# Competitive X-ray and Optical Cooling in the Collisionless Shocks of WR 140

A. M. T. Pollock  Department of Physics and Astronomy, University of
Sheffield, Sheffield S3 7RH, UK  M. F. Corcoran  CRESST and X-ray Astrophysics
Laboratory, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA  The
Catholic University of America, 620 Michigan Ave., N.E. Washington, DC 20064,
USA  I. R. Stevens  School of Physics and Astronomy, University of Birmingham,
Edgbaston, Birmingham, B15 2TT, UK  C. M. P. Russell  The Catholic University
of America, 620 Michigan Ave., N.E. Washington, DC 20064, USA  K. Hamaguchi
CRESST and X-ray Astrophysics Laboratory, NASA/Goddard Space Flight Center,
Greenbelt, MD 20771, USA  Department of Physics, University of Maryland,
Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA  P. M.
Williams  Institute for Astronomy, University of Edinburgh, Royal Observatory,
Edinburgh EH9 3HJ, UK  A. F. J. Moffat  Département de physique and Centre de
Recherche en Astrophysique du Québec (CRAQ), Université de Montréal, C.P.
6128, Succ. Centre-Ville, Montréal, Québec, H3C 3J7, Canada  G. Weigelt  Max-
Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany  V.
Shenavrin  Sternberg Astronomical Institute, Moscow State University,
Universitetskii pr. 13, Moscow, 119992 Russia  N. D. Richardson  Embry-Riddle
Aeronautical University, Physics and Astronomy Department, 3700 Willow Creek
Road, Prescott, AZ 86301, USA  D. Espinoza  The Catholic University of
America, 620 Michigan Ave., N.E. Washington, DC 20064, USA  S. A. Drake
CRESST and X-ray Astrophysics Laboratory, NASA/Goddard Space Flight Center,
Greenbelt, MD 20771, USA  Emeritus

###### Abstract

WR 140 is a long-period, highly eccentric Wolf-Rayet star binary system with
exceptionally well-determined orbital and stellar parameters. Bright, variable
X-ray emission is generated in shocks produced by the collision of the winds
of the WC7pd+O5.5fc component stars. We discuss the variations in the context
of the colliding-wind model using broad-band spectrometry from the RXTE,
Swift, and NICER observatories obtained over 20 years and nearly 1000
observations through 3 consecutive 7.94-year orbits including 3 periastron
passages. The X-ray luminosity varies as expected with the inverse of the
stellar separation over most of the orbit: departures near periastron are
produced when cooling shifts to excess optical emission in C III $\lambda
5696$ in particular. We use X-ray absorption to estimate mass-loss rates for
both stars and to constrain the system morphology. The absorption maximum
coincides closely with inferior conjunction of the WC star and provides
evidence of the ion-reflection mechanism that underlies the formation of
collisionless shocks governed by magnetic fields probably generated by the
Weibel instability. Comparisons with K-band emission and He I $\lambda$10830
absorption show that both are correlated after periastron with the asymmetric
X-ray absorption. Dust appears within a few days of periastron suggesting
formation within shocked gas near the stagnation point. X-ray flares seen in
$\eta$ Car have not occurred in WR 140, suggesting the absence of large-scale
wind inhomogeneities. Relatively constant soft emission revealed during the
X-ray minimum is probably not from recombining plasma entrained in outflowing
shocked gas.

plasmas — shock waves — stars: Wolf-Rayet — stars: individual (WR 140 (catalog
HD 193793)) — X-rays: stars

##  1 WR 140: A Colliding-Wind Binary Laboratory

Massive stars, though extremely rare in the local Universe, are important
cosmic engines which generate those chemicals critical for planetary
habitability. There are many open questions about how these unusual stars
evolve and die, mostly having to do with mass and angular momentum loss during
their short lives (e.g. Meynet & Maeder, 2003), and how such losses depends on
the (evolving) underlying stellar parameters of effective gravity, temperature
and chemical abundance, and on initial rotation rate and other complicating
factors. Additionally, the majority of massive stars either have binary
companions or were part of a multiple system at some point in their history
(Sana et al., 2012), so that binary-driven mass exchange and loss can play an
important evolutionary role (Vanbeveren et al., 1979; Eldridge et al., 2008),
and may play a key role in forming massive gamma-ray burst progenitors by
enhancing the stellar rotation rate (Langer et al., 2010). Massive binaries
are the progenitors of the gravitational wave mergers seen by LIGO, but the
evolutionary pathway between progenitor massive binary systems and LIGO
sources is uncertain, and an area of current interest (see, for example,
Kruckow et al., 2018).

Observations of massive binaries serve as the touchstone for models of stellar
structure and evolution in the upper Hertzsprung-Russell Diagram, since the
mass and radius of stars in binary systems can be directly measured using
simple Newtonian mechanics and Euclidean geometry, as long as the observer is
fortuitously oriented with respect to the orbital plane of the system, or
clever enough. Massive binaries provide an observational connection between
the underlying stellar parameters and stellar wind mass loss (for example,
Corcoran & Heap, 1990). Wind properties (densities and terminal velocities)
have been determined using radio measures of thermal free-free emission
(Wright & Barlow, 1975); analysis of UV spectra of P-Cygni profiles in
resonance lines (Snow & Morton, 1976); and through measures of broad optical
emission lines (Leitherer, 1988). However, each of these methods carries its
own assumptions, biases, and uncertainties.

Study of the orbital dependence of the X-ray emission from massive colliding-
wind binaries is an independent and increasingly important means for
constraining the properties of stellar wind mass-loss. This is because the
localized “bow-shock” created where the winds from massive binary companions
collide produces high-temperature gas which emits in the thermal X-ray band
(0.1–10 keV). Because the X-ray emission occurs near the apex of the
colliding-wind shock, it can be used as a probe of local conditions of the
stellar winds in situ. The X-ray emission measures, temperatures and
absorption column densities derived from analysis of the X-ray spectrum as a
function of orbital phase provide unique measures of the dependence with
distance from the photospheres of the densities and speeds of the stellar
winds. Theoretical modeling of X-rays produced by colliding-wind shocks dates
back more than forty years (Prilutskii & Usov, 1976; Cherepashchuk, 1976) and
has remained an active area of research as computational resources and
numerical models have become more sophisticated (e.g. Stevens et al., 1992;
Usov, 1992; Pittard, 2007; Pittard & Parkin, 2010; Parkin & Gosset, 2011;
Russell et al., 2013).

The small number of highly eccentric, long-period WR+O binaries are a
particularly important means to establish the connection between stellar wind
properties and stellar parameters through X-ray variability studies. Such
systems offer a number of observational advantages. Since the stellar
separation varies as the stars pass from apastron to periastron and back
again, the emission measure of the shocked material along the wind collision
boundary varies with orbital phase and constrains the spatial wind density
distribution from apastron through periastron passage and back again. X-ray
temperatures constrain the local stellar wind velocities of the upstream pre-
shocked gas near the point of impact as a function of stellar separation.
Variations in X-ray absorption, produced by the unshocked stellar winds as the
stars orbit each other, constrain mass loss rates and the geometry of both the
shocked and unshocked winds. In addition, because the stars are well separated
for most of the orbit, mass transfer might only occur now near periastron,
although a modest amount has probably taken place earlier over the course of
WR 140’s evolution (Thomas et al., 2021).

The outstanding example of an eccentric, long-period, X-ray-variable
colliding-wind binary is undoubtedly WR 140 (HD 193793), a WC7pd+O5.5fc binary
of period $7.94$ years and eccentricity $0.900$. Its exceptional nature was
first recognized via periodic dust formation events (Williams et al., 1978,
1987, 1990, 1994; Williams, 1996; Williams et al., 2009). This periodic
outpouring of dust served as the “smoking gun” to establish the system’s long-
period and extreme eccentricity which is one of the highest of all known
stellar binary systems111There are 38 binary systems with orbital
eccentricity$>0.89$ in the 9th Catalog of Spectroscopic Binaries (Pourbaix et
al., 2004) of which WR 140 is the only WR binary. Worth noting, the peculiar
massive long-period binary $\eta$ Car also has a high orbital eccentricity
(near 0.9, Madura et al., 2012, though it has not been directly measured). The
catalogued system with the highest eccentricity is the low-mass binary HD
137763 ($P=889.95$ days, $e=0.976$).). Its orbit and the properties of both
stars have been well established from ground-based observations (Dougherty et
al., 2005; Monnier et al., 2011; Fahed et al., 2011). New analysis by Thomas
et al. (2021), hereafter T21, using optical interferometry from the Center for
High Angular Resolution Astronomy (CHARA) Array, combined with archival
interferometry and new and archival stellar spectra, has provided precise
values for the orbital elements and stellar masses. As a result of these
detailed studies, WR 140 has the best established stellar and orbital
parameters of any WR-type binary, rivalling other very high-eccentricity
systems of assorted spectral type discussed, for example, by Farrington et al.
(2018).

In a wider context, the shocks generated by the wind interactions in massive
stellar binary systems and WR 140 in particular (Pollock et al., 2005) are
prime and arguably optimal exemplars of the physics of collisionless shocks.
Collisionless shocks play important roles throughout the Universe in the
dynamics of plasmas across the widest range of settings (e.g. Marcowith et
al., 2016; Dimmock et al., 2019) from the flow of the solar wind into the
Earth’s magnetosphere and later into the heliopause; through supernova
remnants blasting into the interstellar medium; to merging clusters of
galaxies. The behaviour of all these systems is governed by interlocking
varieties of physics that encompass one or more of shock formation,
development and dissipation; independent ion and electron heating and cooling,
excitation and emission; non-thermal particle acceleration; dust formation;
magnetic field generation and reconnection; plasma waves; turbulence; and
dynamical instabilities. WR 140 exhibits many of these in tightly constrained
conditions. It is bright, nearby and unobscured enough to offer observers
unrivalled opportunities for the remote study of shock physics to contrast and
complement measurements made in solar system space and laboratories on earth.
By virtue of the combination of this precision with its exceptional
brightness, X-ray emission from WR 140 currently serves as a uniquely valuable
resource for the study of the behavior of collisionless astrophysical shocks
under predictable, repeatable, time-dependent physical conditions.

WR 140 was first detected as a luminous X-ray source on 1984 May 19 by the
EXOSAT observatory (Pollock, 1985), at what subsequently proved to be orbital
phase $0.889$, and has been observed many times since by X-ray observatories
like ROSAT (Pollock et al., 1995), ASCA (Koyama et al., 1994; Zhekov &
Skinner, 2000), XMM-Newton (De Becker et al., 2011), CHANDRA (Pollock et al.,
2005) and Suzaku (Sugawara et al., 2015). WR 140 is the brightest X-ray source
among all single or binary massive stars, rivaled only by $\eta$ Car with
which it shares a similar range of observed count rates in many instruments.
While the X-ray brightness of WR 140 has obvious advantages, at the same time
care is required regarding the choice of observing modes in order to avoid
where possible adverse instrumental effects such as photon pile-up.

Here we report detailed X-ray monitoring of the system from observations with
RXTE, Swift, and NICER, emphasizing the broad-band variations revealed as the
stars revolve in their orbits, on timescales of days to weeks, over 3 orbital
cycles according to the orbital and stellar parameters given in Table 1. Most
have been accurately determined through observations except perhaps the more
uncertain O-star mass loss, for which we have adopted the preferred smallest
of the clumping-free rates reported by Pittard & Dougherty (2006). Also given,
to inform the discussion below, are shock-cone opening angles, $\theta_{S}$,
and the shock stand-off distance from the WC7 star as a fraction of the binary
separation, $D$. These were derived from analytical geometrical models of
radiative and adiabatic binary shock formation (Canto et al., 1996; Gayley,
2009) and depend on the momentum flux ratio, $\eta$. Their rigor and
applicability were assessed by Pittard & Dawson (2018) based on 2D numerical
fluid simulations.

We investigate variations of the emergent X-rays in the intensity and spectrum
of the shock emission as modulated by photoelectric absorption during transfer
through cooler pre-shock wind and the interstellar medium, on timescales
according to orbital phase from hours and days to years and beyond, over the
three most recent orbital cycles that span the first 20 years of the 21st
century. As expected, in common with longer-wavelength regimes, X-ray events
move much more quickly near periastron than at other phases, so we requested
observations at increasingly higher cadence in order to sample appropriate
details of the system’s emerging behaviour when the stars are close.
Ultimately nearly a thousand separate observations have been accumulated and
analyzed.

In WR 140’s eccentric 7.94-year orbit, the succession of Keplerian events of
geometrical relevance occur within a few months of periastron: the O star is
in front at $-129$ days; followed by quadrature when the stars are sideways on
with the WC star moving towards the observer at $-10$ days; the WC star in
front at $+9$ days; and quadrature with the WC star moving away at $+104$
days. These times are accurate to about a day near periastron and a week
otherwise. Between periastron and apastron, the distance between the companion
stars varies from 1.5 to 27.5 AU, similar to the separations of Mars and
Neptune from the Sun.

The paper is organized as follows: Section 2 presents an overview of the X-ray
satellite observatories, RXTE, Swift, and NICER, and their work on WR 140. In
Section 3 we derive a suitable spectral model for WR 140 which we then use
consistently to model the spectra from all three observatories. In Section 4,
we present the full X-ray lightcurve from 2001 through 2020, and discuss the
variations of the spectral parameters as a function of time and orbital phase
paying special attention in Section 5 to the mechanisms of shock formation and
cooling in WR 140. Section 6 discusses the implications for the understanding
of the mass loss from the WR and O components, and we summarize the main
results in Section 7.

Table 1: Adopted Orbital and Stellar Parameters Parameter | Value | Reference or Comment
---|---|---
Period (days) | 2895$\pm 0.17$ | T21 (from Table 3, “Adopted Fit”)
eccentricity | 0.9883 $\pm$ 0.0013 | T21
Time of Periastron Passage (MJD) | 60637.23 $\pm$ 0.53 | Best fit $T_{o}$ from T21
$\omega_{\mbox{WR}}$ (degrees) | 227.44 $\pm$ 0.52 | T21
$\Omega$ (degrees) | 353.87 $\pm$ 0.67 | T21
$i$ (degrees) | 119.07 | T21
$a$ (AU) | 13.55$\pm$ 0.21 | T21
$M_{WR}$ (M⊙) | 10.31 $\pm$ 0.45 | T21
$M_{O}$ (M⊙) | 29.27 $\pm$ 1.14 | T21
$\dot{M}_{WR}$ ($10^{-6}$M⊙ yr-1) | 43.0 | Pittard & Dougherty (2006)
$\dot{M}_{O}$ ($10^{-6}$M⊙ yr-1) | 0.8 | Pittard & Dougherty (2006)
$V_{\infty,WR}$ (km s-1) | 2860 | Setia Gunawan et al. (2001)
$V_{\infty,O}$ (km s-1) | 3100 | Setia Gunawan et al. (2001)
$\eta$ | 49.6 |  $=(\dot{M}_{WR}V_{\infty,WR}$)/($\dot{M}_{O}V_{\infty,O}$)
Adiabatic-Shock Opening Angle (degrees)aaTheoretical asymptotic opening half-angle determined by $\eta$ | 41.3 |  Gayley (2009) equation (11)
Radiative-Shock Opening Angle (degrees)aaTheoretical asymptotic opening half-angle determined by $\eta$ | 31.7 |  Canto et al. (1996) equation (28)
WR-Shock Stand-off DistancebbFraction of binary separation determined by $\eta$ | 0.876 |  Canto et al. (1996) equation (27)
Distance (pc) | 1518 | Gaia DR2 & T21
$v$ | $7.07$ | Massey (1984)
$b-v$ | $+0.27$ | Massey (1984)
$N_{H}$ ($10^{21}$ cm${}^{-2})$ | 4.3 | Interstellar absorption column density

##  2 The Observations

There are a total of 940 observations of WR 140 by RXTE, Swift or NICER, for a
total exposure of 1342.0 ksec, included here. Table 2 summarizes the
observations for each of the missions.

###  2.1 RXTE

The Rossi X-ray Timing Explorer (RXTE, Bradt et al., 1993), which operated
between 1995 December and 2012 January, was a satellite observatory with the
flexibility to observe variable X-ray emitting cosmic objects on timescales
from microseconds to years. The primary instrument, the Proportional Counter
Array (PCA, Jahoda et al., 2006; Shaposhnikov et al., 2012), was an array of
collimated, non-imaging proportional counters with a field-of-view of about
$1^{\circ}$, sensitive to X-rays emitted in the $\sim 3-60$ keV band. This
band includes a significant fraction of the absorbed emission generated within
WR 140’s wind-wind collision shock which falls almost entirely between $0.5$
and $10$ keV. However, the lack of soft response below 3 keV made RXTE
insensitive to column density variations at relatively low values of
$N_{H}\lesssim 10^{22}$ cm-2. Also, RXTE’s wide field-of-view means that PCA
spectra are contaminated by cosmic background at a level dependent on
satellite roll angle. RXTE had limited spectral resolution ($E/\Delta E$ =
3.45 - 6.15) between 3 and 8 keV, too coarse for studies of emission lines.

The first observation of WR 140 by RXTE was obtained on 2000 December 09, 63
days before WR 140’s periastron passage (which occurred on 2001 February 10),
after which RXTE observed the system approximately once per week for just over
two years. After a two year hiatus starting in 2003 March, observations
resumed on 2005 March 08, 39 days after apastron ($\phi=$ 0.513), and
continued for six years until 2011 December 23, just before end of mission, at
a variable cadence of a few observations per month to one per day during the
periastron passage and X-ray minimum in 2009 January. As for many space
observatories, RXTE observing time was awarded on an annual basis so that its
cumulative WR 140 campaign comprised 8 separate proposals after being
initiated to inform the context of two CHANDRA observations of WR 140 being
made at the time and whose success they helped guarantee. These data have been
discussed previously (Corcoran et al., 2011; Pollock, 2012). Most recently,
Zhekov (2021) analyzed these data (along with CHANDRA X-ray spectra) and
suggested that the stellar winds are significantly clumped and/or non-
spherically symmetric.

Though the PCA consists of 5 individual Proportional Counter Units (PCUs,
conventionally numbered 0–4), we concentrate here on data from PCU-2, which
provides the most complete and reliable data, and in particular, the data
obtained in Layer 1 of PCU-2, where most of the X-rays from a relatively soft
source like WR 140 are measured. We obtained and analyzed these data from the
RXTE data archive at the HEASARC, NASA’s archive of high energy space mission
data. For each observation, we created individual responses for and
instrumental background estimates of the PCU-2 layer 1 data using software
tools (pcarsp and pcabackest) provided by the RXTE Guest Observer Facility and
distributed with the HEASARC’s HEASoft software package. Note that the
background estimates provided by pcabackest provide estimates of the internal
detector background and external charged particle background and do not
account for cosmic background. Thus the amount of residual cosmic “sky”
background included in the $\approx 1^{\circ}$ field of view of PCU-2 will be
different than the amount of residual cosmic background in imaging
observations (such as the Swift XRT in photon-counting mode) or non-imaging
instruments with narrower fields of view (like NICER). Difference in cosmic
background in the different instruments complicates comparison between the
various observatories. We used calibrations from the most recent version of
the PCA calibration data (version 20120110) obtained from the HEASARC RXTE
Calibration Database (CALDB).

Table 2: Summary of the Observations

Instr. | Num. Obs. | Tot. Expo. | Obs. Start | Obs. End | Min. Expo. | Max. Expo. | Min. Sep.
---|---|---|---|---|---|---|---
|  | ksec | MJD | MJD | s | s | day
RXTE PCA | 533 | 510 | 51887 | 55919 | 16 | 2192 | 0.55
Swift PC | 145 | 313 | 54689 | 57891 | 376 | 19760 | 0.06
Swift WT | 173 | 391 | 54843 | 58588 | 79 | 18648 | 0.07
NICER XTI | 89 | 128 | 58074 | 59002 | 57 | 4501 | 0.05

Note. — Tot. Expos. is the sum of the exposures for the individual
observations; Obs. Start, End are the start and stop of the observing
campaigns in MJD; Min., Max. Expo. are the minimum and maximum exposure for
individual observations; Min. Sep. is the minimum separation between
consecutive observations

###  2.2 Swift

We used the X-ray Telescope (XRT, Burrows et al., 2000) on the Neil Gehrels
Swift observatory (Swift, Gehrels et al., 2004) to monitor changes in the
X-ray spectrum. Swift was used to augment the RXTE data since the XRT’s softer
instrumental sensitivity and better spectral resolution allow for more precise
determination of column densities than possible with RXTE. On the other hand,
the XRT is prone to light leaks at low energies, which can complicate analysis
of the soft part of the X-ray spectrum where the effect of wind absorption is
most pronounced. This contamination, known as optical loading, has been
particularly relevant in the treatment of the soft “relic” component (Sugawara
et al., 2015, Section 4.5 below) revealed during WR 140’s X-ray minimum near
periastron.

The XRT is also susceptible to photon pile-up in imaging (“Photon-Counting”,
hereafter PC) mode observations if more than one X-ray photon strikes a pixel
of the XRT detector before readout, reducing the observed count rate and
distorting the spectrum. The count-rate threshold above which this becomes
significant is about $0.5~{}\mathrm{cts}~{}\mathrm{s}^{-1}$ and applies to
most of WR 140’s orbit except the minimum near periastron. This was not
understood during the early XRT observations. Though data analysis methods
available to mitigate the problem have been used, the XRT’s alternative
“Windowed-Timing” mode (hereafter WT), was later usually judged preferable.
Its faster readout incurs the loss of spatial information in one direction
leading to higher backgrounds and more difficult treatment of bad detector
columns.

The Swift XRT observations of WR 140 started on 2008 August 11, with sporadic
phase coverage. The last observation we analyze here was taken on 2018 April
05. Swift, along with Suzaku (Sugawara et al., 2015), provided critical
measurements of the variation in the WR 140’s soft X-ray spectrum near the
2009 periastron passage since only Swift and Suzaku were available to measure
the WR 140 X-ray spectrum below 3 keV at that time222WR 140 violated viewing
constraints of XMM-Newton, and mitigation of photon pileup in the CHANDRA ACIS
camera would have resulted in prohibitively long exposures. In addition, at
that time it was unclear if the RXTE mission would be extended beyond February
2009; if not, it would have been up to Swift alone to monitor the details of
the recovery of WR 140’s X-ray flux from the X-ray minimum state..

The Swift data were downloaded from the HEASARC data archive, then reprocessed
using the standard pipeline software (xrtpipeline, part of the Swift XRTDAS
software distributed with the HEASoft Analysis package). We calculated
individual effective areas for the PC and WT mode data. We visually inspected
each observation and defined valid “good-time” intervals from extracted
lightcurves, avoiding times of large excursions in count rates produced by
background fluctuations or other, non-source-related variations. We then
extracted spectra and lightcurves from the X-ray events which fell within
these good time intervals. For the PC-mode data, source spectra were extracted
from a circular region of radius $1.1^{\prime}$ centered on WR 140. Background
was extracted from an annulus between $2.7^{\prime}$ and $8.3^{\prime}$, whose
inner boundary extends beyond the Swift PC-mode 90% encircled energy radius,
and which contained no visible X-ray sources. For each PC-mode spectrum we
calculated observation-specific effective areas using the xrtmkarf task
distributed with the Swift XRTDAS, and used the standard XRT PC-mode response
function from version 20170501 of the Swift XRT CALDB in the spectral
analysis.

For the WT mode data, neither pileup nor optical loading is a significant
issue. For data in windowed-timing mode, source photons were extracted from a
region extending to $1.1^{\prime}$ around the source in the 1-D spatially
compressed image, while background was extracted from an apparently source-
free region extending to $1.1^{\prime}$ in the 1-D spatially compressed image.
Because of the compression in the spatial dimension, the background spectrum
in the windowed-timing mode data depends on the spacecraft roll angle since
cosmic sources and bad detector columns included in the spatially-compressed
vary with roll angle. Thus the WT mode backgrounds are in general different
from the backgrounds in photon-counting mode but, from examination of a few
selected datasets at different roll angles, we estimate that the variation
between background levels in different WT observations is probably less than
$5\%$. We computed individual, observation-specific effective areas for all
the WT-mode data and analyzed the data using the standard WT-mode response
function. Comparison of net fluxes derived from PC-mode data with those
derived from the analysis of net WT-mode data indicates that the net WT-mode
data are in general 40% brighter than the net PC-mode data, presumably due to
an under-estimation of background contamination in the WT-mode data.

###  2.3 NICER

The Neutron Star Interior Composition Explorer (NICER, Arzoumanian et al.,
2014) is an X-ray astronomy facility which was installed on the International
Space Station ( ISS) in June 2017. NICER’s primary mission is to obtain high-
time resolved X-ray spectrometry in the 0.2–12 keV band with moderate spectral
resolution of cosmic X-ray sources, primarily of X-ray binary pulsars. NICER’s
X-ray Timing Instrument (XTI, Prigozhin et al., 2016) is comprised of a co-
aligned array of 52 Focal Plane Modules, each consisting of a matched pair of
X-ray “concentrator” (XRC) optics a silicon drift detector (SDD) for readout.
Each XRC optic collects X-rays over a roughly 30 arcmin2 region of the sky
centered on the target of interest in the 0.2–12 keV energy band and
concentrates them onto an SDD. NICER’s combination of large effective area,
restricted field of view and broad bandpass in the thermal X-ray range makes
it especially well-suited to observe X-ray variables like long-period
colliding wind binaries (and other sources) in addition to X-ray pulsars.

The NICER data were extracted from the clean, merged photon events files,
using data obtained outside of the South Atlantic Anomaly at sun angles of
$>40^{\circ}$ to avoid stray-light contamination, using the NICERDAS software
package distributed with HEASoft. We used standard NICER event cleaning
criteria333see the help file for nimaketime for a description of the standard
data screening criteria. to clean each observation. NICER is subject to a
varying charged particle environment at the high-inclination ISS orbit, which
is most noticeable at high energies, so we extracted lightcurves in the
$0.4-10$ keV band for all the NICER observations and visually inspected them
to exclude intervals of large rapid increases in count rate produced by the
variable charged particle environment. In addition, low-energy events produce
a “noise spike” at energies $\lesssim 0.4$ keV. Therefore, in our analysis, we
extracted and fit spectra in the 0.4–10 keV band, which has good overlap with
Swift and RXTE and excludes the NICER spectral bands most affected by
background issues. For each observation we estimated background using the
nibackgen3C50 tool444See
https://heasarc.gsfc.nasa.gov/docs/nicer/tools/nicer_bkg_est_tools.html.
(Remillard et al., 2021) provided by the NICER Guest Observer Facility, which
estimates background from a library of spectra extracted from blank-field
observations, using rates at energies beyond the XRC cutoff and other proxies.
We subtracted this background estimate from the observed spectrum for each
observation before fitting.

##  3 Determining a Spectral Template Model

In order to determine a uniform set of phase-dependent broadband X-ray
spectral parameters from the moderate resolution data delivered by RXTE,
Swift, and NICER we created a template model of the spectrum using high-
resolution CHANDRA grating spectrometer data, as these contain the most
detailed information on the combination of lines and continuum. In particular,
we chose three CHANDRA ObsIDs, 6286, 5419 and 6287, obtained over a two week
period in 2006 March and April, only 14 months (0.15 in orbital phase) after
the stars passed apastron (on 2005-01-28). These spectra show the plasma in
its most relaxed condition, and stellar wind absorption at or near its lowest.
The total exposure time of the combined spectrum is 141 ks. Because of the
resemblance of the spectrum to thermal emission, we used a simple combination
of plasma models in collisional equilibrium with the same adjustments for
velocity broadening and non-solar abundances and subject to absorption by the
interstellar medium and the stellar winds, and used XSPEC (Dorman & Arnaud,
2001) to fit the combined set of 12 MEG and HEG first-order spectra.

The model we adopted was selected for its ability to reproduce the morphology
of the spectrum, so it does not necessarily represent a realistic description
of the actual physics of the plasma which is more likely to be out of
equilibrium as discussed, for example, by Pollock et al. (2005). In XSPEC
notation, the model is (TBabs(bvapec1 \+ bvapec2 \+ bvapec3), where TBabs is
the “Tuebingen-Boulder ISM absorption model” (Wilms et al., 2000, which was
used to estimate the combination of ISM and stellar wind absorption columns to
the X-ray source), and the three bvapec components are non-solar-abundance
("v"), doppler-broadened ("b") plasma emission models (Smith et al.,
2001)555see http://atomdb.org.. When absorption becomes high as the Wolf-Rayet
star moves in front of the colliding-wind source a weak additional soft
component not captured by the template model becomes visible, amounting to
less than 0.25% of the maximum count rate. Known by Sugawara et al. (2015) as
the “relic” component, its behavior is discussed below in section 4.5.

Abundances were held in common for the three thermal emission components and
are mostly representative of the shocked wind of the chemically-evolved WC7
star with a minor contribution, amounting to less than 10% according to
Pittard & Stevens (2002), from the shocked wind of the less chemically-evolved
O star. In order to accommodate this, with hydrogen absent in the WC7 star and
replaced by helium, the abundances of the CHANDRA emission model were fixed:
helium to a high value; carbon to a number fraction
$\mathrm{C}/\mathrm{He}=0.4$; and nitrogen to zero.

The reference template model parameters from the CHANDRA fit are given in
Table 3 including the best-fit abundances used for all three emission
components, given with respect to solar abundances (Anders & Grevesse, 1989)
and as number and mass fractions. The best-fit emission measures of the three
thermal components to the HETGS spectra were fixed at values adjusted
downwards by an indicative factor of 1.061 calculated from the relative binary
separation of the orbit between apastron and the later mean epoch of
observation. With density estimates based on parameters in Table 1, these
emission measures equate to volumes of less than 1% of a characteristic volume
given by $(1-\cos{\theta_{S}})D^{3}$. Other than the relic component, the
luminosity scaling factor was one of the two free parameters of the template
model along with the absorbing column density whose initial value was also
thought to be characteristic of low values at apastron or maximum binary
separation, although expectations at the outset were ill-defined of its
overall phase dependence. The line-velocity structure was also frozen in the
template model, since line velocity broadening is only of relevance at high
(grating) resolution. The HETG spectrum and template model, including the 3
individual emission components representing emission from the shocked gas in
the wind collision region, is shown in Figure 1.

Figure 1: CHANDRA HETG combined $\pm 1$st order MEG spectra from the ObsIDs 6286, 5419, 6287 of WR 140 (black) closest to apastron and the standard template model (red). Strong lines in the 1–20 Å region are marked among which those of Ne X and O VIII are particularly strong.  Table 3: X-ray Spectrum Template Model  Parameter | Unit | Initial Value | Type
---|---|---|---
nH | 1022 cm-2 | 0.50 |
kT1 | keV | 3.68 | Fixed
EM1 | 1053 cm-3 | 3.87 | Fixed
kT2 | keV | 1.14 | Fixed
EM2 | 1053 cm-3 | 1.42 | Fixed
kT3 | keV | 0.41 | Fixed
EM3 | 1053 cm-3 | 1.54 | Fixed
Velocity Shift | 1000 km s-1 | $-1.37$ | Fixed
Line Broadening | 100 km s-1 | 5.78 | Fixed
Normalization factor |  | 1.0 |
Fixed Emission Abundances by number, N, and mass fraction, X
| N/N⊙ | N | X
He | 1000 | 1. | 0.548
C | 65247 | 0.242 | 0.398
N | 0 | 0. | 0.
O | 1938 | $1.69\times 10^{-2}$ | $3.70\times 10^{-2}$
Ne | 3139 | $3.95\times 10^{-3}$ | $1.09\times 10^{-2}$
Mg | 1061 | $4.13\times 10^{-4}$ | $1.37\times 10^{-3}$
Al | 976 | $2.95\times 10^{-5}$ | $1.09\times 10^{-4}$
Si | 881 | $3.20\times 10^{-4}$ | $1.23\times 10^{-3}$
S | 713 | $1.18\times 10^{-4}$ | $5.18\times 10^{-4}$
Ar | 602 | $2.24\times 10^{-5}$ | $1.22\times 10^{-4}$
Ca | 374 | $8.75\times 10^{-6}$ | $4.80\times 10^{-5}$
Fe | 297 | $1.42\times 10^{-4}$ | $1.09\times 10^{-3}$
Ni | 385 | $7.02\times 10^{-6}$ | $5.64\times 10^{-5}$

We then fit this “standard” X-ray spectrum model to each individual spectrum
from the RXTE, and Swift observations, fitting for the overall column
densities, using an overall constant to adjust the flux normalization of the
model, with the temperatures and relative emission measures of the emission
model fixed. We found that this was adequate to generate acceptable fits to
the low-resolution RXTE spectra and the relatively low precision Swift and
NICER spectra (null hypothesis probablilty $>0.05$) which therefore gave no
evidence of any change with orbital phase of the adopted equivalent plasma
temperatures although this conclusion is ripe for exploration with high
resolution data.

We used an automated Python script to fit the data, using pyxspec, the Python
version of the XSPEC spectral analysis package. We recorded values of all
variable parameters, namely those not fixed in Table 3, for each spectrum and
calculated observed and absorption-corrected fluxes in the 2–10 keV band for
all observations. We adopted the 2–10 keV band as standard, since it is
consistent with the harder response of RXTE that does not extend much below 2
keV and includes the bulk of the colliding-wind emission. Any intrinsic
emission from the individual stellar winds is also likely to be mostly
confined to the soft band below 2 keV although even this is weak in WR 140:
the residual soft emission near periastron discussed in Section 4.5 below
amounts to less than 2% of the colliding-wind emission in the same band
observed at apastron.

##  4 X-ray variability in WR 140

###  4.1 Cross-Calibration and Cosmic Background

One important objective of instrumental calibration procedures is to enable
stable, robust and consistent estimates of physical parameters. Comparisons of
results for calibration standards such as the IACHEC group’s work on the
supernova remnant 1E 0102.2-7219 (Plucinsky et al., 2017), show that different
instruments usually agree to within a few percent with some energy dependence.
Similar considerations apply to measurements of WR 140.

We found that there were flux offsets between observations from different
instruments for observations which overlap in phase and in time. In addition
to the cross-calibration uncertainties, flux offsets arise because of the
different amount of cosmic X-ray background (diffuse X-ray background along
with other possible cosmic sources) included in the non-imaging observations
by RXTE, NICER, and Swift in WT mode, since all these instruments have
different fields-of-view in addition to different sensitivities. The imaging
Swift PC-mode data allow the most accurate account for cosmic background since
background is directly determined from source-free regions of the PC image. We
therefore corrected the RXTE, NICER and Swift WT mode fluxes to the PC fluxes.
We found that we needed to subtract an additional background flux of 0.50
$\times 10^{-11}$ ergs cm-2 s-1 from the RXTE 2–10 keV band fluxes, and 0.70
$\times 10^{-11}$ ergs cm-2 s-1 from the NICER fluxes, and 0.80 $\times
10^{-11}$ ergs cm-2 s-1 from the Swift WT mode data to bring them into
agreement with the Swift PC-mode data. In addition, we needed to divide the
background-corrected RXTE fluxes by a scale factor of 1.35 to match the Swift
PC-mode data in order to bring the amplitude of variation of the RXTE data
into agreement with the Swift PC-mode data in the regions near X-ray maximum.

###  4.2 X-ray Flux Variations in the 2–10 keV Band

In what follows, times and phases are calculated using the following
ephemeris:

$T_{o}(JD)=2454846.7270+2895.00E$

where $E$ is the cycle count, the period is given by T21, and the epoch
$T_{o}$ (2454846.7270 = 2009-01-15 05:26:52 UTC) corresponds to the time of
periastron passage from T21, but 2 orbital cycles earlier. We adopt this value
of $T_{o}$ since this periastron passage was densely monitored by both RXTE
and Swift.

Figure 2: The RXTE, Swift, and NICER lightcurve of WR 140, 2000-2020. The time
zero point corresponds to the periastron passage JD 2454846.727 = 2009-01-15
05:26. The gray points are the RXTE fluxes advanced by one period. The black
dashed vertical lines are times of periastron passages, while the gray dashed
curves show the expected $1/D$ variation in flux for an unobscured adiabatic
system of colliding winds.

Figure 3: Comparison of the two minima observed by RXTE in 2001 (gray circles)
and 2009 (black circles). Also shown are the timings of quadratures and
conjunctions, with periastron passage in black. WC-star inferior conjunction
occurs very close in time to the minimum of the X-ray flux a significant
fraction of which is due to the cosmic X-ray background. The gray dashed curve
shows a model flux inversely proportional to the stellar separation ($D$).
Figure 4: Comparison of NICER and Swift contemporanous 2–10 keV X-ray fluxes
around the 2016 minimum. RXTE fluxes from the 2009 minimum are also shown.
Swift PC-mode data are shown as filled blue circles, while WT-mode data are
shown as open blue circles.

Figure 2 shows the complete RXTE, Swift, and NICER 2–10 keV band X-ray flux
curve of WR 140 covering three periastron passages. The general characteristic
of WR 140’s X-ray flux curve is a gradual increase in X-ray brightness as the
stars approach periastron, followed by a rapid decline to a brief, sharp
minimum, a quick recovery from the minimum, and a gradual decline in
brightness up to apastron. While this is similar to the X-ray variation seen
in WR 140’s “sister star”, $\eta$ Car666An interesting numerological
coincidence between these sister binaries: in 2009 WR 140 reached its X-ray
minimum on 24 January 2009, just 8 days after $\eta$ Car began its own X-ray
“deep minimum” phase (on 16 January 2009) near its periastron passage. This
coincidence will not happen again for another 400 years. The next time the
X-ray minima will be similarly coincident will be in 2413 CE, when $\eta$
Car’s minimum will occur on 29 July, just three days before WR 140’s own X-ray
minimum on 1 August. , another long-period, highly eccentric colliding wind
binary, it is worth noting that, unlike $\eta$ Car, there are no strong, rapid
($\sim$weeks) X-ray variations (“flaring”, Moffat & Corcoran, 2009) of the
X-ray brightness seen in WR 140 just prior to the start of its X-ray minimum.
As shown in Figures 2 and 3, the X-ray fluxes from the two orbits observed by
RXTE agree very well with each other at all common phases. In addition the
depth and duration of WR 140’s X-ray minima are nearly constant from one
orbital cycle to another. This can also be contrasted with $\eta$ Car which
shows significant changes in the duration of X-ray minimum from cycle to cycle
(Corcoran et al., 2010, 2017).

If the cooling of the shocked gas is effectively adiabatic and wind absorption
is minimal, the luminosity of X-ray flux with phase is expected to vary
inversely with $D$, the separation between the two stars (Usov, 1992; Stevens
et al., 1992). In the figures the gray dashed curve represents a $1/D$
variation and it is clear that near X-ray maximum & minimum the X-ray
brightness curve does not follow the expected $1/D$ variation. As can be seen
more clearly in Figure 3, the deviation from the $1/D$ dependence in the X-ray
flux starts about 120 days prior to periastron passage, i.e. around the time
of superior conjunction of the WC star.

Figure 4 shows the Swift X-ray fluxes in the 2–10 keV band around the 2016
minimum, along with NICER 2–10 keV band fluxes. NICER began observations in
July 2017, so that observations started after periastron passage ($\phi=2.1$).
There is good agreement between the Swift and NICER contemporaneous fluxes. As
shown in Figure 2 and in Figure 4, the NICER fluxes seem to be about 10% below
the projected level of the RXTE fluxes at these phases (but in good agreement
with the Swift fluxes in the area of overlap).

The exceptional X-ray brightness of WR 140 enables accurate assessment of its
variability. Even the first few isolated observations of WR 140 with EXOSAT,
ROSAT, and ASCA showed that variability was an obvious feature of its
behaviour in line with broad expectations of the eccentric binary colliding-
wind model. The detailed monitoring built up since over the last two decades
through nearly a thousand separate observations with RXTE, Swift, and NICER
allows a fairly complete picture to be drawn of the phase-dependent balance
between downstream shock emission from the interacting winds and upstream
foreground absorption during transfer principally through the more powerful
wind of the WC star. As the ensemble of data under consideration here shows no
evidence of changes in the equivalent temperature structure of the emission,
discussion may properly be framed in terms of the independent measures of
luminosity and absorption of the X-ray emission with reference where necessary
to where this simple scheme fails, notably at low energies near periastron.

The X-ray observations also show that the X-ray spectrum of WR 140 is
repeatable at all phases between orbital cycles in both emission and
absorption and varies smoothly and monotonically between a few turning points
that emerge due to boundary conditions of macroscopic orbital dynamics or
microscopic X-ray emission physics. Of particular note is the absence of
flares or other short-term episodes. Instances of apparent rapid variability
between individual exposures visible in some of the figures are invariably due
to instrumental instabilities. These ideas will be subject to stricter test in
work underway on the ensemble of the few dozen X-ray observations of WR 140 of
much higher statistical weight at scattered phases made with other
instruments.

###  4.3 Orbital Dependence of WR 140’s X-ray Luminosity

As shown chronologically for the different instruments in Figure 5 and in
folded form near periastron in Figure 6, the intrinsic X-ray luminosity of WR
140 evolves smoothly as a function of binary phase. At apastron, when the
binary system is at its maximum separation, the X-ray luminosity is a minimum.
During the subsequent long, nearly 4-year approach to periastron, covered in
its entirety from 2005 March by RXTE, the luminosity gradually increases in
inverse proportion to the binary separation until about 6 months before
periastron when it has doubled, behaviour confirmed in its later stages by the
long-term Swift campaign initiated 16 months before the next periastron
passage in 2016 December. After this point, the luminosity continues its
steadily accelerating increase, though now slower than expected from the
inverse binary separation, until reaching a maximum, not at periastron, but
about 20 days beforehand after which a rapid decrease occurs by about a factor
of five over about 20 days. This unexpected decrease corresponds closely, as
shown below, with the complementary increase of excess emission in the C III
$\lambda$5696 optical emission line in WR 140 (Fahed et al., 2011).

Spectral properties close to the X-ray minimum have been relatively hard to
establish for a combination of reasons: the observed count rates are lowered
even further than just the decreasing luminosity by heavy and changing
absorption during the transit of the WC star; the unresolved RXTE background
becomes much more significant; and the appearance of the relic component.
Despite these challenges, it is clear the minimum is relatively flat for 10-15
days near periastron and conjunction before recovery gets underway.
Furthermore, in common with the rest of the X-ray orbit, there is little
evidence of the type of secular changes seen during repeated observations of
$\eta$ Car’s X-ray minimum.

Despite fewer observations and the higher absorption described below, the
recovery after periastron generally mirrors its previous evolution with some
asymmetry as the luminosity appears to reach its local maximum perhaps 10 days
later than expected from its counterpart before periastron. A few weeks later,
symmetry in luminosity seems to have been established with good agreement
between the three instruments during a steady decrease towards apastron
inversely proportional to the binary separation.

Figure 5: X-ray luminosity in the 2–10 keV band corrected for interstellar and
circumstellar absorption assuming the distance in Table 1. The dashed line
shows a $1/D$ variation. Figure 6: X-ray luminosity in the 2–10 keV band
corrected for absorption in the interval 300 days around periastron passage.
The red points show the observed (i.e. absorbed) luminosity from the RXTE and
Swift observations.

###  4.4 Orbital dependence of WR 140’s X-ray absorption

As shown in Figure 7 on a logarithmic column-density scale, the variable X-ray
absorption observed in WR 140 has a complex structure of high dynamic range
that is asymmetric with orbital phase. Agreement is good between measurements
by RXTE and Swift near the periastron passages of 2009 and 2016, indicating
that the wind absorption stayed repeatable with orbital phase over at least
the last two orbital cycles. NICER and Swift also agree well at common phases.

Figure 7: Top: Column density variations from best fits to RXTE, Swift and
NICER spectra. A horizontal dashed blue line shows the column density far from
periastron, i.e. $N_{H}=4.6\times 10^{21}$ cm-2, which represents the
interstellar column to the system without additional wind absorption. Bottom:
Same as above emphasizing the 300 day interval around periastron passage. Red,
green and black vertical lines mark times of conjunctions, quadratures and
periastron passage, respectively.

The variations in column density are consistent with general expectations of
the colliding-wind shock model in which the upstream O-star wind is confined
by the more powerful WC-star wind within a cone-shaped boundary having a half-
opening angle relative to the line of centers of $\theta_{S}\approx
32\mbox{${}^{\circ}$}$ – 41∘according to the rough radiative and adiabatic
estimates in Table 1. The X-ray emission occurs in the intervening interaction
region that forms an extensive interface between the two upstream winds of
dimension comparable with the binary separation. The carbon-rich WC-star wind
is responsible for most of the absorption around the orbit, shown by the
maximum within a few days of WC-star inferior conjunction when the WC-star is
in front of the system’s center-of-mass, the stagnation point and its stellar
companion. The high eccentricity and the longitude of periastron $\omega$
determine that the WC star is nearer the observer for only about 138 days
including periastron, while the O star is in front for the remaining 2757
days, including apastron.

Significant absorption path lengths through the wind of the O star occur near
its inferior conjunction for orbital inclinations $\sin{i}>\cos{\theta_{S}}$,
i.e., $i>58^{\circ}$. For WR 140, although Table 1 suggests that
$\sin{i}\approx\cos{\theta_{S}}$, the obvious transition in the column density
measurements over the short interval between the two conjunctions shows that
the winds of both stars are involved, allowing among other things estimates to
be made below of the system geometry. Other slower variations with orbital
phase are partly due to changing absorption path lengths through the two
winds.

A basis of the hydrodynamic models often used for simulations of colliding-
wind systems is the absence of any information to the flow of upstream gas
that would signal the presence of shocks further downstream. In this case,
foreground absorption is identical to that of single stars, allowing the
construction of simple geometrical models. The column density integrated along
a path entirely through the terminal velocity flow of a wind from a point
$\vec{R}_{x}$ to a distant observer takes the concise form

$N_{x}~{}\mathrm{cm}^{-2}=4.31\times 10^{23}\frac{\dot{M}_{-6}}{\mu
v_{8}}\frac{\Theta}{b}+N_{\mathrm{ISM}}$ (1)

where $\dot{M}_{-6}\times 10^{-6}$ M⊙ yr-1 is the mass-loss rate; $\mu$ is the
mean atomic weight; $v_{8}\times 1000$ km s-1 is the wind terminal velocity;
$\Theta$ radians is the aspect angle between the vector joining the stars and
the line-of-sight; $b=R_{x}\sin{\Theta}$ $R_{\odot}$ is the impact parameter;
and $N_{\mathrm{ISM}}$ is the constant interstellar term. In WR 140, the
geometrical terms are accurately defined by the well-constrained orbit.

Although the X-ray source is likely to be comparable in size to the binary
separation, for simplicity we have calculated indicative column densities
along single lines-of-sight from the stagnation point as a function of phase.
The single-point approximation provided good fits to all the data considered
here and has been widely used in the literature for the analysis of colliding-
wind systems. Its use is justified by examples that we have calculated of
X-ray sources extended along the analytical shell interface of Canto et al.
(1996). More sophisticated approximations are likely to require detailed
dynamical simulations. For example, in order to anticipate the type of work
that will be required and to illustrate for present purposes the system
geometry at significant phases in the column density curve from the beginning
of the Swift campaign, Figure 8 shows density distributions in the orbital
plane of WR 140 from 3-D smoothed-particle hydrodynamics simulations (Russell
et al., 2013) based on the parameters in Table 1.

Figure 8: Simulated density distributions of WR 140 in the orbital plane at
$500$ days (left), $50$ days (middle) and $22$ days before periastron passage
from a dynamic 3-D smoothed-particle hydrodynamics fluid model (2021, C.
Russell et al., in prep.). The arrow represents the observer’s line-of-sight
projected onto the orbital plane with the spatial scale in units of the semi-
major axis, $a$. The half-opening angle of the shock cone in this simulation
is about $40\mbox{${}^{\circ}$}$. At $-500$ days the leading edge of the shock
cone around the O star has recently crossed the observer’s line-of-sight. The
shock cone takes about $450$ days to pass the line-of-sight. Between $-50$ and
$-22$ days, the trailing edge of the shock cone passes the line-of-sight which
shortly afterwards encounters the dense unshocked wind of the WC7 star,
causing a rapid increase in column density as the stagnation point of the
shock passes close to and behind the WC7 star.

####  4.4.1 Absorption by the O-star wind

While maximum absorption close to WC-star conjunction was already evident from
the earliest observations with RXTE, the orbital dependence at the lowest
columns has only been revealed with the soft X-ray capabilities of the Swift
XRT campaign that began in 2015 August, about a year and a half before the
most recent periastron. In the observations from the beginning of the campaign
in the approach to O-star conjunction 129 days before periastron and beyond,
the observed column increased slowly but steadily by about 20% over the course
of a year or more until 50 or 60 days before periastron, when a rapid increase
in column began. As shown in Figure 9, when the shocks around the O star are
directed towards the observer and the WC7-star wind makes its smallest
contribution, this lowest part of the absorption curve observed so far between
500 and 80 days before periastron is well modelled by a combination of a
constant component due to the interstellar medium and a term linear in
$\Theta/b$ following Eq. (1) for the O star. With this model, the estimate of
the constant interstellar term is $(4.64\pm 0.07)\times 10^{21}$ cm-2,
consistent with the interstellar column in the direction of WR 140 derived
from WR 140’s colour excess or Ly$\alpha$ absorption. For $\mu_{O5}=1.30$, the
linear term yields an O-star mass-loss rate of $\dot{M}_{O5}=(3.7\pm
0.3)\times 10^{-7}$ M⊙ yr-1, about half the smooth-wind value adopted in Table
1, which was the lowest among several alternatives discussed by Pittard &
Dougherty (2006).

Figure 9: X-ray absorption column density observed in WR 140 with the Swift
XRT as a function of the column-density integral through the O-star wind given
by ratio of the aspect angle ($\Theta$) to impact parameter $b$ in the range
500-80 days before periastron passage. The dashed line is the linear fit to
the data, $(3.956\times\Theta/b+0.464)\times 10^{22}$ cm-2. Figure 10: X-ray
absorption column density observed in WR 140 with Swift and NICER as a
function of the column-density integral through the WC-star wind at all
available phases including those associated with the O star shown in Figure 9.

####  4.4.2 Transition between O-star and WC-star winds

An interesting and perhaps unexpected feature revealed by both the
measurements and the simple model of this highly eccentric binary is that the
conjunction of the O star does not coincide with an absorption maximum.
Instead, as a result of the rapidly decreasing binary separation, the
absorption maximum would have been reached about 100 days later, a month or so
before periastron, if other events did not intervene.

The extended episode of low absorption ends between O-star conjunction and
quadrature with a rapid increase in column density of more than an order of
magnitude in a month as the line-of-sight passes from the O-star wind into the
WC-star wind, presumably via an intermediate direct view of shocked gas as the
line of sight encounters the wall of the shock cone. The transition begins
slowly about 60 days before periastron before increasing rapidly until an
inflection point 22 days before periastron when the line-of-sight starts to
pass predominantly through the WC-star wind. These phases mark the angular
positions with respect to the system axis of the two shock discontinuities
corresponding to aspect angles of $34.6\mbox{${}^{\circ}$}$ at the inner
O-star shock and $61.2\mbox{${}^{\circ}$}$ at the outer WC-star shock. A
contact discontinuity, whose existence might be doubtful in a collisionless
plasma, would be located at some intermediate value. In any case, this
estimate of the angular extent of the shock is within a few degrees of the
theoretical values given in Table 1. It agrees well with the estimate of
$34\mbox{${}^{\circ}$}\pm 1\mbox{${}^{\circ}$}$ for the angle of the contact
discontinuity inside the shock[s] derived from He I$~{}\lambda$10830
absorption (Williams et al., 2021) and is reproduced with reasonable success
by the fluid simulations shown in Figure 8.

####  4.4.3 Absorption by the WC-star wind

Once the WC-star wind intervenes, absorption becomes much stronger due to the
appearance of material enriched in carbon and oxygen and a higher mass-loss
rate which combine easily to outweigh the greater distance of the shock from
the Wolf-Rayet star. It should be borne in mind that in order to make a fair
comparison of absorption at all orbital phases, the same solar abundance
photoelectric model has been used throughout and any mass-loss rate estimates
need to take this into account. When the 30–40 day transition is over, the
column density continues to increase for another 30 days at a slower but more
regular pace through quadrature and periastron to reach a maximum close to WC-
star inferior conjunction. At this point, for absorbing material of Table 3
emission abundances with $\mu_{WC7}=5.73$ and correspondingly higher
photoelectric cross-sections, the implied mass-loss rate is
$\dot{M}_{WC7}=1.7\times 10^{-5}$ M⊙ yr-1, a factor of 3 smaller than the
value given in Table 1.

The post-periastron orbital dynamics are slow in comparison so that the aspect
angle of $61.2\mbox{${}^{\circ}$}$ marking the WC-star shock encountered 22
days before periastron is reached only 654 days afterwards at much greater
orbital separation. The binary dynamics of this highly eccentric system are
therefore the major cause of the comparatively slow decrease in absorption
over years after WC-star conjunction compared with the rapid evolution over a
month before. However, in contrast to the absorption through the O-star wind,
the same type of simple linear geometrical model has no success reproducing
the higher, longer-lived WC-star absorption. Instead, the absorption follows
the distinctive locus in the $N_{x}-\Theta/b$ plane shown in Figure 10 that
was constructed from all the available column density measurements made with
Swift and NICER from 502 days before periastron to 1261 days after. This
amounts to 61% of the orbit where the stars are moving at their slowest
leading to the expectation that the small unexplored part of the locus at the
lowest column densities will take just over 3 years to complete and probably
close.

The locus consists of two loops: an upper, rapid, roughly horizontal loop
associated with the WC-star wind and high column densities that lasts about 70
days when the stars are moving at their greatest orbital velocities; and a
lower, slower, roughly vertical loop associated with the O-star wind and lower
column densities that otherwise occupies nearly the whole orbit. The locations
of periastron, conjunctions and quadrature are marked. The two loops coincide
close to the inflection point that marks the end of the rapidly ascending
transition between the winds of the O star and WC star. Once the highest
values have built up relatively slowly towards WC-star conjunction, the column
density stays roughly constant for nearly three weeks despite a large
reduction in $\Theta/b$. This behaviour strongly suggests the presence of a
large amount of absorbing material not connected with the line-of-sight
through the undisturbed upstream wind but instead with the shock itself. This
matter is discussed further below where we suggest that reflected ions are
responsible.

####  4.4.4 Transition between WC-star and O-star winds

The rapid transition between O-star wind and WC-star wind intervening in the
lines-of-sight to the X-ray source observed a few weeks before periastron
through the sharp increase in column density over a month must have a
counterpart in the opposite direction after periastron in which the lines-of-
sight move from WC-star wind to O-star wind. Neglecting the curvature of the
shock fronts, it is plausible that this could take place roughly near the
corresponding orientations between aspect angles $61.2\mbox{${}^{\circ}$}$ and
$34.6\mbox{${}^{\circ}$}$. If so, it would involve a slowly decreasing column
density starting 654 days after periastron and lasting for more than half the
entire orbit over years rather than weeks. The observations taken so far are
consistent with this idea with the latest NICER measurements showing gradually
falling column densities to values still significantly greater than the lowest
values seen at the beginning of the Swift campaign. This trend should continue
through apastron and require precise measurements to follow its progress for
the next few years and complete the loop which might include a shallow local
minimum a few months after the binary separation starts to decrease again.

###  4.5 The “Relic” Component

Analysis of Suzaku X-ray spectra during the X-ray minimum associated with the
2009 periastron passage by Sugawara et al. (2015) uncovered a soft component
below about 2 keV, which they suggested was a relic of cooling plasma from the
wind collision. This “relic” component was seen in spectra obtained on
2009-01-04 and 2009-01-13, at orbital phases of -0.004 and 0.001,
respectively. The relic component seems similar to residual soft emission
revealed in other systems at orbital phases when the colliding-wind emission
suffers severe photoelectric absorption: relevant examples include
$\gamma^{2}$ Velorum (Hartman et al., 2004), the brightest Wolf-Rayet star in
the sky and also a WC+O binary system; and $\eta$ Car (Hamaguchi et al., 2007)
where a so-called “Central Constant Emission” component emerges at its deep
X-ray minimum.

Figure 11 shows a well-exposed XMM-Newton EPIC-pn X-ray spectrum of WR 140
taken two days before maximum X-ray absorption at the inferior conjunction of
the WC7 star. It was retrieved from the XMM-Newton Science
Archive777http://nxsa.esac.esa.int/nxsa-web/ under ObsID 0790850201. It shows
clear distinction between the hard colliding-wind emission in which the line
emission from Fe XXV remains prominent above the highly absorbed continuum,
and the soft relic component. The relic is composed of narrow features that
are resolved even with the limited spectral capabilities of the EPIC-pn
instrument and whose energies are well-determined enough to enable the
identifications suggested in Figure 11 following Sugawara et al. (2015).

Figure 11:  XMM-Newton EPIC-pn energy spectrum of WR 140 observed about a week
after periastron passage in 2016 showing most clearly the relic component
emission below 2 keV and suggested identifications for some of its narrow
features displayed on a logarithmic scale in energy.  Figure 12:  The X-ray
count rate in the relic band (0.4 – 2.0 keV) from Swift XRT observations
including only grade 0 events above 0.4 keV, compared to the 2 – 10 keV
colliding wind emission from the grade 0 events. The relic component is
visible from 25 days before periastron passage to about 50 days afterwards,
during times of high absorption. The XMM-Newton spectrum in Figure 11 was
taken close to conjuction

The Swift monitoring observations around the 2016 periastron passage provide a
measure of the appearance of this component and its temporal behavior once
account is taken of the effects of PC-mode optical loading. The XMM-Newton
data shown in Figure 11 do not suffer from this effect. The XRT was switched
to PC mode once the count rate had fallen sufficiently as WR 140 approached
its minimum for pile-up no longer to be significant, since PC-mode provided a
directly-determined background estimate, important when the X-ray source was
faint. Initial inspection of the lowest-energy data then showed erratic
variability which proved to be confined to multiple-pixel (as opposed to
single-pixel) X-ray events as classified by event grade. Event grade is
assigned early during data processing to show the number and pattern of
neighboring detector pixels contributing to the recognition and reconstruction
of an individual X-ray photon. Single pixel events are classified as grade 0
while multiples are doubles with grades 1-4; triples with grades 5-8; or
quadruples with grades 9-12. Composite spectra for doubles, triples and
quadruples accumulated during the minimum showed the narrow low-energy peaks
at 2, 3 and 4 times the event threshold, respectively, characteristic of
optical loading affecting optically bright targets in tailored calibration
work. Single grade 0 events with energies below 0.4 keV were excluded for the
same reason.

Figure 12 shows the variations of the grade-0 selected count rates in soft
($0.4<E<2.0$ keV) and hard ($2.0<E<10.0$ keV) bands as a function of phase
near periastron passage and WR conjunction a few days later. The soft band
includes the relic component while the hard band is dominated by the thermal
emission from the colliding wind shock. The relic component is revealed about
10 – 15 days before periastron due to combination of increasing absorption and
decreasing luminosity of the colliding-wind shocks, and is visible for about
50 days after periastron until absorption and luminosity have recovered for
low-energy events again to be dominated by emission from the wind-wind
collision. During the 50-d minimum, although the relic component is
responsible for only a handful of counts in each observation, there is some
statistical evidence for variability. The accumulated spectrum closely
resembles that seen at occasional relevant phases during much longer
observations with CHANDRA, XMM-Newton, and Suzaku.

##  5 The C III $\lambda 5696$ Connection

As the stars in WR 140 approach and pass periastron, significant excess
emission appears superimposed on the strong flat-topped C III $\lambda$5696
emission line characteristic of WC stars (Hervieux, 1995; Marchenko et al.,
2003; Fahed et al., 2011). The excess has complex and well-resolved velocity
structure that moves rapidly from blue to red across the line as the intensity
strengthens and fades through periastron and beyond. Similar excesses are also
seen in C III $\lambda 5696$ in other WC colliding-wind binaries (e.g., Hill
et al., 2018) and in other lines in WR 140 such as He I$~{}\lambda$10830
(Williams et al., 2021). It has been natural to suppose such optical and
infrared excesses to originate some way downstream in the wind collision zone
after shocked WC-star plasma has had time to cool to an appropriate
temperature ($T\lesssim 10^{5}$ K) with the velocity profile formed in the
continuously changing orientation of the shocked flow wrapping around the O
star as the system revolves in its orbit.

However, three observational arguments suggest instead a closer connection
between X-rays and C III $\lambda 5696$ concerning, in turn, their correlated
temporal behavior; the comparative luminosities; and the observed velocity
profiles; all considered in the context of the succession of orbital events of
quadrature, periastron and conjunction that occur so close together in WR
140’s highly eccentric but accurately-defined orbit when shocked gas flows
away on time scales $D/v_{\infty}\sim 1$ day or less. During this crucial part
of the orbit, many things are changing rapidly at once on a daily basis with
the sharp fall in intrinsic X-ray luminosity and sharp rise in absorption,
combining to produce a steeply declining X-ray count rate as the strength of
the C III $\lambda 5696$ line increases before turning points throw the system
into reverse.

###  5.1 Anti-correlated variability of X-ray and C III $\lambda 5696$

Figure 13 compares the evolution of the equivalent widths of C III $\lambda
5696$ during the 2009 periastron passage (from Table 7 in Fahed et al., 2011)
with the 2–10 keV X-ray flux measured during that time by RXTE. This shows an
exceptionally tight correlation between the observed drop in X-ray flux and
the strengthening C III before periastron: formally, the Pearson correlation
coefficient = $-0.963$ in the interval between 2008-12-18 and 2009-01-21.
About 20 days before periastron, a step occurs in the X-ray decline mimicking
closely a similarly subtly-shaped feature in the strengthening C III line. The
lack of any apparent lag between the two morphologies coupled with the timing
of the turning points of C III maximum and X-ray minimum close to periastron
suggests a common central origin of both types of radiation.

Figure 13: Comparison of the equivalent width of the C III $\lambda 5696$
excess and the X-ray flux seen by RXTE during the 2009 periastron passage of
WR 140. The asymmetry in the X-ray curve is mostly due to photoelectric
absorption by the WC-star wind traced by the RXTE hardness ratio, HR.

###  5.2 Luminosities of X-rays and C III $\lambda 5696$

We converted the C III $\lambda 5696$ excess equivalent widths reported by
Fahed et al. (2011) to luminosities to compare to the phase-dependent
intrinsic X-ray luminosities and assess the relative importance of the X-ray
and C III in the overall shock energy budget during the few weeks around
periastron when the excess appears. For WR 140 values of $V=6.85$ and
$A_{V}=2.01$ and the standard calibration of the $V$-magnitude intensity scale
of $f_{\lambda}=3.64\times 10^{-9}$ erg cm-2 s-1 Å-1 at $V=0$ gives a
conversion factor of 1.16$\times 10^{34}$ erg s-1 Å-1 for a distance of 1.52
kpc to WR 140. Figure 14 shows immediately the close complementary
relationship between the X-ray and C III luminosities in which the central
X-ray deficit seen in Figure 5 is almost exactly compensated by C III. The
combined luminosity $L_{X+CIII}=L_{X}+L_{CIII}$ formed by these two components
of the energy budget and derived by interpolation is also shown and closely
resembles the ideal $1/D$ prediction of colliding-wind theory. The combined
luminosity observed at periastron, where the C III $\lambda 5696$ excess
peaks, is $L_{X+C~{}III}=1.8\pm 0.1\times 10^{35}~{}$ergs s-1and the X-ray
luminosity observed at apastron, in the expected absence of a C III excess, is
$L_{X}=1\times 10^{34}$ ergs s-1. Their ratio, $18\pm 1$, is consistent with
the value of $(1+e)/(1-e)=18.9$, where $e$ is the orbital eccentricity,
expected if the $1/D$ prediction applies around the entire orbit of WR 140.
This is encouraging, though it should be borne in mind that the error given in
the ratio, determined by the reported uncertainty in the C III equivalent
width, is probably an underestimate due to unknown systematic errors that
apply, for example, to the reddening correction.

Figure 14: Comparison of the 0.5–10.0 X-ray luminosity and the luminosity of
the C IIIline excess, both corrected for absorption, and the combined (Lx + C
III) luminosity. The dashed line is a $1/D$ variation scaled by eye to the
data.

###  5.3 Velocity structure of the C III excess

Information about the dynamics and location of the material radiating in the C
III $\lambda 5696$ line is available by considering, in addition to its
intensity, the variable velocity profiles of the excess shown in Figure 3 and
plotted in Figure 5 of Fahed et al. (2011). The observations illustrated there
fall conveniently into separate groups according to orbital geometry. Before
quadrature, when the WC star is behind its O-star companion, the excess,
though faint in its early development, is nearly all confined as expected to
negative velocities as the radiating material flows towards the observer. A
week later, in a set of 3 observations more-or-less at quadrature, the excess
is distributed roughly evenly between blue and red velocities. The maximum
observed red shift is reached within perhaps 2 or 3 days of conjunction when
the WC star is directly in front of its companion and shocked material is
flowing away.

##  6 Discussion

RXTE, Swift, and NICER X-ray monitoring observations of WR 140 have confirmed
that its X-ray properties varied in a predictable way over the 4 orbital
cycles between 2000 and 2020. They show that the shock conditions and
radiation transfer vary repeatably as a function of orbital phase and
therefore provide a rich and detailed set of measurements on which improved
understanding of the underlying physics may be built. Appropriate 3D models
combining orbital and gas dynamics with the physics of shock formation and
dissipation are likely to be a challenging enterprise but whose boundary
conditions are now more clearly defined by the results presented here
concerning the cooling mechanisms of collisionless shocks under different
conditions and the geometry of the interacting winds.

With its uniquely well-determined 3D highly-eccentric orbit, WR 140 presents
optimum opportunities for the study of its collisionless shocks in an
astrophysical setting whose variable physical conditions of density,
temperature, wind and orbital velocities and viewing angle remain under the
simple control of gravity and orbital geometry.

The physical justification for classifying WR 140’s shocks as collisionless
(Pollock et al., 2005) and therefore regulated by collective electromagnetic
processes as opposed to gas collisions rests on the long mean-free-paths for
Coulomb collisions that pertain in the plasmas that constitute the winds of
the hot stars. Conclusive supporting evidence for a collisionless
classification comes from WR 140’s status as a strong non-thermal synchrotron
radio source (White & Becker, 1995a). The relativistic electrons and magnetic
fields required are both common properties of collisionless shock physics
(e.g. Marcowith et al., 2016) that do not arise in the collisional regime.

###  6.1 Magnetic Conditions in the Shocks of WR 140.

Though Marcowith et al. (2016) argue that the background upstream magnetic
field plays a pivotal role in the formation and dissipation of collisionless
shocks, particle-in-cell simulations (Kato & Takabe, 2008) show that the
Weibel instability also operates in interacting unmagnetised plasmas to
generate magnetic fields whose energy density amounts to 1% or 2% of the
upstream bulk kinetic energy density. At the stagnation point in the terminal-
velocity regime in that case

$\frac{1}{8\pi}B^{2}=W_{B}\frac{1}{2}\rho V\infty^{2}$ (2)

suggesting a shock-generated field of

$B\approx 1141\frac{1}{R_{X}}(W_{B}\dot{M}_{-6}V_{8})^{\frac{1}{2}}G$ (3)

where $W_{B}$ is the fractional magnetic-field energy density and otherwise
the units are those of equation (1) including $R_{X}$ in solar radii. Shock-
generated fields in initially unmagnetized media have been successfully
reproduced in the laboratory (Huntington et al., 2017) and are an alternative
to the common practice following Weber & Davis (1967) of extrapolating a
stellar field into the wind, especially since strong surface fields are rare
in O stars (Grunhut et al., 2017) and undetected so far in Wolf-Rayet stars
(de la Chevrotière et al., 2014). At periastron, equation (3) implies a field
of $0.05-0.1~{}G$ at the stagnation point, and a shock dissipation scale
length defined by the proton gyroradius of a few km. This field is about two
orders of magnitude greater than those typically encountered in interplanetary
space in front of the Earth’s magnetosphere.

###  6.2 Competitive Shock Cooling

The combination of X-ray and C III $\lambda 5696$ luminosities in the shock
energy budget suggests that the ideal $1/D$ prediction of colliding-wind
theory might still make reasonable sense for WR 140. If scalable geometry also
applies, the O-star shock would lie only 36 $R_{\odot}$ from the center of the
star at periastron, only a few radii above the stellar surface. The evident
competition between X-ray and C III $\lambda 5696$ cooling in such extreme
conditions could conceivably be density or radiation dependent (Martins &
Hillier, 2012) if some other mechanism is excluded like charge exchange due to
mixing between the two winds (Pollock, 2012). However, when it is understood
that lines at long wavelengths often classified as recombination lines can
provide cooling under certain conditions to rival or surpass the X-ray
luminosity, it will be necessary to consider other transitions such as He I
$\lambda 5876$ (Marchenko et al., 2003) and He I $\lambda 10830$ for which
Williams et al. (2021) have shown the importance of extensive phase coverage.
Pending these assessments, it does not yet seem necessary to appeal to the
suggestion of a variable effective mass-loss rate due to clumping effects
(Zhekov, 2021) to account for the unexpected decrease in WR 140’s X-ray
luminosity near periastron. Rather, the plasma has found another way to cool.

Future observations would be able to establish more firmly the nature of the
cooling competition in at least three respects: first, more complete phase
coverage including templates; second, simultaneous X-ray and optical line
velocity profiles; and third, how close the C III emission peak is to the 2024
November 22 periastron in comparison with the 1-day flow time. These will all
allow judgement of whether the rival cooling mechanisms compete on
microscopic, as seems likely, or macroscopic scales.

In other WC+O binary systems of shorter period and smaller separation, WR 42,
WR 48 and WR 79 (Hill et al., 2002) and WR 113 (Hill et al., 2018), the
competition may have been decided in favour of C III $\lambda 5696$ by their
luminous excesses and weak or undetected X-ray luminosities.

###  6.3 X-ray Absorption Tomography

While the X-ray luminosity can be be considered almost an integrated
thermodynamic state variable that responds to externally imposed conditions
like an ideal astrophysical Carnot cycle, the observed absorption of the X-ray
spectrum is sensitive to the morphology of whatever cold gas intervenes
between source and observer. The model spectrum used to estimate the
absorption as a function of phase simply incorporated a single line-of-sight
column density to the stagnation point in the flow. This is adequate for the
current campaign in which the scarce resource of observing time was shared
between multiple observations to yield spectra of modest statistical weight at
many different phases. The X-ray source is almost certainly extended on the
scale of the binary separation. Though its detailed spatial form is not known,
it is small enough for sharp features to appear in Figure 7 that delineate the
morphology of the cool gas as the orbit rotates. Notably, the duration of the
transition between O-star and WC-star winds implies that the post-shock gas
occupies a significant angular size of $26\mbox{${}^{\circ}$}$ which Figure 8
suggests is due in about equal measure to the angular extent of the post-shock
gas and the curvature of the shock front. As a consequence, the implication is
that the shock has not suffered collapse at this point close to periastron
from radiative losses.

The measurements made separately near both stellar conjunctions have enabled
the estimates above of the mass-loss rates of both companion stars of
$\dot{M}_{WC7}=1.7\times 10^{-5}$ M⊙ yr-1 and $\dot{M}_{O5}=3.7\times 10^{-7}$
M⊙ yr-1 implying a measured value of $\eta=44$ that is reasonably close to the
wind-balance parameter adopted in Table 1. This looks encouraging, though
there remain challenges for future, 3D dynamical models to resolve in
accounting for the phase-dependent absorption through the WC-star wind where
the simple absorption model of Eq. 1 breaks down.

The simple model of the phase-dependent O-star wind absorption implies
consistent mass-loss rate estimates from measurements made over more than a
year. The mass-loss rate may be low and dependent on elemental abundances that
take no account of any mass-exchange that may have taken place in the course
of the binary system’s evolution but it does have the merit of demonstrating
the sensitivity of X-ray absorption measurements of colliding-wind systems for
making realistic clumping-free estimates of the mass-loss rates of the O stars
in these systems and determining the extent of the absorbing media.

By contrast, point estimates following the same procedure of the WC-star mass-
loss rate from its absorption lead to inconsistent values depending on orbital
phase that differ by a factor of a few. In the formation and dissipation
mechanisms of collisionless shocks, it becomes necessary to consider instead
the established importance of reflected ions as described, for example, by
Burgess & Scholer (2015) and Madanian et al. (2021b). Reflected ions form a
“sheath” of cool material around the collisionless shock, and, for WR140, the
sheath on the WC7-side of the shock would consist largely of He & C rich
material with large X-ray opacity. Observations of collisionless shocks in
supernovae suggest that the reflected-ion fraction increases with Mach number,
reaching up to 50% or more of the material entering the shock (Ghavamian et
al., 2013). The similarities between collisionless shocks in colliding-wind
binaries and supernovae was emphasized earlier (Pollock et al., 2005).

Figure 10 shows that, at the highest columns observed, there’s relatively
little change of $N_{x}$ with $\theta/b$, indicating a thick source of
absorbing material which remains relatively independent of the orbital
geometry as the stars move from O star inferior conjunction through WC star
inferior conjunction and beyond. Zhekov (2021) used 2D hydrodynamic models of
WR 140’s RXTE data precisely to argue for an additional absorption component,
although leaving its origin open. In this orbital phase range, the WC star is
in front of the shock boundary, so it seems natural to suggest that the outer
surface of WR 140’s collisionless shocks are enveloped in a sheath of
reflected ions through which the X-rays from the colliding wind shock pass and
that dominates the observed absorption in the range of maximum absorption,
$0.01<\theta/b<0.02$, shown in Figure 10. The ionization state and chemical
abundance of the reflected ion sheath would be similar to upstream WC7 wind
and present an immediate additional absorption to the X-rays originating
immediately on the other side of the shock discontinuity. Because X-ray
absorption would occur mainly in the enriched carbon content of the WC-star
material, this would be the first direct detection outside the solar system of
the reflection of heavy ions in high Mach-number collisionless shocks, and an
astrophysical analog to the He II reflected ion sheath in the magnetosphere
directly detected by Madanian et al. (2021a). In order to satisfy mass
continuity the sheath would also have some dynamical structure that involves
flow parallel to the shock that might be visible in the velocity structure of
long-wavelength absorption lines in either stellar continuum at favourable
orbital phases as discussed below for He I $\lambda$10830\. In WR 140 it also
becomes possible to explore the shock formation process involving ion
reflection as a function of density and velocity shear driven by the orbital
motion of the stars.

####  6.3.1 X-ray Absorption and Dust

We compared the column density variations to the $K$-band lightcurve in Figure
15 for contemporaneous data taken as part of the 2016 periastron passage
observing campaign. The $K$-band lightcurve, a measure of the brightness of
the periodic dust formation, is shown in orange. The $K$-band brightness
increases almost exactly at periastron passage (although it’s not clear why
the dust appears so precisely here and not sometime before or after), which
suggests that dust nucleation begins very near periastron or that it first
becomes visible to the observer at periastron passage. In either case there’s
no physical reason why this coincidence would occur, unless the cold, dust-
forming gas is embedded within the hot shocked gas and somehow shielded from
the harsh radiative environment near the WC7 and O5 stars (as suggested by
Williams et al., 2009) and the X-ray emission of the shocked gas in the
collision zone. As noted above, the rapid increase in X-ray column density
begins about 50 days before periastron passage. About one month after
periastron passage, the decline in K-band brightness is (unexpectedly) very
similar to the decline in column density. The fading in $K$-band brightness is
believed to be due to the cooling of dust in the dust shell as it expands away
from WR 140. The similarity between the decline in $K$-band brightness and
decline in X-ray column may indicate a physical connection between the X-ray
absorption and the dust shell, i.e. it may be that some of the X-ray
absorption arises in the dust shell itself, as well as in the unshocked wind
of the WC star.

In Figure 15, the relative $K$-band flux is derived from the $K$-band
magnitudes as $F_{K}=10^{-K/2.5}$, where $F_{K}$ is the relative $K$-band flux
and $K$ the $K$-band magnitude. The $K$-band increase starts within five days
of periastron passage (unfortunately there is no $K$-band data in the interval
$\approx\pm 2.5$ days around periastron passage in 2016). The increase in
$K$-band brightness occurs well after the start of the increase in X-ray
column density, and maximum $K$-band brightness occurs after maximum X-ray
absorption (which, as noted, occurs very near superior conjunction of the O
star). The $K$-band brightness does not reach its maximum until about 70 days
after periastron. Assuming the speed of the dust is 1600 km s-1(Williams et
al., 1990), after 70 days the dust has moved 65 AU, about 5 times the semi-
major axis of WR 140. After $K$-band brightness reaches its maximum, it begins
to decline exponentially, with an e-folding time of about 153 days. In the
$H-$band and other short-wavelength IR bands, the brightness starts to decline
shortly after dust formation ends (Williams et al., 1990). At longer IR bands,
the brightness maximum is reached at later orbital phases and the decline is
slower, as the dust cools and the peak emission moves to longer wavelengths.

Figure 15: Comparison of the X-ray column density derived from Swift and NICER
spectra, with the variation in relative K-band flux vs. orbital phase around
the 2016 periastron passage. The decline in $N_{H}$ is well correlated with
the decline in relative K-band flux.

####  6.3.2 X-ray and He I $\lambda$10830 Absorption

Williams et al. (2021) describes the variation of the P-Cygni He I
$\lambda$10830 line near the 2009 and 2016 periastron passages. The He I
$\lambda$10830 emission and absorption components are primarily produced by
the He-rich wind of the WC7 star. This line is both very bright, with a flux
exceeding the 2 – 10 keV X-ray flux for most of the orbit and complex, showing
an emission sub-peak which varies with orbital phase in strength and radial
velocity. The P-Cygni absorption is seen in the radial velocity range
$-3000~{}\mbox{km~{}s${}^{-1}$}<V<-2000~{}\mbox{km~{}s${}^{-1}$}$, and so is
produced by He-rich gas from the WC7 star lying along the line of sight in
front of the stars. We compared the equivalent widths of the He I
$\lambda$10830 P-Cygni absorption (given in Tables 1 & 2 of Williams et al.
2021) to the X-ray absorption column measured from the Swift and NICER spectra
(see Fig. 16).

Figure 16: Comparison of the equivalent width of the He I 1.083$\mu$ P-Cygni
absorption component from Williams et al. (2021) to the X-ray column densities
as measured from the analysis of the Swift and NICER spectra versus orbital
phase.

As discussed by Williams et al., the observed variation in the equivalent
width of the He I absorption is mostly due to absorption variations in the WC7
wind along the line of sight to the O star, since the amount of WC7 material
in front of the O star varies systematically as the orientation and separation
of the stars change with orbital motion. There’s an interval of (mostly) weak
absorption near the time of inferior conjunction of the O star since near this
phase O star is mostly viewed through its own lower-density wind which fills
the shock cavity. Starting at roughly $\phi\approx 0.98$ (when the trailing
arm of the colliding wind bow shock passes the observer’s line of sight) both
stars and the colliding wind shock are viewed through the dense wind of the
WC7 star and the X-ray column and He I absorption increase rapidly, reach
maxima near superior conjunction of the O star, and then gradually decline.
The variation in X-ray column is larger than the observed variation in He I
equivalent width; a drop by about a factor of 50 in X-ray column corresponds
to a decline of about a factor of 2 in He I equivalent width. This may suggest
that some of the absorption is filled in by high velocity, blueshifted
emission. As discussed by Williams et al., there’s a spectrum showing
anomalously strong He I absorption near the inferior conjunction of the O star
(near $\phi\approx 0.96$), and anomalously weak absorption near the second
quadrature (near $\phi\approx 1.04$). These probably arise from stochastic
density variations produced by instabilities in the WC7 wind near the
colliding-wind bow shock, as noted by Williams et al. (2021).

###  6.4 The Relic Component

The Swift data presented in Figure 12 show that the relic component can be
first seen about 25 days prior to periastron passage up to 50 days after
periastron passage, when absorption is high enough that the colliding wind
component is a negligible contributor to the emission in the 0.4-2.0 keV band.
The Swift data also show that the flux of this component is not strongly
variable through this interval. Sugawara et al. (2015) suggested that this
component is radiative recombination continua produced by the shocked wind as
it cools (perhaps as a precursor to dust formation), but this seems unlikely
given the Swift observations. In this 75 day interval around periastron the
stellar winds have flowed out a distance $\sim$124 AU. Assuming the
recombining gas is entrained in the wind, it’s difficult to see how this gas
could show a relatively constant X-ray brightness while moving such a large
distance while experiencing large changes in density and temperature. The
Swift observations of the relic component suggest that this is instead a soft,
relatively constant source. This source has a flux of 1.1$\times 10^{-12}$
ergs cm-2 s-1, corresponding to a luminosity of 2.9$\times 10^{32}$ ergs s-1.
The X-ray flux from the embedded shocks in the O star wind should be
approximately 1.4$\times 10^{32}$ erg s-1, since the luminosity of the O5.5fc
star is $L_{O}\approx$ 3.5$\times 10^{5}L_{\odot}$ (Thomas et al., 2021) using
the canonical relation for X-ray luminosity from embedded wind shocks in O
stars, $L_{x}/L_{bol}\approx 10^{-7}$. It’s unlikely that the O5.5fc star is
the source of the “relic” component, however, since near periastron passage
the star is behind the WC7 star, so that any soft emission in its wind would
suffer significant, and significantly variable, absorption by the wind of the
WC7 star. Another alternative is that this emission is produced by embedded
shocks within the wind of the WC7 star, which seems unlikely since in general
single WC7 stars are very weak X-ray sources. The emission could be produced
by a third unresolved O-type star in the system, but this also seems unlikely
since the star would need to be similarly bright as the O5.5fc star. $\eta$
Car shows soft, constant X-ray emission from the “Outer Debris Field”, the
shell of ejecta produced by the eruption of the star in the 1840’s. Unresolved
ejecta near the star from some past outburst of WR 140 could also reveal
itself as the “relic” component, but there’s no recorded outburst of WR 140,
so this alternative seems unlikely as well. Perhaps the most likely
explanation is that this source is similar to the “Central Constant Emission”
component seen in $\eta$ Car (Hamaguchi et al., 2007), which is produced by
residual hot shocked gas trapped between the distorted shock cone near
periastron passage (Russell et al., 2016).

###  6.5 Comparison with $\eta$ Car

Long-period, eccentric massive binaries are hard to detect unless they present
evidence of wind-wind collision emission. This is because the stars in these
systems spend most of their time near apastron, in accordance with Kepler’s
second law. In the case of WR 140, for example, it takes the component star
1220 days (about 40% of the orbital period) to travel $\pm 0.05$ in orbital
phase around apastron, while around periastron the same interval in phase is
covered in only 25 days (about 1% of the orbital period). Because stellar
radial velocity variations are minimal at apastron, and photocenter variations
non-existent, it’s difficult or nearly impossible to identify such systems
using classical radial velocity, photometric or proper-motion surveys in the
absence of colliding-wind effects. Such systems can be identified, as in the
case of WR 140 and other carbon-rich “dustars” (like WR 125 and WR 19) via
periodic brightening in the IR caused by dust formation in the compressed wind
collision near periastron. But it usually requires a bit of patience and/or
luck in order to catch such dust formation episodes as they are occurring. The
X-ray emission produced by colliding winds is a more constant tracer, since
X-rays are produced through most of the orbit and since single WR stars are
usually weak X-ray sources.

Both WR 140 and $\eta$ Car are now understood as long-period, highly-eccentric
binary systems and first recognized as such based on variations produced by
their wind-wind collision regions. In both cases, periodic variations in the
IR were reported – but the nature of these variations was rather mysterious
and their ties to a putative companion star unclear. In both WR 140 and $\eta$
Car, such periodic photometric variations were initially discussed in terms of
“shell events” (periodic ejection of shells of material from a – perhaps
single – star). Early X-ray observations of the stars revealed unusually
bright X-ray flux, whose origin was also at first unclear, but which is now
recognized as a clear sign of the presence of hot shocked gas produced by a
wind-wind collision. Establishing strictly periodic photometric variability
though long, painstaking campaigns in the IR (Moffat et al., 1987) and radio
(White & Becker, 1995b), coupled with sporadic X-ray observations (Pollock,
1985; Williams et al., 1990) made a convincing case for the presence of
another star in WR 140, confirmed by subsequent observations in the radio and
optical, along with high-resolution ground-based radial-velocity studies which
spatially and spectrally resolved the orbital motions of the two stars (and
even showed emission from the ionized gas in the bow shock). Similarly in the
case of $\eta$ Car, observations of periodic variations in the equivalent
width of the He I $\lambda$10830 emission line over half a century, along with
Paschen line variations (Damineli, 1996; Damineli et al., 1997), and hard
(Seward & Chlebowski, 1982), variable (Ishibashi et al., 1999) X-ray emission
provided persuasive evidence that $\eta$ Car is also a long-period, highly
eccentric binary (even though $\eta$ Car’s companion star has not been
directly seen).

Figure 17: Left: Comparison of the 2–10 keV X-ray lightcurve of WR 140 from
RXTE, Swift and NICER, to the 2–10 keV RXTE and Swift fluxes for $\eta$ Car,
normalized at apastron. $\eta$ Car is about an order of magnitude brighter
than WR 140 at apastron. The phases for $\eta$ Car are calculated using the
periastron passage epoch $T_{o}=$ JD 2,456,874.4 from Teodoro et al. (2016)
and the X-ray period, 2023.7 days, and fluxes from Corcoran et al. (2017). The
lightcurves for each binary have been combined and smoothed using a 5-point
boxcar for display purposes. Right: The phase interval near periastron
passages for the two binaries.

The X-ray behavior of $\eta$ Car and WR 140 shows similar variation with
orbital phase – long, slow rise in flux, a sudden drop accompanied by an
increase in absorption, a brief flux minimum, the appearance of a soft
component during the minimum – but also important differences. The 2-10 keV
X-ray minimum in $\eta$ Car appears flat-bottomed (mostly due to the presence
of circumstellar X-ray background emission) and to last for 30–60 days before
increasing in flux. WR 140’s X-ray minimum state in the same band only lasts
for about 10 days once the minimum is reached. Figure 17 compares the X-ray
flux variations of WR 140 and $\eta$ Car, normalized to their fluxes at
apastron. Although $\eta$ Car is about an order of magnitude brighter in the
2–10 keV band (and about 15$\times$ brighter in X-ray luminosity), the ratio
of X-ray flux at maximum to X-ray flux at apastron is about a factor of two
greater for WR 140 compared to $\eta$ Car. These differences may be due to
differences in orbital eccentricity, if the orbital eccentricity of $\eta$ Car
is lower than the eccentricity of WR 140 ($e=$0.90). Other important
differences that shape the X-ray lightcurves are the relative terminal stellar
wind speeds $V_{\infty}$ of the component stars in the binary ($V_{\infty}$ is
about a factor of 8 different for the stars in $\eta$ Car, and nearly the same
for the two stars in WR 140), along with wind (and circumstellar) absorption.

On approach to X-ray maximum, $\eta$ Car’s X-ray flux shows large variations
on timescales of weeks to days (Corcoran et al., 1997; Moffat & Corcoran,
2009). This variability has not been seen in any of the pre-minimum phase
intervals for WR 140, and flux variations (apparently stochastic) appear to be
$<10-20$% at any phase. Moffat & Corcoran (2009) suggested that the flux
variations in $\eta$ Car are driven by large, stochastic overdensities
(“clumps”) in the massive, slow wind of the LBV primary, $\eta$ Car-A. If this
is the case, the relative smoothness of the WR 140’s X-ray lightcurve may
reflect the smoothness of the wind of the WC7 star, perhaps because its
higher-velocity wind helps reduce out any perturbations before they can grow
substantially.

##  7 Conclusions

In the 66 years since the initial suggestion by Gold (Temple, 1955, p103) that
shock discontinuities occur in low-density plasmas on scales far shorter than
their long Coulomb collisional mean-free-paths, collisionless shocks have
become recognised as central for the understanding of gas dynamics throughout
the Universe. Similarly, in the 45 years since the predictions by Prilutskii &
Usov (1976) and Cherepashchuk (1976) that Wolf-Rayet binary systems should be
bright sources of X-rays from shocked gas produced by the dynamical
interaction of two counterstreaming supersonic stellar-wind plasmas,
observations have confirmed their high luminosities among hot-star X-ray
sources. WR 140 is the preeminent example that unites these two themes for its
exceptional X-ray brightness among other observational riches and the
precision with which its orbital and stellar parameters are known, allowing
the boundary conditions to be accurately defined under which the collisionless
shocks arise.

The accumulation of nearly 1000 X-ray observations and nearly complete phase
coverage have allowed some progress to be made towards a coherent
understanding of the physics underlying its collisionless shocks and the
various instruments that have been employed. WR 140 is bright enough in the
X-ray band for statistical errors to be smaller than residual low-levels of
systematic calibration errors. In order to exploit the promise of high-
precision collisionless-shock physics enabled by WR 140, attention has
variously been necessary to instrumental features such as X-ray pile-up,
optical loading, background contamination and cross-calibration. Within these
limits and within the framework of a colliding-wind binary model in which the
shocks are understood to be collisionless, a clear and consistent set of
conclusions has emerged from campaigns with RXTE, Swift, and NICER in the
first 20 years of the 21st century regarding WR 140’s behaviour as a function
of the phase of its highly eccentric 7.94-year orbit:

  * •

X-ray emission and absorption from WR 140 are repeatable with orbital phase

  * •

The smooth X-ray lightcurve shows no evidence of instabilities or other short-
term variability or of changes in its effective temperature

  * •

Shock X-ray luminosity is inversely proportional to binary separation for most
of the orbit

  * •

Luminosity departures near periastron are largely restored in a switch from
X-rays to excess optical line emission that probably operates on a microscopic
level

  * •

The shock energy budget probably also involves magnetic-field generation
through the Weibel instability

  * •

Foreground X-ray absorption occurs upstream in the wind terminal-velocity
regimes of both WC7 and O5 stars according to phase allowing clumping-free
estimates of their mass-loss rates and the interstellar absorption

  * •

Features in the X-ray absorption curve arise from the geometry of the shock
system

  * •

Shock-reflected ions would naturally explain a substantial part of the X-ray
absorption by the WC-star wind

  * •

Dust-powered K-band photometry and He I $1.083\mu$ absorption are correlated
in their own fashion with the falling X-ray absorption after periastron

  * •

Residual soft X-rays revealed near periastron are less variable than the bulk
shock emission and their origin remains uncertain

The full physical implications of the considerable body of accumulated data on
WR 140 including the conclusions listed above will require detailed models to
be built. In this, we are happy to anticipate sharing with modelers whatever
data or summary parameters they may require. In the specific context of
collisionless shocks, it is an open question how successful fluid models might
be or whether kinetic particle-in-cell calculations are necessary or even
feasible. In either case, the shock continuity equations that determine post-
shock conditions on the basis of things we know probably need to face
adjustments that conceivably involve, for example, reflected ions; magnetic-
field generation; non-thermal particle acceleration; or cooling competition.
The presence of a sheath of reflected ions could also provide an alternative
dense environment cooler than shocked gas that might be worth considering as a
possible site for dust formation.

As evident from WR 140, the utility of complete and repeated phase coverage
should encourage similar efforts in other binary systems. These might be
especially worthwhile in objects for which even currently available piecemeal
work has already shown to have interesting behavior such as V444 Cygni (Lomax
et al., 2015) or $\gamma^{2}$ Velorum (Schild et al., 2004).

Future work on WR 140 itself should immediately entail absorption measurements
to close the vertical loop in Figure 10 to trace the comparatively slow
transition between WC-star and O-star winds and to seek a global absorption
minimum to test the reliability of the interstellar component estimated above.
More important will be plans to explore further the complementary relationship
established here between competitive means of plasma cooling in at least two
ways: by establishing precise timing of the total radiative luminosity
compared with the key orbital event of periastron; and by comparing the
velocity profiles of the emission lines at short X-ray wavelengths and long
optical or IR wavelengths. These will help to determine the extent to which
the X-ray and excess optical emission arise in the same physical space and
establish how prompt are electron and ionic heating.

The current data suggest that WR 140’s X-ray properties are highly predictable
and that it could or should therefore serve as a calibration source both for
high-energy instruments and for numerical models of shock formation. In any
case, the way seems open for WR 140 to become a key reference point for the
study of collisionless shocks. The space physics and astrophysics communities
might join forces in devising ideas for observations and models to exploit the
richness of its observational variety to advance understanding of physical
processes that operate throughout the Universe.

We would especially like to acknowledge the RXTE, Swift, and NICER teams, for
their heroic efforts in scheduling these observations. We’d also like to
acknowledge the project scientists, Jean Swank, Neil Gehrels, Brad Cenko,
Keith Gendreau and Zaven Arzoumanian for granting director’s discretionary
time to help define these lightcurves. This work made use of data supplied by
the UK Swift Science Data Centre at the University of Leicester. We’d also
like to thank the anonymous and unsung peer reviewers who awarded time to
these observing programs. This research was supported through NASA cooperative
agreement NNG06EO960A. This research made use of the Astrophysics Data System
and the HEASARC archive. We express our appreciation to the amateur
astronomers for their dedication and herculean efforts to observe WR 140
during its 2009 periastron passage. This work has made use of data from the
European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia),
processed by the Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. A. F. J. Moffat is grateful
for financial aid from NSERC (Canada). D. Espinoza gratefully acknowledges
support from NASA grants #80NSSC19K1451 and #80NSSC21K0092, and SAO grant
#GO9-20015A thru NASA. M. F. Corcoran is supported under the CRESST-II
cooperative agreement #80GSFC17M0002 with the NASA/Goddard Space Flight
Center. C. M. P. Russell was supported by SAO grant #GO0-21006A through NASA;
this support is gratefully acknowledged. RXTE(PCA), Swift(XRT), NICER(XTI).

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##  Appendix A Sample Spectra

To show the differences in spectral resolution and energy sensitivity, we show
sample spectra in the orbital phase range $0.1<\phi<0.4$ in 18. This phase
range was chosen because it’s the only range sampled by all 3 instruments, and
also because there’s relatively little variation in flux within this range. To
improve statistics, these spectra are combined from all the spectra for a
given instrument in this phase range. The the RXTE-PCA spectrum is combined
from net spectra, where the net spectrum has been accumulating after
correcting individual RXTE-PCA spectra for estimated instrumental background.
No background correction has been applied to either the NICER-XTI or Swift-XRT
spectra.

Figure 18:  Comparison of combined spectra from the 3 instruments (NICER-XTI,
Swift-XRT and RXTE-PCA) in a common interval of WR 140’s orbital phase
($0.1<\phi<0.4$). Some strong lines are marked in the NICER-XTI and Swift-XRT
spectrum (the poor spectral resolution of the RXTE-PCA neans it’s incapable of
resolving line features, though the Fe XXV feature does show up as an apparent
“shelf” near 6.7 keV). The Swift-XRT PC-mode data are not shown because there
were only 4 PC-mode observations in this phase interval.

Table 4: Log of RXTE Observations and Fluxes  Sequence | MJD | Phase | Expo. | Net Rate | Rate Error | Bkg Rate | Flux | Error
---|---|---|---|---|---|---|---|---
|  |  | s | cts/s | cts/s | cts/s | 10-11 ergs/s/cm2 | 10-11 ergs/s/cm2
2000120902 | 51887.106 | 1.978 | 1472.0 | 6.56 | 0.11 | 12.29 | 5.19 | 0.17
2000121607 | 51894.334 | 1.980 | 1440.0 | 6.65 | 0.12 | 13.02 | 5.56 | 0.18
2000122305 | 51901.252 | 1.983 | 1248.0 | 6.87 | 0.12 | 12.21 | 5.67 | 0.19
2000123004 | 51908.194 | 1.985 | 1440.0 | 6.71 | 0.12 | 12.91 | 5.56 | 0.18
2001010608 | 51915.365 | 1.988 | 1584.0 | 7.07 | 0.11 | 12.64 | 5.15 | 0.15
2001011406 | 51923.266 | 1.990 | 304.0 | 5.73 | 0.24 | 11.55 | 3.52 | 0.28
2001011919 | 51928.827 | 1.992 | 1024.0 | 5.49 | 0.13 | 13.10 | 3.54 | 0.17
2001012722 | 51936.930 | 1.995 | 1440.0 | 3.85 | 0.11 | 12.63 | 2.32 | 0.13
2001020316 | 51943.681 | 1.997 | 1536.0 | 2.45 | 0.10 | 13.08 | 1.21 | 0.12
2001021016 | 51950.675 | 2.000 | 1328.0 | 1.46 | 0.10 | 11.85 | 0.51 | 0.11
2001021713 | 51957.566 | 2.002 | 1392.0 | 0.99 | 0.10 | 11.95 | 0.24 | 0.11
2001022405 | 51964.253 | 2.004 | 1584.0 | 1.16 | 0.10 | 13.62 | 0.40 | 0.12
2001030319 | 51971.817 | 2.007 | 1472.0 | 2.00 | 0.10 | 12.16 | 0.96 | 0.12
2001031005 | 51978.257 | 2.009 | 1280.0 | 3.18 | 0.11 | 12.49 | 1.53 | 0.12
2001031810 | 51986.455 | 2.012 | 1360.0 | 3.23 | 0.11 | 12.09 | 1.90 | 0.13
2001032516 | 51993.695 | 2.015 | 1392.0 | 3.84 | 0.11 | 12.60 | 2.28 | 0.13
2001033109 | 51999.418 | 2.017 | 1472.0 | 3.69 | 0.11 | 13.30 | 2.29 | 0.14
2001040722 | 52006.914 | 2.019 | 224.0 | 4.32 | 0.28 | 13.53 | 2.70 | 0.36
2001041415 | 52013.665 | 2.022 | 1440.0 | 3.96 | 0.11 | 12.87 | 2.51 | 0.14
2001042119 | 52020.821 | 2.024 | 944.0 | 3.98 | 0.13 | 12.34 | 2.47 | 0.17
2001042811 | 52027.503 | 2.026 | 1376.0 | 3.81 | 0.11 | 12.36 | 2.44 | 0.14
2001050515 | 52034.592 | 2.029 | 608.0 | 4.20 | 0.17 | 12.47 | 2.77 | 0.22
2001051202 | 52041.105 | 2.031 | 1456.0 | 3.86 | 0.11 | 12.73 | 2.58 | 0.15
2001051920 | 52048.862 | 2.034 | 1472.0 | 3.90 | 0.10 | 11.62 | 2.78 | 0.15
2001052620 | 52055.871 | 2.036 | 1344.0 | 3.51 | 0.11 | 11.57 | 2.54 | 0.16
2001060205 | 52062.241 | 2.038 | 1392.0 | 3.26 | 0.10 | 11.62 | 2.23 | 0.15
2001060914 | 52069.599 | 2.041 | 1312.0 | 3.38 | 0.11 | 12.29 | 2.23 | 0.15
2001061620 | 52076.869 | 2.043 | 1456.0 | 3.35 | 0.10 | 11.75 | 2.24 | 0.14
2001062315 | 52083.646 | 2.046 | 1424.0 | 3.51 | 0.11 | 12.50 | 2.33 | 0.15
2001063023 | 52090.972 | 2.048 | 1008.0 | 3.46 | 0.13 | 13.84 | 2.43 | 0.19
2001070702 | 52097.104 | 2.050 | 1120.0 | 3.14 | 0.12 | 13.08 | 2.13 | 0.17
2001071505 | 52105.254 | 2.053 | 1216.0 | 2.83 | 0.11 | 12.04 | 2.18 | 0.18
2001072114 | 52111.609 | 2.055 | 1600.0 | 3.22 | 0.10 | 12.59 | 2.21 | 0.14
2001072716 | 52117.703 | 2.058 | 1344.0 | 2.96 | 0.11 | 12.14 | 2.10 | 0.16
2001080416 | 52125.697 | 2.060 | 1552.0 | 2.86 | 0.10 | 13.85 | 2.15 | 0.17
2001081001 | 52131.074 | 2.062 | 1296.0 | 2.82 | 0.11 | 11.70 | 2.05 | 0.17
2001081812 | 52139.547 | 2.065 | 1488.0 | 3.08 | 0.10 | 11.44 | 2.02 | 0.14
2001082420 | 52145.857 | 2.067 | 1184.0 | 2.80 | 0.11 | 11.91 | 2.03 | 0.17
2001090303 | 52155.137 | 2.070 | 960.0 | 2.75 | 0.12 | 11.68 | 1.98 | 0.19
2001090817 | 52160.753 | 2.072 | 1456.0 | 2.82 | 0.11 | 13.79 | 2.09 | 0.17
2001091415 | 52166.642 | 2.074 | 1680.0 | 2.94 | 0.10 | 14.30 | 2.16 | 0.16
2001092215 | 52174.650 | 2.077 | 1472.0 | 2.74 | 0.10 | 13.02 | 1.82 | 0.15
2001093004 | 52182.190 | 2.080 | 1312.0 | 2.61 | 0.10 | 11.65 | 1.75 | 0.15
2001100700 | 52189.014 | 2.082 | 1424.0 | 2.71 | 0.10 | 11.83 | 1.79 | 0.15
2001101322 | 52195.958 | 2.085 | 1216.0 | 2.77 | 0.11 | 12.06 | 1.94 | 0.17
2001101923 | 52201.980 | 2.087 | 288.0 | 2.28 | 0.23 | 12.63 | 1.67 | 0.37
2001102621 | 52208.901 | 2.089 | 1312.0 | 2.89 | 0.11 | 12.15 | 1.95 | 0.16
2001110305 | 52216.243 | 2.092 | 1632.0 | 2.81 | 0.10 | 12.52 | 1.92 | 0.14
2001111016 | 52223.710 | 2.094 | 1584.0 | 2.89 | 0.09 | 11.34 | 1.92 | 0.14
2001111712 | 52230.515 | 2.096 | 1440.0 | 2.58 | 0.10 | 11.74 | 1.79 | 0.15
2001112520 | 52238.847 | 2.099 | 1648.0 | 2.93 | 0.10 | 12.36 | 1.91 | 0.14
2001120318 | 52246.780 | 2.102 | 1264.0 | 2.45 | 0.11 | 11.88 | 1.76 | 0.17
2001121011 | 52253.489 | 2.104 | 912.0 | 2.71 | 0.12 | 11.06 | 1.71 | 0.17
2001121819 | 52261.827 | 2.107 | 1232.0 | 2.43 | 0.11 | 11.20 | 1.84 | 0.17
2001122500 | 52268.022 | 2.109 | 1408.0 | 2.48 | 0.10 | 11.25 | 1.69 | 0.15
2001123003 | 52273.175 | 2.111 | 1504.0 | 2.15 | 0.10 | 11.69 | 1.64 | 0.16
2002010610 | 52280.466 | 2.114 | 1456.0 | 2.35 | 0.10 | 10.93 | 1.73 | 0.16
2002011316 | 52287.718 | 2.116 | 1968.0 | 2.40 | 0.09 | 12.30 | 1.70 | 0.14
2002011903 | 52293.143 | 2.118 | 688.0 | 2.57 | 0.14 | 11.05 | 1.67 | 0.20
2002012715 | 52301.656 | 2.121 | 1040.0 | 2.19 | 0.12 | 11.78 | 1.66 | 0.20
2002020213 | 52307.574 | 2.123 | 1232.0 | 2.66 | 0.11 | 12.73 | 1.63 | 0.15
2002020916 | 52314.709 | 2.126 | 1296.0 | 2.45 | 0.10 | 11.07 | 1.55 | 0.15
2002021611 | 52321.509 | 2.128 | 1872.0 | 2.53 | 0.09 | 11.40 | 1.62 | 0.12
2002022400 | 52329.040 | 2.131 | 1232.0 | 2.26 | 0.11 | 11.62 | 1.48 | 0.16
2002030300 | 52336.018 | 2.133 | 1424.0 | 2.03 | 0.10 | 12.13 | 1.42 | 0.16
2002030908 | 52342.379 | 2.135 | 1296.0 | 2.12 | 0.10 | 12.13 | 1.56 | 0.18
2002031707 | 52350.306 | 2.138 | 928.0 | 1.90 | 0.13 | 12.96 | 1.36 | 0.21
2002032313 | 52356.549 | 2.140 | 336.0 | 1.83 | 0.20 | 11.98 | 1.45 | 0.37
2002033108 | 52364.374 | 2.143 | 1648.0 | 2.42 | 0.10 | 12.60 | 1.61 | 0.14
2002040811 | 52372.493 | 2.146 | 1296.0 | 2.04 | 0.10 | 11.09 | 1.49 | 0.17
2002042101 | 52385.078 | 2.150 | 1456.0 | 2.13 | 0.10 | 11.04 | 1.50 | 0.15
2002042706 | 52391.282 | 2.152 | 1520.0 | 2.17 | 0.10 | 11.91 | 1.51 | 0.15
2002050518 | 52399.793 | 2.155 | 1008.0 | 2.13 | 0.11 | 10.94 | 1.39 | 0.17
2002051203 | 52406.148 | 2.157 | 1328.0 | 2.13 | 0.10 | 11.39 | 1.48 | 0.16
2002052006 | 52414.265 | 2.160 | 1296.0 | 1.84 | 0.11 | 13.21 | 1.51 | 0.20
2002052719 | 52421.834 | 2.163 | 1712.0 | 2.06 | 0.09 | 10.97 | 1.50 | 0.15
2002060202 | 52427.119 | 2.164 | 1488.0 | 2.34 | 0.10 | 11.31 | 1.50 | 0.14
2002060823 | 52433.971 | 2.167 | 1472.0 | 2.27 | 0.10 | 11.19 | 1.41 | 0.14
2002061714 | 52442.601 | 2.170 | 1312.0 | 2.37 | 0.11 | 12.29 | 1.36 | 0.14
2002062513 | 52450.583 | 2.172 | 1424.0 | 2.08 | 0.10 | 11.12 | 1.29 | 0.14
2002070122 | 52456.939 | 2.175 | 1680.0 | 1.92 | 0.09 | 11.94 | 1.22 | 0.14
2002070809 | 52463.413 | 2.177 | 720.0 | 2.22 | 0.14 | 11.03 | 1.46 | 0.21
2002071520 | 52470.850 | 2.179 | 1776.0 | 2.19 | 0.09 | 11.39 | 1.34 | 0.12
2002072300 | 52478.042 | 2.182 | 1984.0 | 2.19 | 0.08 | 10.80 | 1.33 | 0.11
2002073011 | 52485.493 | 2.185 | 1328.0 | 2.33 | 0.10 | 11.20 | 1.52 | 0.15
2002080509 | 52491.420 | 2.187 | 1312.0 | 2.32 | 0.10 | 11.28 | 1.46 | 0.15
2002081207 | 52498.338 | 2.189 | 864.0 | 1.98 | 0.13 | 11.63 | 1.35 | 0.20
2002081901 | 52505.052 | 2.191 | 1360.0 | 1.89 | 0.10 | 11.39 | 1.31 | 0.16
2002082419 | 52510.819 | 2.193 | 1632.0 | 1.82 | 0.09 | 10.78 | 1.21 | 0.14
2002090202 | 52519.130 | 2.196 | 1152.0 | 1.97 | 0.11 | 10.91 | 1.32 | 0.17
2002090912 | 52526.510 | 2.199 | 1312.0 | 2.25 | 0.10 | 11.43 | 1.37 | 0.14
2002091719 | 52534.805 | 2.202 | 2192.0 | 2.02 | 0.08 | 10.76 | 1.38 | 0.12
2002092312 | 52540.542 | 2.204 | 800.0 | 2.22 | 0.13 | 11.22 | 1.25 | 0.17
2002093001 | 52547.052 | 2.206 | 1552.0 | 1.76 | 0.09 | 11.75 | 1.09 | 0.14
2002100800 | 52555.019 | 2.209 | 1248.0 | 2.03 | 0.10 | 11.57 | 1.22 | 0.15
2002101422 | 52561.933 | 2.211 | 560.0 | 1.70 | 0.15 | 11.73 | 1.13 | 0.25
2002101823 | 52565.992 | 2.212 | 912.0 | 1.65 | 0.12 | 11.59 | 1.32 | 0.23
2002102716 | 52574.678 | 2.215 | 1792.0 | 1.96 | 0.09 | 12.40 | 1.36 | 0.15
2002110411 | 52582.505 | 2.218 | 1488.0 | 1.91 | 0.10 | 12.82 | 1.08 | 0.14
2002111111 | 52589.485 | 2.220 | 1872.0 | 2.13 | 0.09 | 11.61 | 1.21 | 0.12
2002111803 | 52596.141 | 2.223 | 1200.0 | 2.12 | 0.11 | 11.37 | 1.19 | 0.14
2002112706 | 52605.282 | 2.226 | 1424.0 | 2.11 | 0.10 | 10.86 | 1.47 | 0.15
2002120416 | 52612.688 | 2.228 | 928.0 | 2.01 | 0.12 | 11.66 | 1.33 | 0.19
2002120913 | 52617.554 | 2.230 | 1136.0 | 1.79 | 0.11 | 11.11 | 1.14 | 0.17
2002121605 | 52624.255 | 2.232 | 1488.0 | 1.97 | 0.10 | 11.61 | 1.29 | 0.15
2002122609 | 52634.396 | 2.236 | 1360.0 | 2.26 | 0.10 | 12.15 | 1.18 | 0.13
2002123101 | 52639.081 | 2.238 | 1408.0 | 1.60 | 0.10 | 11.24 | 1.06 | 0.16
2003010603 | 52645.133 | 2.240 | 784.0 | 2.08 | 0.13 | 11.69 | 1.31 | 0.20
2003011415 | 52653.672 | 2.243 | 1648.0 | 1.82 | 0.09 | 11.87 | 1.34 | 0.16
2003012023 | 52659.987 | 2.245 | 1264.0 | 1.50 | 0.10 | 10.84 | 1.18 | 0.19
2003012707 | 52666.331 | 2.247 | 1440.0 | 2.27 | 0.10 | 11.34 | 1.22 | 0.13
2003020217 | 52672.726 | 2.249 | 1040.0 | 1.46 | 0.11 | 10.89 | 1.03 | 0.19
2003021102 | 52681.127 | 2.252 | 1504.0 | 1.47 | 0.09 | 10.79 | 1.00 | 0.16
2003021511 | 52685.478 | 2.254 | 1376.0 | 1.51 | 0.10 | 11.05 | 0.99 | 0.16
2003022514 | 52695.605 | 2.257 | 1376.0 | 1.76 | 0.10 | 12.56 | 1.14 | 0.16