11institutetext: Villanova University, Mendel Science Center 263B, 800 E.
Lancaster Ave., Villanova PA 19085, USA, 11email<EMAIL_ADDRESS>(corresponding author)

Anton Pannekoek Institute, University of Amsterdam, Postbus 94249, 1090 GE
Amsterdam, NL; 11email<EMAIL_ADDRESS>(corresponding author)

# High-Resolution Spectroscopy of X-ray Binaries

Joey Neilsen and Nathalie Degenaar

###### Abstract

X-ray binaries, as bright local sources with short variability timescales for
a wide range of accretion processes, represent ideal targets for high-
resolution X-ray spectroscopy. In this chapter, we present a high-resolution
X-ray spectral perspective on X-ray binaries, focusing on black holes and
neutron stars. The majority of the chapter is devoted to observational and
theoretical signatures of mass ejection via accretion disk winds: we discuss
their appearance (including an overview of photoionization and thermodynamic
processes that determine their visibility in X-ray spectra) and their life
cycles (including efforts to constrain their time-dependent mass loss rates),
and we provide a broad overview of the primary accretion disk wind driving
mechanisms that have been considered in the literature: (1) radiation
pressure, where radiation accelerates a wind by scattering off electrons or
atoms in the disk or its atmosphere; (2) thermal driving, where Compton
heating of the outer accretion disk causes gas thermal velocities to exceed
the local escape speed; and (3) magnetohydrodynamic processes, where gas may
be ejected from the disk via magnetic pressure gradients or magnetocentrifugal
effects. We then turn to spectroscopic constraints on the geometry of
accreting systems, from relativistically blurred emission lines to dipping
sources, clumpy, structured stellar winds, and baryonic jets. We conclude with
discussions of measurements of the interstellar medium and the potential of
next-generation high-resolution X-ray spectroscopy for X-ray binaries.

##  12.1 Introduction

X-ray binaries (XRBs) consist of a compact object (white dwarf, neutron star,
or black hole) accreting from a stellar companion and powered by the resulting
release of gravitational energy, and their accretion processes are as rich and
complex as the evolutionary histories that produce them. Beyond differences
due to the type of compact object, the behavior of XRBs depends on the binary
mass ratio, separation and orbital period; the mass, temperature, winds, and
evolutionary stage of the donor star; and the spin and magnetic field of the
compact object. Leaving aside the extensive sub-classifications (for a recent
review, see Bahramian2022, ), we note that XRBs are categorized as low- or
high-mass X-ray binaries (LMXB or HMXB, depending on whether the companion
star is less or greater than some threshold mass $\sim 3M_{\odot}$) and as
persistent or transient (depending on whether their accretion is continuous or
episodic). X-ray binaries also exhibit a wide variety of “accretion states”
Remillard2006 , corresponding to different luminosity, spectra, and
configurations of the accretion flow. Overall, they provide an excellent set
of opportunities to understand the physics of accretion via X-ray
spectroscopy.

If X-ray astronomy was already photon-starved (note, for example, that
compared to optical CCDs, X-ray detectors are typically designed to record the
details of each individual event), the push to higher spectral
resolution—distributing observed counts across a much larger number of energy
bins—presents a significant observational challenge. Herein lies one of the
great advantages of Galactic X-ray binaries for high-resolution spectroscopy:
their sheer proximity! Compared to more luminous but much more distant AGN,
for example, XRBs provide many more photons per second. Furthermore, their
much shorter variability timescales McHardy2006  make it possible to track
major changes in their accretion flows on human timescales: a career, a PhD
thesis, a summer internship, a 1 ks snapshot. At the high luminosities typical
of Galactic transients, these facts facilitate high-resolution spectral
variability studies at scales that simply aren’t currently feasible in other
systems Nowak2017 . Nevertheless, much of the underlying physics we discuss
below, such as wind driving mechanisms (§12.2.1) may apply to AGN and ULX
studies; we refer the interested reader to Chapters 10 and 14 of this volume
by Gallo & Miller and Pinto, respectively.

The bulk of this chapter focuses on what we have learned about accretion from
high-resolution X-ray spectroscopy of black hole and neutron star X-ray
binaries. Much of our discussion concerns studies of accretion disk winds and
the accretion-ejection connection (Section 12.2). In addition, we review what
high-resolution X-ray spectra have taught us about the accretion geometry in
these systems (Section 12.3), and how these allow us to study the gas and dust
properties of the interstellar medium (ISM; Section 12.4). Finally, we provide
an outlook of what the next generation of high-resolution spectroscopic
instruments may bring us (Section 12.5).

##  12.2 Accretion and Ejection

The most sensitive indicators of mass loss from cosmic sources are the
resonance absorption lines of abundant ions Brandt2000 .

…one would expect the mass flow rate and wind density to be strong functions
of the luminosity, such that the actual structure of the wind (i.e., density
and size) can change as a function of the luminosity Lee2002 .

One particularly fruitful avenue for study of accretion physics has come from
work on the “disk-jet connection,” i.e., the relationship between accretion
states, accretion disks, and relativistic jets. Black hole transients, for
example, typically follow a well-established pattern in their outbursts. They
leave quiescence in radiatively-inefficient, spectrally-hard states with
strong Comptonization and optically-thick jets but transition to more thermal
states as they rise (and then fall again) in luminosity; transient
relativistic ejections may be observed at this state transition Esin1997 ;
Gallo2003 ; Corbel2003 ; Fender2004 ; Fender2004b ; Fender2009 . Similar
outburst patterns have been observed in neutron star LMXBs and accreting white
dwarfs (cataclysmic variables or CVs) Kording2008 .

Perhaps the most significant contribution of high-resolution X-ray spectra in
this context is the unambiguous discovery of accretion disk winds in black
hole outbursts. CCD spectra had revealed absorption lines in some bright X-ray
sources (e.g., Ebisawa1997, ; Kotani1997, ), but without the resolution to
measure Doppler shifts, it was not possible to determine whether those lines
represented extended atmospheres or outflows. With grating spectra provided by
Chandra Canizares2005 ; Brinkman2000  and XMM-Newton denHerder2001 , it became
clear that they were produced in gas flowing away from the compact object (at
least in many cases, but see Section 12.3). These outflows typically have
blueshifts of a few hundred to a few thousand km s-1 (Figure 12.1; see also
Table 12.1), which can complicate the determination of an accretion disk
origin when the companion star is a strong source of stellar winds. Therefore,
most of our observational knowledge about disk winds in XRBs (and hence our
focus here) comes from LMXBs, since their companion stars do not exhibit
strong winds. Disk winds are often envisioned as biconical, roughly equatorial
outflows (see Figure 12.2). They are also typically highly ionized, such that
hydrogen- and helium-like iron tend to dominate the spectra with strong lines
at $\sim 7$ keV and 6.7 keV, respectively.

Figure 12.1: Blueshifted absorption lines from an accretion disk wind in the
black hole LMXB GRO J1655–40 from Miller2006b . The black curve with blue
error bars is the Chandra HETGS spectrum, while the red curve is the best fit
model adjusted to zero Doppler shift. High-resolution spectra like these allow
sensitive diagnostics of the dynamics, temperature, ionization, and even
density of absorbing gas.

It was already evident from simulations of accretion disk winds (e.g.
Begelman1983, ) that photoionized accretion disk winds would play a
significant role in both the physics of accretion onto compact objects and
efforts to understand them, and this prediction was quickly confirmed with
early high-resolution X-ray observations. For instance, in the 2000 discovery
of P-Cygni lines in Circinus X-1, Brandt2000  noted the likely connection to
the high luminosity of the source. Extending this suggestion, in 2002 Lee2002
estimated the mass loss rate in the accretion disk wind in GRS 1915+105,
finding it to be comparable to the accretion rate onto the black hole (see
also Higginbottom2017, ). In the two decades since, high-resolution
observations of X-ray binaries have significantly enhanced our understanding
of the connections between accretion and ejection processes, and in 2016
Fender2016  argued that winds could eject more than half the accreted matter
during black hole outbursts111Kosec2020  found a 70% mass loss rate in the
neutron star LMXB Her X-1.. The details tend to vary somewhat, however,
depending on the system properties, particularly the nature of the compact
object and whether the source is persistent or transient222Of course, whether
the compact object is a black hole, neutron star, or white dwarf is related to
whether it is persistent or transient via a combination of accretion physics
and stellar and binary evolution.. Here we focus mostly on black holes and
neutron stars, but again many of the physical principles apply to CVs as well.

As this text is concerned primarily with X-ray spectroscopy, we also focus on
high-energy observations. However, there is a long and growing list of
optical, infrared, and UV observations of winds in XRBs (e.g.,
Bandyopadhyay1997, ; Knigge1997b, ; Rahoui2014, ; Munoz-Darias2018, ; Jimenez-
Ibarra2019, ; Sanchez-Sierras2020, ; Cuneo2020, ; Munoz-Darias2020, ;
CastroSegura2022, ; MataSanchez2022, ; Panizo-Espinar2022, ) that clearly
indicate that X-rays provide an incomplete picture of ionized outflows from
compact objects. Munoz-Darias2022  have recently argued, for example, that
accretion disk winds are likely multiphase outflows, with hot and cold gas
coexisting. As next-generation X-ray missions offer higher spectral resolution
and sensitivity, connecting the dots between different ouflow phases and
filling in the details of the behavior of winds in black hole outbursts should
be a top priority (see §12.5).

###  12.2.1 Black Holes

Following the early detections described above (a more detailed census is
given in Table 12.1), studies of accretion disk winds around stellar mass
black holes have largely followed two parallel but closely-related tracks: (1)
quantifying the time-dependent mass loss rate $\dot{M}_{w}$ in these ionized
winds and their effect on the accretion flow and the accretion state, and (2)
determining the driving or launching mechanism. As detailed below, our ability
to measure $\dot{M}_{w}$ is ultimately limited by our knowledge of the
geometry and structure of these outflows: the launch radius and (number)
density profile $n(R)$ are essential for robust estimates of mass loss rates.
But because these same parameters are also needed to infer the dominant
physical processes that launched any particular wind, it is not possible to
fully disentangle questions of the origin of disk winds from questions of
their role in systems with accreting black holes.

#### Photoionization

In either case, we need to be able to infer the ionization state of outflowing
gas from a series of line features in a high-resolution spectrum. In X-ray
observations of stellar mass black holes, these are most commonly absorption
lines, but emission lines are also possible depending on the orientation and
geometry of the source and the wind (e.g., King2015, ; Sanchez-Sierras2020, ).
Here we present a brief overview of the physics of photoionization. For a more
detailed description of astrophysical plasmas, we refer the reader to Chapter
8 of this volume by Kallman.

Consider a shell of gas of uniform electron number density $n$ at a distance
$R$ from a point source with ionizing luminosity $L$; let the shell have
thickness $\Delta R$ and therefore equivalent hydrogen column density

$N_{\rm H}=n\Delta R.$ (12.1)

To see why a full accounting of the ionization state of the gas is necessary,
imagine that this shell is ionized to the point that it produces only a single
detectable line (e.g., the Fe xxvi Lyman-$\alpha$ line333The Ly$\alpha$ line
is a doublet, but this does not change the overall argument.: the transition
from $n=1\rightarrow n=2$ in hydrogen-like iron). Following Draine2011 , the
line center optical depth is given by

$\tau_{0}=\frac{\sqrt{\pi}e^{2}}{m_{e}c^{2}}\frac{N_{\ell}f_{\ell
u}\lambda_{\ell u}}{b},$ (12.2)

where $e$ and $m_{e}$ are the charge and mass of the electron, $c$ is the
speed of light, $N_{\ell}$ is the column density of Fe atoms in the lower
level ($\ell$, here $n=1$), $\lambda_{\ell u}$ and $f_{\ell u}$ are the
wavelength and the oscillator strength for the transition from $\ell$ to the
upper level $u$ ($n=2)$, and $b=\sqrt{2}\sigma_{V}$ is the Doppler parameter
in km s-1. Note that this equation neglects stimulated emission.

The important detail is that the depth of the line (and its equivalent width)
depends only on the column density of Fe atoms in the $\ell$ level, not on the
equivalent hydrogen column density. This is related only indirectly, via
Kallman2009 :

$N_{\ell}=N_{\rm H}A_{j}x_{ij},$ (12.3)

where $A_{j}$ is the elemental abundance and $x_{ij}$ is the ion fraction
(i.e., the fraction of Fe atoms in the hydrogen-like state). In short, to
infer the total column density of material along the line of sight, we need
detailed information about electron populations in all the relevant ionization
states of its abundant elements.

Per Tarter1969 , this ionization equilibrium is especially sensitive to the
ionization parameter

$\xi=\frac{L}{nR^{2}}$ (12.4)

as well as the spectrum of the ionizing radiation field. To model a series of
ionized lines, we supply a continuum model to photoionization codes like xstar
Kallman1982 ; Kallman2001 ; Bautista2001 , cloudy Ferland1998 , or pion
Kaastra1996 ; mehdipour2015 . These calculate the physical conditions in gas
in photoionization equilibrium, accounting for Compton heating and cooling,
photoionization and recombination processes, and so on, making it possible to
fit line spectra for $\xi$ and $N_{\rm H}$ directly.

If our shell subtends solid angle $\Omega$ and has velocity $v$, the
associated mass loss rate will be Lee2002 ; Reynolds2012

$\dot{M}_{w}=4\pi m_{p}vnR^{2}\frac{\Omega}{4\pi},$ (12.5)

where $m_{p}$ is the mass of the proton. It can be difficult to constrain $n$
and $R$ directly from observations (see 12.2.1), but following Lee2002  it is
possible to use Equation 12.4 to rewrite Equation 12.5 in terms of observables
as

$\dot{M}_{w}=4\pi m_{p}v\frac{L}{\xi}\frac{\Omega}{4\pi}.$ (12.6)

#### Inferring Evolving Winds in Outbursts

The first X-ray observations of accretion disk winds in X-ray binaries also
brought the first evidence of their variability. Schulz2002a  discovered
P-Cygni profiles around the neutron star Cir X-1 that effectively shifted
between pure absorption and pure emission over the course of their Chandra
HETGS observations. While some changes in the appearance of P-Cygni profiles
can be explained by varying the illumination or orientation of the outflow,
Schulz2002a  found that changes in the structure or density of the wind were
required to explain the line variability in Cir X-1.

Figure 12.2: Cartoon of an accretion disk wind from Tomaru2018 . The wind is
largely equatorial, with the densest regions and largest equivalent widths
observed at high inclination, near the plane of the disk. This geometry is
consistent with observational constraints from Sidoli2001 ; Boirin2003 ;
DiazTrigo2006 ; Ponti2012  and is similar to models often used for disk winds
in CVs Knigge1995 ; Knigge1997 ; Matthews2015 .

Miller2006a  reported a similar result from the 2003 outburst of the black
hole LMXB H1743–322. A series of Chandra HETGS observations revealed Fe xxv
and Fe xxvi absorption lines that varied from one pointing to the next, likely
from an accretion disk wind with a mass loss rate roughly $\sim 5\%$ of the
Eddington rate. Interestingly, within all four observations, the lines
appeared to be stronger at lower X-ray flux. One observation in particular,
however, showed even stronger variability centered around a $\sim 300$ s
oscillation in the X-ray lightcurve. Flux-resolved grating spectroscopy of
this oscillation revealed changes not only in the depth of the lines but also
in their ratio: the depth of the Fe xxv line increased much more than the
depth of the Fe xxvi line at low flux. As noted by Miller2006a , this could be
explained by a decrease in the ionization of the gas at low flux, but it could
also be indicative of changes in the density structure or geometry of the
absorption, e.g., an inhomogeneous wind. Neilsen2011  pushed similar
techniques further, measuring wind variability in GRS 1915+105 on timescales
of seconds but also finding evidence of fast structural variability.

As the catalog of accretion disk wind sources grew, it became clear that these
outflows exhibited long-term variability in addition to the faster changes
described above. For instance, Miller2008  noted that absorption lines from
accretion disk winds were stronger during softer (e.g., disk-dominated)
states. This pattern was reflected in observations of H1743–322 Miller2006a
and GRO J1655–40 Miller2006b  as well as archival observations of GRS
1915+105. These latter observations were published in detail in Neilsen2009b ,
who characterized the state dependence as broad emission lines in harder
states (consistent with reflection) and narrow absorption lines in softer
states.

Figure 12.3: Observations of accretion disk winds in high inclination black
hole X-ray binaries from Ponti2012 . Background gray points show the hardness-
intensity trajectories of outbursts. Circles show wind detections, with symbol
size scaling with absorption line equivalent width. Triangles indicate non-
detections, again with symbol size proportional to the upper limit on any line
equivalent width.

If accretion disk winds vary by state, it is natural to wonder whether there
is a connection between winds and radio jets (given the well-characterized
link between jets and X-ray hard states, e.g., Fender1999, ; Fender2004, ;
Fender2009, ). This connection must be complex, because both Lee2002  and
Miller2006a  reported non-zero radio flux coincident with detections of
absorption lines. Miller2008  suggested that an anticorrelation between winds
and jets might relate to changes in the wind density and its effect on the
magnetic field configuration in the inner disk. In contrast, Neilsen2009b
interpreted the state dependence of accretion disk winds as evidence of a
material tradeoff between winds and jets, in which mass loss in winds from the
outer accretion disk (see §12.2.1) effectively reduces the amount of matter
fed into the jet launched from the inner disk.

The picture of this anticorrelation is substantially enhanced with additional
data. Ponti2012  performed a systematic search for accretion disk wind
absorption lines (specifically Fe xxv and Fe xxvi) in X-ray observations of
black hole X-ray binaries. In systems seen at high inclination, they found
that iron absorption lines were preferentially detected in softer states,
generally at higher luminosity (see Figure 12.3), matching the early trend
described in Miller2008 ; Neilsen2009b . Interestingly, they detected no
significant hot wind absorption in any system at low inclination, which is
consistent with the idea of disk winds as equatorial outflows (e.g.,
Boirin2003, ; DiazTrigo2006, ). The only apparent counterexample is a warm
absorber in GX 339-4 Miller2004 , but this is apparent only in Ne, O, and Mg
below 1.5 keV and its origin is not entirely clear (but see Luo2014, ). See
Table 12.1 for an updated census of winds in BH XRBs.

While Ponti2012  has often been cited as evidence that X-ray absorbing
accretion disk winds are never found in X-ray hard states or that jets and
such winds cannot coexist, the historical record described above requires a
more nuanced view. Miller2006a  found strong radio activity coincident with
X-ray absorption lines in H1743–322, and Homan2016  reported similar results
at high luminosity in GRS 1915+105, V404 Cyg, GX 13+1, Sco X-1, and Cir X-1.
Thus it seems clear that any interaction between winds and jets—whether
mediated by mass loss or changes in the magnetic field configuration—must at
the very least be gradual, so that both outflows can be observed
simultaneously.

Regardless of the precise timescale for the transition to wind-dominated
states, Figure 12.3 (taken from Ponti2012, ) suggested that there is a real
trend in the observability of absorption lines in black hole outbursts. The
discovery of X-ray absorption lines in Chandra HETGS observations of 4U
1630–47 during its 2012-2013 outburst lent additional credibility to the idea
that winds can be reliably detected in soft states of high-inclination systems
Neilsen2013 ; Neilsen2014 ; see also Miller2015 ; Trueba2019 . But if that
fact is generally accepted, the apparent absence of winds in hard states is
still not fully understood, partly because several processes can affect their
observability, including (1) overionization, (2) thermodynamics, and (3) time
evolution.

Overionization: Implicit in our discussion of ionization balance and the
definition of the ionization parameter $\xi$ (Equation 12.4) is the shape of
the ionizing spectrum. Consider two identical shells of gas equidistant from
X-ray sources with luminosity $L;$ let one be illuminated by a blackbody
spectrum and the other by a power law spectrum. The gas shells will have the
same ionization parameter but very different ion fractions. These depend on
the integral of the photon rate spectrum over the ionization cross section
$\sigma_{i}(E)$ of the relevant charge state, i.e.:

$\Phi_{i}=\int_{\chi_{i}}^{\infty}\frac{L_{E}}{E}\sigma_{i}(E)dE,$ (12.7)

where $E$ is energy, $L_{E}$ is the monochromatic luminosity and $\chi_{i}$ is
the ionization threshold for charge state $i$. For a given luminosity, a
harder/shallower spectrum will generally ionize each charge state shell more
effectively. For ionization parameters of interest here, $\log(\xi)\approx
4-5$, a harder ionizing spectrum will typically lead to weaker iron absorption
lines.

The idea behind “overionization” as an explanation for the apparent absence of
winds in spectrally hard states (e.g., Neilsen2012b, ; Miller2012, ;
Neilsen2013, ; Ponti2015, ; Shidatsu2019, ; Petrucci2021, ) is that winds
might be present during these states but—given their harder spectra—too
ionized to produce detectable absorption lines. The difficulty with
overionization is that for a given luminosity, a harder spectrum may have
fewer ionizing photons than a softer spectrum due to the factor of $E^{-1}$ in
Equation 12.7. Moreover, from Figure 12.3, much of the hard state at issue
actually has lower luminosity than the soft states where winds are ubiquitous.
Accordingly, one should expect a given parcel of gas to have a lower
ionization parameter during the hard state, which can compensate for the shift
in the ionization balance444Given the differences in luminosity, a proper
statistical analysis of the presence or absence of winds in different outburst
states needs to account for the 7 keV sensitivity of each individual
observation.. Even power law spectra at higher luminosities have repeatedly
proven insufficient to fully ionize disk winds present in soft states
Neilsen2012b ; Ponti2015 . Thus, though the details of ionization are
certainly important, overionization is not likely to be the primary driver of
the state dependence of hot winds in black hole X-ray binaries (Done2018, ,
reached a similar conclusion based on models of thermally driven winds).
However, overionization may play a more important role in optical winds (e.g.,
Munoz-Darias2019, ).

Thermodynamics: In order to detect Fe xxv and Fe xxvi absorption lines (or any
other particular line series) from our shell, it needs to maintain an
appropriate temperature and ionization parameter over the course of an
observation. This is not particularly likely if the shell is not in a stable
thermal and ionization equilibrium. The question is then whether—given all the
relevant heating, cooling, and ionization processes—such an equilibrium is
more or less likely during hard states than soft states. This has been studied
extensively, and while it is still necessary to account for the actual
radiation field in any specific observation, the broad conclusion is fairly
robust that gas capable of producing hot iron absorption lines is probably
thermally unstable during spectrally hard states (e.g., Chakravorty2013, ;
Chakravorty2016, ; Bianchi2017, ; Petrucci2021, ; Chakravorty2023, ).

Typically thermal stability is diagnosed by inspecting stability curves: the
set of points corresponding to thermal equilibrium in a plot of $T$ vs $\xi/T$
Krolik1981 . The stability curve partitions the parameter space: to the left
of the curve, the cooling rate exceeds the heating rate, while the reverse is
true to the right of the curve. Our shell will only be in a thermodynamically
stable equilibrium where the slope of the stability curve is positive (as this
is where thermally perturbed gas will return to equilibrium)555As discussed by
(Proga2022, , see also 101), this analysis is appropriate for steady
illumination of an optically thin medium; alternative stability curves give
similar results in the case of time dependence or non-negligible attenuation..
Consider the example shown in Figure 12.4. Ponti2015  observed the neutron
star AX J1745.6–2901 on numerous occasions with XMM-Newton and NuSTAR, finding
absorption lines—likely from an accretion disk atmosphere—during soft states
and none during hard states. Bianchi2017  used their constructed hard and soft
SEDs to compute stability curves for this absorbing gas.

Figure 12.4: Stability curves for a disk atmosphere in AX J1745.6–2901,
adapted from Bianchi2017 . The red curve represents thermal equilibrium for
gas illuminated by the soft spectrum observed by XMM-Newton and NuSTAR
Ponti2015 . The best-fit parameters for the absorber are shown as a red
circle, which lies on the stability curve where the slope is positive. The
blue curve, on the other hand, corresponds to thermal equilibrium for gas
illuminated by the hard state. Adjusting for the luminosity of the hard state,
the same disk atmosphere would be thermodynamically unstable (see the point
labeled “Hard,” where the slope is negative). Gas under these conditions would
rapidly evolve to one of the points labeled “H1” or “H2.”

As shown, they found that the absorber lay on the stable portion of the
stability curve during the soft state, but that the same gas would be
thermodynamically unstable during the hard state. Thus, during the hard state,
the same gas would rapidly evolve to a much higher or much lower temperature
and ionization than observed in the soft state. As hard spectra often render
$\log(\xi)=3-5$ gas thermodynamically unstable, this is a very compelling
explanation666One important complicating factor noted by Done2018  is that
state changes in the broadband spectrum lead to changes in the Compton
temperature (see §12.2.1). One consequence is that thermally driven winds may
be launched from different locations in the disk during hard and soft states.
If the value $nR^{2}$ is not preserved in the wind during a state transition,
then it becomes much more difficult to predict the expected temperature and
ionization of the wind in the hard state. Robust conclusions about
overionization thermal instability may therefore depend on the inferred
driving mechanism. of X-ray visibility trends for accretion disk winds. It is
worth noting that Higginbottom2020  performed radiation hydrodynamic
simulations of disk winds, including a self-consistent ionization and
frequency structure, including radiative driving (see below) and thermal
instabilities but still found that hot winds should be detectable in hard
states at a high inclination ($i>75^{\circ}$). The source of this discrepancy
is not clear, since Miller2012  placed tight upper limits on absorption line
equivalent widths in hard states of H1743–322.

Nevertheless, thermodynamic instabilities also offer an appealing way to
account for the fact that winds are rarely detected as X-ray absorption lines
during hard states, but that they are detectable in the optical and infrared
during these states. For example, Munoz-Darias2016  detected P-Cygni profiles
of optical emission lines coincident with radio jet emission during the 2015
outburst of V404 Cygni, and Munoz-Darias2018  found similar results during
likely hard states of V4641 Sgr. Munoz-Darias2019  observed cold optical winds
throughout the rising and decaying hard states in MAXI J1820–070 (but not in
the soft state) and suggested that these outflows are a common feature of
accreting black hole systems. Interestingly, Sanchez-Sierras2020  found
evidence for a relatively steady (i.e., state-independent) wind in NIR spectra
of the same outburst. But finally, Munoz-Darias2022  have reported the
simultaneous detection of X-ray and optical signatures of accretion disk winds
in V404 Cyg; they argue that the data are consistent with a multiphase
outflow, i.e., hot and cold gas coexisting in a single wind (see also
Waters2021, ). Therefore disappearance of X-ray absorption lines need not
indicate the disappearance of the wind itself.

Time Evolution: In other words, the fact that accretion disk winds may be very
difficult to observe in the X-ray during spectrally hard states does not mean
that they are not present during these states. Indeed, Tetarenko2018  argued
that massive accretion disk winds shape the lightcurves of black hole
outbursts, including during the hard state. As noted above, optical and IR
spectra of black hole disk winds in hard states help to reveal how the high-
energy signatures of these outflows may be shaped by thermodynamic
instability.

But there are also several definitive instances of state-dependent evolution
of hot accretion disk winds that cannot be explained by ionization or
thermodynamics. For example, two observations of an accretion disk wind in the
2005 outburst of GRO J1655–40 were inconsistent with a static wind
Neilsen2012b . In addition, Gatuzz2019  showed that overionization and thermal
instabilities could not account for the disappearance of the accretion disk
wind in the 2012-2013 outburst of 4U 1630–47 (see Neilsen2013, ; Neilsen2014,
).

While these examples do not pertain directly to the apparent absence of winds
in most spectrally hard states, they provide compelling evidence that the
physical properties of accretion disk winds evolve significantly over the
course of black hole outbursts. Theoretically, this does not come as a
surprise: depending on the driving or launch mechanism of the wind, the mass
loss rate is expected to change with accretion state (e.g., the geometry and
spectrum of the accretion flow). For instance, Ponti2012  noted that if the
wind is driven by irradiation or Compton heating of the outer accretion disk
(i.e., “thermal driving”), any changes in the illumination of the outer
disk—such as might be caused by an increase in the disk scale height during
hard states—could lead to less effective wind driving. As discussed above and
below, changes in the broadband X-ray spectrum are also expected to affect
thermal wind launching, introducing a time-dependent $\dot{M}_{w}$ (see also
Done2018, ). But magnetohydrodynamic (MHD) winds may also evolve during
outbursts: Fukumura2021  inferred changes in the wind density profile in
different accretion states, though the theoretical basis for those changes is
not understood.

In summary, there is strong evidence that photoionization, thermodynamics, and
true physical time dependence all shape the appearance of accretion disk winds
in X-ray binaries. Now we turn to the driving mechanisms, which (in addition
to being important in their own right), will shed some additional light on the
physical time dependence of winds.

#### Wind Driving Mechanisms

From the preceding discussion, it should be clear that efforts to interpret
the results of Neilsen2009b ; Ponti2012  and understand the mass loss rate in
winds, we need to understand the physical processes that launch these outflows
from the accretion disk in the first place. There has been a significant
effort in recent years to infer these mechanisms based on observations (e.g.,
Miller2006b, ; Netzer2006, ; Kallman2009, ; Neilsen2013, ; Neilsen2016, ;
Shidatsu2016, ; Kalemci2016, ; Fukumura2017, ; Fukumura2021, ; Tomaru2022, ).
Following decades of literature, we shall consider three main driving
mechanisms: (1) radiation pressure, (2) thermal driving, and (3) MHD
processes. It is common in observational papers to consider these mechanisms
separately, though (a) hybrid winds are allowed and often distinct from the
main categories Proga2000 ; Proga2003 ; Waters2018 ; Done2018 ; Shidatsu2019 ;
Higginbottom2020 , and (b) all three mechanisms may be operating at some level
in the disk at any given moment. Here we briefly discuss each mechanism in
turn and discuss the overlap between them as it arises. Efforts to determine
the (dominant) driving mechanisms of winds are typically a process of
elimination, so where possible, we focus on observational diagnostics of and
constraints on the driving mechanism.

Radiation Pressure: In a radiation pressure driven wind, photons scatter off
atoms or electrons in the vicinity of the compact object, accelerating the gas
until it reaches some terminal speed in excess of the local escape velocity.
Here the process that accelerates the wind is the transfer of momentum from
the radiation field to the gas Reynolds2012 . This mechanism seems intuitively
relevant for X-ray binaries, which often reach high luminosities and therefore
might be expected to launch radiatively-driven winds efficiently.

The reality is rather more complicated. Briefly, radiation driving requires a
source of opacity for scattering, and is therefore especially sensitive to the
ionization state of the gas Vitello1988 . For a fully ionized gas, that
opacity is due to electron scattering. At lower temperatures, there is
significantly more opacity in atomic lines, so that resonant scattering or
“line driving” (e.g., Murray1995, ) is much more effective at launching winds
from accretion disks. This is especially the case for the UV, where the line
opacity is particularly high. To be quantitative, the line force can exceed
that due to electron scattering by $\lesssim 2000\times$ Castor1975 ;
Abbott1982 ; Gayley1995 .

In detailed radiation hydrodynamic simulations, Proga2002  found that
radiation pressure could only effectively drive winds in LMXBs when the
central luminosity is within a factor of $\sim 2$ of the Eddington
limit777Ueda2004  argued for the effectiveness of radiation-driven winds at
similar luminosities on the idea that for the purposes of gas kinetics,
radiation pressure reduces the effective mass of the compact object, and that
the gas is effectively unbound at high Eddington ratios., but that such winds
are best described as thermally driven (see below) with assistance from
electron scattering (see also Higginbottom2020, ). Line driving was not
effective at ionization parameters $\log(\xi)\gtrsim 3$ due to the reduction
in UV opacity. Thus when we encounter a wind absorption line system with a
measured high ionization parameter in X-ray binaries, we typically disregard
radiation pressure as a viable driving mechanism for that particular outflow.

Practically speaking, this criterion rules out radiation pressure as the
source of winds in most black hole and neutron star X-ray binaries, with a few
notable exceptions. For example, Ueda2004  argued that the wind in the neutron
star GX 13+1 (see below) could be explained as a radiatively-driven wind
launched at high Eddington ratio, though Tomaru2020a  recently modeled Chandra
HETGS 1st- and 3rd-order spectra of this source as a radiative-thermal wind.
Proga2005  argued that line driving is the most plausible origin for disk
winds in CVs (see also Pereyra2004, , and references therein).

Figure 12.5: Calculations from Tomaru2020b  showing the radial velocity
profile (left) and fractional ionic column densities (i.e., scaled to the
total; right) for a thermal-radiative wind in H1743–322. These profiles are
computed with Monte Carlo radiative transfer using a radiation hydrodynamic
simulation as input. In the right panel, red and green indicate Fe xxvi and Fe
xxv, respectively, while the black curve shows the total column density. The
blueshift and ionization are strong functions of position, so comparing these
models to data permits estimates of the location and turbulent velocity in the
wind (see their Figure 9).

Thermal Driving: If the accretion disk is sufficiently heated by X-rays from
the inner accretion flow, the average thermal velocity of the irradiated disk
surface can exceed the local escape velocity, especially in the outer disk
where matter is less tightly bound to the central source Begelman1983 . Here
we briefly follow Rahoui2010  to cover the important points. Matter in the
disk can be heated to the Compton temperature

$T_{C}=\frac{1}{4k_{B}}\frac{\int_{0}^{\infty}EL_{E}dE}{\int_{0}^{\infty}L_{E}dE},$
(12.8)

where $k_{B}$ is the Boltzmann constant; $T_{C}$ is often in the range
$10^{6}-10^{8}$ K for typical XRB spectra. The characteristic size scale for a
thermally-driven or Compton heated wind is the Compton radius $R_{IC}$, where
the local escape velocity equals the thermal velocity at the Compton
temperature:

$R_{IC}=\frac{9.8\times 10^{17}}{T_{C}}\frac{M}{M_{\odot}}\,{\rm cm},$ (12.9)

where $M$ is the mass of the central object and $T_{C}$ is given in K. The
Compton radius is often comparable to the size of the accretion disk, but
hydrodynamic simulations Woods1996  have indicated that thermal winds can be
launched from radii $R\gtrsim 0.1R_{IC}$; the inclusion of radiation pressure
may enable thermal-radiative winds to be launched from $\sim$anywhere in the
disk at high Eddington ratio Done2018 . Finally, in order for the wind to be
heated fast enough to overcome gravity, the luminosity must exceed a critical
threshold

$L_{\rm cr}=\frac{288L_{\rm Edd}}{\sqrt{T_{C}}},$ (12.10)

where $L_{\rm Edd}$ is the Eddington limit and again $T_{C}$ is given in K.
Because of the appearance of the luminosity and spectral shape in these
equations, thermally-driven winds are naturally dependent on the accretion
state, with a complex tradeoff between the increase in luminosity and decrease
in spectral hardness (and $T_{C}$) as sources head from hard states to soft
states Higginbottom2019 .

With the exception of observations at a high Eddington ratio, the primary
diagnostic of thermal driving is whether or not the X-ray absorber can be
located outside the Compton radius (or the equivalent $0.1-0.2R_{IC}$). If so,
then thermal driving could be the dominant mechanism responsible for the wind.
There are several ways to estimate the location of a wind. Miller2006b ;
Miller2008 ; Kallman2009  used density-sensitive line features to measure the
density of a wind in GRO J1655–40; if $L,$ $n$, and $\xi$ are known, one can
solve Equation 12.4 to determine $R$, though this formulation implicitly
assumes a point source emitter Neilsen2016 . Neilsen2009a  reported a
similarly complex absorber in GRS 1915+105; Ueda2009  found a large
photoionization radius ($\gtrsim 10^{5}r_{g}$), consistent with a
radiative/thermal wind. King2015  found strong emission lines and P-Cygni
profiles at high luminosity in the 2015 outburst of V404 Cyg; ionization
analysis implied a large radius and a wind driven by radiation or irradiation.
Some variability arguments (e.g., Neilsen2011, ; Neilsen2012a, ) have enabled
estimates of the location of X-ray absorbing gas and led to the inference of
thermally driven winds. Neilsen2009b  assumed that the blueshift of absorption
lines in GRS 1915+105 represented the local escape velocity, which placed the
absorption lines in the outer accretion disk. Similarly, the velocity profile
of observed absorption lines may be compared to predictions of models based on
different launch mechanisms (Figure 12.5; Ueda2004, ; Tomaru2020a, ;
Tomaru2020b, ).

Studies of thermally-driven winds have benefited enormously from recent
advances in simulations, which have facilitated direct comparisons between
models and observations Luketic2010 ; Higginbottom2015 ; Higginbottom2018 ;
Shidatsu2019 ; Tomaru2020a ; Tomaru2020b ; Higginbottom2019 ; Higginbottom2020
. As a result, we also have a deeper understanding of the connection between
atomic processes and the bulk behavior of winds. For example, Higginbottom2015
pointed out that the thermodynamic instability discussed in Section 12.2.1 is
where winds are accelerated most efficiently: when plasma becomes thermally
unstable, its temperature rapidly approaches the Compton temperature (see also
Begelman1983, ). The sudden increase in the gas temperature provides a
significant boost to thermal wind launching. Dyda2017  found that winds may
undergo several stages of acceleration if the irradiating flux is sufficient
to drive the thermal equilibrium curve through multiple steep or unstable
branches. Dubus2019  demonstrated that winds themselves may represent a
significant source of disk irradiation if they scatter photons down onto the
disk (see also Kimura2019, ). In short, cutting edge theoretical and
observational studies of thermal winds continue to reveal the rich
relationships between accretion and ejection processes in X-ray binaries.

MHD Winds: The same can be said for studies of winds driven by
magnetohydrodynamic processes. The virtue of this driving mechanism was put
concisely by Proga2003 : “one of the reasons for favoring magnetic fields as
an explanation for mass outflows from accretion disks is the fact that
magnetic fields are very likely crucial for the existence of all accretion
disks.” One recurring theme in studies of disk winds is the connection to
jets, not only owing to the related state dependence of these outflows (see
above), but also because jets are fundamentally magnetic processes. Could
winds and jets be separated only be changes in the magnetic field
configuration? The Blandford-Payne mechanism (Blandford1982, , see below) is
often discussed both as the origin of magnetocentrifugal winds Reynolds2012
and as a source of jets (e.g., Neilsen2014, ). In this context, Miller2006a ;
Miller2008 ; Miller2012  commented on possible magnetic connections between
winds and jets. In a systematic study of AGN and XRBs, King2013  found similar
wind-luminosity and jet-luminosity scaling relations and suggested a common
launching mechanism.

Magnetically-driven winds can be launched from the accretion disk by several
processes, one of the best known being the Blandford-Payne mechanism
Blandford1982 . This mechanism is also known as a magnetocentrifugal wind,
where matter from the rotating disk is flung along poloidal magnetic field
lines Pelletier1992 ; Proga2003 ; Pudritz2007 . As noted by Reynolds2012 , the
terminal velocity of these winds is rather large, typically 2-3 times the
escape velocity at the launch radius and 3-5 times the escape velocity at the
outer edge of the acceleration region. One alternative is magnetic pressure:
when the differential rotation of the accretion disk generates a large
toroidal magnetic field, the gradient of the toroidal field can drive a wind
off the disk (Proga2003, , and references therein). Proga2003  performed a set
of simulations to determine how magnetic fields affect radiation driven winds.
They found that for sufficiently large magnetic fields, a dense, slow,
pressure-driven wind dominates the line-driven component. Interestingly,
Waters2018  found that including strong poloidal fields in simulations of
thermal winds actually suppresses the thermal driving mechanism.

Figure 12.6: Spectral analysis of a rich absorption line spectrum in GRO
J1655–40 from Tomaru2022 . The top panel shows the full absorption line
spectrum including two spectral models with low density $n=\sim 3\times
10^{12}$ cm-3. The bottom panel shows a close-up of the Fe xxii lines at 11.77
Å and 11.92 Å.

Observationally, the first claim of a magnetically-driven wind in an XRB based
on high-resolution spectra was made by Miller2006b , based on a complex
absorption line spectrum in GRO J1655–40 observed by Chandra during a 2005
outburst. As noted above, Miller2006b  used density-sensitive absorption line
features to infer the gas density in the wind (see Figure 12.6). One
constraint in particular came from the detection of Fe xxii absorption lines
at 11.77 Å and 11.92 Å Miller2008 , which represent transitions from the
ground state $2s^{2}2p_{1/2}$ and the metastable $2s^{2}2p_{3/2}$ state into
the $2s^{2}3d_{3/2}$ and $2s^{2}3d_{5/2}$ excited states, respectively.
According to Mauche2003 , the ratio of these two lines is sensitive to the
density in the range $n=10^{12}-10^{15}$ cm-3 because collisional excitation
can enhance the population of the $2s^{2}2p_{3/2}$ state (leading to a
stronger 11.92 Å line). By comparing the observed line ratio to the predicted
density dependence, Miller2008  inferred a density $n=10^{13.7}$ cm-3;
Kallman2009  noted several other transitions that also suggest high density.
Miller2014a  found a similar result in MAXI J1305–704.

Via photoionization modeling Miller2006b ; Miller2008  concluded that the
absorber in GRO J1655–40 lay at $R\gtrsim 10^{9}$ cm from the black hole.
Since the source appeared to be at only a few percent of the Eddington limit
and the wind was highly ionized, such a small radius seemed to rule out both
thermal driving and radiation pressure, leaving magnetic processes as the only
apparently viable origin for the wind888Neilsen2012b  explored the time
dependence of the wind in GRO J1655–40 and found that it likely had at least
one thermally-driven component earlier in the outburst.. The low velocity of
the wind ($\sim 375$ km s-1; Kallman2009, ) in GRO J1655–40 is better matched
to a wind launched by magnetic pressure than rotation, since the escape
velocity at the apparent radius is 15-30$\times$ the observed blueshift;
Neilsen2013  also argued that the data are incompatible with a
magnetocentrifugal wind based on constraints from Reynolds2012 . The
identification of this outflow as a magnetically-driven wind has inspired
significant debate since 2006. Here we will discuss some additional results on
MHD wind models and their applications to spectra of black hole X-ray
binaries, then return to the origin of the wind in of GRO J1655–40.

One of the first additional candidates proposed for an MHD wind was IGR
J17091–3624 King2012 , who found evidence of absorption lines with blueshifts
near $10^{4}$ km s-1. Though thermal driving was possible in this source, the
wind speed was better matched to escape conditions at smaller radii in the
disk. But advances in modeling have also led to more nuanced views of
previously-observed winds. Miller2015  and Miller2016a  perfomed detailed
photoionization modeling of accretion disk winds in GRO J1655–40, H1743–322,
GRS 1915+105, and 4U 1630–47, extending their analysis to the higher-
resolution 3rd order Chandra HETGS spectra (see Figure 12.7) and including not
only multiple ionization/velocity zones but also photoionized emission (which
is expected without fine-tuning of the wind geometry). If the wind structure
is rotating, the absorption lines may be narrow but the emission lines should
be broadened; Miller2015  included this effect by blurring the re-emission
component. These works found that the required emission line blurring was
consistent with Keplerian velocity at the location of the wind inferred via
photoionization analysis. Again, these results indicate that the hot winds are
not only rotating but also found at small radii (suggesting MHD driving).
Trueba2019  reanalyzed 6 Chandra HETGS observations of 4U 1630–47 and found a
similar result, though they also found—like Neilsen2012b —that the winds might
be best described as hybrid thermal/magnetic outflows. More indirectly,
Hartley2002  used the lack of a correlation between source luminosity and wind
activity in two high-state CVs to argue that a non-radiative factor (e.g., MHD
processes) might dominate the wind driving.

One point is worth clarifying before going forward: with the exception of
observations at high luminosity as described above, thermally-driven winds
cannot be launched from small radii. Hot winds found at small radii and
luminosity must therefore be driven by MHD processes. But these act throughout
the disk, so MHD winds can in principle be launched from or extend to large
radii: the detection of wind absorption near the Compton radius is consistent
with a thermal wind but cannot in and of itself rule out a magnetic wind.

This distinction is especially relevant for the application of self-similar
MHD wind models to X-ray spectra of black holes. Fukumura2010a  adapted the
self-similar wind solution of Contopoulos1994  to predict the ionization state
and spectrum of MHD winds in AGN. A key feature of the model is that rather
than being treated as a shell for the purposes of ionization modeling, the
wind originates at small radii and extends over many orders of magnitude in
radius (with corresponding changes in the density, velocity, and ionization of
the gas). These authors applied this model to several supermassive black holes
Fukumura2010b ; Fukumura2015  before arguing Fukumura2017  that it also
explained the dense MHD wind in GRO J1655–40 described above and shown in
Figure 12.6. Fukumura2021  used the same model to fit spectra of GRO J1655–40,
H1743–322, and 4U 1630–47, arguing that the state dependence of winds could be
explained by a decrease in density and a steepening in the density profile
during harder states. Together, these changes effectively serve to render the
wind too ionized to observe in absorption.

Chakravorty2016 ; Chakravorty2023  have explored another set of self-similar
MHD wind models that are based on a solution presented in Ferreira1997 . The
distinction between these winds and the Fukumura2010a  models discussed above
is that in the latter, the initial density of the wind is a free parameter,
while in the former it is an explicit function of the disk scale height and
the radial profile of the disk accretion rate. Chakravorty2016  found that the
wind launching efficiency was too low for “cold” solutions that do not include
heating of the accretion disk surface, but that the geometry of “warm”
solutions matched the observed inclination dependence of winds Ponti2012 .

Figure 12.7: Chandra HETGS 3rd-order spectrum of GRS 1915+105 from Miller2016a
. The data show strong absorption lines with complex energy structure; the
model includes four distinct ionization/velocity zones with associated re-
emission components. See text for details.

Despite the in-depth observational and theoretical work behind the results
above, there is still controversy about evidence for MHD winds in black hole
X-ray binaries (especially GRO J1655–40). Based on X-ray spectra and an
unusual optical/infrared excess, Neilsen2016 ; Shidatsu2016  argued that the
dense wind discovered by Miller2006a  was actually a Compton thick super-
Eddington outflow, and while there are still questions about the geometry and
radiative transfer of the wind and the OIR excess, this would imply that the
intrinsic luminosity of the source must have been much higher. This
distinction has important consequences because the metastable $2s^{2}2p_{3/2}$
state can be populated via UV photoexcitation999Prior studies Miller2008 ;
Fukumura2017  expressly neglected this effect because the apparent Eddington
ratio of GRO J1655–40 is low. as well as collisions (Tomaru2022, , see also
180; 181; 170). Self-consistently accounting for the higher intrinsic
luminosity and SED and allowing the metastable level to be populated by
cascades from radiative excitation lowers the required density in the wind by
more than an order of magnitude Tomaru2022  (pushing the inferred launch
radius to $\sim 10^{11}$ cm). In addition, Tomaru2022  further argued that the
absorption line spectrum in GRO J1655–40 was consistent with an optically
thick thermal wind model based on radiation hydrodynamic simulations (this
model is shown in Figure 12.6, including a close-up of the relevant Fe xxii
lines).

Thus it appears that wind absorption line spectra in black hole X-ray binaries
can be fit with models implying both small Miller2015 ; Miller2016b  and large
Tomaru2022  launch radii, and it seems we are left in a bit of a pickle. But
to the extent that our dilemma is the culmination of decades of advances in
X-ray data, spectral analysis, and numerical simulations, there is still room
for optimism. Will more and more realistic simulations of thermal and magnetic
accretion disk winds reveal observable differences between them? The most
promising development on the horizon appears to be higher spectral resolution,
where the velocity profile of winds may be an important distinguishing factor
(see Section 12.5).

###  12.2.2 Neutron Stars

Having reviewed the basics of disk atmospheres and disk winds in the context
of black hole XRBs we now turn to neutron star systems. Their accretion
properties are overall very similar, which is not surprising because their
gravitational potentials are not too different. Nevertheless, neutron stars
are fundamentally different objects than black holes, given that they have a
solid surface (versus an event horizon) and a magnetic field anchored to it.
Both these properties can impact the surrounding accretion flow, and outflows,
in various ways.

Observationally, thermal radiation from the hot neutron star surface, or a
boundary/spreading layer where matter from the disk splashes into the star,
provides an additional emission component in X-ray spectra. Physically, this
additional reservoir of soft X-ray photons can Compton-cool the corona
burke2017 , illuminate the accretion disk ballantyne2004  and perhaps also
affect the thermal stability criteria of the disk (Section 12.2.1).

The presence of a surface magnetic field can also have a significant impact.
The inner disk may be truncated and plasma channeled onto the magnetic poles
of the neutron star so that it manifests itself as an X-ray pulsar
Bildsten1997 ; Wijnands1998 . The magnitude of this effect depends both on the
pressure exerted by the accretion flow (which scales with the mass-accretion
rate), and the strength of the surface magnetic field. Neutron stars in LMXBs
typically have weak magnetic fields ($\lesssim 10^{9}$ G), apart from a few
exceptions where the magnetic field is stronger ($\simeq 10^{10-12}~{}G$;
Bahramian2022, ). X-ray pulsars in HMXBs, on the other hand, have strong
magnetic fields ($\simeq 10^{12-13}$ G). The stellar magnetic field may also
interact with that of the accretion disk and thereby impact the production of
both jets and disk winds, where again the strength of the surface magnetic
field determines the magnitude of the effect Romanova2009 ; Parfrey2017 ;
Vandeneijnden2021 .

Other differences between neutron stars and black holes that can affect their
accretion and ejection properties are that neutron stars, by definition, are
less massive than black holes ozel2016 . In the context of disk winds, for
instance, mass is one of the parameters that determine where in the disk a
thermal wind can be launched (cf. Eq. 12.9). Moreover, neutron stars appear to
spin (much) slower than black holes in XRBs101010The fastest rotating neutron
star known in a XRB has a spin frequency of 599 Hz disalvo2022 , which
translates into a dimensionless spin parameter of $a\simeq 0.3$ degenaar2015
.. Finally, likely due to observational biases, neutron star LMXBs are
clustered towards smaller orbital periods than their black hole analogues
Bahramian2022 . In reviewing our current observational knowledge of disks and
winds in neutron star XRBs, we will draw parallels with black hole systems to
gauge where their different properties come into play. Table 12.1 gives an
overview of the properties of the disk atmospheres and winds observed in
neutron star (and black hole) XRBs.

#### Observations of disk atmospheres and winds in neutron star systems

For nearly two dozen neutron star XRBs ($\simeq 10\%$ of the currently known
population), ionized absorbers have been detected in X-ray spectra (Table
12.1). Many of these systems are known to be viewed at high inclination, as
evidenced by the detection of eclipses and/or dips (resulting from the central
X-ray source being obscured by either the companion star or the accretion
stream, respectively). For several neutron stars, the X-ray aborption lines
are blue-shifted, showing that plasma is outflowing with velocities in the
range of $\simeq(1-30)\times 10^{3}$ km s-1 ($\simeq 0.004-0.09$c; Table
12.1). Similar to black hole XRBs, there are some neutron star systems that
show wind signatures at other wavelengths but not in X-rays. Examples are the
very bright source Sco X-1 (wind feature in the nIR; Bandyopadhyay1999, ), and
X2127+119 in the globular cluster source M15 (wind feature in the UV;
Ioannou2003, )).

Although disk winds have so far been detected in only a modest fraction
($\simeq$10%) of neutron star LMXBs, it is likely that many disk winds go
undetected, e.g., due to inclination or ionization effects (Section 12.2.1).
Indeed, there is indirect evidence of (highly) non-conservative mass transfer
in several neutron star LMXBs, as inferred from the accelerated orbital decay
of X-ray pulsars Marino2019 ; disalvo2022  and modeling the disk spectral
energy distribution in other systems Ponti2017 ; HS2019 . In black hole
systems there is also indirect evidence for non-conservative mass transfer, as
inferred from transient decay light curves Tetarenko2018 , or modeling the
outburst properties Ziolkowski2018 . Disk winds are an attractive explanation
for the severe mass loss that these systems must be experiencing Dubus2019 .

Similar to the phenomenology seen in black hole systems, the observability of
the ionized absorbers in neutron star LMXBs shows a dependence on accretion
state. This is, for instance, clearly demonstrated by studies of three high-
inclination eclipsing (transient) neutron star low-mass ray binaries across
different states: MXB 1659–28 Ponti2019 , AX J1745.6–2901 (see Figure 12.8;
Ponti2015, ), EXO 0748–676 Ponti2014 . In all cases, the absorber is clearly
seen during soft states, but not during hard states. For the former, the lines
are suggested to be at rest (velocities $\lesssim 200$ km s-1), hence
indicating the absorber is a static ionised atmosphere rather than an
outflowing wind. Indeed, for this system the location of the absorbing plasma
was inferred to be (well) within the Compton radius, hence eliminating the
possibility of a thermal wind Ponti2019 . For the other two sources no
velocity shifts were detected at CCD energy resolution, which sets an upper
limit on the velocity of the absorbing plasma of $\lesssim 10^{3}$ km s-1.
This does not rule out a (slow) wind.

Source | $P_{\textrm{orb}}$ | $N_{\mathrm{Gal}}^{\mathrm{H}}$ | $v_{\mathrm{out}}$ | Class | References
---|---|---|---|---|---
|  | ($10^{21}$ cm-2) | ($10^{3}$ km-2) |  |
Neutron star LMXBs
*1RXS J180408.9–342058a | ? | 2 | 26 | SL | Degenaar2016
*GX340+0b | ? | 2 | 12 | SL,HE | Miller2016a
*4U 1820-30 | 0.19h | 1.3 | 1.2 |  | Costantini2012
*IGR J17062–6143 | 0.63h | 1 | 14 | MP | Degenaar2017 ; vandenEijnden2018
XB1916–053 | 0.83h | 2 | atm | D | Boirin2004 ; Juett2006 ; DiazTrigo2006
|  |  |  |  | Iaria2006 ; zhang2014 ; Trueba2020
1A 1744–-361 | 1.62h | 3 | atm | D | Gavriil2012
4U 1323–62 | 2.93h | 10 | ? | D | Boirin2005 ; church2005 ; Balucinska-Church2009
*XTE J1710–281 | 3.28h | 2 | 0.8 | D,E | Raman2018
EXO 0748$-$676 | 3.82h | 0.9 | $\lesssim 1$ | D,E | DiazTrigo2006 ; vanPeet2009 ; Ponti2014
XB 1254–690 | 3.93h | 2 | atm | D | Boirin2003 ; DiazTrigo2006 ; DiazTrigo2009 ; iaria2007
MXB 1659–298 | 7.12h | 2 | $\lesssim 0.1$ | D,E | Sidoli2001 ; DiazTrigo2006 ; Ponti2018
AX J1745.6$-$2901 | 8.35h | 0.9 | $\lesssim 1$ | D,E | Hyodo2009 ; Ponti2015
*IGR J17591–2342 | 8.80h | 10 | 2.8 | MP | Nowak2019b
X1624–490 | 20.9h | 20 | atm | D | Parmar2002 ; DiazTrigo2006 ; Iaria2007b ; Xiang2009
IGR J17480–2446 | 21.3h | 5.5 | 1–3 | MP | Miller2011
*Swift J1858.6–0814 | 21.3h | 2 | 2 | HE | Buisson2020
GRO J1744–28 | 11.8d | 10 | 8 | SL,SP | (Degenaar2014a, )
Cir X–1 | 16.6d | 20 | 2 | HE | Brandt2000 ; Schulz2002a ; Schulz2008
|  |  |  |  | Dai2007 ; Iaria2007b
GX13+1 | 24.1d | 10 | out | HE | Ueda2001 ; Ueda2004 ; Sidoli2002
|  |  |  |  | DiazTrigo2012 ; Madej2014 ; Dai2014
Neutron star IMXBs and HMXBs
Swift J0243.6+6124 | 1.2d | 7 | $66$ | B,SP,HE | vandenEijnden2019
Her X-1 | 1.7d | 0.15 | $0.2-1$ | IMXB,SP | (Kosec2020, )
1A 0535+262 | 111d | 4.5 | $1.5-3.0$ | B | (Reynolds2010, )
Black hole LMXBs
4U1630–47 | ? | 17 | 0.3 |  | kubota2007 ; DiazTrigo2013 ; DiazTrigo2014
|  |  |  |  | King2013 ; King2014 ; Neilsen2014
H1743–322 | ? | 6.9 | 0.3–0.7 |  | Miller2006a ; King2012
*EXO 1846-031 | ? | 1.4 | 0.3-18 |  | Wang2021
*MAXI J1803-298c | ? | 2.5 | ? | D | Miller2021
*MAXI J1348-630 | ? | 15 | 10 | SL | Wu2023
*MAXI J1631-479 | ? | 17 | 21 | SL | Xu2020
XTE J1650–500 | 7.63h | 0.8 | 0.5 |  | Miller2002b ; Miller2004
MAXI J1305-–704 | 9.74h | 0.2 | -9d |  | Shidatsu2019 ; Miller2014b
*4U 1543-47 | 1.1d | 3.4 | ? | SL | Prabhakar2023
GX339–4 | 1.8d | 3.9 | 0.05–0.5 |  | Miller2004 ; Juett2006
GROJ1655–40 | 2.6d | 5.1 | 0.5 |  | Ueda1998 ; Yamaoka2001 ; Miller2006b ; Miller2008
|  |  |  |  | Netzer2006 ; DiazTrigo2007 ; Sala2007b
|  |  |  |  | Kallman2009 ; Luketic2010 ; Neilsen2012a
IGR J17091–3624 |  $>$4 d | 5.8 | 15 | SL | King2012
*V404 Cyg | 6.5d | 6.4 | 1.5–3 |  | Munoz-Darias2022
GRS 1915+105 | 33.5d | 14 | 0.3–1.4 |  | Kotani2000a ; Lee2002 ; Martocchia2006 ; Ueda2009
|  |  |  |  | Ueda2010 ; Neilsen2009b ; Neilsen2011 ; Neilsen2012b ; Neilsen2018
Table 12.1: List of disk atmosphere and wind detections in neutron star and
black hole X-ray binaries. This is an update of DiazTrigo2016 ; winds reported
since then are indicated by **. The quoted absorption column densities
($N_{\mathrm{Gal}}^{\mathrm{H}}$) are solely meant to be indicative and taken
from HI4PI2016 . Upper limits for outflow velocities typically mean that no
gratings data were available. Source classification: B=BeXRB, D=dipper,
E=eclipser, MP/SP=accreting millisecond/slow X-ray pulsar, HE=high-Eddington
source, SL=outflow inferred based on a single significant line detection.
a Proposed $P_{\mathrm{orb}}\lesssim$3 hr Baglio2016 ; Degenaar2016 .
b GX340+0 is a Z source; in all Z sources where it is known, $P_{\rm
orb}\gtrsim 21$ hr Bahramian2022 .
c Based on the recurrence time of the dips, $P_{\rm orb}$ is expected to be
$\simeq 7$h Xu2021 .
d The minus sign indicates an inflow rather than an outflow.

Whereas the above studies point towards a state dependence for detecting the
ionized absorber in X-rays, there are a few (tentative) X-ray wind signatures
found for neutron stars during hard states. This includes two LMXB pulsars,
IGR J17062–6143 Degenaar2017 ; vandenEijnden2018  and IGR J17591–2342
Nowak2019b . The former accretes at a very low Eddington ratio ($\simeq 0.1$%)
and has a very compact orbit (0.6 hr), hence its disk wind may be driven by
magnetic processes (see Section 12.2.2). The latter has a wider orbit (8.8 hr)
and accreted at only $\simeq 1$% of the Eddington rate during its outburst
Kuiper2020 . During this time it was in a hard X-ray spectral state Kuiper2020
; Manca2023  and it displayed (unusually luminous) radio jet emission
Russell2018 .

Figure 12.8: Comparison between the XMM-Newton (CCD) spectra of the neutron
star LMXB AX J1745.6–2901 taken in hard (black) and soft (red) states. This
clear state-dependence of the observability of the ionized absorber is similar
to the behavior seen in black holes. Figure from Ponti2015 .

#### Wind driving mechanisms for neutron star systems

Accreting neutron stars can launch disk winds via the same physical mechanisms
as discussed for black holes (i.e., radiative, thermal or magnetic processes).
In neutron star systems there are, however, additional means to launch disk
winds. Firstly, winds may be driven by the interaction of the disk and stellar
magnetic field Romanova2009 . Secondly, many neutron stars display
thermonuclear bursts, short but intense flashes of Eddington-limited radiation
Galloway2008  that interact with the accretion flow and can potentially also
launch a temporary disk wind Degenaar2018 .

Disk winds from disk-magnetosphere interaction. Early work on the interaction
of a magnetized star with $\alpha$-type disks revealed that outflows may be
launched at the disk-magnetosphere boundary Lovelace1995 ; Goodson1999 ;
Ustyugova2006 ; Romanova2009 . In these non-relativistic simulations,
conically-shaped winds flow out of the inner disk because in-falling plasma
compresses the neutron star magnetosphere, causing the field lines to inflate
due to the differential rotation between the disk and the star (Romanova2009,
, see Figure 12.9). Such a conical thin wind with a half-opening angle of
$\theta=30-40^{\circ}$ and velocities up to $v=0.1c$ Romanova2009  should be
detectable with high-resolution spectroscopy in low-inclination systems that
harbor a magnetic neutron star.

More recently, the first suites of GRMHD simulations of accretion onto
magnetic neutron stars have been performed. The first calculations for neutron
stars with dipolar magnetic fields Parfrey2017  were further extended to
include more complex magnetic fields Das2022 , motivated by the recent
evidence of multi-polar magnetic fields from pulse-profile modeling (e.g.
Riley2019, ). These GRMHD simulations have not confirmed the presence of the
conical wind patterns seen by earlier non-relativistic calculations
Romanova2009 ; Romanova2012 , but instead find that collimated jet-type
outflows are launched.

Observationally, many of the disk wind detections in neutron star systems are
consistent with thermal driving DiazTrigo2016 . There appear to be, however,
interesting exceptions. For instance, there are a few (potential) disk wind
detections in neutron star LMXBs that have very short orbital periods that
should not allow them to drive thermal winds. Prime examples are 4U1820–30
Costantini2012  and IGR J17062–6143 Degenaar2017 ; vandenEijnden2018 , with
orbital periods of 11.4 and 37.4 min, respectively. As their accretion
luminosity is well below Eddington, these systems may be, by elimination, good
candidates of magnetically-driven winds. In this respect, it is interesting to
note that IGR J17062–6143 is an LMXB pulsar Strohmayer2018  and its accretion
disk appears to be truncated by its magnetic field Degenaar2017 . Several
other pulsars with longer orbital periods have recently been reported to show
disk winds. This includes the weakly magnetic (LMXB) pulsar IGR J17591–2342
Nowak2019b  and the strongly magnetic pulsars GRO J1744–28 Degenaar2014a ,
Swift J0243.6–6124 vandenEijnden2019 , Her X-1 Kosec2022 . It is interesting
to note that the blueshifts of several of these pulsars (IGR J17062–6143,
Swift J0243.6–6124, GRO J1744–28) stand out as high compared to those found in
other neutron star and black hole XRBs where thermal driving might be the
dominant process (see Table 12.1). This is another reason to suspect that
magnetic processes might be involved in driving the disk winds in some neutron
star XRBs

Figure 12.9: Non-relativistic 3D MHD simulations that show the formation of
conical winds from accretion onto a magnetized star Romanova2009 . Shown are
the distribution of matter flux (colors) and sample magnetic field lines at
different times (in the YZ plane). The direction of the stellar magnetic
moment and angular velocity of the rotation is indicated by arrows.

Burst-driven disk winds. Another interesting observational development is that
there are several neutron star LMXBs for which there is evidence of temporary
winds related to bursts (see Figure 12.10; Degenaar2013, ; Pinto2014, ;
Strohmayer2019, ). Their connection to bursts suggests that these disk winds
are purely radiatively driven, or perhaps reveal the impact that radiation can
have on an existing (magnetic or thermally driven) wind (see Section 12.2.1).
These examples all concerned particularly energetic bursts, which may have
promoted wind detection. Perhaps with future instrumentation (see Section
12.5), the impact of bursts on disk winds can be studied more routinely. It
has not been explored in numerical simulations yet what impact bursts may have
on driving or enhancing disk winds.

Figure 12.10: Temporary disk wind detected in the short-period neutron star
system SAX J1808.4–3658 Pinto2014 . The top and bottom panels show the
gratings data recorded before and after an energetic thermonuclear burst,
respectively. The emergence of narrow, blue-shifted emission lines of Ne x and
Fe xxiv suggest that the intense radiation of the burst may have induced a
disk wind Degenaar2018 .

##  12.3 Geometry

…the X-ray luminosity of the source is determined by the wind from the star,
i.e., the highest luminosity states coincide with the strongest wind. It also
confirms the identification of the disk or accretion structure close to the
compact object as the origin for the fluorescent K$\alpha$ line and the
blackbody, and it suggests that these features and the associated accretion
flow structure (i.e., the accretion disk) are anticorrelated with the wind
from the companion. Kallman2019

In addition to outflows, high-resolution spectroscopy of X-ray binaries has
proven to be a powerful probe of the geometry of accreting systems, from the
innermost stable circular orbits of accretion disks to their ionized outer
atmospheres, from the hot accretion columns of white dwarfs to relativistic
jets and the clumpy ionized winds from massive stars. In this section, we
review a selection of these results.

###  12.3.1 Inner Accretion Flows

#### Inner Disks, Reflection, and Spin

X-ray spectral diagnostics of accretion disks in strong gravitational
fields—whether thermal emission or fluorescent iron lines—rely on the
relativistic broadening of emission from the inner flow, a combination of
Doppler boosting and gravitational redshifts (e.g., Reynolds2003, ;
McClintock2006, ). This broadening may be used to measure the inner radius of
the accretion disk (or the spin of a black hole in cases where this radius
corresponds to the innermost stable circular orbit). Because accurate
measurements of the underlying continuum are essential, it is tempting to
think of reflection and black hole spin measurements as largely the domain of
telescopes with low or moderate resolution but significant hard X-ray
sensitivity, like NuSTAR, RXTE, and INTEGRAL. But this is inaccurate both
historically and in practice: high-resolution spectroscopy can play critical
roles in revealing the structure of broad iron lines in X-ray binaries and the
spins of black holes.

First, high-resolution spectra are ideal for disentangling broad and narrow
lines, so they can lead to more powerful and robust probes of broad line
profiles even if reflection is primarily the domain of larger missions with
broader energy ranges Miller2007 . Indeed, one of the first detections of a
relativistically-broadened iron line in an XRB was secured with the help of
the Chandra HETGS: Miller2002a  reported a composite Fe line profile in Cyg
X-1, definitively demonstrating the existence of both a narrow and a broadened
component. Interestingly, Torres2005  argue that microcalorimeter observations
of such broad lines can constrain the precession of the inner accretion disk.
High-resolution spectra have played a similarly important role in uncovering
the origin of broad lines in neutron star X-ray binaries. (Chiang2016, , for
example) used grating spectra to show that there was no narrow line emission
in Ser X-1, effectively requiring a relativistic origin for the line. Though
spin is not a factor because neutron star spacetime is approximately
Schwarzschild, these broad lines can therefore probe the physical scale of the
inner disk (and provide upper limits on the neutron star radius, e.g.,
Cackett2010, ; Ludlam2018, , and references therein).

Second, to the extent that spin and reflection diagnostics are sensitive to
the underlying continuum, they are also sensitive to the inferred level of
interstellar and ionized absorption (see Section 12.4 and discussion in
Nowak2017 ). For missions like NuSTAR and RXTE with little or no soft X-ray
sensitivity, indirect constraints on interstellar absorption are degenerate
with thermal emission from the accretion disk as well as the low energy tail
of any power-law component. High-resolution spectra of absorption edges
facilitate direct measurements of the column densities of gas and dust in the
ISM (e.g., Lee2002, ). Nowak2011  performed a detailed analysis of
observations of Cyg X-1 with Chandra, Suzaku, and RXTE and demonstrated both a
composite line at high resolution and the importance of soft X-ray constraints
on neutral and ionized absorption for modeling the continuum and broad lines.
Again, the presence of coordinated or contemporaneous high-resolution spectra
can enhance the robustness of reflection and spin diagnostics.

#### Central Engines and Boundary Layers

Beyond spin and relativistic diagnostics of the inner edge of the accretion
disk, high-resolution spectra can provide other insights into the nature of
the inner accretion flows around compact objects.

One powerful probe not available in black hole systems is emission from the
boundary layer (or the accretion column in the case of magnetically-driven
accretion). Mukai2017  gives a broad overview of the many subclasses of
accreting white dwarf systems, which we will not review in detail here. We do
note, however, that expected line properties generally vary significantly
depending on the geometry of the emission region, and therefore we should not
be overly quick to generalize between different classes of CVs, e.g., from
dwarf novae to polars (where the configuration of the accretion flow is very
different).

As in black hole and neutron star X-ray binaries, the spectral behavior of CVs
can change with accretion rate. In dwarf novae, for example, high-resolution
spectra typically show strong emission lines in quiescence. XMM-Newton RGS
spectra of OY Car, for example, indicated a multi-temperature plasma with
components at $\sim 3$ keV and $\sim 7$ keV Ramsay2001 . Chandra HETGS spectra
have revealed similar series of strong lines (e.g., Szkody2002, ; Perna2003, ;
Pandel2005, ). According to these sources the lines are consistent with an
origin in the boundary layer itself, i.e., plasma settling onto the white
dwarf from the accretion disk (see Mukai2017, , and references therein for a
more extensive discussion of this point).

Hellier2004 ; Rana2006  discussed the presence of strong fluorescent Fe lines
even in quiescent CVs, which likely indicate reflection off the white dwarf
surface. Hayashi2018  performed Monte Carlo simulations of reflection in
magnetic CVs to study the dependence of the fluorescence features on
parameters like white dwarf mass, spin, viewing angle, abundances, and the
specific accretion rate. But there are also notable changes in the emission
components in dwarf novae between outburst and quiescence. Rana2006  found
that the Fe xxv line was significantly broadened during outburst in some
systems, suggesting outflowing material near the white dwarf surface. Indeed,
Mauche2004b  argued that the Chandra LETGS spectrum of SS Cyg in outburst
comprised continuum emission from the boundary layer, absorbed and scattered
by an outflowing wind.

From the preceding discussion, it is clear that the physical scale of the
inner accretion flow—be it a black hole, neutron star, or white dwarf—is of
central importance for accretion diagnostics. While relativistic modeling and
ionization analysis are common methods for quantifying the size and location
of emitting regions, Trueba2022  developed a novel high-resolution
spectroscopic method for measuring the size scale of the central engine in
accreting compact objects using gravitationally-redshifted absorption lines
from a rotating disk atmosphere. As shown in Figure 12.11, the velocity width
of these absorption lines will depend in part on the size of the X-ray
emitting region. They were able to place $3\sigma$ upper limits of
$<90~{}GM/c^{2}$ on the size of the central engine in the short-period neutron
star LMXB XTE J1710–053. Though it has only been applied in a small number of
systems to date, it seems ideal for microcalorimeters on next-generation X-ray
missions like XRISM and Athena.

###  12.3.2 Outer Limits

#### Outer Accretion Disks

Even in cases where the relevant gas is not close enough to the central engine
to determine its size scale, emission and absorption lines can provide
detailed information about the structure and behavior of accretion disks. One
well-established example of outer accretion flow diagnostics comes from
dipping LMXBs, where early XMM-Newton and Chandra observations revealed the
existence of ionized absorption and emission lines in a number of high-
inclination systems (e.g., Cottam2001a, ; Cottam2001b, ; Sidoli2001, ;
Parmar2002, ; Sidoli2002, ; Jimenez-Garate2003, ; Boirin2005, ). These
observations implied the existence of hot and warm gas extending well above
and below the accretion disk midplane at relatively large radii: the extended
accretion disk corona (ADC) (e.g., Church2004, ; church2005, ; Iaria2006, ;
Schulz2009, ). It is now understood (see vanPeet2009, , and references
therein) that dipping phenomena are caused by transient obscuration of the
central X-ray source by structures in the outer accretion disk, such as the
disk rim, accretion stream, or the bulge at the disk-stream impact point.
Balucinska-Church2011  used Chandra/XMM-Newton grating spectra of Cyg X-2 to
argue that the dips at orbital phase 0.35 could be attributed to structures
opposite the accretion stream impact point. More recently, Psaradaki2018  used
X-ray eclipses to map hot gas above the disk in EXO 0748–676. They found two
separate ionization components; they interpreted the higher ionization emitter
as the extended disk atmosphere, and the cooler gas as clumpy dense gas
related to the accretion stream impact itself. Furthermore, to the extent that
the ADC or other disk atmosphere are azimuthally asymmetric, any associated
emission/absorption features can be expected to vary with orbital phase, a
fact used by Xiang2009  to map the ionization structure and viewing geometry
of the “Big Dipper” 4U 1624–490.

Figure 12.11: Cartoon illustrating geometric velocity broadening from
Trueba2022 . A disk atmosphere sufficiently close to the center will exhibit
velocity broadening that depends on the physical size of the central engine.

Similar techniques can be applied to similar benefit to study the structure of
disks and their environments directly. For example, high-resolution X-ray
spectra have illuminated the behavior of superorbitally-precessing accretion
disks in both low-mass and high-mass X-ray binaries. Jimenez-Garate2002
calculated the expected recombination line emission from an accretion disk
irradiated by a central X-ray source. Based on those calculations, Jimenez-
Garate2002  argued that photoionized emission lines seen in XMM-Newton RGS
observations of Her X-1 likely originated in the disk atmosphere or the
illuminated face of the secondary star. Drawing on 170 ks of Chandra grating
spectra, Ji2009  inferred cool, dense material distributed throughout the disk
in Her X-1. Kosec2022  divided the emission lines in Her X-1 into three
groups, attributed to (1) the outer accretion disk, (2) the disk/magnetosphere
boundary, and (3) X-ray reflection from the accretion curtain. This multi-zone
structure echoes similar results from Neilsen2009b  in LMC X-4, where the
spectral variability properties of different line groups seen by the Chandra
and XMM-Newton gratings could be traced to the inner disk, illuminated outer
disk, or the photoionized stellar wind from the massive donor.

There has also been significant interest in modeling and interpreting narrow
Fe K$\alpha$ lines. Reflection from distant cold gas, for example, is
sensitive to the geometry, ionization, dynamics, and abundances in the
accretion flow George1991 111111With upcoming microcalorimeter missions, it
may even be possible to use Fe K$\alpha$ lines to measure the mass functions
of X-ray binaries DashwoodBrown2022 .. Watanabe2003  reported a sensitive
measurement of the iron line in GX 301–2, including a detection of the
“Compton shoulder,” a faint feature on the red wing of the Fe K$\alpha$ line
due to backscattering of 6.4 keV photons in a Comptonizing medium. In cases
where significant scattering is expected, the Compton shoulder can be used to
measure the column density, electron temperature, orientation, abundances, and
Compton scattering optical depth (e.g., Matt2002, ). Torrejon2010  argued that
the Fe K$\alpha$ line equivalent widths and column densities are consistent
with a spherical distribution of reprocessing material around the compact
object, though Tzanavaris2018  concluded the opposite for a smaller sample of
X-ray binaries. Torrejon2010  also reported a decrease of iron line equivalent
width with luminosity in X-ray binaries (the so-called “X-ray Baldwin effect”)
that they interpreted as the result of photoionization. Finally, they noted
that these lines are ubiquitous in HMXBs but rare in LMXBs, which suggests
that illuminated stellar companions and their winds may play a significant
role in producing K$\alpha$ complexes in X-ray binaries. Follow-up work on
HMXBs by Gimenez-Garcia2015  used XMM-Newton to confirm both the X-ray Baldwin
effect and the contribution of stellar winds.

#### Stellar Winds

It is clear that stellar winds are important for studies of accretion geometry
via fluorescent and recombination lines, but there is also an enormous body of
work devoted to the study of stellar winds in their own right. For the
purposes of this chapter, we focus our attention on massive stars in XRB
systems (particularly Vela X-1 and Cyg X-1, which have received the most
attention in recent decades). By way of demonstrating the impact of stellar
wind physics for XRB studies, Gimenez-Garcia2016  noted that the velocity of
winds from supergiant donors can have a significant impact on the HMXB class.
In other words, stellar winds play an important role in determining the
overall behavior of X-ray binaries! Stellar wind physics also has implications
for binary evolution scenarios: the difficulty of producing a system like Cyg
X-1 (with a rapidly-spinning 21$M_{\odot}$ black hole in close orbit with a
41$M_{\odot}$ O star with enhanced He and Fe abundances) requires significant
adjustments to prescriptions for wind mass loss rates from the black hole
progenitor (Neijssel2021, , and references therein).

In Vela X-1, the presence of ionized circumstellar gas was already apparent
well before the era of high-resolution X-ray spectroscopy. For example, in
1986, Nagase1986  used a series of Tenma spectra to infer a moderately ionized
absorber responsible for an iron edge and emission line. Around the same time,
it was becoming clear how complex the structure of such winds would be in a
binary system, with accretion wakes and photoionization wakes, as well as a
possible accretion stream as sources of large-scale inhomogeneity and clumps
on smaller scales Blondin1990  (see also ElMellah2017, ; ElMellah2018, ).
Winds of massive stars were expected to be clumpy due to instabilities
associated with line driving Lucy1970 ; Lucy1980 , but advances in computation
made it possible to simulate the development of shocks in these winds (e.g.,
Owocki1988, ) and to show how they fragment into clumps (e.g., Oskinova2012, ;
Sundqvist2013, , and references therein). Sako1999  argued that the wind in
Vela X-1 had to be inhomogeneous in order to resolve discrepancies between the
mass loss rates inferred from optical and X-ray spectra, while schulz2002c
drew a similar conclusion based on fluorescent line fluxes. Clumps have also
been invoked to explain variability on timescales of hours Furst2010 ,
absorption dips Hanke2009 , and associated line variability Miskovicova2016 .
In turn, variability measurements can be used to infer the statistical
properties of clumps ElMellah2020 .

High-resolution X-ray spectral studies of Cyg X-1 have been similarly
informative. A number of early Chandra observations (e.g., Marshall2001, ;
Schulz2002, ; Miller2002a, ) showed strong absorption lines at different
orbital phases, while modeling by Feng2003  indicated that the absorption
lines had an extended red wing that was more pronounced in lines from more
highly-ionized ions. Miskovicova2016  found that the line profile actually
varies with orbital phase, appearing as symmetric absorption lines at superior
conjunction but exhibiting full P-Cygni profiles at inferior conjunction.
Miller2005  used orbital phase comparisons to deduce that the X-ray absorbing
portion of the wind must be gravitationally focused: tidal and centrifugal
effects produce a distorted, asymmetric wind, as shown by Friend1982 ;
ElMellah2019  and inferred from optical spectra for Cyg X-1 by Gies1986 .
Hanke2009  described a Chandra HETGS spectrum with a model including two wind
absorption components, which they associated with spherical and focused
regions of the wind. Kallman2019  similarly divided the stellar wind in Cyg
X-3 into a “nebular” component and a “wind” component (see also Paerels2000, ;
Suryanarayanan2022, , and references therein). In Cyg X-1, short-lived dips
are commonly observed when the line of sight intersects the densest region of
the wind, such that flux-resolved spectra can reveal the ionization structure
of clumps in the wind Hirsch2019 . Careful measurements of line velocities
(based on reference energies from an electron beam ion trap) indicate that the
clumps are likely stratified, with denser gas shielding the center and back of
the clumps from ionizing radiation.

In short, as is often the case, the presence of a compact object provides
ample opportunities for studying the structure and behavior of stellar winds,
while also substantially influencing them. A detailed review of the stellar
winds of isolated stars is outside the scope of this chapter, but for a
discussion of high-resolution X-ray spectroscopy and the solar wind, we refer
the interested reader to Chapter 12 of this volume, by L. Gu.

#### Jets

Finally, we turn briefly to spectroscopic constraints on relativistic jets
from X-ray binaries. There are several examples of X-ray jets in X-ray
binaries in the literature (e.g., Corbel2002, ; Steiner2012, ; Espinasse2020,
), but in these cases the X-ray emission arises when jet ejecta interact with
the local environment. The best-known example of a spectroscopically-
identified jet is SS 433. which exhibits Doppler-shifted lines from its
precessing jet. Optical line shifts were attributed to the jet in 1979
Abell1979 ; Fabian1979 ; Milgrom1979 , and Doppler-shifted X-ray emission
lines had been associated with the jet within a decade Watson1986 ; (for a
review of the X-ray literature, see Marshall2013, , and references therein).
Currently, the prevailing interpretation is that the X-ray emission lines
arise in hot thermal plasma in the jet at distances of $\sim 10^{12-13}$ cm
from the compact object (e.g., Brinkmann1991, ; Kotani1996, ; Lopez2006, ;
Marshall2013, ; Medvedev2019, ). The advent of high-resolution X-ray
spectroscopy has produced a number of insights into the X-ray jet from this
important microquasar, including a $\sim 5\times$ smaller opening angle in the
X-ray than in the optical Marshall2002  and a large overabundance of Ni
(suggesting the donor star may have been enriched by the supernova that
created the compact object; Marshall2013, ).

It is clear that the advance to microcalorimeters will further advance our
understanding of the dynamics and structure of jets. But there are also
several results from lower resolution spectra that suggest a similar cause for
optimism. For example, Migliari2002  found hot iron line emission in Chandra
CCD spectra of the jet at distances of $>10^{17}$ cm from the compact object
(long after adiabatic cooling should have rendered the gas undetectable in
X-rays; Marshall2002, ). This result implies that there is continued heating
of the atomic component of the jet long past the initial acceleration region.
More recently, Middleton2021  identified a time lag in NuSTAR observations SS
433 that—due to its narrow energy range–could only be attributed to atomic
processes. Sensitive observations of this lag with next-generation facilities
will reveal its origin in more detail.

More broadly, diagnostics of baryonic jets represent an open question for
high-resolution X-ray spectra. In particular, it is notable that there are so
few detections of atomic transitions clearly associated with outflowing jets.
DiazTrigo2013b  reported detecting relativistically Doppler-shifted emission
lines in 4U 1630–47 using XMM-Newton CCD spectra, though Chandra grating
observations of 4U 1630–47 in different accretion states did not show similar
emission lines Neilsen2014 . If confirmed, this would have represented only
the second clear case of baryons in a jet from an XRB out of a population of
dozens. Next-generation spectra may resolve the question of baryonic jets, but
it remains to be seen whether they do so by detecting faint relativistic lines
or by revealing baryonic jets to be intrinsically rare.

##  12.4 ISM

In this section, we briefly lay out how high-resolution X-ray spectroscopy can
be leveraged to study the ISM. For a more extensive overview, the reader is
referred to the recent review of Costantini & Corrales Costantini2022 .

Bright X-ray binaries provide an excellent backdrop to study the composition
and structure of the ISM at high spectral resolution. Gas along the line of
sight to these sources leads to photoelectric edges in X-ray spectra. By
comparing the optical depth in these edges to the continuum absorption, it is
possible to: (1) measure ISM and stellar abundances (e.g., Lee2002, ;
Juett2003a, ), (2) infer the contributions of interstellar gas vs. absorption
local to the binary (e.g., Juett2001, ; Juett2003a, ), (3) quantify the
depletion of interstellar gas into dust grains (e.g., Juett2006, ; Pinto2010,
, see below), and (4) map the spatial distribution of cold, warm, and hot
interstellar gas (e.g., Paerels2001, ; Pinto2010, ; Gatuzz2018, ).

In addition to photoelectric edges, the X-ray spectra of X-ray binaries are
imprinted with extinction features from solid dust particles present in the
ISM. If X-ray photons interact with electrons inside a dust grain (rather than
gas phase atoms), the energy levels can be modified by the effect of
neighboring atoms, resulting in an interference pattern referred to as “X-ray
absorption fine structure” (XAFS). The details of such features depend on the
energy of electrons and the complexity of the compound, hence allowing us to
study the physical properties of interstellar dust such as its chemical
composition, the size of the dust grains Corrales2016  and their crystallinity
Zeegers2017 ; Zeegers2019 . Bright X-ray binaries provide sufficiently high-
quality data to detect these extinction features and can reveal potential
differences in the dust properties of the ISM in different Galactic
environments Lee2005 ; Lee2009 . The chemical composition of interstellar dust
appears to be dominated by carbon and silicates, hence the most prominent
extinction features are of Si, Mg, O, and Fe (which are the main constituents
of silicates). These features have been studied in detail with current X-ray
missions Lee2002 ; Costantini2012 ; Pinto2013 ; Valencic2015 ; Zeegers2017 ;
Zeegers2019 . Future missions like Athena with higher sensitivity may be able
to study similar structures and compositions using edges of less abundant
species.

Another aspect of interstellar dust that is relevant for high-resolution X-ray
spectroscopy is dust scattering halos. These halos consist of X-rays from the
binary that are scattered into our line of sight by intervening dust screens,
and have been observed around a number of XRBs on a variety of angular scales
Audley2001 ; Ling2009 ; Tiengo2010 ; Xiang2011 ; McCollough2013 ; Kalemci2018
; Jin2019 ; Sguera2020 ; Lamer2021 . In addition to practical considerations
(e.g., the size of the dust scattering halo compared to the spatial resolution
of the instrument Nowak2011, ; Nowak2017, ), through XAFS the structure and
distribution of dust grains affect both the intensity profile of dust
scattering halos and the shape and depth of photoelectric edges
(Costantini2022, , and references therein). Future missions that combine
sensitivity with spatial and spectral resolution will therefore have the best
opportunity to probe the properties of interstellar dust.

##  12.5 Future and Outlook

Finally, we turn to the future: what can we hope to learn from high-resolution
spectroscopy of X-ray binaries with next-generation facilities? As of this
writing, there is particular interest in microcalorimeters on XRISM and
Athena. The improved sensitivity and spectral resolution of these facilities
will be a game changer for all the XRB studies discussed in this chapter. In
particular, the ability to compute absorption and emission diagnostics as
described in the preceding sections will be greatly enhanced by the reduced
time to detect line features, enabling faster constraints on the behavior and
geometry of gas in variable systems and more robust detections of weaker
lines. Since at the time of writing, the Athena mission is in a re-definition
stage, the discussion below is focused on XRISM.

The launch of XRISM Tashiro2020  is anticipated in Spring 2023. It carries a
soft X-ray spectrometer, Resolve, which offers a constant $<7$ eV FWHM
spectral resolution over the entire 0.3–12 keV bandpass and an effective area
of 160 (210) cm-2 at 1 (6) keV. The spectral resolution of Resolve is a factor
20–40 higher than the CCD instruments on board Chandra and XMM-Newton, while
it has substantially increased the collecting area and bandpass over the
grating instruments on these missions. Whereas previous studies have shown
that hot plasmas in X-ray binaries can have very high velocities, some of the
gas may have much smaller characteristic motions of the order of $\simeq$100
km s-1 and hence remain unresolved with current instrumentation.

Figure 12.12: Simulated XRISM/Resolve spectrum of the black hole XRB GRS
1915+105 (50 ks) based on the best Chandra/HETG model Miller2016b  shown in
Figure 12.7. Reproduced with permission from XRISM2020 .

Disk winds. For X-ray binaries, it remains to be established what the relative
importance of thermal and magnetic processes is in driving their disk winds.
The increased spectral resolution of new instrumentation will make it possible
to separate complexes of lines (Figure 12.12). This, in turn, will allow us to
accurately measure velocities, to separate distinct wind zones, and to measure
launching radii. These are all key indicators of the underlying launch
mechanism, as discussed in Section 12.2.1. Also, by virtue of a broad pass
band, density-sensitive lines from intermediate charge states become
accessible; these enable direct measurements of the density so that the
absorption radius can be derived from the photoionization parameter. Wind
launch radii can also be measured independently from the velocity broadening
of the emission components in lines that have a P-Cygni profile. Furthermore,
high-resolution spectrometers may shed new light on whether or not disk winds
are intrinsically transient: if the apparent disappearance in the hard state
is due to lower column densities and higher ionization, the increased
sensitivity and resolution of XRISM/Resolve compared to current
instrumentation may detect hot X-ray winds in hard states.

In this context, it is worth noting that X-ray polarimetry missions will also
contribute to advancing studies of XRB disk winds, albeit less directly. For
instance, IXPE has already started to put constraints on the magnetic field
topology in disks Krawczynski2019 ; Krawczynski2022 , which facilitates
further advancement in numerical simulations of disk accretion and any
resulting outflows.

Geometry. We may also expect to see large strides in understanding the
accretion geometry in X-ray binaries. For instance, the scale height of the
outer disk and the extent to which it might be flared, can potentially be
revealed by studying narrow emission lines in high-inclination dipping X-ray
binaries. For stellar winds, the highly increased velocity resolution enabled
by XRISM will allow the separation of lines produced close to the compact
object from those excited in the larger stellar wind. Moreover, it will allow
a precise detection of velocity shifts as a function of the orbital phase.
Improved measures of the ionization, density and temperature of the accreting
material will enhance detailed comparisons to hydrodynamic simulations.
Furthermore, the increased sensitivity of next-generation missions will
facilitate studies of wind structure and clumping in many more systems and on
short timescales Lomaeva2020 .

ISM. High-resolution X-ray spectroscopy studies of the ISM will also take a
leap with new spectrometers. For instance, XRISM provides access to dense
environments of the Galaxy ($N_{H}\simeq 1-10\times
10^{22}~{}\mathrm{cm}^{-2}$) near the Galactic Center or molecular clouds,
which is currently uncharted territory. XRISM will allow to compare the
spectral features of interstellar dust (especially for heavier elements such
as Ca, S, and Fe) to material absorption measured in the lab XRISM2020 .

As detailed in the pages above, the strength of high-resolution spectroscopy
lies in the power to illuminate the physical conditions in gas and dust and,
accordingly, reveal the physical processes that produce them. In X-ray
binaries, these processes—accretion and ejection, ionization, and so on—vary
from sub-second timescales to years and decades. Building on existing high-
resolution X-ray spectra, next-generation facilities will rewrite our
understanding of accretion physics by probing shorter timescales with superior
constraints on the ionization and dynamics of gas and dust around compact
objects.

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