# Geocoronal Solar Wind Charge Exchange Process Associated with the
2006-December-13 Coronal Mass Ejection Event

###### Abstract

We report the discovery of a geocoronal solar wind charge exchange (SWCX)
event corresponding to the well-known 2006 December 13th coronal mass ejection
(CME) event. Strong evidence for the charge exchange origin of this transient
diffuse emission is provided by prominent non-thermal emission lines at
energies of $\rm O^{7+}$, $\rm Ne^{9+}$, $\rm Mg^{11+}$, $\rm Si^{12+}$, $\rm
Si^{13+}$. Especially, a 0.53 keV emission line that most likely arises from
the $\rm N^{5+}$ $1s^{1}5p^{1}\to 1s^{2}$ transition is detected. Previously,
the forecastability of SWCX occurrence with proton flares has been disputed.
In this particular event, we found that the SWCX signal coincided with the
arrival of the magnetic cloud inside CME, triggered with a time delay after
the proton flux fluctuation as the CME shock front passed through the Earth.
Moreover, a spacecraft orbital modulation in SWCX light curve suggests that
the emission arises close to the Earth. The line of sight was found to always
pass through the northern magnetospheric cusp. The SWCX intensity was high
when the line of sight passed the dusk side of the cusp, suggesting an
azimuthal anisotropy in the flow of solar-wind ions inside the cusp. An
axisymmetric SWCX emission model is found to underestimate the observed peak
intensity by a factor of about 50. We suggest this discrepancy is related to
the azimuthal anisotropy of the solar-wind flow in the cusp.

JGR: Space Physics

Institute of Space and Astronautical Science, Japan Aerospace Exploration
Agency, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 252-5210 National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 International
Center for Quantum-field Measurement Systems for Studies of the Universe and
Particles (WPI,QUP), High Energy Accelerator Research Organization, 1-1 Oho,
Tsukuba, Ibaraki 300-3256

Yu<EMAIL_ADDRESS>
We discover a solar wind charge exchange event with Suzaku X-ray satellite
driven by the 2006-December-13th coronal mass ejection.

The SWCX occurence time coincides with the CME magnetic cloud arrival. It is a
useful knowledge in space weather forecasting.

We modeled the light curve variation of the SWCX. The result indicates that
the solar-wind flow is anisotropic in the cusp.

## Plain Language Summary

We discovered compelling observational evidence of the coronal mass ejection
(CME) interacting with Earth’s magnetosphere by the Suzaku satellite. The
signal arises from a process called charge exchange, in which heavily charged
ions within the CME interact with neutral hydrogen within Earth’s
magnetosphere. This specific process, known as solar wind charge exchange
(SWCX), was associated with the CME event occurred on 2006 December 13th
during the solar minimum. This event provided us with a unique opportunity to
gain insights into the interplanetary consequences of CMEs. Despite a delay
relative to the shock wave associated with the CME, the SWCX coincided with
the arrival of a magnetic cloud. This suggests that solar wind ions were
guided along magnetic field lines into a region near Earth called the cusp,
through a process known as magnetic reconnection. Additionally, we observed
that SWCX emissions were most pronounced when the satellite’s line of sight
passed through the dusk region of the cusp. This indicates that the CME ejecta
may have followed a path along the Parker spiral – a magnetic field pattern
twisted by solar rotation – resulting in the solar wind arriving from a
direction distinct from that of the Sun.

##  1 Introduction

Charge exchange (CX) process was first observed from comet Hyakutake [Lisse .
(1996)] arising from the interaction between cometary neutrals and solar wind
ions [Cravens (1997)]. Nowadays, we have realized that CX event can arise in
various scenarios, such as the shock rim of supernova remnants [Lallement
(2009), Katsuda . (2011), Katsuda . (2012), Cumbee . (2014)], the interface
between stellar wind and surrounding interstellar medium in starburst galaxies
[Pollock (2007), Tsuru . (2007), J. Liu . (2011)], merger or accretion shocks
inside galaxy clusters [Walker . (2015), Fabian . (2011), Gu . (2015)], and
solar wind charge exchange (SWCX) with the planetary neutrals [Snowden .
(2004), Cravens . (2003), Dennerl . (2006), Hui . (2009)] and interplanetary
heliosphere [Cravens (2000), Koutroumpa . (2006), Galeazzi . (2014), Ringuette
. (2021)].

Geocoronal SWCX results from solar wind ions interacting with the neutrals in
Earth’s atmosphere, leading to transient non-thermal emission lines exceeding
the diffuse X-ray background spectrum [Fujimoto . (2007), Ezoe . (2010),
Cravens . (2001), Carter Sembay (2008), Carter . (2010), Ezoe . (2011),
Ishikawa . (2013), Ishi . (2019), Asakura . (2021)]. A significant concern in
studying geocoronal SWCX events is forecasting their occurrence through solar
activity indicators. Solar wind proton flux has been observed to correlate
with the charge exchange emission on timescales of about half a day [Fujimoto
. (2007), Carter . (2010)] or within two hours [Ezoe . (2011), Ishikawa .
(2013)]. However, Ishi2019 demonstrates a SWCX event associated with a coronal
mass ejection (CME) that lacks significant time coincidence with proton flux
but instead shows a positive correlation with alpha flux.

Such complication is due to the diverse phenomena triggered by CME eruptions,
including electromagnetic flares in various energy bands from radio to gamma-
ray [Benz (2017), Del Zanna Mason (2018)], solar energetic particles (SEPs)
[Desai Giacalone (2016)], highly ionized heavy ions [Lepri Zurbuchen (2004),
Zurbuchen Richardson (2006)], and shock waves [Nindos . (2011), Verscharen .
(2019)] reaching Earth with different time delays from the solar surface. The
timescales for X-ray brightening are short (minutes to hours [Shibata Magara
(2011)]), while impulsive SEP events last a few hours, and large-scale gradual
SEP events can persist for several days [Reames (1999), Desai Giacalone
(2016)]. Solar wind (SW), categorized as slow wind (approximately 400 $\rm km\
s^{-1}$), fast wind (around 700-800 $\rm km\ s^{-1}$), and coronal mass
ejections (CMEs) with speeds up to 2000 $\rm km\ s^{-1}$, approaches Earth
over several days or weeks [McComas . (1998), Viall Borovsky (2020),
Verscharen . (2019)]. This makes it challenging to establish clear
correlations between different tracers, especially during frequent solar
flares.

Modeling the SWCX spectrum is another challenge, considering uncertainties in
the CX cross section, ionic composition of the solar wind, relative velocity
between solar wind and neutrals, and the SWCX interaction geometry with the
magnetosphere.

Theoretical approaches to calculate the CX cross section include quantum-
mechanical methods [Nolte . (2012)], atomic-orbital close-coupling [Fritsch
Lin (1991)], classical trajectory Monte Carlo [Abrines Percival (1966), Olson
Salop (1977)], and multi-channel Landau-Zener method [Janev Winter (1985)].
However, laboratory measurements of the CX cross section are limited to a
small number of ions [Fite . (1962), Meyer . (1979), Meyer . (1985), Crandall
. (1979), Ali . (2005), Wargelin . (2005), Greenwood . (2000), Defay . (2013),
Fogle . (2014), Beiersdorfer . (2003), Mullen . (2017), Mullen . (2016),
Cumbee . (2018)]. Consequently, integrated astronomical data analysis software
often relies on scaling relations [Gu . (2016), Olson Salop (1977)] or
empirical formulae to estimate these values [Smith . (2012)].

The SW ionic composition and velocity are determined by factors such as the
solar flare temperature, plasma equilibrium state at the moment it becomes
collisionless, acceleration and release mechanisms [Viall Borovsky (2020)], as
well as deceleration during propagation and the first ionization potential
fractionation status under ponderomotive forces induced by magneto-
hydrodynamic waves [Laming (2015)]. If SW velocity and CX cross section are
accurately constrained, the SWCX spectrum observation can serve as a remote
sensor for highly ionized ions in the solar wind, complementing in-situ ion
composition spectrometers [Gloeckler . (1998)].

The poorly understood geometry of the geocoronal SWCX interaction is also a
critical aspect. Studies often assume that solar wind ions fill the
magnetosheath, with further penetration resisted by magnetic pressure at the
magnetopause [Ezoe . (2011), Carter . (2010), Ishikawa . (2013), Ishi .
(2019)]. However, magnetohydrodynamic (MHD) simulations show prominent X-rays
from CX collisions between solar wind ions and Earth’s exospheric neutrals in
the cusp region [Robertson . (2006)]. Observations by Suzaku, pointing towards
the North pole, indicated that X-ray intensity variation is anti-correlated
with the geocentric distance from the point where the geomagnetic field first
opens to space, suggesting SWCX emission can penetrate deeper than the
magnetosheath near the cusp region [Fujimoto . (2007)].

In this study, we present a unique case of geocoronal SWCX observed by the
Suzaku satellite, associated with a well-distinguished source CME occurring on
December 13th, 2006. The solar environment was near solar minimum at the time,
minimizing contamination from other events and offering a valuable opportunity
to study the space weather consequences of the CME. Especially, the
satellite’s line-of-sight was directed towards the North pole which allows a
cusp observation. Section 2 provides a comprehensive background description of
in-situ measurements for this CME event. Section 3 describes the data
reduction details for Suzaku observations. We report the SWCX spectrum
detected by Suzaku in section 4 and explore the time coincidences with
interplanetary and Earth magnetic fields in section 5. Furthermore, we discuss
the SWCX geometry modeling in section 6. Summary and conclusion are given in
section 7.

Figure 1: A schematic of the CME propagation. (a) Initially, the solar flare
occurs and the CME is launched near the solar surface as a result of magnetic
reconnection, which is observed (in part) as abrupt enhancements of soft X-ray
and proton flux [Zurbuchen Richardson (2006), Shibata Magara (2011)]. (b) The
CME propagates the interplanetary space (ICME) towards the Earth with the
magnetic flux rope as its core. The turbulent sheath forms behind the CME
shock front and reaches the Earth in advance of the MC. (c) As a result of
reconnection between the flux rope and Earth’s magnetic field, the heavily
ionized ions are streamed into the magnetosphere, particularly to the polar
regions, along the magnetic field lines. The artistic drawing is contributed
by courtesy of designer Xuelei Chuai.

##  2 CME Event on 2006 December 13

The CME event that occurred on 2006 December 13 was one of the largest halo
CMEs since the intense solar activity in 2003. This CME was associated with
the X3.4-class solar flare, emanating from NOAA active region 10930, which was
accompanied by the radio bursts, SEP event, and MC passage. This flare event
has been studied in detail from both observational and theoretical points of
view, which is summarized in HinodeReviewTeam2019 and Toriumi2019.

The coronal observations from the Large Angle Spectroscopic Coronagraph and
the Extreme ultraviolet Imaging Telescope aboard the Solar and Heliospheric
Observatory shows a strong EUV brightening at 02:30 UT, followed by a dimming
and forming into a ring of dense material around 03:06 UT [Y. Liu . (2008)].
The CME initial velocity is 1774 $\rm km\ s^{-1}$ near the Sun according to
the coronagraph height-time observation. After the abrupt formation, the CME
ejecta propagates into the space and its interplanetary CME (ICME)
consequences, including low-energy and high-energy electrons, protons, MC,
were measured in-situ by the STEREO and ACE satellite at 1 AU [Mewaldt .
(2008)]. At 14:38 UT on December 14, about 36 hours later than the CME
outburst, a preceding shock passed the spacecraft at an average speed of
$\sim$1160 $\rm km\ s^{-1}$ as suggested by simultaneous enhancements in the
electron flux and magnetic field strength. This speed has decreased compared
with the initial velocity near the Sun but larger than the shock speed as
calculated according to mass conservation across the shock at 1 AU ($\sim$1030
$\rm km\ s^{-1}$)[Y. Liu . (2008)]. Following the preceding shock and magnetic
fluctuation period, the detected magnetic field shows clear rotation,
indicating that spacecraft seems to cross the MC interior[Y. Liu . (2008),
Kataoka . (2009)]. The shock downstream of the ICME was detected later on
17:23 UT on December 16 with a sharp but short duration jump in the proton
flux and magnetic field strength. The shock was finally detected by the
Ulysses with a speed of 870 $\rm km\ s^{-1}$ at a distance of 2.73 AU to the
Sun and to the $117^{\circ}$ east and $74^{\circ}$ south of the Earth at 17:02
UT on December 17 [Richardson . (2005)]. But other signatures of ICME, such as
enhanced helium abundances, decreased proton temperature, or smooth strong
magnetic fields were not detected at Ulysses.

Figure 2: (a) and (b) shows the images of the observation 801032010 and
701060010. The green frames enclose the CDD regions where the energy spectra
were extracted from. (c): Energy spectra for the observation 801032010,
generated separately for the time intervals [A-G] defined from the light
curves shown in Figure 4 (b). (d): Energy spectra for the observation
701060010 that compare the quiescent and flare time periods defined from the
light curves shown in Figure 4 (d). Models fitting to the diffuse X-ray
background break down to three major components: unresolved point sources in
the cosmic X-ray background (gray dashed lines), hot plasma in the galactic
gaseous halo (purple dashed line), and warm-hot gas in the local hot bubble
(blue dashed line).  Figure 3: (a) Net SWCX spectrum and the fitted Gaussian
models for the back-side and front-side illuminated CCDs. $blue$ cross: data
from XIS1, $black$ cross: merged data from XIS0, XIS2, and XIS3. (b)-1 shows
the fit of CX model in SPEX. Comparisons of the SPEX-CX model in terms of
metal abundance, collisional velocity, and plasma temperature are shown in
(b)-2, (b)-3, and (b)-4. Parmeters configuration for (b)-2: ionization
temperature $kT=1.04\rm\ keV$ and collision velocity $v=592.5\rm\ km\ s^{-1}$,
and solar abundance for elements other than C, N, Ne, Mg, Si; for (b)-3, solar
abundance and relative velocity $v=592.5\rm\ km\ s^{-1}$; for (b)-4, solar
abundance and ionization temperature $kT=1.04\rm\ keV$. (c)-1 shows the fit of
VACX2 model incorporated in XSPEC. Comparisons of the XSPEC-VACX2 model in
terms of metal abundance and collisional velocity are shown in (c)-2, (c)-3.
Parameters configuration for (c)-2: plasma temperature $kT=1.05\rm\ keV$, and
solar abundance for elements other than C, N, Ne, Mg, Si; for (c)-3, solar
abundances are set for all elements. Figure 4: The light curves for the Suzaku
X-ray background emission and other solar activity tracers. During the
observation 801032010/701060010 period: Proton flux observed by GOES
satellite, alpha to proton density ratio, and proton density measured by ACE
satellite are shown in (a)/(c); Count rate of the Suzaku X-ray background
emission, soft X-ray flux measured by GOES satellite, and the magnetic field
strength measured by ACE satellite are shown in (b)/(d).  Figure 5: A sketch
(not drawn to scale) of the Earth, magnetosphere, Suzaku orbit, cusp region,
and the definition of $\vec{r}_{\rm mp}$ where the line of sight meets the
last$-$closed geomagnetic field line.  Figure 6: (a) Time history of the
counting rate for $\rm O^{7+}$ emission line, plotted together with $r_{\rm
mp}$, the radial distance from the Earth center of the position where the
magnetic field is open to out space for the first time along the line of site.
(b) The X-ray intensity and $r_{\rm mp}$ plotted as functions of the azimuth
angle of the $r_{\rm mp}$ point in the GSM coordinate. The figure shows only
for cycle 2 of (a).

##  3 SWCX event captured by Suzaku Observations

We analysed the Suzaku observations that covers the time period since CME
formation to its passage across the Earth, including two individual datesets
with ObsIDs 801032010 and 701060010.

###  3.1 observation 801032010

The observation (obsID:801032010) was originally targeted on the galaxy
cluster Abell 1555, with a few point-sources discernable in the 0.5-2 keV
image, as shown in Figure 2 (a). The exposure time of observation, from
2006-Dec-12 22:16 UT to 2006-Dec-13 18:38 UT, has covered the CME-accompanied
X3.4 flare at 2006-Dec-13 02:14 UT and enabled a tracking of detector response
since the onset of solar flare.

We select the background region to exclude any contribution from the discrete
sources and extract the light curve and energy spectrum of the diffuse
background. No significant flare is observed in the light curve of the dark
sky data (selected with the criteria ELV$>$5 & DYE_ELV$>$20 & SUN_ALT$<$0)
except for a moderate orbital modulation around the solar flare phase. But the
sunlit Earth phase data (selected with the criteria ELV$<$0 & SUN_ALT$>$0) has
shown significant enhancement during the solar flare period near 02:14 UT on
2006 December 13, which reflects the solar flare photons scattered in the
Earth atmosphere. We further divided the light curve of the flare period into
small segments and found an abrupt emergence of line emission at $\sim$ 1.5
keV (indicated as [D] period in Figure 4 (b), and the spectrum shown in Figure
2 (b). Confirming that the decay time constant of the 1.5 keV line is
comparable to that of the solar flare X-ray fluxes in 1-8 Å energy range,
rather than that of the proton fluxes detected by GOES satellite, we conclude
that this line emission is originated from the fluorescent instrumental Al
$\rm K\alpha$ line (1.486 keV) created by secondary X-ray photons scattered
inside the telescope.

Besides, Suzaku detected an excess of blended line emissions in the 3-7 keV
energy range during the solar flare period, which are probably originated from
solar flare photons diffusely reflected by the Earth atmosphere that were
partially collected by the telescope. The line emission at 6.62 keV prominent
enough to be recognized as highly ionized Fe XXV line, which is also seen in
the Earth albedo spectrum extracted from the sunlit Earth data, supports this
conjecture.

###  3.2 observation 701060010

The observation (obsID:701060010) was pointed towards a Seyfert 1 galaxy, 3C
390.3, with two bright sources in the field of view, as shown in the full-band
image in Figure 2 (c). The timespan of the observation is from 2006-Dec-14
03:25 UT to 2006-Dec-16 03:19 UT, which contains the time period when the ICME
shock and MC passed by the Earth at around 2006-Dec-14 14:38 UT. We also
noticed an X1.5 flare detected by GOES starting from 22:07 UT on December 14
(see Figure 4 (d)).

We select only the background region to extract the light curve and energy
spectrum of the diffuse X-ray background emission. As seen in Figure 4 (d),
the light curve of Suzaku dark sky between 2006-Dec-15 0h and 6h shows
significant orbital modulation during the flare phase with a higher count
rates at maxima compared to the quiescent phase. A spectral excess is also
clearly observed in the flare phase in comparison with the spectrum of the
quiescent state. The excess emission is dominated by individual lines in 0.5-2
keV energy range.

All four Suzaku XIS detectors have sensed the transient SWCX excess emission
during the flare state. We extracted the energy spectra during the flare and
quiescent periods for both back-side and front-side illuminated CCD detectors.
We merged the spectra for the front-side illuminated sensor XIS0, XIS2, and
XIS3 to obtain a spectrum with higher signal-to-noise ratio. The corresponding
response files, ancillary files, and non-X-ray background files were also
combined using the ASCA ftool command addascaspec. The energy spectra
extracted in the quiescent period were finally subtracted from the source
spectra to exhibit the charge exchange excess for further modelling of the net
SWCX spectrum. The net SWCX spectra after background subtraction for both
types of CCDs are shown in Figure 3 (a).

##  4 Geocoronal SWCX energy spectrum

Figure 3 shows the SWCX energy spectrum fitted with multiple models for both
front-side and back-side illuminated CCDs. Table 1 shows the fitted centroid
energies and flux of the emission lines and their probable identifications. We
found that excess emission lines with fitted centroid energies around 0.652
keV ($\rm O^{7+}$), 1.02 keV ($\rm Ne^{9+}$), 1.32 keV ($\rm Ne^{9+}$), 1.47
keV ($\rm Mg^{11+}$), 1.86 keV ($\rm Si^{12+}$), and 1.97 keV ($\rm Si^{13+}$)
are typically seen in the observed geocoronal SWCX spectrum. Specially, we
observed an unusual emission line at about 0.53 keV. It is most likely the
$\rm N^{5+}$ $1s^{1}5p^{1}\to 1s^{2}$ transition which provides a strong
evidence that the excess emission is of a non-thermal origin. Another
possibility is that there is fluorescent emission of $\rm O$ K$\alpha$ line at
0.525 keV reflected inside the Earth atmosphere. However, we do not observe
comparable amount of $\rm N$ K$\alpha$ line at 0.392 keV which is another
fluorescent line expected to emerge as seen in the Earth albedo spectrum.
Therefore, the 0.53 keV line is not very likely to arise from the Earth
atmosphere fluorescence. Besides, the emission around $\sim$0.8 keV has a
broad energy distribution and has been usually recognized as the Fe-L shell
complex. The fit with CX models, however, suggested that this bump at
$\sim$0.8 keV is possibly contributed by oxygen (see Figure 3 (b)-1 and
(c)-1). Another point worthy of discussion is the 1.32 keV $\rm Ne^{9+}$ line,
around this energy the line could also be recognized as 1.329 keV $\rm
Mg^{10+}$, whereas the CX model favors to fit the 1.32 keV line with $\rm
Ne^{9+}$.

In Table 1 we show the best-fitted temperature and metal abundances with the
CX model in SPEX and XSPEC. Both models are based on the collisional
ionization equilibrium assumption, which may not hold for rapidly expanding
CME plasmas that have not reached the equilibrium state when becoming
collisionless. The fit results show significant degeneracies among the
temperature, velocity, and metal abundances in SPEX-CX model. The XSPEC-VACX2
model suggests a larger collisional velocity, or higher element abundance
ratio to oxygen for heavier ions than SPEX-CX model.

Table 1: Model fit parameters for SWCX spectrum Model | Energy | Line Identification | Surface Brightness |  Flux ratio to $\rm O^{7+}$
---|---|---|---|---
Gaussian | (eV) |  |  ($\rm photons\ cm^{-2}\ s^{-1}\ str^{-1}$) |
| $530_{-15}^{+4}$ |  $\rm N^{5+}$ $1s^{1}5p^{1}\to 1s^{2}$ (533 eV) | $2.4_{-0.5}^{+0.5}$ | $0.42$
| $647_{-4}^{+5}$ |  $\rm O^{7+}$ $2p^{1}\to 1s^{1}$ (653 eV) | $5.7_{-0.6}^{+0.6}$ | $1$
| $813_{-29}^{+16}$ |  $\rm Fe^{16+}$ $2p^{5}3d^{1}\to 2p^{6}$ (826 eV,812 eV) | $2.6_{-0.4}^{+0.4}$ | $0.46$
| $1028_{-4}^{+5}$ |  $\rm Ne^{9+}$ $2p^{1}\to 1s^{1}$ (1.022 keV) | $1.39_{-0.18}^{+0.18}$ | $0.24$
| $1089_{-87}^{+67}$ |  $\rm Fe^{23+}$ $1s^{2}3s^{1}\to 1s^{2}2p^{1}$ (1.085 keV), $\rm Fe^{17+}$, $\rm Fe^{21+}$ | $1.1_{-0.2}^{+0.2}$ | $0.19$
| $1320_{-10}^{+9}$ |  $\rm Ne^{9+}$ $6p^{1}\to 1s^{1}$ (1.324 keV) | $0.57_{-0.10}^{+0.10}$ | $0.10$
| $1460_{-5}^{+6}$ |  $\rm Mg^{11+}$ $2p^{1}\to 1s^{1}$ (1.472 keV) | $0.8_{-0.1}^{+0.1}$ | $0.14$
| $1857_{-22}^{+23}$ |  $\rm Si^{12+}$ $1s^{1}2p^{1}\to 1s^{2}$ (1.865 keV) | $0.6_{-0.2}^{+0.2}$ | $0.10$
| $1973_{-36}^{+26}$ |  $\rm Si^{13+}$ $2p^{1}\to 1s^{1}$ (2.006 keV) | $0.2_{-0.1}^{+0.1}$ | $0.035$
Model | kT (keV) | Abundance |  Velocity ($\rm km\ s^{-1}$) | $\chi^{2}/d.o.f$
CX | $1.04_{-0.01}^{+0.01}$ |  Solar $\rm abundance^{\dagger}$ | $592_{-56}^{+113}$ | 4.54
(SPEX) | $1.14_{-0.02}^{+0.02}$ |  $\rm C/C_{\odot}=8.2_{-0.9}^{+0.9}$ $\rm N/N_{\odot}=6.7_{-0.6}^{+0.7}$ | $232_{-25}^{+45}$ | 4.16
|  |  $\rm Ne/Ne_{\odot}=0.8_{-0.05}^{+0.05}$ $\rm Mg/Mg_{\odot}=0.91_{-0.07}^{+0.08}$ $\rm Si/Si_{\odot}=0.43_{-0.06}^{+0.07}$ |  |
VACX2 | 1.16 | Solar abundance | 448.617 | 3.62
(XSPEC) | 1.05 |  $\rm C/C_{\odot}=3.67245$ $\rm N/N_{\odot}=5.26688$ | 854.947 | 3.22
|  |  $\rm Ne/Ne_{\odot}=1.90699$ $\rm Mg/Mg_{\odot}=4.15255$ $\rm Si/Si_{\odot}=1.78754$ |  |
† Solar abundance refers to the abundance in the solar photosphere [Anders
Grevesse (1989)].

##  5 SWCX as a result of the interaction between the interplanetary and Earth
magnetic field

We found two observational evidences suggesting that the observed SWCX
emission is associated with the interplanetary and Earth magnetic field: (1) A
time coincidence between the arrival of the magnetic cloud (MC) and the SWCX
occurence. (2) An orbital modulation in SWCX light curve.

Figure 4 shows the light curves of the soft X-ray and proton flux detected by
GOES, and magnetic field strength, alpha to proton density ratio, and proton
density measured in-situ by ACE, together with the SWCX emission detected by
Suzaku. The SWCX flaring starts around 2006-Dec-15th 00:00 UT, which is right
after the ACE magnetic field strength entering a smooth transition phase,
indicating the passage of an MC [Y. Liu . (2008)]. Before the MC phase, ACE
also detected significant fluctuation in the field strength and the proton
density between 14:00 to 24:00 UT on 2006-Dec-14th, corresponding to the
turbulent sheath of the CME shock front. This is consistent with the CME
propagation in the standard flare model illustrated in Figure 1, in which the
magnetic reconnection between the coronal loops launches a CME with a magnetic
flux rope as its skeleton. When arriving at the Earth, the flux rope and Earth
field could reconnect so that the heavily ionized ions are streamed into the
magnetosphere, particularly to the polar regions, along the magnetic field
lines.

Furthermore, we find that the X-ray background intensity has a significant
time variation associated with the satellite orbital motion during the SWCX
occurence period, shown in Figure 6 (a). We reason that this time variation
indicates that the source emission region is located close to the observer.
Assuming the source distance is $D$, the maximum physics size the telescope
can observe within the field of view (FoV with angular size $\theta$) is
$D\theta$. Having witnessed the time variation of the diffuse emission
suggests the source moves in and out of the telescope FoV as satellite orbits
around and the source region extension must be smaller than the orbit diameter
$2R_{\rm orb}$. The distance is thus constrained to be $D<2R_{\rm
orb}/\theta=370R_{\rm E}$, where $R_{\rm E}$ is the diameter of the Earth on
the equator plane. Given that the observation was pointed towards the
direction of the North pole, it is likely that the line of sight passed
through the cusp region of the Earth’s magnetic field. We define the $r_{\rm
mp}$ as the geocentric distance of the point where geomagnetic field becomes
open to space for the first time along the line of sight starting from the
spacecraft, and estimate $r_{\rm mp}$ using Tsyganenko geomagnetic field (T96)
model [Tsyganenko (1995), Tsyganenko Sitnov (2005)] and geopack libraries.
Figure 5 shows a sketch of the $r_{\rm mp}$ definition related to the
magnetosphere geometry. The solar wind ram pressure is chosen to be $4.3\rm\
nPa$, with the proton density $3.59\rm\ cm^{-3}$ and proton velocity
$846.52\rm\ km\ s^{-1}$ as measured by ACE, and the interplanetary magnetic
field strength of $B_{y}\sim 11\rm\ nT$ and $B_{z}\sim-13\rm\ nT$, and $Dst$
index $\sim-153\rm\ nT$ adopted as the input parameters of the model.

As shown in Figure 6 (a), $r_{\rm mp}$ is in the range of 1.5 to $\sim 3R_{\rm
E}$, which is much smaller than the outer boundary of Earth magnetosphere, 10
$R_{\rm E}$, throughout the whole orbit period, suggesting the satellite line
of sight passed through the cusp region. The strong SWCX emission could be
explained by the penetration of solar-wind ions to the cusp region [Walsh .
(2016)] where the neutral hydrogen density is high, with the solar wind being
resisted to penetrate into any deeper region below $r_{\rm mp}$ due to the
strong magnetic pressure. If the neutral hydrogen density is the dominant
factor determining the SWCX intensity, the maximum emission is expected at the
lowest $r_{\rm mp}$ point, which is, however, not the case. On the other hand,
variation in solar wind ion density dominated by gravity-pressure balance in
the ionosphere is less likely to account for the SWCX intensity orbital
dependence, either, since the solar wind will stop falling below the
ionosphere boundary $\sim 2.5R_{\rm E}$. Therefore, radial variation in
neutral hydrogen or solar wind ion density cannot account for the observed
light curve and another mechanism is necessary. Azimuthal solar wind ion
intensity non-uniformity inside the cusp region provides one possible
solution. In Figure 6 (b), we plot the X-ray intensity and $r_{\rm mp}$ as
functions of the azimuthal angle of the $r_{\rm mp}$ position in GSM
(geocentric solar magnetospheric coordinates) for the second orbital cycle,
showing that the SWCX intensity is high when the satellite line of sight
passes through the dusk side of the cusp, which means an azimuthal asymmetry
exist in the solar wind density distribution in the cusp. Such density
gradient may be related to the Parker spiral-type propagation of solar wind
enhancement in the planetary space [Koutroumpa . (2007)] in which scenario the
solar wind enhancement due to a CME event first arrives from the dusk side of
the Earth. However, the azimuthal angle of the hit point in GSM is likely
$<90^{\circ}$, while the peak of the X-ray intensity is at $\sim 130^{\circ}$.
We consider it is necessary to model solar wind transportation with azimuthal
non-uniformity in the cusp.

##  6 Modelling the orbital modulation of the SWCX count rate

The surface brightness of SWCX, $S$ is estimated by integrating the emission
intensity per volume along the line of sight $s$,

$S=\frac{1}{4\pi}\int_{s_{0}}^{s_{1}}{\alpha n_{\rm H}(s)n_{\rm ion}(s)v_{\rm
col}ds}.$ (1)

Then the observed intensity, $R$, is obtained by convolving $S$ with the
telescope and detector response functions, and is approximately, $R=A\Omega
S$, where $A$ and $\Omega$ are, respectively, the effective area and the field
of view of the instrument. For CX emission line of certain ions, for example,
$O^{8+}$, the ion density is estimated by solar wind ion density and ionic
abundance, $n_{\rm ion}=n_{sw}\chi_{O^{8+}}$.

$v_{\rm col}$ is the relative collisional speed between solar wind ions and
neutral atoms in the Earth atmosphere. Here we assume $v_{\rm col}=500\rm\ km\
s^{-1}$, a speed smaller than the 1 AU speed of the CME shock, $\sim$1030 $\rm
km\ s^{-1}$ [Y. Liu . (2008)], and neglect the thermal velocity. The charge
exchange cross section, $\alpha$, is chosen as $5\times 10^{-15}\rm\ cm^{2}$
for $O^{8+}+H$ collisions at $v_{\rm col}=500\rm\ km\ s^{-1}$ [Lee . (2004),
Kimura Lane (1987)].

The neutral hydrogen density along line-of-sight $n_{\rm H}(s)$ is a function
of the position in the Earth coordinate, which, more specifically, is a
function the distance from the Earth center, i.e. $n_{\rm H}(s)=n_{\rm
H}(r(s))$. We use the geocoronal model proposed by OStgaard2003 as an
approximation to the neutral hydrogen density distribution in the Earth
atmosphere, $n_{\rm H}(r)=10000e^{-r/1.02}+70e^{-r/8.2}$, where $r$ is in the
unit of $R_{\rm E}$ and $n_{\rm H}(r)$ in the unit of $\rm cm^{-3}$. The model
is based on the measurements of the Lyman $\alpha$ column brightness by the
Geocoronal Imager on board the IMAGE satellite at high altitudes ($>$ 3.5
$R_{\rm E}$) where the neutral hydrogen is considered as an optical thin
medium. Our estimation of neutral hydrogen density may suffer from large
uncertainty due to the following reasons: (1) The variation of solar Lyman
$\alpha$ flux itself from solar minimum to solar maximum is about a factor of
1.5 on average to 2.1 maximum; (2) We extrapolate the empirical model to
smaller altitudes where the medium is no longer optically thin and more
complex analysis including radiative transfer is required; (3) Asymmetric
exosphere, ”magnetotail”, may present higher densities at high altitudes in
the night-side than day-side direction under the radiation pressure.

The solar-wind ion density, $n_{\rm sw}(s)$, is also a function of the
position in the Earth coordinate. Walsh2016 showed the ion density as a
function of the distance from the Earth center using numerical simulations.
Their result shows that the density drops from $\sim 9R_{\rm E}$ to $\sim
6R_{\rm E}$, and stays constant down to $\sim 2.5R_{\rm E}$, then becomes
zero. According to ACE satellite we found the proton density of the CME shock
peaked around 15 $\rm cm^{-3}$. We thus normalize the $n_{\rm sw}(s)$ at the
outer boundary of the magnetosphere to be 15 $\rm cm^{-3}$ and use the radial
profile in Walsh2016 as the solar-wind ion density radial dependence along
line of sight in our model. As discussed in the previous section, we need to
introduce density gradient from sun side to anti-sun side with in the cusp. We
have no physical model for this, though. We thus assume a simple toy model, in
which the density is also a function of $\Theta$ defined in the previous
section, $n_{\rm ion}(s)=n_{\rm ion}(r(s),\Theta(s))$. The solar-wind ion
density orbital modulation function is defined as
$f(\Theta)=Me^{-\frac{1}{2}\frac{(\Theta-\mu)^{2}}{\sigma^{2}}}$, where
$\mu=0.5,\sigma=0.5$, and M is a normalization factor. $\mu$ is chosen to be
0.5 such that the solar-wind density is the highest when the satellite moves
closest to the sun. The abundance of $O^{8+}$ ions is estimated as its
photospheric value, $8.51\times 10^{-4}$ [Anders Grevesse (1989)].

With the assumptions discussed above, the model predicts $\rm O^{7+}$ the
count rate to be 0.01 $\rm cts\ s^{-1}$. On the other hand, from the energy
spectrum, we estimate the observed $\rm O^{7+}$ count rate at the peak of
figure 6 (a) to be $\sim 0.5\ {\rm cts\ s^{-1}}$, which exceeds the model
predication by a factor about 50. This large discrepancy could be related the
non-uniformity of the flow in the cusp region as discussed in section 5. If
the plasma flow is confined in 1/50 of the whole cusp volume, the density is
likely enhaced by this factor compared to the prediction with the uniform
model from Walsh2016. In figure 6 (b), the FWHM of the peak is about 0.8
radian, which is about 1/8 of $2\pi$. A factor of 50 times change in volume
can be explained if the plasma is compressed in two directions with this
ratio.

##  7 Summary and conclusion

We report an unique case of SWCX event caused by the well-known
2006-December-13 CME, which is captured by Suzaku observation with a line-of-
sight cutting through the cusp region. Significant non-thermal emission lines
from $\rm O^{7+}$, $\rm Ne^{9+}$, $\rm Mg^{11+}$, $\rm Si^{12+}$, $\rm
Si^{13+}$, and probably, $\rm N^{5+}$ $1s^{1}5p^{1}\to 1s^{2}$ transition are
detected and we fit the SWCX spectrum with CX models. We find a time
coincidence between the arrival of CME magnetic cloud and the SWCX occurrence,
suggesting that the solar wind ions can be streamed onto the Earth field lines
via magnetic reconnection. The time variation of the X-ray emission suggests
non-uniformity of the solar wind flow in the cusp region which enhances the
X-ray surface brightness by a factor of $\sim 50$. The SWCX is bright in the
dusk side of the cusp and we conjecture that this is related to the Parker
spiral-type propagation of the solar wind.

## Open Research Section

Suzaku archive data available from the DARTS/Suzaku Public Data list
(https://data.darts.isas.jaxa.jp/pub/Astro_Browse/publications/suzaku/public_list.html)
were used in the creation of this manuscript. The Tsyganenko Geomagnetic Field
Model and GEOPACK libraries are published on Github
https://github.com/tsssss/geopack.

###### Acknowledgements.

We thank professor Hiroya Yamaguchi and Yuichiro Ezoe for insightful
discussions and KAKENHI grants: JP20KK0072 (PI: S. Toriumi), JP21H01124 (PI:
T. Yokoyama), and JP21H04492 (PI: K. Kusano).

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# The Size-Mass relation at Rest-Frame $1.5\mu$m from JWST/NIRCam in the
COSMOS-WEB and PRIMER-COSMOS fields

Marco Martorano Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281
S9, 9000 Gent, Belgium  Arjen van der Wel Sterrenkundig Observatorium,
Universiteit Gent, Krijgslaan 281 S9, 9000 Gent, Belgium  Maarten Baes
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000 Gent,
Belgium  Eric F. Bell Department of Astronomy, University of Michigan, 1085
South University Avenue, Ann Arbor, MI 48109-1107, USA  Gabriel Brammer Cosmic
Dawn Center (DAWN), Niels Bohr Institute, University of Copenhagen, Jagtvej
128, Kø benhavn N, DK-2200, Denmark  Marijn Franx Leiden Observatory, Leiden
University, P.O. Box 9513, 2300 RA, Leiden, The Netherlands  Angelos Nersesian
STAR Institute, Université de Liège, Quartier Agora, Allée du six Aout 19c,
B-4000 Liege, Belgium  Sterrenkundig Observatorium, Universiteit Gent,
Krijgslaan 281 S9, 9000 Gent, Belgium Marco Martorano<EMAIL_ADDRESS>
###### Abstract

We present the galaxy stellar mass - size relation in the rest-frame near-IR
($1.5~{}\mu{\text{m}}$) and its evolution with redshift up to $z=2.5$. Sérsic
profiles are measured for $\sim$ $26\,000$ galaxies with stellar masses
$M_{\star}>10^{9}~{}{\text{M}}_{\odot}$ from JWST/NIRCam F277W and F444W
imaging provided by the COSMOS-WEB and PRIMER surveys, using coordinates,
redshifts, colors and stellar mass estimates from the COSMOS2020 catalog. The
new rest-frame near-IR effective radii are generally smaller than previously
measured rest-frame optical sizes, on average by 0.14 dex, with no significant
dependence on redshift. For quiescent galaxies this size offset does not
depend on stellar mass, but for star-forming galaxies the offset increases
from -0.1 dex at $M_{\star}=10^{9.5}~{}{\text{M}}_{\odot}$ to -0.25 dex at
$M_{\star}>10^{11}~{}{\text{M}}_{\odot}$. That is, we find that the near-IR
stellar mass - size relation for star-forming galaxies is flatter in the rest-
frame near-IR than in the rest-frame optical at all redshifts $0.5<z<2.5$. The
general pace of size evolution is the same in the near-IR as previously
demonstrated in the optical, with slower evolution
($R_{\text{e}}\propto(1+z)^{-0.7}$) for $L^{*}$ star-forming galaxies and
faster evolution ($R_{\text{e}}\propto(1+z)^{-1.3}$) for $L^{*}$ quiescent
galaxies. Massive ($M_{\star}>10^{11}~{}{\text{M}}_{\odot}$) star-forming
galaxies evolve in size almost as fast as quiescent galaxies. Low-mass
($M_{\star}<10^{10}~{}{\text{M}}_{\odot}$) quiescent galaxies evolve as slow
as star-forming galaxies. Our main conclusion is that the size evolution
narrative as it has emerged over the past two decades does not radically
change when accessing with JWST the rest-frame near-IR, a better proxy of the
underlying stellar mass distribution.

Galaxy structure - Galaxy evolution - Galaxy luminosities - Galaxy quenching

††software:  astropy (Astropy_v0.2; Astropy_v2; Astropy_v5), GalfitM
(haussler13; vika13), SEP (bertin96; barbary16)

splitbox SBsplitbox tablenum SIXtablenum

##  1 INTRODUCTION

The size of a galaxy retains information about its evolutionary history, and
is partially a reflection of the properties of the host dark matter halo, most
notably the virial radius and the angular momentum (fall80; dalcanton97;
mo98). Galaxy sizes are therefore a key ingredient of the various well-known
scaling relations such as the size-stellar mass relation (e.g. shen03; van-
der-wel14; whitaker17; mowla19a; dimauro19; Nedkova21; magnelli23; shen23;
ward24; cutler24) and the fundamental plane (kormendy77; djorgovski87;
dressler87).

Parametric fits can give estimates of galaxies’ size at the expense of having
some sensitivity to the parametric form, but with the advantage of being less
sensitive to PSF smearing and noise effects than non-parametric methods (for a
complete review see conselice14). Sérsic fits are the most common profiles
adopted to fit galaxies. These are parameterized by flux, half-light radius
($R_{\text{e}}$), and Sérsic index ($n$) which quantifies the concentration of
the light profile.

While the Sérsic index remains relatively constant when moving from optical
wavelengths to the near-IR (kelvin12; kennedy15; martorano23; yao23), the
half-light radius is significantly influenced by color gradients due to
stellar population variations and attenuation by dust (sandage72; peletier90;
de-jong96a). Numerous low redshift studies have analyzed the wavelength-
dependent behavior of $R_{\text{e}}$ (e.g., kelvin12; haussler13; pastrav13;
vika13; vulcani14; kennedy15; lange15; baes20; nersesian23). The general
result is that galaxy sizes are smaller at longer wavelengths, regardless of
type or mass. The implied color gradients are varyingly attributed to
gradients in age, metallicity, star-formation activity and dust attenuation,
depending on the type and mass of the galaxy.

Spatially resolved imaging is essential to study structural evolution at large
look-back time to provide stringent constraints on galaxy evolution models.
Only the Hubble Space Telescope (HST) and the James Webb Space Telescope
(JWST) have sufficient spatial resolution ($\approx 1~{}{\text{kpc}}$) and
stability of the point spread function to accurately quantify the light
profiles of such distant galaxies. HST has been extensively used over the past
two decades to map the size evolution at rest-frame UV and optical wavelengths
(daddi05; trujillo06b; zirm07; van-dokkum08; van-der-wel08b; newman12; van-
der-wel14; shibuya15; mowla19a; mowla19b; Nedkova21; cutler22), where
attenuation by dust and the outshining by young populations present
significant obstacles for interpreting the observed sizes. Now that JWST
provides us with rest-frame near-IR observations of high-redshift galaxies, we
can estimate sizes at longer wavelengths where dust attenuation is much less
severe and the outshining effect lessened, such that gradients in the dust
content and stellar population properties are suppressed.

The first estimates of rest-frame near-IR galaxy sizes from JWST by suess22
found a systematic 9% reduction in the sizes at 4.4$\mu{\text{m}}$ compared to
those at 1.5$~{}\mu{\text{m}}$ (both in the observed frame) in the redshift
range $z=1-2.5$. The general result that galaxies are smaller in the rest-
frame near-IR compared to the rest-frame optical was subsequently confirmed
(ito24; ormerod24; cutler24), displaying the same behavior as for present-day
galaxies (evans94; mollenhoff06; kelvin14).

In this work, we present rest-frame 1.5$~{}\mu{\text{m}}$ effective radius
measurements for $\sim$$26\,000$ galaxies with stellar masses $M_{\star}\geq
10^{9}~{}{\text{M}}_{\odot}$ in the redshift range $z=0.5-2.5$ that fall in
the COSMOS-WEB (casey22; casey23) and PRIMER-COSMOS (dunlop21) JWST
footprints. We take advantage of these new measurements to determine the rest-
frame near-IR size-mass relation and its evolution with redshift for the
general galaxy population, allowing for a direct comparison with the well-
established results obtained in the rest-frame optical wavelength regime.

The paper is structured as follows: in Section 2 we briefly present the
cataloged data used in this work along with an overview of the JWST
observations. Section 3 follows with an explanation of the fitting technique
adopted to retrieve galaxies’ sizes. In Section 4 we present the size-mass
relation and the redshift evolution of the median size of galaxies. This is
followed by a discussion in Section LABEL:sec:discussion. Finally, in Section
LABEL:sec:conclusion, we summarize our findings and draw our conclusions. We
adopt a flat $\Lambda$CDM cosmology with H${}_{0}=70~{}$km s${}^{-1}~{}$Mpc-1,
$\Omega_{m}=0.3$.

##  2 DATA AND SAMPLE SELECTION

In this section we describe the parent catalog that we used to select target
galaxies, and their basic properties (redshifts, stellar masses, star-
formation activity). We also describe the JWST data used to fit near-IR light
profiles.

###  2.1 COSMOS2020

The parent sample is drawn from the COSMOS2020-CLASSIC catalog presented by
weaver22. It contains multi-wavelength ($0.15~{}\mu m$ to $\sim 8~{}\mu m$)
observations of over 1.7 million sources in the 2 deg2 COSMOS field
(scoville07; koekemoer07) from several ground-based (i.e. Subaru/HSC and
VISTA) and space-based (i.e. HST and Spitzer) observatories. The catalog
includes stellar population parameters obtained from broadband photometry SED
fitting with the codes LePhare (arnouts02; ilbert06) and Eazy (brammer08).
Here we use the redshifts and stellar population parameters from LePhare as
those are preferred by the authors (weaver22). Eazy provides the corresponding
rest-frame colors U$-$V and V$-$J. Mixing stellar masses from LePhare with
rest-frame colors from Eazy does not bias our results: the Eazy stellar mass
estimates produce the same conclusions but weaver22 prefer LePhare because of
its lower redshift bias fraction. Furthermore, the LePhare stellar-mass
estimates are closer to those used by van-der-wel14 that we use as a
comparison sample in this work (Appendix LABEL:app-sec:_Fast-LePhare).

###  2.2 JWST observations

Figure 1: Overview of the footprints of the surveys used in this work: the
black square shows the full COSMOS2020 field; the red contours represent the
COSMOS2020 field observed with HST-ACS/F814W. The green area identifies the
CANDELS-COSMOS field. Blue and magenta lines are used to identify,
respectively, the JWST footprints of the COSMOS-WEB and PRIMER-COSMOS
programs. Grey dots in the background show the position of galaxies identified
in the COSMOS2020 catalog while darker dots highlight the position of galaxies
observed in the Long Wavelength Channel of JWST/NIRCam.

A region of $\approx 0.54$ deg2 roughly in the middle of the $\approx 2$ deg2
COSMOS field (Fig. 1) is covered by JWST/NIRCam imaging from the COSMOS-WEB
program (GO:1727, casey23). COSMOS-WEB provides imaging with F115W and F150W
in the Short Wavelength Channel and with F277W and F444W in the Long
Wavelength Channel. The 5$\sigma$ depth reached is between 27.61 and 28.18
ABmag for the filter F444W depending on the number of exposures (casey23).
Currently, slightly more than half of the $\approx 0.54$ deg2 area has been
observed, and will be used in this work.

The CANDELS-COSMOS field (grogin11; koekemoer11), consisting of a deeper but
smaller field within COSMOS, was observed by JWST as part of the PRIMER
program (GO:1827, dunlop21) with ten different JWST/NIRCam filters and a F444W
depth up to 28.17 ABmag (cutler24) for the regions with the highest exposures.

Data from these two programs were processed with grizli (grizli) to create
mosaics and weight maps with a pixel scale of
$0.05\text{\,}\mathrm{\SIUnitSymbolArcsecond}$/pix. The mosaics are publicly
available on The DAWN JWST Archive (DJA) (valentino23). For this work we
retrieve cutouts for each galaxy from the Interactive Map Interface (hausen22)
available on the DJA. Focusing on the rest-frame near-IR, in this paper we
only use the Long Wavelength Channel filters F277W and F444W. As described
below noise properties and PSF are tested and well-understood for this
dataset.

Figure 2: JWST/NIRCam imaging examples for 16 galaxies selected to be
representative of the median characteristics of the sample. The top four rows
show galaxies at $z\sim 1$ while bottom four rows at $z\sim 2$. For each
galaxy the COSMOS2020 ID, the LePhare stellar mass and redshift are indicated.
Filters F150W and F444W are shown as representatives of the optical and near-
IR wavelengths. The RGB frame is obtained by combining the filters F277W,
F150W and F115W with a Richardoson-Lucy deconvolution.

Figure 2 shows JWST/NIRCam imaging for 16 galaxies in the sample selected to
be representative of the median characteristics of galaxies across the full
mass and redshift range (see Sec. LABEL:sec:discussion for further
discussion). JWST/NIRCam Short Wavelength channel filters F115W and F150W are
used only for visualization and are not used for quantitive analysis in this
work.

###  2.3 Galaxy selection

Figure 3: Stellar Mass - redshift distribution of the sample of galaxies for
which GalfitM light profiles were fit, color-coded with the SNR measured from
the JWST/NIRCam F277W image. The solid black line shows the stellar mass
completeness limit from weaver22. The dashed line shows the lower-mass limit
adopted in this paper.

Since this paper aims to present near-IR sizes at rest-frame
1.5$\mu{\text{m}}$ the wavelength coverage of the F277W and F444W filters
impose a redshift range of $z=0.5-2.5$ to avoid the effects of extrapolation.
The rest-frame wavelength corresponding to the pivot wavelength of F277W is
1.85$~{}\mu{\text{m}}$ at $z=0.5$ and of F444W 1.26$~{}\mu{\text{m}}$ for
$z=2.5$.

Among the over 1.7 million sources in the COSMOS2020-CLASSIC catalog, we
select those $75\,765$ galaxies (ACS$\\_$MU$\\_$CLASS=1; this flag rejects
stellar-like objects) in this redshift range that have a positive HST/F814W
flux and that fall within the available JWST/NIRCam F277W and F444W imaging
footprints (Fig. 1).

In Figure 3 we show the mass-redshift distribution of these galaxies. The
adopted stellar mass limit for our sample
($M_{\star}~{}=~{}10^{9}~{}{\text{M}}_{\odot}$) leaves us with $32\,002$
galaxies.

We remove from our sample $4\,912$ objects ($\sim$15$\%$) due to differences
between the identification, deblending and segmentation between the source
catalog from weaver22 and our work based on the much higher resolution NIRCam
imaging (see 3.1). This rejection does not bias our sample since these targets
are evenly distributed across the full mass and redshift range. Moreover,
mismatches are often related to nearby bright sources and/or severe blending
that prevent robust profile fits in the first place. NIRCam-selected catalogs
will eventually produce a clear improvement in object selection and
characterization but this is beyond the scope of this work.

Size estimates may be biased due to the contributions from central point
sources from Active Galactic Nuclei (AGN). Star-like objects were already
removed from the sample, so that the most obvious AGN are automatically
omitted. But AGN contributions in the mid-IR still have to be addressed since
chang17 showed that an AGN fraction $>50\%$ induce a radius decrease up to
$50\%$. We match our sample to the publicly available catalog presented in
chang17, who fit MAGPHYS on the COSMOS2015 (laigle16) photometry for $36\,000$
sources in the COSMOS field. We find, and remove from our sample, 45 galaxies
with the median of the posterior distribution of the AGN fraction larger than
$50\%$. Since these 45 galaxies show no obvious bias in the size distribution
we conclude that more moderate AGN contributions will not affect our results
either.

###  2.4 Separating Star-Forming and Quiescent Galaxies

Figure 4: UVJ diagram for our selected sample of galaxies color coded with the
Sérsic index measured at rest-frame 1.5$~{}\mu{\text{m}}$. Solid lines
identify the quiescent locus in the UVJ plane as described in the text.

The COSMOS2020 SED fits from weaver22 do not include mid- or far-IR
photometric data, consequently, the resulting SFRs are not robust enough to be
efficiently used to divide galaxies in star-forming and quiescent. Instead, we
separate star-forming and quiescent galaxies based on their rest-frame $U-V$
and $V-J$ colors.

williams09 defined selection criteria to separate the quiescent and the star-
forming population from the UVJ diagram. muzzin13 adapted the exact
constraints to better match their rest-frame photometry. But we find that
those cuts do not work well for the current rest-frame photometry. This
difference originates from two main factors: the COSMOS2020 photometry is
different from the one used in muzzin13 despite the similar sample (different
methodology for photometry retrieval, several new filters, updated
zeropoints); the templates used for SED fitting in COSMOS2020 are different
from those used by muzzin13 leading to different rest-frame colors. These two
effects combined necessitate new color cuts to maximize the separation between
the two galaxy types. Note that drawing these separation lines has always been
a heuristic process. In Figure 4 we present the UVJ diagram and the new color
cuts adopted to optimize the separation between the two types. The quiescent
region is finally identified as:

$z<1.5:\;\;\;U-V>1.3;\;\;U-V>0.48+0.88(V-J)$ (1) $z\geq
1.5:\;\;\;U-V>1;\;\,\;\;\;U-V>0.35+0.80(V-J)$ (2)

The original muzzin13 color classification only leads substantially different
sample separation at $z>2$, due to the many quiescent galaxies with relatively
blue colors.

##  3 Light Profile Fits

In this section we present the steps light fitting procedure with GalfitM
(haussler13; vika13), a further developed version of Galfit (peng02; peng10).

###  3.1 Cutouts

For each galaxy we create F277W and F444W cutouts such that the number of
pixels not associated with a source in the F444W segmentation map (created
with SEP, bertin96; barbary16, assuming a detection threshold of 3$\sigma$, a
minimum area of 5 pixels and a minimum contrast ratio used for object
deblending of 0.02) is at least 100 times the number of pixels that are
associated with object segments. In addition, we impose a minimum size of
$8\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ and a maximum size of
$20\text{\,}\mathrm{\SIUnitSymbolArcsecond}$. A posteriori we verify that
99%(50%) of the cutouts are at least 12(37) times larger than $R_{\text{e}}$,
which guarantees that uncertainties in background estimates propagate into
uncertainties in $R_{\rm{e}}$ by less than 5%($<$1%) (see Fig. 6 in george24).
The 1% of galaxies with cutouts smaller than 12 times $R_{\text{e}}$ are large
($R_{\text{e}}>5~{}{\text{kpc}}$) low-mass galaxies
($M_{\star}<10^{10}~{}{\text{M}}_{\odot}$) mostly at $z<1.5$. A systematic
$5\%$ variation in the size of these targets have a negligible effect
($<0.5\%$) on the median stellar mass-size relation presented in §4.1.

For each cutout we use the available weight (inverse variance) image to
compute an error map. Masks are created based on the segmentation map,
including those sources that are more than a magnitude fainter than the target
as also done in martorano23. Sources brighter than this threshold are included
in the GalfitM profile fit as separate objects, along with the target itself
and fitted simultaneously. SEP provides us with an initial estimate for
GalfitM of the semi-major and minor axis of the galaxies as well as their
center coordinates.

Figure 5: Curves of growth for the theoretical PSF profile (WebbPSF; solid
black lines) and our stacked PSF (StackPSF; solid red line) constructed from
50 stellar light profiles (light grey lines) in the two NIRCam filters F277W
(left panel) and F444W (right panel). In the lower panels, we show the
residuals of the curve of growth of our PSF with respect to the theoretical
one. The empirical PSFs are significantly broader than the theoretical PSFs.

We find 144 galaxies to have at least 1 pixel with flux zero within a square
of side 7 pixels from the center recovered with SEP. These pixels can either
be bad pixels masked by the pipeline used to create the mosaics or gaps in the
footprint. Since the effect on the fit produced by a masked pixel in the inner
part of the galaxy can be large, we decided to remove these 144 sources from
our sample.

Figure 6: _Left two columns:_ Galaxy 472142 (from COSMOS2020) in JWST/NIRCam
filters F277W and F444W. We show, from top to bottom, the image , the 2D light
model from GalfitM and the residuals of the fit. _Middle columns:_ COSMOS2020
ID 615747. _Right columns:_ COSMOS2020 ID 515598. Cutouts are presented in the
same size used for the morphological fit performed with GalfitM.

###  3.2 The Point Spread Function

GalfitM generates Sérsic profiles that are convolved with the Point-Spread-
Function (PSF) of the filter investigated and subsequently fitted to the
image. As several works pointed out (nardiello22; weaver24; zhuang23; ji23),
we also find the PSF in the mosaics to be broader than the theoretical PSFs
from WebbPSF (perrin14), which is primarily the result of the data reduction
process (shifting, weighting and stacking). To minimize the systematic effects
that a wrongly calibrated PSF can induce, we create empirical PSFs. We
visually select 50 stars across the mosaic that are not saturated and that
overlap flux density distribution with the sample galaxies as the PSF might be
flux dependent. Sub-pixel precisions of the centers of the stars are
determined by SEP run on $8\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ cutouts.
The flux is normalized in each cutout to the flux measured within a
$0.3\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ circle around the SEP center.
After masking any other source in the cutout, we compute the background as the
median flux per pixel in an annulus with inner radius
$2.5\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ and outer radius
$3\text{\,}\mathrm{\SIUnitSymbolArcsecond}$. This median background is
subtracted from all the pixels. Each cutout is then upsampled by a factor 10
and cropped to a square of $6\text{\,}\mathrm{\SIUnitSymbolArcsecond}$
centered with sub-pixel resolution. We then produce a median stack (on a
pixel-by-pixel basis) of the 50 upsampled, background-subtracted cutouts. Our
final empirical PSF is then produced by a normalization such that the total
flux in the $6\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ square matches that of
the theoretical PSF (generated via WebbPSF) in the same area. Exposures from
COSMOS-WEB and PRIMER-COSMOS have the same pointing position angle
(differences are $<1$ degree), so that the stacked stars are well-aligned.

In Figure 5 we compare our empirical PSF with the theoretical WebbPSF PSF. The
large differences in enclosed light (up to $\approx 20$% at
$0.07\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ for F277W) imply that the
WebbPSF PSF cannot be used in combination with these mosaics to infer accurate
structural properties of galaxies. As referred to before, these differences
can be attributed to the weighting and stacking procedure of multiple
exposures in the data reduction pipeline and do not in any way reflect an
error in the WebbPSF models.

The variation in stellar light profiles reflects, for one, spatial variation
in the PSF. The median and 16-84 percentile ranges in the radius encircling
half of the stellar light profile are
$$0.105(16)\text{\,}\mathrm{\SIUnitSymbolArcsecond}$($0.122(22)\text{\,}\mathrm{\SIUnitSymbolArcsecond}$)$.
We interpret the scatter among the stellar profiles as the uncertainty in the
PSF width ($15\%$ and $18\%$ in F277W F444W). These variations are comparable
to the 20% spatial variation across the detector itself found by nardiello22.
The $0.016\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ and
$0.022\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ are propagated into the galaxy
size uncertainties, by adding in quadrature to the formal fitting
uncertainties. The PSF uncertainty dominates the random uncertainty for small
objects $\lesssim 1$ kpc, but does not affect the median trends that are the
main result of this paper.

###  3.3 Profile Fits with GalfitM

The convolution box used by GalfitM is set to be 200 pixels per side. Despite
slowing down the computation, the large convolution box was adopted to
encompass even the largest sources. We can then use the same convolution box
for all the targets avoiding the introduction of systematics due to the use of
different convolution boxes for different galaxies.

Sérsic profile fits are independently fitted to the F277W and F444W images,
allowing the Sérsic index to span the range 0.2 - 10 with an initial guess of
2.3. The x and y coordinates of the galaxies’ centers are limited to lie
within a distance of 5 pixels from the SEP-based centers. The effective radius
is limited to values between 0.01 and 200 pixels with the initial value
defined as the semi-major axis of the SEP ellipse. Axis ratio and position
angle are left as free parameters with no constraints. The mosaics are
background-subtracted, but to allow for remaining background patterns across
the mosaic we adopt a constant background with GalfitM as a free parameter.

We find that the fits reach the numerical convergence for both JWST/NIRCam
filters for $26\,003$ galaxies ($96\%$ of the available sample).

We find, and remove, one galaxy with a retrieved Sérsic index within $10^{-3}$
from the boundaries of the parameter space suggesting the sampler got stuck
there.

For 514 sources GalfitM produces a fit with $\chi_{reduced}^{2}>3$. A visual
inspection of these fits reveals that for the vast majority (506) the
$\chi_{reduced}^{2}$ is driven by those galaxies fitted simultaneously with
the target, and not by the target itself. We refit these sources, masking the
nearby galaxies and we find that they converge properly, with much lower
$\chi_{reduced}^{2}$ for 497 out of 506. The remainder are omitted from the
final sample.

Visual inspection by MM of all $26\,003$ fitted galaxies shows 36 mergers and
2 lensing systems that are not properly fitted and, therefore, discarded (6
mergers and the 2 lensing systems were among those fits with
$\chi_{reduced}^{2}>3$). We further reject 5 galaxies that were only partially
covered by the NIRCam mosaics, leaving the fitting results unreliable. Our
final sample with reliable Sérsic profiles includes $25\,960$ galaxies of
which $3\,082$ are quiescent and $22\,878$ are star-forming.

In Figure 6 we show the GalfitM fitting results for three randomly selected
galaxies. Although low redshift high-mass galaxies are bright and extended,
our pipeline uses sufficiently large cutouts to enable accurate background
estimates. At the same time, for low-mass high redshift galaxies we see that
the SNR is sufficiently high for a precise size estimate (larger than 30 (50)
for 84% (50%) of galaxies with $M_{\star}<9.5~{}{\text{M}}_{\odot}$ and
redshift $z>2$).

The uncertainties retrieved for Sérsic index ($n$) and effective radius are
systematically underestimated by GalfitM (van-der-wel12). Following the
prescriptions in van-der-wel12 and martorano23, we reassess the uncertainties:
we adopt a baseline uncertainty of 0.1 dex on the Sérsic index for galaxies
with SNR = 50 and on $R_{\text{e}}$ for galaxies with SNR = 20, and compute
the final uncertainties as $\propto 1/\sqrt{\rm{SNR}}$. This methodology is
based on an analysis of HST/WFC3 data (van-der-wel12). The SNR of JWST/NIRCam
is much higher, producing, at times, very small uncertainties. In fact, for
$\sim 32\%(5\%)$ of the galaxies the GalfitM uncertainty on
$R_{\text{e}}$($n$) is larger than the SNR-based value, and we retain the
former.

The rest-frame 1.5$~{}\mu{\text{m}}$ $R_{\text{e}}$ and $n$ are calculated by
fitting a straight line to the values of $R_{\text{e}}$ and $n$ in F277W and
F444W, using the respective pivot wavelengths. This fit is repeated 100 times,
sampling from the F277W and F444W $R_{\text{e}}$ and $n$ uncertainties,
adopting the median values of the $R_{\text{e}}$ and $n$ polynomials at
1.5$~{}\mu{\text{m}}$ as the estimates and half of the 16th-84th percentile
range as the 1$\sigma$ uncertainty.

##  4 RESULTS

###  4.1 Size-Mass Distribution

Figure 7: Size-Mass distribution at rest-frame 1.5$\mu{\text{m}}$ in four
redshift bins. Galaxies are color-coded as quiescent (red) or star-forming
(blue). Solid lines show the medians in mass bins of 0.5 dex for the two
populations and the combined sample (black). Error bars represent the
statistical uncertainty ($\sigma/\sqrt{N}$) while shaded areas highlight the
16-84 percentile intervals of the distributions. The median uncertainty on the
rest-frame 1.5$\mu{\text{m}}$ size for star-forming and quiescent galaxies is
shown in the bottom right corner of each panel. The 16-50-84 percentile values
are reported in Table 4.1. Dashed lines show the median relations in the rest-
frame optical (0.5$\mu{\text{m}}$) from van-der-wel14 with shifted stellar
mass values to account for systematic differences with the stellar masses used
in this paper (see text and Appendix LABEL:app-sec:_Fast-LePhare for details).
Error bars in the bottom right corner represent the typical uncertainty of the
individual size estimates. In the bottom panels we show the offset between the
median rest-frame near-IR and optical sizes. The overall offset for each
redshift bin and galaxy type is indicated by the dotted horizontal lines.
Table 1: Median stellar mass ($M_{\star,\text{med}}$) and 16-50-84 percentiles
of the effective radii (log10($R_{\text{e}}$/kpc)) presented in Figure 7
respectively for the population as a whole (upper table), the star-forming
population (central table) and the quiescent population (lower table) divided
in mass and redshift bins.