# Additional Evidence for Super-Virial Hot Phase in Milky Way CGM

Rebecca L. McClain,1 Smita Mathur,1,2 Sanskriti Das,3 Yair Krongold 4 and
Anjali Gupta 5
1Department of Astronomy, The Ohio State University, 140 West 18th Avenue,
Columbus, OH 43210, USA
2Center for Cosmology and Astro-Particle Physics, The Ohio State University,
191 West Woodruff Avenue, Columbus, OH 43210, USA
3Kavli Institute for Particle Astrophysics & Cosmology, Stanford University,
452 Lomita Mall, Stanford, CA 94305, USA
4Instituto de Astronomia, Universidad Nacional Autonoma de Mexico, 04510
Mexico City, Mexico
5Columbus State Community College, 550 E Spring Street, Columbus, OH 43210,
USA E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

# Super-virial Hot Phase in Milky Way Circumgalactic Medium: Further Evidences

Rebecca L. McClain,1 Smita Mathur,1,2 Sanskriti Das,3 Yair Krongold 4 and
Anjali Gupta 5
1Department of Astronomy, The Ohio State University, 140 West 18th Avenue,
Columbus, OH 43210, USA
2Center for Cosmology and Astro-Particle Physics, The Ohio State University,
191 West Woodruff Avenue, Columbus, OH 43210, USA
3Kavli Institute for Particle Astrophysics & Cosmology, Stanford University,
452 Lomita Mall, Stanford, CA 94305, USA
4Instituto de Astronomia, Universidad Nacional Autonoma de Mexico, 04510
Mexico City, Mexico
5Columbus State Community College, 550 E Spring Street, Columbus, OH 43210,
USA E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Recent discoveries of a super-virial hot phase of the Milky Way circumgalactic
medium (CGM) has launched new questions regarding the multi-phase structure of
the CGM around the Galaxy. We use 1.05 Ms of archival Chandra/HETG
observations to characterize highly ionized metal absorption at z=0 along the
line of sight of the quasar NGC 3783. We detect two distinct temperature
phases with T${}_{1}=5.83^{+0.15}_{-0.07}$ K, warm-hot virial temperature, and
T${}_{2}=6.61^{+0.12}_{-0.06}$ K, hot super-virial temperature. The super-
virial hot phase coexisting with the warm-hot virial phase has been detected
in absorption along only two other sightlines and in one stacking analysis.
There is scatter in temperature of the hot as well as warm-hot gas. Similar to
previous observations, we detect super-solar abundance ratios of metals in the
hot phase, with a Ne/O ratio 2$\sigma$ above solar mixtures. These new
detections continue the mystery of the mechanism behind the super-virial hot
phase, but provide evidence that this is a true property of the CGM rather
than an isolated observation. The super-virial CGM could hold the key to
understanding the physical and chemical history of the Milky Way.

###### keywords:

Galaxy: evolution – Galaxy: abundances – Galaxy: halo – X-rays: diffuse
background – X-rays: individual: NGC 3783 – quasars: absorption lines

††pubyear: 2023††pagerange: Additional Evidence for Super-Virial Hot Phase in
Milky Way CGM–A

##  1 Introduction

The circumgalactic medium (CGM) plays an important role in the structure and
evolution of spiral galaxies, surrounding the stellar and gaseous components
of the galactic disk (Tumlinson et al., 2017). As the gas from the
intergalactic medium (IGM) accretes onto the galaxy, it is shock heated to the
virial temperature of the galaxy (Oppenheimer et al., 2016). Stellar and AGN
(active galactic nucleus) feedback processes expel gas from the disk of the
galaxy and into the CGM, bounded by the galaxy’s virial radius, or beyond to
the IGM. These mechanisms enrich, excite, and mix the CGM, where the gas cools
and falls back down onto the disk of the galaxy, providing new material for
star formation to take place. Understanding these processes, the global
structure, and the interactions between the galaxy, the CGM, and the IGM has
become a topic of great discussion in observational (Tumlinson et al., 2017;
Mathur, 2022) and theoretical (Oppenheimer et al., 2016; Corlies &
Schiminovich, 2016) work and the field has shown great development.

Extending out to the Milky Way’s virial radius of about 220 kpc, the CGM
contains a considerable amount of mass and may account for the missing baryons
and metals in the Galaxy (Gupta et al., 2012). The majority of the matter in
the CGM is shown to be in the warm-hot phase at the virial temperature of
$\sim$106 K, and it is diffuse, extended, massive, and anisotropic (Snowden et
al., 2000; Henley et al., 2010; Henley & Shelton, 2013; Gupta et al., 2012,
2014, 2017; Nicastro et al., 2016; Gatuzz & Churazov, 2018; Kaaret et al.,
2020).

More recent discoveries revealed a hotter, super-virial temperature phase
along several different lines of sight in both X-ray absorption (Das et al.,
2019a, 2021; Lara-DI et al., 2023), and X-ray emission (Das et al., 2019b;
Bhattacharyya et al., 2022; Bluem et al., 2022; Gupta et al., 2021, 2023) with
temperatures up to $\sim$$10^{7}$ K. Simultaneous analysis in emission and
absorption yield a multi-phase model with temperature disagreement toward the
same direction (Das et al., 2019a, b, 2021; Bhattacharyya et al., 2022). This
indicates that absorption and emission spectroscopy probe different regions of
the CGM, with emission probing denser regions and absorption probing more
diffuse gas. Extensive all-sky emission analysis has shown that the hot phase
is universal, seen all across the Galaxy (Bluem et al., 2022; Gupta et al.,
2023). However, we cannot assume that the ubiquity of this phase in emission
can be similarly applied to absorption. The super-virial hot phase has only
been detected in absorption along two individual sightlines (Das et al.,
2019a, 2021) and one stacking analysis (Lara-DI et al., 2023). The stack of
observations indicates a universality of the super-virial phase, but we do not
yet have enough information to claim the true distribution of the highly-
ionized CGM. Thus, we aim to answer this question by adding to the collection
of absorption observations in a new direction and drawing a more clear picture
for the homogeneity or anisotropy of the super-virial hot phase.

In this paper we analyze CGM absorption towards NGC 3783, a bright quasar away
from the direction of the Galactic Center ($l=287.46^{\circ}$,
$b=+22.95^{\circ}$). The previous single-sightline CGM absorption papers (Das
et al., 2019a, 2021) used featureless blazars as their background continuum,
but NGC 3783 is a Seyfert galaxy meaning that is has a more complicated
spectrum of its own (Krongold et al., 2003). Due to the source’s low redshift
of z=0.0097, the intrinsic warm absorbers (WA) features are very close to the
CGM absorption lines that we are interested in observing. The signal from the
WAs is significantly stronger and broader than the CGM signal, making it
challenging to separate the two. However, the spectral resolution of Chandra
gratings is sufficiently high such that we can distinguish the WA features
from the z=0 lines, allowing us to probe the Milky Way CGM.

Section 2 of this paper outlines the data analysis of grating spectra from
Chandra and XMM-Newton, revealing the multi-phase properties of the highly
ionized CGM along this line of sight toward NGC 3783. Section 3 outlines our
initial motivation for the two-phase model used in Section 4, which describes
the spectral modeling conducted to determine the physical and chemical
properties of the distinct phases. Section 5 discusses the implications of our
analysis, the remaining open questions, and a prediction for the upcoming
XRISM mission. We finally summarize our results in Section 6.

##  2 Data Reduction and Analysis

###  2.1 Chandra

NGC 3783 is a bright quasar that has been repeatedly observed by X-ray
telescopes. We analyze the archival Chandra data to study the z=0 Milky Way
CGM absorption of the quasar emission in the wavelength range of 4-22 Å,
probing absorption lines of H-like and He-like ions of sulfur (S), silicon
(Si), magnesium (Mg), neon (Ne), and oxygen (O).

####  2.1.1 Chandra Data Reduction

We extract the data necessary for this analysis from the Chandra public data
archive, taken with the high energy transmission grating (HETG) spectra on
ACIS-S. Of the ten available ACIS-HETG archived observations of NGC 3783, we
choose to include eight111ObsID: 373, 2090, 2091, 2092, 2093, 2094, 14991,
15626. The two omitted observations were taken while NGC 3783 was obscured in
2016 (Kaastra et al., 2018), decreasing the signal-to-noise (S/N) to a value
below the required level for this analysis.

We follow the standard data reduction tools and threads for grating spectra in
CIAO222https://asc.harvard.edu/ciao/ (Chandra Interactive Analysis of
Observations). This produces a source spectrum, background spectrum, response
matrix (RMF) and auxiliary response file (ARF) for each ObsID used. We
consider only the first-order spectrum of the medium-energy grating (MEG) arm
of HETG, combining the positive and the negative first order spectra of all
ObsIDs using the command combine_grating_spectra. We then combine the
resulting positive stack and negative stack spectra to obtain one spectrum
representing the sum of the first-order spectra of eight observations. The
total exposure time for these observations is 1.05 Ms.

All relevant spectral analysis is conducted with Xspec in Heasoft
6.30.1333https://heasarc.gsfc.nasa.gov/docs/software/heasoft/.

####  2.1.2 Line Fitting

The Chandra observations of NGC 3783 span 13 years of observation, making
global continuum fitting difficult due to the flux variations and the presence
of the warm absorbers in the source over that time. Instead, we simplify our
analysis by fitting a local continuum around each absorption line of interest,
listed in Table 1, within a region of about $\pm$0.25 Å around the expected
central wavelength. Each local continuum is fit with a simple power law, with
the normalization and the photon index as free parameters. We do not include a
commonly used neutral absorber from the disk of the Galaxy (TBabs in Xspec) in
our model because there is no significant contribution to the continuum within
the small range of wavelengths we consider. We place no constraints on either
power law parameter to begin with, allowing Xspec to choose the best values.
The presence of a strong absorption line pulls the continuum down to
nonphysical levels when all parameters are free to vary. Thus we fix the
photon index to the best fit value while the normalization is adjusted by eye
to fit the local continuum more accurately.

After determining the continuum parameters, we add a Gaussian absorption
profile to the model with a negative normalization. We set a variable central
wavelength for each of the lines, within a small range of possible values due
to the presence of nearby strong quasar warm absorber features. We also fix
the Gaussian width to be $10^{-5}$ Å because these lines are expected to be
unresolved by Chandra/HETG.

The resulting best fit equivalent width (EW) of each absorption line is shown
in Table 1 and the Gaussian profiles are shown in Figure 1. Several of the
absorption lines are noticeably shifted from their expected wavelength,
particularly Ne ix K$\alpha$ and O viii, shown by the vertical dashed line in
each panel in Figure 1. We assume this to be insignificant due to the fact
that the observed wavelength shift is within $\sim$1 MEG wavelength resolution
element of 23 mÅ.

We detect z=0 absorption lines of O vii K$\alpha$, O vii K$\beta$, O viii
K$\alpha$, Ne ix K$\alpha$, and Ne x K$\alpha$ with 4.2$\sigma$, 2.3$\sigma$,
2.5$\sigma$, 4.1$\sigma$, and 4.5$\sigma$ significance respectively. We also
detect Ne ix K$\beta$ with 2.7$\sigma$ significance, but there is some
contamination from Fe L-shell features from the intrinsic WA within 0.04 Å of
the central Ne ix K$\beta$ wavelength. For this reason, we choose not to
include it in our subsequent analysis. However, our detection is included in
Figure 1. We provide 3$\sigma$ upper limits on the EW of S xvi K$\alpha$, Si
xiv K$\alpha$, Si xiii K$\alpha$, Mg xii K$\alpha$, and Mg xi K$\alpha$, since
they were not significantly detected in this data set (<2$\sigma$). This high-
significance detection of Ne x is strong evidence in itself for the presence
of super-virial hot gas.

Figure 1: Best fit Gaussian profiles for the Chandra/HETG data for each of the detected z $\approx 0$ absorption lines. All spectra are folded with the line spread function of Chandra/HETG and normalized by the best-fitted local continuum. Several of the lines are redshifted or blueshifted from their expected rest wavelengths, $\lambda_{\text{rest}}$ (vertical dashed line), but the offset is consistent with $\lambda_{\text{rest}}$ within one resolution element. Ne ix K$\beta$ is detected, but is contaminated by a Fe L-shell WA feature at $\sim$$\lambda=11.51$, making it difficult to model in our later analysis. The equivalent widths and implied column densities of each of the lines are shown in Table 1. Table 1: Observed ions in the CGM with their corresponding rest wavelength $\lambda_{\text{rest}}$, rest energy E, oscillator strength fjk, fit wavelength $\lambda_{\text{obs}}$, measured equivalent width EW, and associated column density N. EW${}_{\text{T1}}$ and EW${}_{\text{T2}}$ denote the equivalent width contributions of the lower and higher temperature gas phase respectively, determined by the non-solar two-component PHASE model. The errors quoted are 1$\sigma$ uncertainties for the parameter. 3$\sigma$ upper limits are quoted for the lines with less than 2$\sigma$ detections. Ion | Transition |  $\lambda_{\text{rest}}$ (Å) | E (keV) | fjk |  $\lambda_{\text{obs}}$ (Å) | EW (mÅ) | N $\left(\times 10^{15}\text{ cm}^{-2}\right)$ | EW${}_{\text{T}1}$ (mÅ) | EW${}_{\text{T}2}$ (mÅ)
---|---|---|---|---|---|---|---|---|---
S xvi | K$\alpha$ | 4.729 | 2.62 | 0.274 | 4.734 | < 3.70 | < 52.72 | - | -
Si xiv | K$\alpha$ | 6.182 | 2.01 | 0.240 | 6.180 | < 2.86 | < 35.26 | - | -
Si xiii | K$\alpha$ | 6.648 | 1.87 | 0.747 | 6.655 | < 2.16 | < 7.39 | - | -
Mg xii | K$\alpha$ | 8.419 | 1.48 | 0.276 | 8.415 | < 3.64 | < 21.02 | - | -
Mg xi | K$\alpha$ | 9.169 | 1.35 | 0.741 | 9.165 | < 3.83 | < 6.95 | - | -
Ne ix | K$\beta$ | 11.547 | 1.08 | 0.149 | 11.544 | 2.95${}^{+1.71}_{-1.09}$ | 16.79${}^{+9.73}_{-6.20}$ | 1.10${}^{+0.44}_{-1.10}$ | 1.95${}^{+0.96}_{-0.89}$
Ne x | K$\alpha$ | 12.134 | 1.02 | 0.276 | 12.130 | 5.49 $\pm$ 1.21 | 15.28 $\pm$ 3.37 | - | 4.29${}^{+1.54}_{-1.75}$
Ne ix | K$\alpha$ | 13.447 | 0.92 | 0.720 | 13.464 | 8.55 $\pm$ 2.09 | $24.98^{+16.12}_{-4.54}$ | 4.56${}^{+1.29}_{-1.66}$ | 7.92${}^{+2.07}_{-2.69}$
O vii | K$\beta$ | 18.627 | 0.67 | 0.146 | 18.630 | 7.61 $\pm$ 3.25 | 16.97 $\pm$ 7.25 | 6.93${}^{+1.21}_{-1.31}$ | -
O viii | K$\alpha$ | 18.969 | 0.70 | 0.278 | 18.960 | $8.55^{+3.45}_{-3.48}$ | $9.66^{+3.90}_{-3.93}$ | - | 5.41${}^{+2.25}_{-2.34}$
O vii | K$\alpha$ | 21.602 | 0.57 | 0.645 | 21.603 | $19.79^{+4.03}_{-4.70}$ | $24.40^{+13.50}_{-6.00}$ | 23.49${}^{+5.82}_{-6.23}$ | 2.34${}^{+1.34}_{-1.13}$

We are able to isolate only the Milky Way CGM absorption for fitting and
modeling due to the high spectral resolution of Chandra. Figure 2 shows the
separation of the z=0 CGM absorption line from the quasar warm absorber (WA)
line for Ne x. The source NGC 3783 is at z=0.0097, but the Ne x WA line is
blueshifted from the quasar to due to the outflow velocity (Krongold et al.,
2003), with the observed WA redshift z=0.0075. This results in a wavelength
separation of 0.09 Å between the z=0 line and the intrinsic WA line. All other
lines are similarly separated, allowing us to minimize the contamination from
the WA features in our analysis, even for such a small redshift. Any other
possible contamination from other WA lines (i.e. Fe L-shell or Ca xvi
transitions) is negligible, except in the case of Ne ix K$\beta$ as discussed
above.

Figure 2: Chandra/HETG spectrum around the z=0 wavelength of the Ne x line,
showing the separation between the z=0 CGM absorption and the intrinsic
z=0.0075 warm absorber (WA) feature of NGC 3783. The z=0 Ne x Gaussian profile
is plotted in red. The wavelength separation between the CGM Ne x line and the
WA line is 0.09 Å which allows us to isolate the z=0 Ne x absorption in the
Milky Way from the WA.

O vii K$\alpha$ was previously detected in Gupta et al. (2012) in their
analysis of the same Chandra archival data of NGC 3783 to study the virial
warm-hot gas of the Milky Way CGM. Their measured EW for this lines is
$14.4\pm 2.5$ mÅ while our measurement in this analysis gives an EW of
$19.79^{+4.03}_{-4.70}$. The difference in detection significance is likely
due to our choice of a simple background continuum while Gupta et al. (2012)
chose a more complicated model to fit the continuum. However, there is still
agreement between the two values within 1$\sigma$. The other lines detected in
Gupta et al. (2012) also shows agreement with our own measurements. Fang et
al. (2015) analyzed XMM-Newton observations of a collection of quasars to
study O vii K$\alpha$ CGM absorption, obtaining an EW of $23.30\pm 6.65$ mÅ
and $19.82\pm 6.61$ mÅ with two different evaluation methods along the NGC
3783 sightline. Our results remain consistent with these previous detections,
providing more agreement and confidence in our new results.

###  2.2 XMM-Newton

We briefly look at the XMM-Newton Reflection Grating Spectrometer (RGS)
observations of NGC 3783 from the XMM-Newton Science Archive by stacking the
observations of the unobscured quasar with a sufficient exposure time for the
best possible S/N444Obs ID: 0112210101, 0112210201, 112210501. We reduce the
raw data with XMM-Newton Scientific Analysis System (SAS) and stack the
resulting RGS1 and RGS2 spectra using the command rgscombine. The resulting
combined observations have a total exposure time of 316 ks.

We fit the O vii K$\alpha$ line with a two-Gaussian model, one at the O vii
K$\alpha$ wavelength, and one centered at 21.72 Å, consistent with the model
in Fang et al. (2015) with EW = 23.81${}^{+7.21}_{-6.26}$ mÅ. The spectrum
around the O vii K$\alpha$ line is shown in the left panel of Figure 3,
normalized by the power law + Gaussian continuum. The S/N is still too low to
make any new detections, so we instead overlay our Chandra best fit on the
XMM-Newton data for the Ne x line, shown in the right panel of Figure 3. This
model has all the same parameters as the Chandra model, but with the power law
normalization adjusted to account for continuum variability between the two
observations. We see that the Ne x line strength in XMM-Newton is similar to
that in the Chandra observations.

Although we were unable to confirm our other detections or fit any new
absorption lines, there is agreement between the two data sets in the
existence of highly ionized metal absorption in the CGM.

Figure 3: Normalized XMM-Newton spectra for O vii K$\alpha$ (left) and Ne x
(right) with the best model plotted in red. The O vii K$\alpha$ model is an
independent fit to the XMM-Newton data, with a power law + Gaussian (centered
at 21.72 Å) continuum consistent with Fang et al. (2015). The Ne x model is
the best fit Chandra model in Figure 1 with an adjusted continuum
normalization. The S/N in the XMM-Newton data is significantly lower than the
Chandra data, so we do not expect an independent measurement of Ne x, or other
absorption lines. However, the O vii K$\alpha$ Chandra model is consistent
with the XMM-Newton data and the previous measurements.

##  3 Model-Independent Results

With our detections of highly ionized Ne and O absorption, we want to estimate
the temperature of the gas containing these metals in comparison with the
known warm-hot virial phase of the Milky Way CGM. The temperature can be
determined based on the EW and column densities (N) measured from the
spectroscopic analysis in Section 2.

We use the linear part of the curve of growth to determine the column
densities of all of the unsaturated detected lines, given by Equation 1.

$N_{i}=1.13\times 10^{12}\frac{EW_{i}}{\lambda_{jk}f_{jk}}$ (1)

where $N_{i}$ is the column density of the ion in cm-2, $EW_{i}$ is the
equivalent width of the $i$-th ion in cm, $f_{jk}$ is the dimensionless
oscillator strength of the given transition from the $j$-th to $k$-th atomic
level, and $\lambda_{jk}$ is the wavelength of the absorption line in cm. The
column densities calculated in this manner for each absorption line are shown
in Table 1.

Based on our measured EWs for O vii and Ne ix lines, we see that O vii
K$\alpha$ and Ne ix K$\alpha$ are both saturated. When calculating the column
densities for these lines, we combine the information from the K$\alpha$ and
K$\beta$ lines as previously done in Williams et al. (2005), Gupta et al.
(2012), Das et al. (2021), and Mathur (2022). These values are quoted in Table
1. This method gives column densities larger than would be calculated with the
linear curve of growth analysis.

In combination with the ionization fractions of each of the ions as a function
of temperature ($f_{\text{ion}}(\text{T})$, taken from CHIANTI Atomic
Database555https://www.chiantidatabase.org/ (Dere et al., 1997; Del Zanna et
al., 2021)), we determine the approximate temperatures of the gas containing
these metals. This can only be done for the cases where we have detections of
two ions of the same species (O vii, O viii, Ne ix, and Ne x). The ratio of
the ionization fractions of the same species as a function of temperature is
equal to the ratio of the column densities previously calculated. For example:

$\frac{f_{\text{Ne\,{ix}}}(\text{T})}{f_{\text{Ne\,{x}}}(\text{T})}=\frac{\text{N}_{\text{Ne\,{ix}}}}{\text{N}_{\text{Ne\,{x}}}}$
(2)

For simplicity, we assume that all of the Ne ix and Ne x are produced by one
temperature component while all of the O vii and O viii are produced by
another. Previous observations show that the ions are mixed between phases
(Das et al., 2019a, 2021), but we follow this simple assumption solely for the
purpose of informing our formal model in Section 4.

Under this assumption, we calculate the approximate temperatures of this two-
phase CGM model. The O vii/O viii ratio implies log(T${}_{1})=6.23\pm 0.05$ K.
The Ne ix/Ne x ratio implies log(T${}_{2})=6.55^{+0.04}_{-0.05}$ K. Because
there is no 1$\sigma$ overlap in temperatures of these phases, we see that
there are indeed two distinct phases along this line of sight, one near the
virial temperature (O vii/O viii) and one at super-virial temperature (Ne
ix/Ne x). Without modeling, there is no way to know how much each temperature
component contributes to the overall EW of the lines, but this estimation
gives us enough evidence to conclude that two distinct phases of the CGM are
necessary to simultaneously produce the observed amount of metal absorption.

With these model-independent temperature calculations, we can estimate the
total column density of both Ne ix and O vii, which gives an absolute
abundance ratio estimation of Ne/O = $1.24^{+1.10}_{-0.52}$, compared to a
solar ratio of Ne/O = $0.23\pm 0.03$. This implies the existence of Ne
abundances up to 2$\sigma$ above the solar prescriptions of Asplund et al.
(2021) along the sightline of NGC 3783.

##  4 PHASE Modeling

We use the hybrid-ionization model PHASE (models of collisionally ionized gas
perturbed by photoionization by the meta-galactic radiation field, at a given
redshift; Krongold et al. (2003), Das et al. (2019b), Das et al. (2021)) to
model the detected absorption lines in Chandra. As discussed above, we do not
include the Ne ix K$\beta$ line because the proximity and potential
contamination of the Fe line does not allow for accurate modeling. The
parameters in PHASE are temperature T, hydrogen column density
N${}_{\text{H}}$, redshift, non-thermal velocity, ionization parameter, and
the abundances relative to solar of various metals (including Ne and O,
detected in our analysis). We set the ionization parameter $U$ in all of our
models to be $U=10^{-3.9}$, the lowest value allowed by PHASE. At this value,
the photoionization is negligible, and the model is effectively a collisional
ionization model only, as expected for the CGM. The non-thermal velocity is
set to be zero for all absorption lines and the redshift is set based on the
existing wavelength offset of the Gaussian best fit for each of the lines as
discussed in Section 2.1.

We choose a two-component PHASE model with a power law continuum (powerlaw *
PHASE1 * PHASE2) to account for the different temperature phases determined
above. Due to the low redshift of NGC 3783, the quasar warm absorbers have a
small wavelength separation from the CGM absorption lines, creating added
difficulty in a global PHASE fit. Additionally, since there is no appropriate
global continuum fit used in this analysis as discussed above, we limit our
fitted wavelength range to be small such that only the z=0 absorption line
itself is included. This completely removes the effects of the warm absorbers
and other emission or absorption lines that are beyond the focus of this
analysis. We set the local continuum levels to be the same as the chosen
parameters in the Gaussian best fit, ultimately only allowing
N${}_{\text{H}}$, T, and Ne abundance to vary in PHASE.

###  4.1 Solar Relative Abundances

In the first fit, we fix the relative abundances of all metals in both of the
defined PHASE components to be solar, ab(X) = 1 for all elements X. We call
this our "solar" model. The only metals that are detected in our analysis are
O and Ne, but PHASE considers the non-detection of the included S, Si, and Mg
lines in the fitting process. Each of the lines are fit simultaneously with
interdependent variable parameters. Only the local continuum and redshift are
unique to the line.

The resulting best-fitted parameters are listed in Table 2, with a final fit
$\chi^{2}/$dof = $81.17/121$. Most notable is the determined temperatures of
log(T$)_{1}=5.83^{+0.15}_{-0.07}$ K and log(T$)_{2}=6.61^{+0.12}_{-0.06}$ K,
consistent with a two-phase CGM model with a virial and super-virial phase, as
expected. Including only PHASE1, $\chi^{2}/$dof = $96.61/121$, and including
only PHASE2, $\chi^{2}/$dof = $103.50/121$, showing that a two-temperature
component model is statistically the best fit to the data. With this model,
PHASE fits the O  lines appropriately, giving EWs consistent with our Gaussian
fits. However, the model fits the Ne x absorption line poorly, with an EW of
1.85${}^{+0.55}_{-0.83}$ mÅ, underestimating the strength of the Ne x line by
about 3$\sigma$ from the Gaussian model. This difference indicates a non-solar
mixture of metals, since even with a higher temperature, PHASE cannot
replicate the amount of Ne x present under the assumption of solar abundance
ratios. The full solar fit is shown with a dotted line in Figure 4. Note the
underproduction of Ne x in the top left panel.

Because the Ne x is underestimated in PHASE2 with a solar model, our model
suggests a non-solar Ne/O abundance ratio to account for the differences in Ne
and O absorption. A variation in any other PHASE parameters is not sufficient.

###  4.2 Non-Solar Relative Abundances

Allowing super-solar abundance ratios, as necessitated by the results of the
solar model, gives the "non-solar" model quoted in Table 2. We freeze the
temperatures at their best-fitted values in the solar model, instead varying
the metal abundances for both PHASE components. The ionization parameter,
redshift, and non-thermal velocity are still fixed to be as defined in the
solar model, and N${}_{\text{H}}$ remains variable.

PHASE assumes a solar absolute metallicity when determining the value of
N${}_{\text{H}}$, but we do not measure a true metallicity along this line of
sight. Therefore, we refer to all metal abundances as relative ratios. In our
model, the Ne abundance varies relative to O, which is held fixed at solar
metallicity. The O lines were fit well in our solar model, so we take this as
a good approximation. We do not have enough information to be able to vary
both ab(Ne) and ab(O) relative to solar in PHASE as these are the only
detected metals.

The resulting best fit has $\chi^{2}/$dof = $75.48/121$, a significant
improvement over the solar model. PHASE1, dependent on Ne ix, requires no
change in Ne abundance, fit well with ab(Ne)${}_{1}=1.00^{+2.49}$. We fixed
the abundance to be solar or above, so there is no 1$\sigma$ lower limit on
this value. However, PHASE2, defined largely by the overabundant Ne x,
requires ab(Ne)${}_{2}=5.51^{+7.47}_{-2.84}$ (or
$[\text{Ne/O]}=0.75^{+0.38}_{-0.30}$ following Asplund et al. (2021)). This is
$\sim$2$\sigma$ above solar abundances. When we force Ne/O to be the same
between the two fit components, we get ab(Ne) $=3.59^{+3.16}_{-1.64},$
consistent within 1$\sigma$ with our best fit. There must be super-solar Ne
abundances in the super-virial hot phase of the CGM along the line of sight of
NGC 3783.

Allowing N${}_{\text{H}}$, T, and ab(Ne) to vary simultaneously from our best
fit values results in parameters within 1$\sigma$ of those quoted in Table 2.
Thus our choice to freeze the temperatures in PHASE2 does not impact our
results with significance.

The non-solar model for each of the detected lines is shown in Figure 4 with
each of the PHASE component contributions highlighted in different colors. The
top panel shows the spectrum folded with the line spread function of
Chandra/HETG, while the bottom panel shows the unfolded spectrum. We see that
all of the Ne x and O viii absorption comes from the hot phase, while almost
all of the O vii comes from the warm-hot phase. Ne ix K$\alpha$ is split
between both phases. Here, the Ne x line is well fit with the high Ne
abundance, consistent with the Gaussian fit. The Ne ix K$\beta$ line was not
included in the PHASE-modeled data, but the resulting predicted EW for Ne ix
K$\beta$ is consistent with our Gaussian fit measurement. The two temperature
component contributions to the EW are shown in Table 1. With this consistency,
we can conclude that Ne ix K$\beta$ is likely not contaminated by the local Fe
lines, but their proximity still complicates the independent modeling.

Table 2: PHASE best fit model parameters and their 1$\sigma$ uncertainties for
all detected CGM absorption lines with both solar and non-solar abundance
ratios. The values with no quoted errors were fixed during the modeling and
thus have no associated uncertainty. The EW of the resulting absorption lines
of the non-solar model are shown in Table 1.

| Parameter |  | Values
---|---|---|---
|  |  | Solar | Non-Solar
PHASE1 | log(N${}_{\text{H}}$)1 |  |  $20.20^{+0.22}_{-0.28}$ cm-2 |  $20.10_{-0.31}^{+0.22}$ cm-2
log(T)1 |  |  $5.83^{+0.15}_{-0.07}$ K | 5.83 K
ab(Ne)1 |  | 1.00 | $1.00^{+2.49}_{*}$
PHASE2 | log(N${}_{\text{H}}$)2 |  |  $19.92^{+0.15}_{-0.18}$ cm-2 |  $19.65^{+0.22}_{-0.31}$ cm-2
log(T)2 |  |  $6.61^{+0.12}_{-0.06}$ K | 6.61 K
ab(Ne)2 |  | 1.00 | $5.51^{+7.47}_{-2.84}$

  * •

* The lower limit of ab(Ne)1 is pegged at 1.

Figure 4: Non-solar PHASE models for the detected absorption lines in the
Chandra spectrum. The spectrum folded with the line spread function of
Chandra/HETG is shown in the top row and the unfolded spectrum is shown in the
bottom row. Both spectra have been normalized by the best-fitted local
continuum. The best-fitted two-T PHASE model is shown in black solid lines,
with the separate contributions from the lower temperature PHASE component,
PHASE1 (red), and the higher temperature PHASE component, PHASE2 (blue). All
of the Ne x and O viii is produced by the super-virial temperature component,
while all of the O vii is produced by the virial temperature component. The
solar fit is also plotted with a dotted black line, showing that solar
abundances poorly fit the Ne x line, indicating the necessity for non-solar
Ne/O abundance in the hot component.

At fixed T and fixed ab(O), N${}_{\text{H}}$ is anti-correlated with ab(Ne) in
the hot phase (PHASE2). The hot phase is characterized dominantly by Ne x and
O viii. The O  lines are sensitive to the changes in N${}_{\text{H}}$, not in
changes to ab(Ne), while Ne  is sensitive to changes in both parameters.
Leaving log(N${}_{\text{H}}$)2 and ab(Ne)2 free, PHASE chooses a combination
that best fits both ions. Increasing N${}_{\text{H}}$ decreases the necessary
ab(Ne) to fit Ne x, but also increases the strength of the O viii line. We
have no prior knowledge of the expected hydrogen column density of the super-
virial hot phase, so we can make no distinction between the chosen values in
the solar and non-solar model. If, however, N${}_{\text{H}}$ is higher than
our best-fit modeled value (still assuming fixed T and solar ab(O)), this
would imply a lower—only $1\sigma$ super-solar—Ne/O than currently predicted.

We find no similar correlation between the temperatures of PHASE1 and PHASE2
nor between the temperature and Ne/O of PHASE2.

##  5 Discussion

We find that two distinct temperature phases coexist in the Milky Way CGM
along the line of sight of NGC 3783 at temperatures at and above the virial
temperature, with an overabundance of Ne in only the hot phase. This the
fourth detection of the super-virial hot phase and the third detection of
super-solar abundance ratios in absorption from the CGM. An in-depth
discussion of the possible explanations for the super-virial temperatures and
metal enrichment within the CGM has already been outlined in Das et al.
(2019a) and Das et al. (2021), thus we will only reiterate the important and
relevant information here.

###  5.1 Implications for CGM Structure

We have now detected the super-virial phase in absorption on four accounts,
three individual sightlines with high S/N data and one stack of low S/N data
towards other sightlines. Each of these studies has detected super-virial
temperatures based on the presence of different highly ionized (H-like)
metals, e.g., O viii, Ne x, Si xiv, S xvi. Even with this now seemingly
universal property, there is still significant scatter in temperature within
the super-virial phase and the well-understood virial phase as depicted in
Figure 5. In these observations, we see three distinct phases in
temperature—sub-virial, virial, and super-virial—with almost an order of
magnitude variation in the super-virial phase and about a factor of 3 scatter
in the virial phase. This temperature scatter has also been observed in
emission (Das et al., 2019b; Gupta et al., 2023; Bhattacharyya et al., 2022).
The consistent observation indicates that regions of gas in the CGM can be
much hotter than the volume-filling virial phase, but is not homogeneously
mixed or heated.

Figure 5: A summary of the current absorption detections of the warm (sub-
virial), warm-hot (virial), and hot (super-virial) phases of the Milky Way
CGM. The width of the band represents the 1$\sigma$ uncertainty (3$\sigma$ for
Mrk 421) on the measured temperature. The coexistence of three distinct phases
of the highly-ionized CGM has been observed along three individual sightlines
and in a stack of 46 low S/N galaxies. There is large scatter across orders of
magnitude in temperature, even within each phase. [1] Das et al. (2021), [2]
Das et al. (2019a), [3] Lara-DI et al. 2023, in preparation.

In a stack of 46 quasar sightlines, Lara-DI et al. (2023) detect Si xiv and S
xvi associated with the super-virial hot component of the Milky Way CGM at
temperatures of T $\approx 10^{7.5}$ K (temperature determination described in
Lara-DI et al. 2023, in preparation). However, they do not detect any Ne x in
their resulting spectrum, which has been necessary to constrain the hot
temperature in the other studies, including this one. The main reason that Ne
x is detectable is because of an overabundance of Ne, increasing the strength
of the faint lines. This may be indicative of inhomogeneous mixing of metals,
with some regions of the CGM being more Ne-rich than others.

The CGM of the Milky Way is not uniform, it is patchy in chemical composition
and temperature. Galactic feedback and outflow processes cause heating and
turbulence in the CGM. In turn, turbulence can affect the heating, cooling,
and mixing of the CGM gas. What we observe is the complex effects of all of
these interactions, which combine to create the multi-phase structure of the
highly ionized CGM.

There are still many open questions regarding this phase-structure and the
mechanisms powering the CGM. What processes are able to sustainably heat the
gas to such hot temperatures observed? We see that the virial and super-virial
phases coexist along the line of sight, but where does the hotter gas reside
along that line? Given the likely solar Ne/O in the warm-hot component, but
significantly super-solar Ne/O in the hot phase, we speculate that the two
phases might not be co-spatial, and might arise from different physical
processes. For example, the hot phase may occupy the extra-planar region of
the Galaxy, while the warm-hot phase may fill the extended region out to the
virial radius. Of course, adding more lines of sight to this group of analysis
will allow us to probe more of the hot phase structure around the CGM and
explore more of the metal mixtures that exist around the Galaxy.

This super-virial phase and non-solar chemical composition is still new.
However, in the absence of non-detections of the super-virial phase, we are
confident in its universal presence in the Milky Way CGM. In their analysis of
3-D hydrodynamical simulations, Vijayan & Li (2022) were able to reproduce the
hot multi-phase gas in the CGM. They find that, in the case of high star
formation rates, an asymmetric distribution of temperature and metallicity
exists inside and outside the produced biconical outflow, which may relate to
the wide range of temperatures (Figure 5) and metal ratios in our
observations. The temperature that we measure along the sightline of NGC 3783
(log(T)$=6.61^{+0.12}_{-0.06}$ K) is reproduced in the extra-planar regions in
Vijayan & Li (2022) and is a direct result of the stellar feedback in the
galaxy. The combination of theory, simulations, and observations will allow us
to shed light on the processes governing the Milky Way CGM. Understanding the
nature of the super-virial hot phase, and the amount of baryonic matter and
metals contained in it, is important for understanding the CGM formation, and
thus, galactic evolution.

###  5.2 XRISM Prediction

With the upcoming XRISM mission, new doors are opening in the field of X-ray
astronomy and an understanding the capabilities of the instruments in
achieving our science is necessary. XRISM could be used to study the Milky Way
CGM in greater depth, helping us understand the underlying mechanisms causing
the observations we have obtained thus far. With the planned observations of
NGC 3783, the results of this analysis could be confirmed and expanded with
the better spectral resolution and higher effective area of XRISM. We simulate
XRISM/Resolve 7 eV resolution observations of NGC 3783 based on our non-solar
PHASE model to explore the potential results of new observations under the
same analysis.

The source is inherently variable, meaning that the observed flux changes over
time, influencing the quality of the received data. We simulate an observation
with 200 ks of integration time at the measured flux of the Chandra data
($1.72^{+0.005}_{-0.003}\times 10^{-11}$ erg/cm2/s between 0.295 and 2.4 keV).
The resulting spectrum is shown in Figure 6 (middle row). We bin the spectrum
for visual effect, but the quality of the data at 200 ks is roughly the same
as 1 Ms of Chandra data, with an EW limit of 1.82 mÅ.

Figure 6: Simulated XRISM/Resolve 7 eV resolution observations showing
predicted detections of Ne lines along the NGC 3783 line of sight. Top: The
PHASE model used to simulate the XRISM spectra. Middle: 200ks integration
time. Bottom: 600ks integration time, representing an observation at 3 times
the flux of the middle panel. Both spectra are folded with the line spread
function of XRISM/Resolve. An observation at a time when NGC 3783 has a higher
flux will increase the S/N in the data, increasing the significance of
detections and allowing us to measure new lines not currently detected in
Chandra data.

However, at energies below about 0.7 keV (wavelengths at which the O lines can
be detected), the effective area of XRISM/Resolve is below 100 cm2. This means
that we are not able to detect O absorption lines with the same level of
significance as Chandra. The 200 ks XRISM simulation measures O vii K$\alpha$
with an EW of 27.31${}^{+7.41}_{-7.37}$ mÅ, which has a lower significance
(3.71$\sigma$) and larger uncertainties than our Chandra measurement. Thus, at
longer wavelengths, Chandra is preferred when compared to a shorter XRISM
observation.

Archival ROSAT observations of NGC 3783 obtained a flux up to $5.66\times
10^{-11}$ erg/s/cm2 (Salvato et al., 2018) in the range 0.1-2.4 keV,
approximately 3 times higher than our Chandra observations. This would be
equivalent to observing for 3 times longer, yielding a spectrum with a higher
S/N and more significant detections of the absorption lines of interest. We
simulate another XRISM spectrum, instead with 600 ks of exposure time to
predict the results from a higher flux observation, also shown in Figure 6
(bottom row). With the longer exposure time, many of the absorption lines
would be detected with more significance, which can be noticed by eye in the
spectrum. This would allow for more precise measurements of line strengths,
metal abundances, and temperature in the CGM.

We suggest that NGC 3783 be monitored over time (with Swift, for example) and
observed with XRISM at a period of high flux. This would allow us to detect
more of the lines predicted by PHASE and confirm the existence of the super-
virial temperature gas with different metals. Our PHASE model predicts many
additional lines that could be potentially detected with as little as 200 ks
of integration time. All of the lines with PHASE-predicted equivalent widths
within the wavelength range of XRISM/Resolve are listed in Table 3. Detections
of additional z=0 metals in the spectrum would allow us to better constrain
the CGM metal mixture along this line of sight, giving us more than just Ne
and O to add to our understanding of the thermal and chemical structure of the
CGM.

##  6 Conclusions

In this paper, we present deep Chandra/HETG observations of NGC 3783 that show
z=0 metal line absorption from the Milky Way CGM.

  * •

We fit the continuum around each of the absorption lines with a simple power
law and add a Gaussian profile to determine EW of each detected absorption
line. We see agreement when comparing to previous analysis of Chandra (Gupta
et al., 2012) and XMM-Newton (Fang et al., 2015) data of NGC 3783.

  * •

We use PHASE to properly model the spectrum and determine the temperatures of
the two detected CGM phases to be T1=$5.83^{+0.15}_{-0.07}$ K, warm-hot virial
temperature, and T${}_{2}=6.61^{+0.12}_{-0.06}$ K, hot super-virial
temperature.

  * •

We detect a super-solar Ne abundance of ab(Ne)${}_{2}=5.51^{+7.47}_{-2.84}$
relative to solar, or $[\text{Ne/O]}=0.75^{+0.38}_{-0.30}$, which is
$\sim$2$\sigma$ above solar in the hot phase, and an abundance consistent with
solar in the warm-hot phase. However, if the total N${}_{\text{H}}$ is higher
than predicted, our models call for a Ne abundance closer to solar with
ab(Ne)2 $\approx$ 2.

  * •

We make predictions for upcoming XRISM/Resolve observations and find that the
same quality of data can be achieved with XRISM in only 200 ks, compared to 1
Ms with Chandra. We also suggest that, in order to maximize CGM absorption
line detections, NGC 3783 be observed in a high flux state.

In conjunction with the previous absorption observations of the Milky Way CGM
hot phase, this analysis shows that the hot super-virial phase can be seen
around the Galaxy and provides confidence in the multi-phase structure of the
CGM. However, as discussed in Section 5, there remains variation even within
the super-virial phase. Determining the underlying mechanisms behind the
existence of the hot phase will require more observational and theoretical
work in the development of this field.

## Acknowledgements

SM is grateful for the grant provided by the National Aeronautics and Space
Administration (NASA) through Chandra Award Number AR0-21016X issued by the
Chandra X-ray Center, which is operated by the Smithsonian Astrophysical
Observatory, for and on behalf of the National Aeronautics Space
Administration under contract NAS8-03060. S.M. is also grateful for the NASA
ADAP grant no. 80NSSC22K1121. S.D. acknowledges support from the KIPAC
Fellowship of Kavli Institute for Particle Astrophysics and Cosmology,
Stanford University. AG gratefully acknowledges support through the NASA ADAP
grant no. 80NSSC18K0419. YK acknowledges support from UNAM PAPIIT grant no.
IN102023.

## Data Availability

All data used in the presented analysis is available online via the Chandra
Data Archive (CDA) and the XMM-Newton Science Archive (XSA). The relevant
ObsID numbers are provided below:

Chandra: 373, 2090, 2091, 2092, 2093, 2094, 14991, 15626

XMM-Newton: 0112210101, 0112210201, 112210501

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##  Appendix A PHASE Predictions

Our non-solar PHASE model predicts the presence of many absorption lines, most
of which are outside the wavelength range of Chandra or require a higher S/N
than available with the current data. We provide a list of those predictions
with the expected EW and N and their associate uncertainties. We only include
those in the wavelength range of XRISM, as the Resolve instrument will provide
the best opportunity to observe these lines.

The quoted column densities are the totals for each ion. They have not been
calculated with Equation 1, as in Table 1, but are simply an output of PHASE.

Table 3: Predicted equivalent widths and column densities for all absorption lines in our non-solar 2-component PHASE model within the wavelength range of XRISM/Resolve. The quoted EW is the total EW for each of the lines, the sum of both phase contributions. N${}_{\text{tot}}$ represents the total column density of the ion. Many of these lines should be detectable with XRISM when NGC 3783 is in a high flux state. Element | Ion |  $\lambda$ (Å) | EW (mÅ) | N${}_{\text{tot}}$ $\left(\times 10^{15}\text{ cm}^{-2}\right)$
---|---|---|---|---
C |  C v | 40.267 | 29.14${}^{+6.13}_{-6.37}$ | 37.10${}^{+23.80}_{-18.70}$
C v | 34.973 | 12.39${}^{+1.50}_{-2.23}$
C v | 33.426 | 8.47${}^{+1.52}_{-2.47}$
C vi | 33.736 | 11.34${}^{+1.96}_{-2.90}$ | 7.74${}^{+4.96}_{-3.91}$
C vi | 28.466 | 3.35${}^{+1.38}_{-1.46}$
N |  N vi | 28.787 | 13.56${}^{+2.68}_{-3.11}$ | 11.70${}^{+7.50}_{-5.91}$
N vi | 24.898 | 5.09${}^{+1.28}_{-1.80}$
O |  O vii | 21.601 | 25.83${}^{+7.16}_{-7.36}$ | 94.10${}^{+60.40}_{-47.55}$
O vii | 18.627 | 6.93${}^{+1.21}_{-1.31}$
O vii | 17.768 | 4.76${}^{+0.82}_{-1.22}$
O vii | 17.396 | 3.34${}^{+0.81}_{-1.11}$
O viii | 18.969 | 5.41${}^{+2.25}_{-2.34}$ | 5.43${}^{+3.60}_{-2.74}$
Ne |  Ne ix | 13.447 | 12.48${}^{+3.36}_{-4.35}$ | 20.51${}^{+5.18}_{-4.05}$
Ne ix | 11.544 | 3.05${}^{+1.40}_{-2.55}$
Ne x | 12.134 | 4.29${}^{+1.54}_{-1.75}$ | 11.70${}^{+7.70}_{-5.94}$
Ar |  Ar ix | 35.024 | 2.24${}^{+1.05}_{-1.03}$ | 0.46${}^{+0.29}_{-0.23}$
Ca |  Ca xi | 30.471 | 2.38${}^{+1.32}_{-1.15}$ | 0.12${}^{+0.07}_{-0.06}$
Fe |  Fe xvii | 15.014 | 3.14${}^{+1.73}_{-1.49}$ | 0.66${}^{+0.43}_{-0.33}$