# The COS-Holes Survey: Connecting Galaxy Black Hole Mass with the State of
the CGM

Samantha L. Garza Department of Astronomy, University of Washington, Seattle,
WA, 98195  Jessica K. Werk Department of Astronomy, University of Washington,
Seattle, WA, 98195  Benjamin D. Oppenheimer Center for Astrophysics and Space
Astronomy, 389 UCB, Boulder, CO, 80309, USA  Kirill Tchernyshyov Department of
Astronomy, University of Washington, Seattle, WA, 98195  N. Nicole Sanchez
Carnegie Observatories, 813 Santa Barbara Street, Pasadena, California, 91101
USA  California Institute of Technology, TAPIR 350-17, 1200 E. California
Boulevard, Pasadena, California, 91125-0001 USA  Yakov Faerman Department of
Astronomy, University of Washington, Seattle, WA, 98195  Kate H. R. Rubin
Department of Astronomy, San Diego State University, San Diego, CA 92182 USA
Department of Astronomy $\&$ Astrophysics, University of California, San
Diego, La Jolla, CA 92093, USA  Misty C. Bentz Department of Physics and
Astronomy, Georgia State University, Atlanta, GA 30303, USA  Jonathan J.
Davies Department of Physics and Astronomy, University College London, Gower
Street, London WC1E 6BT, UK  Joseph N. Burchett Department of Astronomy, New
Mexico State University, Las Cruces, NW, 88003  Robert A. Crain Astrophysics
Research Institute, Liverpool John Moores University, 146 Brownlow Hill,
Liverpool, L3 5RF  J. Xavier Prochaska Department of Astronomy and
Astrophysics, University of California, Santa Cruz, CA 95064, USA  Kavli
Institute for the Physics and Mathematics of the Universe (Kavli IPMU), 5-1-5
Kashiwanoha, Kashiwa, 277-8583, Japan  Division of Science, National
Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

###### Abstract

We present an analysis of HST/COS/G160M observations of C IV in the inner
circumgalactic medium (CGM) of a novel sample of eight z$\sim$0, L$\approx$L⋆
galaxies, paired with UV-bright QSOs at impact parameters
($R_{\mathrm{proj}}$) between 25-130 kpc. The galaxies in this stellar-mass-
controlled sample (log10M⋆/M⊙ $\sim$ 10.2-10.9 M⊙) host super-massive black
holes (SMBHs) with dynamically-measured masses spanning log10MBH/M⊙ $\sim$
6.8-8.4; this allows us to compare our results with models of galaxy formation
where the integrated feedback history from the SMBH alters the CGM over long
timescales. We find that the C IV column density measurements (NCIV) (average
log10NCIV,CH = 13.94$\pm$0.09 cm-2) are largely consistent with existing
measurements from other surveys of NCIV in the CGM (average log10NCIV,Lit =
13.90$\pm$0.08 cm-2), but do not show obvious variation as a function of the
SMBH mass. In contrast, specific star-formation rate (sSFR) is highly
correlated with the ionized content of the CGM. We find a large spread in sSFR
for galaxies with log10MBH/M⊙ $>$ 7.0, where the CGM C IV content shows clear
dependence on galaxy sSFR but not MBH. Our results do not indicate an obvious
causal link between CGM C IV and the mass of the galaxy’s SMBH; however
through comparisons to the EAGLE, Romulus25, $\&$ IllustrisTNG simulations, we
find that our sample is likely too small to constrain such causality.

galaxies: formation - galaxies: halos - intergalactic medium -
quasars:absorption lines

††facilities: Hubble Space Telescope/Cosmic Origins Spectrograph††software:
ArviZ (Martin et al., 2023), astropy (Astropy Collaboration et al., 2013,
2018, 2022), JAX (Bradbury et al., 2018), LIFELINES (Davidson-Pilon, 2024),
linetools (Prochaska et al., 2017a), matplotlib (Hunter, 2007), numpy (Harris
et al., 2020), NumPyro (Phan et al., 2019; Bingham et al., 2019), pandas
(pandas development team, 2024), pPXF (Cappellari, 2023), PyIGM (Prochaska et
al., 2017b), scipy (Virtanen et al., 2020), NADA (Lee, 2020), veeper
(Burchett, 2024).

##  1 Introduction

For decades, absorption-line experiments using bright background quasars
(QSOs) have been recognized as an efficient way of studying diffuse gaseous
atmospheres of the Milky Way and other galaxies (e.g. Bahcall & Spitzer, 1969;
Bergeron, 1986; Werk et al., 2013). With the more recent addition of results
from HST/COS, astronomers have established that this diffuse outer part of
galaxies, called the circumgalactic medium (CGM), is a highly-ionized,
massive, spatially extended reservoir of both fuel for future star formation
and the byproducts of stellar evolution (Lehner & Howk, 2011; Peeples et al.,
2014; Werk et al., 2014; Tumlinson et al., 2017). The properties of the CGM,
particularly the highly ionized CGM traced by O VI, are linked to the star-
forming properties of host galaxies (e.g. Tumlinson et al., 2011; Tchernyshyov
et al., 2022). For this reason, the CGM can serve as an excellent testing
ground for astrophysical models of galaxy-scale feedback. In this work, we
focus on testing the cumulative effect of feedback from supermassive black
holes (SMBHs) on the content of the cool CGM.

It is well-known that the properties of galactic SMBHs correlate with their
parent galaxy properties. For example, Kormendy & Richstone (1995) found that
black hole masses scale linearly with the absolute luminosity of the host
bulge (or elliptical galaxy). This result inspired many investigations into
other scaling relationships between these galaxy properties and their
corresponding central black hole properties, which found an indirect link
between galaxy formation and the growth of their SMBHs (Haehnelt et al., 1998;
Magorrian et al., 1998; Saglia et al., 2016). In particular, both the relation
between the mass of the central SMBH and the stellar dispersion of its host
galaxy’s bulge, MBH-$\rm\sigma$, and the bulge mass-MBH correlation (Silk &
Rees, 1998; Ferrarese & Merritt, 2000; Gebhardt et al., 2000; Häring & Rix,
2004; Reines & Volonteri, 2015), reflect the assertion that the mass of the
SMBH is a fundamental property of a galaxy, reflective of its history
(Kormendy & Ho, 2013; van den Bosch, 2016). To extend this further, we posit
that there can be a significant (and observable) alteration of the CGM content
of galaxies due to black hole activity over time due to the cumulative effect
of the processes associated with black hole growth such as those envisioned in
most kinetic-mode feedback scenarios (e.g., Best & Heckman, 2012).

Recently, analytical studies have shown that maintaining the large observed
column densities of highly ionized gas in the CGM, traced by far ultraviolet
(FUV) transitions like O VI, for longer than a Gyr requires a significant
source of energy that cannot be supplied by galactic supernovae and stellar
winds alone (Mathews & Prochaska, 2017, but see Faerman et al. (2020, 2022)).
If these are the only energy sources, McQuinn & Werk (2018) asserts that much
of a galaxy’s energy budget must be expended in the CGM (rather than the ISM).
SMBHs may provide a promising source of far-reaching intermittent feedback
shocks that can keep the gas in the CGM warm and highly ionized (T $>10^{5}$).
More specifically, the energy released from building a SMBH not only exceeds
the binding energy of the gas in the bulge (by orders of magnitude), but can
easily exceed the binding energy of the entire gaseous halo (Oppenheimer,
2018). Therefore, even with a low efficiency of the SMBH rest mass energy
being imparted to the gaseous halo over its history, the mass and the
energetics of the CGM can be significantly affected.

In combination with established black hole scaling relations, these arguments
imply that the mass of a SMBH may be a key determinant for the content and
kinematics of the CGM around L⋆ galaxies. There are already established
physical links (i.e. scaling relationships) for galaxies on black hole scales
(sub-pc) and stellar-disk scales (kpc). If these relationships are combined
with the expectation that the extended gaseous halos of galaxies fuel their
star formation, it is possible that the evolution of a galaxy’s central black
hole likewise physically links to the properties of galactic gas on CGM scales
(tens to hundreds of kpc). Our present survey, which we call COS-Holes, seeks
to examine whether such a correlation exists between the pc-scale physics of
black hole growth and the global, kpc-scale gas flows of the CGM that fuels
star formation (Oppenheimer et al., 2020; Nelson et al., 2018a; Sanchez et
al., 2019).

In the last five years, simulation work has already suggested that feedback
from a galaxy’s SMBH impacts the content and ionization state of its CGM, but
they have differing views on the role the SMBH ultimately plays. Results from
studies using the cosmological simulations TNG (Nelson et al., 2018b), EAGLE
(Davies et al., 2019; Oppenheimer et al., 2020), and Romulus (Tremmel et al.,
2017) suggest that the SMBH at the center of galaxies enriches the CGM by
driving metals out of the disk and into the halo. However in EAGLE and TNG,
galaxies that host more massive BHs can provide a significant amount of energy
over time which transport baryons beyond the virial radius, ultimately
reducing gas accretion, overall star formation, and the total density of the
CGM. Using O VI, demonstrated to be a sensitive probe of SMBH feedback,
Sanchez et al. (2019) reports a contrasting view to the role of the SMBH
outlined above. Results from Romulus do not show evacuation of CGM gas into
the IGM, but rather suggest that galaxies with more massive BHs are more
likely to have a more-metal enriched (higher ion column density) CGM. Due to
these opposing simulation predictions, it is imperative to empirically test
the role SMBH feedback plays (if any) in setting the content of the CGM.

This work examines the observed relationship, if any, between black hole
growth over long timescales (parameterized by a dynamically-measured SMBH
mass) and the gas content and kinematics within the extended halos of
galaxies. In addition, we compare these observations to predictions from
cosmological simulations. Our novel sample of stellar- and halo-mass
controlled nearby galaxies ($z<$ 0.005; Figure 1) host a wide range of
dynamically resolved SMBHs (log10 MBH $\sim$ 6.8-8.4) and FUV bright QSOs at
impact parameters between 25 $<$ Rproj $<$ 130 kpc.

This paper proceeds as follows: §2 describes the sample selection §2.1, FUV
spectroscopy §2.1.1, and data reduction and analysis for the COS-Holes sample
§2.3; §3 presents the BH mass estimates for archival data collected to
increase the sample size; §4 presents general trends for the COS-Holes sample
(§4.1), the radial profile for the COS-Holes+Literature sample (§4.2),
multivariate analysis and statistics done on the sample (§4.2.1), and the
minimum mass of carbon seen in the CGM of the sample (§4.3); §5 describes the
three simulations used in this paper (§5.1) and presents the results of the
simulated values compared to the results of the combined sample (§5.3); §6
presents a discussion of sSFR dependence in C IV ionization (§6.1) and whether
BHs evacuate their CGMs or not (§6.2); lastly we present a summary of our
conclusions in §7. In this work, we assume a flat-universe $\Lambda$CDM
cosmology with $H_{0}$ = 67.8 km s-1 Mpc-1 and $\Omega_{m}$ = 0.308 (Planck
Collaboration et al., 2016).

##  2 Observation and Data Analysis

###  2.1 Sample Selection

Figure 1: Top: SDSS images of each of the 8 target galaxies in the sample, with exception of NGC 1097, with the image from ESO. The physical scale (in kpc) in each galaxy’s rest-frame is shown at the top of its 6’$\times$6’ stamp. The targeted QSOs lie outside of the shown FOV; blue arrows and text display the direction, and distance to each FUV-bright QSO. One galaxy, NGC 4258, has two UV-bright QSOs at $<$130 kpc. Bottom: Target figure showing the distribution of QSO position angles (blue x’s) on the sky with respect to the target galaxies (shifted to the center, yellow star). On the left, the radial coordinate (Rproj) is in physical kpc at the galaxy redshift, and on the right, this coordinate is translated to the fraction of galaxy’s virial radius, Rproj/R200c, at which the sightline intercepts the halo. No knowledge of galaxy disk orientation or inclination with respect to the sightline is implied here.  Table 1: Galaxy Sample Properties Galaxy | RA | Dec | $z$ | Morph | D | sSFR | M∗ | M200c | MBH
---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) |  |  | (Mpc) | (log10 yr-1) | (log10M⊙) | (log10M⊙) | (log10M⊙)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
NGC 1097 | 41.579 | -30.275 | 0.0042 | SB(s)b | 14.50 a | -9.7 | 10.5 | 11.75 | 8.14$\pm$0.090
NGC 3414 | 162.818 | 27.975 | 0.0049 | S0 | 25.20$\pm$2.74 b | -11.8 | 10.8 | 12.29 | 8.40 $\pm$ 0.07
NGC 3489 | 165.078 | 13.901 | 0.0022 | SABa | 11.98 c | -11.2 | 10.2 | 11.45 | 6.77$\pm$0.065
NGC 3627 | 170.063 | 12.991 | 0.0024 | SAB(s)b | 10.05$\pm$1.09 b | -10.3 | 10.8 | 12.41 | 6.92$\pm$0.048
NGC 4026 | 179.855 | 50.962 | 0.0033 | S0 | 13.35 c | -12.2 | 10.4 | 11.66 | 8.26$\pm$0.120
NGC 4258 | 184.740 | 47.304 | 0.0015 | SABbc | 7.27$\pm$0.50 b | -10.9 | 10.9 | 12.51 | 7.58$\pm$0.030
NGC 4564 | 189.113 | 11.439 | 0.0038 | S0 | 15.94 c | -12.4 | 10.4 | 11.63 | 7.94$\pm$0.140
NGC 4736 | 192.721 | 41.121 | 0.0010 | Sab | 5.00$\pm$0.79 b | -10.7 | 10.6 | 11.94 | 6.83$\pm$0.120
Table 2: Background QSO Properties QSO | RA | Dec | z | Rproj | Rproj/R200c | Mag | Mag | NORB
---|---|---|---|---|---|---|---|---
| (deg) | (deg) |  | (kpc) |  | (FUV) | (NUV) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
UVQSJ024649.87-300741.5 | 41.707792 | -30.128194 | 0.524 | 55.66 | 0.32 | 18.46 | 17.9 | 4
SDSSJ105115.75+280527.1 | 162.81564 | 28.090865 | 0.423 | 40.50 | 0.15 | 18.2 | 17.75 | 4
SDSSJ110139.76+142953.4 | 165.4157 | 14.498172 | 0.635 | 110.00 | 0.80 | 18.99 | 18.70 | 7
SDSSJ112304.91+125748.0 | 170.77049 | 12.963349 | 0.315 | 120.00 | 0.42 | 18.76 | 18.34 | 6
SDSSJ115901.72+510630.7 | 179.75718 | 51.108554 | 0.524 | 37.38 | 0.23 | 18.72 | 18.36 | 4
SDSSJ122046.61+464347.5 | 185.19421 | 46.729881 | 0.707 | 69.78 | 0.22 | 18.82 | 18.21 | 6
UVQSJ122208.10+461250.1 | 185.53375 | 46.213917 | 0.111 | 130.30 | 0.42 | 18.30 | 18.11 | 4
LBQS-1235+1123 | 189.43571 | 11.116143 | 0.949 | 123.10 | 0.77 | 18.99 | 17.93 | 7
SDSSJ124939.06+412243.5 | 192.41277 | 41.378773 | 0.368 | 25.52 | 0.13 | 18.62 | 18.55 | 6

The COS-Holes Survey consists of nine UV-bright QSOs, z $<$ 0.005, probing the
halos of eight galaxies at impact parameters Rproj $\sim$ 25-130 kpc as seen
in Figure 1. To build the survey, we cross-matched the SDSS DR14 QSO catalog
(Pâris et al., 2018) and the UVQS (Monroe et al., 2016) QSO catalogs with
several published catalogs of galaxy BH masses (Kormendy & Ho, 2013; McConnell
& Ma, 2013; Bentz & Katz, 2015; Läsker et al., 2016; van den Bosch, 2016;
Terrazas et al., 2017) to search for FUV bright QSOs (GALEX
M${}_{\mathrm{FUV}}<$ 19) within 150 kpc projected distance from the galaxies
in their rest frames. By design, the resulting sample contains galaxies that
have dynamically determined SMBH masses (e.g. through stellar dynamics,
ionized gas dynamics, CO molecular gas disk dynamics, maser disk dynamics etc)
determined. We note that we did not select our galaxies based on assembly
history or morphology. We acknowledge that recent results have shown that
disruptions in the disk (either by merger or similar event) can be an
important factor for how BHs grow and affect the CGM (Davies et al., 2022,
2024); however testing for these morphological differences in the galaxies and
how that affects the properties of the CGM is beyond the scope of this work.
The property cuts implemented for our sample, as described below, were
strategically made to match similar cuts made for previous surveys searching
for highly ionized gas (COS-Halos; Tumlinson et al., 2011; Werk et al., 2012)
within the cool and intermediate temperature phase of the CGM (Tumlinson et
al., 2017); what sets our sample apart, however, is our focus on galaxies that
have accurately measured BH masses in order to determine how they impact the
state of the CGM.

To start, we eliminate from the sample any galaxies in dense cluster
environments (e.g. Virgo) which have already been shown to possess
significantly less gas than galaxies in more isolated environments (Yoon et
al., 2012; Burchett et al., 2018). We check the GALEX NUV magnitudes of our
targets for large values of NUV-FUV colors, which would potentially indicate
the presence of a strong Lyman Limit system (N${}_{\mathrm{HI}}\geqslant
10^{17}$ cm-2; LLS) along the line of sight that may have contaminated our
transitions of interest. We note that this process does not introduce a bias
to the sample selection since the LLS absorption would be at unrelated higher
redshifts than our targets.

It is known that AGN feedback can be highly directional and not necessarily
aligned with the spin axis of the galaxy (Bentz et al., 2023). However, we
choose not to include QSOs that probe the halos of galaxies with black holes
that are currently accreting as Seyferts or quasars themselves, as done in
Berg et al. (2018). Instead, we are more interested in the long term effects
the black hole has on the halo and and thus selected galaxies based on their
stellar mass, redshift, and having a dynamically-measured black-hole mass
available. None of the galaxies in our sample is classified as an AGN in the
mid-infrared photometrically-selected sample of Asmus et al. (2020), using a
method that has a 90% reliability in selecting AGN (Assef et al., 2018). We
note however, that many of our galaxies do exhibit LINER-like emission in
their central regions, possibly indicating a low-luminosity, accretion-powered
active nucleus (e.g. Molina et al., 2018). LINER emission is quite common
among nearby, L⋆ spiral galaxies, and it can be related to AGN phenomena,
although this relation is uncertain and poorly-quantified (Ho et al., 1997).

In addition, there can be an azimuthal dependence of ion absorption in disk
dominated galaxies. For example, it has been shown that there is a strong
azimuthal dependence with Mg II (Bordoloi et al., 2011), but for O VI the
correlation along the major and minor axes are less clear (Kacprzak et al.,
2019). These dependencies have not been demonstrated for C IV and
investigating them in the COS-Holes sample is beyond the scope of this work.
Moreover, as seen in Figure 1, some of our galaxies are too face on to report
accurate azimuthal angles. The remaining galaxies have azimuthal angles
consistent with a random distribution, and thus any azimuthal angle dependence
of CGM CIV will not play a significant role in driving the trends (or lack
thereof) we observe.

Finally, the nearby galaxy NGC 4258 which has a highly accurate BH-mass
measurement from megamaser kinematics (Miyoshi et al., 1995), is
serendipitously intersected by two inner-CGM QSO sightlines at 70 and 130 kpc.
We include both QSO targets in our final sample because it offers a rare
opportunity to study subtle variations (e.g. column density, kinematics, etc.)
within a single halo.

We selected a sample of galaxies with stellar masses spanning a narrow range
around M* ($\approx 10^{10.5}$ M⊙), since stellar mass has been found to
correlate with ionized CGM content (e.g. Tchernyshyov et al. (2022)). We
estimate the halo masses of our sample by following the same method as
outlined in CGM2 by Tchernyshyov et al. (2022). Using the stellar mass-halo
relation, as defined in Tab J1 of Behroozi et al. (2019), in combination with
the approach laid out in Hu & Kravtsov (2003), we convert the halo masses to
match the convention where the average mass density within the halo radius is
200 times the critical density of the universe. We denote these halo masses
and the corresponding virial radii as M200c and R200c. The final range of
stellar and halo masses for the sample are log10M⋆/M⊙ $\sim$ 10.2-10.9 and
log10Mhalo/M⊙ $\sim$ 11.45-12.51 respectively. We note that a stellar mass of
$\approx$1010.5 M⊙, is representative of L⋆ galaxies, but also can also be a
transitional stellar mass in terms of sSFR which is known to correlate with
CGM properties in intermediate ionization states (Tchernyshyov et al., 2023).
However, by keeping the range of stellar and halo masses relatively small we
minimize the scatter due to these properties and enable a controlled
examination of the role SMBHs and SFR play in shaping the properties of the
CGM. The galaxy and QSO properties for the sample can be found in Tables 1 and
2 respectively.

####  2.1.1 Star Formation Rates

We obtain star formation rates (SFRs) for the COS-Holes sample from Terrazas
et al. (2017) in §4. For the three galaxies in our survey not included in
their sample (NGC 3489, NGC4026, and NGC 4564), we calculate their
corresponding SFRs using the same methodology; we summarize the procedure here
but a detailed description can be found in Bell (2003) and Terrazas et al.
(2016). We calculate far-infrared (FIR) SFRs by using Eq. (A1) in Bell (2003)
which uses 60 and 100 $\rm\mu$m IRAS fluxes to estimate the FIR flux. We then
estimate the total infrared (TIR) flux via TIR = 2 $\times$ FIR (Bell, 2003).
Finally, the TIR-derived SFR is calculated using Eq. 12 in Kennicutt & Evans
(2012):

$\log_{10}\rm
SFR_{\mathrm{TIR}}(M_{\odot}\mathrm{yr}^{-1})=\log_{10}L_{\mathrm{TIR}}-43.41$
(1)

where LTIR is the TIR luminosity calculated from the TIR flux estimates and
distances to the galaxy (for consistency we use the same distances presented
in (Terrazas et al., 2017); for more detailed information, see Table 1). We
note that for NGC 3489, only 65 and 90 $\mu$m fluxes from AKARI were available
on NED111The NASA/IPAC Extragalactic Database (NED) is funded by the National
Aeronautics and Space Administration and operated by the California Institute
of Technology. and we use those values to calculate its respective SFR. To
present the calculated SFRs as log10sSFRs (which range between -12.4 and -9.7)
in Table 1, we divide them by the stellar mass of the galaxy. Typical stellar
mass uncertainties derived from SDSS photometry are $\pm$50$\%$ (Blanton &
Roweis, 2007; Kauffmann et al., 2003) (approximately 0.2 dex) and the SFR
errors derived from infrared photemetry are approximately 0.2-0.3 dex (Rieke
et al., 2009; Terrazas et al., 2017).

###  2.2 COS Spectroscopy

The quasar spectra for the COS-Holes survey were taken using the G160M grating
on the Cosmic Origins Spectrograph (COS; Froning & Green, 2009; Green et al.,
2012) on the Hubble Space Telescope as a part of a 55-orbit Cycle 29 HST
Program (PID$\\#$16650). The primary spectral features of interest were
absorption lines from the doublets C IV ($\lambda\lambda$1548, 1550) and Si IV
($\lambda\lambda$1393, 1402).

C IV is the highest ionization state transition available at these low
redshifts (z $<$ 0.005) where dynamical black hole masses are available, and
is easily detectable in the UV. We note that C IV is an “intermediate” ion
with a potential energy of 47.89 eV required to ionize C III into C IV. In
collisional ionization equilibrium (CIE) C IV reaches a peak ion fraction at a
temperature of 1.2$\times 10^{5}$ K (105.1) and falls rapidly at higher
temperatures, with less than 10$\%$ at 1.6$\times 10^{5}$ K (105.2) (Gnat &
Sternberg, 2007). In photoionization equilibrium (PIE), it peaks at a density
of nH $\approx$ 2$\times 10^{-5}$ cm-3 at $z=$ 0 (Haardt & Madau, 2012a;
Khaire & Srianand, 2019). Thus, in CGM conditions, it can form either through
photo-ionization or collisional ionization (Tumlinson et al., 2017). In EAGLE,
Oppenheimer et al. (2020) found that C IV is a very good tracer of CGM gas
between T$=10{{}^{4}}-10{{}^{5}}$ K and n${}_{H}=10^{-5}-10^{-3}$ cm-3. While
it is beyond the scope of this work to constrain the precise phase of C IV, we
highlight that we are explicitly avoiding characterization of the hot CGM (T
$\approx$ 106 K).

The COS-Holes QSOs have FUV magnitudes of 18.2 - 19.0 and redshifts ranging
from 0.3 $-$ 0.9, and we observed each target QSO for between 4 and 7 orbits
in G160M with a central wavelength of 1577 Å. Our exposure times were
calculated to detect a 40 mÅ feature at 2$\sigma$, consistent with detected C
IV around $\sim$ 0.1 - 1 L⋆ galaxies in the literature (Borthakur et al.,
2013; Bordoloi et al., 2014; Burchett et al., 2016). All spectra achieved a
S/N of 10 - 12 per resel at the wavelengths of C IV.

We combine the CALCOS-generated x1D files using v3.1.1 of the COADD_X1D
routine provided by the COS-GTO team (Danforth et al., 2016), which properly
treats the error arrays of the input files using Poisson statistics. The code
aligns the different exposures by determining a constant offset determined by
cross-correlating strong ISM lines in a 10Å wide region of the spectrum. The
COS line-spread function (LSF) is well described by a Gaussian convolved with
a power law that extends to many tens of pixels beyond the line center (Green
et al., 2012). These broad wings affect both the precision of our equivalent
width measurements and complicate assessments of line saturation. We mediate
these effects by fitting absorption lines with Voigt profiles that incorporate
the COS LSF. Each COS resolution element at R $\sim$18,000 covers 16 km s-1
and is sampled by six raw pixels. We perform our analysis on the data binned
by three native spectral pixels to a dispersion of $\Delta\lambda$ $\approx$
0.0367 Å. The resulting science-grade spectra are characterized by a FWHM
$\approx$ 16 km s-1. We perform continuum fitting with the linetools
package222https://doi.org/10.5281/zenodo.1036773, an open-source code for
analysis of 1D spectra.

###  2.3 Absorption Line Measurements

This section describes the methods used to measure and calculate key
observational properties, presented in Table 3. §4 discusses the column
densities versus key galaxy parameters (Figure 3).

####  2.3.1 Line identification with PyIGM

We manually assign line identifications and redshifts to all absorption
features in the spectra using the PyIGM IGMGuesses
GUI333https://doi.org/10.5281/zenodo.1045480. To make sure that we correctly
attribute absorption to a COS-Holes galaxy’s CGM rather than another absorber
at a different redshift, we implement the following methodology. First, we
identify absorption features at $z$ = 0, the redshift of the Milky Way. We
then identify any “proximate” absorption at the redshift of the QSO observed.
Finally, we examine the spectra for Lyman series lines at redshifts $<z_{\rm
QSO}$ to find serendipitous absorption systems. After identifying these
features, we move to the redshift of the target galaxy to look for any
absorption features within $\sim$300 km/s associated with C IV
($\lambda\lambda$1548, 1550), similar to the COS-Halos Survey (Werk et al.,
2013). For this paper we specifically focus on C IV identifications and
analysis even though other ions (e.g, Si IV $\lambda\lambda$1393, 1402) were
observable; in future work we plan on analysing other ion absorption features
present. We obtain preliminary line profile fits including the following
parameters: central velocity $v$, column density $N$, and Doppler parameter,
$b$; we then input these user specified parameters into a Voigt profile
fitting program.

####  2.3.2 Voigt Profile Fitting

Figure 2: Representative C IV absorption feature of a QSO-galaxy pair
(SDSSJ1051-NGC 3414) set in the rest frame of the galaxy. The colored line
represents the Voigt profile fit due to the $\lambda\lambda$1548 1550 lines in
the top and bottom panels respectively. The values in the labels correspond to
the following: ionic species, wavelength, absorption feature redshift, column
density (log10NCIV) [cm-2], and doppler parameter [km s-1]. In the bottom left
hand corner of the figure is the reduced chi squared for the fit made to each
absorption feature. The spectra for the rest of the COS-Holes sample are
presented in Appendix A.

Based on the identifications from PyIGM IGMGuesses GUI, we measure C IV column
densities, Doppler parameter, and the relative velocity of the absorption
components using Voigt profile fitting with the package
veeper444https://zenodo.org/doi/10.5281/zenodo.10993983, which uses
scipy.optimize.least_squares555https://doi.org/10.1038/s41592-019-0686-2 to
perfrom a least squares minimization. In five of our QSO-galaxy line-of-sight
pairs we detect C IV while the other four were non-detections and we report
them as upper limits. In the spectral regions with no detected metal
absorption, we calculate a 2$\sigma$ upper limit on the column density as
estimated by the apparent optical depth method (AODM) with the linetools
XSpectrum1D package666https://doi.org/10.5281/zenodo.1036773 over a 100 km s-1
velocity span centered on the galaxy redshift. By default, we use the stronger
line at 1548Å to estimate $2\sigma$ equivalent width upper limits, similar to
the AOD method, using linetools XSpectrum1D, but in cases where there is
blending or contamination, we use the 1550Å line. When multiple absorption
components are found in a galaxy’s search window, their column densities are
summed, and then this total column density is associated with the galaxy.
Figure 2 displays the line profile for the C IV ($\lambda\lambda$1548, 1550)
absorption doublet for NGC 3414 as a representative Voigt profile for the
entire COS-Holes sample. The spectra showing C IV (or upper limits) for the
rest of the survey are presented in Appendix A.

Table 3: COS-Holes Measurements Galaxy | QSO ID | $z_{\mathrm{abs}}$ | log10NCIV | $b$ | EW | $|v_{\mathrm{rel}}|$
---|---|---|---|---|---|---
|  |  | (cm-2) | (km s-1) | (mÅ) | (km s-1)
(1) | (2) | (3) | (4) | (5) | (6) | (7)
NGC 1097 | UVQSJ0246 | 0.00426 | 14.14$\pm$0.05 | 55.60$\pm$7.58 | 323.84$\pm$33.38 | 2.01
NGC 1097 | UVQSJ0246 | 0.00471 | 13.71$\pm$0.10 | 15.36$\pm$6.09 | 109.54$\pm$27.27 | 145.38
NGC 3414 | SDSSJ1051 | 0.00443 | 13.88$\pm$0.05 | 35.26$\pm$6.06 | 235.30$\pm$26.86 | 148.32
NGC 3489 | SDSSJ1101 | 0.00229 | 13.44$\pm$0.10 | 22.95$\pm$8.90 | 106.52$\pm$19.55 | 30.88
NGC 3627 | SDSSJ1123 | 0.00287 | 13.89$\pm$0.07 | 85.00$\pm$18.33 | 230.70$\pm$41.64 | 152.24
NGC 4026 | SDSSJ1159 | 0.0033 |  $<$13.24 |  |  $<$73.10 | 0
NGC 4258 | SDSSJ1220 | 0.001494 |  $<$13.47 |  |  $<$60.32 | 0
NGC 4258 | UVQSJ1222 | 0.001494 |  $<$13.39 |  |  $<$50.20 | 0
NGC 4564 | LBQS-1235 | 0.0038 |  $<$13.40 |  |  $<$58.21 | 0
NGC 4736 | SDSSJ1249 | 0.00054 | 13.75$\pm$0.05 | 32.39$\pm$6.30 | 186.38$\pm$17.07 | 148.55
NGC 4736 | SDSSJ1249 | 0.00083 | 13.48$\pm$0.10 | 11.53$\pm$6.33 | 95.97$\pm$12.53 | 47.32
NGC 4736 | SDSSJ1249 | 0.00111 | 13.86$\pm$0.05 | 37.78$\pm$5.91 | 217.64$\pm$19.25 | 43.94

##  3 Archival Observations & BH Mass Estimations

We increase our sample size with CGM C IV measurements using published HST/COS
data from Borthakur et al. (2013) (starbursts), Werk et al. (2013) (COS-
Halos), Bordoloi et al. (2014) (COS-Dwarfs), and Lehner et al. (2020) (Project
AMIGA). M31 has a measured SMBH mass of log10MBH/M⊙ = 8.15 $\pm$ 0.24 (Davis
et al., 2017) and a stellar mass of log10M⋆/M⊙ = 10.9 $\pm$ 0.22 (Williams et
al., 2017), both of which are within range of the COS-Holes galaxy properties.
Through the use of several QSO sightlines, it has a well studied CGM (Project
AMIGA; Lehner et al. (2020)). To match the COS-Holes sample we only include
sightlines from Project AMIGA if their corresponding impact parameter was
$\leq$ 150 kpc and did not have any contamination from the Magellanic Stream;
for a more detailed explanation of how this contamination was removed, see
Lehner et al. (2020). If a sightline contained C IV and had multiple
absorption features, we sum the measured NCIV to present a total column
density, similar to COS-Halos. We note that having a plethora of QSO
sightlines provides the opportunity to compare single QSO-galaxy sightline
derived CGM properties to a galaxy with multiple sightlines. However, with
this reduced sample of Project AMIGA observations, we choose to take an
average of the column densities to represent a singular mean NCIV for the
Project AMIGA observations. This allows us to have a consistent Literature
sample and not bias any results towards features seen in M31.

Similarly to M31, we only include NCIV measurements from galaxies if they had
a stellar mass that fell within the range of our COS-Holes observations
(log10M⋆/M⊙ = $10^{10}-10^{11}$); by making these cuts we add four galaxies
from Borthakur et al. (2013), five from Bordoloi et al. (2014), and two from
Werk et al. (2013) (COS-Halos) to the Literature sample. Since galaxies from
these surveys do not have dynamically measured BH masses, we estimate the SMBH
mass for each galaxy using the following approximation from Eq. 7 in
Piotrowska et al. (2022); Saglia et al. (2016):

$\rm log_{10}\rm M_{\mathrm{BH}}=5.246\times\rm log_{10}\sigma_{c}-3.77$ (2)

where $\sigma_{c}$ is the central stellar velocity dispersion of the galaxy,
or the random line-of-sight motion of stars due to the galaxy’s gravitational
potential well.

We obtain central stellar velocity dispersion measurements from the SDSS DR7
value-added catalog777gal_info_dr7_v5_2 (Abdurro’uf et al., 2022) for our
selected sample of galaxies from Borthakur et al. (2013) and Bordoloi et al.
(2014). These SDSS $\sigma_{c}$ values are the superposition of many
individual stellar spectra that were Doppler shifted due to the star’s motion
within each galaxy and their measurements were made by analyzing the
integrated spectrum of the whole galaxy. We acknowledge that estimating
measurements for $\sigma_{c}$ can be complex due to several components that
can dominate the integrated spectra, either from different stellar populations
and/or kinematics in the bulge and the disk. However, these complexities were
taken into account in the SDSS catalog where velocity dispersion estimates
were only measured for spheroidal systems whose spectra satisfied certain
specifications (e.g. galaxy type, $z<$ 0.4, etc). In addition, it is
recommended to only use SDSS velocity dispersion measurements $>$ 70 km s-1
(due to the SDSS instrumental resolution) for spectra with a median per-pixel
S/N $>$ 10; for more information about how these velocity dispersions were
measured and how their biases were corrected see Bernardi (2007).

All the galaxies from Borthakur et al. (2013) and Bordoloi et al. (2014) (nine
total) have median per-pixel S/N $>$ 10 and the average $\sigma_{\rm c}$ value
for the galaxies with velocity dispersion measurements $>$ 70 km s-1 is
111.59$\pm$17.18 km s-1. Four galaxies from Bordoloi et al. (2014) have
stellar velocity dispersion measurements $<$ 70 km s-1. We report these as
upper limits and use 70 km s-1 in our log10MBH/M⊙ estimates which correspond
to a value of $<$ 5.91. As this is close to the lower bound of the BH mass
range for the COS-Holes survey, and the SDSS fiber spectra is not sensitive to
BH estimates lower than this value, we do not believe that adding these BH
mass estimations bias the new combined sample. For those galaxies drawn from
the COS-Halos sample (Werk et al., 2013), where SDSS fiber spectra of the
galaxies were not available, we use the python package
pPXF888https://pypi.org/project/ppxf/ to analyze the Keck LRIS spectra (COS-
Halos; Werk et al., 2012). This package calculates a central velocity
dispersion from the optical LRIS spectrum; for more clarification on
techniques see Koss et al. (2022). The uncertainties on the BH masses for the
literature sample are roughly a factor of five larger than those from the COS-
Holes sample with dynamically-measured BH-masses.

We use the package KaplanMeierFitter from the python package
LIFELINES999https://doi.org/10.5281/zenodo.10456828 which implements
Greenwood’s uncertainty estimate, to determine the average log10MBH/M⊙ for
both the literature and the COS-Holes sample. Kaplan-Meier is a non-parametric
technique of estimating the survival probability of a set of data and is
useful since it assumes that censored observations (upper limits) have the
same survival prospects as observations that continue to be followed. For the
literature sample, with 95$\%$ confidence intervals, we find the average
log10MBH/M⊙ to be 7.40(6.10, 7.71); this is comparable to the COS-Holes
average log10MBH/M⊙ of 7.58(6.77, 8.255). This sample of 12 additional
galaxies adds a wider range of galaxies black hole masses to the sample and
statistical power to our analysis, especially in §4.2. The collective
information for the additional Literature sample can be seen in Appendix B in
Tables 6 and 7 respectively.

##  4 Observational Results

Figure 3: Measured C IV column densities versus log10MBH. Each data point is
colored with by the specific star formation rate (sSFR) and each marker size
corresponds to the respective impact parameter. Unfilled circles represent
2$\sigma$ upper limits. There is a wide spread in the C IV column densities as
black hole mass increases; interestingly, there is a slight trend with sSFR
and column density. Galaxies with low observed column density
(log10N${}_{\mathrm{CIV}}\leq$ 13.5) tend to be less star forming (sSFR
$\lesssim$ -11.0) than galaxies with higher observed column density.  Figure
4: C IV column densities assembled from previous QSO absorption line surveys
probing the CGM of low-z, log10M⋆/M⊙ = $10^{10}-10^{11}$ galaxies, including
Borthakur et al. (2013), Bordoloi et al. (2014), Werk et al. (2013), and
Lehner et al. (2020) along side our COS-Holes detections. Each observation is
colored by its corresponding SMBH mass, whether that be their dynamically
measured BH mass or estimated using Equation 2. The dark grey line is a linear
regression fit for the combined COS-Holes+Literature sample and is
characterized by Equation 3 with the shaded grey region representing a 95$\%$
confidence interval. We find there is a wide scatter in the COS-
Holes+Literature radial profiles as impact parameter increases. From this
relation alone, we see very little observational evidence that feedback from a
SMBH heavily impacts the ionization state of its CGM. Figure 5: Investigating
the role sSFR plays in driving the ionization content of the CGM across the
combined sample’s range of SMBH masses. Top panels: log10sSFR as a function of
log10MBH (left panel) and log10MBH normalized by the stellar mass (right
panel) colored by $\Delta$log10NCIV (C IV column density corrected for impact
parameter). We present our upper limit observations that have higher column
densities than those predicted by our model (Equation 8) as having a
$\Delta$log10NCIV of zero (yellow coloring). Stars with arrows pointing to the
left represent upper limits on the log10MBH estimations; for a more detailed
description of how these BH masses were estimated, see §3. Bottom panel:
log10sSFR as a function of $\Delta$log10NCIV colored by log10MBH. The dark
grey line is a linear regression, similar to the fit for Figure 4, and
characterized by Equation 8 with 95$\%$ confidence intervals (the shaded grey
region). This strong correlation between sSFR and C IV suggests that sSFR is
more closely tied to the ionization state of the CGM than the BH mass. Figure
6: C IV column density as a function of Rproj,100 colored by log10sSFR for the
COS-Holes+Literature sample. The grey line is characterized by Equation 10 and
has 95$\%$ confidence intervals depicted as the grey shaded regions. The other
solid lines represent an evaluation of a single fit for column density as a
function of Rproj,100 at different values of log10sSFR. The value of log10sSFR
is denoted by their color and label. As log10 sSFR increases from -9.0 to
-12.0, the regression intercept increases and closely follows the gradient of
the observations. This is further evidence showing how dominant sSFR is within
the combined sample.

In this section we examine the effects of SMBH feedback on the state of the
CGM in $\sim$L⋆ galaxies by examining the observational data. The section
proceeds as follows: we investigate the relationship, if any, between NCIV and
MBH for the COS-Holes sample §4.1; §4.2 describes analysis for the COS-Holes
survey with the addition of a subset of published literature observations; and
§4.3 shows our estimate of the minimum mass of carbon in the CGM of our
sample.

###  4.1 COS-Holes General Trends

In Figure 3, we show our measured NCIV for each line of sight versus MBH; each
point is colored by its specific star formation rate (sSFR) and the size
scales by impact parameter. We note that the two sightlines that intersect the
halo of NGC 4258, colored in grey, are upper limits; even though the upper-
limit observations are consistent with each other, studying the variations
within this single halo is not possible with these two sightlines. For
galaxies with a log10M${}_{\rm BH}<$ 7.0 we find a 100$\%$ covering fraction
and a 33$\%$ covering fraction for galaxies with a log10M${}_{\rm BH}>$ 7.0.
However, as black hole mass increases we show a large scatter of $>$1 dex in C
IV column density for this range of MBH. Due to this wide scatter and how
small the sample size is, we suggest that there is no strong identifiable
relationship between these two particular properties seen in the COS-Holes
observations.

Interestingly, there is a different correlation with another galaxy property;
across the MBH range of our sample, galaxies that have low observed C IV
column density (log10N${}_{\mathrm{CIV}}\lesssim$ 13.5 cm-2) are less star
forming (log10sSFR/M⋆ $<$ -11) than galaxies with higher observed column
density. Its difficult to determine if this trend is due to sample selection
and if its causally or significantly correlated, since several factors could
be influencing the C IV content of the CGM. Even so, it raises the question,
how much is the SMBH feedback really impacting observed NCIV in the CGM and do
other galaxy parameters, like sSFR, play a larger role in setting the
ionization state?

###  4.2 COS-Holes & Archival Data

To examine if a relationship dependent on BH mass is observable in the radial
profile, we show log10NCIV versus impact parameter for COS-Holes and the 12
additional literature observations (§3) in Figure 4. Similar to Figure 3 the
COS-Holes observations are represented by the circles and the literature
observations are depicted as stars; all the observations are colored by their
SMBH masses. Log10NCIV weakly declines with the impact parameter within 150
kpc, a trend that has been discussed in a number of previous works (e.g.
Bordoloi et al., 2014). Although there is significant scatter ($>$ 1 dex) in
the combined samples, we find that the average C IV column density of the
literature sample detections (average log10NCIV,Lit = 13.98$\pm$0.08 cm-2) is
comparable to the average C IV column density of the COS-Holes sample (average
log10NCIV,COS-Holes = 13.94$\pm$0.09 cm-2). We find a 52$\%$ covering fraction
for galaxies in the combined sample with C IV absorption above log10NCIV =
13.5 cm-2.

To characterize the radial profile for the combined samples and get a
quantifiable constraint on the observed scatter mentioned above, we fit the
relation between impact parameter and column density with a linear model (the
dark grey line with a dark grey line where the shaded grey region represents
the 95% confidence intervals). The mean column density at some $R_{\rm proj}$
is:

$\log_{10}{\rm N_{C\,IV}/cm^{-2}}=\alpha{\rm R_{proj}/kpc}+\beta.$ (3)

From examining the distribution of column density measurements in narrow
$R_{proj}$ ranges in Figure 4, it is clear that there is column density
scatter beyond what can be explained by the observational uncertainties. We
model this additional scatter about the $\log_{10}$ mean column density trend
as a Gaussian distribution with mean zero and standard deviation $\sigma$. The
prior probability distributions over these parameters are:

$\displaystyle\alpha$ $\displaystyle\sim\text{Normal}(0,1^{2})$ (4)
$\displaystyle\beta$ $\displaystyle\sim\text{Uniform}(10,16)$ (5)
$\displaystyle\sigma$ $\displaystyle\sim\text{Gamma}(2,4),$ (6)

where the gamma distribution parameters are the shape and rate, respectively.
The priors over $\alpha$ and $\beta$ are broad but not infinite. The prior
over $\sigma$ is moderately informative: it has a mean of $1/2$ and a standard
deviation of $1/\sqrt{2}\approx 0.7$.

The dataset includes three kinds of measurements which require different
likelihood functions: detections, upper limits, and lower limits. The
likelihood for a detection is assumed to be a normal distribution with known
mean and standard deviation. The result of convolution with the scatter term
is also a normal distribution. The likelihood for an upper limit is an
improper uniform distribution between negative infinity and the upper limit
value. The convolution with the scatter term is the cumulative distribution
function of a normal distribution with the mean column density trend and
standard deviation $\sigma$. The likelihood and convolution with the scatter
term for lower limits are similar to those of upper limits, but done in the
opposite direction.

We implement this model using the NumPyro101010https://github.com/pyro-
ppl/numpyro probabilitistic programming library, which relies on
JAX111111https://jax.readthedocs.io/en/latest/, and
ArviZ121212https://doi.org/10.5281/zenodo.10436212. To infer values of
$\alpha$, $\beta$, and $\sigma$, we run MCMC using the No-U-Turn Sampler
(NUTS) and collect samples from the posterior probability distribution. The
best-fit coefficients with 95$\%$ confidence intervals are $\alpha$ = -0.0057
(-0.016, 0.0042) and $\beta$ = 14.08 (13.08, 14.93) respectively. Using this
linear model we place constraints on the scatter in the combined COS-
Holes+Literature sample and find that the slope of this relation is consistent
with zero within error bars.

####  4.2.1 Is sSFR Directly Linked to the C IV Content of the CGM?

To investigate the possible trend suggested in Figure 3 between column density
and other galaxy properties, we present the combined COS-Holes+Literature
sample in three different ways as shown in Figure 5. In the top left panel we
investigate sSFR as a function of black hole mass colored by
$\Delta$log10NCIV. These $\Delta$ log10NCIV values, which marginalize the
large scatter in the radial profile (§4.2, were calculated by subtracting the
observed column densities by values estimated from the best fit line depicted
in Figure 4 (Equation 3) and is characterized by the following equation:

$\Delta\rm log_{10}\rm N_{\mathrm{CIV}}=\rm log_{10}N_{\rm CIV,obs}-\rm
log_{10}N_{\mathrm{CIV,Eq3}}.$ (7)

We choose to color the data using these corrected column densities to
normalize the observations with respect to impact parameter for the combined
sample so we can focus on only four parameters: sSFR, MBH, M⋆ and NCIV. A
similar relation is shown in the top right panel, where we present sSFR as a
function of black hole mass normalized by stellar mass colored by $\Delta$
log10NCIV. In both of the top panels there is a clear branching occurring at
log10MBH $>$ 7.0 (log10(MBH/M⋆) $\gtrsim$ -3.5); galaxies that have a
log10sSFR greater than -11.0 appear to have an excess of C IV column density,
while galaxies that have a log10sSFR less than -11.0 seem to have much lower C
IV column densities.

However, when we show sSFR as a function of $\Delta$log10NCIV colored by black
hole mass in the bottom panel, we see that this branching falls away to reveal
a correlation between sSFR and column density. We fit a linear regression to
this relation, using the same method and packages as described for Equation 3,
and is characterized by the following equation:

$\rm log_{10}\rm sSFR/\rm yr^{-1}=\alpha\rm\Delta log_{10}\rm N_{\rm CIV}/\rm
cm^{-2}+\beta.$ (8)

The best-fit coefficients with 95$\%$ confidence intervals are $\alpha$ = 1.8
(1.1, 2.5) and $\beta$ = -11.30 (-11.74, -10.88) respectively. Within this
relation, we do not see any trends with respect to black hole mass, suggesting
that the CGM properties are only loosely tied to black hole growth,if at all.
In the CGM of our combined sample, the sSFR is more closely coupled with
conditions in galactic atmospheres. Since CGM properties vary as a function of
galaxy properties in various and complex ways, quantifying which of these is
the primary driver of the ionization state is challenging. We present two
methods of analysis in which we attempt to quantify the correlations seen
within the combined sample, so we can further build our understanding of how
CGM properties scale with galaxy properties.

####  4.2.2 Bayesian Analysis

Table 4: Multivariate Linear Regression Coefficients coeff | mean | $\sigma$ | 95$\%$ CI
---|---|---|---
(1) | (2) | (3) | (4)
Equation 9
$\alpha$ (slope) | -0.87 | 0.49 | (-1.85, 0.09)
$\gamma$ (log10sSFR coeff) | 0.57 | 0.21 | (0.16, 0.98)
$\delta$ (log10M⋆ coeff) | -0.57 | 0.88 | (-3.20, 1.25)
$\epsilon$ (log10MBH coeff) | 0.26 | 0.33 | (-0.43, 0.76)
$\beta$ (intercept) | 14.04 | 0.44 | (13.14, 14.88)
Equation 10
$\alpha$ (slope) | -0.84 | 0.45 | (-1.73, 0.05)
$\gamma$ (log10sSFR coeff) | 0.49 | 0.17 | (0.17, 0.84)
$\beta$ (intercept) | 14.13 | 0.38 | (13.37, 14.89)

To examine the effect of Rproj, sSFR, M⋆, and MBH on the C IV column density
at increasing impact parameter, we perform several multivariate linear
regression analyses. Building upon the Bayseian linear regression model
discussed in §4.2, we include the galaxy properties mentioned above. We center
log10sSFR/yr-1, log10M⋆/M⊙, and log10MBH/M⊙ at -11.0 (typical dividing point
between star-forming and quenched galaxies), 10.5 (middle of the range for the
combined sample), and 7.0 (middle of the range for our combined sample and
point at which branching is seen in top panels of Figure 5) respectively. This
operation makes the intercept $\beta$ more interpretable but has essentially
no effect on the linear relation slopes. We also divide Rproj by 100
(Rproj,100) so that all properties used in the regression would have a similar
dynamic range. In addition, we acknowledge that there are some upper limit MBH
estimations for a few of our galaxies in the combined sample, however our
multivariate linear regression treats these as detections; due to the error
bars for these upper limits, this should not affect the best fit in a
substantial way. The equation for our multivariate regression is described by
the following:

$\begin{split}\log_{10}{\rm N_{C\,IV}/cm^{-2}}=\alpha{\rm R_{proj,100}/kpc}\\\
\ +\ \gamma{\rm\log_{10}(sSFR-(-11.0))/\rm yr^{-1}}\\\ +\delta{\ log_{10}(\rm
M_{\star}-10.5)/\rm M_{\odot}}\\\ +\ \epsilon{\log_{10}(\rm M_{\rm
BH}-7.0)/\rm M_{\odot}}+\beta.\end{split}$ (9)

Looking at the best fit mean coefficients and their standard deviations, given
in Table 4, we can immediately rule out strong correlations with log10M⋆ and
log10MBH. Both of these parameters’ mean coefficients have significance less
than 1$\sigma$ and are unlikely to be driving the regression or impacting the
ionization. The most dominant galaxy parameter, which is greater than zero
with a significance of nearly 3$\sigma$, is log10sSFR and is likely the main
driving component in this relation. To test this assertion, we run a similar
multivariate linear regression, but only including Rproj and sSFR, where the
coefficients and statistics are shown in the bottom half of Table 4 and is
characterized by the following equation:

$\begin{split}\log_{10}{\rm N_{C\,IV}/cm^{-2}}=\alpha{\rm R_{proj,100}/kpc}\\\
\ +\ \gamma{\rm\log_{10}(sSFR-(-11.0))/\rm yr^{-1}}+\beta.\end{split}$ (10)

This relation is shown in Figure 6 as the grey line with its 95$\%$ confidence
intervals depicted as the grey shaded regions. The coefficients and standard
deviations for the new regression remain essentially the same with log10M⋆ and
log10MBH removed, confirming that they are subdominant in setting the
ionization content of the CGM of our combined sample. This is further
demonstrated by the other multivariate linear regressions included in Figure 6
where log10NCIV is plotted as a function of Rproj,100 colored by log10sSFR;
each line evaluates a single fit for column density as a function of Rproj,100
at different values of log10sSFR. As the value of sSFR increases, the
regression intercept increases and changes the relation substantially, and
follows the gradient of the observations, showing how dominant sSFR is within
the combined sample. Based on the strong correlation seen in Figure 5, we
suggest that sSFR of a galaxy is directly linked to the C IV content of the
CGM.

####  4.2.3 Frequentist Analysis

We also investigate the relationship between log10NCIV, log10MBH, and
log10sSFR using frequentist non-parameteric tests. We first use Kendall’s rank
correlation test (also known as a $\tau$ test) to check for a dependence
between column density and black hole mass. Specifically, we use the cenken
function in the NADA R package (Lee, 2020), which can handle censoring (i.e.,
non-detections). The test $p$-value for a correlation between log10NCIV and
log10MBH is greater than 0.05, indicating no evidence for a dependence. The
test $p$-value for log10NCIV and log10sSFR is 0.017, which would correspond to
about $2.3\sigma$ for a normal distribution: a somewhat significant
correlation.

We repeat these tests on an impact-parameter-trend-corrected column density,
$\Delta$log10NCIV. The cenken function in NADA provides the Akritas-Theil-Sen
estimator for the slope and the Turnbull estimator for the intercept of the
linear relation between two variables. We use this functionality to determine
the linear relation between log10NCIV and Rproj, use that linear relation to
get a predicted log10NCIV for each observation, and subtract that from the
observed value to get $\Delta$log10NCIV. We then run Kendall’s rank
correlation tests from the previous paragraph replacing log10NCIV with
$\Delta$log10NCIV.

For $\Delta$log10NCIV and log10MBH, we find a $\tau$ of 0.33 and a p-value of
0.85; for $\Delta$log10NCIV and log10sSFR we find a $\tau$ and p-value of 0.40
and 0.0094, respectively. The results for NCIV and $\Delta$log10NCIV are
comparable and consistent with results from §4.2.2, where we see no
correlation between C IV column density and black hole mass, but there is a
possible correlation with sSFR. This further supports our earlier conclusion
that the SMBH does not have as significant effect on the state of the CGM as
predicted, and that sSFR, with the stronger correlation, is more directly
linked with the C IV content of the CGM.

###  4.3 Minimum Mass of Carbon in the CGM

Following the methods used in Bordoloi et al. (2014), we estimate the carbon
mass in the CGM around our sample of $\sim$L⋆ galaxies. Bordoloi et al. (2014)
obtained their upper limit on carbon mass (Mcarbon) by applying a conservative
ionization correction (assuming $f_{\rm CIV}$ = 0.3) to their values of C IV
mass (MCIV); these estimates were made by assuming ionization equilibrium and
including collisional- and photo-ionization using the CLOUDY photoionization
code (Ferland et al., 1998; Chatzikos et al., 2023). The minimum carbon mass
can be written as:

$\begin{split}M_{\rm carbon}\gtrsim 1.12\times
10^{6}\rm\>M_{\odot}\left(\frac{N_{\rm CIV,\>mean}}{10^{14}\>\rm
cm^{-2}}\right)\\\ \times\left(\frac{\rm R_{\rm proj}}{110\>\rm
kpc}\right){{}^{2}}\times\left(\frac{0.3}{f_{\rm CIV}}\right)\times\rm
C_{f}.\end{split}$ (11)

This calculation assumes that these galaxies conform to global stellar
metallicity relations and the gas-phase mass-metallicity relation.

Inserting typical values for the COS-Holes sample, R${}_{\rm proj}=$ 140 kpc,
covering fraction Cf131313All Cf values are determined above log10NCIV = 13.5
cm-2 44$\%$, and mean column density of our detections N${}_{\rm CIV,mean}=$
$10^{13.94}$ cm-2, we get a minimum mass of Mcarbon/M${}_{\odot}=$ 7.41
$\times$ $10^{5}$. This is about a factor of 2.5 lower than the Mcarbon value
presented in Bordoloi et al. (2014) found for both star-forming and non star-
forming dwarf galaxies using Voigt profile fitted NCIV (1.9$\times 10^{6}$
M⊙). Comparing this value to the total carbon mass in the ISM of L⋆ galaxies,
we find that our minimum carbon mass is approximately a factor of three lower
(e.g. Peeples et al., 2014).

We repeated this calculation for the whole COS-Holes+Literature sample
(R${}_{\rm proj}=$ 150 kpc, covering fraction C${}_{\rm f}=$ 52$\%$, and mean
column density of our detections N${}_{\rm CIV,mean}=$ $10^{13.98}$ cm-2) and
just the star-forming galaxies (log10sSFR/yr-1 $\geq$ -11) in the COS-
Holes+Literature sample (R${}_{\rm proj}=$ 150 kpc, covering fraction
C${}_{\rm f}=$ 60$\%$, and mean column density of our detections N${}_{\rm
CIV,mean}=$ $10^{14.17}$ cm-2) to find a minimum mass of carbon for both
samples to be 1.11 $\times$ $10^{6}$ M⊙ and 1.98 $\times$ $10^{6}$ M⊙
respectively. These values are comparable to those reported in Bordoloi et al.
(2014); the combined COS-Holes + Literature sample has a carbon mass 1.7 times
lower than the value reported for both star-forming and non-star forming
galaxies (1.9$\times 10^{6}$ M⊙), while the the star-forming-galaxy-only
combined sample has a carbon mass only a factor of 1.3 lower (2.6$\times
10^{6}$ M⊙).

##  5 Simulation Results

In this section we compare the observational results of the combined COS-
Holes+Literature sample to results from simulations. The section proceeds as
follows: we describe the three simulations in §5.1.1,5.1.2, and 5.1.3 and
discuss their various C IV column density predictions in §5.2; we compare the
combined COS-Holes+Literature sample to simulated values from our three
simulations in §5.3; and in §5.3.1 we mimic the COS-Holes survey across all
three simulations used in §5.3.

###  5.1 Simulation Descriptions

Here, we briefly describe the three simulations to which we will compare our
results. For more details on these well-known and widely used simulations, we
refer the reader to the citations referenced throughout these sections.

####  5.1.1 Evolution and Assembly of GaLaxies and their Environments (EAGLE)

We compare our observations to a sample galaxies from the EAGLE main
‘Reference’ simulation volume (Ref-L100N1504), originally published in (Schaye
et al., 2015; Crain et al., 2015). This (100 comoving Mpc)3, $1504^{3}$ dark
matter and smooth particle hydrodynamic (SPH) particle run uses a heavily
modified version of the N-body code GADGET (Springel, 2005). EAGLE applies the
pressure-entropy SPH formulation from (Hopkins, 2013), extra parameters
referred to as ANARCHY (Schaye et al., 2015), and assumes cosmology from the
Planck Collaboration et al. (2013) ($\Omega_{m}$ = 0.307, $\Omega_{\Lambda}$ =
0.693, $H_{0}$ = 67.77 km $\rm s^{-1}~{}Mpc^{-1}$). The initial dark matter
and SPH particle masses are 9.7$\times 10^{6}M_{\odot}$ and 1.8$\times
10^{6}M_{\odot}$ respectively.

EAGLE implements the following subgrid physics modules: radiative cooling
(Wiersma et al., 2009a), star formation (Schaye & Dalla Vecchia, 2008),
stellar evolution and metal enrichment (Wiersma et al., 2009b), stellar
feedback (Dalla Vecchia & Schaye, 2012), BH formation accretion, feedback
(Booth & Schaye, 2009; Rosas-Guevara et al., 2015). In regards to the black
holes, EAGLE follows BHs from seed black hole particles with mass
$10^{5}\textit{h}^{-1}M_{\odot}$ (where h=0.6777) placed at the center of
every halo that exceeds a mass of $10^{10}\textit{h}^{-1}M_{\odot}$. The BH
particles grow via Bondi & Hoyle (1944) gas accretion as well as as mergers
with other BHs using the prescription derived by Booth & Schaye (2009).
Stellar and BH feedback operate via thermal prescriptions that heat
surrounding gas to $10^{7.5}\;$K and $10^{8.5}\;$K, respectively. Further
information on these processes and their calibrations are described in Crain
et al. (2015).

The BH energy feedback rate is calculated by tracking the accretion rate onto
BHs using the efficiency

$\dot{E}_{BH}=\frac{\epsilon_{f}\epsilon_{r}}{1-\epsilon_{r}}\dot{M}_{BH}c^{2}$
(12)

where $\epsilon_{r}=0.1$ is the radiative efficiency of the accretion disk and
$\epsilon_{f}=0.15$ is the thermal feedback efficiency. The combined
efficiency prefactors result in a total BH efficiency of 1.67% of the rest
mass energy accreted onto the BH. The BH feedback operates via a single-mode
thermal prescription that heats surround gas particles to $10^{8.5}\;$K.
Energy is stored until a gas particle or particles can be heated to this
temperature to ensure that the feedback is numerically efficient.

####  5.1.2 Romulus25

We also compare our observations to galaxies from the cosmological volume
Romulus25 (hereafter R25; Tremmel et al., 2017). The Romulus25 (25 Mpc)3
volume was run with a $\Lambda$CDM cosmology from Planck Collaboration et al.
(2016) with $\Omega_{0}$ = 0.3086, $\Lambda$ = 0.6914, $h$ = 0.67,
$\sigma_{8}$ = 0.77. R25 is run using the smooth particle hydrodynamics code,
Charm N-body GrAvity Solver (ChaNGa Menon et al., 2015). ChaNGa adopts the
same models as GASOLINE (Wadsley et al., 2004, 2017), including the following
physical prescriptions: cosmic UV background (Haardt & Madau, 2012b), star
formation (using a Kroupa, 2001 IMF), and blastwave supernova feedback
(Ostriker & McKee, 1988; Stinson et al., 2012a), which includes both SNIa and
SNII (Thielemann et al., 1986; Woosley & Weaver, 1995). R25 has a Plummer
softening length of 250 pc and a mass resolution of $3.4\times
10^{5}M_{\odot}$ and $2.1\times 10^{5}M_{\odot}$ for dark matter and gas,
respectively.

R25 includes independent subgrid physics modules for the black hole formation,
accretion, feedback, and dynamical friction as introduced in Tremmel et al.
(2017). Unlike other simulations that use a threshold halo mass to initiate a
BH seeding, BH seed particles with initial mass $10^{6}M_{\odot}$ are required
to form in dense, extremely low metallicity gas to better model SMBH
populations across galaxy mass scales as described in as described in Tremmel
et al. (2017) §5.1. The BH accretion utilizes a modified Bondi-Hoyle
prescription that considers angular momentum support from nearby gas,
resulting in a different physical growth model which uses fewer free
parameters. Thermal feedback energy from the BH is imparted onto the 32
nearest gas particles every time step in the form

$E_{BH}=\epsilon_{r}\epsilon_{f}\dot{M}_{BH}c^{2}dt,$ (13)

where the radiative and feedback efficiencies are $\epsilon_{r}$ = 0.1 and
$\epsilon_{f}$ = 0.02, resulting in a total rest mass energy efficiency of
0.2%. The energy is released every timestep $dt$ in contrast to the EAGLE
prescription that stores energy until a surrounding gas particle can be heated
to its threshold energy.

To calculate the ion column densities from the Romulus25 galaxy suite, we use
the public analysis software,
Pynbody141414https://pynbody.github.io/pynbody/index.html (Pontzen et al.,
2013). Oxygen and metal enrichment from SN and winds is traced throughout the
integration of the simulation. Then, ionization states are post-processed,
assuming optically thin conditions, collicaiton ionization equilibrium, and a
Haardt & Madau (2012a) UV radiation field. Finally, we create models using the
CLOUDY software package (Stinson et al., 2012b; Ferland et al., 2013) for
varying redshift, temperature, and density to calculate individual ion
fractions for each gas particle in every simulated galaxy.

####  5.1.3 IllustrisTNG

The last cosmological simulation that we compare our galaxies to is the
IllustrisTNG simulation, hereafter TNG. The TNG simulations were run with the
moving mesh code AREPO (Springel, 2010), including a magnetic hydrodynamic
(MHD) solver that is seeded with the cosmologically motivated initial
conditions and then follows the magnetic field self-consistently (Pakmor &
Springel, 2013). TNG utilizes values consistent with the Planck Collaboration
et al. (2016) results ($\Omega_{m}$ = 0.3089, $\Omega_{\Lambda}$ = 0.6911, $h$
= 0.6774).

The (100 Mpc)3 TNG simulation, also known as TNG100, is the middle of the
three TNG volume series, providing a balance of volume and resolution,
particularly for intermediate mass halos. The simulation implements several
subgrid processes as part of the TNG model including primordial/metal-line
radiative cooling on microphysical scales, star formation based on a two-phase
subgrid ISM model, evolution of stellar populations and the expected chemical
enrichment/mass loss, galactic-scale outflows from energy-driven, kinetic
winds from stellar feedback, and the seeding, growth and feedback from BHs
(Pillepich et al., 2018). Black holes seeds with mass $8\times
10^{5}\textit{h}^{-1}M_{\odot}$ are initially seeded in halos of $5\times
10^{10}\textit{h}^{-1}M_{\odot}$.

The black hole prescriptions are introduced in Weinberger et al. (2017). Their
dual-model AGN model, incorporates a ‘thermal’ mode injects thermal energy at
high Eddington accretion rates and ‘kinetic’ mode injects kinetic energy at
low Edditington accretion rates. The feedback efficiency for the thermal mode
uses $\epsilon_{r}=0.1$ $\epsilon_{f}=0.2$ from Equation 12 for a total rest-
mass accretion efficiency of $\sim 2$%, which is distributed thermally over
surrounding gas cells. The kinetic mode injects kinetic “pulses” at a total
efficiency that can achieve $\sim 20$% of the accreted rest-mass energy (via
the physical mechanism of Blandford & Znajek (1977)). Randomly oriented, jet-
like pulsed feedback events apply energy directionally, imparting significant
momentum stored across multiple timesteps to avoid dependence on the
simulation timestep. This low accretion rate, kinetic mode generally dominates
for late growing SMBHs above a threshold mass of $M_{\rm BH}\approx
10^{8.1}\,M_{\odot}$ (Davies et al., 2020; Terrazas et al., 2020).

###  5.2 Simulation Predictions

Using EAGLE, Oppenheimer et al. (2020) asserts that the efficiency with which
a SMBH feedback energy is coupled to the CGM is critical for understanding the
process of secular galaxy formation. This can be thought about in a three step
pathway: (1) the formation of the halo, (2) the rapid growth of the BH, and
(3) the lifting by AGN feedback of the baryonic halo reducing the supply of
fuel for star formation. The last point is evidenced by a decrease in heavy
metals in the CGM (such as C IV). These results were heavily based on the work
by Davies et al. (2019) that published an inverse correlation between MBH and
$\textit{f}_{\mathrm{CGM}}$ in EAGLE, suggesting a link between the BH and the
removal of a significant portion of gas from the halo, essentially reducing
CGM accretion and galactic star formation. Oppenheimer et al. (2020) find that
the galaxy BH mass is generally a good indicator of its past feedback history
at masses above log10MBH/M${}_{\odot}\sim$ 7.0. They used high-cadence
snapshot outputs from the EAGLE simulation to determine that significant AGN
episodes directly lift the CGM and significantly reduce (in some cases
quenching) star formation on a $<100$ Myr timescale. Ion tracers including C
IV take longer ($0.5-2.5$ Gyr) to respond, but this sequence generally happens
at $z>1$ for L⋆ galaxies meaning that this ion is an indicator of CGM gas
content by $z=0$.

TNG shows a dramatic decline in the covering factor of O VI from star-forming
to quenched galaxies, as presented by Nelson et al. (2018b). Davies et al.
(2020) explored both TNG and EAGLE to determine how CGM mass depends on BH
mass, finding that the BH feedback energy released during the low-Eddington
kinetic mode in TNG is most strongly anti-correlated with the gas content of
halos in the mass range corresponding to our samples explored here. Hence, the
BH mass itself is not directly deterministic for baryon lifting in TNG, but
the energy released during the kinetic mode (Davies et al., 2020; Voit et al.,
2023). This manifests itself in a strong anti-correlation between BH and CGM
mass, but for BH masses that are above $10^{8}\;M_{\odot}$ where kinetic mode
(and therefore baryon lifting) operate in TNG. Taking these results together,
BH feedback drives the results of star-forming (less massive BHs) galaxies
having higher O VI column density compared to quiescent (more massive BHs)
galaxies (Nelson et al., 2018b). Hence, the driving force depleting ionized
oxygen (and mostly likely C IV as well) is the ejection of mass from the CGM
due to black hole feedback.

In contrast, Sanchez et al. (2019) uses R25 to examine the effects of SMBH
feedback and star formation history (SFH) on the column densities of O VI in
the CGM of galaxies. They determine that the host galaxy’s SMBH transports
metal-rich gas out of the galaxy disk where metals are formed and propagates
it into the CGM. From these results they posit that galaxies with lower mass
BHs (which have experienced less accretion and therefore less feedback) are
likely to have a lower metallicity CGM and vice versa for galaxies with higher
mass BHs leading them to have more metal-enriched material in their host CGM.
Therefore, SMBH feedback impacts the total metal mass in the CGM (but not the
total gas mass) and may play a critical role in galaxy quenching (Sanchez et
al., 2021). In a follow up paper, Sanchez et al. (in prep) measure the SMBH
masses and CGM metal content from a sample of galaxies from R25. They find
higher CGM metal fractions in galaxies with more massive black holes (compared
to their host’s stellar dispersion). In further contrast to EAGLE and TNG,
Sanchez et al. (in prep) find no correlation between $M_{\mathrm{BH}}$ and
$\textit{f}_{CGM}$ indicating that in their galaxies, the SMBH’s influence is
more local, impacting the galaxy’s disk and enriching the CGM without
evacuating gas from the halo.

All of these simulations support the idea that SMBHs transport gas and metals
into the CGM of the host galaxy. However, they differ on their predictions of
how the mass of the SMBH regulates the amount of C IV present in the CGM. The
COS-Holes survey provides the opportunity to constrain these feedback
processes by comparing EAGLE, R25, and TNG predictions. §5.3 compares these
theoretical SMBH feedback prescriptions with our observations.

###  5.3 Comparison to Simulations

Figure 7: Column densities of the combined COS-Holes+Literature sample versus
impact parameter compared to predictions from the EAGLE (top panel), R25
(middle panel) and TNG (bottom panel) simulations. Blue represents the “high”
mass black hole sample (log10M${}_{\mathrm{BH}}>$ 7.0 $M_{\odot}$) while pink
refers to the “low” mass black hole sample (log10MBH $\leq$ 7.0 M⊙). The
corresponding blue and pink lines are the median C IV radial profile
predictions from each simulation (also split based on black hole mass) each
with 16-84$\%$ confidence spreads represented as the shaded region around each
prediction. Like previous figures, unfilled markers represent an upper limit
for that observation. Combined sample column densities agree reasonably with
predictions from EAGLE and TNG and lie above the R25 predictions.

We begin our comparison to simulations by showing the entire observed sample
(COS-Holes+Literature; log10MBH = 5.91 - 8.4 M⊙) to the three simulations. In
Figure 7, we split the observations into two bins divided by log10MBH = 7.0, a
“low”-MBH sample (10 observations, log10MBH $\leq$ 7.0) and a “high”-MBH
sample (11 observations, log10MBH $>$ 7.0). This split is strategically made
to take advantage of the range of BH masses that make up the combined COS-
Holes+Literature sample, but to also investigate the question, “do galaxies
with similar stellar masses, but hosting differing SMBH masses show different
CGM metal contents?”

We first make a broad-brush type comparison between data and simulations by
choosing all galaxies with stellar masses between log10M⋆/M⊙ =
$10^{10}-10^{11}$ in the three simulations, and dividing the samples into two
MBH bins in Fig. 7. This means that the split black hole mass is different
amongst the simulations as they have different MBH distributions as discussed
in §5.1. In EAGLE there are 1993 central galaxies at z $=$ 0.00 with a
dividing MBH=$10^{7.10}$ M⊙. In R25 there are 52 central galaxies at z $=$
0.05 with a dividing MBH=$10^{7.6}$ M⊙. In TNG there are 3049 central galaxies
at z $=$ 0.00 with a dividing MBH=$10^{8.12}$ M⊙. The distribution of black
hole masses for TNG is narrower and more massive than the distributions for
EAGLE and R25; see §5.3.1 for more details. For EAGLE and TNG the C IV column
density radial profiles were calculated using a projection along the $z$ axis
with a total depth of 2 Mpc, while for R25, they were averaged down to R200c.
We choose to plot the simulations predicted column densities versus the true
projected impact parameter, Rproj [kpc], since it is a more direct measurement
that does not rely on estimations from an indirectly observable property (like
using Rproj/R200c which uses dark matter mass).

The radial profiles shown in the top panel of Figure 7 show that the EAGLE
simulation results are in reasonable agreement with the COS-Holes$+$Literature
absorption observations. Interestingly that there is no discernible difference
in the low and high BH mass samples (average log10NCIV = 13.6 cm-2 for both
samples). We note that Oppenheimer et al. (2020) predicted an anti-correlation
between C IV and MBH, but we do not see such a correlation here. This likely
is a result of the slightly larger stellar mass range probed by our COS-Holes
galaxy sample compared to that of Oppenheimer et al. 2020 ($10^{10-11}$ M⊙ vs.
$10^{10.2-10.7}$ M⊙; Oppenheimer et al., 2020). Additionally, they found a
measurable difference in the reduction of C IV column densities for only the
highest quartile of BH masses, whereas here, we have divided the sample into
two, leading us to have similar radial profiles for the split samples.

In the middle panel of Figure 7 where the observations are compared to NCIV
values from R25, we see that the mean predicted column density (log10NCIV =
12.8 cm-2) is on average $\sim$1 dex below our combined sample; thus, there is
little agreement between the combined sample and those predicted by R25. We
see more of a difference between the low and high mass sample R25 predictions
than EAGLE until $\sim$90 kpc where the two samples become more indiscernible.
These results are comparable to averaged radial profiles presented in Fig 14
of Sanchez et al. (in prep) (log10NCIV vs log10(Rproj/R200c)) at the same BH
mass split but are under predicting the C IV column density observed.

For TNG, in the last panel of Figure 7, we see the largest differentiation
between the low and high samples (average log10NCIV = 14.0 and 13.1 cm-2
respectively), which reasonably overlaps with the C IV column densities for
the combined sample. Interestingly, TNG has a much larger spread for their
high-mass sample than any other simulation and sample. While we do see a
population of low C IV values for high MBH, there is also a population with
high C IV for high MBH. A fuller investigation determining why there is such a
spread in C IV for high black hole masses is beyond the scope of this paper.

We note these general trends between each of the simulations, but we cannot
directly compare them to the COS-Holes survey without reproducing the observed
survey, which we now do in §5.3.1.

####  5.3.1 Mocking up the COS-Holes Survey

We create a mock up of the COS-Holes Survey of the nine sight lines by using
the SMOHALOS (Simulation Mocker Of Hubble Absorption Line Observational
Surveys) used first in Oppenheimer et al. (2016) across the three simulations.
In our implementation here, SMOHALOS matches the impact parameter, stellar
mass, and SFR of observed galaxies using a selection of central galaxies taken
from $z=0.00$ simulation outputs. We also attempt to match black hole mass,
but only divide the sample into two using a black hole mass split, MBH,split
that is defined differently for each simulation based on the distribution of
simulated MBH values. In SMOHALOS, the 1-$\sigma$ range of BH masses in EAGLE
spans $10^{6.65}-10^{7.94}{\rm M}_{\odot}$, in R25 spans
$10^{7.27}-10^{8.35}{\rm M}_{\odot}$, and in TNG spans
$10^{7.94}-10^{8.43}{\rm M}_{\odot}$. Briefly, we choose a sight line by
selecting a random pixel in a C IV column density map at an impact parameter
within 5 kpc of an observed sight line around a simulated galaxy that matches
the observed galaxy. We use a projection along the $z$ axis with a total depth
of 2 Mpc. SMOHALOS selects a matching simulated galaxy by taking the observed
galaxy values and adding a random error assuming a Gaussian dispersion, then
finding the simulated galaxy that best fits the observed galaxy’s dispersed
values. We assume dispersions of 0.3 dex to M⋆ and 0.5 dex to SFR, therefore
ensuring we are selecting galaxies that are similar to the COS-Holes sample
but have a random scatter based on reasonable uncertainties in stellar masses
and star formation rates.

We run SMOHALOS for 100 realizations, reporting the results in Table 5. We
first report the median C IV column density from our observations noting the
large range on the high MBH sample due to upper limits (cf. Fig. 3) indicating
the uncertainty in which the sample has more C IV. For the simulations, we are
not limited by upper limits, therefore we present the equivalent of noiseless
column densities for the median and $1-\sigma$ spread in their distribution.

Table 5: SMOHALOS Simulation C IV Comparison Dataset | MBH(split) | Low MBH | High MBH
---|---|---|---
|  | NCIV [cm-2] | NCIV [cm-2]
(1) | (2) | (3) | (4)
Observed | 7.6 | $13.44-13.47$ | $<13.40-13.88$
EAGLE | 7.49 | $13.59^{+0.63}_{-1.15}$ | $13.71^{+0.53}_{-1.06}$
R25 | 8.10 | $12.75^{+1.05}_{-0.77}$ | $12.78^{+0.64}_{-0.63}$
TNG | 8.23 | $13.85^{+0.69}_{-1.49}$ | $13.79^{+0.78}_{-2.61}$

The first result to note is how each simulation compares with the observed
dataset. EAGLE has values that are consistent with both samples, R25 has
values that are significantly lower than observations, and TNG agrees best
with the high MBH sample but appears to over-predict the low MBH sample. In
detail, TNG predicts the largest reduction in C IV with MBH while EAGLE
predicts the largest increase. This agrees with the trends in Fig. 7, but we
note the SMOHALOS sample as well as the split $M_{\rm BH}$ are different. By
selecting matched galaxies, we are sampling a distribution that has a much
smaller difference than, for example TNG would predict for a typical galaxy in
the bottom panel of that figure.

The second result to note is that the simulations all show $0.12$ dex or less
differences in their log10NCIV medians indicating that a COS-Holes is not
large enough to distinguish the different behaviours across the simulations.
Even if there exists different C IV absorption patterns relating to MBH, our
SMOHALOS exploration finds that COS-Holes is too insensitive due to its small
sample size and heterogeneous sample of galaxies.

Finally, we estimate the number of sightlines needed to distinguish between
different C IV distributions as a function of BH mass by replicating the
results from R25. For a set sample size, we interpolate a C IV column density
from a random impact parameter (between 0 and 150 kpc) and assign it to either
the low or high BH mass sample to create a uniform sample. We fit these random
replications to a linear regression model for increasing sample sizes
iteratively to create a distribution. We determine that at least 60 sightlines
for each high and low mass sample would be needed to distinguish between the
samples with a 2$\sigma$ confidence and over 100 sightlines in each sample to
tell with a 3$\sigma$ confidence.

##  6 Discussion

###  6.1 $\Delta$NCIV Dependence on sSFR

We find a $>$2$\sigma$ correlation between the impact-parameter-corrected
column density ($\Delta$NCIV) and sSFR, as shown in Figure 5. In the top
panels of Figure 5, we see a distinct split in $\Delta$NCIV between star-
forming and non-starforming galaxies at log10M${}_{\mathrm{BH}}>$ 7.0. This
dividing point occurs at log10sSFR $\approx$ -11.0. This is consistent with
star-forming (log10sSFR$>-11.0$) and passive (log10sSFR$<-11.0$) galaxies in
the COS-Halos survey (Tumlinson et al., 2011). COS-Halos found that star-
forming galaxies exhibited an OVI covering fraction $>$80%, and higher NOVI
than their passive galaxy counterparts (fC $\approx$ 30%). Building off of
these results, subsequent studies (Johnson et al., 2015; Zahedy et al., 2019;
Tchernyshyov et al., 2023) have established an evident dichotomy in the amount
of O VI present in star-forming and passive galaxies. Controlling for
stellar/halo mass, Tchernyshyov et al. (2023) demonstrated that this dichotomy
persists at high statistical significance. For the first time, we tentatively
confirm with $>2\sigma$ significance that this correlation exists in the C IV-
bearing gas phase as well, even when we control for other potential variables
(see §4 for a discussion of our multivariate analysis).

There is little C IV coverage in other surveys of L⋆ galaxies, and our current
sample size is only 21 galaxies. The CIViL⋆ survey (Berg et al., 2022) will
fill this gap in previous COS absorption-galaxy studies by adding NUV data
covering C IV for many of the L⋆ galaxies of COS-Halos and other surveys which
also have O VI coverage. With the addition of data from this survey, we will
be able to test whether C IV acts more like O VI than a tracer of the photo-
ionized, 104K gas phase. Our current sample indicates that C IV is more O VI-
like than “low-ion-like,” where low-ionization state gas traced by singly and
doubly ionized species shows no correlation with galaxy star-forming
properties (Werk et al., 2013).

While we find a clear trend that exists between $\Delta$NCIV and sSFR (4.2.1),
we note a possible second order connection between the sSFR and $M_{\rm BH}$
as they relate to NCIV (Figure 5, top panels). As discussed above galaxies
with higher sSFRs and MBHs show higher C IV content in the CGM, while galaxies
with similarly high black hole masses but low sSFR maintain lower C IV column
densities. This split trend could indicate that the relationship between sSFR
and black hole mass could result in varying NCIV possibly connected to
overmassive or undermassive black hole characteristics; however, other
evolutionary factors such as galaxy formation time may also play a role (e.g.
Sharma et al. (2020) connects overmassive black hole formation to earlier
galaxy formation).

Results using EAGLE and TNG, have shown that there is an inter-relationship
between intrinsic galaxy halo properties and the properties of the central
galaxy such as sSFR (Davies et al., 2019, 2020). In these simulations,
galaxies with overmassive BHs are more likely to be quenched, and vice vera
(Davies et al., 2020, Fig 2), and these quenched systems almost always have an
evacuated CGM; due to the BH’s influence on the CGM of the central galaxy
through suppressing cooling the total sSFR is reduced. Therefore, sSFR, BH
mass (and its subsequent growth), and the CGM are highly interconnected.
However, for our current sample (including the additional literature values),
is too small to directly test these interdependent relationships seen in
simulations. Exploring whether this sSFR vs NCIV trend appears cosmological
simulations could shed light on the underlying physics driving this apparent
connection.

###  6.2 Do BHs evacuate their CGM?

Cosmological hydrodynamical simulation suites are now able to self-
consistently recreate an array of galaxy observables (e.g., EAGLE, Schaye et
al. (2015); Illustris-TNG (TNG), Pillepich et al. (2018); Romulus25, Tremmel
et al. (2017)), including not only the galaxy mass function but specific SMBH-
related observables including the AGN luminosity function (EAGLE, Rosas-
Guevara et al., 2016) and the M${}_{\mathrm{BH}}-\sigma$ relation
(IllustrisTNG, Sijacki et al. (2015); Romulus25, Tremmel et al. (2015)). From
these simulations, numerical and analytical calculations predict that even a
small percentage of the energy from SMBH assembly, when coupled to its
surrounding halo, will unbind the CGM from the dark matter halo (Davies et
al., 2019; Oppenheimer et al., 2020). This evacuation of the CGM has a
preventative effect such that the reduction in CGM gas density leads to long
cooling times for the gas in the inner halo (Davies et al., 2020); meanwhile,
this lower global gas density (not short lived cavities or bubbles carved by
AGN-mode feedback) causes galaxies to quench and stay quenched (Davies et al.,
2021).

Both EAGLE (Oppenheimer et al., 2020) and TNG (Nelson et al., 2019) predict
that the ionized gas in the CGM traced by C IV will be far lower-density (and
thus lower measured column density) in galaxies with over-massive black holes
(relative to their stellar mass). In contrast, results from Sanchez et al.
(2019) which used Romulus25 (Tremmel et al., 2017), suggest that galaxies with
high mass BHs will have higher measured column densities (higher metallicity)
in their CGM due to the BH ejecting material out into the diffuse parts of the
halo. The COS-Holes observations directly tests these predictions to quantify
the imprint of different implementations and efficiencies of BH feedback on
the physical state of the CGM.

Comparing between the simulations (Figure 7), EAGLE and TNG agree better with
the combined observed sample than R25. EAGLE appears to perform the best in
matching the column densities of the Low $M_{\rm BH}$ sample as well as
reproducing the $M_{\rm BH}$ values themselves. This may not be the case for
every ion as Nelson et al. (2018b) finds TNG shows better agreement for O VI
around the COS-Halos galaxies than found in EAGLE or EAGLE zoom simulations
(Oppenheimer et al., 2016).

Interestingly, R25 seems to be under predicting the observed C IV column
density. The AGN feedback in R25 has been shown to be more moderate in
comparison to TNG and EAGLE (Tremmel et al., 2019; Chadayammuri et al., 2021;
Jung et al., 2022), possibly due to R25’s lack of metal cooling. Sanchez et
al. (in prep) shows that a result of this less powerful feedback is that the
CGM of these galaxies are significantly less evacuated at these masses.
However, it may be that the metal rich gas evacuated by the SMBH in these
galaxies remains somewhat nearby to the galaxies, <50 kpc, as in the MW-mass
galaxies explored by Sanchez et al. (2019), which may explain the predicted
peak in NCIV around 30-40 kpc and the subsequent decline at high impact
parameter.

Despite the combined sample reasonably aligning with EAGLE and TNG, there is
no striking evidence in the COS-Holes survey that more massive SMBHs have
lower observed column densities, which would indicate this “cleared” CGM
(Oppenheimer et al., 2020) or that more massive SMBHs have a more metal
enriched CGM due to the BH ejecting material out into the halo (Sanchez et
al., 2019). However, we note that from the SMOHALOS exploration (5.3.1), we do
not yet have a sample large enough to determine if SMBHs are impacting the
content or the ionization state of the CGM.

##  7 Summary & Conclusion

The COS-Holes survey, in combination with a detailed comparison to
cosmological simulations, offers the first assessment of the role of BH growth
in the regulation of the baryonic content of extended gaseous halos. Broadly,
our observations, when combined with data from the literature, are in
reasonable agreement with simulation predictions, but do not provide
definitive evidence that SMBH feedback significantly impacts the state of the
CGM, in either evacuation or through metal enrichment. While our results do
not rule out that a galaxy’s central SMBH plays an important role in setting
the state of the CGM, we find that the sSFR is more correlated with properties
of the CGM. Specifically, our key results are:

  1. 1.

There is no identifiable relationship between the C IV content of the CGM and
the mass of the assumed host galaxy’s SMBH. We attribute this lack of a
correlation to both the COS-Holes survey’s small sample size and the large
scatter of $>$1 dex in C IV column density as BH mass increases.

  2. 2.

When we augment the COS-Holes sample of eight galaxies with 12 additional
galaxies from the literature for which we can estimate SMBH masses from
ground-based spectroscopy and which have C IV coverage along paired QSO
sightlines, we again find no significant trend between CGM C IV column
densities and SMBH mass with increasing impact parameter (Figure 4).

  3. 3.

We find that galaxy sSFR is correlated with the ionized content of the CGM as
traced by C IV; this is evidenced by a large spread in sSFR for
log10M${}_{\mathrm{BH}}>$ 7.0, where C IV strength shows clear dependence on
sSFR but not MBH. Our multivariate analysis tentatively confirms, with
$>$2$\sigma$ significance, that a correlation between sSFR and CGM C IV
content exists, similar to that of CGM O VI (Tchernyshyov et al., 2023).
Combined with items 1 and 2, above, our results suggest that the mass of the
SMBH is a subdominant factor in the processes that contribute to the content
or ionization state of the z$\sim$0 CGM and that it is the galaxy sSFR that
that is more tightly tied to the C IV-bearing gas phase of the CGM.

  4. 4.

We compare C IV column densities to simulated column densities from the EAGLE,
R25, and TNG simulations (Figure 7). Upon splitting the combined sample into
two SMBH mass bins, we find there are only small differences in median column
densities between different simulations. The combined COS-Holes + Literature
sample measurements of NCIV are in reasonable agreement with predictions from
EAGLE and TNG, but are higher than predictions from R25.

  5. 5.

We create a mock up of the nine lines of sight from the COS-Holes Survey in
all three simulations: EAGLE, R25, and TNG. We conclude that COS-Holes does
not contain enough QSO-galaxy pairs to distinguish the different behaviours
across all three simulations. To do so, the sample size would need to be
increased from 9 lines of sight to 120 lines of sight. See §5.3.1 and Table 5
for further details.

Since we targeted nearby, spatially extended galaxies with ancillary data
(e.g., resolved ALMA and VLA maps of the molecular and neutral ISM, rotation
curves, stellar population ages, and metallicity gradients), our QSO
spectroscopy will enable a variety of studies well beyond the scope of the
goals of this paper. For example, our observed absorption line kinematics will
aid in differentiating between material recently launched from the central
galaxy via feedback and gas accreting from the larger-scale environment (Bowen
et al., 2016; Ho et al., 2017). Closer to the purview of the paper, this COS
spectroscopy will also be crucial for differentiating between other AGN
feedback prescriptions invoked in models and simulations that are in the
public domain in addition to EAGLE and R25 described and used throughout this
paper; these include TNG with dramatic SMBH feedback (Pillepich et al., 2018;
Nelson et al., 2019) and the FIRE simulations suite (Anglés-Alcázar et al.,
2017; Pandya et al., 2021). Given the significant investment in observational
resources required to establish independent and well-constrained SMBH mass
measurements and the rarity of UV-bright QSOs, it is unlikely that additional
sightlines will become available until the next generation of ELTs and HWO are
in active use. However, these future UV observatories will be pivotal for
increasing the sample size and allowing us to test the effect of SMBH feedback
on the state of the CGM.

Based on observations with the NASA/ESA Hubble Space Telescope obtained at the
Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Incorporated, under NASA contract
NAS5- 26555. Support for Program number HST-GO-16650 was provided through a
grant from the STScI under NASA contract NAS5- 26555. This research has made
use of the NASA/IPAC Extragalactic Database (NED), which is operated by the
Jet Propulsion Laboratory, California Institute of Technology, under contract
with the National Aeronautics and Space Administration. We thank an anonymous
referee for their insightful comments with helped improve the clarity of this
paper. S.L.G recognizes the unceded traditional lands of the Duwamish and
Puget Sound Salish Tribes, on which she is grateful to love and work. S.L.G.
also thanks Trystyn Berg for their enlightening science discussions on this
topic and their valuable input. NNS acknowledges support from NSF MPS-Ascend
award ID 2212959 and NASA award SMD-21-75544133. MCB gratefully acknowledges
support from the NSF through grant AST-2009230. KHRR acknowledges partial
support from NSF grant AST-2009417. YF acknowledges support by NASA award
19-ATP19-0023 and NSF award AST-2007012. Data Availability: HST/COS spectra
can be found on in MAST: http://dx.doi.org/10.17909/njhs-4a40 (catalog
doi:10.17909/njhs-4a40).

##  Appendix A C IV Absorption Profiles

Figure 8: The remaining C IV absorption features for the COS-Holes survey.
Same conventions are used as described in Figure 2.

Figure 8 presents absorption line profiles for the COS-Holes sample. Some
items of note are: (1) for NGC 4026 (QSO: SDSSJ1159) there is a prominent
blend in $\lambda$1550 which we identified corresponds to H I $\lambda$1215 at
z = 0.28; due to this contamination and no features in $\lambda$1548 we report
an upper limit for the C IV column density; (2) for NGC 4258 (QSO: SDSSJ1220
and SDSSJ1222) and NGC 4564 (QSO: SDSSJ1235) we do not detect any C IV
absorption, and report only upper limits on C IV column density.

##  Appendix B Literature Sample Galaxy and QSO Tables

Table 6: Literature Sample Galaxy Information Galaxy | RA | Dec | z | sSFR | M∗ | MBH | Ref
---|---|---|---|---|---|---|---
| (deg) | (deg) |  | (log10yr-1) | (log10M⊙) | (log10M⊙) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
J102846.43+391842.9 | 157.194 | 39.312 | 0.1135 | -9.8 | 10.5 | 7.16 $\pm$ 0.35 | a
J132150.89+033034.1 | 200.462 | 3.509 | 0.0816 | -10.3 | 10.8 | 7.63 $\pm$ 0.12 | a
J140502.20+470525.9 | 211.259 | 47.091 | 0.1452 | -9.0 | 10.4 | 7.4 $\pm$ 0.43 | a
J154527.12+484642.2 | 236.363 | 48.778 | 0.0752 | -10.5 | 10.5 | 6.11 $\pm$ 0.52 | a
J0925+4535_227_334 | 141.379 | 45.533 | 0.014 | -10.3 | 10.0 |  $<$5.91 | b
J0959+0503_318_13 | 149.813 | 5.068 | 0.059 | -9.9 | 10.0 | 6.13 $\pm$ 0.52 | b
J1121+0325_73_198 | 170.362 | 3.445 | 0.023 | -10.2 | 10.1 |  $<$5.91 | b
J1211+3657_312_196 | 182.761 | 36.998 | 0.023 | -9.8 | 10.1 |  $<$5.91 | b
PG1202+281_165_95 | 181.183 | 27.878 | 0.051 | -12.1 | 10.0 |  $<$5.91 | b
J0910+1014_34_46 | 137.626 | 10.24 | 0.1427 | -9.5 | 10.61 | 7.71 $\pm$ 0.22 | c
J1619+3342_113_40 | 244.831 | 33.706 | 0.1414 | -9.9 | 10.1 | 6.16 $\pm$ 0.44 | c
M31 | 10.685 | 41.269 | -0.00099 | -11.1 | 10.9 | 8.15 $\pm$ 0.24 | d
Table 7: Literature Sample QSO Information QSO | RA | Dec | z | Rproj |  $R_{\mathrm{proj}}$/R200c | log10NCIV | Ref
---|---|---|---|---|---|---|---
| (deg) | (deg) |  | (kpc) |  | (cm-2) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
J102847.00+391800.4 | 157.2 | 39.3 | 0.473 | 88.7 | 0.52 | 14.65 $\pm$ 0.04 | a
J132144.97+033055.7 | 200.44 | 3.52 | 0.269 | 140.2 | 0.52 | <14.06 | a
J140505.77+470441.1 | 211.27 | 47.08 | 1.24 | 146.9 | 0.90 | 14.25 $\pm$ 0.08 | a
J154530.23+484608.9 | 236.38 | 48.77 | 0.399 | 64.7 | 0.37 | <13.79 | a
J09525+4535 | 141.478 | 45.596 | 0.329 | 95.0 | 0.76 | 13.56 $\pm$ 0.06 | b
J0959+0503 | 149.815 | 5.065 | 0.162 | 14.0 | 0.11 | >14.69 | b
PG1202+281 | 181.175 | 27.903 | 0.165 | 92.0 | 0.73 | 13.58 $\pm$ 0.10 | b
J1121+0325 | 170.309 | 3.43 | 0.152 | 89.0 | 0.68 | <13.45 | b
J1211+3657 | 182.811 | 36.961 | 0.171 | 90.0 | 0.68 | <13.17 | b
J0910+1014 | 137.624 | 10.237 | 0.462 | 112.0 | 0.58 | 14.1 $\pm$ 0.09 | c
J1619+3342 | 244.819 | 33.711 | 0.47 | 97.0 | 0.72 | 13.9 $\pm$ 0.03 | c
HS0033+4300 | 9.096 | 43.278 | 0.12 | 30.5 | 0.133 | 14.1 $\pm$ 0.05 | d
HS0058+4213 | 15.38 | 42.493 | 0.19 | 48.6 | 0.211 | 13.33 $\pm$ 0.18 | d
RX_J0043.6+3725 | 10.927 | 37.422 | 0.08 | 50.5 | 0.22 | 13.85 $\pm$ 0.03 | d
Zw535.012 | 9.087 | 45.665 | 0.048 | 59.7 | 0.26 | 12.99 $\pm$ 0.30 | d
RX_J0050.8+3536 | 12.711 | 35.612 | 0.058 | 77.1 | 0.335 | 13.45 $\pm$ 0.07 | d
IRAS_F00040+4325 | 1.652 | 43.708 | 0.163 | 93 | 0.404 | 13.23 $\pm$ 0.11 | d
MRK352 | 14.972 | 31.827 | 0.015 | 131.7 | 0.573 | 13.5 $\pm$ 0.15 | d
RX_J0043.6+3725 | 10.927 | 37.422 | 0.08 | 50.5 | 0.22 | <12.92 | d
RXS_J0118.8+3836 | 19.706 | 38.606 | 0.216 | 97.2 | 0.423 | <12.9 | d
RX_J0028.1+3103 | 7.045 | 31.063 | 0.5 | 139.1 | 0.605 | <13.11 | d
Project AMIGA Avg |  |  |  | 77.79 | 0.33 | 13.34 $\pm$ 0.20 | d

We increase our COS-Holes sample size by adding values from Lehner et al.
(2020) (Project AMIGA), Werk et al. (2013) (COS-Halos), Borthakur et al.
(2013) (starbursts), and Bordoloi et al. (2014) (COS-Dwarfs). Project AMIGA
(M31; log10M${}_{\star}=$9$\pm$2 $\times$ 1010 M⊙, Williams et al. (2017);
log10MBH = 8.15 $\pm$ 0.24, Davis et al. (2017); total SFR = 0.7 M⊙ yr-1,
Lewis et al. (2015)) was specifically designed to span M31’s project major and
minor axis and intermediate orientations, thus it provides the unique
opportunity to probe one high mass SMBH galaxy at increasing impact parameter.
It is important to mention that there were data values that had possible
contamination from the Magellanic Stream, however we only plot values they
denote as uncontaminated; for more a more detailed explanation of how this
contamination was removed see Lehner et al. (2020). Using this smaller sample
of Project AMIGA observations, we take an average of the detections to report
mean Project AMIGA column density. We use this single data point to represent
the Project AMIGA observations.

We also include Borthakur et al. (2013) which found highly ionized gas traced
by C IV in 80$\%$ of their starburst galaxies. They assert that it is
extremely unlikely that these absorbers were photoionized from either the
metagalactic background or the stellar radiation from the starburst; using
CLOUDY models, they suggest that this observed C IV would arise from shock-
ionization and be accelerated by the ram pressure of the wind and thus
enriching the CGM. Similar high detections of C IV were seen in Bordoloi et
al. (2014), where they detected the ion out to 100 kpc in their sample of
sub-L⋆ galaxies. They find that strong C IV absorption observations were
detected around star-forming galaxies and they are kinematically consistent
with being bound to the dark matter halos of their hosts. In conclusion, they
assert that the metallic content of the CGM around their galaxy sample is best
explained by the addition of strong outflows in addition to tidal debris and
ram pressure stripping. Taken together, both of these archival studies support
the idea that energy-driven feedback is needed to explain the presence of
highly ionized ions, such as C IV in the CGM. Thus, they are interesting
samples to compare and expand upon the COS-Holes observations.

In addition, we also include Werk et al. (2013) which presented column density
measurements of the CGM from QSO-galaxy pairs (low-z, L $\approx$ L⋆) drawn
from the COS-Halos survey. One of their main results is finding that column
densities derived for intermediate ionization state metal lines decrease with
increasing impact parameter; they interpret this trend to mean there is a
decline in the metal surface density profle of the CGM within its inner
160kpc. They also see that the gas kinematics derived from Voigt profile fits
to their observations suggest that the CGM is mostly bound to its host
galaxy’s dark matter halo similar to results seen in Bordoloi et al. (2014).
The collective information for Werk et al. (2013) and the rest of our
additional literature sample can be seen in Table 6 and 7 respectively.

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