# Revealing the Gas Recycling in the Circumgalactic Medium (CGM) Utilizing a
Luminous Ly$\alpha$ nebula around a Type-II Quasar at $z=2.6$ with the Keck
Cosmic Web Imager (KCWI)

Shiwu Zhang  Department of Astronomy, Tsinghua University, Beijing 100084,
China  Zheng Cai  Department of Astronomy, Tsinghua University, Beijing
100084, China  Dandan Xu  Department of Astronomy, Tsinghua University,
Beijing 100084, China  Andrea Afruni  Departamento de Astronomía, Universidad
de Chile, Casilla 36-D, Santiago, Chile  Yunjing Wu  Department of Astronomy,
Tsinghua University, Beijing 100084, China  Steward Observatory, University of
Arizona, 933 N Cherry Ave, Tucson, AZ 85721, USA  Wuji Wang  Astronomisches
Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg,
Mönchhofstr. 12-14, 69120 Heidelberg, Germany  Fabrizio Arrigoni Battaia  Max-
Planck-Institut für Astrophysik, Karl-Schwarzschild-Str 1, D-85748 Garching
bei München, Germany  Mingyu Li  Department of Astronomy, Tsinghua University,
Beijing 100084, China  Sen Wang  Department of Astronomy, Tsinghua University,
Beijing 100084, China  Xianzhi Bi  Beijing Royal School, Beijing 102209, China

###### Abstract

How galaxies acquire material from the circumgalactic medium (CGM) is a key
question in galaxy evolution. Recent observations and simulations show that
gas recycling could be an important avenue for star formation. This paper
presents Keck Cosmic Web Imager (KCWI) integral field unit spectroscopic
observations on a type-II quasar, Q1517+0055 at $z=2.65$, a pilot study of our
Ly$\alpha$ nebulae sample at $z\approx 2$. We revealed diffuse emission of the
Ly$\alpha$ $1216$, He ii $1640$, and C iv $1549$ on the projected physical
scale of 122 kpc, 45 kpc, and 79 kpc, respectively. The total Ly$\alpha$
luminosity is $L_{\rm Ly\alpha}=3.04\pm 0.02\times 10^{44}\ {\rm erg\
s^{-1}}$. The line ratio diagnostics shows that ${\rm HeII/Ly\alpha}\approx
0.08$ and ${\rm CIV/Ly\alpha}\approx 0.28$, consistent with the
photoionization including recombination and photon punmping. We also identify
the associated H i and C iv absorption from the spectra. By fitting the
spectra, we derive both the column density and the velocity. We find that the
velocity profile from both the absorption and the He ii emission exhibit
increasing trends. Moreover, both the line ratio diagnostic from the emission
and the column density ratio from the absorption confirm that the cool gas
metallicity is $\geq Z_{\odot}$. From detailed modeling and estimation, gas
recycling might be a more plausible interpretation compared with the scenario
of a powerful outflow.

Quasar; Circumgalactic Medium; Ly$\alpha$ nebulae; Gas Recycling;

††facilities: Keck-II (KCWI)††software: astropy (Astropy Collaboration et al.,
2022), Cloudy (Ferland et al., 2017), vorbin (Cappellari & Copin, 2003),
Linetools (Prochaska et al., 2017)

##  1 Introduction

The gas diffusing in the dark matter halo is the circumgalactic medium (CGM)
which plays a key role in galaxy formation and evolution (Tumlinson et al.,
2017). As the link between the intergalactic medium (IGM) and galaxies, CGM
has been confirmed to contain multi-phase gas including the hot gas ($T\geq
10^{5}$ K) observed by the X-ray emission (Anderson et al., 2016, 2013), the
cool gas ($T\sim 10^{4}$ K) observed by the UV-optical line emissions (Cai et
al., 2017, 2019; Arrigoni Battaia et al., 2019; Borisova et al., 2016), and
the cold gas ($T\sim 10-100$ K) observed by radio/submillimeter emissions
(Emonts et al., 2018, 2019). Hydrodynamical simulations (Kereš et al., 2005;
Anglés-Alcázar et al., 2017; Suresh et al., 2015; Wang et al., 2022; Lu et
al., 2022) have shown that the mass, energy, and metals exchange between the
galaxy and the CGM/IGM is complex. Despite the great theoretical and
observational efforts, the origin, the cooling mechanisms, and the detailed
dynamical processes of the CGM are still under investigation.

In the modern paradigm of how galaxies obtain their gas, the well-accepted
picture is that the galaxy could not only accrete the hot gas isotropically
(Nelson et al., 2013; Stern et al., 2020) but also obtain the cool gas through
filaments in the form of inspiraling stream (Kereš et al., 2005; Dekel et al.,
2009). Nevertheless, beyond this sketch, studies indicate that gas recycling
could also be an important avenue for the galaxy to sustain star formation
(Anglés-Alcázar et al., 2017; Oppenheimer et al., 2010). In the so-called
recycling scenario, the metal-enriched gas is firstly ejected to the CGM by
the outflow, and then falls back to the galaxy (Ford et al., 2014; Christensen
et al., 2016). This phenomenon has been studied in both observations and
simulations at low-$z$ (Rubin et al., 2012; Oppenheimer et al., 2010).
Hydrodynamical simulations show that the gas recycling could exceed the cold-
mode accretion at $z=0$ and reshape the stellar mass function (SMF) of the
galaxy (Oppenheimer et al., 2010). Rubin et al. (2012) present the detection
of the metal-enriched accretion with the Mg ii and Fe ii absorption at $z\leq
1$. For high-$z$, the cosmological simulations show that recycled gas is an
important source to regulate star formation. FIRE simulations show that the
recycled gas can take a fraction more than 50% of the total accreted material
at $z\approx 2$ (Anglés-Alcázar et al., 2017). Also, Wang et al. (2022) using
IllustrisTNG simulations demonstrate a closely entangled fate between the CGM
gas recycling and episodic star formation. Nevertheless, the direct detection
of gas recycling at high-$z$ is rare.

Ly$\alpha$ nebulae are good laboratories allowing us to directly study the
cool gas in the CGM. By observing the Enormous Ly$\alpha$ nebula (ELAN),
MAMMOTH-1, Zhang et al. (2022) present the first direct imaging on the
recycled inflow in a massive system with halo mass of $10^{13}M_{\odot}$ at
$z=2.3$. They find that the cool gas is enriched to $Z_{\odot}$ by the
previous outflow, which is flowing back to the galaxy in the form of
inspiraling streams. Furthermore, the gas inflow rate is estimated to be
$\dot{M}_{\rm in}\approx 713\ M_{\odot}$ yr-1, fully covering the star
formation rate (SFR) of the central galaxy. These observations also indicate
that the recycled inflow could be important for enriching the star-forming
environment in massive systems at high-$z$.

Here, we present a pilot study targeting a type-II quasar, Q1517+0555, at
$z=2.65$ with the Keck Cosmic Web Imager (KCWI) instrument on Keck Telescope.
This source is selected from a type-II quasar candidate catalog (Alexandroff
et al., 2013). After 2-hr exposure with Keck/KCWI which is a blue-sensitive
integral field spectrograph (IFS), we detect not only extended Ly$\alpha$
emission line, but also extended C iv and He ii emission lines. Besides, we
also find the H i and C iv absorption associated with the emission. After
analyzing the absorption, we conclude that the absorption could trace the
metal-enriched cool gas inflowing into the galaxy.

This paper is organized as follows: we present the information of observations
in Sec. 2 where the details about the systemic redshift of the source and the
process of the data reduction are also given. In Sec. 3, we show the detailed
results of Ly$\alpha$, He ii, and C iv emissions with the H i and C iv
absorption. In Sec. 4, the possible powering mechanism and the possible
explanations of our observations are discussed. Conclusions are provided in
Sec. 5. The $\Lambda$CDM cosmology with $\Omega_{\rm m}=0.3$,
$\Omega_{\Lambda}=0.7$, and $h=0.7$ is assumed.

##  2 Observations

###  2.1 KCWI observations

We obtained the IFS observations of the Q1517+0055 with the KCWI mounted on
the Keck-II telescope (Morrissey et al., 2018). The medium slicer with the
field of view (FoV) of $16^{\prime\prime}\times 20^{\prime\prime}$ was
employed for observations. It yields a spatial resolution of
$0.7^{\prime\prime}$ along the slicer direction with the seeing-limited
condition of $0.6^{\prime\prime}$. The KCWI/BM grating with the wavelength
range of $3500\ {\rm\AA}-6200\ {\rm\AA}$ was employed. This configuration
yields a slit-limited spectral resolution of $R\approx 4000$, corresponding to
a velocity resolution with the full width of half maximum (FWHM) of 75 km s-1
(rest-frame 22.7 km s-1), completely resolving the kinematics of the cool gas
of the Ly$\alpha$ nebula.

To fully reveal the morphology and kinematics, we performed a 2-hours on-
source exposure. This yields a 2-$\sigma$ surface brightness (SB) of
$8.4\times 10^{-19}$ erg s-1 cm-2 arcsec-2 at $\lambda\approx 4400\ {\rm\AA}$,
assuming a wavelength bin of $1\ {\rm\AA}$. At $\lambda=5800\ {\rm\AA}$, our
observations yields the 2-$\sigma$ surface brightness of $6.5\times 10^{-19}$
erg s-1 cm-2 arcsec-2 in a bin of $1\ {\rm\AA}$.

###  2.2 Data Reduction

The standard KCWI pipeline 111https://github.com/Keck-
DataReductionPipelines/KcwiDRP was employed to reduce the data. We first
subtract the bias, correct the pixel-to-pixel variation with the flat-field
images, and remove the cosmic rays. Then the geometric transformation and the
wavelength calibration with ThAr arc images are conducted. We use the twilight
flats to correct the slice-to-slice variance. The spectrophotometric standard
star is adopted to calibrate the flux of the individual image of the cube.

The systemic redshift is calculated from the He ii line which is non-resonant.
By fitting the He ii emission, we have $\lambda_{\rm HeII}=5983.2\pm 0.3$ Å,
corresponding to a systemic redshift of $z_{\rm sys}=2.6474\pm 0.0002$ with
the rest-frame wavelength of He ii equal to $1640.4\ {\rm\AA}$.

The optimal-extraction method for faint, extended sources extracting (Borisova
et al., 2016; Arrigoni Battaia et al., 2019; Cai et al., 2019) is applied to
generate the pseudo narrowband images for the Ly$\alpha$, He ii, and C iv
emissions. We extract the sub-cubes by centering on the redshifted line
centers and fixing the wavelength bin size of $\Delta\lambda=\pm 20\
{\rm\AA}$. With the systemic redshift of $z_{\rm sys}=2.6474\pm 0.0002$, the
wavelength coverage of the sub-cubes are fixed to be $4410-4450\ {\rm\AA}$,
$5963-6003\ {\rm\AA}$, and $5631-5671\ {\rm\AA}$. Then, we apply the Gaussian
kernel with ${\rm FWHM=0.7^{\prime\prime}}$, same as the spatial resolution
along the slicer direction, to smooth the sub-cubes. We construct the three-
dimensional segmentation masks, containing the value of zero or one to select
the connected voxels which have the $S/N$ above the user-defined thresholds. a
threshold of $S/N=2$ is employed. Such threshold has been tested extensively
in previous IFS studies (Borisova et al., 2016; Cantalupo et al., 2019;
Arrigoni Battaia et al., 2019).

##  3 Results

###  3.1 Morphology and Emission

Figure 1: Panel A: Optimally extracted images of the Ly$\alpha$, He ii, and C
iv emissions. White contours represent the 2$\sigma$ noise level. The three
emission lines are detected on the scale of 122 kpc, 45 kpc, and 79 kpc,
respectively. Middle: The flux-weighted velocity maps. Right: The flux-
weighted dispersion map. Panel B: The map of spatial bins coded by the color.
Black contours represent noise levels of [2$\sigma$, 5$\sigma$, 10$\sigma$,
20$\sigma$, 40$\sigma$] of the Ly$\alpha$ emission. Panel C: The SB profile of
the Ly$\alpha$ (red), He ii (blue), and C iv (green) emissions compared with
the PSF (black). The Moffat profile is employed to model the PSF with the
spatial resolution of $0.7^{\prime\prime}$. The flux peak of the PSF is
normalized to align with the He ii emission.

The pseudo narrowband images of the Ly$\alpha$, He ii, and C iv emissions are
shown in Fig. 1. The nebular emissions are enclosed in white contours which
represent $S/N=2$. By comparing the SB profile with the point spread function
(PSF) shown in Fig. 1, we find that the Ly$\alpha$, He ii, and C iv emissions
are all extended. Within the 2$\sigma$ contours, the spatial extent of the
three diffuse emissions is 122 kpc, 45 kpc, and 79 kpc, respectively.

The integrated fluxes of the three diffuse emissions are $F_{\rm
Ly\alpha}=5.30\pm 0.02\times 10^{-15}$ erg s-1 cm-2, $F_{\rm HeII}=2.79\pm
0.08\times 10^{-16}$ erg s-1 cm-2, and $F_{\rm CIV}=2.02\pm 0.01\times
10^{-15}$ erg s-1 cm-2. With the luminosity distance of $D_{\rm L}\approx
21868$ Mpc at $z_{\rm sys}$, these fluxes correspond to the luminosities of
$L_{\rm Ly\alpha}=3.04\pm 0.02\times 10^{44}$ erg s-1, $L_{\rm HeII}=1.60\pm
0.04\times 10^{43}$ erg s-1, and $L_{\rm CIV}=11.53\pm 0.05\times 10^{43}$ erg
s-1, respectively.

Figure 2: The spectra of the Ly$\alpha$, He ii, and C iv lines in bin-0. We
use the Gaussian profile and the voigt profile to fit the emission and the
absorption, respectively. Blue dashed lines represent the emission component
and the orange solid lines are the best fits (including the absorption). For C
iv absorption, the overshoot of the model to the data in the velocity range of
$-500\ {\rm km\ s^{-1}}\leq v\leq 0\ {\rm km\ s^{-1}}$ is the consequence of
reaching the smallest residual. Red dashed lines mark the zero point for each
emission with the systemic redshift. The results clearly demonstrate that our
fittings are consistent with the observed spectra.

###  3.2 Spectral Analysis

Here, we present the result of the spatially resolved spectra. We use the
Voronoi binning technique (Cappellari & Copin, 2003) to spatially bin the IFS
data. This technique adaptively bins the pixel of the input IFS data to reach
a user-defined $S/N$ threshold. We set the $S/N$ threshold to $S/N=25$
estimated from the wavelength range of $4410-4450\ {\rm\AA}$ which fully
covers the Ly$\alpha$ emission. Note that this $S/N$ threshold is derived from
the un-optimally-extracted image. By adopting the $S/N=25$, the Voronoi
binning gives 69 spatial bins in total (Fig. 1). The spectra of the
Ly$\alpha$, He ii, and C iv emissions from the bin-0 are shown in Fig. 2 as an
example. The He ii emission clearly shows one peak while both the Ly$\alpha$
and C iv emissions show two peaks with an enhanced redshifted peak. Since
Ly$\alpha$ line exhibits different features from the He ii emission line, such
features are not likely to be caused by the gas kinematics. Moreover, the
scattering could also play a role as the resonant lines, Ly$\alpha$ and C iv,
are more extended than He ii. Whereas, the resonant scattering is hard to
reproduce the observed spectral features of Ly$\alpha$ and C iv since it
requires the outflow with constant velocity (Chang et al., 2022) which is
unnatural on the CGM scale. Actually, recent works (Wang et al., 2021; Kolwa
et al., 2019) find Ly$\alpha$ nebulae around high-redshift radio galaxies
associated with the H i and the C iv absorption with line features similar to
our results. Moreover, the absorption features are seen at the similar
redshift for both Ly$\alpha$ and C iv lines. Thus, the absorption scenario is
more favored.

Figure 3: The parameter maps by fitting the spectra of the Ly$\alpha$ and the
C iv. The black contours denote the emission region with the noise level of
[2$\sigma$, 5$\sigma$, 20$\sigma$, 40$\sigma$, 60$\sigma$]. For Both emissions
and absorption, the spatial bins with $S/N<3$ are removed. The spatial bins
within the central 10 kpc are also removed to avoid the influence of the PSF.

In addition, Alexandroff et al. (2013) show that the Q1517+0055 is a type-II
quasar which has no significant broad component. By fitting the spectra
extracted from bin-0 where the flux peaks, we find that the line width (FWHM)
of the Ly$\alpha$, C iv, and He ii emissions are $\rm FWHM_{Ly\alpha}=503\pm
17\ km\ s^{-1}$, $\rm FWHM_{CIV}=482\pm 23\ km\ s^{-1}$, and $\rm
FWHM_{HeII}=459\pm 12\ km\ s^{-1}$, respectively. Compared with the threshold
of $\rm FWHM_{CIV}<2000\ km\ s^{-1}$ used to select the type-II quasar
(Alexandroff et al., 2013), our measured line width is about four times
smaller. This result suggests that the emissions are more likely to have no
significant broad components.

The spectra extracted from 69 spatial bins are fitted. We follow the same
procedure as Kolwa et al. (2019) and Wang et al. (2021) to fit spectra. We use
the Gaussian function in the python package ASTROPY222https://www.astropy.org/
and Voigt function in the software
LineTools333https://linetools.readthedocs.io/en/latest/# to model the emission
and absorption. The emergent emission is
$F_{\lambda}=F_{\lambda,0}e^{-\tau_{\lambda}}$. The unabsorbed flux
$F_{\lambda,0}$ is shown in Eq. 1.

$F_{\lambda,0}=Ae^{-0.5(\lambda-\lambda_{\rm emis})^{2}/\sigma^{2}}$ (1)

where $A$ is the amplitude, $\lambda_{\rm emis}$ is the line center, and
$\sigma$ is the line dispersion. The absorption is quantified by the optical
depth, $\tau_{\lambda}$, which is shown in Eq. 2.

$\tau_{\lambda}=\frac{N\sqrt{\pi}e^{2}f\lambda_{0}}{bm_{\mathrm{e}}c}H(a,u)$
(2)

where $N$ is the column density, $e$ is the electron charge, $m_{e}$ is the
electron mass, $c$ is the speed of light, and $f$ is the oscillator strength.
$H(a,u)$ is the Hjerting function where $a=\Gamma\lambda_{\rm abs}/4\pi cb$
and $u=(\lambda-\lambda_{\rm abs})/b\lambda_{\rm abs}$. $\Gamma$ is the
Lorentzian width and $b$ is the Doppler parameter.

To fit the spectrum of Ly$\alpha$, He iiand C iv, we initialize $A$ as the
peak flux of each spectrum, $\lambda_{\rm abs}$ as the observed wavelength at
the systemic redshift, $z_{\rm sys}=2.6474\pm 0.0002$, and $\sigma$ as the
width which corresponds to the result of primary fitting of He ii. The column
density, $N_{\rm HI}$, is constrained to a conservative range of
$10^{12}$—$10^{20}$ cm-2 by following the Kolwa et al. (2019). The initial
guess of the column density is taken as $N_{\rm HI}=10^{16}$ cm-2 which is the
mean of boundaries in log space. The Doppler parameter, $b$, is constrained in
the range of 45—200 km s-1 where the lower limit corresponds to the spectral
resolution of FWHM=75 km s-1. To fit the spectrum of C iv doublet, the
emission flux ratio between the two lines is set to be
$A_{1}/A_{2}=f_{1}/f_{2}\approx 2$ (Kolwa et al., 2019; Wang et al., 2021)
where the initial value of $A_{1}$ is set to be the peak flux in the spectrum.
The C iv column density is constrained in the range of 1013—1016 cm-2 by
following Wang et al. (2021) with the 1014.5 cm-2 as the initial guess. The
initial value of $\lambda_{\rm emis}$ and $\lambda_{\rm abs}$ for C iv are set
in the same way as Ly$\alpha$. We present the initial value and range of
fitting parameters in Tab. 1, 2, and 3. The best-fitting parameters are shown
in Tab. 4 and 5.

After pairing fitting parameters to corresponding spatial bins, we get
parameter maps (Fig. 3). For maps derived from fitting both the emission and
the absorption, bins with the $(S/N)_{i}<3$ are removed where $(S/N)_{i}$
denotes the signal-to-noise ratio at bin $i$.

###  3.3 CGM kinematics

Figure 4: The absolute value of the line-of-sight velocity profile of the
Ly$\alpha$ and C iv absorption, and the He ii emission. The black dots are
from observations. The red dashed lines are the linear fitting to the black
dots in the radius range of $10\ {\rm kpc}\leq R\leq 30\ {\rm kpc}$. The red
shadow denotes the 1-$\sigma$ uncertainty of the fitting. The fitting
indicates that the profile of the Ly$\alpha$ and C iv roughly have an
increasing trend and the profile of the He ii is constant.

We plot radial profiles of the absolute value of the line-of-sight velocity
(referred as velocity profile in the following) yielded from the Ly$\alpha$
and C iv absorption and the He ii emission (Fig. 4). The velocity is converted
from the wavelength of the absorption/emission by

$v=\frac{\lambda-\lambda_{r}(1+z_{\rm sys})}{\lambda_{r}(1+z_{\rm sys})}c$ (3)

where $\lambda$ is the observed wavelength of the line, $\lambda_{r}$ is
wavelength of the line in the rest-frame, $z_{\rm sys}=2.6474\pm 0.0002$ is
the systemic redshift of Q1517+0055, and $c$ is the speed of the light. The
radius of the point is measured as the distance between the quasar and the
spatial bin center. We remove the velocities from spatial bins with the radius
of $R\leq 10\ {\rm kpc}$ to avoid the influence of the PSF.

We fit the velocity profiles in the range of $10\ {\rm kpc}<R\leq 30\ {\rm
kpc}$ with a linear model. The best-fitting slopes are shown in Tab. 6. From
the fitting results, we find that the profiles of Ly$\alpha$ and C iv have an
increasing trend up to 30 kpc. For He ii, the profile is consistent with a
constant model within the 1-$\sigma$ uncertainty. Moreover, The slopes yielded
from the Ly$\alpha$ and C iv absorption are consistent with each other within
1-$\sigma$ uncertainty, which implies that the two absorptions might trace the
same flow of gas. The increasing velocity profile could be a natural result of
the gas inflow, which has been studied in observations (Zhang et al., 2022),
simulations (Wang et al., 2022), and semi-analytic models (Afruni et al.,
2019; Lan & Mo, 2019). In sec. 4.3, we present a detailed discussion.

##  4 Discussion

###  4.1 Photoionization Model

The powering mechanism of these diffuse emissions could be inferred from the
line ratio diagnostics. We calculate the line ratio based on the fitted
emission line (blue dashed lines in Fig. 2) in each spatial bin (Fig. 1). The
velocity range used to extract the fluxes is set to $-1000\ {\rm km\
s^{-1}}\leq\Delta v\leq 1000\ {\rm km\ s^{-1}}$ which fully covers the
emission lines. Then, the CLOUDY simulations (Ferland et al., 2017) are used
as follows. We apply the built-in AGN template as the incident radiation. The
UV slope of the AGN template is adopted as $\alpha_{\rm uv}=-2$ to keep
consistent with observations. As for model parameters, we follow previous work
(Cai et al., 2017; Arrigoni Battaia et al., 2015) to set the ionization
parameter, $log(U)$, in the range of $-3-0$ with a step of 0.06, the
metallicity, $Z$, in the set of [$10^{-3}$, $10^{-2}$, $10^{-1}$, $1$,
$10$]$Z_{\odot}$, the column density, $log(N_{\rm H}/{\rm cm^{-2}})$, in the
range of $18-20$ with a step of $1$, the hydrogen number density, $log(n_{\rm
H}/{\rm cm^{-3}})$, in the range of $-3-1$ with a step of $1$. Both the
recombination radiation from the CGM and the resonant scattering of AGN’s
photons are included in the model. We show both the photoionization model
(color dots) and observations (black dots) in Fig. 5, Left. Because of the
high ratio between C iv and Ly$\alpha$ (C iv/Ly$\alpha\approx 0.28$), the
observed line ratio could be consistent with models of $Z\geq Z_{\odot}$.
Considering that no significant broad component contaminates the emission (see
Sec.3.2), this consistency between the observed line ratios and the solar-
metallicity model indicates that the cool gas in the CGM is metal-enriched.

Actually, under the photoionization scenario, the absorption also yields high
metallicity. Fig. 5, Right presents the observed column density ratios profile
of the H i and C iv (black dots) versus the modeled column density ratios by
CLOUDY simulations (red dashed lines). The observed column density ratio
profile indicates metallicity of $Z\geq Z_{\odot}$ out to 30 kpc.

In fact, the metal-enriched CGM has been prevalently revealed by recent
observations on the diffuse emission (Guo et al., 2021; Fossati et al., 2021;
Marques-Chaves et al., 2019; Kolwa et al., 2019) and absorption (Prochaska &
Hennawi, 2009; Prochaska et al., 2014). Both Marques-Chaves et al. (2019) and
Kolwa et al. (2019) reveal that the CGM could reach solar metallicity or
beyond though observing the Ly$\alpha$ and C iv nebulae. Our observations are
consistent with these results, which indicates that the CGM could be highly
metal-enriched at the cosmic noon.

Figure 5: Left: The comparison of observed line ratios (black) and modeled
line ratios (colored). The color and size of modeled points denote the
metallicity and the ionization parameter, respectively. Black upper limits are
from bins without C iv and He ii emissions. The consistency between
observations and models indicates that diffuse emissions should be powered by
photoionization with the metallicity of $Z\geq Z_{\odot}$. Right: The column
density ratio profile produced by fitting the absorption. The red dashed line
denotes the column density ratios with metallicity of $Z_{\odot}$ from CLOUDY
simulations. This figure shows that the cool gas traced by the absorption has
the metallicity of $\geq Z_{\odot}$ out to 30 kpc.

###  4.2 Outflow scenario

The previous section reveals that the CGM of Q1517+0055 is enriched to about
solar metallicity. Such high metallicity could be due to the AGN feedback.
Under this scenario, the outflowing gas should be accelerated out to roughly
30 kpc to match our observations. In terms of the theory, although some
hydrodynamic simulations demonstrate that the outflow could be accelerating on
the scale of 10 kpc (Mitchell et al., 2020), most simulations of the
accelerating outflow only focus on the scale of $\leq 1$ kpc (Tanner & Weaver,
2022). In terms of the observations, the accelerating outflows are only
observed on the scale of hundreds of parsec to 1 kpc (Santoro et al., 2020; He
et al., 2022). Although Rupke et al. (2019) directly imaging the AGN feedback
on the physical scale of 100 kpc at $z\approx 0.5$, previous observations
reveal that the outflow is mostly decelerating on the large scale (Kacprzak et
al., 2019; Ng et al., 2019; Rupke et al., 2019).

Besides, we also calculate the coupling efficiency ($f_{c}$) which is the
ratio between the outflow energy rate ($\dot{E}_{\rm out}$) and the active
galactic nucleus (AGN) luminosity ($L_{\rm AGN}$). This value describes the
efficiency of the AGN luminosity coupling to the interstellar medium (ISM) or
CGM. By fitting the spectral energy distribution (SED) of Q1517+0055 with
cigale (Boquien et al., 2019), we derive the AGN luminosity to be $L_{\rm
AGN}=8.0\times 10^{45}$ erg s-1. For $\dot{E}_{\rm out}$, we follow previous
works (Harrison et al., 2012, 2014) to calculate the upper limit and the lower
limit.

For the upper limit, we adopt the energy-conserved model that assumes an
inefficient cooling process. This model gives (Harrison et al., 2012, 2014;
Cai et al., 2017)

$\dot{E}_{\rm out}=1.5\times 10^{46}R^{2}_{\rm out}v^{3}_{\rm out}n_{e}\ {\rm
erg\ s^{-1}}$ (4)

where $R_{\rm out}$ is the outflow radii in the unit of 10 kpc, $v_{\rm out}$
is the outflow velocity in the unit of 1000 km s-1, and $n_{e}$ is the
electron number density in the unit of 0.5 cm-3. By adopting our observational
results, $R_{\rm out}=$39 kpc (half the spatial extent of C iv emission),
$v_{\rm out}=320$ km s-1 (the max velocity yielded from the H i absorption),
and assuming electron density of $n_{e}=1.5\ {\rm cm^{-3}}$, we calculate the
upper limit of $\dot{E}_{\rm out}$ to be $2.3\times 10^{46}$ erg s-1.

For the lower limit, we adopt the model which assumes the outflow extending
from 0 kpc to where we see the extended emission. The $\dot{E}_{\rm out}$ is
given by (Harrison et al., 2012, 2014; Cano-Díaz et al., 2012; Greene et al.,
2012)

$\dot{E}_{\rm out}=\frac{1}{2}\dot{M}_{\rm out}(v_{\rm
out}^{2}+3\sigma_{v}^{2})$ (5)

where $\dot{M}_{\rm out}$ is the outflow mass rate and $\sigma_{v}$ is the
velocity dispersion. For $\dot{M}_{\rm out}$, we have $\dot{M}_{\rm
out}=M_{\rm out}v_{\rm out}/R_{\rm out}$ where $M_{\rm out}$ is the outflow
mass. Following Zhang et al. (2022), we derive the outflow mass to be
$\dot{E}_{\rm out}=1.4\times 10^{45}$ erg s-1. Then, the outflow energy rate
is adopted as the mean of the upper limit and lower limit in the log space
(Harrison et al., 2012, 2014), which is $\dot{E}_{\rm out}=5.7\times 10^{45}$
erg s-1.

Given the outflow energy rate and AGN luminosity, we calculate the coupling
efficiency to be $f_{c}=0.7$. The results are shown in Fig. 6. Compared with
previous observations and simulations (Harrison et al., 2018), the lower limit
of $f_{c}$ for our observations is slightly higher than the largest $f_{c}$
predicted by simulations. The mean $f_{c}$ for our observations is about five
times larger than this largest value. Based on the discussion and estimations
above, we note that the extremely powerful AGN feedback might be an
interpretation of our observations. Such feedback should be able to accelerate
the gas on the scale out to 30 kpc and have the $f_{c}$ reaching $\approx
0.7$.

Figure 6: A comparison of the coupling efficiency calculated from our
observations, assuming an AGN outflow model (red star) and other observations
(black dots) and simulations (dashed lines) (Harrison et al., 2018). The error
bar of our result represents the upper and lower limit. The coupling
efficiency of $f_{c}\approx 0.7$ is higher than those from simulations and
previous observations.

###  4.3 Inflow scenario

Figure 7: Left: The line-of-sight velocity profile gotten by fitting spectra.
Here, we only show the absolute value of the velocity. The errorbar of the
velocity is from the fitting while the errorbar of the radius represents the
1$\sigma$ scatter of the spatial bin. The red line is the simulated line-of-
sight velocity profile from our model. The red shadow represents the $2\sigma$
scatter. This figure shows that the velocity profile increases and then drops
down from the inside out, which can be reproduced by the inflow model. Right:
The trajectories of the inflowing cloud. The color codes the inflowing time.
This set of trajectories is yielded by ranging the fitting parameters in the
$2\sigma$ range. The dashed line marks the direction of the sightline.
$\theta_{\rm los}$ is the angle describing the direction of the sightline.
This result means that our inflow model can produce the inspiraling inflow
seen in both observations (Zhang et al., 2022) and simulations (Wang et al.,
2022).

In fact, the observed increasing velocity profile can be produced by the gas
inflow. Such kinematics is not proposed for the first time. The CGM kinematics
has been studied by observations (Weidinger et al., 2004, 2005; Arrigoni
Battaia et al., 2018; Zhang et al., 2022), simulations (Wang et al., 2022),
and semi-analytical models (Afruni et al., 2019, 2022; Lan & Mo, 2019). Zhang
et al. (2022) observe the Ly$\alpha$ nebula with the diffuse He ii and C iv
emissions around a type-II quasar at $z=2.3$, revealing an increasing velocity
profile in the nebula which represents the metal-enriched inflow. Wang et al.
(2022) found similar infalling CGM gas behavior in the IllustrisTNG
simulations. The cool circumgalactic gas speeds up as it inflows from larger
radii. Both Afruni et al. (2019) and Lan & Mo (2019) construct a semi-analytic
model showing the cool gas cloud could accelerate in the CGM.

To understand the physics of the observed kinematics, an inspiraling inflow
model with the gas angular momentum included is constructed in this work.

Afruni et al. (2019) and Lan & Mo (2019) construct the semi-analytic model
describing the radial motion of the cool gas inflow in the CGM. Their inflow
model shows that the cool gas motion is controlled by the gravitational force
of the dark matter halo and the drag force of the hot gas. The radial motion
is described by Eq. 6 (Eq. 12 in Afruni et al. (2019)),

$\frac{dv_{r}}{dt}=\frac{GM(r)}{r^{2}}-\frac{\pi r_{\rm cool}^{2}\rho_{\rm
hot}(r)v_{r}^{2}}{m_{\rm cool}}$ (6)

where $G$ is the gravitational constant, $v_{r}$ is the velocity of the cool
gas relative to the hot gas, $M(r)$ is the mass within the radius of $r$
following the Navarro Frenk White (NFW) profile (Afruni et al., 2019), $r_{\rm
cool}$ is the radius of the cool gas cloud assuming that the cloud is
spherical, $\rho_{\rm hot}(r)$ is the density of the hot gas, and $m_{\rm
cool}$ is the mass of the cool gas cloud. For the hot gas density, we have
$\rho_{\rm hot}=f_{\rm hot}\rho_{\rm bar}$ where $\rho_{\rm bar}$ is the
baryon density and $f_{\rm hot}$ is the hot gas fraction. Since there is
almost no observational constraint for the hot gas fraction at high-$z$,
$f_{\rm cor}$ is set to be a free parameter here. Details about how $\rho_{\rm
bar}$ and $r_{\rm cool}$ are derived are shown in (Afruni et al., 2019). On
the right side of Eq. 6, the first term represents the gravity of the halo,
and the second term represents the drag force of the hot gas.

Since the tangential motion of the cool gas cloud is also important, we
include it in the model. The equation of the drag force should be modified
because it is determined by the relative velocity. The Eq. 6 is changed to

$\frac{dv_{r}}{dt}=\frac{GM(r)}{r^{2}}-\frac{\pi r_{\rm cool}^{2}\rho_{\rm
hot}(r)v^{\prime}v_{r}}{m_{\rm cool}}-\frac{v_{t}^{2}}{r}-\frac{dm_{\rm
cool}}{dt}\frac{v_{r}}{m_{\rm cool}}$ (7)

where $v_{t}$ is the tangential velocity and $v^{\prime}=\sqrt{(v_{t}-v_{\rm
hot})^{2}+v_{r}^{2}}$ is the velocity of the cool gas relative to the hot gas,
$v_{\rm hot}$ is the rotation velocity of the hot gas. On the right side of
Eq. 7, the first term is the gravitational force from the halo, and the second
term is the projection of the drag force in the radial direction. The newly
added two terms ($v_{t}^{2}/r$, $\frac{dm_{\rm cool}}{dt}\frac{v_{r}}{m_{\rm
cool}}$) represent the centripetal force due to the tangential motion and the
mass change of the cool gas cloud, respectively. The equation describing the
tangential motion is

$\frac{dv_{t}}{dt}=-\frac{\pi r^{2}\rho_{\rm hot}(r)v^{\prime}(v_{t}-v_{\rm
hot})}{m_{\rm cool}}-\frac{dm_{\rm cool}}{dt}\frac{v_{t}}{m_{\rm
cool}}-\frac{v_{r}v_{t}}{r}$ (8)

where, on the right side, the first term is the projection of the drag force
in the tangential direction, the second term represents the mass change, and
the third term represents the influence of the tangential motion. The equation
describing the mass change of the cool gas is

$\frac{dm_{\rm cool}}{dt}=-\alpha m_{\rm cool}$ (9)

where $\alpha$ is the evaporation rate describing the mass loss rate of the
cool gas cloud (Afruni et al., 2019).

The dark matter halo mass is needed for the inflow model. By fitting the
spectral energy distribution (SED) of Q1517+0055, we derive the stellar mass
of the host galaxy to be ${\rm log}(M_{\star}/M_{\odot})=10.5^{+0.1}_{-0.1}$.
Through the stellar-mass-to-halo-mass relation of Lu et al. (2014), we get the
halo mass of Q1517+0055 to be ${\rm log}(M_{\rm
h}/M_{\odot})=12.1^{+0.3}_{-0.1}$.

To model the hot gas rotation, we use the result of Danovich et al. (2015)
which studies the angular momentum of CGM at $z=1.5\sim 4$ in cosmological
simulations. In their simulations, the systems have the halo mass of
1011.4∼12.2 $M_{\odot}$ at $z\approx 2$, which are consistent with our
observations. To compare with the observed line-of-sight velocity, we further
introduce the angle of sightline, $\theta_{\rm los}$, which is used for the
projection (Fig. 7, right). The rotation and density profile of the hot corona
are shown in Fig. 8.

Based on the description above, the inspiraling inflow model has seven free
parameters. They are the initial infalling radius, $r_{\rm init}$, the initial
radial velocity of the cloud, $v_{\rm r,init}$, the initial tangential
velocity of the cloud, $v_{\rm init,t}$, the initial mass of the cloud,
$m_{\rm cool,init}$, the mass evaporation rate, $\alpha$, the hot corona
fraction, $f_{\rm cor}$, and the angle of the sightline, $\theta_{\rm los}$.
We then fit the observed line-of-sight velocity profile (Fig. 7) using a
Markov chain Monte Carlo (MCMC) analysis. Considering that the velocity
profile of Ly$\alpha$ not only exhibits a similar trend with C iv but also is
observed at the largest radius, we only use the velocity profile of Ly$\alpha$
here. Eq. 10 denotes the logarithm of the likelihood used for performing the
MCMC.

$\ln\mathcal{L}=-\frac{1}{2}\Sigma_{i}\frac{(v_{\rm obs}(r_{i})-v_{\rm
model}(r_{i}))^{2}}{\sigma^{2}_{\rm obs}(r_{i})}$ (10)

The prior of free parameters are shown in Tab. 7. The fitting results are
shown in Fig. 7 (left). The reduced $\chi^{2}$ is $\chi_{r}^{2}\approx 1.3$
which indicates the modified model is consistent with our observations.

The corner plot of the best-fitting parameters are shown in Fig. 9. The best-
fit initial radius, $r_{\rm init}=66.22^{+1.54}_{-1.19}$ kpc, is within the
halo virial radius of 87 kpc. We note that the initial radius is limited by
observations. The velocities are only observed up to 50 kpc. The best-fit
initial radial velocity and tangential velocity of the cool cloud are $v_{\rm
r,init}=130.37^{+2.5}_{-2.08}$ km s-1 and $v_{\rm
t,init}=163.44^{+2.18}_{-2.49}$ km s-1, respectively. Wang et al. (2022) show
that the cool CGM gas could gain angular momentum from the large-scale
environment through galaxy fly-by interactions which lead the gas velocity to
be $0-200$ km s-1. In fact, recent observations have revealed the CGM inflow
with a radial velocity of $\sim 300$ km s-1 at $z\approx 2$ (Fu et al., 2021).
The best-fitting radial velocity and tangential velocity are comparable to
both simulations and observations. For the evaporation rate, our best-fit
value is $\alpha=1.56^{+0.05}_{-0.04}$ Gyr-1 which is similar to the low-$z$
results (Afruni et al., 2019). For the mass of the cool cloud, we find that
our best-fitting value is ${\rm log}(m_{\rm
cl}/M_{\odot})=6.04^{+0.02}_{-0.03}$. This mass is two orders of magnitude
larger than the cool cloud mass estimated by Afruni et al. (2019) but roughly
consistent with the cool cloud mass yielded by Afruni et al. (2022). For the
hot corona fraction, we derive $f_{\rm hot}=0.36^{+0.02}_{-0.02}$ which is
consistent with cosmological simulations (Machado et al., 2018). Note that,
from Fig. 9, the cloud mass degenerates with the evaporation rate and the hot
corona fraction ($f_{\rm hot}$). We, thus, prefer not to have strong claims
for these quantities.

From the inflow model, the velocity profile can be explained by the
competition between the halo gravity and the drag force. The projection effect
also plays a role here. When the cool gas cloud starts to fall into the
galaxy, the initial velocity is small. The cloud is firstly accelerated due to
the halo gravity at this stage. Since the drag force exerted by the hot gas is
proportional to $v^{\prime 2}$ (Eq. 6), at the stage when the velocity of the
cloud is large enough near the central region, the drag force of the hot gas
and the loss of cool cloud mass begin to take control leading to the
deceleration. In addition, the evaporation of the gas is also an important
effect influencing the cloud motion. Moreover, the inspiraling trajectory of
the gas inflow seen in both observations (Zhang et al., 2022) and simulations
(Wang et al., 2022; Stewart et al., 2017) is the natural consequence after
considering the tangential motion of both the cool gas and the hot gas (Fig.
7, right).

We should note that our inflow model is simplified which only includes one gas
cloud into consideration. In fact, the inflow should be a “continuous flow”
with multiple clouds. These clouds could have different kinematics due to the
gas shock. Since the detailed study of the gas shock is beyond this work, we
present a brief discussion here.

To induce the shock, the gas velocity should exceed the local sound speed
($c_{s}$) which is (Yun et al., 2019)

$c_{s}=\sqrt{\frac{\gamma k_{\rm B}T_{\rm gas}}{\mu m_{\rm p}}}$ (11)

where $T_{\rm gas}$ is the gas temperature, $k_{\rm B}$ is the Boltzmann
constant, $\gamma=5/3$ is the adiabatic index for the monatomic gas, and $\mu
m_{\rm p}$ is the average particle mass. $m_{\rm p}$ is the proton mass. For
CGM, we have $\mu m_{\rm p}\approx 0.6m_{\rm p}$ (Yun et al., 2019; Gritton et
al., 2017). In our case, the cloud is moving in the diffuse hot corona. Since
the hot corona is virialized (Afruni et al., 2019), the temperature of the hot
corona is

$T_{\rm gas}=\frac{\mu m_{\rm p}GM_{\rm h}}{2k_{\rm B}r_{\rm vir}}$ (12)

where $M_{\rm h}$ is the halo mass and $r_{\rm vir}$ is the virial radius of
the halo. Given $M_{\rm h}=10^{12.1}\ M_{\odot}$ and $r_{\rm vir}=87$ kpc, we
have $T_{\rm gas}=2.3\times 10^{6}\ {\rm K}$. From Eq. 11, we have
$c_{s}\approx 228$ km s-1. This local sound speed is roughly consistent with
the largest value of the observed velocities, which indicates that the cloud
is hard to induce the shock. Nevertheless, considering that the observed
velocity is only a projection of the gas velocity, the gas velocity should be
larger than the observed velocity. Thus, for the “continuous flow” of the gas
cloud, a small fraction of the cloud could be influenced by the shock.

For most of the clouds, since they do not induce shock, they should have
similar kinematics with each other (Fig. 7). For the small fraction of clouds
influenced by the shock, we present the qualitative discussion.

On the one hand, the gas shock could slow down the inflowing gas by
dissipating the kinetic energy. This will then make the velocity profile in
the radius of $10\ {\rm kpc}\leq r\leq 30\ {\rm kpc}$ steeper. On the other
hand, the drag force is proportional to the velocity squared. Since the cloud
is slowed down by the shock, the drag force could be reduced. This result will
in turn flatten the velocity profile in the inner region. Combining these two
effects, the velocity profile (Fig. 7, left) might not change too much after
considering the shock. Moreover, the shock could also induce gas heating by
converting the kinetic energy to the thermal energy of the gas, which might
accelerate the evaporation of the cool cloud. Nevertheless, for Q1517+0055,
the gas is metal-enriched to about solar metallicity. The heated gas could
also be efficiently cooled down through the emission from the highly ionized
metal atoms such as the C iv emission. To reach a more solid conclusion,
detailed hydrodynamical simulations and inflow models are needed to figure out
the impact of the shock.

###  4.4 CGM Gas Recycling

Discussions above show that the metal-enriched cool gas is more likely to
inflow to Q1517+0055. Such cool gas is undergoing the gas recycling process.
By combining the results of Zhang et al. (2022) and this work, we show a
possible physical picture in Fig. 10. At the beginning, the metal-enriched gas
born in the star-forming region of the galaxy is ejected to the CGM through
feedback. After cooling through the UV line emission, the enriched gas starts
to fall back to the galaxy given that thermal pressure cannot support the
gravity of the halo. Meanwhile, satellite galaxies fly by to further bring
angular momentum to the CGM gas leading to the inspiraling form of the inflow
(Wang et al., 2022).

We demonstrate that gas recycling could be a non-negligible process in the
metal-enriched CGM around high-$z$ quasars. To fully reveal the details of gas
recycling, more observations on the CGM diffuse emissions are needed.

##  5 Conclusions

In this paper, we present the discovery of a Ly$\alpha$ nebulae around the
type-II quasar, Q1517+0055. Our main findings are summarized as follows:

  * •

Above the $2\sigma$ surface brightness limit, we reveal the diffuse emissions
of Ly$\alpha$, He ii, and C iv on the physical scale of 122 kpc, 45 kpc, and
79 kpc, respectively (Fig. 1, left). The total Ly$\alpha$ luminosity is
$L_{\rm Ly\alpha}=3.04\pm 0.02\times 10^{44}\ {\rm erg\ s^{-1}}$. From the
spectra, we find that the Ly$\alpha$ and C iv emissions exhibit double peaks
which are caused by the associated Ly$\alpha$ and C iv absorption (Fig. 2).

  * •

By fitting the absorption, we find that the velocity of the absorption has an
increasing trend (Fig. 4). We construct an inspiraling inflow model which
explains the velocity profile as the consequence of the competition between
the halo gravity and the drag force of the hot gas. The model shows that gas
evaporation is also an important effect in determining the cloud motion.

  * •

From the line ratio diagnostic, we find that the observed line ratios between
the diffuse emissions are ${\rm HeII/Ly\alpha}\approx 0.08$ and ${\rm
CIV/Ly\alpha}\approx 0.28$, consistent with the photoionization scenario with
recombination and photon pumping included (Fig. 5, Left). By comparing ratios
of both the emission and column density, we find the cool gas in the CGM is
metal-enriched with the metallicity of $Z\geq Z_{\odot}$.

  * •

Comparing with the scenario of a powerful outflow, the inflow seems to be a
more natural interpretation. Gas recycling could be a non-negligible process
for high-$z$ quasars. More observations on the CGM diffuse emission are needed
to directly image this process.

Acknowledgments: We thank the anonymous referee for reading the paper
carefully and providing comments that helped improve and strengthen this
paper. We would like to also thank Helmut Dannerbauer for his contribution for
obtaining the submillimeter data for the series of this work. Z. C., S. Z., Y.
W., and M. L. are supported by the National Key R&D Program of China (grant
No. 2018YFA0404503), the National Science Foundation of China (grant No.
12073014), and Tsinghua University Initiative Scientific Research Program (No.
20223080023). X. D. and S. W. are supported by Tsinghua University Initiative
Scientific Research Program (grant No. 2019Z07L02017). This work is based on
observations made with the Keck-II Telescope. The data were obtained from Keck
Observatory Archive.

Figure 8: Left: The rotation profile of the hot gas in the CGM. We construct
this rotation profile by following the result of Danovich et al. (2015) which
study the angular momentum of the CGM gas for galaxies at $z=1\sim 3$. Right:
The density profile of the hot gas. This density profile is constructed by
following the Eq. 6 in Afruni et al. (2019). Figure 9: Corner plot of the MCMC
results for the fitting parameters. The one and two-dimensional posterior
probabilities for the seven free parameters are shown. We initialize the
twenty-five Markov chains and iterate each chain for twenty-thousand steps.
The first fifty steps are discarded for burn-in. After the iteration, the
results converge. Figure 10: The physical picture of the gas recycling. The
main galaxy first ejects the metal-enriched materials to the CGM. After
cooling, the metal-enriched gas cools and begins to fall back to the main
galaxy. Under the influence of the satellite galaxy and the hot gas, the
falling material forms the inspiraling stream. The competition between the
gravity of the halo and the drag force of the hot gas lead to the cool gas
accelerating at first and then decelerating. Ly$\alpha$
---
| Absoprtion | Emission
$\lambda_{\rm abs}$ [${\rm\AA}$] |  $N_{\rm HI}$ [cm-2] |  $b$ [km s-1] | $f$ |  $\Gamma$ [$\times 10^{8}$ s-1] |  $\lambda_{\rm emis}$ [${\rm\AA}$] |  $A$ [erg s-1 cm-2 ${\rm\AA^{-1}}$] |  $\sigma$ [km s-1]
initial value | 4434 | $10^{16}$ | 100 | 0.4162 | 6.258 | 4434 | $F_{\rm peak}$ | 300
range | [4419, 4449] | [$10^{12}$, $10^{20}$] | [45, 200] | 0.4162 | 6.258 | [4419, 4449] | [100%, 200%]$F_{\rm peak}$ | [100, 600]
Table 1: The initial value and range of fitting parameters for Ly$\alpha$. The
initial value of the wavelength corresponds to the systemic redshift.The
wavelength range corresponds to -1000 km s${}^{-1}\sim$ 1000 km s-1 centering
on the line center. $F_{\rm peak}$ denotes the peak flux in the spectrum
extracted from each spatial bin.

CIV
---
| Absoprtion | Emission
$\lambda_{\rm abs}$ [$\rm\AA$] |  $N_{\rm CIV}$ [cm-2] |  $b$ [km s-1] | $f$ |  $\Gamma$ [$\times 10^{8}$ s-1] |  $\lambda_{\rm emis}$ [$\rm\AA$] |  $A$ [erg s-1 cm-2 $\AA^{-1}$] |  $\sigma$ [km s-1]
initial value | 5646, 5653 | $10^{14.5}$ | 100 | 0.1899, 0.0948 | 2.643, 2.628 | 5646, 5653 | $F_{\rm peak}$ | 300
range | [5627, 5671] | [$10^{13}$, $10^{16}$] | [45, 200] | 0.1899, 0.0948 | 2.643, 2.628 | [5627, 5671] | [100%, 200%]$F_{\rm peak}$ | [100, 600]
Table 2: The initial value and range of fitting parameters for C iv. Since C
iv is a doublet, two initial values are given corresponding to the doublet of
$1548\AA$ and $1550\AA$. The lower limit of the wavelength range corresponds
to -1000 km s-1 centering on $\lambda=5646\AA$ and the upper limit of the
wavelength range corresponds to 1000 km s-1 centering on $\lambda=5653\AA$.
HeII
---
| Emission
$\lambda_{\rm emis}$ [$\AA$] |  $A$ [erg s-1 cm-2 $\AA^{-1}$] |  $\sigma$ [km s-1]
initial value | 5983 | $F_{\rm peak}$ | 300
range | [5963, 6003] | [100%, 200%]$F_{\rm peak}$ | [100, 600]
Table 3: The initial value and range of fitting parameters of He ii. The setting is the same as the Ly$\alpha$. Ly$\alpha$ | CIV | HeII
---|---|---
log(NHI/cm-2) |  $\lambda_{\rm abs,Ly\alpha}$ [$\AA$] |  $\lambda_{\rm emis,Ly\alpha}$ [$\AA$] | log(NCIV/cm-2) |  $\lambda_{\rm abs,CIV}$ [$\AA$] |  $\lambda_{\rm emis,CIV}$ [$\AA$] |  $\lambda_{\rm emis,HeII}$ [$\AA$]
14.4$\pm$0.2 | 4433.1$\pm$0.2 | 4435.0$\pm$0.1 | 14.9$\pm$0.2 | 5647.7$\pm$0.5 | 5649.1$\pm$0.1 | 5981.9$\pm$0.4
14.4$\pm$0.2 | 4433.2$\pm$0.2 | 4435.1$\pm$0.1 | 14.8$\pm$0.4 | 5647.1$\pm$0.6 | 5649.1$\pm$0.1 | 5982.1$\pm$0.3
14.5$\pm$0.2 | 4433.3$\pm$0.3 | 4436.2$\pm$0.1 | 14.9$\pm$0.2 | 5647.1$\pm$0.4 | 5648.8$\pm$0.2 | 5981.4$\pm$0.3
14.4$\pm$0.2 | 4433.4$\pm$0.2 | 4436.2$\pm$0.1 | 14.9$\pm$0.2 | 5647.5$\pm$0.5 | 5648.4$\pm$0.2 | 5982.0$\pm$0.3
14.2$\pm$0.2 | 4433.0$\pm$0.2 | 4435.4$\pm$0.3 | 14.8$\pm$0.4 | 5647.4$\pm$0.5 | 5648.6$\pm$0.1 | 5982.8$\pm$0.3
14.2$\pm$0.2 | 4432.6$\pm$0.4 | 4436.2$\pm$0.0 | 14.8$\pm$0.2 | 5647.4$\pm$0.5 | 5648.4$\pm$0.1 | 5982.1$\pm$0.3
14.0$\pm$0.2 | 4433.1$\pm$0.3 | 4436.1$\pm$0.1 | 14.9$\pm$0.0 | 5647.7$\pm$0.3 | 5648.2$\pm$0.1 | 5981.8$\pm$0.4
14.2$\pm$0.2 | 4432.9$\pm$0.3 | 4435.4$\pm$0.2 | 14.8$\pm$0.4 | 5647.3$\pm$0.5 | 5648.7$\pm$0.1 | 5983.2$\pm$0.3
14.2$\pm$0.2 | 4433.1$\pm$0.3 | 4435.9$\pm$0.1 | 14.8$\pm$0.4 | 5648.2$\pm$0.3 | 5648.0$\pm$0.1 |
14.6$\pm$0.2 | 4432.9$\pm$0.3 | 4434.6$\pm$0.1 | 14.7$\pm$0.4 | 5648.1$\pm$0.4 | 5649.9$\pm$0.1 |
14.2$\pm$0.2 | 4433.2$\pm$0.3 | 4435.9$\pm$0.1 |  |  |  |
14.7$\pm$0.3 | 4433.1$\pm$0.4 | 4435.9$\pm$0.1 |  |  | 5650.6$\pm$0.6 |
14.3$\pm$0.0 | 4432.3$\pm$0.2 | 4435.2$\pm$0.1 | 14.8$\pm$0.4 | 5647.5$\pm$0.4 | 5648.4$\pm$0.1 | 5982.9$\pm$0.3
14.3$\pm$0.3 | 4432.3$\pm$0.3 | 4435.1$\pm$0.2 | 13.9$\pm$0.4 | 5647.1$\pm$1.2 | 5651.6$\pm$0.2 |
14.5$\pm$0.2 | 4431.4$\pm$0.5 | 4435.0$\pm$0.1 | 14.8$\pm$0.2 | 5647.8$\pm$0.3 | 5648.5$\pm$0.2 |
14.4$\pm$0.2 | 4432.4$\pm$0.3 | 4434.7$\pm$0.1 | 14.8$\pm$0.3 | 5647.2$\pm$0.5 | 5648.4$\pm$0.1 | 5983.1$\pm$0.3
13.6$\pm$0.2 | 4433.5$\pm$0.2 | 4435.6$\pm$0.1 |  |  |  |
13.7$\pm$0.2 | 4433.0$\pm$0.6 | 4435.6$\pm$0.1 | 14.7$\pm$0.2 | 5647.9$\pm$0.5 | 5648.1$\pm$0.4 |
14.4$\pm$0.3 | 4431.9$\pm$0.5 | 4434.7$\pm$0.2 | 14.9$\pm$0.1 | 5647.1$\pm$0.4 | 5648.4$\pm$0.1 | 5983.6$\pm$0.2
14.2$\pm$0.2 | 4432.3$\pm$0.5 | 4436.2$\pm$0.1 | 14.3$\pm$0.1 | 5646.5$\pm$0.3 | 5651.5$\pm$0.2 | 5983.7$\pm$0.3
|  | 4433.4$\pm$0.4 |  |  |  |
14.2$\pm$0.2 | 4433.5$\pm$0.2 | 4435.8$\pm$0.1 | 14.8$\pm$0.4 | 5649.2$\pm$0.8 | 5645.0$\pm$0.0 | 5978.2$\pm$1.1
|  | 4435.0$\pm$0.2 |  |  |  |
14.1$\pm$0.2 | 4430.1$\pm$0.6 | 4432.8$\pm$0.6 |  |  |  |
14.4$\pm$0.1 | 4429.8$\pm$0.6 | 4433.9$\pm$0.1 |  |  | 5648.4$\pm$0.5 |
14.2$\pm$0.3 | 4430.2$\pm$0.7 | 4434.1$\pm$0.1 | 14.5$\pm$0.2 | 5647.2$\pm$0.4 | 5647.6$\pm$0.2 |
14.4$\pm$0.2 | 4429.4$\pm$0.7 | 4433.8$\pm$0.1 | 14.6$\pm$0.4 | 5646.4$\pm$0.8 | 5647.2$\pm$0.2 |
14.3$\pm$0.0 | 4431.0$\pm$0.3 | 4435.7$\pm$0.1 | 13.8$\pm$0.3 | 5646.8$\pm$0.8 | 5651.4$\pm$0.2 | 5983.8$\pm$0.3
14.2$\pm$0.2 | 4433.4$\pm$0.1 | 4436.1$\pm$0.1 |  |  | 5648.8$\pm$0.4 |
14.1$\pm$0.1 | 4433.4$\pm$0.2 | 4436.0$\pm$0.1 |  |  | 5646.2$\pm$0.3 |
14.7$\pm$0.3 | 4433.2$\pm$0.3 | 4436.4$\pm$0.2 | 14.6$\pm$0.2 | 5648.0$\pm$0.4 | 5649.4$\pm$0.2 |
|  | 4431.1$\pm$0.5 |  |  |  |
14.8$\pm$0.2 | 4433.4$\pm$0.2 | 4436.0$\pm$0.1 | 14.9$\pm$0.0 | 5647.8$\pm$0.2 | 5648.0$\pm$0.1 | 5981.8$\pm$0.4
Table 4: The fitting parameters of the Ly$\alpha$, He ii, and C iv lines. The log($\rm N_{\rm HI}$/cm-2), log($\rm N_{\rm CIV}$/cm-2), $\lambda_{\rm abs,Ly\alpha}$, and $\lambda_{\rm abs,CIV}$ are from fitting the absorption. The $\lambda_{\rm emis,Ly\alpha}$, $\lambda_{\rm emis,CIV}$, and $\lambda_{\rm emis,HeII}$ are from fitting the emissions. The blanks in the column are the parameter that is neglected according to the selection criteria from the Sec. 3.2. Ly$\alpha$ | CIV | HeII
---|---|---
log(NHI/cm-2) |  $\lambda_{\rm abs,Ly\alpha}$ [$\AA$] |  $\lambda_{\rm emis,Ly\alpha}$ [$\AA$] | log(NCIV/cm-2) |  $\lambda_{\rm abs,CIV}$ [$\AA$] |  $\lambda_{\rm emis,CIV}$ [$\AA$] |  $\lambda_{\rm emis,HeII}$ [$\AA$]
14.8$\pm$0.2 | 4433.4$\pm$0.2 | 4436.0$\pm$0.1 | 14.9$\pm$0.0 | 5647.8$\pm$0.2 | 5648.0$\pm$0.1 | 5981.8$\pm$0.4
14.5$\pm$0.2 | 4433.4$\pm$0.2 | 4436.1$\pm$0.2 | 14.2$\pm$0.3 | 5647.4$\pm$0.8 | 5652.8$\pm$0.3 | 5981.3$\pm$0.4
14.8$\pm$0.2 | 4433.1$\pm$0.2 | 4436.4$\pm$0.1 | 14.9$\pm$0.0 | 5647.1$\pm$0.3 | 5649.2$\pm$0.2 | 5981.6$\pm$0.4
14.2$\pm$0.2 | 4433.3$\pm$0.2 | 4436.1$\pm$0.2 | 14.8$\pm$0.4 | 5647.6$\pm$0.3 | 5649.2$\pm$0.1 | 5983.0$\pm$0.4
|  | 4432.5$\pm$0.3 |  |  |  |
14.4$\pm$0.2 | 4429.4$\pm$0.8 | 4434.0$\pm$0.1 | 14.6$\pm$0.0 | 5645.4$\pm$0.5 | 5647.2$\pm$0.1 | 5983.8$\pm$0.4
|  | 4433.0$\pm$0.1 |  |  |  |
|  | 4433.6$\pm$0.2 |  |  | 5646.5$\pm$0.8 |
14.0$\pm$0.2 | 4433.5$\pm$0.2 | 4436.4$\pm$0.3 |  |  | 5646.2$\pm$0.4 | 5984.5$\pm$0.9
14.1$\pm$0.2 | 4433.5$\pm$0.1 | 4436.2$\pm$0.3 | 14.5$\pm$0.1 | 5650.0$\pm$0.5 | 5648.7$\pm$0.4 |
14.1$\pm$0.2 | 4433.5$\pm$0.2 | 4436.0$\pm$0.2 | 14.7$\pm$0.3 | 5648.2$\pm$0.4 | 5648.3$\pm$0.2 | 5985.0$\pm$0.5
|  | 4437.9$\pm$0.4 |  |  |  |
14.0$\pm$0.2 | 4432.5$\pm$0.6 | 4432.7$\pm$0.1 |  |  |  |
14.4$\pm$0.2 | 4429.5$\pm$1.0 | 4434.0$\pm$0.1 | 14.5$\pm$0.0 | 5645.2$\pm$0.4 | 5647.3$\pm$0.1 | 5984.0$\pm$0.5
14.3$\pm$0.3 | 4433.5$\pm$0.2 | 4436.8$\pm$0.1 | 14.8$\pm$0.2 | 5647.2$\pm$1.3 | 5648.8$\pm$0.2 | 5983.7$\pm$0.5
14.5$\pm$0.2 | 4433.3$\pm$0.2 | 4436.3$\pm$0.1 | 14.9$\pm$0.2 | 5647.3$\pm$0.4 | 5649.4$\pm$0.1 | 5981.6$\pm$0.4
14.4$\pm$0.3 | 4430.7$\pm$0.8 | 4434.9$\pm$0.1 | 13.7$\pm$0.3 | 5647.1$\pm$0.9 | 5651.2$\pm$0.2 | 5984.1$\pm$0.3
14.3$\pm$0.3 | 4432.1$\pm$0.4 | 4435.8$\pm$0.1 | 14.8$\pm$0.2 | 5647.7$\pm$0.3 | 5649.1$\pm$0.1 | 5983.9$\pm$0.3
14.4$\pm$0.2 | 4431.2$\pm$0.6 | 4434.1$\pm$0.0 | 14.1$\pm$0.3 | 5646.7$\pm$1.6 | 5649.1$\pm$0.2 | 5983.4$\pm$0.6
14.3$\pm$0.2 | 4433.6$\pm$0.3 | 4436.6$\pm$0.1 | 14.5$\pm$0.1 | 5647.3$\pm$0.4 | 5651.9$\pm$0.3 | 5983.5$\pm$0.4
|  | 4438.9$\pm$0.2 |  |  |  |
14.2$\pm$0.2 | 4433.2$\pm$0.2 | 4435.9$\pm$0.2 | 14.5$\pm$0.3 | 5648.4$\pm$0.4 | 5649.9$\pm$0.1 | 5983.6$\pm$0.4
14.2$\pm$0.3 | 4433.4$\pm$0.1 | 4436.1$\pm$0.2 | 14.1$\pm$0.3 | 5646.8$\pm$1.4 | 5652.6$\pm$0.2 | 5982.5$\pm$0.4
14.2$\pm$0.3 | 4433.4$\pm$0.2 | 4435.0$\pm$0.4 | 14.8$\pm$0.4 | 5647.5$\pm$0.4 | 5649.6$\pm$0.2 | 5983.2$\pm$0.5
14.4$\pm$0.2 | 4431.6$\pm$0.5 | 4435.1$\pm$0.1 | 14.5$\pm$0.2 | 5649.4$\pm$0.5 | 5650.0$\pm$0.1 |
14.3$\pm$0.1 | 4431.6$\pm$0.4 | 4435.3$\pm$0.1 | 14.5$\pm$0.2 | 5648.5$\pm$0.4 | 5649.3$\pm$0.2 | 5983.9$\pm$1.5
14.4$\pm$0.3 | 4433.2$\pm$0.2 | 4434.7$\pm$0.1 | 14.6$\pm$0.2 | 5649.3$\pm$0.3 | 5649.8$\pm$0.1 | 5982.3$\pm$0.6
14.3$\pm$0.2 | 4433.0$\pm$0.2 | 4435.6$\pm$0.2 | 14.0$\pm$0.2 | 5648.5$\pm$1.2 | 5652.6$\pm$0.2 | 5984.6$\pm$0.5
14.2$\pm$0.2 | 4433.5$\pm$0.7 | 4437.4$\pm$0.1 | 14.8$\pm$0.0 | 5647.5$\pm$0.3 | 5651.0$\pm$0.2 | 5984.6$\pm$0.6
|  | 4432.6$\pm$0.3 |  |  |  |
14.3$\pm$0.2 | 4433.0$\pm$0.2 | 4435.8$\pm$0.7 | 14.1$\pm$0.3 | 5646.8$\pm$2.0 | 5653.2$\pm$0.4 |
14.2$\pm$0.2 | 4430.8$\pm$0.7 | 4434.6$\pm$0.3 |  |  |  |
|  | 4432.7$\pm$0.1 |  |  |  |
|  | 4437.6$\pm$0.2 |  |  |  |
14.3$\pm$0.3 | 4431.7$\pm$0.4 | 4434.6$\pm$0.3 |  |  |  |
|  | 4436.1$\pm$0.5 |  |  |  |
Table 5: Continued | Ly$\alpha$ | C iv | He ii
---|---|---|---
k [km s-1 kpc-1] | $8.3\pm 3.4$ | $4.2\pm 2.3$ | $1.6\pm 3.3$
Table 6: The best-fitting slopes of the velocity profile with the radius of $10\ {\rm kpc}\leq R\leq 30\ {\rm kpc}$. The slopes of the Ly$\alpha$ and C iv have positive values while the slope of He ii is around zero. | initial value | range
---|---|---
$r_{\rm init}$ [kpc] | $r_{\rm vir}$ | [0, 3$r_{\rm vir}$]
$v_{\rm r,init}$ [km s-1] | 0.00 | [-800, +800]
$v_{\rm t,init}$ [km s-1] | 0.00 | [-800, +800]
${\rm log}(m_{\rm cool}/M_{\odot})$ | 5.00 | [2, 8]
$\alpha$ [Gyr-1] | 1.71 | [0, 10]
$\theta$ [rad] | $\pi/2$ | [0, $\pi$]
$f_{\rm hot}$ | 0.35 | [0, 1]
Table 7: The initial value and prior of free parameters input into the MCMC.
Quiet large priors are given to the seven free parameters. For the initial
radial velocity and tangential velocity, the minus means the negative
direction.

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