# Compact and Quiescent Circumgalactic Medium and Ly$\alpha$ Halos around
Extremely Red Quasars (ERQs)

Jarred Gillette,1 Marie Wingyee Lau,1 Fred Hamann,1 Serena Perrotta,2 David S.
N. Rupke,3 Dominika Wylezalek,4 Nadia L. Zakamska,5 and Andrey Vayner5
1Department of Physics & Astronomy, University of California, Riverside, CA
92521, USA
2Center for Astrophysics and Space Sciences, University of California, San
Diego, CA 92093, USA
3Department of Physics, Rhodes College, Memphis, TN 38112, USA
4Astronomical Calculation Institute, University of Heidelberg, D-69120
Heidelberg, Germany
5Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD
21218, USA E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Red quasars may represent a young stage of galaxy evolution that provide
important feedback to their host galaxies. We are studying a population of
extremely red quasars (ERQs) with exceptionally fast and powerful outflows, at
median redshift $z$ = 2.6. We present Keck/KCWI integral field spectra of 11
ERQs, which have a median color $i-W3$ = 5.9 mag, median $\left\langle
L_{\text{bol}}\right\rangle$ $\approx$ 5 $\times$ $10^{47}$ erg s-1,
Ly$\alpha$ halo luminosity $\left\langle L_{\text{halo}}\right\rangle$ $=$ 5
$\times$ $10^{43}$ erg s-1, and maximum linear size $>128$ kpc. The ERQ halos
are generally similar to those of blue quasars, following known trends with
$L_{\text{bol}}$ in halo properties. ERQs have halo symmetries similar to
Type-I blue quasars, suggesting Type-I spatial orientations. ERQ $\left\langle
L_{\text{halo}}\right\rangle$ is $\sim$2 dex below blue quasars, which is
marginal due to scatter, but consistent with obscuration lowering photon
escape fractions. ERQ halos tend to have more compact and circularly symmetric
inner regions than blue quasars, with median exponential scale lengths of
$\sim$9 kpc, compared to $\sim$16 kpc for blue quasars. When we include the
central regions not available in blue quasar studies (due to PSF problems),
the true median ERQ halo scale length is just $\sim$6 kpc. ERQ halos are also
kinematically quiet, with median velocity dispersion 293 km s-1, consistent
with expected virial speeds. Overall we find no evidence for feedback on
circumgalactic scales, and the current episode of quasar activity, perhaps due
to long outflow travel times, has not been around long enough to affect the
circumgalactic medium. We confirm the narrow Ly$\alpha$ emission spikes found
in ERQ aperture spectra are halo features, and are useful for systemic
redshifts and measuring outflow speeds in other features.

###### keywords:

galaxies: active – quasars: emission lines – galaxies: intergalactic medium –
galaxies: halos – galaxies: evolution – galaxies: high-redshift

††pubyear: 2023††pagerange: Compact and Quiescent Circumgalactic Medium and
Ly$\alpha$ Halos around Extremely Red Quasars (ERQs)–Compact and Quiescent
Circumgalactic Medium and Ly$\alpha$ Halos around Extremely Red Quasars (ERQs)

##  1 Introduction

Quasars are supermassive black holes which grow as they rapidly accrete
infalling material at the center of their host galaxy. At high redshift,
accretion can coincide with galactic assembly via galaxy mergers, or streams
of infalling gas. Major merger activity could trigger both star formation and
growth of the central black hole (Hopkins et al., 2006, 2008; Somerville et
al., 2008; Glikman et al., 2015). The process of infalling gas, cold-mode
accretion, may also be a dominant mechanism for supplying matter for the
formation of galaxies, triggering starbursts, and fueling quasars (Kereš et
al., 2009; Dekel et al., 2009; Faucher-Giguère & Kereš, 2011; Fumagalli et
al., 2014). Accretion by infall can coincide with outflows as the subsequent
galaxy activity generates feedback, influencing the galaxy’s formation (Costa
et al., 2014; Nelson et al., 2015; Suresh et al., 2019). A possible
evolutionary scheme is where the central back hole grows in obscurity until
feedback generates outflows, which clear the obscuring interstellar medium, to
reveal a luminous quasar (Sanders et al., 1988; Di Matteo et al., 2005;
Hopkins et al., 2006, 2008, 2016; Rupke & Veilleux, 2011, 2013; Liu et al.,
2013; Stacey et al., 2022).

Red quasars are important for testing the hypothesis that obscured quasars may
be in a young evolution phase. Young quasars may be reddened by dust created
in a major starburst inside the galaxies, triggered by a merger or cold-mode
accretion. They may show signs of early evolution such as rapid accretion or
more powerful outflows from the quasar, or more infall from the intergalactic
medium, as they transition in to blue quasars. Studies of red/obscured quasars
have found many to be in mergers or high-accretion phases (Glikman et al.,
2015; Wu et al., 2018; Zakamska et al., 2019). Extremely Red Quasars (ERQs)
display powerful outflow signatures, and are interesting candidates for
studying a young quasar phase in the galaxy/quasar evolution scheme (Hamann et
al., 2017).

ERQs were first discovered among the Baryon Oscillation Spectroscopic Survey
(BOSS, Pâris et al., 2017) in the Sloan Digital Sky Survey-III (SDSS,
Eisenstein et al., 2011) and the ALLWISE data release (Cutri et al., 2011,
2013) of the Wide-field Infrared Survey Explorer (WISE, Wright et al., 2010).
They were initially described in Ross et al. (2015), and were further refined
in Hamann et al. (2017) to $\sim$200 objects, characterized by their extremely
red colors ($i-W3$ $>4.6$ mag; Hamann et al., 2017). Currently known ERQs are
at comic noon redshifts $z$ $\sim$ 2$-$4, and are on the high end of quasar
bolometric luminosities $L_{bol}$ > $10^{47}$ erg s-1.

ERQs exhibit other extreme spectral properties that make them unique compared
to other red quasar samples, beyond being extremely red. Many have unusually
strong and/or blueshifted broad emission lines, with C IV rest equivalent
widths > 100 Å, and peculiar wingless profiles with high kurtosis (Monadi &
Bird, 2022). They also frequently have unusual emission line flux ratios (e.g.
high N V $\lambda$1240/Ly$\alpha$ or N V $\lambda$1240/C IV $\lambda$1549).
These broad line features indicate outflow properties controlled by accretion,
and reside on scales of tens of parsecs (Zhang et al., 2017; Alexandroff et
al., 2018). ERQs also have the most blueshifted [O III] $\lambda$5007 emission
lines ever reported, with speeds > 6000 km s-1 (Zakamska et al., 2016;
Perrotta et al., 2019). [O III] is significant because it traces gases on
galactic scales, at tens of kpc, and are low density forbidden transitions
(Hamann et al., 2011; Vayner et al., 2021). Outflows at these galactic scales
carry energy that could generate feedback in the host galaxy. This suite of
properties found in ERQ spectra indicate more extreme physical conditions than
what are found in typical quasar populations, and beyond orientation effects.

Understanding ERQs and their evolutionary nature has launched a multi-faceted
study of their physical environments. ERQ host galaxies have been directly
imaged with Hubble Space Telescope to look for signs of merger activity
(Zakamska et al., 2019). Major merger activity was not found in most of their
objects, but observations of high redshift quasars have added difficulty
subtracting point-spread function in two dimensional imaging. Another approach
is to study the kinematics and physical extent of the outflowing gas,
specifically, the [O III] emission (Perrotta et al. (2019); Vayner et al.
(2021); Lau et al. in preparation). Past studies have found [O III] outflows
to be spatially compact, not extended to circumgalactic regions, and at kpc
scales of the nuclear regions of host galaxies (Vayner et al., 2021). A third
method of investigating ERQ environments is through their halo emission. The
circumgalactic medium (CGM) has an important role in understanding the
evolution of galaxies (Tumlinson et al., 2017), and is the site of interaction
for outflows from galaxies and the inflows from the intergalactic medium.

High redshift quasars have been found to have large gas reservoirs in the CGM,
observed in fluorescent Ly$\alpha$ emission, and have been interpreted as
filaments or inflowing gas in cold-mode accretion (Borisova et al., 2016a;
Arrigoni Battaia et al., 2019; Cai et al., 2019). ERQs are a well defined and
uniform sample from BOSS, and make good targets for studying their Ly$\alpha$
halos for quasar evolution.

In this paper, we aim to investigate whether ERQs represent an earlier
evolutionary stage compared to regular luminous blue quasars, which are
characterized by strong rest-UV emission lines and blue color across the rest-
frame mid-UV to Near-IR spectral range. With the embedded quasar evolution
scheme, we investigate ERQs for evidence they are different or unusual from
normal blue quasars at the same redshifts and luminosities. This could be
evidence for feedback, but also signatures of more intense infall or chaotic
mergers, more/less asymmetries, and/or suppressed Ly$\alpha$ halo emission due
to the quasar obscuration. Detailed analysis of the Ly$\alpha$ emission from
ERQs can provide key insights into this question.

Secondarily we want to investigate the spatial origin of a peculiar, and
narrow, Ly$\alpha$ emission component frequently seen in spatially unresolved
ERQ spectra. It often appears as a “spike” on top of the broad Ly$\alpha$
emission, and it’s narrow width (FWHM < 1,000 km s-1) indicates the emission
is far from the quasar’s broad line region (BLR). The spike sometimes
coincides with the rest frame of other narrow emission lines (e.g. He II and
narrow [O III], Hamann et al. (2017) and Perrotta et al. (2019),
respectively). We want to determine whether this sharp feature originates in
the extended inner-halo region, as hypothesized in Hamann et al. (2017), and
discussed or used in Perrotta et al. (2019) and Lau et al. (2022). This
investigation is motivated from observations that many broad emission lines in
ERQs are often blueshifted, and involved in outflow, that would typically be
at the systemic in other quasar populations (Hamann et al., 2017; Perrotta et
al., 2019). This blueshifting would systemically bias automated redshift
estimates generated in BOSS, making outflows appear weaker. If the source of
the Ly$\alpha$ spike is far from the galactic center, where outflows would
take place, and is extended in the galactic halo, then it would not be
involved in strong outflows and would provide a better systemic redshift
estimate. Confirming the narrow Ly$\alpha$ emission can be used as a better
systemic redshift of ERQs also confirms outflows hypothesized in the
discussions aforementioned, and helps constrain velocities for future work on
ERQ outflows (J. Gillette et al. 2023b in preparation).

Our team already analyzed one Ly$\alpha$ halo from our sample that is the
reddest known ERQ (J0006+1215, in Lau et al. (2022)), which displays an
extremely fast [O III] $\lambda$5007 outflow at $\sim$6000 km s-1 (Perrotta et
al., 2019). The Ly$\alpha$ halo spans $\sim$100 kpc, and the narrow Ly$\alpha$
emission spike in the quasar spectrum originates from the inner halo. It is
kinematically quiet, with velocity dispersion of $\sim$300 km s-1 and no
broadening above the dark matter circular velocity down to the spatially
resolved limit $\sim$6 kpc from the quasar. Lau et al. (2022), hereafter L22,
proposed that the He II $\lambda$1640/Ly$\alpha$ ratio of the inner halo and
the asymmetry level of the overall halo in J0006+1215 are dissimilar to Type-
II quasars, suggesting unique physical conditions for J0006+1215 that are
beyond orientation differences from other quasar populations. We note the
Type-I/II quasar classification dichotomy, because other studies find that
Type-IIs tend to show more asymmetric halos, consistent with more edge-on
views of the quasar. It also correlates strongly with the level of obscuration
toward the nucleus Greene et al. (2014), and we want to distinguish ERQs from
obscured quasar populations explained by orientation effects.

In this paper we analyze Ly$\alpha$ halos of a sample of ERQs, and compare
them to those around other quasars as a unique population. It is organized as
follows. Section 2 describes the selection method for ERQ observations, their
data reduction, calibration, and post-processing. Section 3 describes the
measured halo properties of ERQ sample, such as the extended line emission
surrounding the quasar, and analysis results of size, morphology, surface
brightness (SB), and kinematics of the extended emission. In Section 4 we
discuss implications for quasar youth, feedback, and further for quasar
studies. Section 5 concludes the paper. Throughout this paper we adopt a
$\Lambda$-CDM cosmology with $H_{0}$ = 69.6 km s-1 Mpc-1, $\Omega_{\text{M}}$
= 0.286 and $\Omega_{\Lambda}$ = 0.714, as adopted by the online cosmology
calculator developed by Wright (2006). All magnitudes are on the AB system.
Reported wavelengths are in vacuum and in the heliocentric frame.

##  2 Target Selection, Observations, and Data Reduction

Here we summarize the KCWI observations, data reduction, and post-processing
for the full sample of 12 ERQs, following the procedures described in detail
by L22. Our aim is to test whether the most extreme properties of ERQs
correlate in any way with particular or unusual Ly$\alpha$ halo properties.
Our second goal is to test the suggestion in Hamann et al. (2017) that the
narrow Ly$\alpha$ spikes in the BOSS spectra of some ERQs are halo emission.

###  2.1 Sample Selection

We select targets for our study from the sample of 205 ERQs in Hamann et al.
(2017), and in the redshift range $2.0\leq z\leq 3.6$, all have coverage of
the Ly$\alpha$ feature at rest-frame 1215.7Å. ERQs showing a narrow Ly$\alpha$
emission in the profile of their BOSS spectra, by visual inspection, were
prioritized during observing to determine if the emission originates from an
extended halo. We also prioritize ERQs in Perrotta et al. (2019), which have
[O III] measurements, which were shown to have color-correlated powerful
outflows at tens of kpc scales, and may be more likely to show evidence of
feedback in the halo. We also prefer the reddest available ERQs. We chose the
best available targets subject to weather and scheduling constraints, and
prioritize targets fitting several of the criteria above.

Finally, after applying our selection criteria to our four nights we present a
total sample of 12 ERQs, with redshifts $2.31\leq z\leq 3.14$. Half of them
have the narrow component in their Ly$\alpha$ emission. The median reddening
of the sample is $i-W3\approx 5.9$, Table 1 contains basic sample properties.

###  2.2 Observations

We observed our final sample of 11 ERQs using the Keck Cosmic Web Imager
(KCWI, Morrissey et al., 2018), on the Keck II telescope. KCWI is a wide
field, integral field spectrograph optimized for observing low-surface
brightness targets. It provides both spatial and spectral information for
resolved targets, allowing us to make pseudo-narrow-band images and obtaining
spectra from individual spatial-pixels, or “spaxels.”

Observations were conducted over four nights from 2018 to 2020, with identical
instrument configuration across the sample. Observation details are noted in
Table 1. Conditions during observation often varied through any night, but our
work had typical seeing FWHM of about (0.8-1.4) arcseconds. KCWI currently has
only a blue filter, and we used the BL grating, which has the best efficiency
and widest wavelength bandpass ($\Delta\lambda\approx$ 2,000Å). KCWI uses a
“slicer” to slice the field of view into rows or columns before going to the
grating. Slicers come in three different sizes to optimize field of view,
spectral resolution, and spatial sampling. We used the medium slicer to have
considerable field of view, spectral resolution comparable to SDSS, and
sufficient spatial sampling. This configuration yields a field of view of 15.7
arcsec $\times$ 18.9 arcsec, corresponding to a physical scale of
approximately 128 kpc $\times$ 154 kpc at our sample’s median redshift
($z_{em}\approx 2.61$). With 24 slices, the instrument configuration provides
a spatial sampling of 0.68 arcsec, and seeing limited, along the slices. Each
exposure was dithered 0.35 arcsec across slices to sub-sample the long spatial
dimension of the output spaxels, which have sizes of 0.68 arcsec $\times$ 0.29
arcsec. The spectral resolution is $R=1800$. The full spectral range is
approximately 3500 to 5625Å, which is ample for coverage of the Ly$\alpha$
emission profile across a wide range of quasar redshifts, $2.0\leq z\leq 3.6$.
We used exposures of 20 minutes, optimally integrating for 2 to 3 hours total,
and varied depending on target availability, observing conditions, and
priority of the object. We calibrated using arclamps and spectroscopic
standard stars at the beginning and end of each night.

###  2.3 Data Reduction & Post Processing

We adopted the data reduction and post-processing approaches described in
detail in L22. Here we only provide a summary of the major steps. We used the
KCWI Data Extraction and Reduction Pipeline (KDERP, https://github.com/Keck-
DataReductionPipelines/KcwiDRP) written in the Interactive Data Language (IDL)
for flat-fielding, cosmic-ray removal, and for the first-pass instrument noise
removal and background subtraction. We made sure that no prominent skyline
residuals are present near Ly$\alpha$ in each spectrum. We then used CWITools
(O’Sullivan et al., 2020), and the IDL library IFSFIT (Rupke & To, 2021), for
the second-pass background subtraction and removing internally scattered
light. Specifically, IFSFIT uses a spatially-unresolved quasar emission
template, generated from a one arcsecond aperture around the object, and is
scaled to subtract all emission from the quasar at every spaxel position. A
key step that was customized for half of the sample was the quasar template
which is subtracted to leave only halo emission in the residual, described in
Section 2.4. We also used CWITools’ simplified algorithm to subtract any
foreground continuum sources convolved with the point spread function.

###  2.4 Narrow Halo Emission

L22 confirmed that the narrow Ly$\alpha$ “spike” emission in ERQ spectra
originates in the halo. In Section 3.1 we further confirm this in the rest of
our ERQ sample. This insight into the emission’s origin allows us to treat the
emission differently in processing the spectra and images. For objects with no
spike the PSF spectral template removes all emission within the seeing disk
resulting in a hollow at the quasar position in the SB map, like in blue
quasar studies.

We followed the procedure for generating quasar spectral templates as
described in L22, and made customisations to the quasar template for each ERQ
identified to have narrow Ly$\alpha$ emission. We isolated the feature within
the one arcsecond template by interpolating underneath the narrow line,
effectively “clipping” it, and left the extended emission in the residual.
Examples of this template interpolation is shown in Figure 1 (see also L22).
In cases where the spectral location and profile shape of the spike was more
ambiguous, we compared extracted spectra from gradually larger aperture sizes.
We confirmed the spike was the only emission that increases with larger
aperture size, and interpolated underneath its narrow profile.

###  2.5 Line Variability

We inspected ERQ spectra for variability between our KCWI observations and the
BOSS catalog. The median time between observations is two years at rest frame
of the the median ERQ. In general, characteristics of line profiles do not
significantly change between SDSS and our observations, in agreement with
comments in L22. Similarities between these observations indicate the unusual
profile features that distinguish ERQs from typical quasars persist beyond two
years in the quasar frame, and are consistent with other observations of ERQs
from Hamann et al. (2017).

Table 1: ERQ properties in our program. $z_{em}$ is from the SDSS DR12Q BOSS
catalog emission-line measurements, $z_{halo}$ is computed from the Ly$\alpha$
line emission from the extended halo. C IV FWHM is from emission line fitting
done in Hamann et al. (2017). [O III] emission blueshift measurements, when
available, are from Perrotta et al. (2019), and blueshifted from CO emission
measurements by F. Hamann et al. (2023 in prep.), and will be later discussed
in Gillette et al. (2023b in prep.). Bolometric luminosity is estimated from
the W3 magnitude. ERQ J0834+0159 was observed under cloudy conditions, and is
omitted from analysis of Ly$\alpha$ halos.
Notes. a Quasars with their narrow Ly$\alpha$ component clipped from the quasar emission template. b Redshift approximated by Ly$\alpha$ line peak from an inner 1-arcsec aperture spectrum. c Blueshift relative to a redshift approximated by Ly$\alpha$ line peak from an inner 1-arcsec aperture spectrum. ERQ Name | RA | Dec | zem | zhalo | C IV FWHM | [O III] v98 | W3 | i-W3 | Bolometric Luminosity | Observation Date | Exposure Time
---|---|---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) |  |  | (km s-1) | (km s-1) | (mag) | (mag) | (erg/s) |  | (s)
J0006+1215a | 00:06:10.67 | 12:15:01.2 | 2.31 | 2.3184 | 4540$\pm$200 |  $-$6224.99 | 14.1 | 8.0 | 7.58e+47 | 2019-10-02 | 4,200.0
J0220+0137a | 02:20:52.11 | 01:37:11.1 | 3.14 | 3.1375 | 2613$\pm$161 | … | 15.8 | 6.2 | 3.68e+47 | 2019-10-02 | 8,400.0
J0834+0159 | 08:34:48.48 | 01:59:21.2 | 2.59 | 2.5882b | 2863$\pm$65 |  $-$4426.08 | 14.9 | 6.0 | 4.98e+47 | 2019-03-02 | 6,000.0
J1145+5742a | 11:45:08.00 | 57:42:58.6 | 2.79 | 2.8747 | 9103$\pm$446 | … | 14.3 | 4.8 | 1.14e+48 | 2019-03-02 | 10,800.0
J1232+0912 | 12:32:41.75 | 09:12:09.3 | 2.38 | 2.4034 | 4787$\pm$52 |  $-$7026.20 | 14.3 | 6.8 | 6.33e+47 | 2020-05-26 | 4,800.0
J1451+0132a | 14:51:13.61 | 01:32:34.1 | 2.77 | 2.8130 | 6231$\pm$156 | … | 14.7 | 5.7 | 6.78e+47 | 2019-03-02 | 10,800.0
J1451+2338a | 14:51:48.01 | 23:38:45.4 | 2.62 | 2.6348 | 4166$\pm$124 | … | 15.0 | 5.5 | 4.56e+47 | 2020-05-26 | 8,400.0
J1652+1728a | 16:52:02.61 | 17:28:52.3 | 2.94 | 2.9548 | 2403$\pm$45 |  $-$2534.00c | 14.9 | 5.4 | 6.80e+47 | 2020-05-26 | 4,800.0
J1705+2736 | 17:05:58.56 | 27:36:24.7 | 2.45 | 2.4461 | 1301$\pm$22 | … | 15.5 | 5.1 | 2.43e+47 | 2020-05-26 | 3,600.0
J2215$-$0056 | 22:15:24.03 |  $-$00:56:43.8 | 2.51 | 2.5074 | 4280$\pm$112 |  $-$3876.95 | 16.0 | 6.2 | 1.51e+47 | 2019-10-02 | 8,400.0
J2254+2327 | 22:54:38.33 | 23:27:14.5 | 3.09 | 3.0825 | 4412$\pm$146 | … | 16.5 | 5.5 | 1.68e+47 | 2018-10-05 | 10,800.0
J2323$-$0100 | 23:23:26.17 |  $-$01:00:33.1 | 2.36 | 2.3831 | 3989$\pm$62 |  $-$6458.03 | 15.2 | 7.2 | 2.88e+47 | 2019-10-02 | 7,800.0
Median | … | … | 2.61 | 2.6348 | 4223 | … | 15.0 | 5.9 | 4.56e+47 | … | …
Table 2: ERQ measurements of the Ly$\alpha$ halo luminosity and morphology. Area covered and size are shown as lower limits when extended halo is detected to the edge of the FOV. Ly$\alpha$ halo luminosities are measured from modified PSF subtraction, as referenced in Section 2.4.  ERQ Name | Area Covered | Maximum Linear Size | Halo Luminosity | Peak to Quasar Distance | Centroid to Quasar Distance | $e_{\text{weight}}$ | $e_{\text{unweight}}$
---|---|---|---|---|---|---|---
| (kpc2) | (kpc) | (erg/s) | (kpc) | (kpc) |  |
J0006+1215a | 6851 | 140 | 5.00e+43 | 3.44 | 5.56 | 0.44 | 0.69
J0220+0137a | >5693 | >104 | 6.26e+43 | 5.04 | 9.59 | 0.35 | 0.66
J1145+5742a | >10529 | >148 | 9.97e+43 | 2.31 | 17.09 | 0.74 | 0.71
J1232+0912 | 6016 | 119 | 5.40e+43 | 6.83 | 6.17 | 0.72 | 0.64
J1451+0132a | >9970 | >148 | 2.29e+44 | 0.00 | 4.00 | 0.43 | 0.59
J1451+2338a | >11645 | >157 | 3.80e+44 | 5.29 | 2.87 | 0.57 | 0.59
J1652+1728a | >8596 | >128 | 2.14e+44 | 2.30 | 3.72 | 0.46 | 0.49
J1705+2736 | >6703 | >122 | 2.37e+43 | 4.81 | 23.15 | 0.91 | 0.78
J2215$-$0056 | 3812 | 114 | 9.78e+42 | 28.91 | 21.50 | 0.87 | 0.85
J2254+2327 | 2181 | 80 | 9.36e+42 | 8.18 | 8.41 | 0.65 | 0.67
J2323$-$0100 | >3640 | >137 | 3.08e+42 | 9.97 | 19.95 | 0.86 | 0.65
Median | >6702 | >128 | 5.40e+43 | 5.04 | 6.50 | 0.65 | 0.66

Figure 1: Example spectral templates extracted from an inner 1 arcsecond
aperture spectra near Ly$\alpha$ of, from left to right, J1145+5742,
J1451+2338, and J1652+1728. The spectrum is shown in black, the interpolation
function is in dashed green, and the “clipped” narrow feature in the spectrum
is replaced by the thick red line segment. All emission lines are labelled
from the rest frame of the Ly$\alpha$ extended halo emission. Function fitting
procedures would become convoluted by absorption in the Ly$\alpha$ forest, and
so the interpolation function was hand-fit to account for smooth emission
features and continuum on the red side of Ly$\alpha$ and deep absorption on
the blue side. In the first panel, J1145+5742 has a straightforward and
distinct separation between the broad and narrow emission components. The
second panel shows J1451+2338, shown to have blended broad emission lines from
Ly$\alpha$ and N V $\lambda 1240$. The third panel of J1652+1728 also has
unusual emission lines, and the blueshifted central emission of Ly$\alpha$
caused uncertainties in clipping the narrow emission. We do not assume this
interpolation function describes any characteristics of the broad emission,
but simply isolates the emission from the narrow component of Ly$\alpha$.

###  2.6 Sample Properties

Table 1 lists basic properties of the sample, measured redshift of the
Ly$\alpha$ emission, and details of the observations. We include the SDSS BOSS
catalog emission-line redshift measurements $z_{em}$, and $z_{halo}$ computed
from the extended Ly$\alpha$ halo emission centroid, without the quasar
emission. We include C IV FWHM, measured from C IV $\lambda$1549 emission-line
profile fitting done in Hamann et al. (2017), and when available [O III]
$\lambda$5007 emission blueshift from Perrotta et al. (2019). We include
catalog magnitudes and color ($W3$ and $i-W3$), and our computed bolometric
luminosities ($L_{bol}$). We apply galactic extinction corrections to all
luminosity and SB measurements.

ERQs are heavily extincted in the visible and UV, but the amount of extinction
is difficult to determine. In Hamann et al. (2017) it is estimated that the
median SED is suppressed in ERQs by three magnitudes in the rest-frame UV, in
comparison to normal blue quasars. Uncertain extinction in ERQs also makes
bolometric luminosities difficult to determine. Therefore, we assume ERQs have
intrinsic SEDs like typical blue quasars, and use their measured WISE $W$3
fluxes (assumed to be unaffected by extinction) to estimate the bolometric
luminosities, similar to the ERQ luminosities computed by Perrotta et al.
(2019).

We compare the medians quantities from our sample to medians from other
surveys of blue quasars, discussion of these comparisons are in Section 3.4.
One quasar, J0834+0159, was observed under cloudy conditions, and was omitted
from analysis of Ly$\alpha$ halos. We do not have detection of other extended
emission lines such as C IV $\lambda$1549 or He II $\lambda$1640 except for
J0006+1215, which is discussed in L22.

###  2.7 Halo Detection

We used an optimal extraction algorithm for detecting diffuse emission in
Ly$\alpha$ instead of pseudo narrowband images to obtain morphology and
kinematics of the halo. This algorithm takes into account pixels of the three
dimensional data cube, or “voxels,” that are of good signal to noise (S/N > 2)
and connected at sides, edges, or corners to each other. Our algorithm is
described with more detail in L22, which followed algorithms in Borisova et
al. (2016b); Arrigoni Battaia et al. (2019); Cai et al. (2019); Farina et al.
(2019). Our surface brightness’s $1\sigma$ limit, and root-mean-square value,
are measured in a 1-arcsec aperture for a single 1-angstrom channel. Surface
brightness maps probe the halo Ly$\alpha$ emission down to a median $1\sigma$
SB limit of 2.16 $\times$ $10^{-19}$ erg s-1 cm-2 arcsec-2, across spatial
scales from 40 kpc to $>80$ kpc from the quasars. Surface brightness root-
mean-square has median of 2.26 $\times$ $10^{-19}$ erg s-1 cm-2 arcsec-2, for
a channel in rest-frame wavelengths between 1255 and 1275 Å, and where there
are no prominent quasar emission lines.

##  3 Measurements & Results

To investigate the environment of ERQs, we measure basic properties of the
Ly$\alpha$ halo emission, such as surface brightness, linear size, and
velocity dispersion. Peculiarities in halo properties compared to blue quasars
may be evidence ERQ inhabit a different quasar evolutionary phase.

Panels in Figure 2 show, from left to right, halo surface brightness, 1st
velocity moment of the line flux distribution (i.e. velocity shift), velocity
dispersion, circularly-averaged surface brightness (SB) radial profile, and
spatially-integrated spectrum, for 11 of the 12 observed ERQs. J0834+0159 was
observed under cloudy conditions, and is not included in the Figure 2 and
subsequent tables. Tables 2 - 4 list a variety of properties measured from
these maps.

###  3.1 Morphology & Brightness Maps

Morphology measurements such as extent and asymmetry may give insights into
the gaseous environment of the quasar, and could be influenced by large scale
structure, the presence of merger activity, and quasar luminosity.

Morphology of ERQ Ly$\alpha$ halos varies across the sample, with some halos
extending to the edge of the FOV (> 60-70 kpc), and others compact near the
central quasar ($\sim$40 kpc). These Ly$\alpha$ halos also show varying
asymmetry. We present Ly$\alpha$ SB maps in the first column of Figure 2. One
unique aspect of this project is showing continuous halo emission down to zero
projected distance from the quasar, and thus the six ERQs with Ly$\alpha$
spikes do not show a hollow due to our quasar PSF subtraction (Section 2.4).

Table 2 presents the measured projected distance from the quasar to the
Ly$\alpha$ halo emission peak, and to the halo centroid. The median distance
from quasar to peak in our sample is $r_{\text{peak}}=5.0$ kpc, and the median
distance from quasar to halo centroid is $r_{\text{centroid}}=6.5$ kpc.
Uncertainty in these projected distances is about half a pixel in size, or
$\sim$1 kpc. The position of the Ly$\alpha$ halo centroid is used in analysis
of spatial asymmetry in this section, and the position of the halo peak is
used in analysis of aperture kinematics in Section 3.2.

Six of the halos extend beyond the FOV, and $>55$ kpc from the central quasar.
Our sample has a median maximum linear size $>128$ kpc, and median halo
luminosity 5.40 $\times$ $10^{43}$ erg s-1.

We quantify the asymmetry level of the morphology of the Ly$\alpha$ halo with
the elliptical eccentricity parameters $e_{\text{weight}}$ and
$e_{\text{unweight}}$ (identical to L22). We define $e_{\text{weight}}$ using
flux-weighted second-order spatial moments with respect to the Ly$\alpha$ halo
centroid, and follow the formula in O’Sullivan & Chen (2020).
$e_{\text{unweight}}$ uses flux-unweighted spatial moments with respect to the
quasar position. Values of $e\approx 0$ correspond to circular morphologies,
and values near 1 correspond to being more elliptical. Parameter
$e_{\text{weight}}$ is defined as
$e_{\text{weight}}=\sqrt{1-\alpha_{\text{weight}}^{2}}$, where the flux-
weighted eccentricity parameter $\alpha_{\text{weight}}$ is defined in
Arrigoni Battaia et al. (2019) or Cai et al. (2019). $e_{\text{weight}}$ tends
to characterize central regions of the halo with high SB. Conversely,
$e_{\text{unweight}}$ is defined as
$e_{\text{unweight}}=\sqrt{1-\alpha_{\text{unweight}}^{2}}$, where the flux
unweighted eccentricity parameter $\alpha_{\text{unweight}}$ is defined in den
Brok et al. (2020) or Mackenzie et al. (2021). $e_{\text{unweight}}$ better
describes the large-scale shape of the diffuse halo surrounding the quasar
position.

Large differences between $e_{\text{weight}}$ and $e_{\text{unweight}}$ could
indicate significant changes from inner halo to extended regions that could be
affected by filamentary structures. For example, J1145+5742 has a luminous
Ly$\alpha$ halo that extends East from the quasar position, and is visibly
asymmetric about the halo centroid, with a measured $e_{\text{weight}}\approx
0.74$. Asymmetric extending of the halo away from the quasar position is also
reflected in the large $e_{\text{unweight}}\approx 0.71$. An unusual case is
J2323$-$0100, which displays an asymmetric halo with a patch of emission to
the North-West that causes the Ly$\alpha$ halo centroid to be offset. This
offset away from the luminous bulk of halo emission results in a large
$e_{\text{weight}}\approx 0.86$. Considering the more diffuse mission around
the quasar position, the asymmetry is more moderate, and thus has lower
$e_{\text{unweight}}\approx 0.65$. Median eccentricities for the optimally
extracted halos (11 objects) are $e_{\text{weight}}=0.65$ and
$e_{\text{unweight}}=0.66$. $e_{\text{unweight}}$ values larger than
$e_{\text{weight}}$ could reflect the sample generally having a more
circularly symmetric inner halo, where the flux is strongest, versus the
slightly more asymmetric outer halo. These median eccentricity values are
comparable to each other, but are given further context by comparing values to
other quasar samples in Section 3.4.

To characterize the radial extent of the Ly$\alpha$ halo, we calculate the
circularly averaged SB radial profiles for the ERQ sample (Figure 2, 4th
column). While optimally extracted line maps yield measurements of morphology
and kinematics, they do not allow direct comparison with other samples because
other surveys used pseudo-narrowband imaging to compute their radial profiles.
Therefore, we choose to generate a pseudo-narrowband image with fixed width to
recover all possible fluxes in extended regions. Using a similar method to
other studies, we adopt a fixed wavelength width of $\pm 1,000$ km s-1
centered at the Ly$\alpha$ rest wavelength. For the full sample of ERQs, the
median SB in the innermost annulus (2$-$4 kpc) is 1.53 $\times 10^{-14}$ erg
s-1 cm-2 arcsec-2, and 1.61 $\times 10^{-16}$ erg s-1 cm-2 arcsec-2 in the
most distant annulus (32$-$63 kpc). Six of the 11 ERQs which have modified PSF
subtraction, due to the presence of a Ly$\alpha$ spike in their spectra, have
an inner annulus (2$-$4 kpc) median SB 11.4 $\times 10^{-14}$ erg s-1 cm-2
arcsec-2, and most distant annulus (32$-$63 kpc) median SB 4.69 $\times
10^{-16}$ erg s-1 cm-2 arcsec-2. We calculate the averaged SB at each radial
distance measured by annuli centered on the quasar position for each ERQ, as
well as the full sample median (Table 3). We compute a full sample SB median
omitting the inner region data in order to compare these ERQ radial profiles
with the spike to other samples, which cannot perform modified PSF
subtraction. To demonstrate the potential difference between our quasars and
other samples, we compute the median radial profile of the sub-sample of six
ERQs, where a Ly$\alpha$ spike is present in the spectra and modified PSF
subtraction was performed. SB of ERQs with detected Ly$\alpha$ emission
increases monotonically as the radial distance decreases, indicating that the
innermost regions are the most luminous part of these halo. ERQs with the
Ly$\alpha$ spike emission demonstrate the most centrally concentrated
emission.

We use an exponential fit to the binned radial profiles,
SB${}_{\text{Ly}\alpha}(r)=C_{e}\text{exp}(-r/r_{h})$, where $C_{e}$ is the
normalization, $r$ is the projected distance from the quasar, and $r_{h}$ the
scale length of the profile. Figure 2 shows the fits of this model in the
fourth column, and appear to reasonably describe the the radial SB profile.
For individual ERQs, a steep decline in SB near their inner regions (<4kpc)
appear only for ERQs with quasar PSF subtraction that did not involve clipping
the Ly$\alpha$ spike. Offset between the profile fit and data in the outer
regions (>32kpc, eg. J1451+0132 and J1652+1728) are generally from ERQs with
an asymmetric shape in the Ly$\alpha$ halo at large scales. These profiles are
better fit by exponential functions than power laws, and show that SB steeply
declines at large distances from the quasar. Table 3 presents averaged SB at
each annular bin and exponential fit parameters. Our full sample median
exponential scale length is $r_{h}=9.4$ kpc, and the median of the six ERQ
with a Ly$\alpha$ spike have $r_{h}=8.7$ kpc. Generally, ERQ Ly$\alpha$ halos
are more centrally concentrated than blue quasar samples, and ERQs that have
the Ly$\alpha$ spike are the most compact of our sample. Section 3.4 will have
further discussion of quasar population comparisons.

Table 3: Our sample’s Ly$\alpha$ halo circularly averaged surface brightness radial profiles. The first five columns make up the data points for radial profiles in Figure 2. For modeling the radial profiles, the inner radius (2-4)kpc is not included when there is no inner halo clipped from the quasar PSF spectral-template, shown in parentheses. The last two columns are the parameters from exponential-profile fit to the radial profile data. Median-errors shown are the standard deviation of the values that compose the median. ERQ Name | Radii Brightness | Radii Brightness | Radii Brightness | Radii Brightness | Radii Brightness | Exponential Amplitude | Exponential Scale Length
---|---|---|---|---|---|---|---
| (2-4) kpc | (4-8) kpc | (8-16) kpc | (16-32) kpc | (32-63) kpc |  |
| (erg/s/cm${}^{{}^{2}}$/arcsec${}^{{}^{2}}$) | (erg/s/cm${}^{{}^{2}}$/arcsec${}^{{}^{2}}$) | (erg/s/cm${}^{{}^{2}}$/arcsec${}^{{}^{2}}$) | (erg/s/cm${}^{{}^{2}}$/arcsec${}^{{}^{2}}$) | (erg/s/cm${}^{{}^{2}}$/arcsec${}^{{}^{2}}$) | (erg/s/cm${}^{{}^{2}}$/arcsec${}^{{}^{2}}$) | (kpc)
J0006+1215a | 1.63e-14 | 1.22e-14 | 5.88e-15 | 1.48e-15 | 1.78e-16 | (2.36 $\pm$ 0.04)e-14 | 8.6 $\pm$ 0.1
J0220+0137a | 1.43e-14 | 1.28e-14 | 7.68e-15 | 1.93e-15 |  $-$4.76e-17 | (2.50 $\pm$ 0.05)e-14 | 9.4 $\pm$ 0.1
J1145+5742a | 2.16e-14 | 1.60e-14 | 7.09e-15 | 2.49e-15 | 7.98e-16 | (2.43 $\pm$ 0.02)e-14 | 10.8 $\pm$ 0.1
J1232+0912 | (1.03e-15) | 9.25e-15 | 6.75e-15 | 2.60e-15 | 1.61e-16 | (1.77 $\pm$ 0.11)e-14 | 11.9 $\pm$ 0.5
J1451+0132a | 2.10e-13 | 8.23e-14 | 1.53e-14 | 3.85e-15 | 3.13e-16 | (4.68 $\pm$ 0.02)e-13 | 3.51 $\pm$ 0.01
J1451+2338a | 8.46e-14 | 8.59e-14 | 4.01e-14 | 9.42e-15 | 1.22e-15 | (1.57 $\pm$ 0.02)e-13 | 8.7 $\pm$ 0.1
J1652+1728a | 1.46e-13 | 7.26e-14 | 1.92e-14 | 4.96e-15 | 6.25e-16 | (2.41 $\pm$ 0.03)e-13 | 5.01 $\pm$ 0.04
J1705+2736 | (6.69e-15) | 2.39e-15 | 1.50e-15 | 7.85e-16 | 7.91e-17 | (3.82 $\pm$ 0.52)e-15 | 13.9 $\pm$ 1.3
J2215$-$0056 | (1.23e-16) | 1.33e-15 | 6.67e-16 | 4.69e-16 | 8.05e-17 | (1.64 $\pm$ 0.17)e-15 | 16.9 $\pm$ 1.4
J2254+2327 | (3.15e-15) | 7.91e-15 | 2.24e-15 | 5.39e-16 |  $-$2.10e-16 | (2.07 $\pm$ 0.22)e-14 | 5.7 $\pm$ 0.3
J2323$-$0100 | ($-$1.59e-16) | 4.14e-16 | 3.77e-16 | 1.28e-16 |  $-$2.48e-17 | (1.02 $\pm$ 0.19)e-15 | 10.5 $\pm$ 1.4
Median | 1.53e-14 | 1.22e-14 | 6.75e-15 | 1.93e-15 | 1.61e-16 | (2.36 $\pm$ 0.14)e-14 | 9.4 $\pm$ 3.7
Table 4: Halo kinematics measured from several methods from different columns in Figure 2. Measurements in the first column refers to the standard deviation of the 1st velocity-moments, computed from the emission line flux distribution at each spaxel. The second and third column refer to dispersion as computed by a single Gaussian fit to each Voronoi-bin in the velocity dispersion map. 2nd velocity-moments are not computed because there is not enough signal to reliably compute higher velocity-moments. The final column shows results from fitting a single Gaussian to the total integrated halo. ERQ Name | Spatial Standard Deviation of | Spatial Median of | Spatial Standard Deviation of | Spatially-Integrated
---|---|---|---|---
| Velocity Centroid | Velocity Dispersion | Velocity Dispersion | Velocity Dispersion
| (km s-1) | (km s-1) | (km s-1) | (km s-1)
J0006+1215a | 238 | 275 | 73 | 293
J0220+0137a | 456 | 259 | 44 | 264
J1145+5742a | 288 | 491 | 124 | 526
J1232+0912 | 231 | 424 | 114 | 393
J1451+0132a | 264 | 420 | 82 | 467
J1451+2338a | 331 | 401 | 112 | 354
J1652+1728a | 393 | 542 | 194 | 526
J1705+2736 | 424 | 251 | 108 | 235
J2215$-$0056 | 301 | 220 | 122 | 292
J2254+2327 | 195 | 374 | 216 | 261
J2323$-$0100 | 280 | 266 | 201 | 225
Median | 288 | 374 | 114 | 293

Figure 2: Full sample of ERQ Ly$\alpha$ halos after subtracting the quasar,
and the best available measurements, where the Ly$\alpha$ spike was isolated
in six quasar spectra before subtraction. First column shows the optimally
extracted halo, second is the 1st moment halo velocity map, third is Voronoi
binned velocity dispersion, fourth is the circularly averaged surface
brightness radial profile, and the fifth is the total integrated Ly$\alpha$
halo spectrum. For all 2D maps, the plus is the location of the quasar. For
the surface brightness panels the PSF size is indicated as a circle in the
upper left corner, the diamond is the centroid of halo emission, the cross
symbol is the location of peak Ly$\alpha$ halo emission when the Ly$\alpha$
spike is left in the residual map. For the surface brightness radial profiles
hollow circles represent negative values that were included for profile
fitting, and plotted as absolute values. They have also been corrected for
cosmological dimming for comparison to other samples. The integrated halo
spectrum shows a Gaussian that was fit to determine the overall halo velocity
dispersion. Zero velocity is defined as the centroid of integrated halo
emission, without removing the Ly$\alpha$ spike in quasar subtraction.
J0220+0137 has a cloud in the eastern edge of the FOV which is likely a
foreground source not physically related to the quasar, and is omitted in
measuring Ly$\alpha$ halo emission.

Figure 3: continued

. J1652+1728’s integrated halo centroid is offset from zero velocity because
we define zero from the outer halo. J2215$-$0056 has a cloud in the north of
the quasar which appears to be associated with the quasar as part of the same
large scale structure, and blueshifts the spatially-integrated halo spectra.
The associated object is omitted in measuring the ERQ’s total Ly$\alpha$ halo
emission.

Figure 4: continued

.

###  3.2 Kinematics

Here we describe our kinematic measurements of the halos in our sample.
Because of the multi-dimensional measurements of integral field spectroscopy,
we can present the kinematics in both the integrated halo emission and
spatially-resolved spectra.

Figure 2’s fifth column shows the spatially integrated spectra and a single
Gaussian fit to the Ly$\alpha$ halo emission. We define zero velocity by the
emission centroid of the spatially-integrated halo, without clipping the
narrow-emission spike from the spectral template. For the case of
J2215$-$0056, we integrate the halo including the extended object to the
north. Across the sample our integrated-halo emission spectra generally have
similar narrow shapes, with a median spatially-integrated spectrum velocity
dispersion of 293 km s-1. J1145+5742 has narrow absorption that is blueshifted
from the centroid in its Ly$\alpha$ halo spectrum. But in spite of the
absorption, the fit centroid is consistent with the Ly$\alpha$ halo emission
peak. For J1652+1728, the Gaussian fit captures the line width for
approximating dispersion, but the narrow Ly$\alpha$ halo emission in the
central region is blueshifted relative the outer halo, blueshifting the total
spatially-integrated spectrum. This centrally concentrated blueshifting, which
is seen in J1652+1728’s 1st moment velocity map, is also seen in the
Ly$\alpha$ emission profile from the central arcsec aperture in Figure 1 & 6.
Blueshifted central emission causes uncertainties in what to clip as halo
emission when subtracting the quasar. Table 4’s fifth column shows the
resulting velocity dispersion from a Gaussian fit to the integrated halo
emission.

Figure 5 displays evidence of an extended Ly$\alpha$ emitter (LAE) whose
emission centroid coincides with absorption in the quasar spectrum. The
centroid of the LAE is $\sim$30 kpc projected distance from the halo peak, and
spectroscopically < $-500$ km s-1 from the redshift measured by the Ly$\alpha$
halo. At higher redshifts (3 < $z$ < 4.5) LAEs with similar velocity offset
and clustering are suggested to be star-forming galaxies orbiting in the
quasar halo potential (Fossati et al., 2021). It is uncertain if the extended
emitter is powered by quasar radiation.

Figure 5: Aperture spectra of J2215$-$0056’s halo and the associated
Ly$\alpha$ emitter (LAE). The left panel displays the same SB map from Fig. 2,
over-plotted with the apertures used to generate emission spectra. The plus
symbol is the location of the quasar, and the cross symbol is the location of
peak brightness for the LAE. The aperture used to extract the halo emission
includes the quasar position, but is offset to avoid the LAE. The second
aperture above the quasar is used to generate the LAE spectrum. The right
panel is the quasar spectra for J2215$-$0056, the extracted aperture spectra
from the left panel, and a singe Gaussian fit to the halo emission. In black
is J2215$-$0056’s quasar spectrum, generated using a 1 arcsecond aperture from
the non-PSF subtracted data, blue is the LAE emission, orange is the aperture
spectrum of Ly$\alpha$ halo emission, and black is a Gaussian fit to the halo
emission. Ly$\alpha$ halo emission is scaled with a constant for visualization
and comparison to the other spectra. There is sharp and narrow absorption in
the quasar spectrum that visibly aligns with the LAE spectrum centroid. Our
extracted halo emission may also display absorption at the same spectral
location. There is no strong emission detected near the boundary of these
emitters, nor is there a smooth and continuous transition from the halo
emission profile to the LAE profile, to suggest there is a luminous arm
directly connecting the objects.

We describe kinematics at each spatial position around the quasar in 2D maps.
Figure 2’s second column shows velocity centroid maps, which are the 1st-
moments in velocity space of the flux distribution at each spatial position.
Our velocity maps use the same detection region and PSF from the SB maps. We
measured relatively low velocity shifts of the halos, at hundreds of km s-1,
and do not exhibit energetic outflows of thousands of km s-1.

Table 4 lists the spatial velocity-centroid standard deviation for each ERQ,
other computed quantities of velocity dispersion, and their median. The first
column is the standard deviation of the 1st velocity-moment centroid, with a
sample median of 288 km s-1. Second is the median velocity dispersion for each
object, from the Voronoi-binned velocity dispersion maps in Figure 2, and
their respective standard deviation in the third column. Our sample median of
the spatial velocity dispersion and its standard deviation are 374 and 114 km
s-1 respectively. Finally we show the dispersion of the Gaussian-fit to the
spatially integrated Ly$\alpha$ halo emission, with a median of 293 km s-1.
Discussion and analysis of these quantities is in Section 4.5.

Our data do not have sufficient signal-to-noise ratios to measure halo
velocity dispersion using second velocity moments (see L22 for more
discussion). We instead use Gaussian fits to a Voronoi-binned map (see Rupke
et al. (2019)). Figure 2’s third column shows the final Ly$\alpha$ Gaussian
velocity dispersion maps. These maps are generally smaller than the other maps
of SB and velocity shift, but as an independent detection method they confirm
the general morphology of the extended halo. In the case of J2215$-$0056, the
northern emitting region has unusually uniform dispersion across its area,
unlike any other extended emission cloud we detect. It is not clear if this
Ly$\alpha$ emitter is a distinct object. For J2215$-$0056 we determine the
systemic redshift by extracting the extended halo excluding the extended
object. The remaining ERQ Ly$\alpha$ halos show relatively low dispersion
across their maps, in the hundreds of km s-1.

Some ERQs show a velocity gradient from one edge of the halo to the other of
$\sim$1,000 km s-1 (e.g., J1232+0912 and J1451+0132), and the coherent
transition from redshift to blueshift helps confirm the measured velocities
are valid. A rotating disc of $\sim$100 kpc size is not expected to have
formed by $z\sim 2$ (e.g., DeFelippis et al., 2020; Huscher et al., 2021). One
ERQ, J0220+0137, has a kinematically distinct cloud at the eastern boundary of
the FOV, $\sim$65 kpc from the quasar, and shifted in velocity space about
$-$1,500 km s-1 from the Ly$\alpha$ halo redshift. The kinematic separation
makes it unlikely to be of the quasar halo diffuse gas, and it is omitted in
measuring the Ly$\alpha$ halo emission. ERQs J1451+2338 and J1652+1728 have a
noticeable circular patch at the center of their 1st velocity-moment map, and
are likely the residual from imperfect quasar subtraction caused by
complexities in their Ly$\alpha$ profile.

###  3.3 Blueshifted Absorption

Figure 6 shows aperture and annular spectra of selected ERQs, to further
understand the spatial and spectral distribution of Ly$\alpha$ emission and
absorption features. One ERQ shows definite blueshifted absorption,
J1145+5742, similar to what was found in J0006+1215, by L22. J1145+5742 has
strong absorption features in its integrated spectra, and consistently shows
deep and narrow absorption in apertures across the FOV, out to $\sim$50 kpc,
blueshifted at $-$400 km s-1. In its inner halo spectrum, only within $\sim$25
kpc, there is blueshifted absorption at about $-$950 km s-1. J1451+0132 has
blueshifted absorption in its emission profile of the innermost and spatially
unresolved inner halo, at $\sim$800 km s-1 and $\sim$1250 km s-1, but not in
the outer halo profile. These blueshifted absorption features resemble those
of spatially resolved Ly$\alpha$ halo spectra that require outflows (e.g., Li
et al., 2021).

J1652+2736 has more unique profile features. It has primarily blueshifted
central halo emission from apertures within 15$-$20 kpc of the quasar (about
$-$900 km s-1), and has gradually redshifted and more symmetric Ly$\alpha$
halo emission at larger annular radii. Its aperture spectra reveal that the
asymmetric emission profile in the integrated Ly$\alpha$ halo is not from
blueshifted absorption, but from the central halo emission being blueshifted,
relative to the extended halo.

Our data show evidence of multi-component emission, and likely also affected
by absorption. Overall, we do not find evidence for strong absorption in the
Ly$\alpha$ halo emission profiles. The intrinsic emission profile of
Ly$\alpha$ is not known for these quasars in order to model the level of
absorption (e.g., Wang et al., 2021), and analysis of the environment which
may cause absorption is beyond the scope of this work.

Figure 6: Aperture spectra of Ly$\alpha$ halo emission for J0220+0137,
J1145+5742, J1652+1728, and J1705+2736. The left column displays the same 1st
moment velocity map from Fig. 2, over-plotted with the apertures used to
generate Ly$\alpha$ emission spectra. The plus symbol is the location of the
quasar, and the cross symbol is the peak of the Ly$\alpha$ halo emission. For
J0220+0137 & J1145+5742, circular aperture boundaries are drawn to define
three regions, one innermost region, a middle transition region, and an outer
halo region, which includes all emission outside the circular apertures.
J1652+1728 has an additional subdivision to show a quiescent circular region
of the middle halo ($\sim$20 kpc), which lacks clumpy inflows/outflows. For
J1705+2736, the halo is bisected into a northern and southern region for
analysis. The right panel is the corresponding quasar’s Ly$\alpha$ emission
spectra from each halo region, and each spectra is scaled with a constant for
visualization and comparison to the other regions’ emission profile.
J0220+0132 is an example of a complex profile that is revealed after it’s
divided into apertures, instead of the smoothed emission features in ’s
integrated halo spectra. A flat emission spectrum between 100-400 km s-1 is
seen in the innermost halo ($\leq\sim$20 kpc), perhaps by a combination of
multi-component gas kinematics and/or absorption, and is otherwise lost in the
total integrated halo spectrum shown in Fig. 2. J1145+5742 displays strong
absorption at $-$400 km s-1 across the $\sim$120 kpc span of the halo, and
weaker absorption at $-$950 km s-1 across $\leq\sim$50 kpc. Ly$\alpha$’s
emission profile shape remains consistent across the $\sim$120 kpc span of the
halo. J1652+1728’s Ly$\alpha$ emission profile displays a rapid transition
beyond $\sim$20 kpc from the quasar, and becomes sharper peaked and
symmetrically broader at its base. This symmetric broadening is likely from
the patches of red and blueshifted clumps in the outer regions of the velocity
map. The inner halo region’s peak emission is blueshifted to $\sim$900 km s-1,
and displays absorption at the the redshift of the peak outer-halo emission.
J1705+2736 shows moderate blueshifting in the southern lobe of the Ly$\alpha$
halo, and becomes more narrow. The northern halo emission profile may be
asymmetrically broadened on the red side by redshifted clumps at the outer
boundary of the halo.

###  3.4 Comparisons to Blue Quasars

We have a full sample of eleven ERQ Ly$\alpha$ halos. One of the main goals of
our study is to compare the Ly$\alpha$ halos around ERQs to Type-I blue
quasars roughly matched to the ERQs in redshift and luminosity ($\geq 10^{47}$
ergs s-1, at cosmic noon). Our focus is on Type-I quasars, but we also include
Type-IIs for some of the comparisons, as described below. Our median ERQ
luminosity of $L_{\text{bol}}=5\times 10^{47}$erg s-1 and $z=2.61$ is only
slightly more luminous than other samples we compare. We use the same method
described in Section 4.5 to recalculate all of the blue quasar sample
luminosities for consistency. Combining the four blue quasar samples, they
have a range of medians $L_{\text{bol}}\approx 1.0-4.0\times 10^{47}$erg s-1
and $z\approx 2.3-3.2$, totaling 108 quasars (Cai et al. (2019); Arrigoni
Battaia et al. (2019); Borisova et al. (2016a); Mackenzie et al. (2021)).

We recalculate all of the blue quasar sample luminosities in the same way as
ERQs, using W3 photometry to estimate bolometric luminosities (see Section
2.6).

Our comparison samples are the following. We take the quasar sample from Cai
et al. (2019), consisting of 16 blue quasars of median $z=2.3$, and
$L_{\text{bol}}=10^{47.2}$erg s-1. We take the 61 blue quasars from Arrigoni
Battaia et al. (2019), with median $z=3.2$ and $L_{\text{bol}}=10^{47.4}$erg
s-1. Borisova et al. (2016a) sample consists of 19 luminous blue quasars of
median $z=3.2$ and median bolometric luminosity $10^{47.6}$ erg s-1. Mackenzie
et al. (2021) have 12 blue quasars of median $z=3.2$, and are on the fainter
side of these samples, with median $L_{\text{bol}}=10^{47.0}$erg s-1. den Brok
et al. (2020) sample consists of four Type-II quasars of median $z=3.4$ and
median $L_{\text{bol}}=10^{46.7}$erg s-1. We verify that the intrinsic
bolometric luminosities estimated based on mid-IR luminosities are similar to
those estimated with X-ray luminosities, and the correction factors modeled in
Shen et al. (2020). A final Type-II quasar from Sanderson et al. (2021) is at
$z=3.2$, which is a mid-IR-only source not detected in the optical.

Figure 7 shows the relationship between the halo luminosity and the bolometric
luminosity of the quasar. In order to make these comparisons, we verified that
masking or not masking the inner 1-arcsecond yields similar halo luminosities,
within about 10 per cent of the total halo luminosity. We also assessed
changes in computed halo luminosity with or without Ly$\alpha$ spike clipping.
Four of six ERQs with a spike showed an increase in computed halo luminosity
of 20$-$40 percent. Halo luminosities of J1451+0132 & J1652+1728 more than
doubled, each increasing by factors of $\sim$2.25. When subtracting the
emission of the quasar, the shape of the spectral template that is subtracted
is important for determining the residual halo emission. Halo emission is not
as distinct in typical blue quasar spectra, and does not change the spectral
template shape (ref. Sections 2.3 & 2.4, and Figure 1). Most of ERQ Ly$\alpha$
halo emission is concentrated in the inner halo regions near the quasar PSF,
so modifications to the spike are more important for ERQ Ly$\alpha$ halo
luminosity.

Figure 7: Computed logarithmic bolometric luminosity vs logarithmic Ly$\alpha$
halo luminosity of various literature samples and our ERQs. Upper and lower
limits are shown with arrows. Brown pluses are the individual ERQs, and the
large brown plus is the median of our sample. Blue quasar samples have median
values shown as the large pink circle, dark blue star, light blue triangle,
and the dark green downward triangle symbol. Individual quasars from other
samples shown as small gray symbols matching their median symbol. There is
significant overlap of individual quasars in our sample and luminous blue
quasar samples. The median of these samples shows a positive luminosity trend
for bolometric luminosity and Ly$\alpha$ halo luminosity across all samples.

Our ERQ median is $L_{\text{halo}}=5.40\times 10^{43}$ergs s-1, where the
luminous blue quasar populations have medians in the range
$L_{\text{halo}}\approx 5-10\times 10^{43}$ergs s-1. L22 noted that the
Ly$\alpha$ halo luminosity around the reddest quasar in our sample,
J0006+1215, is roughly three times lower than expected from the matched blue
quasar samples. In our larger sample, the second reddest ERQ, J2323$-$0100,
stands out for having the lowest halo luminosity, roughly 10 times lower than
expected from the blue quasars (see Table 2 and Fig. 7). However, the full
range of ERQ halo luminosities in our study falls within the range of those
for blue quasars. We also find that the ERQs follow a weak trend for larger
halo luminosity around quasars with larger bolometric luminosity that was
noted previously in blue quasars by Mackenzie et al. (2021).

Figure 8 shows the maximum linear size vs bolometric luminosity. Many of the
ERQs are shown with only lower limits on their maximum halo size, because they
exceed the field of view of KCWI (see also Table 2 and Section 3.1). We
compare samples from Borisova et al. (2016a), Arrigoni Battaia et al. (2019),
Cai et al. (2019), and Mackenzie et al. (2021). For Arrigoni Battaia et al.
(2019) we estimate a maximum linear size for each quasar from the sum of
maximal radial extent for the halo plus $\sqrt{(\text{covered area})/\pi}$. It
was noted in Arrigoni Battaia et al. (2019) that the size of blue quasar
nebulae did not increase significantly with longer exposure time, confirming
our size measurements are mostly insensitive to integration time. We report
the maximum linear size as lower limits when the halo SB map extends to the
edge of the FOV. Similarly to the luminosity trend, ERQs populate the high-
luminosity region of a positive trend with the maximum linear size of
Ly$\alpha$ halos and bolometric luminosities.

Figure 8: Computed logarithmic bolometric luminosity vs maximum linear size of
the halo, using identical color and symbol legend as Figure 7. Lower limits
are shown for medians computed from samples that contain halos extending to
the edge of the field of view. There is overlap of individual quasars with
other samples, and a weak positive luminosity trend can be seen across the
medians of the samples.

Figure 9 shows the surface brightness radial profile of ERQs pseudo-narrowband
images, the median radial profiles of ERQs and several blue quasar samples,
and the median exponential scale length of each quasar sample. Each point on
the radial curve shows the average SB of an annulus centered on the quasar.
Table 3 presents the data for our sample. An important feature we take
advantage of is that obscuration behaves as a coronagraph, and allows probing
of the inner-most regions of the halo. Six ERQs have had their quasar emission
subtracted without the Ly$\alpha$ spike, and we measure their SB at smaller
projected distances from the quasar than the blue quasar samples. For
comparison, we take the median SB radial profile from Borisova et al. (2016a),
Arrigoni Battaia et al. (2019), and Cai et al. (2019). The Borisova et al.
(2016a) radial profile is obtained from Marino et al. (2019). All samples have
comparable size of the point-spread function corresponding to a FWHM of 1.4
arcsec or 12 kpc. For our ERQ sample we present two median radial profiles.
One median is for ERQs which can probe to zero projected distance, and the
other is omitting the central 1-arcsecond region ($\sim$4 kpc radius), for
comparison to other quasar studies that do not have the Ly$\alpha$ spike.

Figure 9: Circularly averaged surface brightness radial profiles of our sample
of ERQs in comparison with other samples of blue quasars at comparable
redshift and luminosity. The bold brown line is the ERQ sample median at each
surface brightness bin for which there is detected halo emission. Thin brown
lines are the individual ERQs. Other colors correspond to the other samples of
blue quasars, pink, blue, and light blue for Cai et al. (2019), Arrigoni
Battaia et al. (2019), and Borisova et al. (2016b), respectively. Across the
top of the figure shows the exponential scale lengths, color coded to match
each sample. Notice that the scale lengths of ERQs are shorter than blue
quasar samples, and thus have profiles that fall off more rapidly at large
distances. Also notice that ERQs with higher surface brightness tend to have
detectable Ly$\alpha$-spike halo emission down to the central projected radius
from the quasar. Negative values of surface brightness from Fig. 2 are not
shown in this figure. All surface brightnesses are corrected for cosmological
dimming.

Along the top of Figure 9 we also present the exponential scale length fit to
the median radial profiles. We fit an exponential function defined in Section
3.1 to the median SB radial profile, and record fit values in Table 3.
Exponential scale length probes the brighter inner halo region, in contrast to
the maximum linear size which depends on more diffuse low-SB emission. Our
full sample’s median radial profile, omitting the innermost bin (0$-$4 kpc)
for comparison with blue quasar samples, has a scale lenth $r_{h}=9.0$ kpc.
Median profile scale lengths for other blue quasar samples are 13.5, 15.7, and
18.7 kpc for Borisova et al. (2016a), Arrigoni Battaia et al. (2019), and Cai
et al. (2019), respectively. For ERQs with a Ly$\alpha$ spike we can probe
deeper to the inner halo regions, at projected distance 0$-$4 kpc, because of
modified PSF subtraction (ref. Sections 2.3 & 2.4). Considering only the ERQs
with a Ly$\alpha$ spike, we can compute a scale length of their median profile
$r_{h}=5.9$ kpc. ERQs are generally more luminous than blue quasars, and there
should be a natural tendency for more luminous quasars to have larger halos,
as everything scales with higher luminosity. Despite this intuitive tendency,
ERQ Ly$\alpha$ halos are characteristically more compact in their inner
regions than those of luminous blue quasars.

Figure 10 compares ERQ Ly$\alpha$ halo spatially-integrated velocity
dispersion vs bolometric luminosity with those from blue quasars which have
measured spatially integrated velocity dispersion in the literature. We did
not have enough signal to compute 2nd-moment velocity dispersions for the halo
maps. Our ERQ velocity dispersions for direct comparison are computed from the
Gaussian fits to the total integrated halo spectrum, shown in the last column
of Figure 2, and are tabulated in the last column of Table 4. Other samples
compute a 2nd-moment velocity dispersion, but Cai et al. (2019) also reports a
velocity dispersion from spatially integrated velocity dispersion for the
integrated halo spectrum, which we can directly compare. Line fitting of the
integrated spectrum is a more robust dispersion measurement than moment maps
(see discussion in O’Sullivan et al. (2020)). Our ERQ sample’s median
integrated Ly$\alpha$ halo dispersion is $293$ km s-1. Cai et al. (2019)
measured their sample median of $269$ km s-1. We see the halo velocity
dispersion of ERQs follow the distribution of the luminous blue quasars of Cai
et al. (2019). Both distributions generally follow a trend for larger
dispersion in more luminous quasars.

Figure 10: Comparison of logarithmic bolometric luminosity vs spatially
integrated Ly$\alpha$ halo velocity dispersion for samples which it was
measured, using identical legend as Figure 7. Halo velocity dispersion for
this comparison is taken from a Gaussian fit to the spatially integrated halo
spectrum, shown as the last column in Figure 2. Cai et al. (2019) is the only
blue quasar survey from the blue quasar surveys we have considered in this
paper also computed integrated halo velocity dispersion. There is a positive
luminosity trend among individual quasars, but the trend is uncertain for the
two sample medians available for this analysis.

Finally, Figure 11 presents morphology of halos vs bolometric luminosity, with
two different eccentricity parameters. Different surveys used different
parameters to characterize morphology for their population. We present ERQs
with both of these parameters computed to compare with as many as possible. We
take $e_{\text{unweight}}$ values from, Borisova et al. (2016a), den Brok et
al. (2020), Mackenzie et al. (2021), and Sanderson et al. (2021). We take the
computed $e_{\text{weight}}$ from Arrigoni Battaia et al. (2019) and Cai et
al. (2019). Their $e_{\text{weight}}$ is calculated with a 1-arcsecond region
centered on the quasar masked to avoid residuals from point spread function
subtraction. All samples we compare also mask the central 1-arcsecond region
for their computed $e_{\text{weight}}$ or $e_{\text{unweight}}$, except for
den Brok et al. (2020) and Sanderson et al. (2021). The two samples with no
masking are so obscured they did not need point spread function subtraction to
measure the halo.

Figure 11: Logarithmic bolometric luminosity vs Ly$\alpha$ halo eccentricity,
flux weighted and unweighted, for samples which have the respective
measurements to compare. In addition to the identical symbols as Figure 7,
Type-II quasars from den Brok et al. (2020) are shown in box symbols with
their median shown as the large light green box, and an upper limit of an
individual Type-II in Sanderson et al. (2021) is shown as a purple star.
Eccentricity of zero is circular, and values near one are more elliptical.
Plotted ERQ eccentricity values are computed with the central 1 arcsecond
masked to compare with the other samples that use standard PSF subtraction,
and Table 2 shows the eccentricity values calculated without masking the
central 1 arcsecond. Flux-unweighted eccentricity is a measure of the outer
halo shape, whereas the flux-weighted eccentricity is more strongly influenced
by the brighter inner halo regions. In the flux unweighted plot there is some
separation between the populations of Type-I and Type-II quasar samples, which
is more clear in the median symbols.

For our data in Figure 11, we also mask the inner 1-arcsecond of the quasar
for plotted measurements, for fair comparison with other surveys which did not
probe the inner halo as we have. Table 2 presents our best possible
eccentricity measurements, without the inner 1-arcsecond masked. Without
masking, our ERQ sample has median weighted and unweighted eccentricities of
$e_{\text{weight}}=0.65$ and $e_{\text{unweight}}=0.66$. We give these values
context by comparing them to other typical quasar values available in the
literature.

Flux unweighted eccentricity is insensitive to strong central emission, and
thus can describe morphology at large scales. Blue quasar samples have
$e_{\text{unweight}}\approx 0.7$, and are comparable to the less luminous
population seen in Mackenzie et al. (2021). Our ERQs tend to have morphologies
like blue Type-I quasar samples.

There is significant scatter in $e_{\text{weight}}$ measurements among each
sample, but medians of these populations show ERQs have more circular symmetry
to other blue quasar Ly$\alpha$ halo surveys. Blue quasar samples have
$e_{\text{weight}}\approx 0.7-0.9$. Luminous quasar medians are larger than
the ERQ median and most individual ERQs, tabulated in Table 2.

We include Type-II quasars in this morphology comparison, because other
studies find that Type-IIs tend to show more asymmetric halos, consistent with
more edge-on views of the quasar asymmetric illumination patterns in the
normal Type-I/II dichotomy (den Brok et al., 2020). Samples of Type-II quasars
have an unweighted eccentricity as high as $e_{\text{unweight}}\approx 0.8$
(den Brok et al., 2020; Sorini et al., 2021). The ERQ in our sample with
narrowest C IV emission line FWHM, J1705+2736, is similar to the other Type-
IIs, and has the largest unweighted eccentricity in our sample with
$e_{\text{unweight}}=0.78$. J1705+2736 also has the largest flux weighted
eccentricity of our sample, and greater than of most of the Type-I blue
quasars, with $e_{\text{weight}}=0.91$.

##  4 Discussion

ERQs could represent a brief transition phase in galactic and quasar
evolution, characterized by an obscured galactic/quasar environment and
potentially extreme feedback via outflows (see Section 1). Our main goal is to
determine if ERQs differ from normal blue quasars in significant ways that
might identify them as a distinct, and potentially more youthful,
galactic/quasar population. We obtained Keck KCWI data for 11 ERQs to measure
their basic Ly$\alpha$ halo properties. In this section we will discuss our
results for the full sample.

###  4.1 Quasar Systemic Redshift & Future Work

Systemic redshifts are uniquely difficult to determine for ERQs due to
frequent blueshifted/fast-outflowing emission-lines that are typically used as
redshift indicators, such as [O III] $\lambda$5007 and broad emission lines
(Hamann et al. 2017; Perrotta et al. 2019; Gillette et al. 2023b in prep.).
Our study confirms the result in L22 that the narrow Ly$\alpha$ spike present
in aperture spectra of some ERQs are the same redshift and emission profile as
the inner halo emission, and therefore this spike also forms in the inner halo
and is a good indicator of ERQ systemic redshifts. L22 used the Ly$\alpha$
spike redshift in the reddest ERQ, J0006+1215, to show the centroid of the
broad C IV $\lambda$1549 emission line is blueshifted by 2240 km s-1. Hamann
et al. (2017) provides other examples of large broad emission-line blueshifts
in ERQs based on the Ly$\alpha$ spike, claiming that large blueshifts are more
common in ERQs than luminous blue quasars. We present a more complete
discussion of blueshifts and their implications for ERQ outflows in a
forthcoming paper, Gillette et al. (2023b in prep.).

###  4.2 Circularly Symmetric and Compact Halos

Overall we find that ERQs and blue quasars both exhibit a wide range of
Ly$\alpha$ halo properties and there is considerable overlap between these
samples. The main differences identified by our study are in the halo
morphologies. In particular, the ERQs tend to have 1) more compact and
centrally concentrated SB profiles, and 2) more circularly symmetric central
regions. Fig. 9 shows other samples which have circularly averaged SB radial
profiles measured have median exponential scale lengths between 13.5 and 18.7
kpc, and the scale length of the median profile of our full sample is 9.0 kpc.
When considering only ERQs that exhibit a Ly$\alpha$ spike, the median
profile’s exponential scale length is only 6.0 kpc. Fig. 11 shows the flux-
weighted elliptical eccentricities of our sample are much smaller, probing the
inner halo, and meaning more circularly symmetric.

Reasons for ERQs having more compact and more circular morphology are unclear.
They are possibly related to a younger evolution stage than blue quasars, for
example, if the outflows from ERQs (e.g., Perrotta et al. 2019; Gillette et
al. 2023b in prep.) have not had time yet to distort and disperse the gas in
their inner halo. Compact and circular morphology also supports the argument
that ERQs do have Type-I orientation in spite of their obscuration.

###  4.3 Type-I versus Type-II Quasars

We can gain insights into the dust distribution around ERQs from the halo
morphology being more similar to Type-I blue quasar samples than Type-II
samples. Previous studies have shown that Type-IIs tend to have more
asymmetric Ly$\alpha$ halos, consistent with Type-IIs having a more edge-on
view of the asymmetric (bipolar) radiation pattern of quasars in the standard
Type-I/II dichotomy (Antonucci, 1993; Urry & Padovani, 1995; Netzer, 2015; den
Brok et al., 2020).

Gas distribution asymmetry is evident in the eccentricity parameters plotted
in Fig. 11, although the sample sizes are small and there is considerable
overlap in values between samples. ERQs tend to have more symmetric halo
morphologies than Type-I blue quasars, making them even more different from
the Type-IIs.

One ERQ in our sample, J1705+2736, has considerable asymmetry in its outer
Ly$\alpha$ halo morphology, and has an asymmetric and luminous arm that
extends >70 kpc from the quasar. J1705+2736 has substantially narrower FWHM(C
IV) than the other ERQs, similar to other Type-II quasars, although FWHM(C IV)
alone is known not to be a good discriminator for Type-I versus Type-II
classification (Greene et al., 2014; Hamann et al., 2017). Fig. 6 shows
J1705+2736’s extended emission, that is uniformly blueshifted from the central
halo by about $-$100 km s-1, and out to $>$70 kpc in the southern direction.

Thus it appears that the large line-of-sight extinctions toward ERQs cannot be
attributed to viewing effects analogous to Type-IIs in the simplified picture
of Type-IIs versus Type-I quasars. Our conclusion that ERQs are more similar
to Type-I’s is supported by the finding in L22 that the He II/Ly$\alpha$ line
ratio in the ERQ J0006+1215 (the only ERQ for which those lines are measured)
is more similar to Type-I blue quasars than Type-IIs (see section 4.5 in L22
for more discussion).

###  4.4 No Evidence of Halo Feedback

Figure 10 reveals ERQs appear to follow the same trend as blue quasars for
larger velocity dispersions around quasars with larger bolometric luminosity.
Overall the halos are kinematically quiet, with integrated velocity dispersion
in the range 225$-$526 km s-1, similar to matched blue quasars.

We compare these velocity dispersions with emission-line broadening expected
from the orbital motions of gas in the host galaxy’s dark matter halo. Our
sample is on the high end of quasar luminosities, and further studies have
found that obscured quasars and hyperluminous quasars may on average reside in
more massive halos, typically $10^{13}h^{-1}M_{\odot}$ (DiPompeo et al., 2017;
Geach et al., 2019). We assume a dark matter halo profile from Navarro et al.
(1997), and halo concentration parameter of 4, from the COLOSSUS software and
references
therein.111https://bdiemer.bitbucket.io/colossus/halo_concentration.html We
then use the halotools software to calculate the circular velocity for an
upper limit for the projected 1D
velocity.222https://halotools.readthedocs.io/en/latest/api/halotools.empirical_models.
NFWProfile.html Halo gas with dispersion above $379$ km s-1 could be
considered fast moving, and corresponds to 1D circular velocity of 536 km s-1.
Table 4 presents our integrated Ly$\alpha$ halo dispersion. Velocity
dispersions of our sample have a median dispersion of 293 km s-1, are within a
few hundred km s-1 of each other, and none are above the fast moving circular
velocity estimate. Quiet kinematics do not rule out the possibility of youth
in ERQs, because they may have had less time for energetic outflows to extend
outward to generate feedback in the inner halo.

Across the sample we generally do not find Ly$\alpha$ halo emission-line
broadening above the expected dark matter halo velocities down to $\sim$0.7
arcsec or $\sim$6 kpc radius. Episodic lifetimes of quasars are typically
$10^{5}-10^{7}$ yrs (e.g., Khrykin et al., 2021). With most Ly$\alpha$ halo
outflow speeds $\sim$400 km s-1 they can at most only travel to $\sim$4 kpc.
Therefore any Ly$\alpha$ emission on circumgalactic scales are not outflowing
due to the present quasar episode. Spatially resolved velocity dispersion
beyond 20$-$30 kpc is more commonly measured in ERQs with a Ly$\alpha$ spike.
These more extended halos gradually decrease velocity dispersion toward the
edges, away from the quasar. Instances of extended clouds (eg. J1145+5742 and
J1451+0132) also show a decrease in dispersion farther along the extended arm,
but J0006+1215 shows increasing dispersion with increasing distance along its
extended arm. We do not find evidence for large velocity dispersion in the
Ly$\alpha$ halos that may be caused by outflows and feedback effects from the
central quasar, but an absence of fast outflows in our sample has no
implications on the quasar evolutionary stage.

In conclusion, the quiet kinematics, and the compact and circular symmetry
discussed in Section 4.2, are evidence against feedback being present at CGM
halo scales, now or in the past.

###  4.5 General Halo Properties

If ERQs are in younger host galaxies, then they may have different ionizing
escape fractions compared to typical blue quasars. If the galaxy is dusty,
then the escape fraction could be lower. But if the dust distributions are
clumpy, then they may have substantial ionization escape fractions.
Luminosities of the Ly$\alpha$ halos are comparable to typical luminous blue
quasars of similar redshift in Fig. 7. We also see in Fig. 8 that ERQ halo
linear size is within the size distributions in other samples of luminous
quasars. The median ERQ halo luminosity is offset roughly two times lower than
expected from the blue quasar data, but this does not appear significant given
the small sample size and the width of the halo luminosity distributions
spanning nearly a factor of 100. Thus the appearance of narrow Ly$\alpha$
emission spikes in ERQ spectra can be attributed to extinction toward the
central quasar, and not from unusually bright halo emission, relative to the
central quasars.

If the Ly$\alpha$ halo emissions are powered by hydrogen-ionizing radiation
from the central quasars, the similar halo luminosities between ERQs and blue
quasars might indicate that similar fractions of the H-ionizing photons
emitted by the quasars escape to the circumgalactic medium in ERQs. This
similarity is notable because of the much larger line-of-sight extinctions
observed in ERQs, estimated to be typically $\sim$3 mags or a factor of
$\sim$16 in the near UV around 1500 Å to 2000 Å (Hamann et al., 2017). One
possible explanation is that other lines-of-sight toward ERQs have lower
extinctions than we observe, allowing their ionizing photons to escape in
quantities similar to blue quasars. Another possibility is that the dust
distributions are clumpy and inhomogeneous, which can permit larger UV photon
escape fractions than expected from the extinctions along direct lines of
sight to the central source, due to scattering. The general notion that dust
scattering plays an important role is consistent with the large UV
polarizations found in some ERQs by Alexandroff et al. (2018); however, they
attribute their results to a particular axisymmetric scattering geometry that
might conflict with our finding that ERQs tend to have circularly symmetric
halos, resembling Type-I blue quasars (Section 4.3).

An important caveat to keep in mind for the $L_{halo}$ comparisons is that
Ly$\alpha$ halos around quasars are generally believed to be at least partly
matter bounded, meaning that the observed luminosities depend at least partly
on the amount of halo gas available for ionisation, not simply on the flux or
escape fraction of ionising photons emitted by the quasar. ERQs show a weaker
than expected Ly$\alpha$ halo luminosity for their bolometric luminosity,
which could be evidence of matter bounded halo emission (Dempsey & Zakamska
2018, also Fig. 7). In an ionization bounded scenario we expect the luminosity
of the halo to scale linearly with bolometric luminosity, but when a halo is
matter bounded there is no dependence. However, real quasars can show a weak
dependence of the halo properties on the bolometric luminosity, and any
relation between Ly$\alpha$ halo luminosities and extinction toward the
quasars will also be weak.

A unique feature of our study is that extreme obscuration allows us to map the
2D halo emissions all the way down to the quasar positions, and possibly down
to galactic emission, in roughly half of our ERQ sample. ERQs that exhibit the
Ly$\alpha$ spike show similar inner halo characteristics as J0006+1215 in L22,
but vary in their outer region symmetry and morphology beyond 20$-$30 kpc from
the emission peak. ERQs without the spike are most luminous around the central
region of the quasar, and tend to be less extended to outer regions beyond
30$-$40 kpc from the halo emission peak (see Fig. 2).

###  4.6 Multi-component Emission

In several ERQs with spatially resolved measurements, a transition at
$\sim$20$-$30 kpc from the quasar frequently occurs (e.g., a drop off in SB,
change in blueshift, or velocity dispersion). This transition leads us to
define a boundary of inner-halo and outer-halo Ly$\alpha$ emission. This
boundary could be evidence of a 2-component halo structure of compact and
extended gas (e.g., J1145+5742 and J1652+1728). L22 showed a halo transition
phase 20$-$30 kpc from the position of ERQ J0006+1215, defining an inner and
outer halo component. The inner region is more coherent, circularly symmetric,
and has quiet gas kinematics, and the outer region has more asymmetric and
disrupted kinematics. One possibility is that the outer halo is inflowing CGM
gas, and the inner halo is dominated by outflow (see section 4.2 in L22 for
more discussion). This is further supported in multi-component JWST
observations of J1652+1728, which found complex gas kinematics and outflows on
kpc scales (Vayner et al., 2023). Figure 6 shows aperture spectra of ERQs with
distinct inner and outer halo emission regions that show different kinematics
from each other.

Many of our ERQ Ly$\alpha$ halos show a smooth gradient in their velocity
shift from one side of the halo to the other, with zero velocity centered near
the halo emission peak. None have extreme velocities consistent with powerful
outflow. In cosmological radiation-hydrodynamic simulations from Costa et al.
(2022) quasar driven outflows on circumgalactic scales move $\sim$1,000 km
s-1, and are also less dense than most Ly$\alpha$ emitting gas.

In summary, our comparison of ERQ Ly$\alpha$ halo properties to blue quasars
has revealed many similarities, and some contrasting characteristics that
distinguish them from simple orientation effects. Extended morphology of halos
around ERQs appear similar to those of blue quasars, but the inner halo is
more circularly compact. Future work with larger samples and/or deeper maps
could help resolve the evolution/youth question. Further exploration into ERQs
as an evolutionary stage (eg., Perrotta et al. 2023 and Hamann et al. 2023)
will investigate the host galaxies for comparison to blue quasars.

##  5 Conclusions

We present a sample of 11 ERQs observed with KCWI Integral Field Spectroscopy,
which have median redshift $z$ $=$ 2.6, a median color of $i-W3$ $=$ 5.9 mag,
and median bolometric luminosity $L_{\text{bol}}$ $\approx$ 5 $\times$
$10^{47}$ erg s-1. Except for one ERQ observed under cloudy conditions, all
have detected Ly$\alpha$ halos, and have a median halo luminosity
$L_{\text{halo}}$ $=$ 5.83 $\times$ $10^{43}$ erg s-1.

The median of Ly$\alpha$ emission’s maximum linear size is >128 kpc, and
exponential scale length of the circularly averaged SB radial profile median
is $9.0$ kpc. Morphology is generally circular around the inner halo regions,
with a median flux-weighted eccentricity of $e_{\text{weight}}=0.65$ and
unweighted $e_{\text{unweight}}=0.66$. One ERQ in our sample, J1705+2736, that
has substantially narrower emission line widths, has the most asymmetric
morphology in its outer halo with $e_{\text{unweight}}=0.78$, and compared to
the rest of the ERQ sample has the most asymmetric inner halo with
$e_{\text{weight}}=0.91$.

Kinematics of the halos are relatively calm, with velocity shifts of the
Ly$\alpha$ emission centroid to be in the hundreds of km s-1, and much weaker
than the shifts found in [O III] for ERQs in the thousands of km s-1 by
Perrotta et al. (2019). Velocity maps are coherent, with some showing a
gradual gradient from red to blue velocity shifts across the halo. Dispersion
of the halo emission is also quiet, with a spatial median dispersion of 374 km
s-1, and standard deviation of 114 km s-1.

Our measured quantities of size, luminosity, blueshift, and dispersion show
ERQs are mostly similar to those obtained in blue quasar surveys. ERQs
generally follow luminosity trends that are seen across faint to luminous blue
quasar samples for halo linear-size, luminosity, and velocity dispersion.
However, ERQs do stand apart from similarly luminous blue quasars in that
their halos are more circularly compact.

Most of the statements and inferences about ERQ populations made in L22 are
supported by this work with the addition of 10 other Ly$\alpha$ halos,
summarized below:

  * •

We do not see a color correlation with Ly$\alpha$ luminosity or kinematics
across our sample.

  * •

At circumgalactic scales we do not find clear evidence of feedback based on
the circularly symmetric inner halos and low velocity dispersions (see
Sections 4.2 & 4.4).

  * •

Ly$\alpha$ halo velocity dispersions are mostly consistent with circular
velocities of halo gas at a typical dark matter halo mass (see Section 4.4).

  * •

Our sample’s illumination patterns are similar to other blue quasars based on
Ly$\alpha$ halo morphologies, characterized by elliptical eccentricity
parameters (see Section 3.4).

  * •

ERQ halos are more circularly concentrated, and could mean they have had less
time to extend by outflows from the innermost unresolved regions (see Section
4.2).

  * •

Obscuration acting as a chronograph allows for measurements of narrow
Ly$\alpha$ emission lines, and these lines can be used as systemic redshift
estimators for constraining broad line emission blueshifts and outflows (see
Section 4.1).

## Acknowledgements

JG, MWL, and FH acknowledge support from the USA National Science Foundation
grant AST-1911066. NLZ and AV acknowledge support from the NASA Astrophysics
Data Analysis Program Grant 80NSSC21K1569. The data presented herein were
obtained at the W. M. Keck Observatory, which is operated as a scientific
partnership among the California Institute of Technology, the University of
California and the National Aeronautics and Space Administration. The
Observatory was made possible by the generous financial support of the W. M.
Keck Foundation. Data presented herein were partially obtained using the
California Institute of Technology Remote Observing Facility. The authors wish
to recognize and acknowledge the very significant cultural role and reverence
that the summit of Maunakea has always had within the indigenous Hawaiian
community. We are most fortunate to have the opportunity to conduct
observations from this mountain.

## Data Availability

The data are available upon request.

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