# Extremely broad Ly$\alpha$ line emission from the molecular intra-group
medium in Stephan’s Quintet: evidence for a turbulent cascade in a highly
clumpy multi-phase medium?

P. Guillard  Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de
Paris, 98bis bd Arago, 75014 Paris, France  Institut Universitaire de France,
Ministère de l’Enseignement Supérieur et de la Recherche, 1 rue Descartes,
75231 Paris Cedex 05, France  P. N Appleton  Caltech/IPAC, MC 6-313, 1200 E.
California Blvd., Pasadena, CA 91125, USA  F. Boulanger  Laboratoire de
Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne
Université, Université de Paris, 75005 Paris, France  J. M. Shull  CASA,
Astrophysical and Planetary Sciences Dept., University of Colorado, UCB-389,
Boulder, CO 80309, USA  M. D. Lehnert  Sorbonne Université, CNRS, UMR 7095,
Institut d’Astrophysique de Paris, 98bis bd Arago, 75014 Paris, France  G.
Pineau des Forets  Observatoire de Paris, PSL University, Sorbonne Université,
LERMA, 75014 Paris, France  Université Paris Saclay, CNRS, Institut
d’Astrophysique Spatiale, 91405 Orsay, France  E. Falgarone  Laboratoire de
Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne
Université, Université de Paris, 75005 Paris, France  M.E. Cluver  Centre for
Astrophysics and Supercomputing, Swinburne University of Technology, John
Street, Hawthorn 3122, Victoria, Australia  Department of Physics and
Astronomy, University of the Western Cape, Robert Sobukwe Road, Bellville,
South Africa  C.K. Xu  IPAC, Caltech, MC 100-22, 1200 E. California Blvd.,
Pasadena, CA 91125, USA  Chinese Academy of Sciences South America Center for
Astronomy, National Astronomical Observatories, CAS, Beijing 100101, China
S.C. Gallagher  Department of Physics and Astronomy, University of Western
Ontario, London, ON N6A 3K7, Canada  P.A. Duc  Université de Strasbourg, CNRS,
Observatoire astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France

(Received February, 2021; Revised September 20th, 2021; Accepted October 18th,
2021)

###### Abstract

We present Hubble Space Telescope Cosmic Origin Spectrograph (COS) UV line
spectroscopy and integral-field unit (IFU) observations of the intra-group
medium in Stephan’s Quintet (SQ). SQ hosts a 30 kpc long shocked ridge
triggered by a galaxy collision at a relative velocity of 1000 km s-1, where
large amounts of molecular gas coexist with a hot, X-ray emitting, plasma. COS
spectroscopy at five positions sampling the diverse environments of the SQ
intra-group medium reveals very broad ($\approx 2000$ km s-1) Ly$\alpha$ line
emission with complex line shapes. The Ly$\alpha$ line profiles are similar to
or much broader than those of H$\beta$, [C ii]157.7$\mu$m and CO (1-0)
emission. The extreme breadth of the Ly$\alpha$ emission, compared with
H$\beta$, implies resonance scattering within the observed structure.
Scattering indicates that the neutral gas of the intra-group medium is clumpy,
with a significant surface covering factor. We observe significant variations
in the Ly$\alpha$/H$\beta$ flux ratio between positions and velocity
components. From the mean line ratio averaged over positions and velocities,
we estimate the effective escape fraction of Ly$\alpha$ photons to be $\approx
10-30$%. Remarkably, over more than four orders of magnitude in temperature,
the powers radiated by X-rays, Ly$\alpha$, H2, [C ii] are comparable within a
factor of a few, assuming that the ratio of the Ly$\alpha$ to H2 fluxes over
the whole shocked intra-group medium stay in line with those observed at those
five positions. Both shocks and mixing layers could contribute to the energy
dissipation associated with a turbulent energy cascade. Our results may be
relevant for the cooling of gas at high redshifts, where the metal content is
lower than in this local system, and a high amplitude of turbulence is more
common.

galaxies: high-redshift – galaxies: formation and evolution – galaxies:
kinematics and dynamics – galaxies: ISM – galaxies: active – ISM: general –
ISM: structure – turbulence

††journal: ApJ††journal: ApJ

##  1 Introduction

Galaxy interactions are important phases of their evolution, often involving
high-speed shocks and dissipation or large amounts of kinetic energy. Many of
these interactions are observed in infrared (IR) and visible light to trigger
bursts of star-formation. The dissipation of kinetic energy affects the gas
cooling and how, when, and where star formation proceeds. To make headway in
our understanding of the conversion of molecular gas to stars, it is crucial
to determine the mechanism and rate of gas cooling.

Stephan’s Quintet (HCG 92, hereafter SQ) is a compact group of five
interacting galaxies (Arp, 1973) with a complex dynamical history, involving
multiple galaxy collisions (Moles et al., 1997; Renaud et al., 2010; Hwang et
al., 2012; Duc et al., 2018). It is an ideal laboratory for the study of
galaxy interactions and their impact on the physical state and energetics of
the gas, especially the dissipation of merger-driven turbulence isolated
against the dark sky (Guillard et al., 2009). It is one of the few
extragalactic sources where one can spatially separate star forming regions
from shocked gas. When excluding the large foreground dwarf galaxy NGC 7320,
the main group is dominated by four large massive galaxies. Three of them, NGC
7317, NGC 7318a and NGC 7319, have heliocentric radial velocities in the range
V${}_{helio}=6599-6747$ km s-1, and together they define the main barycentric
velocity of the group (at around 6600 km s-1). A fourth galaxy, NGC 7318b
(Vhelio = 5774 km s-1, is often described as an intruder galaxy because it
appears to be colliding into NGC 7319’s tidal tail in the intra-group medium
at a relative velocity of $\approx\\!1000$ km s-1(see Fig 1 and Xu et al.,
2003).

The collision of NGC 7318b with the gas in the intra-group medium is believed
to be responsible for a striking feature of the group, namely a galaxy-wide
shock ($\approx 15\times 35$ kpc2; Fig. 1) seen at many wavelengths. A ridge
of X-ray (O’Sullivan et al., 2009) and radio synchrotron (Allen & Hartsuiker,
1972) emission from the hot ($6\times 10^{6}\,$K) post-shock plasma is
associated with the group-wide shock. Surprisingly, Spitzer IRS spectroscopy
revealed that the mid-IR spectrum in the intra-group medium is dominated by
the rotational lines of $\rm H_{2}$ (see red contours on Fig. 1), with very
weak dust emission from star formation (Appleton et al., 2006; Cluver et al.,
2010). Over the shock region, no H i emission is detected, but optical line
emission from ionized gas is observed at the velocity of NGC 7319’s H i tidal
tail (Sulentic et al., 2001).

The weakness of the mid-IR tracers of star-formation (dust features and
ionized gas lines) relative to the H2 lines suggests that, despite the large
H2 mass estimated to be $\approx 5\times 10^{9}\,$M⊙ (Guillard et al., 2012),
the star formation rate is on average very low in the shock ($<0.07\,$M⊙ yr-1,
Cluver et al., 2010). This is a factor 40 below the star formation rate
expected from the Schmidt-Kennicutt relation (Guillard et al., 2012). Deep
HST/WFC3 H$\alpha$ imaging of SQ reveals many compact H$\alpha$ knots and
filaments spread over the shock, as well as a diffuse, underlying component
(Gallagher et al., 2001). Extensive Gemini optical spectroscopy of 50
H$\alpha$ knots in the group (Konstantopoulos et al., 2014) shows that both
photo-ionization and shock excitation are present (see also Xu et al., 2003,
for earlier long-slit optical spectroscopy), a result that is also confirmed
by IFU spectroscopy (Duarte Puertas et al., 2019). Some knots are star
clusters (masses from $10^{4}$ to a few $10^{5}\,$M⊙, Gallagher et al., 2001;
Fedotov et al., 2011), while others show very strong [Oiii]$\lambda\,5007\,$Å
and [Oi]$\lambda\,6300\,$Å emission, and very broad (FWHM up to $\approx
700\,$km s-1), complex optical emission line profiles, consistent with pure
shock excitation (Konstantopoulos et al., 2014).

Spitzer and Herschel have shown that the H2, [C ii]$\lambda 158\mu$m and [O
i]$\lambda 63\mu$m IR lines are important coolants of the shocked gas
(Appleton et al., 2013, 2017). Guillard et al. (2009) proposed a model in
which this line emission is powered by the dissipation of kinetic energy,
through a turbulent cascade of energy, from the galaxy-wide shock down to low-
velocity shocks within molecular gas. GALEX imaging of SQ (Xu et al., 2005)
shows that most of the UV emission in the intra-group medium ridge is
associated with an arc-like structure to the South-East of the intruder NGC
7318, which spatially correlates with a chain of H$\alpha$ knots. The broad-
band UV emission at the center of the shock, where the H2 emission peaks, is
extended and corresponds to a radiation field of average intensity
$G_{UV}=1.4$ Habing (Guillard et al., 2010).

This paper complements the rich array of SQ observations by presenting UV
spectra obtained with HST COS, focusing on the Ly$\alpha$ line emission. We
assess the origin of the Ly$\alpha$ photons and their contribution to the
energy budget of the SQ galaxy collision. The comparison of the line profiles
with those of CO, [C ii] and H$\beta$ provide insight on the structure of the
multiphase ISM in SQ.

We assumed a distance to Stephan’s Quintet of 94 Mpc for H0 = 70 km s-1 Mpc-1,
and a group systemic heliocentric velocity of 6600 km s-1.

##  2 Observations and data reduction

###  2.1 Observed COS line-of-sights

We chose to perform deep COS spectroscopy of 5 regions in the intra-group
medium of SQ, as shown on Fig. 1, for which we have very high signal-to-noise
optical spectra from Gemini. The COS pointings are also associated with
CO(1-0) line emission detected with the NOEMA interferometer, as well as the
30m single-dish for positions 1, 2, 5 and 7. The optical line properties
derived from Gemini, the slit positions associated with the COS beams, and the
CO(1-0) line properties are gathered in Table 4. Our five pointings were also
chosen to probe diverse environments. As the background HST WFC3 image in Fig.
1 shows, positions 1, 2 and 7 are associated with bright H$\alpha$ knots in
the intra-group medium ridge, while positions 3 and 5 are not. Positions 1, 2
and 5 are associated with very broad optical line emission, with line ratios
consistent with pure shock excitation (see Fig. 10 in Konstantopoulos et al.,
2014). Position 5 lies in the so-called bridge between NGC 7319 and the ridge,
and shows faint, diffuse H$\alpha$ emission filling up the COS beam,
associated with NGC 7319’s tidal tail. Position 3 points towards a region of
the ridge devoid of compact H$\alpha$ emission. The associated Gemini slit is
slightly offset from the COS beam and hits a bright H$\alpha$ knot, whose
excitation is consistent with that of an H ii region, so comparison between
COS and Gemini data at this position may not be meaningful. Position 7 is
located in the SQ-A starburst region in the Northern region of the ridge, and
is one of the two brightest star-forming regions in the intra-group medium of
SQ. This region is known to combine photo-ionization from star formation and
shocks. Indeed, for instance, optical Gemini spectra show strong variation in
the H$\alpha$/N ii line ratio as a function of gas velocity. In this paper, to
characterize the dissipation of turbulence in the intra-group medium
environment of SQ, we focus on regions known to be shock-dominated.

###  2.2 Reduction of COS spectroscopic data

SQ was observed with the medium-resolution far-UV G130M (Ly$\alpha$) and G160M
(Civ) gratings of HST-COS on 2014 November 9 for a total of 15 orbits.
Descriptions of the COS instrument and on-orbit performance characteristics
can be found in (Green et al., 2012; Osterman et al., 2011), as well as in the
COS Instrument Handbook. In order to achieve continuous spectral coverage
across the G130M bandpass (1135-1440 Å) and to minimise fixed-pattern noise,
we made observations at two central wavelength settings (1291 Å and 1300 Å)
with four focal-plane offset locations in each grating setting (i.e. FP-POS =
1, 2, 3, 4). This combination of grating settings ensures the highest signal-
to-noise observations at the shortest wavelengths available to the G130M mode
at a resolving power of $R=\lambda/\Delta\lambda\approx 16,000$ (about 17 km
s-1velocity resolution for a point source). For every sightline, COS
observations yielded a continuous spectrum spanning $\lambda\approx 1150-1800$
Å. The calibration of the wavelength scale with updated dispersion solutions
ensures a velocity accuracy of 7 km s-1. The exposure times were chosen to
achieve a signal-to-noise ratio (S/N) of 7–15 per resolution element (7
pixels, $\approx 0.07\AA$, ${\rm FWHM}=15\ \mbox{{\rm km}\,{\rm s}${}^{-1}$}$
for a point source) at $\lambda\approx 1300$ Å, depending on the velocity
range. We note that the spectral resolution could be significantly lower for
extended sources, as low as $R=1450$ for G130M if the emission uniformly fills
the COS beam. In particular, this may be the case for positions 3 and 5, which
do not show an associated compact H$\alpha$ source within the COS aperture.
The target positions, grism configurations and individual exposure times are
presented in Table 1. We plot the spectra binned to the standard 7 pixels.

We started our data reduction from the x1d.fits files produced by the COS
calibration pipeline, CalCOS111see HST COS Instrument Handbook for more
details:
http://www.stsci.edu/hst/cos/documents/handbooks/current/cos_cover.html.,
downloaded from MAST. To assess the contamination of the spectra by geocoronal
airglow lines, we have filtered the data in time in order to produce spectra
utilizing only data taken during orbital night time. To do that, we used the
TimeFilter routine from the COSTOOLS
package222https://github.com/spacetelescope/costools to select night time data
in the COS corrtag files, and then re-extracted the data into x1d spectra. The
comparison between the night-only and full datasets did not yield significant
improvement because the redshift of the source (0.02) shifts the Ly$\alpha$
line to 1240 Å, in between the geocoronal Ly$\alpha$ and [O i] lines. The data
have then been aligned and coadded with the COADD_X1D.pro V3.3 IDL routine
provided by STScI333available at
http://casa.colorado.edu/~danforth/science/cos/costools. To take into account
the strong wings of the non-Gaussian, Line Spread Function (LSF) of COS, we
have used the COS_LSF.pro IDL routine to produce a LSF model at the nearest
tabulated wavelength value. The COS exposures for each regions were
deconvolved using the LSF appropriate for corresponding grating setting and
for the central wavelengths of the Ly$\alpha$ and Civ emission lines. The
absolute flux calibration steps are described in detail in the COS data
handbook444https://hst-docs.stsci.edu/cosdhb/chapter-3-cos-calibration, and
are expected to of the order of $\pm 5$% for G130M and G160M (errors are
dominated by fixed pattern noise in the UV detectors and uncertainties in the
time-dependent sensitivity correction).

###  2.3 Visible light IFU spectroscopy

We also present Integral Field Unit (IFU) observations made with the George
and Cynthia Mitchell Spectrograph (hereafter GCMS, formerly known as VIRUS-P)
mounted on the 2.7 m Harlan J. Smith Telescope at McDonald Observatory (Hill
et al., 2008; Blanc, 2013). The IFU uses a 246 fiber bundle, with each fiber
covering $4\farcs 16$ on the sky, which makes it sensitive to faint extended
emission. We used a 3-point dither pattern to completely cover the 2.82
arcmin2 field of view, and to fill in gaps between the fibers. Observations
were obtained on 1 Oct 2011 with an integration time of one hour at each of
the three dither positions. We used the VP2 blue grating, which has a spectral
resolution of $\sim 1.6$ Å ($\sim$ 100 km s-1) and covers the wavelength range
$\sim 4700$ to $\sim 5350$ Å. The data reduction was performed using the
VACCINE software package (Adams et al., 2011), and these data were further
flux calibrated using a bootstrapping method which compares each fiber
response to a calibrated SDSS b-image of the galaxy (e.g. Joshi et al., 2019).
Wavelength calibration was performed using lamp spectra obtained at the
beginning of the observing run.

Figure 1: HST Wide Field Camera 3 F665N image of the inner SQ group with Spitzer IRS H2 (0-0) S(3) 9.6$\mu$m line flux contours in red from Cluver et al. (2010). This emission from warm molecular hydrogen highlights the North-South shocked ridge of the intra-group medium, as well as an extension towards NGC 7319, called ”the bridge”. The blue circles are the COS apertures (2.5” in diameter) corresponding to 1.1 kpc at a distance $D=94$ Mpc. The positions, observing parameters and integration times are listed in Table 1. Table 1: COS observation log: MAST archive name, positions, COS gratings, central wavelength and individual exposure times for each of the 5 positions observed. COS target | RA | Dec | Grating | $\lambda_{cen}$ | Exp. time
---|---|---|---|---|---
(MAST) | (J2000) | (J2000) |  | [Å] | [seconds]
HCG92-1 | 22 35 59.765 | +33 58 21.33 | G130M | 1096 | 1287.872
|  |  | G130M | 1222 | 1437.696
|  |  | G160M | 1611 | 3180.512
|  |  | G160M | 1623 | 3673.536
HCG92-2 | 22 36 00.032 | +33 58 06.75 | G130M | 1096 | 1287.936
|  |  | G130M | 1222 | 1437.760
|  |  | G160M | 1611 | 3180.544
|  |  | G160M | 1623 | 3673.568
HCG92-3 | 22 35 59.439 | +33 58 34.80 | G130M | 1096 | 1429.056
|  |  | G130M | 1222 | 1447.840
|  |  | G160M | 1611 | 3180.576
|  |  | G160M | 1623 | 3673.568
HCG92-5 | 22 36 01.222 | +33 58 22.74 | G130M | 1096 | 1366.016
|  |  | G130M | 1222 | 1359.552
|  |  | G160M | 1611 | 3180.640
|  |  | G160M | 1623 | 3671.584
HCG92-7 | 22 35 58.953 | +33 58 49.96 | G130M | 1096 | 600.000
|  |  | G130M | 1222 | 599.712
|  |  | G160M | 1611 | 1102.656
|  |  | G160M | 1623 | 1303.712
Table 2: Observed Ly$\alpha$, H$\beta$ and H2 line fluxes and line ratios for the COS lines of sight. COS target |  $F_{Ly\alpha}$: Ly$\alpha$ FluxaaUncorrected for Ly$\alpha$ absorption. Some of the profiles show evidence of absorption (see text).  |  $F_{H\beta}$: H$\beta$ fluxbbSum of the observed line flux estimated on a $4\times 4$ arcsec2 square aperture from the Mitchell Spectrograph IFU data, scaled to the circular COS aperture of 2.5” in diameter assuming constant surface brightness. | FH2: H2 flux ccSum of the (0-0) S(0) + (0-0) S(1) + (0-0) S(2) + (0-0) S(3) pure rotational H2 line fluxes derived from extractions of $5.5\times 5.5$ arcsec2 from Spitzer IRS data (Appleton et al., 2017), scaled down to the circular COS aperture of 2.5” in diameter assuming constant surface brightness. |  $F_{Ly\alpha}$/$F_{H\beta}$ |  $F_{Ly\alpha}$/FH2
---|---|---|---|---|---
| [$10^{-18}\,$W m-2] | [$10^{-19}\,$W m-2] | [$10^{-18}\,$W m-2] |  |
HCG92-1 (ridge) | $5.3\pm 0.5$ | $1.7\pm 0.2$ | $6.7\pm 0.8$ | $30.9\pm 3.4$ | $0.77\pm 0.12$
HCG92-2 (ridge) | $5.2\pm 0.5$ | $2.4\pm 0.2$ | $7.3\pm 0.9$ | $22.0\pm 2.5$ | $0.71\pm 0.11$
HCG92-3 (ridge) | $1.1\pm 0.1$ | $1.6\pm 0.3$ | $5.8\pm 0.7$ | $7.0\pm 1.2$ | $0.19\pm 0.03$
HCG92-5 (bridge) | $0.4\pm 0.1$ | $0.8\pm 0.1$ | $5.5\pm 0.6$ | $4.7\pm 0.9$ | $0.07\pm 0.02$
HCG92-7 (SQ-A) | $1.3\pm 0.1$ | $6.7\pm 0.1$ | $7.0\pm 0.8$ | $1.8\pm 0.2$ | $0.17\pm 0.02$
all (stacked) | $13.3\pm 0.2$ | $13.2\pm 0.4$ | $32.3\pm 1.7$ | $10.1\pm 1.4$ | $0.41\pm 0.03$
Table 3: Observed Ly$\alpha$ line kinematical properties for the COS lines of
sight.

COS target |  $W_{10}$(Ly$\alpha$)aaWidths at 10%, 20% and 50% of maximum flux. |  $W_{20}$(Ly$\alpha$)aaWidths at 10%, 20% and 50% of maximum flux. |  $W_{50}$(Ly$\alpha$)aaWidths at 10%, 20% and 50% of maximum flux.
---|---|---|---
| [km s-1] | [km s-1] | [km s-1]
HCG92-1 | $1910\pm 40$ | $1690\pm 20$ | $1290\pm 40$
HCG92-2 | $2120\pm 40$ | $1080\pm 20$ | $690\pm 20$
HCG92-3 | $2000\pm 40$ | $1770\pm 20$ | $570\pm 20$
HCG92-5 | $1120\pm 40$ | $930\pm 40$ | $350\pm 20$
HCG92-7 | $1480\pm 40$ | $530\pm 40$ | $220\pm 20$
all (stacked) | $2650\pm 40$ | $1820\pm 20$ | $595\pm 15$

Note. — $W_{10}$ has been computed after smoothing the spectra to 80 km s-1 to
increase the SNR in the line wings, and is close to the Full Width at Zero
Intensity of the line. In case of the presence of several velocity components,
only the widest component is listed.

Table 4: CO (1-0) line properties extracted at the positions of the COS apertures and optical line properties derived from Gemini spectroscopy at the nearest position of the HST COS apertures. COS target |  $I_{\rm CO}$aaParameters estimated from the CO (1-0) spectrum extracted from the IRAM NOEMA interferometer data (Guillard et al. in prep.) on a beam size $4.2\times 3.9$ arcsec2: integrated intensity, central velocity and velocity dispersion. |  $v_{\rm CO}$aaParameters estimated from the CO (1-0) spectrum extracted from the IRAM NOEMA interferometer data (Guillard et al. in prep.) on a beam size $4.2\times 3.9$ arcsec2: integrated intensity, central velocity and velocity dispersion. |  $\sigma_{\rm CO}$aaParameters estimated from the CO (1-0) spectrum extracted from the IRAM NOEMA interferometer data (Guillard et al. in prep.) on a beam size $4.2\times 3.9$ arcsec2: integrated intensity, central velocity and velocity dispersion. | Gemini IdbbClosest Gemini slit ID from Konstantopoulos et al. (2014). The star indicates when the Gemini slit is slightly offset from the COS aperture.  | F(H$\alpha$) ccH$\alpha$ flux and optical line ratios from Konstantopoulos et al. (2014).  | [Nii]/H$\alpha$ccH$\alpha$ flux and optical line ratios from Konstantopoulos et al. (2014).  |  [O i]/H$\alpha$ccH$\alpha$ flux and optical line ratios from Konstantopoulos et al. (2014).  | H$\beta$/H$\alpha$ccH$\alpha$ flux and optical line ratios from Konstantopoulos et al. (2014).
---|---|---|---|---|---|---|---|---
| [Jy km s-1] | [km s-1] | [km s-1] |  | [$10^{-18}\,$W m-2] |  |  |
HCG92-1 (ridge) | $2.6\pm 0.2$ | 6084.9 | 28.8 | 15053∗ | $0.0774\pm 0.0058$ | $0.168\pm 0.001$ | $0.251\pm 0.002$ | $0.320\pm 0.002$
HCG92-2 (ridge) | $1.8\pm 0.2$ | 6080.1 | 30.6 | 12002 | $0.2553\pm 0.0180$ | $0.141\pm 0.001$ | $0.203\pm 0.002$ | $0.145\pm 0.003$
HCG92-3 (ridge) | $2.2\pm 0.3$ | 6260.0 | 35.7 | 14006∗ | $0.0639\pm 0.0016$ | $0.129\pm 0.001$ | $0.025\pm 0.001$ | $0.241\pm 0.001$
HCG92-5 (bridge) | $1.1\pm 0.3$ | 6350.0 | 67.8 | 20001 | $0.0276\pm 0.0007$ | $0.210\pm 0.002$ | $0.217\pm 0.001$ | $0.460\pm 0.002$
HCG92-7 (SQ-A) | $4.3\pm 0.3$ | 6736.8 | 19.8 | 30109 | $1.0383\pm 0.0032$ | $0.051\pm 0.001$ | $0.217\pm 0.001$ | $0.197\pm 0.002$

Figure 2: Comparison of Ly$\alpha$ (red), H$\beta$ (green), and CO (1-0)
(blue) line profiles for the 5 positions observed. The CO (1-0) PdBI spectra
are extracted at the COS positions over an ellipsoidal beam of $4.3\times 3.5$
arcsec2, P.A = 100 degrees. The Ly$\alpha$ CO(1-0), H$\beta$ spectra have
respectively a velocity resolution of 20, 30, and 100 km s-1.

Figure 3: Comparison of Ly$\alpha$ (red) , Herschel [C ii] spectra, and IRAM
single-dish 30m CO(1-0) line profiles for the 5 positions observed. For
position 3, where no IRAM 30m data is available, we added the comparison to
the H$\beta$ line taken with the GCMS (VIRUS-P) IFU Spectrograph.

##  3 Extremely broad Ly$\alpha$ line and kinematics of the ionized medium

###  3.1 Individual COS pointings: line fluxes and kinematics

We detect strong and broad Ly$\alpha$ (1215.67 Å) emission from all the five
observed regions shown in Fig. 1. The Ly$\alpha$ line profiles for each of the
5 observed positions, shown in Fig. 2a-e and 3a-e (in red), have complex,
multi-peaked profiles. The observed coordinates and integrated Ly$\alpha$ and
molecular hydrogen (H2) line fluxes for each region are presented in Table 2.
Our observations involve only a few COS sight-lines and therefore provide a
sparse view of the Ly$\alpha$ emission across the intra-group medium. It is
therefore not possible to quantify the total Ly$\alpha$ luminosity from the
intra-group medium, and we will restrict our analysis to the comparison of
line fluxes at the COS positions.

The Ly$\alpha$ flux averaged over the 5 COS beams amounts to $\approx 40$% of
the warm H2 IR line emission (see last column of Table 1), which is the
dominant cooling channel in the shocked intra-group medium (Appleton et al.,
2017) and similar to that of the [C ii] line and X-rays as well (see Table 1
in Guillard et al., 2009, for a summary of the energy budget across gas
phases). Remarkably, on average, the Ly$\alpha$ line luminosity is comparable
to that of much cooler and hotter gas, assuming that the ratio of Ly$\alpha$
to H2 emissions is the same over the whole shocked intra-group medium. Sect.
5.3 discusses the implications of this observational result on the properties
of kinetic energy dissipation in the intra-group medium of SQ. We also note
that the Ly$\alpha$ flux varies by a factor of $\approx 10$, between the
bridge (faintest) and the ridge 1 (brightest) positions.

In Table 3, we gather our measurements of the widths of the Ly$\alpha$ lines
for the five observed positions, as well as for the stacked spectrum. There is
a large variation of the widths of the Ly$\alpha$ lines, with Full Width at
Zero Intensity (FWZI) up to $\approx 2100$ km s-1. This is remarkable, given
that the COS beam is sampling a small region of intergalactic space between
the galaxies (the 2.5 arcsec beam diameter corresponds to 1.1 kpc)555Stephan’s
Quintet is assumed to be at a distance of 94 Mpc. This suggests that the COS
beams likely probe the same large-scale organised structure in the filament
seen at other wavelengths, rather than small individual emission regions. This
becomes clear when we compare the Ly$\alpha$ profiles with H$\beta$ lines,
shown as red and green profiles respectively on Fig. 2, and with [C
ii]157.7$\mu$m lines (Appleton et al., 2013), shown as yellow profiles on Fig.
3. In many cases, the complex Ly$\alpha$ profile shapes track approximately
the main kinematic features from the other lines which are known to show
large-scale coherence (see for example Rodríguez-Baras et al. 2014; Duarte
Puertas et al. 2019).

Fig. 2 and 3 show the varying velocity, profile shapes, line widths, and
strength of the Ly$\alpha$ emission, compared with other line profiles at the
same positions. The broadest Ly$\alpha$ line we observed is seen in Fig. 2a
and 3a, obtained at position HCG92-1 (see Fig. 1, and Table 3), near the
center of the giant H2 emitting filament. In this profile, the Ly$\alpha$
emission tracks quite well the shape of the H$\beta$ and [C ii] profiles at
low heliocentric velocity, but deviates strongly at higher velocities. The
Ly$\alpha$ emission extends to at least V${}_{helio}=7600$ km s-1, whereas
both the [C ii] and H$\beta$ emission fall almost to zero flux at velocities
of no more than 7300 km s-1, compared to the barycentric systemic velocity of
6600 km s-1. The excess emission seen above 7300 km s-1 may be evidence of
resonant scattering and bulk motions of the scattering medium, which is common
in Ly$\alpha$ systems (see Sect. 5.2 for a discussion of the origin of the
line broadening). This is supported by the observation that the line profiles,
taken with both the Mitchell Spectrograph and Herschel generally occupy a more
limited range of radial velocities compared with the Ly$\alpha$ emission,
despite being taken over larger beam sampling areas than the COS data, i.e.
$4\times 4$ arcsec2 for GCMS and $9.4\times 9.4$ arcsec2 for the [C
ii]157.7$\mu$m line, see Appleton et al. (2013).

Other examples of possible resonant scattering wings in the Ly$\alpha$
profiles compared with the [C ii] and H$\beta$ emission lines are the blue
wing seen in HCG-2 (Fig. 3b) at V${}_{helio}<5800$ km s-1and the blue wing in
HCG-5 (Fig. 3d). In both cases, the Ly$\alpha$ emission extends significantly
blueward of the H$\beta$ line by velocities of up to 200-300 km s-1.

###  3.2 Comparison with CO (1-0) line profiles

We compare the Ly$\alpha$ and H$\beta$ lines with CO (1-0) line profiles
obtained respectively with the IRAM NOEMA interferometer and the single-dish
IRAM 30m telescope (from Guillard et al., 2012), respectively in Fig. 2 and 3.
Our CO (1-0) observations with the IRAM NOEMA interferometer, which will be
presented in a companion paper (Guillard et al. in prep.), show giant, kpc-
scale molecular complexes of a few $10^{8}\,$M⊙ in the shock, some of them
associated with H$\alpha$-emitting regions. From the cleaned CO (1-0) line
emission map, we have extracted spectra within beams centered on the COS
positions, using a synthesized beam of $4.3\times 3.5$ arcsec2, of position
angle P.A.=100∘. We used the IRAM GILDAS mapping suite of
routines666https://www.iram.fr/IRAMFR/GILDAS/doc/pdf/map.pdf to perform the
extractions, and then exported the spectra into fits files. The line
parameters are gathered in Table 2. The CO (1-0) line intensity was computed
by integrating the line profile, and the central velocity and line velocity
dispersion were computed after a Gaussian fit to the profile. The comparison
between the CO (1-0) and Ly$\alpha$ line profiles is shown in Fig. 2 with the
caveat that the NOEMA beam is twice as large as the COS beam. It is striking
that the CO lines detected with NOEMA are much narrower than the Ly$\alpha$
lines, except in the Northern star-forming region (SQ-A, position 7) where the
main CO velocity component at 6700 km s-1 matches the Ly$\alpha$ profile.
Those molecular complexes are much larger than the small scale structure of
the neutral gas through which Ly$\alpha$ photons scatter out of the intra-
group medium. However, the spatial resolution of the NOEMA observations being
1.8 kpc, those giant molecular complexes could well break down into much
smaller clumps with sometimes large shear motions between them ($\approx 100$
km s-1). We also note that there may be a more diffuse, extended molecular
component, which may be filtered-out by the interferometer. This is
illustrated on Fig. 3 where we compare the Ly$\alpha$ and [C ii] line profiles
with CO(1-0) from single-dish IRAM 30m data. In this case, the single-dish CO
line profiles are much broader than the interferometric data.

###  3.3 Overview of the Large-scale motions of the intra-group medium gas

Part of the complexity of the Ly$\alpha$ line profiles can be understood when
the full picture of the ionized gas (as measured optically) is explored. Other
authors have presented 2-dimensional spectral maps of the optical emission
lines in Stephan’s Quintet (Iglesias-Páramo et al., 2012; Konstantopoulos et
al., 2014; Rodríguez-Baras et al., 2014; Duarte Puertas et al., 2019), but we
will use our own data from the GCMS spectrograph to provide an overview and
context for the observed profiles. In Fig. 4, we show a sequence of
representative H$\beta$ surface-brightness emission maps for the inner SQ
group. For context, the radial velocity of the intruder galaxy, NGC 7318b is
Vsys= 5774 km s-1, and it is thought to be entering the group from behind with
a blue-shifted discrepant velocity of almost 1000 km s-1 relative to the rest
of the group members and the group-wide gas (Xu et al., 2003; Hwang et al.,
2012). A component of the ionized gas (Fig. 4a and b) follows the spiral arm
and H ii regions seen in NGC 7318b, as expected if some of the gas was part of
that galaxy. Gas is also seen from the nucleus and northern disk of NGC 7319,
(Fig. 4c, d and e), but with significant emission from the main North-South
shocked filament. Gas at intermediate velocities (Fig. 4c and d) is spread
along the filament, but also in the bridge between NGC 7318b and NGC 7319. The
bridge is fragmentary in nature at H$\beta$, and occupies as narrower range of
velocities compared with the main filament. The pile-up of gas with such a
wide range of velocities along such a narrow structure in the main filament is
a unique and remarkable feature of the Stephan’s Quintet system.

Figure 4: Contours of H$\beta$ surface brightness emission (in red) from
Stephan’s Quintet based on the Mitchell Spectrograph observations covering the
full range of heliocentric velocities from 5291 to 7123 km s-1 in which
emission was detected. Each sub-figure (a to f) shows the integrated surface
brightness of the emission in units of
$2.5,5,10,15,20,25,30,40,50~{}$and$~{}60~{}\times~{}10^{-18}~{}erg~{}s^{-1}~{}cm^{-2}~{}arcsec^{-2}$
over the range of velocities indicated. Subfigure (b) cover the velocity range
which includes the intruder galaxy (Vsys=5774 km s-1), whereas the barycenter
of the group (Vsys=6600 km s-1) is represented in panel (e). Gas is also seen
at intermediate velocities in the bridge between the main filament and the
Seyfert galaxy NGC 7319 (panels c and d). Note a possible outflow from NGC
7319. All of the contours are projected against the HST WFC3 F665N (H$\alpha$)
greyscale image of the system.

###  3.4 Stacked spectra and the detection of the
Civ$\lambda\\!\lambda$1548,1550Å doublet

In Fig. 5 we show the averaged spectra of both Ly$\alpha$ and the
Civ$\lambda$1549Åline, stacked over the five observed positions. We found all
ten G160M integrations setting (two wavelengths per position) free of strong
fixed pattern noise features and thus suitable for co-addition. The Civ line
detected on the stacked spectra is centered around the heliocentric recession
velocity of the intra-group gas ($\approx$ 6000 km s-1) and is very broad
(FWHM $>1000$ km s-1). The profiles of the stacked Ly$\alpha$ and Civ lines
also show some similarities, with, for Ly$\alpha$, a brighter low-velocity
component around $6000-6200$ km s-1and a fainter shoulder around $6300-7000$
km s-1. We note that the noise in the stacked spectrum is not Gaussian,
indicating that some low-level pattern noise is present, which makes the
estimate of the S/N ratio of the line uncertain. The individual spectra are
not very useful and show weak detections ($\approx 2\sigma$) for all five
positions.

##  4 Absorption and scattering of Ly$\alpha$ photons in the intra-group
medium

By comparing the Ly$\alpha$, H$\beta$, [C ii] and CO spectra, we can deduce at
which velocities along the line of sight the Ly$\alpha$ photons are mostly
absorbed. Generally speaking, looking at Fig 2 and Fig. 3, the Ly$\alpha$ and
[C ii] profiles are sometimes closer in shape than Ly$\alpha$ and H$\beta$.
This result recalls the work of Appleton et al. (2013) showing that most of
the [C ii] line emission is associated with the warm ($T>100$ K) molecular gas
(H2), and that the [C ii] emission cannot be accounted for by recombination in
the warm ionized medium. Therefore, both [C ii] and Ly$\alpha$ trace gas
heated by mechanical energy dissipation.

There are four possible examples of where Ly$\alpha$ absorption is taking
place. In Fig. 3b and c we see that the high velocity component of the double
profile seen in both H$\beta$ and [C ii] is significantly suppressed compared
with the low-velocity component. For Fig. 2b in particular, the peak in the
H$\beta$ profile falls close to a strong dip in the Ly$\alpha$ profile, which
appears as two small wings on either side of the dip. For Fig. 3c, the feature
seen in both [C ii] and H$\beta$ is largely suppressed above 6500 km s-1.
Also, in Fig. 2d and 3d, the Ly$\alpha$ profile is shifted blueward of the
main [C ii] and H$\beta$ peaks, suggestive of absorbing gas centered at Vhelio
= 6500-6700 km s-1. Asymmetric Ly$\alpha$ profiles like this are often
associated with radial outflows in galaxies (e.g. Heckman et al., 2011). The
COS pointing (HCG92-5) samples the gas in the so-called ”AGN bridge” (Cluver
et al., 2010), a linear H2 filament that is apparently separate from the main
collisional shock in SQ. A strong shear in the velocity field of the [C ii]
emission was noted by Appleton et al. (2013) in that region. The spectrum of
the CO (1-0) emission from that direction (see Fig. 2d and Fig. 3d), shows
significant CO emission at the high velocity side of the profile, which would
be consistent with absorption. Finally, HCG92-7 shows, in Fig. 3e, the
opposite effect. In this case, again considering the high-velocity component
of the double-horned profile only, we see that the Ly$\alpha$ is significantly
redshifted with respect to the H$\beta$ emission, with a sharp drop in
emission as one approaches the peak of the H$\beta$ (around Vhelio = 6600-6700
km s-1). This may be another example of asymmetric absorption, with resonant
scattering to the red-side of the wings of the kinematics. In summary, we see
that two regions in the main emission-line filament are almost free of
absorption, whereas other regions show strong absorption. Even in those cases,
at least some of the Ly$\alpha$ emission is able to resonantly scatter, and
undergo many scatterings within the gas before eventually escaping into the
wings of the velocity profile where the optical depth is much lower. In Sect.
5.2 we estimate the escape fraction of the Ly$\alpha$ photons and the number
of scatterings, and we discuss the multi-phase structure of the intra-group
medium gas. We also remind that the differences between the Ly$\alpha$ and
H$\beta$ spectral profiles may not only be due to Ly$\alpha$ scattering,
because collisional excitation could also contribute.

Does this interpretation make sense in terms of the expected line ratios for
the hydrogen lines? In Table 2 we also present the H$\beta$ line fluxes and
Ly$\alpha$ to H$\beta$ flux ratios integrated over the 5 different sets of
spectra. It is interesting that HCG92-1 and 2 both show ratios (31 and 22
respectively) consistent with little or no absorption when compared with Case
B recombination (Case B predicts for T = 104 K and typical interstellar
densities a flux ratio F(Ly$\alpha$)/F(H$\beta$) of $\sim$ 33). The lack of
extinction inferred from the line ratio for HCG-1 is entirely consistent with
our previous description of the close similarity between the Ly$\alpha$ and
H$\beta$ line profile shapes. The slightly lower Ly$\alpha$ to H$\beta$ ratio
is consistent with the increased absorption in the red component of the
Ly$\alpha$ profile. For both HCG92-3 and 5, F(Ly$\alpha$)/F(H$\beta$) are
significantly lower than Case B, suggesting stronger absorption, which is
again consistent with the line profiles. Finally, HCG92-7 (which is associated
with the extragalactic Hii regions and contains significant star formation and
dust), shows the highest deviation from Case B (F(Ly$\alpha$)/F(H$\beta$)
$\sim$ 2) suggesting that, at that position, most of the Ly$\alpha$ photons
are absorbed by dust.

Figure 5: Ly$\alpha$ line (red, grism G130M) and Civ doublet (purple, grism
G160M) HST COS spectra stacked over all 5 observed positions in the intra-
group medium of Stephan’s Quintet. The flux of the Civ line has been
multiplied by a factor of 10 for clarity. The widths at 20% and 50% of the
stacked Civ peak flux are, respectively, $1100\pm 60$ and $900\pm 40$ km s-1.

Figure 6: Results from the MAPPINGS V shock models library from Alarie &
Morisset (2019), covering a range in velocities of 50-1000 km s-1. Solid lines
show the contribution of the shock only and dashed lines include the
contribution of the radiative precursor at velocities $V_{s}>100$ km s-1. In
this grid of models, the preshock Hydrogen density is $n_{\rm H}$= 10 H cm-3
and the pre-shock magnetic field intensity is $B=1\,\mu$G. Left: Line fluxes
normalized to $\mu m_{H}nV_{s}^{3}$ as a function of the shock velocity
$V_{s}$, $\mu=1.3$ is the mean molecular weight for neutral gas, and $m_{\rm
H}$ the atomic mass unit. For weakly-magnetized shocks like those presented
here, $\rho V_{s}^{3}$ is close to the total radiative flux of the shock.
Right: Line emissivity ratios to H$\beta$ flux versus shock velocities, with
the same chemical abundances (Solar) and shock parameters as Allen et al.
(2008). The grey bands show Ly$\alpha$/H$\beta$ ratios for the three positions
(1, 2 and 5) associated to broad optical line emission and shock excitation,
and the value averaged over all positions (see Table 4). The orange and green
bands show respectively the range of observed H$\alpha$/H$\beta$ ratios and
the stacked Civ/H$\beta$ value with a $\pm 20$ % uncertainty. The blue band
show the $3\sigma$ upper limit on the Ovi/H$\beta$ ratio.

##  5 Origin and properties of the Ly$\alpha$ emission in the intergalactic
medium of SQ

###  5.1 Shocks and turbulent mixing layers

Strong Ly$\alpha$ line emission, with typical FWHM of 200-1500 km s-1, is
often observed in high redshift galaxies (e.g. Tapken et al., 2007), where
Ly$\alpha$ photons produced by powerful starbursts scatter off neutral gas
carried in outflows. Similar broad Ly$\alpha$ profiles are sometimes seen in
the inner regions of Ly$\alpha$ nebulae associated with luminous high-z
quasars (e.g. Ginolfi et al., 2018). However, these extreme conditions are the
antithesis of those seen in the SQ filament, where the star formation activity
is very weak and, globally, the Ly$\alpha$ emission is mainly powered by
dissipation of mechanical energy. In this section, we argue that both
radiative shocks and turbulent mixing layers may contribute to powering the
observed Ly$\alpha$ line emission.

Shocks having velocities high enough to reach temperatures capable of
collisionally exciting electronic states of atomic Hydrogen (above $10^{4}$ K)
are a strong source of Ly$\alpha$ photons (e.g. Shull & McKee, 1979; Dopita &
Sutherland, 1996; Lehmann et al., 2020). Due to collisional ionization of
hydrogen, Ly$\alpha$ and H$\beta$ photons are mostly produced in gas at
temperatures smaller than T$=10^{5}\,$K, with collisional excitation
dominating recombination for T$>10^{4}\,$K (Raga et al., 2015). In the intra-
group medium of SQ, it is likely that a wide distribution of shock velocities
is present (Guillard et al., 2009). In this paper we do not attempt at a
detailed modelling of the line emission from shocks. We rather aim at
qualitatively determining which shocks contribute the most to the Ly$\alpha$
and Civ line emission.

To do so, we use the results from the MAPPINGS V shock code library. The
physics of the models is fully described in Sutherland & Dopita (2017) and the
data in Alarie & Morisset (2019). These shock models are based on Allen et al.
(2008), but the new models extend the predictions for shocks and radiative
precursors to shock velocities smaller than 100 km s-1, as well as up to 1500
km s-1. These models include expanded atomic cooling lines and comprise a wide
range of shock precursor conditions, from completely neutral gas through
partially ionized and fully ionized. Magnetic fields are also included as they
can strongly impact the compression and temperature of the post shocked gas.
Figure 6 shows results from the MAPPINGS V shock models for a neutral atomic
pre-shock gas with density $n_{\rm H}$= 10 H cm-3 and a pre-shock magnetic
field intensity of $B=1\,\mu$G. The pre-shock gas ionisation fraction is
computed from the UV emission generated by the shock. We only show models for
shock velocities above $V_{s}>50$ km s-1 because modelling of H2 line emission
shows that, in SQ, lower velocity shocks are molecular shocks (Guillard et
al., 2009).

The left panel of Figure 6 shows some optical and UV lines fluxes
normalized777See the energy conservation equation Eq. 4 in (Allen et al.,
2008). For negligible magnetic energy, the total radiative flux of the shock
is $F_{tot}=0.5\rho V_{s}^{3}$.  to $\rho V_{s}^{3}$, i.e. the sum of the
kinetic and enthalpy fluxes, where $\rho=1.4$ $n_{\rm H}$$m_{\rm H}$ is the
gas mass density, as a function of the shock velocity $V_{s}$. The solid lines
show the fractional line luminosities from the shock only, while dashed lines
include the contribution of the precursor for shock velocities $V_{s}>100$ km
s-1. Due to collisional ionization of Hydrogen atoms, the fraction of the
shock emission accounted for by Ly$\alpha$ photons is the highest for shock
velocities smaller than 100 km s-1 for which Hydrogen excitation is mainly
collisional. Faster shocks do contribute to Ly$\alpha$ emission but to a
lesser fraction of the total radiated power. For shock velocities typically
above 150 km s-1, the Ly$\alpha$ shock emission comes mainly from the photo-
ionisation of the post-shock gas that has cooled down to $\sim 10^{4}\,$K. The
UV emission produced in fast shocks is also in part processed into Ly$\alpha$
photons by hydrogen photo-ionization in the radiative precursor (Sutherland &
Dopita, 2017). The Civ and Ovi line fractions peak at shock velocities higher
than for Ly$\alpha$, 120 and 200 km s-1 respectively. The contribution of
photo-ionization to the Ly$\alpha$ emission could thus be significant in the
intra-group medium of SQ. This contribution would still be associated with the
dissipation of mechanical energy since in SQ the UV flux is mostly produced by
shocks.

In the right panel of Fig. 6 we show model predictions for strength of various
emission line fluxes normalized to the H$\beta$ line, and we compare them to
the observed values, averaged for the 5 positions. The H$\alpha$/H$\beta$
ratio in the models is always above the case B value (2.86), and slightly
below the stacked value (H$\alpha$/H$\beta$= 4.3), although observations
towards the 5 positions span a large range, i.e. H$\alpha$/H$\beta$= 2.2 –
6.9. The rise of the Ly$\alpha$/H$\beta$ at low velocities ($V_{s}<150$km s-1)
is due to collisional excitation in the post shock gas, since the precursor
gas entering the shock is neutral (Sutherland & Dopita, 2017). We also note
that both the low Civ/H$\beta$ observed ratio and the Ovi/H$\beta$ upper
limit888computed with a $3\sigma$ upper limit on the Ovi line flux measured on
the G130M stacked spectrum. point to shocks below 150 km s-1.

Another contribution to the generation of Ly$\alpha$ emission could be
irradiated molecular shocks at lower velocities than those presented in Fig.
6. Shocks at velocities 30–50 km s-1driven into molecular gas at typical
densities $n_{\rm H}$$=10^{4}$ cm-3 produce a strong Ly$\alpha$ radiation
(Lehmann et al., 2020). However, the Ly$\alpha$/ $L_{T}$ ratio in such
molecular shocks is lower (10–20%) than for the shocks in atomic gas at
similar velocities presented in Fig. 6. In addition to shocks, turbulent
mixing of gas phases is likely to contribute to the emission of UV line
emission (e.g., Slavin et al., 1993; Kwak & Shelton, 2010) and to the overall
energy dissipation in the multiphase medium of SQ. Turbulent mixing layers may
also explain the high Civ/ Ovi line flux ratio ($>0.7$), akin to what is
observed in the circum-galactic medium (e.g. Shull & Slavin, 1994; Fox et al.,
2011).

###  5.2 Scattering of Ly$\alpha$ photons in a highly clumpy medium with large
bulk motions as a source of line broadening

Neufeld (1991) and Charlot & Fall (1993) first emphasized the impact of
clumping and the multi-phase nature of astrophysical media on the Ly$\alpha$
line strength and spectral shape. This paper does not attempt at a
quantitative modelling of the Ly$\alpha$ emission in the multiphase intra-
group medium of SQ. We only present some qualitative suggestions within the
framework of Ly$\alpha$ radiative transfer in a clumpy medium (Zheng &
Miralda‐Escude, 2002; Verhamme et al., 2015; Gronke et al., 2016, 2017).

mean ratio between Ly$\alpha$ and H$\beta$ fluxes measured on stacked spectra
$\approx 10$ (Table 2) may be compared with the intrinsic value $\approx 30$
for hydrogen recombination at temperatures of a few $10^{4}\,$K and $\approx
80$ for collisional excitation in the lowest velocity shocks
($V_{s}<100\mbox{{\rm km}\,{\rm s}${}^{-1}$}\ $) in the right plot of Fig. 6.
From this comparison, we estimate the escape fraction of Ly$\alpha$ photons to
$\sim 10-30\%$. This is an effective value that varies significantly among
regions and within regions with gas velocity.

In an interacting system like SQ, coherent gas flows within the SQ intra-group
medium are likely to contribute to the broadening of the Ly$\alpha$ line
profile. In particular, it is likely that the prominent blue-shifted
scattering wings observed at Positions 2, 3 and 5 are the result of systematic
velocity gradients related to the 3D geometry of the collision between the
intruder and the intra-group medium. More generally, the width of the
Ly$\alpha$ line does not provide a direct constraint on the number of
scatterings and the gas clumping. Further, existing models of Ly$\alpha$
radiative transfer based on micro-turbulence (pure random motions) make
simplifying assumptions that probably do not apply to SQ. With this caveat in
mind, we provide here some indicative numbers based on these models.

In a static medium, the number of scatterings $N_{sc}$ can be estimated from
the observed frequency shift $\Delta\nu=\nu-\nu_{0}$, where $\nu$ and
$\nu_{0}$ are the observed and rest frequencies of the Ly$\alpha$ line, as the
following: $N_{sc}^{1/2}=\Delta\nu/\Delta\nu_{D}\approx(a\tau_{0})^{1/3}$,
where $\Delta\nu_{D}$ is the thermal Doppler broadening, $a$ the damping
parameter, and $\tau_{0}$ the line-center optical depth (see Neufeld, 1990).
Assuming $T=10^{4}$ K and a typical velocity shift of 100 km s-1, we find
$N_{sc}\approx 60$. In a multiphase medium, the Ly$\alpha$ escape fraction
$f_{esc}$ depends on the dust optical depth of the clumps, $\tau_{d}$, and the
covering factor $f_{c}$, i.e. the average number of clumps along the sightline
(Neufeld, 1991). Both the modelling of the dust emission in SQ (Natale et al.,
2010; Guillard et al., 2010) and studies of the molecular gas content
(Guillard et al., 2012; Appleton et al., 2017) converge to an average column
density of $N_{H}\approx 2\times 10^{20}$ cm-2 in the ridge, which translates
into $\tau_{d}\approx 0.5$ at $\lambda=1216$ Å. Following Hansen & Peng Oh
(2006) and Gronke et al. (2017), we find a covering factor $f_{c}\approx 15$
for a fiducial escape fraction $f_{esc}=0.15$, and $N_{sc}\approx 80$. To test
these estimates, more realistic radiative transfer models including coherent
gas velocity gradients would be needed, as well as very high spatial
resolution observations to confirm their presence.

In conclusion, this high escape fraction, combined with the spectral evidence
of Ly$\alpha$ scattering, reflects the clumpy picture that has emerged from
the analysis of SQ observations, mainly the spatial correlation between the
tracers of the hot, warm and cold intra-group medium phases, and the modelling
of the SQ dust emission (Guillard et al., 2010). The neutral gas (dominated by
dusty molecular gas in the ridge) is in clumps with a high velocity dispersion
and large velocity gradients. The clumps are embedded in a hot X-ray emitting,
dust-free, plasma. Within such a clumpy medium, Ly$\alpha$ photons may escape
through multiple scatterings off the clump surfaces (Neufeld, 1991; Gronke et
al., 2017) without being absorbed in the inter-clump dust-free plasma. The
clumps must fill a small fraction of the volume but their surface filling
factor must be close to unity with multiple clumps along a given line of
sight. Further work is needed to model these observations and to assess
whether the differences in spectral shapes observed for the five pointings
could be accounted for by variations in the total column of dusty neutral
(molecular) Hydrogen, the number of clumps along the line of sight and their
kinematics. Note that not only scattering effects but also collisional
excitation could also contribute to explain the differences between the
Ly$\alpha$ and H$\beta$ spectra.

###  5.3 A constant dissipation rate across many orders of magnitude in gas
temperatures: a signpost of a turbulent cascade?

The observations presented in this paper brings another piece to the cooling
budget puzzle of the SQ shocked intra-group medium. Putting together multi-
wavelength line spectroscopy allows us to combine radiative tracers which
spans a wide range of gas temperatures, from $\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}100$ K for rotational
H2 and [C ii] lines, to $5\times 10^{6}$ K for X-rays. Remarkably, over more
than four orders of magnitude in temperature, the powers radiated by the
multi-phase intra-group medium in X-rays, Ly$\alpha$, H2, [C ii] are
comparable within a factor of a few (see also Table 1 in Guillard et al.,
2009, for a summary of the energy budget across gas phases). This indicates
that the dissipation of the kinetic energy in the SQ galaxy-wide collision
involves all gas phases. Dissipation could proceed through shocks with a wide
distribution of velocities and involve turbulent mixing layers. Shocks and
mixing layers can be the combined result of the turbulent energy cascade
within the multiphase intra-group medium. While a specific probability
distribution function of shock velocities is required to make the cooling rate
independent of the gas temperature, models suggest that this may be a generic
property of energy dissipation in turbulent mixing layers (Ji et al., 2019).

##  6 Similarities with the Circum-Galactic Media of distant galaxies

The nature of the emission from the intra-group medium of Stephan’s Quintet
may have implications for our understanding of the observations and nature of
the Circum-Galactic Medium (CGM) surrounding galaxies in the distant universe.
Superficially, there are many similarities between the CGM of galaxies and the
intra-group medium in SQ. The CGM of distant galaxies have evidence for: (1)
bright Ly$\alpha$ emission with broad lines ($\sigma\approx 100-500$ km s-1)
and line profiles which range from simple Gaussians, double-horned, to those
with strong asymmetries (e.g., Leclercq et al., 2017; Vernet et al., 2017;
Leibler et al., 2018; O’Sullivan et al., 2020); (2) emission at a wide range
of frequencies implying that the gas in the CGM is multiphase and contains
cold gas (e.g. Emonts et al., 2016, 2018, 2019; Falkendal et al., 2021); and
(3) line ratios of the UV and optical emission lines that are about the values
expected for recombining, clumpy gas (Leibler et al., 2018; Cantalupo et al.,
2019; Marino et al., 2019). The intra-group medium of SQ is also somewhat
reminiscent of the very broad, shock-powered Ly$\alpha$ and CH+ emission
detected outside galaxies in the distant galaxy group SMMJ02399 at $z=2.8$
(Vidal-García et al., 2021). In all of these ways, there are similarities with
the selected regions of the intra-group medium of SQ we have studied.

Of particular interest is the comparison of the H$\alpha$ and Ly$\alpha$ line
ratios and surface brightnesses between the intra-group medium of SQ and the
ICM of the Slug Nebula and MRC 1138-262 (Leibler et al., 2018; Shimakawa et
al., 2018). In the Slug Nebula and the medium surrounding the radio galaxy,
MRC 1138-262, the Ly$\alpha$ to H$\alpha$ line ratios are about 6 and a few
respectively. These ratios are quite similar to the range of values spanned in
the spectra of the regions of the SQ, less than 1 to almost 10. It is also
worth noting that in the case of the Slug Nebula, the H$\alpha$ line is
consistent with being much narrower than the Ly$\alpha$ emission over the same
region (Leibler et al., 2018) and similar to our findings. These results
suggest that a fraction of the Ly$\alpha$ escapes the nebulae and that
scattering plays an important role in shaping the line profiles. The surface
brightness of the hydrogen lines is also quite different in these objects. In
both the Slug and MRC 1138-262, the surface brightness of H$\alpha$ is
approximately 1-2 orders of magnitude higher than in the emission line regions
we have observed in SQ. The Slug Nebula has a lower surface brightness than
MRC 1138-262 but was also estimated at a much larger distant from the QSO than
that used for MRC 1138-262 (estimated at the faintest surface brightness
levels in the narrow band imaging data; Shimakawa et al., 2018).

Since both the Slug and MRC 1138-262 have been observed in CO transitions, we
can also compare their molecular gas surface densities. Over roughly the same
regions are those used to estimate the H$\alpha$ surface brightnesses, the
Slug has upper limits to its H2 gas mass surface densities, $<$12-25 M⊙ pc-2
(Decarli et al., 2021), while MRC 1138-262 is about 35 M⊙ pc-2 (Emonts et al.,
2016). The mass surface densities of H2 for SQ range from about 10-100 M⊙
pc-2. It is interesting that the molecular gas surface densities of MRC
1138-262 are similar while the H$\alpha$ (and given the similar ratios, the
Ly$\alpha$) surface brightnesses are so different. This can simply be
explained within the context of our analysis that both objects have strong
energy injection into their circumgalactic media (a collision and a high power
radio jet) which drives a turbulent cascade, but MRC 1138-262 hosts a power,
UV luminous AGN which powers its optical emission line gas. The emission from
the Slug nebula is consistent with that expected from photoionized gas
(Decarli et al., 2021) while clearly this is not the case for either the
regions of SQ and MRC 1138-262. The injection of mechanical energy into their
circumgalactic media plays an important role in shaping what we observe,
especially in creating and sustaining dense molecular gas.

##  7 Conclusions

We have used the COS spectrograph on HST to observe Ly$\alpha$ emission from
the intergalactic gas in SQ. The observations sample five positions across the
30 kpc-wide shock. The HST data is compared with CO, [C ii] and H$\beta$
spectra. We summarize the main observational results and outline our
interpretation of the data.

We detect extremely wide Ly$\alpha$ lines with a full width at zero intensity
of $\approx 2000$ km s-1, which exceeds the velocity range of CO, [C ii] and
H$\beta$ line emission. After stacking of the five HST spectra, we also detect
the Civ doublet. We observe significant variations in the Ly$\alpha$ /
H$\beta$ spectral ratio between positions and velocity components. From the
mean line ratio averaged over positions and velocities, we estimate the mean
escape fraction of Ly$\alpha$ photons to be $\sim 10-30\%$. The Ly$\alpha$
lines are systematically broader than the H$\beta$ ones at the same positions,
which we consider as observational evidence for scattering of Ly$\alpha$
photons by the SQ intra-group medium. The difference in velocity spread is
asymmetrical and amounts to $\approx 300$ km s-1 for the blue-shifted
Ly$\alpha$ wings observed at three of the five positions.

The observations provide insight on the structure of the multiphase intra-
group medium in SQ. The high Ly$\alpha$ escape fraction and scattering reflect
the clumpy picture suggested by the spatial correlation between the tracers of
the hot, warm and cold phases of the SQ intra-group medium. The neutral,
mainly molecular, gas is in clumps embedded in the X-ray emitting, hot and
dust-free plasma. Ly$\alpha$ photons must escape through multiple scatterings
off the clumps. Scattering indicates that the intra-group medium is not porous
to Ly$\alpha$ photons, i.e. the neutral gas surface filling factor must be
close to unity with multiple clumps along a given line of sight. A
quantitative comparison with Ly$\alpha$ radiative transfer models is beyond
the scope of this observational paper, but these data suggest that coherent
gas flows within the SQ intra-group medium contribute to the broadening of the
Ly$\alpha$ line profile. In particular, it is likely that the blue-shifted
scattering wings follow from systematic velocity gradients related to the 3D
geometry of the collision between the intruder and the SQ intra-group medium.

The bulk of the Ly$\alpha$ emission must be powered by dissipation of
mechanical energy because the SQ star formation rate is small and the gas
velocities span an exceptionally large range. This conclusion is in line with
optical line ratios measured at our COS pointings. Ly$\alpha$ photons are
emitted by gas at temperatures smaller than the thermal energy threshold for
collisional ionization ($T<10^{5}\,$K). It is likely that both collisional
excitation and recombination of photo-ionized Hydrogen contribute to the
observed emission. Due to collisional ionization of hydrogen atoms, the
fraction of the shock emission accounted for by Ly$\alpha$ photons is the
highest for shock velocities smaller than 100 km s-1. Faster shocks do
contribute to Ly$\alpha$ emission but to a lesser fraction of the total
radiated power. The UV emission produced in fast shocks is in part processed
into Ly$\alpha$ photons in the post-shock and the pre-shock gas. This
contribution of photo-ionized gas to the Ly$\alpha$ emission, which is also
associated with dissipation of mechanical energy, could be significant.

The HST observations complement our view at the energetics of the galaxy-wide
shock created by the collision of high-speed intruder galaxy with the SQ
intra-group medium. The total power emitted in the Ly$\alpha$ line is
comparable to that of much cooler gas in the mid-IR rotational H2and the [C
ii] fine structure lines. The energy radiated in [C ii], H2, Ly$\alpha$ and
X-rays represents cooling from gas spanning four order of magnitudes in
temperature from 100 to $10^{6}\,$K. The observed fluxes are comparable within
a factor of a few, which indicates that roughly the same fraction of energy is
dissipated per logarithmic bin of temperature. This is a remarkable result
that constrains models of the turbulent energy cascade in SQ. It emphasises
the possible contribution from turbulent mixing layers to energy dissipation.

Following the trail of mechanical energy dissipation and gas kinematic in the
turbulent gas on scales smaller than $\approx 1$ kpc (the COS aperture scale)
will be possible with observations of warm molecular and ionized gas with the
James Web Space Telescope, and future UV-optimized telescopes. Such
observations will also to look for coherent anisotropic gas flows, which are
necessary in order to explain the blue scattering wings in the Ly$\alpha$
profiles seen in some of the observed positions.

PG thank the Centre National d’Etudes Spatiales (CNES), the University Pierre
and Marie Curie, and the ”Programme National de Cosmologie and Galaxies”
(PNCG) and the ”Physique Chimie du Milieu Interstellaire” (PCMI) programs of
CNRS/INSU for there financial supports. We thank Daniel Kunth and Brigitte
Rocca for very useful physical and technical discussions about Ly$\alpha$
scattering. Support for Program number HST-GO-13321.001-A was provided by NASA
through a grant from the Space Telescope Science Institute, which is operated
by the Association of Universities for Research in Astronomy, Incorporated,
under NASA contract NAS5-26555. PA thanks Guillermo Blanc (Carnegie
Observatories) and Emily Freeland (formerly Texas A&M University) for
providing assistance with observations, and software/data reduction associated
with the Mitchell Spectrograph. This work used observations carried out under
project number U020 (P.I. Guillard) with the IRAM NOEMA Interferometer,
reduced and analysed with the GILDAS software
(https://www.iram.fr/IRAMFR/GILDAS). IRAM is supported by INSU/CNRS (France),
MPG (Germany) and IGN (Spain). We also thank the referee who has contributed
to improve both the figures and content of the paper.

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