A Semi-Analytical Line Transfer (SALT) model to interpret the spectra of galaxy outflows

2 MB·English

by  C. Scarlata

Draftversion January30,2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
A SEMI–ANALYTICAL LINE TRANSFER (SALT) MODEL TO INTERPRET THE SPECTRA OF GALAXY
OUTFLOWS
C. Scarlata1 and N. Panagia2,3,4
Draft version January 30, 2015
ABSTRACT
5 WepresentaSemi–AnalyticalLineTransfermodel,SALT,tostudythe absorptionandre–emission
1 line profiles from expanding galactic envelopes. The envelopes are described as a superposition of
0 shells with density and velocity varying with the distance from the center. We adopt the Sobolev
2 approximation to describe the interaction between the photons escaping from each shell and the
n remaining of the envelope. We include the effect of multiple scatterings within each shell, properly
a accounting for the atomic structure of the scattering ions. We also account for the effect of a finite
J circular aperture on actual observations. For equal geometries and density distributions, our models
8 reproducethe mainfeaturesofthe profilesgeneratedwithmorecomplicatedtransfercodes. Also,our
2 SALT line profiles nicely reproduce the typical asymmetric resonantabsorptionline profiles observed
in starforming/starburst galaxies whereas these absorption profiles cannot be reproduced with thin

] shellsmovingatafixedoutflowvelocity. Weshowthatscatteredresonantemissionfillsintheresonant
A
absorption profiles, with a strength that is different for each transition. Observationally, the effect
G of resonant filling depends on both the outflow geometry and the size of the outflow relative to the
spectroscopic aperture. Neglecting these effects will lead to incorrect values of gas covering fraction
.
h and column density. When a fluorescent channel is available, the resonant profiles alone cannot be
p used to infer the presence of scattered re–emission. Conversely, the presence of emission lines of
- fluorescent transitions reveals that emission filling cannot be neglected.
o
r Subject headings: galaxies: ISM — ISM: structure
t
s
a
[ 1. INTRODUCTION constraints on the physical properties of galaxy out-

The mechanical and radiative energy (from massive flowsandhowthesedependonthegalaxystar–formation
1
rates, stellar masses, and so on. In order to characterize
v star winds and supernova explosions) injected in the in-
howeffectivefeedbackisinquenchingthestar–formation
2 terstellar medium (ISM) of galaxies is expected to drive
(by, e.g., heating the gas and/or completely remove it
8 gas outflows around regions of active star–formation.
from a galaxy dark matter halo) we need to be able to
2 These outflows are indeed observed both on the scale
7 of individual H II regions as well as on full-galaxy probethekinematicsoftheoutflows,theirdensitystruc-
ture, and their extent. Absorption line studies against
0 scales. Outflows are currently invoked as the princi-
the strong UV continuum produced in the star-forming
. pal mechanism regulating the galactic baryonic cycle
1 regionscanprobetheneutralandionizedcomponentsof
(i.e., the balance between the gas accretion rate and
0 the outflows, with numerous resonant transitions in low
thestar-formationrate)instate-of-the-artgalaxyforma-
5 and high ionization metals (such as, Si II, C II, Mg II,
1 tion models (e.g. Oppenheimer et al. 2010; Dav´e et al. C III, Fe II, andC IV; e.g., Rupke et al. 2005; Martin
: 2011; Lilly et al. 2013). Whether or not the observed
v outflows are actually able to do the job is, however, 2005; Sato et al. 2009; Weiner et al. 2009; Rubin et al.
i 2010; Steidel et al. 1996; Shapley et al. 2003).
X still unclear. In fact, although outflow-regulated models
Recent studies show that outflowing gas moving with
are able to broadly reproduce some of the fundamental
r velocities up to several hundreds of km s−1 is common
a correlations observed in massive galaxies, recent studies
instar–forminggalaxies(e.g.,Pettini et al.2002;Martin
have pointed out the existence of a fundamental prob-
lem with the evolution of low mass (M∗ < 109.5M⊙) 2005). Generally,thesestudiesusestandardabsorption–
lineanalysis(e.gSavage & Sembach1991),wheretheve-
galaxies(Weinmann et al.2012). This difficulty appears
locity of the outflowing material is determined by the
to indicate that crucial feedback processes are modeled
amount of blueshift observed in the resonant absorption
incorrectly, since it is precisely in this low-mass regime
lines (typically UV lines, but absorption of Na–D lines
that feedback-induced outflows are expected to have the
has been used). Recent observations, however, have re-
strongest impact.
vealedthepresenceofnumerousresonantandfluorescent
What is lacking at this point are robust observational
emission lines associated with the blueshifted resonant
1MinnesotaInstituteforAstrophysics,School ofPhysicsand absorptions (e.g., Weiner et al. 2009; France et al. 2010;
Astronomy, University of Minnesota, 316 Church str SE, Min- Rubin et al. 2011; Jones et al. 2012; Erb et al. 2012;
neapolis,MN55455,USA Martin et al. 2012, 2013; Kornei et al. 2013). Although
2Space Telescope Science Institute, 3700 San Martin Drive,
originally interpreted as the result of photoionizationby
Baltimore,MD21218, USA,[email protected]
3INAF–NA, Osservatorio Astronomico di Capodimonte, weakAGNs(e.g.,Weiner et al.2009),theselinesarenow
SalitaMoiariello16,80131Naples,Italy believed to be the result of scattered resonant photons
4 SupernovaLtd,OYV#131,NorthsoundRd.,VirginGorda in an expanding envelope around galaxies (Rubin et al.
VG1150, VirginIslands,UK
2 Scarlata & Panagia
Fig.1.—Sideviewoftheoutflow model. Weconsider asphericalgalaxy(withradiusRSF)surroundedbyanexpandingenvelope with
avelocityincreasingradiallywiththedistancefromthecenter. Forr>RW thegasvelocityisv∞. Theshadedyellowareashowsthesize
oftheapertureofradiusRaper. Thedottedverticallineindicatestheedge-onviewoftheplanewithconstant observedvelocity(vobs).
2011; Erb et al. 2012; Martin et al. 2013). z ∼0.3Lyαemitters. We showhowourmodelisableto
The scattered re–emission into the line of sight affects consistentlyreproducetheprofilesofboththeabsorption
thevelocitymeasurementsbasedonpureabsorptionlines andresonantandfluorescentemissionlinesandthuscon-
analysis, as well as mimic a partial covering fraction of straintheoutflowvelocity–anddensity–fields. Although
the outflowinggas(e.g.,Prochaska et al.2011). Inthese rather simplified, the SALT model can be used to gain
cases, it is crucial to be able to consistently model both a more physical understanding of the outflowing gas, in
the resonant absorption as well as the associated res- both local and high redshift galaxies. We focus here on
onant and (if present) fluorescent emission originating a few specific lines of Si+ ion, however, the models are
from the same ionic species. Steps in this direction have readily applicable to any other ions.
been taken by Rubin et al. (2011), who pioneered the The paper is organized as follows. In Section 2 we
study of outflows in emission using resonantly-scattered present the derivation of the semi analytical line profile
MgII, and Fe lines. Prochaska et al. (2011) used Monte foranoutflowingsphericalshell. Themodeliscompared
Carloradiativetransfertechniquestostudythenatureof withtheobservedstackedspectruminSection3,andthe
resonant absorption and emission for winds, accounting results are discussed in Section 4. We offer our conclu-
for the effects of resonant scattering and fluorescence. sions in Section 5.
InthispaperwegoastepforwardanddevelopaSemi–
AnalyticalLine Transfer(hereafter referredto asSALT) 2. P-CYGNIPROFILEFROMASPHERICALEXPANDING
modeltointerprettheabsorption/scatteredemissionline ENVELOPE
profiles resulting from extended galactic outflows. We In sphericaloutflows, suchas those producedin winds
assume that the Sobolev approximation holds, and we from early type stars, resonant lines are characterized
account for multiple scattering within the outflow with by the well understood P–Cygni profile (e.g., Castor
a simple statistical approach. As an example of an ap- 1970; Castor & Lamers 1979). The profile shows both
plication of the model, we apply SALT to multiple tran- an emission and an absorption component. The absorp-
sitions in the Si+ ion observed in the stack spectrum of tion is created in the material between the source and
3
the observer, while the emission is produced by scatter- introduce the normalized radial coordinate ̺ = r/R
SF
ingphotonsintothe lineofsight. Forsphericaloutflows, (̺= ξ2+s2/R ). AgivenpointPinthe envelopeis
SF
the velocity profile of the absorption component will be identipfied by the pair of coordinates ̺, θ, where θ is the
blueshiftedrelativetothesystemicvelocityofthesource angle between the direction of r and the line of sight to
and will depend on the density and velocity fields of the the observer.
absorbing material. Because of the spherically symmet-
ric geometry, the emission component will be centered
at the systemic velocity of the source and thus will con-
tribute to fill in the absorption at negative velocities.
This effect, well known in the context of stellar winds,
has generally been neglected in the context of absorp-
tion line studies of galaxies. Recently, however, a few
studies have emphasized the importance of properly ac-
counting for scattered re-emission in studies of galaxy
absorption line spectra. These studies have also high-
lighted how the emission line features can be used as
powerful diagnostics of the geometry and physical con-
ditions of galaxy outflows both in the local and high–
redshift Universe (Rubin et al. 2011; Prochaska et al.
2011; Erb et al. 2012; Martin et al. 2013).The goal of
this paper is to present a semi-analytical line transfer
(SALT) modelthatcanbe usedtoconsistently interpret
the absorption and emission line profiles of both reso-
nant and fluorescent transmissions observed in galactic
spectra. The line profiles are modeled for outflow ge-
ometriessimilar to those introducedby the recentworks
Fig.2.— Iso-velocity contours of observed velocity for a shell
ofRubin et al.(2011);Prochaska et al.(2011);Erb et al. moving at radial velocity v. The observed velocity ranges from
(2012); Martin et al. (2013). vobs=v atthecenteroftheshell,tovobs=0attheedge.
In this Section we first describe the basic assumptions
to derive the line profiles in single scattering approxi- We consider a velocity field where the velocity (v) in-
mation Scuderi et al. (following 1992). We then modify creases with r as a power law of exponent γ:
the wind model to include a more realistic description
of the scattering process by relaxing the single scatter-
ing approximation. We also include the possibility of v =v r γ for r ≤R =R v∞ 1/γ; (1)
0 W SF
re-emissionin the fluorescentchannel, different envelope (cid:16)RSF(cid:17) (cid:16) v0 (cid:17)
geometries and effect of a finite aperture.
2.1. The basic model v =v∞ for r ≥RW; (2)
To build our SALT model we start with the simplest where v is the wind velocity at the surface of the star-
0
description for the gas/star configuration. We approxi- forming region (i.e., at RSF), and v∞ is the terminal
mateagalaxyasasphericalsourceofUVradiationwith velocity of the wind at R .
W
radius R (i.e., where the bulk of star-formation oc- When the velocity gradient in the expanding envelope
SF
curs), surrounded by an expanding envelope of gas, ex- is large, photons will interact with the outflowing mate-
tending to R . In the following we will refer to the ex- rial only where the absorbing ions are exactly “at reso-
W
pandingenvelopeasthe“galacticwind”. Prochaskaetal. nance”duetotheirDopplershift(thisisaconditionalso
(2011)usea Monte Carloradiativetransfertechnique to knownas “Sobolev’approximation”,e.g., Grinin 2001).
derive the absorption line profiles resulting from similar In this case, the radiative transport of the line photons
galactic winds. In what follows, we simplify their calcu-
lations by computing semi-analytical expressions for the
line profiles (including the effects of fluorescent emission
and spectroscopic aperture size). Martin et al. (2013)
use a similar outflow model to study the extended scat-
tered emission from galactic outflows at z ∼ 1, consid-
ering the effects of a clumpy expanding medium on the
derived mass outflow rate. Here, we build upon these
works, and we develop a semi-analytical algorithm to
simply but accurately calculate the expected line pro-
files originating in extended outflows. Our results can
be used to easily model galactic extended outflows com-
monly observed in local and high redshift galaxies.
InFigure 1 we show the geometryofthe wind andthe
definition of the coordinate system. The coordinates ξ
and s are given in units of R , so that in Figure 1 the
SF
dashed line tangential to the galaxy has ξ = 1. We also Fig.3.—EnergylevelsofSi+.
4 Scarlata & Panagia
canbe reducedtoalocalproblem,andtheopticaldepth Globally the shell will absorb a fraction E(v) = [1−
for absorption (τ) can be evaluated at the interaction exp(−τ(v))] of the energy that, in terms of observedve-
surface, which is defined in terms of the velocity as: locities(v =v cosθ), willbe redistributedevenlyover
obs
the velocity interval (v , v). Here v is the projec-
min min
v =−c∆ν; (3) tionoftheshellvelocityalongthelineofsighttangential
ν to the galaxy (i.e., at ξ = 1). Following Scuderi et al.
0
(1992), we can compute v as:
where ν is the resonance frequency of the line. The min
0
numericalresultsofProchaskaetal(2011)showthatfor
s(̺(v))
the physical conditions of typical galaxy outflows, the v =v cosθ =v . (8)
min
̺(v)
Sobolev approximation is a justified assumption.
The wind optical depth at the interaction surface, can
Or, setting y =v/v , as:
0
be written as a function of wavelength, wind parame-
ters,andatomicconstants,asfollows(e.g.,Castor1970): y =y(γ−1)/γ(y2/γ −1)1/2. (9)
min
Only shells with intrinsic radial velocities in the range
πe2 n g r/v from vobs and v1 =vobs/cosθ (for ξ =1) can contribute
τ(r)= f λ n (r) 1− u l ; (4) to the absorption at v . Setting x = v /v , y =
mc lu lu l h nlgui1+σµ2 v1/v0 can be computedobbsy solving the equaotbiosn:0 1
where f and λ are the oscillator strength and wave-
length, urlespectivleuly, for the ul transition, µ = cos(θ), y2(1−y−2/γ)=x2. (10)
1 1
and σ = dln(v) −1 (see Table 1 for Si+ atomic data). Thus, we can write the absorption component of the
dln(r)
The expression for the optical depth can be simplified profile, in units of the stellar continuum as:
by assuming that 1) it does not depend on the angle
θ between a radius and the line of sight, 2) the above y1 1−e−τ(y)
I (x)= dy. (11)
velocity law holds, 3) stimulated emission is negligible abs,blue Z y−y
max(x,1) min
(i.e., 1− nugl = 1), and 4) the mass outflow rate is
h nlgui Surfacesofconstantobservedvelocitycanbedescribed
constant, so that n (r) ∝ (vr2)−1. For γ = 1, and with by the equation:
l
these assumptions, we can write:
γ
r
v =v cosθ. (12)
obs 0
πe2 R 3 r (cid:18)RSF(cid:19)
SF
τ(r)= f λ n (5)
lu lu 0
mc (cid:18) r (cid:19) v For the particular case of γ = 1, this equation describes
RSF 3 parallel planes at distance r = RSFvvo0bs cosθ from the
=τ (6) center of the emitting region (see Figure 1).
0
(cid:18) r (cid:19)
and 2.1.1. Single scattering approximation
Resonantphotons absorbedin the envelopecanbe de-
πe2 R
SF tected when re–emitted toward the observer. Assuming
τ = f λ n ; (7)
0 lu lu 0
mc v that a re-emitted photon escapes a given shell without
0
further interactions, we can compute the emission com-
where n is the gas density at R (for γ = 1, n (r) =
0 SF l ponentofthelineprofileasfollows. Ifthephotonsarere–
−3
n r ). emitted isotropically, then they will uniformly cover the
0(cid:16)RSF(cid:17) rangeofprojectedvelocitiesbetween±v. Todescribethe
Now consider a thin shell located at a distance r =
R (v )1/γ, moving with an intrinsic radial velocity v. profile of this emission component, we divide the range
SF v0 of observed velocities into blueward and redward of the
The velocity measured by the observer, i.e. the compo-
systemic velocity. The blue side of the emission profile
nent of the radial velocity along the line of sight to the
originates in the half of the envelope approaching the
observer (v = v cosθ) will depend on the position on
obs observer (i.e., s ≥ 0). For a given observed velocity, the
the shell and in particular on the projected distance to
emission will come from all shells with v >v , and we
thecenter. ThisisshowninFigure2,whereweplotcon- obs
can write:
tours of constant observed (i.e., projected) velocity from
a shell moving outward with radial velocity v. For the y∞ 1−e−τ(y)
sakeof clarity,we showonly the half ofthe shell moving I (x)= dy. (13)
em,blue
towardthe observer. The observedvelocities range from Zmax(x,1) 2y
−v at the projected center of the envelope (where the
The red side of the profile is produced in the unoc-
gas is moving directly toward us) to 0 at the projected
culted, receding portion of the envelope. Because of the
distance r = r (where the shell is moving on the plane
v occultation, however, only shells with velocities larger
of the sky). Obviously, only the portion of the shell in
than v (see Eq.9) will contribute to a given observed
front of the continuum disk (hatched area in Figures 2) min
receding velocity:
willproduceanetabsorptioninthe spectrum(blueward
of the line center) by scattering photons out of the line y∞ 1−e−τ(y)
of sight. I (x)= dy. (14)
em,red
Z 2y
y1
5
Finally,the resultingP-Cygprofileforthe idealspher- outflow, where the density is highest. We account for
ical outflows can be computed as: multiple scatterings within a single shell, as follows.
We define the photon’s escape probability from a shell
I(x)=1−I +I +I . (15) of optical depth τ(v) as (e.g., Mathis 1972):
abs,blue em,blue em,red
β =(1−e−τ)/τ, (17)
2.1.2. Fluorescent emission in single scattering
approximation Thus, for a shell with velocity v, a photon has a prob-
ability β of escaping the shell, and therefore –because
Depending on the energy levels of the particular ionic
of the underlying Sobolev approximation– escaping the
species, the absorption of a resonant photon can result
outflow. Of all photons absorbed at resonance by the
in the production of a fluorescent photon. This occurs
moving shell, a fraction p will be re-emitted in the flu-
when the electron decays into an excited ground level5. F
orescent channel and escape. Of the fraction p of the
As an example, figure 3 shows the energy level diagram photons re-emitted at resonance, a faction 1−βRwill be
of the λ 1190.42 and 1193.28˚A Si+ doublet. Resonant absorbed again before they are able to escape the shell.
and fluorescent transitions are marked with dashed and Of these [p (1 − β)], a fraction p will be converted
R F
dottedlines,respectively. We accountforthefluorescent into fluorescent photons and escape [i.e., p p (1−β)].
F R
channel in the modeling of the line profile as follows. Again, out of the resonantly re–emitted photons, a frac-
For a bound electron, the probability of decaying into tion1−βwillbere–absorbedwithintheshell,contribute
the lower level l is proportional to p = A / A ,
ul ul i ui to the fluorescentre–emissionandescape the outflow. It
whereAui is the spontaneousdecayprobabilityfrPomthe can be easily shown that, for each shell, the fraction of
upperlevelutothelowerleveli. RelevantAui valuesare absorbed photons converted into fluorescent photons is
givenin Table 1. In the single scatteringapproximation,
given by:
the resulting line profile accounting for the emission in
the fluorescent channel becomes: ∞
F (τ)=p [p (1−β)]n, (18)
F F R
nX=0
I(x)=1−I +p (I +I )+p (I +I ),
abs,blue R em,blue em,red F em,blue em,red
(16) while the fraction of absorbed photons that are able to
where p and p are the probabilities that a photon is escape will be:
R F
re–emitted in the resonant and the fluorescent channels,
∞
respectively. When only one fluorescentchannel is avail-
F (τ)=p β [p (1−β)]n. (19)
able, as in the cases considered here, p +p = 1. The R R R
R F
left panel in Figure 4 shows how the line profiles of the nX=0
Si IIdoubletgeneratedinanoutflowingenvelopechange Because p (1−β)<1, the summation of the geometric
R
when the fluorescent channels are taken into account. series in Equations 18 and 19 converges,and
When a fraction of the photons are re–emitted in the
fluorescent transition, the filling effect of the resonant
absorption due to photons scattered in the wind is sub- FF =pF/[1−pR(1−β)] (20a)
stantially reduced for the 1190˚A transition. It is only F =βp /[1−p (1−β)]. (20b)
R R R
minimally reduced for the transition at 1193˚A due to
Figure 5 shows the fraction of absorbed photons that
contamination from the fluorescent re-emitted photons
at 1194.5˚A (see Table 1). Because of the re–emission in escapeinthefluorescentchannelasafunctionoftheshell
opticaldepthforthreerepresentativevaluesofp . Anal-
thefluorescentchannel,the totalequivalentwidthofthe F
ogously to Eqns 13 and 14, the blue and red resonant-
resonantP-Cygniprofile(i.e.,includingboththeabsorp-
emission components become:
tion and emission components) is negative (net absorp-
tion).
y∞ 1−e−τ(y)
2.1.3. Accounting for multiple scatterings Iem,blue,MS(x)= FR(y) dy (21a)
Z 2y
max(x,1)
More realistically, a photon re-emitted with the reso-
y∞ 1−e−τ(y)
nant energy will likely interact with the ions in the shell I (x)= F (y) dy, (21b)
em,red,MS R
where it was created, resulting in multiple scattering Zy1 2y
events of a single photon within a given shell. Multi-
while the blue and red fluorescent components can be
ple scatterings will not change the shape of the absorp-
written as:
tion profile (I ), but will reduce the contribution
abs,blue
of the re–emission in the resonant line, while enhanc-
ingthere–emissioninthe fluorescentchannel(whenthis y∞ 1−e−τ(y)
is available). The number of scatterings will clearly be Iem,blue,MS,F(x)= FF(y) dy (22a)
Z 2y
a function of the ion density at any given point in the max(x,1)
outflow. Thus, for our assumed density profile, this pro- y∞ 1−e−τ(y)
I (x)= F (y) dy. (22b)
cesswillbemoreimportantintheinternalregionsofthe em,red,MS,F F
Z 2y
y1
5 In what follows, fluorescent transitions willbe indicated with Inthe rightpanel ofFigure 4 we show the effect of ac-
an∗. countingformultiplescatteringsonthelineprofilesofthe
6 Scarlata & Panagia
Fig. 4.— Left: Effect of fluorescent channel onthe resonant P-Cygniprofile. TheSi+ doublet lineprofiles areshownwithandwithout
theinclusionof thefluorescent emission(dashed andsolidlinerespectively) forthe single-scatteringapproximation. Thepureabsorption
componentoftheprofileisalsoshownforreference(dottedline). Right: Si+doubletprofilescomputedwithsinglescatteringapproximation
(black)andmultiplescatterings(red).
Fig. 5.—Thefractionofabsorbedresonantphotonsre-emittedin Fig.6.— The P-Cygni line profile changes as function of size
the fluorescent channel after multiple scatterings depends on the ofspectroscopicaperture,fromapureabsorptionprofile(Raper =
gas column density as well as on the transition probability. We RSF),toaclassicP-Cygprofile(Raper=RW). Theprofileswhere
show the calculations for three transitions of Si+, as indicated in computedassumingasphericalexpandingenvelope,γ=1,τ =60,
thelabel. v0 = 25 km s−1 and v∞ = 450 km s−1 (we consider here a line
withnofluorescent transition,suchas,e.g.,SiIIIλ=1260).
SiIIdoublet. Asexpected,there-scatteredemissioncom-
ponentatresonanceisreducedsignificantlycomparedto
the single-scattering approximation resulting in an in-
creased intensity of the fluorescent lines. We note that profile will remain unchangeddue to the presence of the
this effect enhances the contaminationof the SiII 1193˚A aperture. The blue andred scatteredemission, however,
willchange. Infact,forashellofintrinsicvelocityv, the
absorption component from re–emitted fluorescent pho-
tons from the SiII 1190˚A transmission. This enhance- aperture will block those photons scattered at velocities
smallerthanv =vcos(θ ),whereθ issuchthat
ment is particularly prevalent in low resolution spectra. aper aper aper
sin(θ ) = R /r . Clearly, see Figure 1, each shell
aper aper v
will correspond to a different θ .
2.2. Spherical envelope observed with a circular finite aper
In Figure 1 we show the edge-on view of a plane of
aperture
constant v (dotted line). As we saw earlier, only lay-
obs
If the spectroscopic observations are made using an ers with v ≥v will contribute to the emission at v .
obs obs
aperturethatdoesnotincludethefullextentofthescat- Figure 1 shows that the effect of adding a circular aper-
teringenvelope,thentheobservedlineprofilecanchange ture is to remove the contribution at v from all shells
obs
dramatically. Toillustratetheconsequences,weconsider with v >v , where:
up
herethe caseofasphericalenvelopeobservedwithacir-
cularaperture largerthanthe centralsourcebut smaller v
obs
v = . (23)
than the entire envelope, i.e., with Raper ≥ RSF and up cosθaper
R ≤R . We also restrict our analysis to γ =1.
aper W
Clearly, the blueshifted absorption component of the In terms of v , and after a little algebra, we get:
0
7
± one weighted standard deviation. In Figure 7, the
R 2 top panel shows the number of galaxies that entered the
y2 =x2+ aper . (24)
up (cid:18) R (cid:19) stackateachwavelength. Inthestackedspectrumweare
SF
able to clearlyidentify andreliablymeasure the features
Thus, Iaper (x) (see Eq. 13) can be written here as: presented in Tables 2 and 3 and marked in Figure 7.
em,blue
The list includes five absorption lines and four fluores-
yup 1−e−τ(y) centemissionlines. ThelistalsoincludestheC iiiλ1175
I (x)aper = dy; (25) absorption line, which is mainly produced in the stellar
em,blue
Zmax(x,1) 2y photospheres.
If we assume that lines are pure absorption and pure
Analogously, Iaper (x) will be:
em,red emission we could measure the bulk velocity of the gas
from the peak velocity of the lines. We derive the peak
yup 1−e−τ(y)
I (x)aper = dy; (26) positionsbyfittingGaussianlineprofilestotheobserved
em,red
Zy1 2y absorption/emission lines. When two lines of a given
multiplet/ion are blended, we fit them simultaneously
In Figure 6 we show how the P-Cygni profile changes
constraining the width of the Gaussian function to be
with the ratio R /R . In the extreme case of
aper SF the same for both lines. In Figure 8 we zoom–in on the
R /R = 1 (dotted line), i.e., when the aperture
aper SF spectral regions around different transitions in the Si+
is only as large as the source of continuum, the line is
and Si++ ions and plot the resulting best-fit Gaussian
observed only in absorption, and blueshifted relative to
models. The errors on the peak wavelength were com-
the systemic velocity of the galaxy. A component of
puted with a Monte Carlo simulation. We created 1000
scattered re–emitted photons coming from the absorb-
realizationsofthestackedspectrumbychangingtheflux
ing material is contributing to the blue side of the line,
at each wavelength within ±1σ. The new profiles were
but no re–emitted photons are detected on the red side,
fitted with a Gaussian, and the error on the peak wave-
becauseofboththe effectoftheaperture,andthe-often
length was computed as the standard deviation of the
neglected- occultation by the galaxy.
1000 best–fit peak wavelengths.
As the ratio R /R increases, fewer photons scat-
aper SF In Tables 2 and 3 we report the vacuum wavelength
tered toward the observer are blocked by the aperture.
of the considered transitions, the observed peak wave-
As a result, the emission component of the profile (cen-
length of the profiles, as well as the velocity shift be-
tered at the systemic velocity) becomes more and more
tween the galaxy’s rest frame velocity (computed from
pronounced. The shape of the absorption profile also
the Hα) and the peak velocity of the profiles. The stel-
changesbecauseoftheincreasingcontributionofphotons
lar C III velocity is consistent with the systemic veloc-
scattered by material moving toward the observer. It is
ity computed from the Hα emission line profiles. Note
alsoevidentfromFigure6thatthevelocityatmaximum
thatthe peak/troughvelocitiesobtainedfromthe Gaus-
absorption shifts toward higher blueshifted velocities as
sian fits offer an easy mathematical representation of
the the contribution from scattered emission increases
the data but do not add immediate physical meaning.
(i.e., as R /R increases).
aper SF The velocity profiles shown in Figure 8 are typical of
3. APPLICATIONTOREALSPECTRA starforminggalaxiesatbothhighandlowredshifts(e.g.
Shapley et al.2003;Steidel et al.2011;Jones et al.2012;
As an example of its flexibility, we apply the SALT
Heckman et al. 2011; Wofford et al. 2013), where they
model to resonant line profiles observed in a stacked
are usually interpreted as originating in a gas outflow
spectrum of Lyα emitting galaxies. We first summa-
probablydrivenbythecurrentepisodeofstar-formation.
rize the data and the measurements (Section 3.1) and
The results of the Gaussian fits presented in Fig-
then discuss the properties of that outflow that can be
ure 8 would indicate that the gas is moving toward
inferredfromtheabsorptionlineanalysisperformedwith
the observers with velocities –as measured at the max-
the SALT model. imum absorption/emission– ranging between −160 and
−220kms−1. Theaveragevelocitycomputedinthisway
3.1. Data and measurements
from all absorption lines is −185±25 km s−1. The pro-
The average spectrum modeled in this section was filesinFigure8alsoshowabsorptionatvelocitiesashigh
created by stacking Cosmic Origin Spectrograph (COS as −500km s−1, indicating the presence of multiple ve-
Green et al. 2012) medium-resolution spectra of a sam- locity components and/ora velocity gradientin the out-
ple of 25 known z ∼ 0.3 Lyα emitters (Deharveng et al. flowing gas. All detected fluorescent emission lines are
2008; Cowie et al. 2010). The details of the data reduc- blueshiftedwithrespecttothesystemicHαvelocitywith
tion and spectral extraction are presented in Scarlata et peak velocities ranging between −88 and −137km s−1.
al. (2014). For each galaxy, we have accurate redshift With an average outflow velocity of −100±22km s−1,
measurements obtained from the Hα emission line pro- the fluorescent emission components appear to have a
files (Cowie et al. 2011). systematically-lowervelocity shift than the resonant ab-
To create the stacked spectrum, we first blueshift the sorption lines.
observed spectra of individual galaxies into the rest- Resonant photons can be either re–emitted at reso-
frame using the measured Hα velocities. Then, at each nance, or in the fluorescent channel, when available.
wavelength we compute a flux-weighted average and a Thus, the two lines originate in the same gas and will
standard deviation. The mean stacked UV spectrum sharethesamekinematicalproperties. Naively,themea-
(shown after a box-car smoothing of 0.85˚A) is shown sured systematic difference in the bulk velocities of the
in Figure 7, where the shaded gray area corresponds to
8 Scarlata & Panagia
Fig.7.—Compositerest-frameUVspectrumof25z∼0.3Lyα-emittinggalaxies. Multipleabsorptionfeaturesareidentifiedwithvertical
lines. Solidlinesindicatestellarphotosphericabsorptions,dottedanddashedlinesindicatesresonantabsorptionoriginatinginthegalaxy’s
ISM, with dotted and dashed showing low– and high– ionization metal lines, respectively. The top panel shows the number of galaxies
usedtocomputetheaveragespectrumateachwavelength.
9
absorption and fluorescent emission lines could then be respect to the central source. A simple way to imple-
interpreted as an indication that these lines formed in ment this, is by differentially weighting the contribution
two kinematically–distinct components. In the following to the final profile from different portions of the enve-
section, we use SALT to consistently model the scatter- lope. Thus, we introduce a scaling factor – f – to
obsc
ingfromtheoutflowinggas,andshowhowthesystematic the redcomponentofthe scatteredprofile (Eqn14); i.e.,
velocity difference can be the result of a non-symmetric the radiation scattered in the half sphere moving away
outflow. from the observer). Physically, the parameter f can
obsc
be used to mimic a face-on galaxy, where the disk is ab-
3.2. Modeling the line profiles
sorbing part of the radiation emitted by the outflowing
Here we use SALT to model the observed absorp- material(see Section 4). The profile can now be written
tion/emission profiles observedin the stacked spectrum. as:
The free parameters for the models are τ0, v0, and v∞
for the spherical outflow, and τ0, v0, v∞ and Raper, for I(x)asy =1−I +I +f ×I . (27)
the spherical outflow plus aperture. These parameters abs emi,blue obsc emi,red
fully describe the density and velocity field of the galac- f ,representsthefractionofI thatisallowedto
obsc emi,red
tic outflow, and do not depend on the particular transi- reach the observer. We refer to the above profile as the
tion within a given ionic species. We therefore constrain “asymmetric model”, to indicate that the receding half
the model’s free parameters by simultaneously fitting oftheexpandingenvelopeisseenlesseasilythanthe ap-
the four radiative transitions of Si+, observed around proaching front part. The best fit asymmetric outflow
λ = 1190˚A. We chose this spectral region because it model is shown in Figure 9 with the yellow line. This
shows the highest S/N of the stackedspectrum, and be- modelis clearlyable to simultaneously reproduce the rel-
cause of the presence of both two resonant absorption ative intensity of the fluorescent emission and resonant
and the corresponding fluorescent emission lines. To absorption lines, as well as their systematically different
model the observed line profiles we use equation 22b, peak positions.
which accounts multiple scattering within each shell as Wecantestourresultsusingadifferentresonanttran-
explained in section 2. sition in Si+. The resonant line at λ = 1260.42 is ideal
We derive the best-fit parameters for the symmetric for this purpose. As Figure 8 shows, we detect both the
outflow model with and without a view-limiting aper- resonant absorption and the corresponding fluorescent
ture,byperformingaχ2 minimizationontheentiredou- emission. This absorption originates in the same mate-
bletprofile,includingbothabsorptionandemissionlines. rialwherethe Si iiλ1190doubletisproducedandis thus
The models were computed on the same velocity vector perfect to test the parametersof the outflow model (i.e.,
as the data, and then box-car smoothed with the same the density, velocity field, and geometry). In Figure 10
kernel, before proceeding to the computation and mini- weshowtheobservedSiiiλ1260profile,togetherwiththe
mization of the χ2. The best–fit line profiles for the SiII modelprofilecomputedusingthebest-fitoutflowparam-
doubletareshowninFigure9,andthe parametervalues eters derived from our analysis of the 1190–1193˚A dou-
are given in Table 4. The blue and red curves show the blet(i.e.,changingonlythetransitiondependentparam-
best fit for the spherical outflow with and without the eters in the profile equations). Figure 10 shows that the
spectroscopic aperture, respectively. model optimized to fit the Si II doublet fully reproduces
The simplest spherical models (with or without aper- the observed Si iiλ1260 profile as well. In particular, it
ture) well reproduce the depth, shape and central ve- reproduces both the blueshifted absorption component
locities of the blueshifted absorption components of the as well as the intensity and peak wavelengthof the fluo-
resonantdoublet. Thisindicatesthatoursimpleassump- rescentemission. We stressagainthatthe parametersof
tions for the density and velocity fields of the scattering the outflow are kept fixed to the best-fit values given in
materialareadequaterepresentationoftheSi+ distribu- Table 4.
tion. On the other hand, the spherical model with no
limiting aperture fails to reproduce the observedprofiles 4. DISCUSSION
in two key aspects: 1) it substantially overproduces the Near and far–UV spectra include numerous resonant
amount of scattered emission, and 2), due to the sym- metal absorption lines that, combined with the appro-
metry in the considered configuration, it predicts that priate theoretical tools, provide powerful diagnostics for
the emission component of the P-Cygni profile should galactic outflows. High–quality rest–frame UV spec-
be centered at the systemic velocity, while the observa- tra are currently available for nearby individual galax-
tionsshowsthatthepeaksofthefluorescentemissionare ies (e.g., with data from the Hubble Space Telescope),
clearly blueshifted. and stacked spectra of high–redshift galaxies (with data
As we discussed in Section 2.2, the effect of a spectro- from 8m class telescopes). Soon, with the planned 30m
scopic aperture is to selectively decrease the number of telescopes, we will be able to study at high resolution
scatteredphotonsthatareabletoreachtheobserver. As absorption line spectra in individual objects up to the
Figure 9 shows (blue curve), adding an aperture allevi- highest redshifts.
ates the first of the two discrepancies. However,because Resonant blue–shifted UV absorption features are
ofthe intrinsicsymmetryofthe outflowmodel, the scat- commonly modeled as originating in a thin shell
tered re–emission is still centered at zero velocity, and of gas moving at the outflow velocity (as mea-
therefore the model still fails in fully reproducing the sured from the centroids of resonant absorption lines,
observed features. A blueshift in the scattered emission e.g.,Verhamme et al.2006;Schaerer & Verhamme2008;
componentoriginatingin outflowingmaterialcanbe ob- Verhamme et al. 2008; Schaerer et al. 2011). Substan-
tained if the outflow is not spherically symmetric with tial evidence, however, suggests that this description is
10 Scarlata & Panagia
Fig.8.— Zoom inon the spectral regions around the absorption and emissionlinefeatures considered in this work. In each panel, the
dashed vertical lines show the vacuum wavelength of each transition (as indicated by each label). The orange line shows the sum of the
best-fitGaussianprofiles,whilethedot-dashedlineshowsthecontinuum level.
that the re–emissioncomponentfromthe outflowing gas
cannot be neglected, particularly in compact galaxies or
galaxiesathigh–z,wherethespectroscopicaperturemay
include a substantial fraction of the extended scatter-
ing outflow. Neglecting possible contribution from re–
emitted photons may have important consequences for
the determinationofthe gascolumndensityand/orcov-
eringfraction,asrecentlynotedby,e.g.,Prochaska et al.
(2011).
The SALT model discussed in this paper provides a
simple analytical description of the line profiles origi-
nating in the expanding envelopes around galaxies, that
properlyaccountformultiplescatteringofresonantpho-
tons, scattered re-emission, and observational aperture
effects.
4.1. On the use of the absorption profiles as indication
Fig. 9.—Theabsorptionandre–emissionprofilesoftheSiiidou- of covering fraction
bletarewellreproducedwithanasymmetricmodelandaccounting
Inthe approximationofpureabsorptionandwithwell
fortheeffectofthefiniteCOSaperturesize. Bestfitmodelprofiles
totheSiii1190–1193˚Adoubletareshownfordifferentoutflowge- resolved line profiles, the gas apparent optical depth at
ometries,asindicatedinthelabel. AllmodelsshowninthisFigure a given velocity τ(v) is often used to derive the appar-
includemultiplescatteringwithineachshell. ent column density profile (−ln(I(v)/I (v)) = τ(v) ∝
0
fλN(v), e.g. Pettini et al. 2002). However, it is well
too simplistic, as noted already by, e.g., Pettini et al. known that the apparent column density obtained from
(2002). First of all, when the absorption lines are ob- line profiles can be underestimated if undetected satu-
served at high enough spectral resolution, they show rated components contribute at some velocities. When
asymmetric profiles covering a broad range of velocities twoormoretransitionsofagivenspeciesdifferingonlyin
(up to as much as -1000 km s−1, Tremonti et al. 2007; the product of fλ are available, then information about
Diamond-Stanic et al. 2012; Sell et al. 2014). This indi- line saturation can be inferred from the comparison of
cates that the gas is not confined to a thin shell, but the apparentopticaldepth profiles(that shouldbe iden-
rather is distributed in an extended envelope, with ve- tical within the observational errors). If saturation is
locity and density changing with the distance from the present, the line with the highest oscillatorstrength will
galaxy. More realisticmodels ofextended outflows,with result in a lower apparent column density. The previous
velocity and density gradients have been proposed (e.g., reasoning is correct only if the absorbing gas fully cov-
Prochaska et al. 2011; Rubin et al. 2011; Martin et al. ersthe continuumsource. Ifthis is notthe case,the line
2013),andhighlighttheimportanceofproperlyaccount- profilewillalsodependonthegascoveringfraction(f ),
C
ing for the geometry of the outflowing material. aswell astheopticaldepth(i.e.,I/I =1−f (1−e−τ)).
0 C
Second, well defined P–Cigny profiles from resonant Variousworkshaveusedabsorption-lineprofilestodeter-
transitions of MgII, as well as the detection of fluo- mine the gas f , under the assumption that absorption
C
rescent emission associated with resonant transitions of linesaresaturated(i.e.,e−τ →0inI/I ,e.g.Jones et al.
0
Si II, and FeII, are commonly observed (Shapley et al. 2013; Martin & Bouch´e 2009). When the scattering en-
2003; France et al. 2010; Rubin et al. 2011), indicating velopeisincludedinthespectroscopicaperture,however,