The Mass and Momentum Outflow Rates of Photoionized Galactic Outflows
John Chisholm, Christy A. Tremonti, Claus Leitherer, Yanmei Chen
MMNRAS , 1–11 (2016) Preprint 10 May 2017 Compiled using MNRAS L A TEX style file v3.0
The Mass and Momentum Outflow Rates of Photoionized GalacticOutflows
John Chisholm (cid:63) , Christy A. Tremonti , Claus Leitherer , Yanmei Chen Observatoire de Genève, Universitè de Genève, 51 Ch. des Maillettes, 1290 Versoix, Switzerland Astronomy Department, University of Wisconsin, Madison, 475 N. Charter St., WI 53711, USA Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA Department of Astronomy, Nanjing University, Nanjing 210093, China
10 May 2017
ABSTRACT
Galactic outflows are believed to play an important role in regulating star formation in galaxies,but estimates of the outflowing mass and momentum have historically been based on uncertainassumptions. Here, we measure the mass, momentum, and energy outflow rates of sevennearby star-forming galaxies using ultraviolet absorption lines and observationally motivatedestimates for the density, metallicity, and radius of the outflow. Low-mass galaxies generateoutflows faster than their escape velocities with mass outflow rates up to twenty times largerthan their star formation rates. These outflows from low-mass galaxies also have momentalarger than provided from supernovae alone, indicating that multiple momentum sources drivethese outflows. Only 1-20% of the supernovae energy is converted into kinetic energy, andthis fraction decreases with increasing stellar mass such that low-mass galaxies drive moreefficient outflows. We find scaling relations between the outflows and the stellar mass of theirhost galaxies (M ∗ ) at the 2-3 σ significance level. The mass-loading factor, or the mass outflowrate divided by the star formation rate, scales as M − . ∗ and with the circular velocity as v − . .The scaling of the mass-loading factor is similar to recent simulations, but the observationsare a factor of five smaller, possibly indicating that there is a substantial amount of unprobedgas in a different ionization phase. The outflow momenta are consistent with a model wherestar formation drives the outflow while gravity counteracts this acceleration. Key words:
ISM: jets and outflows, galaxies: evolution, galaxies: formation, ultraviolet: ISM
In actively star forming galaxies, high-mass stars inject energy andmomentum into the surrounding gas, heating and accelerating thegas out of star-forming regions as a galactic outflow (Heckmanet al. 2000; Veilleux et al. 2005; Erb 2015). Models suggest thatremoving this residual mass and energy from star-forming regionsregulates star formation in galaxies (Dekel & Silk 1986; White &Frenk 1991; Katz et al. 1996; Hopkins et al. 2014). Consequently,galactic outflows are a ubiquitous component of modern galaxyformation and evolution simulations (Springel & Hernquist 2003;Hopkins et al. 2014; Vogelsberger et al. 2014; Schaye et al. 2015).However, it is computationally infeasible, at the moment, to fullyresolve all of the necessary physics to drive galactic outflows, andsimulations typically scale the mass and energy outflow rates withproperties of their host galaxy, like the star formation rate (SFR)or stellar mass ( M ∗ ; Springel & Hernquist 2003; Oppenheimer &Davé 2006; Somerville & Davé 2015). (cid:63) Contact email: [email protected]
The mass and energy outflow rates are challenging to observe.Outflows are diffuse structures with uncertain geometries that spandifferent ionization states and metallicities (Heckman et al. 1990,2000; Veilleux et al. 2005), which are challenging to observationallyconstrain. Many studies use a single absorption line to trace boththe density and kinematic information of the outflowing gas, butrely on assumptions for the ionization corrections, metallicities,and outflow radii to derive mass outflow rates (Rupke et al. 2005;Martin 2005; Weiner et al. 2009; Rubin et al. 2014; Heckman et al.2015). These assumptions may introduce an order of magnitudescatter into the observed relations (Murray et al. 2007).In a series of papers we have used a sample of nearby star-forming galaxies with ultraviolet spectra from the Cosmic OriginsSpectrograph (COS; Green et al. 2012) on the
Hubble Space Tele-scope to characterize the physical conditions within galactic out-flows. In Chisholm et al. (2015) (hereafter Paper I), we define asample of 48 nearby star-forming galaxies, our method to fit thestellar continuum, and characterize the absorption kinematics. Wethen use the Si ii absorption profiles to find shallow scaling rela-tions between outflow velocities and their host galaxy properties. In © 2016 The Authors a r X i v : . [ a s t r o - ph . GA ] M a y Chisholm et al.
Galaxy name log( M ∗ ) v circ SFR SFR
COS log(O/H)+12 Proposal ID References[log(M (cid:12) )] [km s − ] [M (cid:12) yr − ] [M (cid:12) yr − ] [dex]SBS 1415+437 6.9 18 0.02 0.02 7.6 11579 81 Zw 18 7.2 21 0.02 0.02 7.2 11579 8MRK 1486 9.3 82 3.6 2.5 8.1 12310 2, 6, 10, 11, 12KISSR 1578 9.5 94 3.7 2.1 8.1 11522 3, 14Haro 11 10.1 137 26 12 8.1 13017 1, 7NGC 7714 10.3 156 9.2 3.1 8.5 12604 4, 5, 13IRAS 08339+6517 10.5 179 14 4.7 8.5 12173 9NGC 6090 10.7 202 25 5.5 8.8 12173 9 Table 1.
Derived galaxy properties (see § 2.1 for sample selection details). The first column gives the name of the galaxy, the second column gives the stellarmass ( M ∗ ), the third column gives the circular velocity of the galaxy (v circ ) calculated using a Tully-Fischer relation (Reyes et al. 2011), the forth column givesthe star formation rate of the entire galaxy (SFR), the fifth column corrects the total SFR for the fact that COS resolves a portion of the total galaxy (SFR COS ),the sixth column is the oxygen abundances (log(O/H)+12) taken from Chisholm et al. (2015), the seventh column is the HST proposal ID, and the last columnlists previous references for the data that we use. References for the targets are coded as: (1) Alexandroff et al. (2015), (2) Duval et al. (2016), (3) France et al.(2010), (4) Fox et al. (2013), (5) Fox et al. (2014), (6) Hayes et al. (2014), (7) Heckman et al. (2015), (8) James et al. (2014), (9) Leitherer et al. (2013), (10)Östlin et al. (2014), (11) Pardy et al. (2014), (12) Rivera-Thorsen et al. (2015), (13) Richter et al. (2013), and (14) Wofford et al. (2013).Galaxy name (cid:219) M o /SFR COS (cid:219) E o / (cid:219) E SFR (cid:219) p o / (cid:219) p SFR M o R i (10 M (cid:12) ) (pc)SBS 1415+437 19 ±
17 0 . ± .
18 5 . ± . ± . . ± .
11 3 . ± . . ± .
33 0 . ± .
01 0 . ± .
18 1 45KISSR 1578 2 . ± .
57 0 . ± .
03 1 . ± .
35 2 54Haro 11 1 . ± .
51 0 . ± .
02 0 . ± .
29 14 101NGC 7714 0 . ± .
08 0 . ± .
003 0 . ± .
04 0.34 33IRAS 08339+6517 0 . ± .
03 0 . ± .
004 0 . ± .
03 0.02 13NGC 6090 0 . ± .
18 0 . ± .
006 0 . ± .
09 1.9 63
Table 2.
Derived outflow properties. The first column gives the name of the galaxy, the second column column gives the maximum mass outflow rate dividedby the SFR in the COS aperture ( (cid:219) M o /SFR COS ), the third column the maximum energy outflow rate divided by the energy from supernovae within the COSaperture ( (cid:219) E o / (cid:219) E SFR ), the fourth column gives the maximum momentum outflow rate divided by the direct momentum from supernovae within the COS aperture( (cid:219) p o / (cid:219) p SFR ), the fifth column gives the mass at the inner radius of the outflow, and the last column gives the inner radius of the outflow. We calculate the errorsusing a Monte Carlo method (see § 3.3 for details). All the values for IRAS 08339+6517 are upper limits because the profile is not fit by our model, and weexclude this galaxy from the sample (see § 4.3).
Chisholm et al. (2016a) (hereafter Paper II) we extend this analysisto the O i, Si iii, and Si iv transitions, which span a factor of threein ionization potential, and probe both neutral and ionized gas. Wefind that the moderately ionized Si iv and neutral O i are co-moving,implying that we are observing a single outflowing structure. Wethen use the equivalent width ratios to study the ionization struc-ture of the outflows, and find that the outflow equivalent widthsare reproduced by photoionization models, if the observed O andB stars ionize the outflow. Using these photoionization models, weestimate the ionization structure, the metallicity, and the total hy-drogen density at the base of the outflow. These values vary fromgalaxy-to-galaxy, and each galaxy requires a unique photoioniza-tion model. Finally, in Chisholm et al. (2016b) (hereafter Paper
III )we fit detailed models of the Si iv 1402Å line profile to determinethe acceleration, the radial density structure, and the inner radius ofthe outflow from the starburst NGC 6090. We combine these mea-surements with detailed photoionization models to derive a velocityresolved mass outflow rate with observationally motivated valuesfor the metallicity, ionization correction, and physical extent of theoutflow.Here, we extend the analysis of Paper
III to a sample of 7 nearbystar-forming galaxies with the highest signal-to-noise UV spectra.We first briefly describe the data analysis and how we characterizethe outflow (§ 2). In § 3.2, we then examine the physical picturesuggested by the observations, and use it to inform our calculation of the mass, momentum, and energy outflow rates (§ 3.3). In § 3.3.1 wenormalize the outflow energetics by the mass and energy producedby supernovae, and explore the scaling relations with the stellar massof the galaxies. Finally, in § 4 we compare the values to previousobservations and simulations (§ 4.1), explore the implications ofthese relations for driving galactic outflows (§ 4.2), and discuss agalaxy that our model does not fit (§ 4.3). In a companion paper,we will explore how the physical properties of galactic outflows(metallicity, density, radius and velocity structure) scale with hostgalaxy properties, and their implications for the mass-metallicityrelation and the enrichment of the circum-galactic medium.
The data reduction and methods follow Paper I and Paper
III . Herewe summarize the major steps taken, but refer the reader to thosepapers for details. We first discuss the sample (§ 2.1), the datareduction, and the continuum fitting (§ 2.2). We then discuss howwe fit the line profiles of the Si iv 1402Å doublet to derive importantvelocity-resolved relations (§ 2.3). Finally, in § 2.4 we describe howwe use O i 1302Å, Si ii 1304Å, S ii 1250Å, and Si iv 1402Å columndensities, along with
CLOUDY photoionization models, to derive themetallicities, densities, and ionization corrections of the outflows.
MNRAS , 1–11 (2016) ass and Momentum Outflow Rates We select the eight galaxies from Paper I that have COS spectrawith a signal-to-noise ratio greater than five at 1380 Å (near theSi iv line; the median signal-to-noise ratio of the sample is 11); ameasured central velocity less than 0 at the 1 σ significance for theO i 1302, Si ii 1304, S ii 1250, and Si iv 1402 Å lines; and arenot contaminated by geocoronal emission at both the O i 1302 andSi ii 1304 Å absorption lines. The most crucial, and constraining,requirement is that we cleanly observe all of the transitions becausemultiple transitions with different ionization potentials constrainthe ionization structure and metallicity of the outflow. These cutsproduce a sample of eight high-quality spectra that are kinematicallydefined as outflows. A list of the previous
Hubble Space Telescope proposal identifications and references for each galaxy is given inTable 1.Since COS is a circular aperture spectrograph, the spectral res-olution varies depending on the size of the target, with the resolutionof our sample varying from 21 km s − to 58 km s − , as measuredfrom the Milky Way absorption lines (Paper I). In Paper I we cal-culate the star formation rates (SFR) and stellar masses ( M ∗ ) of thehost galaxies, assuming a Chabrier initial mass function (Chabrier2003), using archival WISE (Wright et al. 2010) and
GALEX (Mar-tin et al. 2005) observations (Buat et al. 2011; Jarrett et al. 2013;Querejeta et al. 2015). These values are recorded in Table 1. Whilethe sample is small, it represents the only high signal-to-noise spec-tra in the HST archive for which we can accurately calculate themass outflow rates.
The COS spectra are processed through the
CalCOS pipeline, ver-sion 2.20.1, and downloaded from the MAST server. The individualexposures are combined and wavelength calibrated following themethods outlined in Wakker et al. (2015). The spectra are normal-ized, binned by 5 pixels (a spacing of 10 km s − ), and smoothed by3 pixels.A linear combination of multi-age, fully theoretical STAR-BURST99 models (Leitherer et al. 1999, 2010), computed using theWM-Basic stellar library and the Geneva stellar evolution trackswith high-mass loss (Meynet et al. 1994), are fit to the spectra fol-lowing the methods of Paper I. We simultaneously fit for the redden-ing along the line-of-sight using a Calzetti extinction law (Calzettiet al. 2000). We use these fits to remove contributions from thestellar continuum, set the zero-velocity of the absorption lines, andto describe the number of ionizing photons in the photoionizationmodels below.
For each galaxy we simultaneously fit the velocity-resolved Si iv op-tical depth ( τ ) and covering fraction (C f ) to describe the variationof the line profile with velocity. The radiative transfer equation de-fines the flux ( F ) at a given velocity in terms of the C f and the τ atthat velocity as F ( v ) = − C f ( v ) + C f ( v ) e − τ ( v ) (1)If there is a doublet, where the transitions share the same C f and theratio of the two optical depths is equal to the ratio of their f -values,then a system of equations solves for both C f and τ independently(Hamann et al. 1997). We use the Si iv doublet to form a system of equations and solve for the velocity-resolved C f and τ in terms ofthe flux of the Si iv doublet as C f ( v ) = F W ( v ) − W ( v ) + S ( v ) − W ( v ) + τ ( v ) = ln (cid:18) C f ( v ) C f ( v ) + F W ( v ) − (cid:19) (2)Where F W is the STARBURST99 continuum normalized flux of theweaker doublet line (Si iv 1402Å), and F S is the continuum normal-ized flux of the stronger doublet line (Si iv 1394Å). The τ and C f errors are calculated by varying the observed fluxes by a Gaussiankernel centered on zero with a standard deviation equal to the erroron the flux measurement. We then recalculate the τ and C f values ateach velocity interval, and repeat the procedure 1000 times to form τ and C f distributions. We take the standard deviation of these dis-tributions as the velocity-resolved τ and C f errors. To increase thesignal-to-noise ratio, we further bin these profiles by two pixels. The τ and C f distributions for each galaxy are shown in § A. Now, wefit physically motivated, velocity-resolved models to the observed τ and C f distributions.To fit the τ profile we assume that the Si iv density ( n ) followsa radial power-law such that n ( r ) = n , (cid:18) r R i (cid:19) α (3)where n , is the Si iv density at the base of the outflow, R i is the ini-tial radius of the outflow, and α is an unknown power-law exponent.As discussed in Paper III , a power-law distribution with α = − as the mass in a thin shell is spread over a suc-cessively larger surface area as it moves out in the flow. This radialdecline may be due to either deviations in geometry from sphericallysymmetric outflow geometries or because mass is removed from theflow as it propagates outward. In the local galaxy M 82, Leroy et al.(2015) find a steep density power-law, with an α between − −
5, implying that the outflow is not a mass-conserving flow. There-fore, Equation 3 is general, and allows for either a mass-conservingoutflow ( α = −
2) or one that does not conserve mass ( α < − f measures the fraction of the continuum area coveredby the absorbing gas, C f will change as the solid angle of theabsorbing clouds change (Martin & Bouché 2009; Steidel et al.2010). We fit the covering fraction with a radial power-law suchthat C f ( r ) = C f ( R i ) (cid:18) r R i (cid:19) γ (4)where C f ( R i ) is the covering fraction of the outflow at R i ,and γ is the power-law exponent that measures the decline of C f withradius. As gas moves away from the continuum source, the totalarea at a given radius increases. If the clouds remain the same size,this geometric dilution will cause C f to fall as r − . However, if theclouds expand adiabatically some of the geometric dilution can beoffset, and C f declines more gradually. In Paper III , we measurea γ of -0.8 from the Si iv profile of NGC 6090, consistent withexpectations of adiabatically expanding clouds in an adiabaticallyexpanding medium. Moreover, Steidel et al. (2010) fit the C f profilesof z ≈ γ values between − . − . β -law (Lamers & MNRAS000
2) or one that does not conserve mass ( α < − f measures the fraction of the continuum area coveredby the absorbing gas, C f will change as the solid angle of theabsorbing clouds change (Martin & Bouché 2009; Steidel et al.2010). We fit the covering fraction with a radial power-law suchthat C f ( r ) = C f ( R i ) (cid:18) r R i (cid:19) γ (4)where C f ( R i ) is the covering fraction of the outflow at R i ,and γ is the power-law exponent that measures the decline of C f withradius. As gas moves away from the continuum source, the totalarea at a given radius increases. If the clouds remain the same size,this geometric dilution will cause C f to fall as r − . However, if theclouds expand adiabatically some of the geometric dilution can beoffset, and C f declines more gradually. In Paper III , we measurea γ of -0.8 from the Si iv profile of NGC 6090, consistent withexpectations of adiabatically expanding clouds in an adiabaticallyexpanding medium. Moreover, Steidel et al. (2010) fit the C f profilesof z ≈ γ values between − . − . β -law (Lamers & MNRAS000 , 1–11 (2016)
Chisholm et al.
Cassinelli 1999) such thatv ( r ) = v ∞ (cid:18) − R i r (cid:19) β (5)where v ∞ is the measured terminal velocity of the outflow. A β -lawis commonly used to describe stellar winds (Lamers & Cassinelli1999). Analytic relations from Murray et al. (2005) suggest thatdriving outflows with optically thin radiation pressure or ram pres-sure lead to a β near − .
5, consistent with the Si iv profile fromNGC 6090 Paper
III . We simplify Equations 3-5 by introducing thenormalized quantities w = v/v ∞ and x = r / R i to give the relationfor the normalized velocity as w = ( − / x ) β .As found in Paper III , the equivalent width ratios of theSi iv 1394Å and Si iv 1402Å lines indicate that the Si iv is notheavily saturated. Therefore, we simultaneously fit the observedvelocity resolved optical depth and covering fraction, assuming aSobolev optical depth (Sobolev 1960; Lamers & Cassinelli 1999;Prochaska et al. 2011; Scarlata & Panagia 2015), as τ ( w ) = π e mc f λ R i v ∞ n , x α dxd w = τ w / β − β ( − w / β ) + α C f ( w ) = C f ( R i ) (cid:0) − w / β (cid:1) γ (6)where m is the mass of the electron, f is the oscillator strength of theSi iv 1402Å line, λ is the restframe wavelength of the Si iv 1402Åline, and τ is a constant term that we define as τ = π e mc f λ R i v ∞ n H , χ Si4 ( Si / H ) (7)where we have replaced n , with the hydrogen density at the baseof the outflow (n H , ), the Si iv ionization fraction of the outflow( χ Si4 ), and the silicon to hydrogen abundance of the outflow (Si/H).These parameters are estimated from the observed column densitiesand
CLOUDY models in § 2.4 below.We fit Equation 6 to the velocity resolved τ and C f distri-butions of the Si iv 1402Å line using MPFIT (Markwardt 2009) tosolve for τ , β , α , γ , C f (R i ). Resonant emission decreases the C f and increases the τ of the outflow (Prochaska et al. 2011), lead-ing to unphysical velocity distributions if the resonance emissionis not accounted for (see gray points in § A). As in Paper III , weuse the Si ii ∗ ∗ emission lines are narrow, and typically onlyoccupy the inner ±
50 km s − of the profile. Therefore, low velocityabsorption–which can also be contaminated with ISM absorptionfrom within the host galaxy–is largely excluded from the fit. Thefitted relations describe the velocity structure of the outflowingSi iv gas, and the profile fits for the full sample are described fullyin a future paper but are shown in § A. While most galaxies havesimilar fit parameters (median plus standard deviation for β , γ , α are 0 . ± . − . ± . − . ± . f distribution which cannot be fit byEquation 6 (see Figure A7). Instead we force a flat unity C f dis-tribution ( γ = 0 and C f (R i ) = 1). Since IRAS 08339+6517 doesnot follow Equation 6, we exclude it from our outflow discussion,but include an upper limit of its mass outflow rate using γ = f (R i ) = 1 on all plots as an X. In § 4.3 we discuss this profilefurther. The column densities of the different transitions trace the ionizationstructure of the outflow. To characterize this ionization structure,we measure column densities (N) of the O i 1302Å, Si ii 1304Å,S ii 1250Å, and Si iv 1402 Å lines. The measured lines are weak:the Si iv doublet equivalent width ratio is greater than 1.3 for allgalaxies (median of 1.7), while the f -value ratio is 2.0, indicatingthat the Si iv 1402Å line is not overly saturated. We measure columndensities assuming that the lines are partially covered, as measuredby C f ( R i ) in Equation 6. Partial coverage is important, especiallyfor low-mass galaxies with low covering fractions; not accountingfor partial coverage artificially decreases N. We determine N byintegrating the optical depth over a by-eye determined velocity rangeusing the following expression N = . × cm − λ [ Å ] f ∫ ln (cid:18) C f ( R i ) C f ( R i ) + F ( v ) − (cid:19) dv (8)where F ( v ) is the STARBURST99 stellar continuum normalized flux.We assume that C f (R i ) remains the same for each of the four tran-sitions, consistent with the result from Paper II that the line width,not the covering fraction, changes from transition to transition.We fit the observed column densities to integrated column den-sities from a large grid of CLOUDY , version 13.03, photoionizationmodels (Ferland et al. 2013), which use the observed
STARBURST99 stellar continuum fit as the ionizing source. Additionally, we use anexpanding spherical geometry with the measured density profilesfrom § 2.3. We create the
CLOUDY models by varying the ioniza-tion parameter, metallicity, and density of the outflow; and tabulatethe column densities for each model. We use
CLOUDY ’s H ii abun-dances, including the Orion dust grain distribution which accountsfor depletion of metals onto grains, from Baldwin et al. (1991).We scale these abundances between 0.01 Z (cid:12) and 2.5 Z (cid:12) to createthe grid of
CLOUDY models. We then infer the best-fit ionizationparameters, metallicities, and densities using a Bayesian approachwith the O i, Si ii, S ii, and Si iv column densities from the obser-vations and the
CLOUDY models (Paper
III ). From these models weestimate χ Si iv , the outflow metallicity (Z o ), and n H , . The ioniza-tion fractions and metallicities convert n H , to the Si iv density atthe base of the outflow (n , ) , which, with the fitted Si iv opticaldepth and maximum Si iv outflow velocity, defines R i (see Equa-tion 7; Paper III ). We can now calculate the masses and energeticsof the outflows.
Here we calculate the mass outflow rates and energetics of thegalactic outflows. In § 3.1 we consider what drives the outflows:energy and momentum from star formation. By comparing the out-flow mass, momentum and energy to the corresponding quantitiesreleased through star formation, we study how efficiently outflowsremove mass and momentum from galaxies. We then consider thephysical situation of galactic outflows by asking: on which physicalscales do we observe outflows (§ 3.2)? The answer to this ques-tion affects how we interpret the energetics of the outflows. Finally,in § 3.3 we calculate the mass outflow rates ( (cid:219) M o ), energy outflowrates ( (cid:219) E o ), and momentum outflow rates ( (cid:219) p o ); and derive how thesequantities scale with the stellar mass of the galaxy (§ 3.3.1). MNRAS , 1–11 (2016) ass and Momentum Outflow Rates Star formation deposits energy and momentum into gas, accelerat-ing it out of star-forming regions (McKee & Ostriker 1977; Dekel &Silk 1986; Murray et al. 2005). Therefore, to know the efficiency ofa galactic outflow one must know the amount of energy depositedinto the surrounding gas by star formation. For example, comparing (cid:219) M o to the mass of stars formed per unit time (SFR) describes howefficiently galaxies convert gas into stars. The ratio of (cid:219) M o to SFRis called the mass-loading factor. Similarly, we normalize the mo-mentum and energy of the outflow by the momentum and energyreleased by star formation. Leitherer et al. (1999) give the energydeposition rate from supernovae as (cid:219) E SFR = × (cid:18) SFR1 M (cid:12) yr − (cid:19) g cm s − (9)and Murray et al. (2005) give the direct momentum deposition fromsupernovae as (cid:219) p SFR = × (cid:18) SFR1 M (cid:12) yr − (cid:19) g cm s − (10)Where both of these relations assume one supernovae per 100 M (cid:12) of stars formed. These relations only include the direct energy andmomentum from supernovae; other energy and momentum sourcesmay change these relations. For (cid:219) p SFR , radiation pressure, the SedovTaylor phase, and stellar winds from massive stars inject at leastas much momentum as supernovae (Leitherer et al. 1999; Kim &Ostriker 2015). Below, we normalize the mass, momentum andenergy outflow rates by their star formation quantities to study howefficiently outflows remove mass, momentum and energy from star-forming regions.
Our observations indicate that the covering fraction declines withradius (C f ∝ r − . ) and the observed gas density drops dramaticallywith radius (n ∝ r − . ). Further, the measured initial radii of the out-flows indicate that they begin nearly at the size of the star-formingregions. However, this does not mean that there is not absorptionfrom larger radii along the line-of-sight. The equivalent widths ofour outflows are typically 6-10 times larger than the equivalentwidths seen from studies of the circum-galactic medium (Steidelet al. 2010; Werk et al. 2013). This means that the circum-galacticabsorption is likely blended within the outflow absorption at low,zero, or positive velocities, contaminating trends of outflow cen-troid velocities, as discussed in Paper I. While warm gas has beenobserved out to 100 kpc in the circum-galactic medium (Steidelet al. 2010; Tumlinson et al. 2011; Werk et al. 2014), a majority ofthe gas we observe at high velocities (< -200 km s − ) likely comesfrom within 300 pc of the star-forming region (Paper III ).Recently, Thompson et al. (2016) proposed a plausible sce-nario that links outflows at small radii to circum-galactic absorptionat large radii. High-energy photons, stellar winds, and supernovaeinject energy and momentum into the surrounding gas, thermalizingsome gas into a hot, 10 K, outflow and accelerating the residualgas out of the star-forming region (Weaver et al. 1977; Chevalier &Clegg 1985; Heckman et al. 2000; Cooper et al. 2008; Bustard et al.2016). The cooler photoionized gas observed here is produced eitherduring the snowplow phase of the hot supernovae ejecta (McKee &Ostriker 1977; Mac Low et al. 1989), or it is ambient gas entrainedin the hot outflow (Cooper et al. 2009). Either way, the photoionized gas is radially accelerated, destroyed and incorporated into the hot-ter outflow on short timescales (Klein et al. 1994; Scannapieco &Brüggen 2015; Brüggen & Scannapieco 2016). This process "mass-loads" the wind, increasing the mass of the hot outflow (Strickland& Heckman 2009), and accounts for the rapid drop in Si iv density(see § 2.3; Paper
III ). The hot mass-loaded phase continues out ofthe disk, where it encounters and interacts with the hot ejecta fromother localized star-forming regions, producing the shocked shell-like structures and filaments seen in recombination lines in M 82(Shopbell & Bland-Hawthorn 1998). This hotter outflow contin-ues out of the galaxy, undetected by the photoionized tracers here,adiabatically and radiatively cooling as it travels out. Eventuallythe hot outflow cools to temperatures near the peak of the coolingcurve where it shocks, reproducing photoionized gas at large radii(Thompson et al. 2016).This physical picture means that the observed outflows arepowered by the local star formation within the COS aperture, andthe outflow properties depend on the local star formation (Bordoloiet al. 2016). Consequently, the driving source of the outflow is notthe global SFR, rather the local SFR. Our global SFRs are calculatedfrom a combination of the FUV and FIR luminosities (Paper I). Wecannot use this method for the local SFRs because we lack high-resolution FUV and FIR imaging. However, we can measure theFUV in our aperture directly from the COS spectra. Assuming thatthe fraction of unobscured-to-total SFR is the same in the COSaperture as in the galaxy as a whole we calculate:SFR
COS = SFR × F COS F GALEX (11)Where SFR is the total SFR calculated using the IR and UV lu-minosities, F COS is the flux in the COS aperture, and F
GALEX isthe
GALEX measured flux. The lowest mass galaxies have similarSFR
COS to their total SFR because the COS aperture encloses allof the
GALEX flux, whereas the higher mass galaxies have spatiallyextended star formation outside of the COS aperture. This modelassumes that the IR light follows the UV light, whereas the SFR ofhigh-mass galaxies may be clumpy. F
COS /F GALEX ranges from 1,for low-mass galaxies, to 0.22, for the highest mass galaxies. TheSFR
COS values for the full sample are given in Table 1.
Here we estimate the mass, energy, and momentum outflow rates. InPaper
III , we calculate the mass outflow rate ( (cid:219) M o ) at each velocityinterval using the profile fitting and the photoionization modellingas (cid:219) M o ( r ) = Ω C f ( r ) v ( r ) ρ ( r ) r (cid:219) M o ( w ) = Ω C f ( R i ) v ∞ µ m p n H , R w ( − w / β ) + γ + α (12)Where µ m p is is the average mass per nucleon, or 1.4 times theproton mass for standard abundances (Asplund et al. 2009); w is thevelocity normalized by v ∞ ; and Ω is the solid angle occupied by theoutflow, which we assume is 4 π because a locally driven outflow isnot yet collimated by the disk. The relations for C f (r) and ρ (r) aretaken from the profile fitting (Equation 2 and Equation 3), and thevalues for n H , and R i are taken from the photoionization modeling(§ 2.4) and Equation 7, respectively. The total mass at each velocityinterval is similarly calculated as M o ( w ) = Ω C f ( R i ) µ m p n H , R (cid:18) − w / β (cid:19) + α + γ (13) MNRAS000
III , we calculate the mass outflow rate ( (cid:219) M o ) at each velocityinterval using the profile fitting and the photoionization modellingas (cid:219) M o ( r ) = Ω C f ( r ) v ( r ) ρ ( r ) r (cid:219) M o ( w ) = Ω C f ( R i ) v ∞ µ m p n H , R w ( − w / β ) + γ + α (12)Where µ m p is is the average mass per nucleon, or 1.4 times theproton mass for standard abundances (Asplund et al. 2009); w is thevelocity normalized by v ∞ ; and Ω is the solid angle occupied by theoutflow, which we assume is 4 π because a locally driven outflow isnot yet collimated by the disk. The relations for C f (r) and ρ (r) aretaken from the profile fitting (Equation 2 and Equation 3), and thevalues for n H , and R i are taken from the photoionization modeling(§ 2.4) and Equation 7, respectively. The total mass at each velocityinterval is similarly calculated as M o ( w ) = Ω C f ( R i ) µ m p n H , R (cid:18) − w / β (cid:19) + α + γ (13) MNRAS000 , 1–11 (2016)
Chisholm et al.
We then calculate the energy outflow rate ( (cid:219) E o ) using Equation 12as (cid:219) E o ( w ) = (cid:219) M o ( w ) v ∞ w (14)and the momentum outflow rate ( (cid:219) p o ) as (cid:219) p o ( w ) = (cid:219) M o ( w ) v ∞ w (15)These four quantities are velocity resolved. Specifically, (cid:219) M o in-creases at low-velocities and decreases at high-velocities, reachinga maximum (cid:219) M o at intermediate velocities. The increase in (cid:219) M o hap-pens as the velocity and radius increase, and the decrease happensas the density and covering fraction decrease (Paper III ). Here, wetake the maximum value of each quantity as the estimate of thequantity. This means that the reported values in Table 1 and in eachfigure are calculated at specific velocities that correspond to theirmaximum values. We choose the maximum value as the representa-tive value because a radially accelerated outflow implies that the (cid:219) M o in each velocity interval is a snapshot of the (cid:219) M o at a given velocity(or equivalently radius or time). Further, if the decrease in densityis due to a phase change (photoionized gas to a hotter phase), thenthe decrease in (cid:219) M o actually represents a transfer of (cid:219) M o from thephotoionized phase to a hotter phase. In this case, the maximum (cid:219) M o represents the time when the photoionized outflow is the largestcontributor to the total (cid:219) M o of the galaxy.The errors of each quantity are calculated by varying the es-timated parameters of Equation 12 by a Gaussian distribution cen-tered on zero with a standard deviation corresponding to the pa-rameters’ measured errors. We then recalculate the (cid:219) M o value withthese Monte Carloed values, and repeat the procedure 1000 times toform a (cid:219) M o distribution. We take the standard deviation of this dis-tribution as the errors on (cid:219) M o and propagate the errors accordinglyfor (cid:219) p o and (cid:219) E o . The errors are larger for low-mass galaxies becausenarrow absorption line profiles are challenging to determine thedensity scaling ( α ), which leads to larger uncertainties in α and (cid:219) M o . We normalize each of the quantities by the SFR, star formationenergy deposition rate (Equation 9) and star formation momentumdeposition rate (Equation 10) within the COS aperture to determinehow efficiently outflows remove these quantities from star-formingregions (see Table 2 for the values). Here, we study how the masses and energetics of outflows scalewith the stellar mass of their host galaxies. With only a sample ofseven galaxies, more high-quality data is required to confirm theserelations, but we do find statistically significant correlations. Asdiscussed in § 4.3, we exclude IRAS08339 from the fits because theline profile does not follow the model of § 2.3, and upper-limits ofthe (cid:219) M o estimates are shown on the plots as an X, assuming γ = f (R i ) =
1. Figure 1 shows the scaling of the mass-loadingfactor with stellar mass. Over-plotted in black is the least-squares fitto the relation, with the 95% confidence interval as the gray region.This trend corresponds to a relation of (cid:219) M o SFR
COS = . ± . (cid:18) M ∗ M (cid:12) (cid:19) − . ± . (16)The fit is significant at the 3 σ significance level (p-value < 0.001),and has a coefficient of determination (R ) of 0.88, where an R of1.0 implies that the fit describes 100% of the variation. The relationhas a residual standard error of 0.26 dex. Figure 1.
The scaling of the maximum mass-loading factor ( (cid:219) M o /SFR COS )with stellar mass ( M ∗ ). The line gives the least squares regression fit tothe circles (see Equation 16), while the gray region is the 95% confidenceinterval of the fit. The X is IRAS 08339+6517, a high-mass merger that isnot fit by the line profile model of Equation 6 (see § 4.3). Several simulations scale the mass-loading factor by the cir-cular velocity (v circ ) of the galaxy (e.g., Somerville & Davé 2015).Since we do not measure v circ for our sample, we rescale M ∗ intov circ using the Tully-Fisher relation from Reyes et al. (2011). Doingthis, we find (cid:219) M o SFR
COS = . ± . (cid:18) v circ
100 km / s (cid:19) − . ± . (17)Similarly, Figure 2 gives the scaling of the momentum efficiencywith M ∗ as (cid:219) p o (cid:219) p SFR = . ± . (cid:18) M ∗ M (cid:12) (cid:19) − . ± . = . ± . (cid:18) v circ
100 km / s (cid:19) − . ± . (18)which is significant at the 2.5 σ level (p-value < 0.006), and has anR of 0.85. Finally, in Figure 3 we show the variation of the outflowenergy efficiency with M ∗ , which has a scaling relation of (cid:219) E o (cid:219) E SFR = . ± . (cid:18) M ∗ M (cid:12) (cid:19) − . ± . = . ± . (cid:18) v circ
100 km / s (cid:19) − . ± . (19)This relation is only significant at the 2 σ level (p-value < 0.01),and has an R of 0.74. We do not consider this relation signifi-cant, but an inverse relation exists such that low-mass galaxies havehigher energy efficiencies (the trend has a Kendall’s τ coefficientof − . MNRAS , 1–11 (2016) ass and Momentum Outflow Rates Figure 2.
The outflow momentum efficiency ( (cid:219) p o / (cid:219) p SFR ) with stellar mass( M ∗ ). The line gives the least squares regression fit to the circles (seeEquation 18), while the gray region is the 95% confidence interval of the fit.The X is IRAS 08339+6517, a high-mass merger that is not fit by the lineprofile model of Equation 6 (see § 4.3). outflows remove mass, momentum and energy from star-formingregions. The most important results of this study are the values of the massoutflow rate, the momentum outflow rate, and the energy outflowrate (Table 2) that are estimated using observationally motivatedvalues for the outflow metallicity, ionization fraction, and radius.Additionally, we use this small sample to find significant (>2.5 σ )scaling relations between the mass (Figure 1) and momentum (Fig-ure 2) of the photoionized outflows and the stellar mass of their hostgalaxies ( M ∗ ).The mass-loading values found here are broadly consistentwith the wide range of mass-loading factors found in the literature(Rupke et al. 2005; Weiner et al. 2009; Rubin et al. 2014). Threeof the galaxies studied here are included in the Heckman et al.(2015) sample, which calculates (cid:219) M o assuming a constant outflowcolumn density of 10 . cm − , a constant outflow metallicity of0.5 Z (cid:12) , and that the outflow radius is a constant factor of two timesthe radius of the star-forming region. Our estimates of the mass-loading factors for these three galaxies are, on average, a factorof three times smaller than theirs, however, the difference has alarge range: between an over-estimate of 1.04 and 5.7 times. Thisdiscrepancy is largely due to our observationally motivated radii,metallicities, and ionization corrections (Paper III ), which vary byfactors of 3, 10 and 3, respectively, for the sample. Heckman et al.(2015) find a statistically weak correlation between (cid:219) M o /SFR andv circ of (cid:219) M o /SFR = 1.8 (v circ /100 km s − ) − . . This relation has Figure 3.
The outflow energy efficiency ( (cid:219) E o / (cid:219) E SFR ) with stellar mass ( M ∗ ).We do not find a significant correlation between (cid:219) E o / (cid:219) E SFR and M ∗ , althoughthere is a trend such that higher mass galaxies have lower (cid:219) E o / (cid:219) E SFR . The Xis IRAS 08339+6517, a high-mass merger that is not fit by the line profilemodel of Equation 6 (see § 4.3). a normalization that is 1.6 times larger and a shallower scalingthan Equation 17. Crucially, by not accounting for galaxy-to-galaxyvariations in the metallicities, ionization corrections and radii, pre-vious studies may introduce up to a factor of 10 scatter into the (cid:219) M o relations, possibly obscuring trends.We also compare these results to relations typically used insimulations. Simulations use a variety of scaling relations to drivegalactic outflows (Somerville & Davé 2015), including scaling themass-loading factor as v − (Oppenheimer & Davé 2008; Dutton2012) or as v − (Benson et al. 2003; Somerville et al. 2008). InFigure 4 we over-plot the Somerville et al. (2008) relation on our (cid:219) M o estimates as a dot-dashed line. This relation is steeper and hasa larger normalization than the observations presented here.Recent high-resolutions simulations produce outflows withoutexplicitly scaling the outflow properties to the host galaxy. One ex-ample of this is the FIRE simulation (Hopkins et al. 2014), whichfinds the mass-loading factor to scale as M ∗− . when they calcu-late (cid:219) M o at 0.25 R vir (Muratov et al. 2015), as shown by the dashedline in Figure 4. The scaling of this relation is statistically similarto Equation 16, but the normalization is 4.6 times larger. However,we caution that the value of (cid:219) M o from the simulations depends onthe radius used to calculate (cid:219) M o , with (cid:219) M o varying by a factor of 4whether it is calculated at R vir or at 0 . vir (Muratov et al. 2015).The discrepancy between our observations and the simulations doesnot necessarily mean that the simulation drives outflows that are toolarge: if other phases like the molecular gas, O vi coronal gas, or hotX-ray-emitting plasma substantially contribute to the mass and mo-mentum of the outflow, than our observed outflows do not accountfor the entire mass outflow. Future simulations that track the phasestructure of outflows (e.g. molecular, photoionzied, transitional, andhot gas) can compare the mass-loading factors in different ioniza- MNRAS000
The outflow energy efficiency ( (cid:219) E o / (cid:219) E SFR ) with stellar mass ( M ∗ ).We do not find a significant correlation between (cid:219) E o / (cid:219) E SFR and M ∗ , althoughthere is a trend such that higher mass galaxies have lower (cid:219) E o / (cid:219) E SFR . The Xis IRAS 08339+6517, a high-mass merger that is not fit by the line profilemodel of Equation 6 (see § 4.3). a normalization that is 1.6 times larger and a shallower scalingthan Equation 17. Crucially, by not accounting for galaxy-to-galaxyvariations in the metallicities, ionization corrections and radii, pre-vious studies may introduce up to a factor of 10 scatter into the (cid:219) M o relations, possibly obscuring trends.We also compare these results to relations typically used insimulations. Simulations use a variety of scaling relations to drivegalactic outflows (Somerville & Davé 2015), including scaling themass-loading factor as v − (Oppenheimer & Davé 2008; Dutton2012) or as v − (Benson et al. 2003; Somerville et al. 2008). InFigure 4 we over-plot the Somerville et al. (2008) relation on our (cid:219) M o estimates as a dot-dashed line. This relation is steeper and hasa larger normalization than the observations presented here.Recent high-resolutions simulations produce outflows withoutexplicitly scaling the outflow properties to the host galaxy. One ex-ample of this is the FIRE simulation (Hopkins et al. 2014), whichfinds the mass-loading factor to scale as M ∗− . when they calcu-late (cid:219) M o at 0.25 R vir (Muratov et al. 2015), as shown by the dashedline in Figure 4. The scaling of this relation is statistically similarto Equation 16, but the normalization is 4.6 times larger. However,we caution that the value of (cid:219) M o from the simulations depends onthe radius used to calculate (cid:219) M o , with (cid:219) M o varying by a factor of 4whether it is calculated at R vir or at 0 . vir (Muratov et al. 2015).The discrepancy between our observations and the simulations doesnot necessarily mean that the simulation drives outflows that are toolarge: if other phases like the molecular gas, O vi coronal gas, or hotX-ray-emitting plasma substantially contribute to the mass and mo-mentum of the outflow, than our observed outflows do not accountfor the entire mass outflow. Future simulations that track the phasestructure of outflows (e.g. molecular, photoionzied, transitional, andhot gas) can compare the mass-loading factors in different ioniza- MNRAS000 , 1–11 (2016)
Chisholm et al.
Figure 4.
Comparison of the observed mass-loading factors ( (cid:219) M o /SFR COS )with typical relations from simulations. The solid line gives the least squaresregression fit to the circles (see Equation 16), while the gray region is the95% confidence interval of the fit. The dashed line shows the best-fit relationfrom the FIRE simulations (calculated at 0.25R vir ; Muratov et al. 2015) andthe dot-dashed line shows the relation from Somerville et al. (2008) (S08).The relations from simulations are typically a factor of five larger than theobserved photoionized outflows. The X is IRAS 08339+6517, a high-massmerger with a line profile that is not fit by our model (see § 4.3). tion phases to determine if the normalization discrepancy lies inunobserved phases or in the assumptions of the simulations.
Driving galactic outflows in simulations is challenging. Cosmolog-ical simulations need to account for entire galaxies with physics ontens of kpc scales as well as detailed physics on sub-pc scales. Inparticular, resolving the size of a supernova blastwave is crucial toaccount for the energy and momentum of outflows because most ofthe supernova energy is radiated away in these small, dense regionswhen they are under-resolved (Katz 1992). The lack of resolutionprompted simulations to use computational methods, like temporar-ily turning off cooling immediately after a supernova or convertingall of the supernova energy into kinetic energy (Navarro & White1993; Rosdahl et al. 2016), to eliminate overcooling. More recently,simulations scale the outflow velocities and mass-loading factors toparameters of the host galaxies (Benson et al. 2003; Oppenheimer& Davé 2008; Vogelsberger et al. 2013; Somerville & Davé 2015),enabling simulations to generate outflows while remaining compu-tationally feasible.Driving outflows using scaling relations has a logical theoreti-cal argument: star formation transfers momentum or energy into thesurrounding gas which accelerates the gas out of the galaxy. If ob-servations can relate the transfer of momentum from star formationto the outflow, then simulations will drive realistic outflows usingmoderate computing resources. Typically, star formation is assumed to drive outflows by imparting momentum to the gas as (cid:219) p o = (cid:219) M o v o = ζ (cid:219) p SFR (20)where v o is the outflow velocity and ζ is the fraction of the totalmomentum produced by star formation ( (cid:219) p SFR ) that is transferred tothe outflow.Our sample has large ζ values: the median momentum of theoutflow is 68% of the momentum that is directly injected by super-novae. Moreover, outflows from galaxies below log( M ∗ ) of 9 havemore momentum than provided by supernovae alone. Stellar winds,the Sedov Taylor phase, and radiation pressure also add momen-tum to the gas, where STARBURST99 models imply that radiationpressure and stellar winds add at least as much momentum as super-novae (Leitherer et al. 1999). Additionally, Equation 10 may under-estimate the total amount of momentum injected by supernovae byup to a factor of 10 during the Sedov-Taylor phase (Hopkins et al.2014; Kim & Ostriker 2015; Kim et al. 2017). These phases arecrucial for understanding the amount of momentum transferred tothe outflow.Regardless, (cid:219) p o / (cid:219) p SFR values greater than one require moresources of momentum than just the direct momentum from su-pernovae to produce the observed outflow momenta (Hopkins et al.2012). The roles of different momentum sources are explored in H iiregions of the Large and Small Magellanic Clouds where observa-tions suggest that pressure from warm gas dominates the energetics,but there are also significant contributions from hot gas pressureand radiation pressure from dust at small radii (Lopez et al. 2011,2014). At a radius of 75 pc, Lopez et al. (2014) find that the domi-nant pressure source changes from radiation pressure to the thermalpressure of warm gas. The lower-mass galaxies tend to have smallR i (Table 2), which may indicate that (cid:219) p SFR is different for theselow-mass galaxies. Further, Equation 10 assumes that the observedstar formation drives the observed outflows. The timescales definedby the velocity law imply that the gas is accelerated to terminalvelocities in 1 −
10 Myr (Equation 5), which is shorter than the100 Myr timescales of the IR and UV SFRs. Therefore, bursty starformation may impart different (cid:219) p o than assumed in Equation 10.Theory typically solves Equation 20 by assuming that v o scaleslinearly with v circ , that (cid:219) p SFR is proportional to the SFR (Equa-tion 10), and that ζ is constant (Murray et al. 2005). Placing theseassumptions into Equation 20 and solving for (cid:219) M o /SFR gives a scal-ing of v − , which is often called a momentum driven outflow(Murray et al. 2005). A similar argument is made using the energyfrom star formation to derive the scaling of the mass-loading for anenergy driven outflow as v − . Simulations often use these relationsto produce galactic outflows (§ 4.1).However, our observations indicate that the situation is morenuanced because the momentum efficiency is not constant with M ∗ . The normalized momentum flux of SBS 1415+437, the low-est mass galaxy, is 20 times larger than the highest mass galaxy,NGC 6090. Furthermore, the scaling of the momentum efficiencywith M ∗ (Equation 18) indicates that momentum is either more eas-ily dissipated in high-mass galaxies, or star formation injects moremomentum in low-mass galaxies.Gravitational drag could dissipate momentum. For example,the inward momentum deposition due to gravity ( (cid:219) p g ) is equal tothe retarding force of gravity (F g ). If we assume a spherical massdistribution, the net force on the outflow is given as (cid:219) p o = (cid:219) p SFR − M o v R i (21)Assuming that the bulk of outflowing mass (M o ) is at R i (Paper MNRAS , 1–11 (2016) ass and Momentum Outflow Rates Figure 5.
A simplified model describing the relationship between the outflowmomentum ( (cid:219) p out ; in units of g cm s − ) and the net force acting on the outflow(see Equation 21; in units of g cm s − ). This simple model uses the observedstar formation momentum to accelerate the outflow while gravity counteractsthis acceleration to describe the observed outflow momenta.III ), we use the R i and M o values from Table 2 to test whether thissimplified model roughly reproduces the observed outflow momenta(Figure 5). This model does have a few limitations. First, the R i values are sufficiently small such that the enclosed regions mightnot sample the full dark matter profile, and the gravitational forcemay not be accurately modeled by v circ . The model also does notaccount for the fact that low-mass galaxies have larger (cid:219) p o than (cid:219) p SFR , implying that supernovae are not the only momentum sourceaccelerating these outflows (see the discussion above). This factis partially offset because low-mass galaxies have lower coveringfractions, possibly reducing the total amount of (cid:219) p SFR transferred tothe outflow. Regardless, this simplified model has a relationship thatis significant at the 3 σ significance, consistent with a unity slope,an R of 0.85 and a Kendall’s τ coefficient of 0.89. A simple modelwhere gravity dissipates momentum from the outflow may explainthe observed decrease in (cid:219) p o / (cid:219) p SFR with increasing M ∗ .The energy efficiencies ( (cid:219) E o / (cid:219) E SFR ) of the outflows range be-tween 0.9-21%, implying that most of the energy from supernovaeis dissipated by gravity, radiated away, or not in the photoionizedphase. The (cid:219) E o / (cid:219) E SFR values are consistent with the 1-10% oftenfound in numerical simulations (Thornton et al. 1998; Efstathiou2000). Importantly, (cid:219) E o / (cid:219) E SFR of the photoionized outflows increaseswith decreasing M ∗ such that low-mass galaxies drive more effi-cient galactic outflows than high-mass galaxies. The combinationof more efficient outflows and shallower potentials means that low-mass galaxies more efficiently remove gas from their star-formingregions (Dekel & Silk 1986).Mass-loading factors above one indicate that the outflows de-plete the gas within the galaxy more than the star formation does.Equation 16 implies that the mass-loading factor exceeds one whenlog( M ∗ ) is less than 9.7. Outflows regulate the gas depletion of low-mass galaxies; star formation regulates the gas depletion ofhigh-mass galaxies. This critical stellar mass is similar to the stellarmass found in Paper I, below which outflow velocities are faster thanescape velocities. In fact, only NGC 7714 and NGC 6090, the twohighest mass galaxies in the sample, do not have Si iv absorptionat velocities greater than three times their v circ , a typical estimateof the escape velocity (Heckman et al. 2000). Since the outflowis accelerated radially, the model presented here defines whetheroutflows escape the gravitational potential differently than previousmodels. In fact, with a radially accelerated outflow, each velocityinterval is a snapshot of the outflow in time (or radius, or velocity)which may be accelerated to higher velocities at later times. Un-fortunately, the density also declines rapidly with radius, making itimpossible to observe whether the outflows from the highest-massgalaxies reach the escape velocity.Galaxies in this sample with log( M ∗ ) less than 9.7 have out-flows that deplete more gas than their star formation does at veloc-ities high enough to completely remove the gas from the galaxies.This may produce the bursty star formation histories of dwarf galax-ies (Mateo 1998) by removing most of the gas in a single burst ofstar formation (Dekel & Silk 1986). Conversely, high-mass galaxiesretain their outflows, and the gas reaccretes onto the galaxy as agalactic fountain (Shapiro & Field 1976), providing a secondarysource of star-forming material. Consequently, galaxies must bemassive to retain outflowing gas, to efficiently convert gas intostars, and to have relatively constant star formation histories. Sincestar formation dominates the gas depletion in galaxies with halomasses greater than 10 . M (cid:12) (Moster et al. 2010), these galaxiesretain a higher fraction of their total baryons as stars (i.e. they havea higher M ∗ /M halo ratio). The observed M ∗ /M halo relation peaksnear 10 M (cid:12) (Moster et al. 2010) and declines at higher massesas AGN feedback becomes important, or as the halo becomes mas-sive enough to shock heat accreting gas to high temperatures (socalled hot-mode accretion; Kereš et al. 2009). Outflows are a signif-icant component of galaxy evolution by shaping their star formationhistories, regulating their gas content, and removing their baryons. A curious outlier to the above trends is the high-mass mergingsystem IRAS 08339+6517. This galaxy has an anomalously lowmass outflow rate, but extremely high outflow velocity. In PaperI we define a group of outflows with maximum velocities greaterthan 750 km s − , that have outflow velocities 32% higher than othergalaxies at similar stellar mass and SFR. IRAS 08339+6517 is theonly galaxy in this sample that is in that high-velocity group. Whatmakes IRAS 08339+6517 such a strange galaxy?The power of the detailed profile fitting presented here is thatwe can differentiate groups of outflows based on the model fits tothe absorption profile. The line profile of IRAS 08339+6517 doesnot fit the prescription in § 2.3 largely because C f does not varycoherently with velocity, as prescribed by the power-law scaling(see Figure A7). This is in sharp contrast to the rest of the sample(see § A), which have similar C f distributions with a C f power-law exponent ( γ ) of -0.88. To derive an upper limit to (cid:219) M o forIRAS 08339+6517, we set the C f distribution by-hand to match theobservations, with γ = f (R i ) = 1.In Paper III we use the observed C f power-law scaling of r − . to approximate the outflow as an ensemble of adiabatically expand-ing clouds in an adiabatically expanding medium. No variation inC f with velocity requires that the outflowing clouds expand at the MNRAS000
A simplified model describing the relationship between the outflowmomentum ( (cid:219) p out ; in units of g cm s − ) and the net force acting on the outflow(see Equation 21; in units of g cm s − ). This simple model uses the observedstar formation momentum to accelerate the outflow while gravity counteractsthis acceleration to describe the observed outflow momenta.III ), we use the R i and M o values from Table 2 to test whether thissimplified model roughly reproduces the observed outflow momenta(Figure 5). This model does have a few limitations. First, the R i values are sufficiently small such that the enclosed regions mightnot sample the full dark matter profile, and the gravitational forcemay not be accurately modeled by v circ . The model also does notaccount for the fact that low-mass galaxies have larger (cid:219) p o than (cid:219) p SFR , implying that supernovae are not the only momentum sourceaccelerating these outflows (see the discussion above). This factis partially offset because low-mass galaxies have lower coveringfractions, possibly reducing the total amount of (cid:219) p SFR transferred tothe outflow. Regardless, this simplified model has a relationship thatis significant at the 3 σ significance, consistent with a unity slope,an R of 0.85 and a Kendall’s τ coefficient of 0.89. A simple modelwhere gravity dissipates momentum from the outflow may explainthe observed decrease in (cid:219) p o / (cid:219) p SFR with increasing M ∗ .The energy efficiencies ( (cid:219) E o / (cid:219) E SFR ) of the outflows range be-tween 0.9-21%, implying that most of the energy from supernovaeis dissipated by gravity, radiated away, or not in the photoionizedphase. The (cid:219) E o / (cid:219) E SFR values are consistent with the 1-10% oftenfound in numerical simulations (Thornton et al. 1998; Efstathiou2000). Importantly, (cid:219) E o / (cid:219) E SFR of the photoionized outflows increaseswith decreasing M ∗ such that low-mass galaxies drive more effi-cient galactic outflows than high-mass galaxies. The combinationof more efficient outflows and shallower potentials means that low-mass galaxies more efficiently remove gas from their star-formingregions (Dekel & Silk 1986).Mass-loading factors above one indicate that the outflows de-plete the gas within the galaxy more than the star formation does.Equation 16 implies that the mass-loading factor exceeds one whenlog( M ∗ ) is less than 9.7. Outflows regulate the gas depletion of low-mass galaxies; star formation regulates the gas depletion ofhigh-mass galaxies. This critical stellar mass is similar to the stellarmass found in Paper I, below which outflow velocities are faster thanescape velocities. In fact, only NGC 7714 and NGC 6090, the twohighest mass galaxies in the sample, do not have Si iv absorptionat velocities greater than three times their v circ , a typical estimateof the escape velocity (Heckman et al. 2000). Since the outflowis accelerated radially, the model presented here defines whetheroutflows escape the gravitational potential differently than previousmodels. In fact, with a radially accelerated outflow, each velocityinterval is a snapshot of the outflow in time (or radius, or velocity)which may be accelerated to higher velocities at later times. Un-fortunately, the density also declines rapidly with radius, making itimpossible to observe whether the outflows from the highest-massgalaxies reach the escape velocity.Galaxies in this sample with log( M ∗ ) less than 9.7 have out-flows that deplete more gas than their star formation does at veloc-ities high enough to completely remove the gas from the galaxies.This may produce the bursty star formation histories of dwarf galax-ies (Mateo 1998) by removing most of the gas in a single burst ofstar formation (Dekel & Silk 1986). Conversely, high-mass galaxiesretain their outflows, and the gas reaccretes onto the galaxy as agalactic fountain (Shapiro & Field 1976), providing a secondarysource of star-forming material. Consequently, galaxies must bemassive to retain outflowing gas, to efficiently convert gas intostars, and to have relatively constant star formation histories. Sincestar formation dominates the gas depletion in galaxies with halomasses greater than 10 . M (cid:12) (Moster et al. 2010), these galaxiesretain a higher fraction of their total baryons as stars (i.e. they havea higher M ∗ /M halo ratio). The observed M ∗ /M halo relation peaksnear 10 M (cid:12) (Moster et al. 2010) and declines at higher massesas AGN feedback becomes important, or as the halo becomes mas-sive enough to shock heat accreting gas to high temperatures (socalled hot-mode accretion; Kereš et al. 2009). Outflows are a signif-icant component of galaxy evolution by shaping their star formationhistories, regulating their gas content, and removing their baryons. A curious outlier to the above trends is the high-mass mergingsystem IRAS 08339+6517. This galaxy has an anomalously lowmass outflow rate, but extremely high outflow velocity. In PaperI we define a group of outflows with maximum velocities greaterthan 750 km s − , that have outflow velocities 32% higher than othergalaxies at similar stellar mass and SFR. IRAS 08339+6517 is theonly galaxy in this sample that is in that high-velocity group. Whatmakes IRAS 08339+6517 such a strange galaxy?The power of the detailed profile fitting presented here is thatwe can differentiate groups of outflows based on the model fits tothe absorption profile. The line profile of IRAS 08339+6517 doesnot fit the prescription in § 2.3 largely because C f does not varycoherently with velocity, as prescribed by the power-law scaling(see Figure A7). This is in sharp contrast to the rest of the sample(see § A), which have similar C f distributions with a C f power-law exponent ( γ ) of -0.88. To derive an upper limit to (cid:219) M o forIRAS 08339+6517, we set the C f distribution by-hand to match theobservations, with γ = f (R i ) = 1.In Paper III we use the observed C f power-law scaling of r − . to approximate the outflow as an ensemble of adiabatically expand-ing clouds in an adiabatically expanding medium. No variation inC f with velocity requires that the outflowing clouds expand at the MNRAS000 , 1–11 (2016) Chisholm et al. same rate as geometric dilution. Alternatively, the high-velocityoutflows might not fit the physical picture presented in § 2.3. Onepossibility is that the absorption does not correspond to outflowinggas, rather tidal interactions have distributed gas at a wide range ofvelocities along the line-of-sight, creating the unity covering of thesource in Figure A7.NGC 7552, another merger with a high-velocity outflow(Si ii velocity of -1043 km s − ), has a similarly flat Si iv C f distribu-tion. Unfortunately, strong geocoronal lines contaminate the O i andSi ii 1304 Å profile, making photoionization models impossible forthis galaxy. While two galaxies do not constitute a complete group,their similarities suggest that the highest velocity outflows have dif-ferent line profiles, and including different types of outflow profilesmay increase the scatter, increase measured velocities, and confusethe derivation of trends between outflow properties and host galaxyproperties. Here we calculate the mass ( (cid:219) M o ), energy ( (cid:219) E o ), and momentum ( (cid:219) p o )outflow rates for a sample of 7 nearby star-forming galaxies. Weuse a Sobolev approximation and detailed photoionization modelsto determine the quantities with fewer assumed parameters thanprevious studies. These observations describe how efficiently pho-toionized outflows remove mass and momentum from star-formingregions. For example, galaxies in the sample with log( M ∗ ) less than9.7 eject more mass in their outflow than they form into stars, atvelocities that exceed their escape velocities. The momentum ofoutflows from low-mass galaxies is greater than the momentum di-rectly injected from supernovae alone, implying that there must beadditional momentum sources driving the outflows. Only 1-20%of the energy released by supernovae is converted into the kineticenergy of the photoionized outflow, the rest is dissipated by gravity,radiated away, or in a different temperature phase. The values ofthe mass-loading factor, (cid:219) p o / (cid:219) p SFR , and (cid:219) E o / (cid:219) E SFR describe how effi-ciently outflows remove gas from galaxies, and demonstrate that theevolution of the gas content of low-mass galaxies is dominated bygalactic outflows.We find a 3 σ relation between the galactic stellar mass andthe mass-loading factor ( (cid:219) M o /SFR; Equation 12 and Figure 1). The (cid:219) p o / (cid:219) p SFR ratio is also correlated at the 2.5 σ significance with M ∗ (Figure 2). The momenta are described by a simple model wherestar formation drives the gas outward while gravity counteractsthe acceleration (Equation 21 and Figure 5). Additionally, low-mass galaxies are more energy efficient than high-mass galaxies,suggesting that dwarfs efficiently remove gas from their star-formingregions. The mass outflow rates presented here are five times weakerthan simulations typically implement, but have similar scalings.This normalization discrepancy is likely because we only observethe photoionized outflow and there is a substantial amount of massin other outflowing phases.In a future paper, we will discuss how the outflow metallicity,inner radius, and density profile changes with star formation rate andstellar mass. These results are crucial to understanding the enrich-ment of the circum-galactic medium, and how outflows transportmetals out of star-forming regions to establish the mass-metallicityrelationship. ACKNOWLEDGMENTS
We thanks the anonymous referee that provided comments andsuggestions that significantly improved the manuscript. JosephCassinelli inspired this work with helpful conversations and notes.We thank Bart Wakker for help with the data reduction.Support for program 13239 was provided by NASA througha grant from the Space Telescope Science Institute, which is oper-ated by the Association of Universities for Research in Astronomy,Inc., under NASA contract NAS 5-26555. All of the data presentedin this paper were obtained from the Mikulski Archive for SpaceTelescopes (MAST). STScI is operated by the Association of Uni-versities for Research in Astronomy, Inc., under NASA contractNAS 5-26555. Support for MAST for non-HST data is provided bythe NASA Office of Space Science via grant NNX09AF08G and byother grants and contracts.
REFERENCES
Alexandroff R. M., Heckman T. M., Borthakur S., Overzier R., Leitherer C.,2015, ApJ, 810, 104Asplund M., Grevesse N., Sauval A. J., Scott P., 2009, ARA&A, 47, 481Baldwin J. A., Ferland G. J., Martin P. G., Corbin M. R., Cota S. A., PetersonB. M., Slettebak A., 1991, ApJ, 374, 580Benson A. J., Bower R. G., Frenk C. S., Lacey C. G., Baugh C. M., Cole S.,2003, ApJ, 599, 38Bordoloi R., Rigby J. R., Tumlinson J., Bayliss M. B., Sharon K., GladdersM. G., Wuyts E., 2016, MNRAS, 458, 1891Brüggen M., Scannapieco E., 2016, preprint, ( arXiv:1602.01843 )Buat V., Giovannoli E., Takeuchi T. T., Heinis S., Yuan F.-T., Burgarella D.,Noll S., Iglesias-Páramo J., 2011, A&A, 529, A22Bustard C., Zweibel E. G., D’Onghia E., 2016, ApJ, 819, 29Calzetti D., Armus L., Bohlin R. C., Kinney A. L., Koornneef J., Storchi-Bergmann T., 2000, ApJ, 533, 682Chabrier G., 2003, PASP, 115, 763Chevalier R. A., Clegg A. W., 1985, Nature, 317, 44Chisholm J., Tremonti C. A., Leitherer C., Chen Y., Wofford A., LundgrenB., 2015, ApJ, 811, 149Chisholm J., Tremonti C. A., Leitherer C., Chen Y., Wofford A., 2016a,MNRAS, 457, 3133Chisholm J., Tremonti Christy A., Leitherer C., Chen Y., 2016b, MNRAS,463, 541Cooper J. L., Bicknell G. V., Sutherland R. S., Bland-Hawthorn J., 2008,ApJ, 674, 157Cooper J. L., Bicknell G. V., Sutherland R. S., Bland-Hawthorn J., 2009,ApJ, 703, 330Dekel A., Silk J., 1986, ApJ, 303, 39Dutton A. A., 2012, MNRAS, 424, 3123Duval F., et al., 2016, A&A, 587, A77Efstathiou G., 2000, MNRAS, 317, 697Erb D. K., 2015, Nature, 523, 169Ferland G. J., et al., 2013, rmxaa, 49, 137Fox A. J., Richter P., Wakker B. P., Lehner N., Howk J. C., Ben Bekhti N.,Bland-Hawthorn J., Lucas S., 2013, ApJ, 772, 110Fox A. J., et al., 2014, ApJ, 787, 147France K., Nell N., Green J. C., Leitherer C., 2010, ApJ, 722, L80Green J. C., et al., 2012, ApJ, 744, 60Hamann F., Barlow T. A., Junkkarinen V., Burbidge E. M., 1997, ApJ, 478,80Hayes M., et al., 2014, ApJ, 782, 6Heckman T. M., Armus L., Miley G. K., 1990, ApJS, 74, 833Heckman T. M., Lehnert M. D., Strickland D. K., Armus L., 2000, ApJS,129, 493Heckman T. M., Alexandroff R. M., Borthakur S., Overzier R., Leitherer C.,2015, ApJ, 809, 147Hopkins P. F., Quataert E., Murray N., 2012, MNRAS, 421, 3522MNRAS , 1–11 (2016) ass and Momentum Outflow Rates Hopkins P. F., Kereš D., Oñorbe J., Faucher-Giguère C.-A., Quataert E.,Murray N., Bullock J. S., 2014, MNRAS, 445, 581James B. L., Aloisi A., Heckman T., Sohn S. T., Wolfe M. A., 2014, ApJ,795, 109Jarrett T. H., et al., 2013, AJ, 145, 6Katz N., 1992, ApJ, 391, 502Katz N., Weinberg D. H., Hernquist L., 1996, ApJS, 105, 19Kereš D., Katz N., Davé R., Fardal M., Weinberg D. H., 2009, MNRAS,396, 2332Kim C.-G., Ostriker E. C., 2015, ApJ, 802, 99Kim C.-G., Ostriker E. C., Raileanu R., 2017, ApJ, 834, 25Klein R. I., McKee C. F., Colella P., 1994, ApJ, 420, 213Lamers H. J. G. L. M., Cassinelli J. P., 1999, Introduction to Stellar Winds.Cambridge, UK: Cambridge University PressLeitherer C., et al., 1999, ApJS, 123, 3Leitherer C., Ortiz Otálvaro P. A., Bresolin F., Kudritzki R.-P., Lo Faro B.,Pauldrach A. W. A., Pettini M., Rix S. A., 2010, ApJS, 189, 309Leitherer C., Chandar R., Tremonti C. A., Wofford A., Schaerer D., 2013,ApJ, 772, 120Leroy A. K., et al., 2015, ApJ, 814, 83Lopez L. A., Krumholz M. R., Bolatto A. D., Prochaska J. X., Ramirez-RuizE., 2011, ApJ, 731, 91Lopez L. A., Krumholz M. R., Bolatto A. D., Prochaska J. X., Ramirez-RuizE., Castro D., 2014, ApJ, 795, 121Mac Low M.-M., McCray R., Norman M. L., 1989, ApJ, 337, 141Markwardt C. B., 2009, in Bohlender D. A., Durand D., Dowler P.,eds, Astronomical Society of the Pacific Conference Series Vol. 411,Astronomical Data Analysis Software and Systems XVIII. p. 251( arXiv:0902.2850 )Martin C. L., 2005, ApJ, 621, 227Martin C. L., Bouché N., 2009, ApJ, 703, 1394Martin D. C., et al., 2005, ApJ, 619, L1Mateo M. L., 1998, ARA&A, 36, 435McKee C. F., Ostriker J. P., 1977, ApJ, 218, 148Meynet G., Maeder A., Schaller G., Schaerer D., Charbonnel C., 1994,A&AS, 103, 97Moster B. P., Somerville R. S., Maulbetsch C., van den Bosch F. C., MacciòA. V., Naab T., Oser L., 2010, ApJ, 710, 903Muratov A. L., Kereš D., Faucher-Giguère C.-A., Hopkins P. F., QuataertE., Murray N., 2015, MNRAS, 454, 2691Murray N., Quataert E., Thompson T. A., 2005, ApJ, 618, 569Murray N., Martin C. L., Quataert E., Thompson T. A., 2007, ApJ, 660, 211Navarro J. F., White S. D. M., 1993, MNRAS, 265, 271Oppenheimer B. D., Davé R., 2006, MNRAS, 373, 1265Oppenheimer B. D., Davé R., 2008, MNRAS, 387, 577Östlin G., et al., 2014, ApJ, 797, 11Pardy S. A., et al., 2014, ApJ, 794, 101Prochaska J. X., Kasen D., Rubin K., 2011, ApJ, 734, 24Querejeta M., et al., 2015, ApJS, 219, 5Reyes R., Mandelbaum R., Gunn J. E., Pizagno J., Lackner C. N., 2011,MNRAS, 417, 2347Richter P., Fox A. J., Wakker B. P., Lehner N., Howk J. C., Bland-HawthornJ., Ben Bekhti N., Fechner C., 2013, ApJ, 772, 111Rivera-Thorsen T. E., et al., 2015, ApJ, 805, 14Rosdahl J., Schaye J., Dubois Y., Kimm T., Teyssier R., 2016, preprint,( arXiv:1609.01296 )Rubin K. H. R., Prochaska J. X., Koo D. C., Phillips A. C., Martin C. L.,Winstrom L. O., 2014, ApJ, 794, 156Rupke D. S., Veilleux S., Sanders D. B., 2005, ApJS, 160, 87Scannapieco E., Brüggen M., 2015, ApJ, 805, 158Scarlata C., Panagia N., 2015, ApJ, 801, 43Schaye J., et al., 2015, MNRAS, 446, 521Shapiro P. R., Field G. B., 1976, ApJ, 205, 762Shopbell P. L., Bland-Hawthorn J., 1998, ApJ, 493, 129Sobolev V. V., 1960, Moving envelopes of stars. "Cambridge: Harvard Uni-versity Press"Somerville R. S., Davé R., 2015, ARA&A, 53, 51 Somerville R. S., Hopkins P. F., Cox T. J., Robertson B. E., Hernquist L.,2008, MNRAS, 391, 481Springel V., Hernquist L., 2003, MNRAS, 339, 312Steidel C. C., Erb D. K., Shapley A. E., Pettini M., Reddy N., BogosavljevićM., Rudie G. C., Rakic O., 2010, ApJ, 717, 289Strickland D. K., Heckman T. M., 2009, ApJ, 697, 2030Thompson T. A., Quataert E., Zhang D., Weinberg D. H., 2016, MNRAS,455, 1830Thornton K., Gaudlitz M., Janka H.-T., Steinmetz M., 1998, ApJ, 500, 95Tumlinson J., et al., 2011, Science, 334, 948Veilleux S., Cecil G., Bland-Hawthorn J., 2005, ARA&A, 43, 769Vogelsberger M., Genel S., Sijacki D., Torrey P., Springel V., Hernquist L.,2013, MNRAS, 436, 3031Vogelsberger M., et al., 2014, MNRAS, 444, 1518Wakker B. P., Hernandez A. K., French D. M., Kim T.-S., OppenheimerB. D., Savage B. D., 2015, ApJ, 814, 40Weaver R., McCray R., Castor J., Shapiro P., Moore R., 1977, ApJ, 218, 377Weiner B. J., et al., 2009, ApJ, 692, 187Werk J. K., Prochaska J. X., Thom C., Tumlinson J., Tripp T. M., O’MearaJ. M., Peeples M. S., 2013, ApJS, 204, 17Werk J. K., et al., 2014, ApJ, 792, 8White S. D. M., Frenk C. S., 1991, ApJ, 379, 52Wofford A., Leitherer C., Salzer J., 2013, ApJ, 765, 118Wright E. L., et al., 2010, AJ, 140, 1868This paper has been typeset from a TEX/L A TEX file prepared by the author.
APPENDIX A: OPTICAL DEPTH AND COVERINGFRACTION PLOTS
Here we include the plots of the velocity-resolved τ (upper panels) andC f (lower panels) for the entire sample. Fits to the lines, using Equation 6are shown by the solid line. The velocity resolution is marked in the upperportion of each panel.MNRAS000
Here we include the plots of the velocity-resolved τ (upper panels) andC f (lower panels) for the entire sample. Fits to the lines, using Equation 6are shown by the solid line. The velocity resolution is marked in the upperportion of each panel.MNRAS000 , 1–11 (2016) Chisholm et al. -250 -200 -150 -100 -50 0Velocity (km/s)012345 (cid:111) -250 -200 -150 -100 -50 0Velocity (km/s)0.00.20.40.60.81.01.2 C f Figure A1.
The velocity resolved Si iv optical depth ( τ ; upper panel) and covering fraction (C f ; lower panel) for SBS1415+437, as derived from Equation 2.The τ is fit (solid line) assuming a Sobolev optical depth, and the C f is fit assuming a radial power-law C f , as given by Equation 6. Gray points are excludedfrom the fit due to contamination of resonance emission. The spectral resolution is given as a bar in the upper portion of each panel.MNRAS , 1–11 (2016) ass and Momentum Outflow Rates -400 -300 -200 -100 0Velocity (km/s)012345 (cid:111) -400 -300 -200 -100 0Velocity (km/s)0.00.20.40.60.81.01.2 C f Figure A2.
Same as Figure A1 but for 1 Zw 18. .MNRAS000
Same as Figure A1 but for 1 Zw 18. .MNRAS000 , 1–11 (2016) Chisholm et al. -400 -300 -200 -100 0Velocity (km/s)012345 (cid:111) -400 -300 -200 -100 0Velocity (km/s)0.00.20.40.60.81.01.2 C f Figure A3.
Same as Figure A1 but for MRK 1486. MNRAS , 1–11 (2016) ass and Momentum Outflow Rates -300 -200 -100 0Velocity (km/s)012345 (cid:111) -300 -200 -100 0Velocity (km/s)0.00.20.40.60.81.01.2 C f Figure A4.
Same as Figure A1 but for KISSR 1578.MNRAS000
Same as Figure A1 but for KISSR 1578.MNRAS000 , 1–11 (2016) Chisholm et al. -400 -300 -200 -100 0Velocity (km/s)012345 (cid:111) -400 -300 -200 -100 0Velocity (km/s)0.00.20.40.60.81.01.2 C f Figure A5.
Same as Figure A1 but for Haro 11. MNRAS , 1–11 (2016) ass and Momentum Outflow Rates -400 -300 -200 -100 0Velocity (km/s)012345 (cid:111) -400 -300 -200 -100 0Velocity (km/s)0.00.20.40.60.81.01.2 C f Figure A6.
Same as Figure A1 but for NGC 7714.MNRAS000
Same as Figure A1 but for NGC 7714.MNRAS000 , 1–11 (2016) Chisholm et al. -500 -400 -300 -200 -100 0Velocity (km/s)012345 (cid:111) -500 -400 -300 -200 -100 0Velocity (km/s)0.00.20.40.60.81.01.2 C f Figure A7.
Same as Figure A1 but for IRAS08449+6517. This galaxy is not included in the analysis because the line profile cannot match the proposed modelof § 2.3 MNRAS , 1–11 (2016) ass and Momentum Outflow Rates -400 -300 -200 -100 0Velocity (km/s)012345 (cid:111) -400 -300 -200 -100 0Velocity (km/s)0.00.20.40.60.81.01.2 C f Figure A8.
Same as Figure A1 but for NGC 6090.MNRAS000