Probing the gaseous halo of galaxies through non-thermal emission from AGN-driven outflows
aa r X i v : . [ a s t r o - ph . GA ] J u l Mon. Not. R. Astron. Soc. , 1–12 (2015) Printed 14 September 2018 (MN L A TEX style file v2.2)
Probing the gaseous halo of galaxies through non-thermal emissionfrom AGN-driven outflows
Xiawei Wang ⋆ and Abraham Loeb Department of Astronomy, Harvard University, 60 Garden St., Cambridge, MA 02138, USA
Accepted 2015 July 17. Received 2015 July 15; in original form 2015 June 16
ABSTRACT
Feedback from outflows driven by active galactic nuclei (AGN) can affect the distribution andproperties of the gaseous halos of galaxies. We study the hydrodynamics and non-thermalemission from the forward outflow shock produced by an AGN-driven outflow. We consider afew possible profiles for the halo gas density, self-consistently constrained by the halo mass,redshift and the disk baryonic concentration of the galaxy. We show that the outflow velocitylevels off at ∼ km s − within the scale of the galaxy disk. Typically, the outflow canreach the virial radius around the time when the AGN shuts off. We show that the outflowsare energy-driven, consistently with observations and recent theoretical findings. The outflowshock lights up the halos of massive galaxies across a broad wavelength range. For Milky Way(MW) mass halos, radio observations by The Jansky Very Large Array ( JVLA ) and
The SquareKilometer Array ( SKA ) and infrared/optical observations by
The James Webb Space Telescope ( JWST ) and
Hubble Space Telescope ( HST ) can detect the emission signal of angular size ∼ ′′ from galaxies out to redshift z ∼ . Millimeter observations by The Atacama LargeMillimeter/submillimeter Array ( ALMA ) are sensitive to non-thermal emission of angular size ∼ ′′ from galaxies at redshift z . , while X-ray observations by Chandra , XMM-Newton and
The Advanced Telescope for High Energy Astrophysics ( ATHENA ) is limited to localgalaxies ( z . . ) with an emission angular size of ∼ ′ . Overall, the extended non-thermalemission provides a new way of probing the gaseous halos of galaxies at high redshifts. Key words: shock waves – galaxies: active – galaxies: haloes – quasars: general – radiocontinuum: general.
Outflows from active galactic nuclei (AGN) regulate blackhole (BH) growth (Silk & Rees 1998; Di Matteo et al. 2005) andmay quench star formation (Springel et al. 2005; Hopkins et al.2008) in galaxies. A great amount of observational evidencehas demonstrated the presence of AGN-driven outflows, in-cluding observations of absorptions in quasars (Ganguly et al.2007; Fu & Stockton 2009; Moe et al. 2009; Villar-Mart´ın et al.2011; Arav et al. 2013; Zakamska & Greene 2014; Arav et al.2015), multiphase outflows in nearby ultraluminous infraredgalaxies (ULIRGs) (Rupke & Veilleux 2011; Sturm et al. 2011;Cicone et al. 2014; Feruglio et al. 2015; Tombesi et al. 2015) andquasars (Carniani et al. 2015; Gofford et al. 2015), and post-starburst galaxies (Tripp et al. 2011). The velocity of AGN-drivenoutflows can reach ∼ km s − on galaxy scale, indicating thatthe outflows are likely to propagate into the halos of galaxies whilethe AGN is active. Here we propose to use AGN-driven outflows asa probe of the halo gas in galaxies.Halo gas has been identified in multiphases (see review ⋆ E-mail: [email protected] by Putman et al. 2012): cold neutral hydrogen detected ashigh velocity clouds (Kalberla et al. 2005; Westmeier et al. 2005;Oosterloo et al. 2007; Saul et al. 2012), warm gas ( T ∼ − K) discovered in deep H α emission line surveys (Putman et al.2003; Lehner et al. 2012), warm-hot gas ( T ∼ − K) detectedin absorption (Wakker & Savage 2009; Prochaska & Hennawi2009; Savage et al. 2011; Marasco et al. 2013; Farina et al. 2014;Ford et al. 2014) and hot gas ( T ∼ K) inferred from X-ray observations in emission and absorption (Bogd´an et al. 2013;Miller & Bregman 2013; Bogd´an et al. 2015). The presence ofwarm-hot and hot halo gas, extending out to the virial radius, isof particular interest since the hot gas is postulated to host a sig-nificant fraction of baryons in the galaxy (Kaufmann et al. 2006).However, the detailed properties and the origin of the extended anddiffuse hot halo gas remain uncertain since there is little evidencefor its existence around spiral galaxies (Putman et al. 2012). Thedetection of halo gas out to virial radius scale is difficult and theextent to which the outflows impact the properties of the halo gasremains uncertain. Therefore, it is important to study the interac-tion between AGN-driven outflows and surrounding gas on differ-ent scales as a probe of the properties of the diffuse hot halo gasand the effectiveness of the feedback mechanism. c (cid:13) X. Wang and A. Loeb
In galaxies with a weaker AGN where the energetics ofAGN activity and star formation are comparable, it remains un-clear whether outflows are dominated by AGN or supernovae (SN)(Hopkins et al. 2015). In this paper, we focus on AGN-driven out-flows. First, our model assumes spherical symmetry, which is morejustified for AGN-driven outflows since they are launched at thecenter of the galaxy whereas SN-driven outflows are distributedthroughout the entire disk. More importantly, as shown later inthe paper, the strongest emission signal comes from more massivegalaxies where AGN feedback is thought to dominate.Previous work on the dynamics of and non-thermal emissionfrom galactic outflows has made simple assumptions about the totalgravitational mass and the gaseous environment in which the out-flow propagates (Furlanetto & Loeb 2001; King 2003; King et al.2011; Faucher-Gigu`ere & Quataert 2012; Nims et al. 2015), andlimited the evolution of the outflows to galactic disk scales(Jiang et al. 2010; Faucher-Gigu`ere & Quataert 2012; Nims et al.2015; Hopkins et al. 2015). In this paper, we explore different gasdensity profiles in galaxy halos and examine the non-thermal emis-sion from the forward shock plowing into the ambient medium indetails. We predict the multiwavelength spectrum and detectabil-ity of the non-thermal emission and discuss how the outflow shockand halo gas affect each other. We propose a new way to probethe gaseous halo using the non-thermal emission from the outflowshocks as they travel through the ambient medium in the galaxyand halo.The paper is organized as follows. In §
2, we describe ourmodel for the halo and gas distribution. In §
3, we analyze the hy-drodynamics of AGN-driven outflows. In §
4, we calculate the non-thermal emissions from shocks produced by outflows. In §
5, weshow numerical results for representative cases and discuss physi-cal significance. Finally in §
6, we summarize our results and dis-cuss their implications.
We approximate the galaxy and halo as spherically symmetric. Theenvironment into which the outflow propagates is decribed below.Here we discuss properties of spherical outflows driven by fast nu-clear wind (Jiang et al. 2010; King & Pounds 2015). The predictedradio emission from outflow shocks as discussed in § We assume that the density distribution of the galaxy in whichthe outflow is initially embedded follows the NFW profile(Navarro et al. 1996): ρ NFW ( R ) = ρ (1 + z ) Ω m Ω m ( z ) δ c c N x (1 + c N x ) , (1)where ρ = 3 H / πG is the critical density today, H isthe Hubble constant today, G is the gravitational constant, x = R/R vir , c N is the concentration parameter which is roughly givenby: c N ≈ z ) − , Ω m = 0 . . δ c is given by δ c =∆ c c N / [3(ln(1 + c N ) − c N / (1 + c N ))] , where ∆ c ≈ π . Ω m ( z ) can be expressed as Ω m ( z ) = Ω m (1 + z ) / [Ω m (1 + z ) + Ω Λ ] , where Ω Λ = 0 . . R vir is the virial radius, writ-ten as R vir = 0 . h − / (cid:2) Ω m ∆ c / π Ω m ( z ) (cid:3) − / M / , / (1 + z/
10) kpc , where h = ( H /
100 km s − ) is the Hubble parameter and M halo = 10 M h , M ⊙ is the halo mass. We obtain the totalmass of the galaxy and dark matter halo within a radius of R by R πR ρ NFW ( R ) dR , which gives: M DM ( R ) = ρ (1 + z ) Ω m Ω m ( z ) δ c R c N (cid:20) ln(1 + c N x ) − c N x c N x (cid:21) . (2)We estimate the BH mass M • self-consistently by the followingsteps (Guillochon & Loeb 2015). First we obtain the total stellarmass in the galaxy M ⋆ determined by M halo (Moster et al. 2010): M ⋆ = M ⋆, ( M halo /M ) γ h M halo /M ) β i ( γ − γ ) /β , (3)where log( M ⋆, /M ⊙ ) = 10 . , log( M /M ⊙ ) = 10 . , γ =7 . , γ = 0 . and β = 0 . . There is no specific bulge mass M bulge for a given halo mass (Kormendy & Ho 2013). Numericalsimulation (Bluck et al. 2014) suggests that the bulge-to-total stel-lar mass ratio B / T = M bulge /M ⋆ is roughly uniformly distributedfrom to . This ratio for the MW is ∼ . (Licquia & Newman2014). Additionally, Fisher & Drory (2011) suggest that ∼ ofall local stellar mass is in bulges and elliptical galaxies. We thenadopt a particular value of B / T ratio to be ∼ in our calcula-tion and multiply this value by M ⋆ to get M bulge to illustrate someexamples. There is likely to be only ellipticals in high mass halos,so it is justified to take a fixed B/T ratio for these systems. We alsoverify that modifying B/T ratio only results in a difference within afactor of . This variation can be cancelled out by the uncertaintyin the fraction of AGN’s luminosity injected into the medium asdiscussed later in the paper. Finally, we obtain the BH mass M • by(McConnell & Ma 2013): log( M • /M ⊙ ) = 8 .
46 + 1 .
05 log (cid:20) M bulge M ⊙ (cid:21) . (4)The underestimation of the M • correlations could be an issue forthe most massive BHs (Kormendy & Ho 2013) but should not af-fect our results on the emission from the outflow shocks in the morecommon galaxies with M • ≪ M ⊙ . We assume that the gas takes up a fraction f g of the total massof the dark matter in a galaxy. We adopt a cosmic mean baryonfraction, which is f g ∼ (Hinshaw et al. 2013). A fraction ofthe baryons f d is concentrated in the disk of the galaxy, and thedisk radius R disk is taken to be ∼ of the virial radius R vir (Shibuya et al. 2015).Our first prescription for the gas density distribution is a bro-ken power-law profile, given by: ρ pl ( R ) = ( C d R − α ( R R disk ) C h R − β ( R disk < R R vir ) (5)where α and β are the power-law indices in the disk and halo com-ponent, respectively. We assume an isothermal sphere for the gaswithin the disk component and fix α = 2 . in our calculation. Theconstants in the density profile C d and C h can be constrained bythe baryon mass budget in the disk component and in total. Con-sequently, β is soley dependent on f d . The constraint on β by f d is shown in Fig.1, where we find that when f d ∼ . , β ∼ ,indicating that the gas in the halo approximately follows the NFW c (cid:13) , 1–12 robing gaseous galaxy halos Figure 1.
Power-law index β of the halo gas density profile as a functionof the baryon fraction of the halo ( − f d ). The dashed lines correspondto values of f d = 0 . , . and . , which we have taken into numericalcalculation in the following sections. profile. From the broken power-law density profile, we estimate thegas number density at − kpc to be − − − cm − , whichis consistent with numerical simulations (Sokołowska et al. 2015)and observations (Bogd´an et al. 2015) of the hot halo gas distribu-tion. The second profile we consider for the halo gas densitydistribution is analogous to that of galaxy clusters, written as(Patej & Loeb 2015): ρ clu ( R ) = Γ f g A ( R/s ) − R/r s [1 + ( s/r s )( R/s ) Γ ] , (6)where A = ρ δ c is the scale parameter, s = R vir , r s = s/c N is thescale radius and Γ is the jump ratio. The density profile recovers toa scaled NFW profile for Γ = 1 . We assume spherical symmetry for the outflow and the ambi-ent medium. Fast wind with velocity ∼ . c is injected into themedium, as inferred from observations of broad absorption lines inquasars (Arav et al. 2013). The wind drives an outer forward shockinto the ambiet medium accelerating the swept-up material and aninner reverse shock into the wind decelerating itself, separated by acontact discontinuity (King & Pounds 2015).The equation of motion of the shell is given by(Furlanetto & Loeb 2001; Faucher-Gigu`ere & Quataert 2012): d R s dt = 4 πR M s ( P t − P ) − GM tot R − v s M s dM s dt , (7)where G is the gravitational constant, and R s , v s and M s are theradius, velocity and mass of the swept-up shell, respectively. M tot is the total gravitational mass inside R s that impedes the expansionof the wind bubble, written as M tot = M DM + M gal + M • + M s / , composed of the mass of dark matter M DM , galaxy M gal ,the central BH M • , and the self-gravity of the shell. The shell mass, M s , satisfies, dM s dt = 4 πρ g R v s , (8) where ρ g is the ambient gas density profile in the galaxy.Hydrostatic equilibrium gives the temperature in the ambientmedium T : dT dR = GM tot m p kR − T n g dn g dR , (9)where m p is the proton mass, k is the Boltzman constant and n g isthe number density profile of the ambient gas. At virial radius R vir , T reaches virial temperature T vir = µm p v / k where µ = 0 . is the mean molecular weight of fully ionized gas and v c is thecircular velocity, given by v c = ( GM halo /R vir ) / . The ambientthermal pressure is given by P = n g kT .The thermal pressure in the shocked wind P t declines due toradiative energy losses and work done on the ambient gas by theexpansion, at a rate: dP t dt = Λ2 πR − P t v s R s , (10)where Λ is the heating and cooling function, composed of energyinjection from the central source and different physical cooling pro-cesses in the shocked wind region: Λ = L in − L ff − L IC − L syn − L p . (11)Energy is continuously injected into the shocked wind during thequasar’s lifetime, taken to be the e-folding time τ Edd ≈ . × yrs (Martini & Weinberg 2001), with a rate of L in , which isassumed to be a fraction of the AGN’s bolometric luminosity f in L AGN . Observations infer f in to be ∼ − (Arav et al.2013; Cicone et al. 2014) and we adopt f in = 5% in our calcula-tion. We assume that L AGN is a fraction f AGN of the Eddingtonluminosity L Edd = 1 . × ( M • /M ⊙ ) erg s − , and adopt f AGN = 0 . in our calculation (Shen et al. 2009).The last four terms in the right hand side of Eqn. 11 ac-count for radiative cooling. L ff is the radiative cooling rate viafree-free emission in the shocked wind. L IC decribes cooling viainverse Compton (IC) scattering off photons in the quasar’s radi-ation field and the cosmic microwave background (CMB). L syn represents synchrotron cooling rate. L p refers to the cooling ofprotons through Coulomb collisions with the electrons. The cool-ing rate can be expressed as µE t /t c , where E t = 2 πR P t isthe thermal energy in the shocked wind and t c is the timescalecorresponding to different cooling processes. The total emissiv-ity of free-free emission is given by (Rybicki & Lightman 1979): ǫ ff = 1 . × − T / , n , ¯ g B , where ¯ g B is the Gaunt fac-tor, T e , = ( T e / K) and n e , = ( n e / − ) are theelectron temperature and number density, respectively. The cor-responding cooling timescale is t ff = kT e /ǫ ff = 4 . × T / , n − , ¯ g − B yr . The IC cooling time of relativistic elec-trons of energy E e in soft photon radiation field can be writtenas (King & Pounds 2015): t IC = 3 m c / πσ T U ph E e , where σ T is the Thomson scattering scross section and U ph is the en-ergy density of soft photons, including AGN photons with en-ergy density U AGN = L AGN / πR c and CMB photons withenergy density U CMB ≈ . × − (1 + z ) erg cm − . Herewe consider the most efficient IC cooling limit and thus leaveout non-relativistic electrons, of which the IC cooling time canbe significantly longer (Faucher-Gigu`ere & Quataert 2012). Weobtain the temperature in the shocked wind by the Rankine-Hugoniot jump condition T e ≈ µm p v / k . The synchrotroncooling timescale is given by t syn = 1 . × B − − T − e, yr ,where B − = ( B/ − G) . If two-temperature plasma ef-fect is taken into account (Faucher-Gigu`ere & Quataert 2012), c (cid:13) , 1–12 X. Wang and A. Loeb then the proton cooling timescale t p can be expressed as: t p ≈ . × R , kpc L − , v / , v / , . yr , where v s , =( v s / km s − ) and L AGN , = ( L AGN / erg s − ) . Next we discuss the non-thermal emission from the outflow shockas it propagates in the ambient medium (Nims et al. 2015).
As the forward shock plows through the ambient medium super-sonically, a broken power-law distribution of non-thermal elec-trons N ( γ ) dγ ∝ γ − p (1 + γ/γ b ) − is generated via Fermi ac-celeration in the shock to produce non-thermal emission, where p is the power-law index. γ b is the break Lorentz factor, whichis obtained by equating the dynamical timescale ∼ R s /v s andthe cooling timescale m e c/ U B + U AGN + U CMB ) σ T γ . Thisgives γ b = 3 m e cv s / σ T R s ( U B + U AGN + U CMB ) , where m e is the electron mass, σ T is the Thomson scattering cross sectionand U B = B / π is the energy density of the magnetic field. Weassume that the total non-thermal luminosity is a fraction of the ki-netic energy of the swept-up material, written as L nt = ǫ nt L kin ≈ ǫ nt ˙ M s v . We calibrate the magnetic field energy density as a frac-tion ξ B of the thermal energy behind the shock in what followssupernova (SN) remnants (Chevalier 1998), giving: U B = ξ B nkT . (12)Observations of radio emitting bubbles from a radio-quiet quasarimply p ∼ (Harrison et al. 2015). By fitting the radio flux frombubbles at ∼ kpc, we obtain ǫ nt ∼ . Coefficients ξ B canbe estimated from observations of late-time radio emission fromrelativistic jets associated with tidal disruption events (Bower et al.2013), synchtrotron emission from shocks between jet and circum-nuclear medium (Metzger et al. 2012) as well as from an anal-ogy with SN remnants (Chevalier 1998). These observations imply ξ B ∼ . .Finally, we calculate the synchrotron emission following thestandard formula from (Pacholczyk 1970; Rybicki & Lightman1979). The emission and absorption coefficients are given by: j syn ν = c B Z γ max γ min F ( x ) N ( γ ) dγ , (13) α syn ν = − c B ν Z γ max γ min γ ddγ (cid:20) N ( γ ) γ (cid:21) F ( x ) dγ , (14)where c = √ e / πm e c , c = √ e / πm c , F ( x ) ≡ x R ∞ x K / ( ξ ) dξ and K / ( x ) is the modified Bessel func-tion of / order. The maximum Lorentz factor γ max is givenby the tighter constraint of equaling the acceleration timescale ξ acc R L c/v (Blandford & Eichler 1987) to either dynamical orcooling timescale, where ξ acc ∼ and R L = γm e c /eB is theLarmor radius. We plot γ max in unit of as a function of outflowshock radius R s for M halo = 10 M ⊙ , f d = 0 . and z = 1 . as a representative example, shown in Fig.2. γ max varies within afactor of ∼ as a result of simultaneously decreasing v s and softphoton energy density with increasing R s . We take the minimumLorentz factor γ min ∼ in our calculation. The synchrotron emis-sion peaks at a frequency of ν syn = 4 . × B − γ Hz , where γ = ( γ/ ) . Figure 2.
The maximum Lorentz factor of non-thermal electrons γ max in unit of as a function of outflow shock radius. We fix M halo =10 M ⊙ , f d = 0 . and z = 1 . as a representative example. The soft photons includes those from the accretion disk and CMB.The energy density of the AGN radiation field is U AGN ≈ . × − L AGN , R − , kpc erg cm − . The CMB photons have an en-ergy density of U CMB ∝ (1+ z ) , which manifests themselves as adominant source of IC scattering at high-redshift (Celotti & Fabian2004). The spectral energy distribution of quasars can be con-strained by observations (Elvis et al. 1994; Marconi et al. 2004;Scott & Stewart 2014). For simplicity, we approximate it as a blackbody spectrum (Ito et al. 2015). We model the CMB photons asa black body with a spectrum peak frequency of ν CMB ≈ . × (1 + z ) Hz. The peak of IC scattering of CMB photons takesplace at a frequency of ν IC ≈ γ ν CMB = 1 . × γ (1+ z ) Hz .The differential rate to produce high-energy photons with energy ǫm e c is given by (Jones 1968; Coppi & Blandford 1990): Q ( ǫ ) = Z dǫ n ( ǫ ) Z dγN ( γ ) K ( ǫ, γ, ǫ ) , (15)where ǫ m e c is the soft photon energy, γm e c is the electron en-ergy and n ( ǫ ) is the number density of soft photons. K ( ǫ, γ, ǫ ) is the Compton kernel, expressed as: K ( ǫ, γ, ǫ ) = 2 πr cγ ǫ [2 κ ln κ + (1 + 2 κ )(1 − κ )+ (4 ǫ γκ ) ǫ γκ ) (1 − κ )] , (16)where κ = ǫ/ [4 ǫ γ ( γ − ǫ )] . The emission coefficient of IC scat-tering can be obtained by: j IC ν = h π ǫQ ( ǫ ) , (17)where h is the Planck constant. In Figures 3–6, we show the dependence of outflow hydrodynamicssolutions and emissions on f d , M halo , z and density profile formu-lation. Since the gas distribution in the intergalactic medium (IGM)is uncertain, we restrict our calculation to halo scale within R vir . c (cid:13) , 1–12 robing gaseous galaxy halos As shown in panel a in Figures 3–6, we find that the swept-up shell decelerates quickly to a roughly constant velocity of ∼ km s − in the disk. As it propagates outside the galaxy intothe halo, the shell accelerates somewhat as a result of the tenu-ously distributed halo gas. The evolution of the shell velocity isconsistent with a self-similar solution, where the shell radius is as-sumed to follow R s ∝ t δ and v s ∝ t δ − . We express the gaspower-law density profile generally as ρ ∝ R γ . For γ < , weobtain M s ∝ R − γ . In the energy-conserving limit, we assumethat ∼ of the injected energy goes to the kinetic energy of theswept-up material, L in t = M s v , and so we have δ = 3 / (5 − γ ) .For power-law index α = 2 in our model, δ = 1 and thus v s ap-proaches a constant in the disk. We can also verify that for halocomponent power-law index β , the outflow accelerates as β > .The acceleration stops as the quasar shuts off and the thermal en-ergy in the shocked wind E t drives the expansion of the shell after-wards. At this point, the outflow reaches the edge of the dark matterhalo and is likely to continue to propagate into the IGM.Panels b and c in Figures 3–6 show the radio flux as a func-tion of shock radius and time, respectively. We scale the timeto the Hubble time t H , which is given by t H ≡ /H ( z ) = H − (cid:2) Ω m (1 + z ) + Ω Λ (cid:3) − / . The chance of finding a galaxywith a given flux is t/t H . We find that for z ∼ , about a few per-cent of the galaxy halos embed outflows reaching R vir . We also cal-ibrate the angular diameter of the outflow shock, given by R s /D A ,where D A is the angular distance.We show snapshots of non-thermal emission taken at twomilestones in panels e and f . At the edge of the galaxy disk, the en-ergy injection from the central source has an age of ∼ yrs. Atthe virial radius, snapshots are taken at the dead quasar remnantswith outflow approaching the edge of the dark matter halo on atimescale of ∼ yrs, which indicates that this population shouldbe ∼ times more abundant. At this point, the outflow no longeroverlaps with the galaxy and there is no galaxy-bubble interactions.We find that the outflows can reach the edge of the halo around theend of quasar’s lifetime. This feature indicates that AGN-drivenoutflows are most abundant during their passage through their hostgalaxy halo.We summarize the detectability of this extended non-thermalemission in Table 1. For a halo of mass M halo = 10 M ⊙ at z = 1 . , we choosethree representative values of f d as motivated by observations(Courtois et al. 2015). We find that the shell velocity is not sen-sitive to f d . The outflow reaches the edge of the halo aroundthe time the energy injection discontinues. With a velocity of ∼ − km s − , the outflow is likely to propagate into theIGM. The non-thermal radio flux at 1 GHz remains at ∼ . mJywithin the disk, independent of f d . As the shell propagates into thehalo, the non-thermal emission diminishes quicker in halos withhigher f d as a result of more tenuous halo gas. For f d = 0 . ,the radio emission is ∼ times fainter than the other two casesand drops below the detection limit of JVLA and
SKA before theoutflow reaches R vir . Observationally, we can distinguish galaxieswith high disk baryonic concentrations by the faint emission fromtheir outflows propagating in the halos. We examine M halo of M ⊙ , M ⊙ and M ⊙ , coveringthe full range from mid to high mass halos. In lower mass halos,the energy input into embedded outflows is much lower due to theself-consistent scaling relation between M • and M halo . The out-flow shock decelerates quicker and may not propagate farther out-side the galactic disks. The short lifetime of outflows in low massgalaxy halos makes them less abundant. Therefore, it would be ob-servationally challenging to identify outflows from low mass halosin terms of both emission intensity and recurrence rate. At z ∼ ,the emission is only detectable in radio band on galaxy scale with aflux ∼ µ Jy. High mass galaxies produce AGN photons of higherenergy density, making the detection more promising.
The hydrodynamics of outflows is insensitive to z . Consequently,outflows reach the edge of its host galaxy and halo at similar veloci-ties for different redshifts. At low redshift z ∼ . , the non-thermalemission is detectable in multiwavelength from radio to X-ray. Forhigh-redshift galaxies at z = 5 , the non-thermal emission is dom-inated by IC scattering off CMB photons. The emission remainsobservable in the radio, infrared and optical bands on halo scale. We compare the broken power-law profile to the gas density profileof galaxy clusters. We find that the outflow velocity and emissionindistinguishable for these gas density profiles. However, outflowscan not reach the edge of the halo for galaxy clusters, excludingthem from halo scale observations in these systems.
Another important dynamics issue is whether the outflow is mo-mentum or energy conserving. In the momentum-driven regime,thermal energy in the shocked wind region is efficiently radiatedaway, while in energy-driven outflows, such radiative losses are in-significant. We compare the timescale of the most efficient radiativecooling processes discussed in § t cool , withthe dynamical timescale of the outflow, given by t dyn = R s /v s , asshown in Fig. 7.The plot shows t cool /t dyn for several representative cases andindicates that for some cases the outflow starts propagating as par-tially momentum-driven. Once the shell reaches ∼
100 pc , thepartially momentum-driven regime breaks down and the shockedwind region no longer cools rapidly. At larger radii, the soft pho-ton energy density is dominated by CMB photons and t cool /t dyn decreases consequently. However, the energy conserving nature re-mains unchanged at larger radii, which is in agreement with re-cent observations (Tombesi et al. 2015) and theoretical calculations(Faucher-Gigu`ere & Quataert 2012; Zubovas & King 2012).These results suggest that most of the wind kinetic energy isconverted to the kinetic energy of the outflow, giving ˙ P / ˙ M s ∼ ˙ P / ˙ M in , where ˙ P rad = L AGN /c is the momentum flux ofAGN’s radiation field and ˙ M in is the mass injection rate of the windfrom the central source (Zubovas & King 2012). We can write themomentum flux of the outflow normalized to AGN’s radiation as ˙ P / ˙ P rad ∼ v in /v s . This relation is illustrated in panel d of Figures3-6. c (cid:13) , 1–12 X. Wang and A. Loeb
Figure 3.
Dependence of outflow hydrodynamics and emission on baryon fraction in the disk f d . We fix M halo = 10 M ⊙ and z = 1 . . Panel a and b show the shell velocity and radio synchrotron flux at 1 GHz as a function of radius. The dotted and dashed vertical lines mark the position of R disk and R vir ,respectively. The upper x-axis of panel b marks the angular diameter of the outflow shock. Panel c shows the radio synchrotron flux as a function of time. Thedashed vertical line corresponds to the point when the AGN shuts off. Time is scaled to the Hubble time t H on the upper x-axis. Panel d demonstrates themomentum flux boost of the shell. The solid lines represent the numerical result while the dashed lines correspond to predictions in the energy-driven regime.Panel e and f illustrate snapshots of non-thermal emission power and flux at R disk and R vir , respectively. The solid, dashed and dotted lines correspond tosynchrotron emission, IC scattering of accretion disk photons and CMB photons, respectively. c (cid:13) , 1–12 robing gaseous galaxy halos Figure 4.
Dependence of outflow hydrodynamics and emission on halo mass M halo . We fix f d = 0 . and z = 1 . . The configuration and physicalsignificance of the subplots are the same as Fig. 3. The dotted vertical lines marks the position of R disk for the three cases in panel a and b .c (cid:13) , 1–12 X. Wang and A. Loeb
Figure 5.
Dependence of outflow hydrodynamics and emission on redshift z . We fix M halo = 10 M ⊙ and f d = 0 . . The configuration and physicalsignificance of the subplots are the same as Fig. 3. The dotted vertical lines marks the position of R disk for the three cases in panel a and b . The right-handy-axis of panel e and f is scaled to a distance of Gpc. c (cid:13) , 1–12 robing gaseous galaxy halos Figure 6.
Dependence of outflow hydrodynamics and emission on gas density profile of galaxy clusters. We fix M halo = 10 M ⊙ and z = 1 . . We comparegalaxy cluster gas density profile with the broken power-law profile ( f d = 0 . ). The configuration and physical significance of the subplots are the same asFig. 3.c (cid:13) , 1–12 X. Wang and A. Loeb z = 0 . z = 1 . z = 5 . Telescopes F ν ( R disk ) ; F ν ( R vir ) detectability F ν ( R disk ) ; F ν ( R vir ) detectability F ν ( R disk ) ; F ν ( R vir ) detectability(mJy) (mJy) (mJy)JVLA 300 ; 0.8 Yes ; Yes 1.0 ; × − Yes ; Yes × − ; × − Yes ; MarginalSKA 300 ; 0.8 Yes ; Yes 1.0 ; × − Yes ; Yes × − ; × − Yes ; MarginalALMA 0.5 ; × − Yes ; Marginal × − ; × − Marginal ; No × − ; × − No ; NoJWST × − ; × − ∗ Yes ; Marginal × − ; × − ∗ Yes ; No × − ; × − No ; YesHST × − ; × − ∗ Yes ; No × − ; × − ∗ Marginal ; No × − ; × − No ; Marginal νF ν ( R disk ) ; νF ν ( R vir ) detectability νF ν ( R disk ) ; νF ν ( R vir ) detectability νF ν ( R disk ) ; νF ν ( R vir ) detecatbility( erg cm − s − ) ( erg cm − s − ) ( erg cm − s − )XMM-Newton − ; × − Marginal ; Marginal × − ; × − No ; No × − ; − No ; NoATHENA − ; × − Yes ; Yes × − ; × − No ; Marginal × − ; − No ; NoChandra × − ; × − No ; Marginal × − ; × − No ; No × − ; − No ; NoNuSTAR × − ; × − No ; No × − ; × − No ; No × − ; − No ; No
Table 1.
Detectability of non-thermal emission from AGN-driven outflow shock.Note: We choose M halo = 10 M ⊙ and f d = 0 . as a representative example for a galaxy halo. For radio, mm/sub-mm, infrared and opticalobservations, we provide values of F ν ( R disk ) and F ν ( R vir ) , which correspond to non-thermal flux at the edge of the disk and halo respectively, inunit of mJy. For X-ray observation, we present νF ν ( R disk ) and νF ν ( R vir ) , in unit of erg cm − s − .The telescope detection limits are as follows:– The Jansky Very Large Array (JVLA) : ∼ µ Jy for 1 σ detection and 12h integration time at most bands (NRAO 2014).– The Square Kilometer Array (SKA-MID) : ∼ . µ Jy RMS sensitivity for 10h integration time (Prandoni & Seymour 2014).–
The Atacama Large Millimeter/submillimeter Array (ALMA) : At observating frequency
GHz, the sensitivity ∼ . µ Jy for 10h integrationtime is calculated by the
ALMA
Sensitivity Calculator (ASC) (https://almascience.eso.org/proposing/sensitivity-calculator).–
The James Webb Space Telescope (JWST) : sensitivity ∼ nJy for wavelength − µ m and ∼ nJy for wavelength − µ m for 10 σ detectionand s integration time (STScI 2013).– Hubble Space Telescope (HST) : sensitivity ∼ − nJy for wavelength . − . µ m for 10 σ detection and s integration time (STScI2013).– Chandra : sensitivity of high resolution camera (HRC) ∼ × − erg cm − s − covering energy range . − keV for 3 σ detection and × s integration time (CXC 2014).– XMM-Newton : ∼ . × − erg cm − s − in . − . keV band (Hasinger et al. 2001).– Advanced Telescope for High Energy Astrophysics (ATHENA) : ∼ × − erg cm − s − in . − keV band in a s deep field(Barcons et al. 2012).– Nuclear Spectroscopic Telescope Array (NuStar) : ∼ × − erg cm − s − in − keV band for 3 σ detection and s integration time(Harrison et al. 2013).* The emission may be contaminated by scattered quasar light (see § We study the hydrodynamics of AGN-driven outflows out to galac-tic halo scales and the resulting non-thermal emission from the fastforward outflow shock propagating into the ambient medium. Wehave found that the outflow decelerates rapidly to a nearly constantvelocity of ∼ km s − within the galaxy disk and acceleratesonce it enters the halo until the central BH shuts off. Around thistime, the outflow can reach the edge of the halo. We have verifiedthat the outflow is energy-conserving on large radii, consistentlywith recent observations (Tombesi et al. 2015) and theoreticalpredictions (Faucher-Gigu`ere & Quataert 2012; Zubovas & King2012). The predicted non-thermal emission from outflow shocksin MW mass halos up to a redshift z of is detectable over abroad range of wavelengths. At z ∼ . , the ′ angular scaleemission is detectable by JVLA and
SKA in radio band,
ALMA inmm/sub-mm band,
JWST and
HST in optical and infrared bands,marginally detectable in X-ray band by
Chandra , XMM-Newton and
ATHENA . At z ∼ , the signal remains observable in radioband and marginally detectable in infrared and optical bands withan angular scale of ∼ ′′ . The detection is promising even at highredshifts ( z ∼ ) in the radio, infrared and optical bands with an angular scale of ∼ ′′ . For lower mass halos the detection shouldlimit within the local Universe.We find that the detailed gas distributions do not significantlyaffect the hydrodynamics of the outflow while the halo mass playsa more important role in regulating the outflow dynamics. Weshow a near universality of the non-thermal emission within thegalaxy disk for different gas distributions of galaxies with samehalo masses, which breaks down on the halo scale as a result ofdistinct density profile for tenuous halo gas. The halo mass deter-mines the intensity of the emission since the BH mass is scaledself-consistently with halo mass. Consequently, non-thermal emis-sion from outflows embedded in low mass halos is ∼ − ordersof magnitude fainter than that in MW mass halos. We conclude thatthe halo mass is the dominant factor in regulating the dynamics andemission of the outflow. In order to distinguish between differentgas density distributions, halo scale observations are required.The predicted non-thermal emission should be an observa-tional signature of the existence of extended gas in galaxy halos ina wide range of redshifts. With this method, one can probe the evo-lution of gaseous halos at early cosmic times. Thermal X-ray emis-sion from free-free cooling at the forward wind shock was proposedto be an observational signature of kpc-scale outflows powered by c (cid:13) , 1–12 robing gaseous galaxy halos Figure 7.
Ratio of radiative cooling timescale in the shocked wind region tooutflow’s dynamical time. The default values of the parameters are: f d =0 . , M halo = 10 M ⊙ and z = 1 . . Each line represents a specificparameter modified from its default value while the other parameters arefixed at the default values. The dotted line separates the momentum andenergy conserving regimes. AGN (Nims et al. 2015). The predicted thermal X-ray luminosityat 1keV band is smaller than our non-thermal X-ray prediction anddinimishes with increasing outflow shock radius given our assump-tion about the gas density profile in the galaxy and halo. Since thetravel time of the outflow shocks is comparable to AGN’s lifetime,most of the detected halos still host an active quasar, targets canbe selected for observations as an AGN. On the other hand, sub-traction of the much brighter emission from the AGN is requiredto measure the extended diffuse emission from the outflow shocks.Radio interferometry can resolve the luminous central source andsubtract emission from it to obtain the extended emission on haloscale. For optical and infrared observations, the extended emissioncan be subtracted using techniques similar to the removal of quasarlight in
HST images (McLeod & Rieke 1995; Bahcall et al. 1997).A source of contamination to the extended non-thermal emis-sion is the scattered quasar light by the surrounding electrons in thehalo (Wise & Sarazin 1990; Young 2000; Holder & Loeb 2004).We find that the optical depth for Thomson scattering throughthe halo is ∼ − , so ∼ − of the observed flux from theAGN is expected to diffuse throughout the halo. For a M ⊙ mass halo, the bolometric luminosity of the scattered radiation is ∼ erg s − , which is comparable to the non-thermal emissionat infrared and optical frequencies from outflow shocks in haloswithin z . and negligible for halos at z ∼ . One possible wayto distinguish the scattered radiation from the non-thermal emis-sion is by polarimetric measurement. Additionally, the scatteredlight is diffused throughout the halo at any given time while theemission from outflow shocks shows a discontinuity at the shockfront. As the outflow propagates farther into the halo, the scatteredquasar light no longer exists as the quasar fades away. There isno contamination from scattered AGN photons in radio band fromradio-quiet quasars, which takes up ∼ of the population, sothe non-thermal emission can be more easily identified in radiowavelength (Nims et al. 2015). Therefore, radio observation is ex-pected to be most effective in detecting the halo scale non-thermalemission from outflows in a wide range of redshifts. It should benoted that the predicted radio emission from outflow shocks exists without the presence of relativistic jets, which account for the radioemission from radio galaxies (Heckman & Best 2014).There are a few uncertainties in our model. First, sphericalsymmetry of both gas distribution and outflow shell is likely to beunrealistic. In fact, the outflow may be collimated from the start orcan propagate along the path of least resistance, forming a bipo-lar or bicone structure. Observations of kpc-scale molecular out-flows suggest a wide-angle biconical geometry (Rupke & Veilleux2011; Feruglio et al. 2015). Biconical outflows with small open-ing angle could have less impact on the ambient medium. Second,the detailed gas distribution is uncertain and can be complicatedby galaxy-to-galaxy variations, which can greatly dependend ongalaxy types as well as the specific gas phase. Finally, we find thatthe terminal velocity of the outflow arriving at the edge of the halois ∼ km s − , which is still large enough for farther propaga-tion of the outflow into the IGM. The propagation dynamics of theoutflow into the IGM is beyond the scope of this paper. Along somedirections gas accretion onto the galaxy could impede the develop-ing outflow (Suresh et al. 2015). ACKNOWLEDGEMENTS
We thank Mark Reid and Lorenzo Sironi for helpful commentson the manuscript. This work was supported in part by NSF grantAST-1312034.
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