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Mon.Not.R.Astron.Soc.000,000–000 (2008) Printed4January2012 (MNLATEXstylefilev2.2) Measures of cosmic-ray energy densities in galaxies Massimo Persic1,2, Yoel Rephaeli3,4 1INAF/Osservatorio Astronomico di Trieste, viaG.B.Tiepolo 11, I-34143 Trieste,Italy 2 2INFN Sezione di Trieste,Trieste,Italy 1 3School of Physics & Astronomy, Tel Aviv University,TelAviv 69978, Israel 0 4Centerfor Astrophysics and Space Sciences, Universityof California at San Diego, La Jolla, CA 92093, USA 2 n a Accepted .............Received............;inoriginalform............ J 1 ABSTRACT ] E The energy density of cosmic ray protons (CRp) in star-forming galaxies can H be estimated from (i) π0-decay γ-ray emission, (ii) synchrotron radio emission, and . h (iii) supernova rates. For most of the galaxies for which values of all these quanti- p ties are known, the three methods yield consistent energy density estimates, ranging - fromO(10−1)eVcm−3 ingalaxieswithlowstar-formationrates,toO(102)eVcm−3 in o galaxies with high star-formationrates.The only cases for which the methods do not r t agree are the composite starburst/Seyfert2 galaxy NGC1068, whose γ-ray emission s a originatesinblack-holeaccretionratherthanstarformation,andtheSmallMagellanic [ Cloud, where the discrepancy between measured and estimated CRp energy density may be due to a small CR confinement volume. 1 v Keywords: Galaxies:cosmicrays–Galaxies:gamma-ray–Galaxies:spiral–Galax- 9 ies: star formation 6 3 0 . 1 1 INTRODUCTION Longair 1994 – but see Beck & Krause 2005 for a critical 0 view). 2 1 Activestarformation ingalaxiesleadstoproductionofcos- The equipartition assumption enables deduction of the : mic ray protons and electrons (CRp, CRe) via the Fermi-I CRp energy density in star forming galaxies, Up (the main v diffusive shock acceleration mechanism in supernova (SN) contributiontotheparticleenergydensity),indirectlyfrom Xi remnants (Fermi 1954; Ginzburg & Syrovatskii 1964; Bell the electron energy density (from radio synchrotron mea- 1978; Protheroe & Clay 2004). surements) if a theoretically motivated injection proton-to- r a Timescales of starburst (SB) activity in galaxies are elecron (p/e) ratio is assumed. comparable to galactic dynamical timescales, τSB ∼τdyn ∼ Another way to derive Up is based on measuring the 108yr.Ontheotherhand,in aSBregion thecharacteristic GeV-TeV γ-ray emission, which is largely from CRp inter- timescales for protons togain energy (bythe Fermi-I accel- actions with ambient gas protons, which produce neutral eration process), andtoloseit bycollisions with thermally- (π0) and charged pions; π0 decays into γ-rays. So γ-ray distributed protons (leading to pion production and decay) measurements provide a direct measurement of U . Only p andadvection, areτ+ τ− 105 yr.Indeed,assuming the recently have such measurements been possible for star- Fermi-Iprocesstobea∼twork∼inaSNremnant,τ+ E/E˙ = forming galaxies – and only for a handful of sources (see (∆E/E)−1∆t = β−1∆t = (10/β0.1)∆t 105y≡r, where below). ∆t 104yrisatypicalSNremnantlifetim∼e,andβ0.1 isthe Third, since energy-loss timescales are shorter than ∼ speed of the SN ejecta in units of 0.1c. The main energy- star-formationtimescales,U canbeestimatedfromtheob- p losstimescaleislargelydeterminedbytheSN-drivenoutflow served rate of core-collapse SN and the deduced residency emanatingfromtheSBregion,i.e.τ− τout 105yr;thus, timeofCRpintheinsterstellarmedium–onceafractionof ∼ ∼ τ+ τ− <<τSB. SNkineticenergythatischanneledintoparticleacceleration ∼ The respective lengths of these timescales suggest that has been assumed. ingalaxies, duringtypicalepisodesofstarformation, abal- This paper describes measures of galactic CR energy ancecanbeachievedbyCRbetweenenergygainsandlosses. densities based on the methods outlined above. Although Underbasichydrostaticandvirialequilibriumconditionsin not strictly independent, these methods are based on very agalaxy, aminimum-energyconfiguration of magnetic field different observables to estimate U : radio emission, HEγ- p andCRmaybeattained;thisisequivalenttohavingCRand rayemission, andtherateofcore-collapse SN.Wefindthat magnetic fields in (approximate) energy equipartition (e.g., thethreemethodsyieldconsistentresultsonU forasample p 2 Persic & Rephaeli of 10 galaxies with widely varying levels of star formation CRe lose energy via Coulomb scattering for γ <γ and via 1 activity from quiescent to intense starbursts. These are the synchrotron cooling for γ >γ . 1 only galaxies for which γ-ray data (plus radio data and SN (ii) We assume equipartition between the energy densities rates) are available (seeTable1).Afterreviewing theradio, ofparticles(CRelectronsandprotons)andmagneticfields, γ-ray, and SN methods (sect.2,3,4), the corresponding val- U + U = B2/8π. This condition may actually be at- p e uesofU arepresentedinsection5.Theresultsarediscussed tained by strong coupling between all the relevant degrees p in section 6 and summarized in section 7. offreedom intheSBregion. Intermsof theCRp/eenergy density ratio, κ, the particle-field equipartition condition is U [1+(1+χ)/κ]=B2/8π, so that p 2 PARTICLES AND MAGNETIC FIELDS 2 7.44 10−21 κ γ2−q250q/2ψ 5+q CRe populations consist of primary (directly accelerated) B = × 1+ 1 . (7) (cid:20) 1+χ 1+χ (q 2) a(q) (cid:21) and secondary (produced via π± decays) electrons. While (cid:2) (cid:3) − the exact form of the steady-state CRe energy spectrum is Inserting Eq.(7) into Eq.(5) we get (dγ) γ2(9−q)/(5+q). notasinglepowerlaw,athighenergiestheflatteningofthe dt syn ∝ 1 Oncethevalueofn isspecified(seeTable1),byequating e,th spectrum due to Coulomb losses can be ignored, justifying Eqs.(5,6) we deduceγ . 1 theuseof theapproximatesingle power-law form. Let then The secondary-to-primary electron ratio χ, which ap- thecombined(primaryplussecondary)CRespectraldensity pearsinEqs.(7),dependsontheinjectionp/enumberratio, distribution bea single power-law rp/e=(mp/me)(qinj−1)/2(seeAppendix),andonthegasop- N (γ) = N (1+χ) γ−q, (1) tical thickness to p-p interactions. Proton-proton (p-p) col- e e,0 lisionsleadtothetheproductionofchargedandneutralpi- wγ2h,eNree,t0hiesealencotrrmonalLizoarteinotnzffaaccttoorroγftisheinptrhimeararyngeeleγct1r≤onγs,≤χ ofonlslo.wAendebleyctµro−nisper−od+ucνeµd+inν¯the.eGdeivcaeynπth−e→brµa−nc+hiνnµg+rν¯ae- is the secondary-to-primary electron ratio, and q 2 is the tiosinp-pcollisio→ns, onlyathirdofthesecollisionsproduce ≥ spectral index (the equality holds in the strong-shock limit electrons. The mean free path of CR protons in a medium of the Fermi-I acceleration process). of density n due to p-p interactions is λ = (σ n )−1; p pp pp p Ignoring the contribution of low-energy electrons with for protons with kinetic energy T fewTeV the cross sec- χγ)m<ecγ21,γγt12heγ1e−lqedctγr,ownheenreerγg2yisdeannsiutyppiesrUcueto=ff wNheo,0se(1ex+- 1ti9o8n4)i.sFσoprpa≃typ5i0camlbSB=am5b×ie1n0t−g2a6s∼cdme2ns(itByanltpru≃sa1it5i0scemt−a3l., act valueRis irrelevant in the the limit of interest γ2 >>γ1. λpp 43kpc. The probability for a single CR proton to ∼ For q>2 and γ2 >>γ1, undergo a pp interaction in its 3D random walk through a region of radius r 0.25kpc (also typical of SB nuclei) Ue ≃Ne,0(1+χ)mec2γ12−q/(q−2). (2) is then √3rs/λpps ∼0.01. We then estimate that in typi- ≃ ForapopulationofelectronsdescribedbyEq.(1),traversing calSBenvironments,characterizedbyrelativelystrongnon- ahomogeneousmagneticfieldofstrengthBinaregionwith relativistic shocks(qinj=2.2, seeAppendix),thesecondary a(andspehmeritictainllgyaeq1uGivHalzensty)nrcahdrioutsrorns lroacdaitaetdionatflauxdisotfafn1ceGHdz, tqouipesrcimenatryenevleircotrnomnernattsi,owisithχ t=ypχic0a√l3va(rlus/eλspnp)p ≃≃01.3c.mF−o3r Jy,standard theory yields and rs 2.5kpc, we find χ 0.03. The higher value found ∼ ≃ for starbursts is in approximate agreement with results of Ne,0(1+χ) = 5.72 10−15 ψ a(q)−1 B−q+21 250q−21 (3) detailed numerical starburst models for energies > 10MeV × (plottedin,e.g.,Paglioneetal.1996;Torres2004;∼Domingo- where a(q) is defined and tabulated in, e.g., Tucker (1975) and ψ is defined as ψ ( rs )−3( d )2(f1GHz). From Santamar´ıa & Torres 2005; De Cea et al. 2009; Rephaeli et ≡ 0.1kpc Mpc Jy al. 2010). Eqs.(2, 3) we then derive To compute the CR p/e energy density, κ (see Ap- Ue ≃ (12+.96χ) ×10−22250q2 ψ (q γ1−2q)+a2(q)B−q+21 . (4) pcleens:di(xi)),thweeealesscutrmone sppoewcetrr-allawindsepxecqteraisfdoredtuhceedCfRrompartthie- − measured synchrotron radiation index α, according to the In order tocompute U from Eq.(4) we need to specify e standard formula q = 2α+1; and (ii) the proton spec- γ and B. To do so we make thefollowing assumptions: e 1 tral index is assumed to be close to the injection value, (i) We assume that the low-energy limit of the electron q q 2.1 2.2, for the dense, CR-producing, SB power-lawspectrum,γ1,marksthetransition(fordecreasing epnv∼ironminjen≃ts host−ed in the central regions of some galax- energy)fromCoulomb((Gould1972;Rephaeli1979)tosyn- ies, and equal to the leaky-box value, q = q +δ 2.7 chrotronlosses.Foranelectronofenergyγ,thesynchrotron p inj ≃ (whereδ 0.5isthediffusionindex)formoretenuous,CR- loss rate is ≃ diffusing, quietly star forming galaxies. Values of κ for our dγ B 2 sample galaxies are reported in Section5. = 1.30 10−21γ2 s−1 (5) − dt syn × (cid:18)µG(cid:19) Finally, we obtain an explicit expression for Up: (cid:0) (cid:1) whereas theCoulomb loss rate is 1 1+χ −1 U = 1+ dγ ln(γ/n ) p 8π (cid:20) κ (cid:21) × = 1.2 10−12n 1.0+ e,th s−1.(6) − dt coul × e,th (cid:20) 75 (cid:21) 4 (cid:0) (cid:1) 7.44 10−21 κ γ2−q250q/2ψ 5+q × 1+ 1 . (8) (Rephaeli1979; Sarazin1999).Wethensimplyassumethat × (cid:20) 1+χ 1+χ (q 2) a(q) (cid:21) (cid:2) (cid:3) − Measures of cosmic-ray energy densities in galaxies 3 Table 1.Star-forminggalaxies:thedata. Object DL[1] rs[2] f1[3G]Hz α[N4T] n[e5,]th L[T6I]R SFR[7] νS[8N] Mg[9a]s L[γ10] τr[e1s1] Notes (Mpc) (kpc) (Jy) (cm−3) (erg/s) (M⊙/yr) (yr−1) (M⊙) (erg/s) (yr) Arp220 74.7 0.25 0.3 0.65 300 45.75 253 3.5 9.24+0.10 <42.25 9.0E+3 SB −0.11 M82 3.4 0.26 10.0 0.71 200 44.26 8.2 0.25 9.37+0.09 40.21+0.10 2.6E+3 SB −0.14 −0.13 NGC253 2.5 0.20 5.6 0.75 400 44.23 7.7 0.12 9.20+0.10 39.76+0.14 2.0E+4 SB −0.11 −0.19 MilkyWay – 4.4 – – 0.01 43.75 2.5 0.02 9.81+0.12 38.91+0.12 2.7E+7 quiescent −0.16 −0.15 M31 0.78 5.17 4.8 0.88 0.01 42.98 0.43 0.01 9.88+0.11 38.66+0.09 4.0E+7 quiescent −0.15 −0.10 M33 0.85 2.79 3.30 0.95 0.03 42.68 0.22 0.003 9.35+0.13 <38.54 2.6E+7 quiescent −0.19 LMC 0.049 3.0 285.0 0.84 0.01 42.45 0.16 0.002 8.86+0.12 37.67+0.05 1.0E+7 quiescent −0.18 −0.05 SMC 0.061 1.53 45.3 0.85 0.01 41.45 0.01 0.001 8.66+0.03 37.04+0.11 4.0E+7 quiescent −0.06 −0.14 NGC4945 3.7 0.22 5.5 0.57 300 44.02 4.7 0.1-0.5 9.64+0.10 40.30+0.12 4.6E+4 SB+Sy2 −0.40 −0.16 NGC1068 16.7 1.18 6.6 0.75 300 45.05 50 0.2-0.4 9.71+0.11 41.32+0.15 1.0E+6 SB+Sy2 −0.19 −0.23 [1]Distance(fromAbdoetal.2011). [2]Effectiveradiusofstar-formingregion.Seetext. DataarefromPersic&Rephaeli2010andrefs.therein(Arp220,M82,NGC253), Beck&Gräve1982(M31),Tabatabaei etal.2007(M33),Weinberg&Nikolaev2001(LMC),Wilkeetal.2003(SMC),Moorwood& Oliva1994(NGC4945), Spinoglioetal.2005(NGC1068). [3]1GHzfluxdensity.DataarefromPersic&Rephaeli 2010andrefs.therein(Arp220,M82,NGC253)), Beck&Gräve1982(M31), Tabatabaei etal.2007(M33),Kleinetal.1989(LMC),Haynes etal.1991(SMC),Elmouttieetal.1997(NGC4945), Ku¨hretal.1981 (NGC1068). [4]Non-thermalspectralradioindex.DataarefromPersic&Rephaeli2010andrefs.therein(Arp220,M82,NGC253), Beck&Gräve 1982(M31), Tabatabaei etal.2007(M33),Kleinetal.1989(LMC),Haynesetal.1991(SMC),Elmouttieetal.1997(NGC4945), Ku¨hretal.1981(NGC1068). [5]Thermalelectrondensity. DataarefromRoyetal.2010(Arp220), Petuchowski etal.1994(M82),Kewleyetal.2000andCarralet al.1994(NGC253),Cox2005(MilkyWay), Beck2000(M31),Jabatabaei etal.2008(M33),Pointsetal.2001(LMC),Sasakietal. 2002(SMC),Spoonetal.2000(NGC4945), Kewleyetal.2000(NGC1068). [6]TotalIR[i.e.,(8−1000)µm] luminosity,inlog(fromAbdoetal.2011). [7]Starformationrate,fromSFR=LIR/(2.2×1043erg/s)(Kennicutt1998). [8]Core-collapseSNrate.DataarefromPersic&Rephaeli2010andreferencestherein(Arp220,M82,NGC253),Diehletal.2006 (MilkyWay), vandenBergh&Tammann1991(M31,M33,SMC,LMC;seealsoPavlidou&Fields2001), Lenainetal.2010and referencestherein(NGC4945,NGC1068).ForNGC1068wealsocomputedanupperlimittotheSNrate(νSN≤0.39)usingMannucci etal.’s(2003)formulaνSN=(2.4±0.1)×10−2[LFIR/(1010L⊙)]yr−1,beingfFIR=1.26×10−11(2.58f60+f100)ergcm−2s−1 (see Helouetal.1988)withf60≃190Jyandf100≃277Jy. [9]Gasmass(neutralplusmolecularhydrogen:MHI+MH2),inlog.Dataarefrom:Torres2004forArp220;Abdoetal.2010aforM82, NGC253,andtheMilkyWay; Abdoetal.2010bforM31andM33;Abdoetal.2010cfortheLMC;Abdoetal.2010dfortheSMC; andLenainetal.2010forNGC4945andNGC1068. [10]High-energy(>100MeV)γ-rayluminosity,inlog(fromAbdoetal.2011). [11]CRpresidencytime. Using Eq.(8), numerical values of U can be obtained from clespectrumisassumed tohavethenon-relativisticstrong- p therelevantobservationalquantitiesforoursamplegalaxies shockindexq=2.AtheoreticalN /N ratio,predictedfrom p e (see Table1); thesevalues are reported in Table2. chargeneutralityoftheinjectedCR,islikelytoholdinthis sourceregion–asisalsotheassumptionofequipartition.A measured radio index α 0.75 in the source region implies ≃ q = 2α+1 2.5 there. This indicates a substantial steep- ≃ 3 ESTIMATING UP FROM γ-RAY EMISSION ening of the CRe spectrum from the injection value q0 = 2 due to diffusion (D γ−δ) effects that cause the steady- Inthissectionwewillreviewsomebasicfeaturesofthemod- ∝ state particle spectral index to be q +δ above some break 0 eling of γ-ray emission from star-forming galaxies, and the energy.Asanexample,thesteady-stateelectronandproton statusof HE/VHEγ-rayobservations. Detectionsof several spectraintheSBregionofNGC253areshowninFig.1.At suchgalaxieshaveenabledmeasurementsofU valueseither p low energies both spectra are flatter, whereas at E >> 1 in SBcores or throughout thedisk. GeV the stronger electron losses result in steeper electron In most SB galaxies, such as thetwo nearby onesM82 spectra. and NGC253, the central SB region (also called the source region) with a radius of 200 300pc, is identified as the Adopting the convection-diffusion model for energetic ∼ − main site of particle acceleration. Here, the injection parti- electron and proton propagation and accounting for all the 4 Persic & Rephaeli emission from p-p–inducedπ0 decay is 10−5 L,[≥q]E = Z g≥[qE] ngas Up dV s−1 (9) V −1−3Density (GeV cm)10−10 kbawtneiotomhdwe)ntt−he1ear(mneidnVint/eetcgdhmr,ea3olp)n−eacmr1etii(scLDslei≥rvuǫistrtyyaenaegddt≥[ηyǫa]n-slgi.tnaa1st(9uer9n)4ei)tna.sreTerogfhyoepbrhdseefoiosrttvroreanitbUsiuo−pnt1iac(olHanlnys- Particle 10−15 hdaiffvuesbioenenmnoudmelerfiocralClyRweoarnkeddCoRutpbpyrsooplavginagtiothne. cBoynvitesctvioerny- nature,this is a direct measurement of U . p The two local SB galaxies M82 and NGC253 are the 10−20 only non-AGN extragalactic sources that have so far been detected in both the GeV (Abdo et al. 2010a) and TeV 10−2 10−1 100 101 102 103 104 E (Gev) (Acciari et al. 2009; Acero et al. 2009) regions. The mea- Figure 1.Properties of the emitting particles inthe central SB sured fluxes and spectra of both galaxies in the two bands region of NGC253 (Rephaeli et al. 2010): steady-state spectra agree with predictions of recent numerical models in which ofprimary(solidline)andsecondary(dot-dashedline)electrons, Up = (102)eVcm−3 in the SB nucleus. The highest-SFR O andofprotons(dashedline). galaxy in the nearby universe, Arp220, was undetected by MAGIC (Albert et al. 2007). HEγ-raydetectionswereobtainedwiththeLargeArea Telescope (LAT) on board the orbiting Fermi telescope for 10−4 a number of low-SFR galaxies: (i) the Andromeda galaxy M31 (Abdo et al. 2010b), with U 0.35eVcm−3; (ii) 10−6 p ≃ the Large Magellanic Cloud (LMC) whose average spec- −1−2−1Flux (GeV cm s)111000−−−11820 et2toert0fug1a3rm0l0a.c,tD)2ee;d0oi(t1rihsa0ipeidd)reu)c;twsth,arieutnyhmdiSemol(dirinasvwdl)lUiicttMpahhteao≃egusceto0ltml.tha2hanpe−tiocbsU0irCtp.i3egl≃oheSuVtB0ds.c/1tm(Sa5Ser−eM-yVf3foCer(cr)mAmt,-ib2−wnd3gghoao(rlAseeaetgxbiiioadnenlos-. NGC1068andNGC4945(Lenainetal.2010).Onlyfluxup- 10−14 perlimitsexistfortheTriangulumgalaxyM33(Abdoetal. 10−16 2010b). For the Milky Way, the modeling of the Galactic dif- 10−18 fuseHEemission alongthelinesoutlinedabovesuggestsan 10−3 10−2 10−1 10E0γ (Gev) 101 102 103 aavl.er2a0g1e1)U.pT≃his1ecVomcmpa−r3es(SwtirtohngUet1ale.V20c1m0−;3Amckeearsmuarendnaett Figure 2.Properties of the emitted radiation inthe central SB Earth (e.g., Webber1987), and wpi∼th (6 3)eVcm−3 in the region of NGC253 (Rephaeli et al. 2010): radiative yields from ± 200pc region of the Galactic Center, as inferred from the electron Compton scattering off the FIR radiation field (dotted ∼ line),electronbremsstrahlungoffambientprotons(dashed line), measured VHEγ-ray emission (based on HESS data: Aha- π0 decay following p-p collisions (dashed-dotted line), and their ronian et al. 2006). sum(solidline). TheU valuesestimatedfromanalysisofGeV-TeVob- p servations are reported in Table2. relevant hadronic and leptonic processes, the steady-state energy distributions of these particles, in both the (active) SB nucleus and the (passive) disk of these galaxies, can be 4 ESTIMATING UP FROM SN RATES determinedwithadetailednumericaltreatmentoncethegas Combining the SN frequency with the residency timescale, distribution is known (e.g., Torres 2004; Persic, Rephaeli & τ , of CR protons that give rise to TeV emission in the res Arieli 2008; Rephaeli, Arieli & Persic 2010). star-forming region, and assuming a bona-fide value of the The relevant electron energy loss processes are energythatgoesintoacceleratingCRparticlesperSNevent, bremsstrahlung, Compton, and synchrotron, whereas for we can obtain a second estimate of U that stems from the protons the main losses are γ-ray emission from π0 decay p link between CR and core-collapse SN. following p-p collisions (see Fig.2); bremsstrahlung losses Thevalueofτ isdeterminedfrom thoseof twoother dominate at lower energies, whereas π0-decay losses domi- res timescales: nateat higherenergies. In theGeV-TeVregion, emission is (i) energy-loss timescale for p-p interactions, τ = mainly from p-p–inducedπ0 decay. (σ cn )−1that,forprotonswithkineticenergyE> 1p0pTeV pp p Theprocedureissimilarwhenstarformationisnotun- for which σ 50mb, can bewritten as ∼ pp dergoing a burst confined to the nuclear region but occurs ≃ throughout thewhole disk. τ 2 105 np −1 yr; (10) For a source with gas number density n , proton en- pp ∼ × 100cm−3 gas (cid:0) (cid:1) ergy density U , and volume V, the integrated hadronic (ii) CRp advection timescale, τ , that characterizes the p out Measures of cosmic-ray energy densities in galaxies 5 removal of CR out of the disk mid-plane region in a fast whichthewindbreaksout,tocomputeτ 9 103yr(be- adv (v 2500kms−1 for M82: Chevalier & Clegg 1985; ing n 102cm−3; and using thelatter and≃ν ×=3.5yr−1 out p SN Seaqui∼st&Odegard1991;Strickland&Heckman2009)SB- in Eq.(≃13), we get U 515eVcm−3 (SN method). p ≈ driven wind, which for a homogeneous distribution of SNe M82. Following Persic etal. (2008; and referencestherein) within theSB nucleusof radius r is s wetakethecentralSBtobearegionwitharadiusof300pc τout = 3×104 0.3rkspc 2500vkoumt s−1 −1 yr. (11) aranddioheeimghistsioofn20h0aspfc,henc=er1s0=Jy26a0npdcα,who0s.7e1n.oTnh-tehelartmtearl (cid:0) (cid:1) (cid:0) (cid:1) 1GHz ≃ (Both timescales are normalized to typical SB conditions.) impliesq 2.42,thatyieldsa 0.09;assumingqp =2.2,we ≃ ≃ Thus, then compute κ 60. From Eqs.(6) and (5), and the value ≃ of n reported in Table1, we derive γ = 4724. From τr−es1 = τp−p1(nHI)+τo−u1t(rs,vout). (12) Eq.(8e,)thwe then obtain B 91µG and Up1 201eVcm−3 During τres, a number νSNτres of SN explode and de- in the SBnucleus (radio m≈ethod). Because ν≈SN =0.25yr−1 pSNosi(tWthooeskleiyne&ticWeenaevregry1o9f95t)h,eiinrteojetchtea,inEteerjst=ell1a0r51meerdgiupmer. aSnBdnτurcelseu∼s,τaonutd≃vou3t×120540y0r k(tmaksi−n1g;nsepe∼Pe1r0si2ccm&−R3eipnhatehlei Arguments based on the CR energy budget in the Galaxy 2010),from Eq.(13)w∼egetUp 95eVcm−3 (SNmethod); ≈ and SN statistics suggest that a fraction η 0.05 0.1 of NGC253. Following Rephaeli et al. (2010, and references ∼ − this energy is available for accelerating particles (e.g., Hig- therein) we assume r = 200pc, f = 5.6Jy, and α s 1GHz ≃ don et al. 1998; Tatischeff 2008). Accordingly, we express 0.75. The latter implies q 2.50, hence a=0.0852; assum- ≃ theCRp energy density as ing q =2.2, we get κ 76. From Eqs.(6) and (5), and the p ≃ valueofn reportedinTable1,wederiveγ =7886.From Up = 85 0.3νSyNr−1 3×τ1re0s4yr 0.η05 10E51eejrg (cid:0)0.3rkspc(cid:1)−3 tEhqe.(s8t)arwbeuer,tsththennuocbletuasin(rBad≈io7m7eµthGodan).dBUeipn≈gν1145=eV0c.1m2−y3r−in1 eV cm−3. (13) and τ τ 3 104yr (being n 102SNcm−3, in the res out p starburst∼nucleu≃s, an×d v 2500 km∼s−1; see Persic & out Rephaeli 2010), we get U ∼75eVcm−3 (SN method); p 5 VALUES OF U IN GALAXIES ≈ P Milky Way. Measurements of Galactic CR indicate U p ≃ In SB galaxies star formation activity is intense in a rel- 1eV at the Sun’s position. The Galactic CRp flux mea- atively small nuclear region, in addition to quiescent, low- sured locally is the result of the superposition of parti- intensity star formation throughout the rest of the galactic cles, accelerated in several sites scattered throughout the disk(whichischaracteristicofnon-SBspiralgalaxies).This Galaxy, that have diffused out into the disk. Accordingly, is the case, for example, in the nearby M82 and NGC253. we view the entire Galaxy as the region where SN oc- ThestarformationrateinthenuclearSBregioncanbesuf- cur, and adopt 15kpc and a thickness of 0.5kpc, so that ficiently high that the main contribution to theCR density rs = 4.4kpc, τres 2 107yr (with np 1cm−3), and comesfrom acceleration (bySNshocks)inthisregion,with νSN = 0.02yr−1, le∼ading×to Up 1eVcm−∼3 (SN method). ≈ radial extent r . The rest of the disk can then be viewed as Alternatively,ifwedirectlycompareourSN-basedestimate s targettothediffusingCR.Innon-SBspiralgalaxies,e.g.the to available measurements of the innermost Galactic re- MilkyWayandtheTriangulumgalaxyM33,starformation gion, we need to estimate the relevant quantities in a nu- proceeds throughout the disk, where both CR sources and clear region with rs = 0.2kpc. The most prominent large- targetgascloudsaredistributed;inthiscase,r isessentially scale distribution of HI gas in the Galaxy is an exponential s thedisk radius. disk with Rd = 3.75kpc coplanar to the stellar disk with For the sample of galaxies detected in γ-rays with nHI = 1cm−3 in the solar neighborhood, i.e. at a Galacto- Fermi/LAT(seeTable1),valuesofUpwerededuceddirectly centric distance R0 = 8kpc (Dehnen & Binney 1998): this bymodellingtheobservedγ-rayemission.UsingEq.(8)and implies that the average density within rs is n¯HI 8cm−3, ≃ Ediqo.(e1m3)is,swioennforwomprCoRvideeleecsttriomnastaensdofthUepsftraotmistmicesaosfuSreNderxa-- rhaetnec,eντSpNp==02.0.52×yr−1016(yDriethhlereet. aTl.he20f0u6ll),dsishkouGldalasicmtiiclaSrlNy plosions. be rescaled to the rs region: In an exponential disk with R =2.5kpc (Dehnen & Binney 1998), r contains 0.3% of Arp220. The starburst activity takes place in a central d s thetotalmass;consequently,ν =0.6 10−4yr−1,leading molecular-gas diskofradius480pcandthickness90pcthat SN accounts for SFR 120M⊙yr−1, and embeds (at a galac- to Up ≈5eVcm−3 (SN method). × ∼ tocentric distance of 200pc) two extreme starburst nuclei M31.Withanaveragevalueofthespectralindex,α=0.88, of radii 68pc and 110pc that account for SFR= 50 and and the (nonthermal) flux (at 2.7 GHz) reported by Beck 35M⊙yr−1, respectively. This scheme, derived from Torres & Gräve (1982), we deduce f1GHz = 4.8Jy, averaged over (2004) and using Eq.4 of Kennicutt (1998), is consistent 19.2kpcradius.Thelattercorrespondsto 3.34exponential with the galaxy-wide IR-inferred SFR 225M⊙yr−1. For length scales (Rd =5.75kpc,averaging VR∼Idatafrom Hou ∼ thediskaloneweassumer 0.25kpc,f 0.3Jy,and etal.2009),i.e.thecorrespondingvolumeencloses 85%of s 1GHz ≃ ≃ ∼ α 0.65, which implies q = 2.30, and hence a 0.09; the mass of the exponential disk, hence most of the stellar e ≃ ≃ assuming q = 2.2 leads to κ 38. From Eqs.(6) and distribution. With an assumed thickness of 0.5kpc, we get p ≃ (5), and the value of n reported in Table1, we derive r =5.17kpc.Themeasuredspectralradioindeximpliesq= e,th s γ = 2650. From Eq.(8) we then obtain B 207µG and 2.76, and a 0.08; assuming q =2.7, we get κ 8. From 1 p U 1027eVcm−3 (radio method). In E≈q.(11) we use Eqs.(6) and≃(5), and the value of n reported i≃n Table1, p e,th ≈ 0.09kpc,thethicknessofthestarburstdiskperpendicularto we derive γ = 1169, and from Eq.(8) we then obtain B 1 ≈ 6 Persic & Rephaeli 2.6µG and U 0.15eVcm−3 (radio method). Taking the p ≈ Table 2.Star-forminggalaxies:CRpenergydensities+. whole disk as a site for SN explosions, the implied average gasdensityisn 0.5cm−3,henceτ τ 3.7 107yr. p res pp Eq.(13) then yiel≃ds Up 0.2eVcm−3 (S∼N me≃thod)×. Object γ-ray radio SN other rs loss ≈ meth. meth. meth. meth. (kpc) mode M33. Star formation - traced by OB associations and HII regions (e.g., Bastian et al. 2007) - and SN occur through- Arp220 – 1027 515 – 0.25 adv outthedisk.FromTabatabaeietal.(2007)wederiveanon- M82 200a,c 201 95 – 0.26 adv thermal radio flux f = 3.3Jy and α = 0.95, averaged 1GHz NGC253 200b,c 145 77 – 0.20 adv over 7.6kpc radius. The latter corresponds to 5.3 exponen- MilkyWay 1d – 1 1j 4.4 pp tiallengthscales(Rd 1.43kpc,fromRegan&Vogel1994), 6e – 5 – 0.2 pp ≃ enclosing97%ofthemassofanexponentialdisk,hencevir- M31 0.36f 0.15 0.7 – 4.77 pp tually the whole stellar distribution. For an assumed thick- M33 <3f 0.38 0.7 – 2.79 pp nessof0.5kpc,wegetr =2.79kpc.Themeasuredspectral LMC 0.25g 0.14 0.2 – 3.0 pp s index implies q = 2.90, and a 0.08; assuming q = 2.7, SMC 0.15h 0.39 1.0 – 1.53 pp p we get κ 11.2. From Eqs.(6)≃and (5), and the value of NGC4945 200i 201 220 – 0.22 adv ≃ NGC1068 – 65 61 – 1.18 pp n reportedinTable1,wederiveγ =1287. FromEq.(8) e,th 1 we then obtain B 4.1µG and U 0.38eVcm−3 (radio p ≈ ≈ method). Given the gas mass reported in Table1, the aver- + ValuesareineVcm−3. agegasdensityisnp 1cm−3,henceτres τpp 2 107yr. (a) Acciari et al. 2009 (see also Persic et al. 2008 and De Cea ∼ ∼ ≃ × Inserting the relevant quantities (see Table1) into Eq.(13), et al. 2009). (b)Acero et al. 2009 (see also Paglione et al. 1996, we then deriveUp 0.7eVcm−3 (SNmethod). Domingo-Santamar´ıa & Torres 2005, and Rephaeli et al. 2010). ≈ LMC. This satellite of the Milky Way can be modeled (c)Abdoetal.2010a.(d)Strongetal.2010.(e)Aharonianetal. 2006.(f)Abdoetal.2010b,withDruryetal.1994inthecaseof as a truncated disk/spheroid with r 3kpc whose half- t ≃ M33.(g)Abdoetal.2010c.(h)Abdoetal.2010d.(i)Lenainet thicknessis also 3kpc(Weinberg&Nikolaev 2001), sowe ≃ al.2010.(j)Webber1987. use r = 3kpc in Eqs.(13,8). The measured spectral radio s indeximpliesq=2.68,anda 0.08;assumingq =2.7,we p ≃ region can bemodeled as aspherical shellwith externalra- get κ 6.7. From Eqs.(6) and (5), and the value of n reporte≃din Table1,wederiveγ1 =1189. Eq.(8)thenyieel,dths diusof1.5kpcandthickness0.3kpc,andmass3.4×109M⊙ B 2.6µG and U 0.14eVcm−3 (radio method). There (Spinoglio et al. 2005). The effective radius is then rs = is n≈o mass outflowpi≈n the LMC, hence τres τpp 107yr 1.2kpc,andtheaveragedensityisnp ∼20cm−3.Themea- (usinganaveragegasdensityofnp 2cm−3∼.)Eq.(1≈3)then sured spectral index implies q ≃ 2.50, hence a = 0.0852 yields Up 0.2eVcm−3 (SN metho≈d). – assuming qp = 2.2, we get κ ≃ 76. From Eqs.(6) and ≈ (5), and the value of n reported in Table1, we derive e,th SMC. This other Milky Way satellite can be modeled as γ = 10161, and from Eq.(8) we then compute B 52µG 1 a bar with an area ≃ 2.5×1.5kpc (Wilke et al. 2003) and and Up 65eVcm−3 (radio method). The CRp r≈esidency l.o.s. extent of 4kpc (following Abdo et al. 2010d), so we time is τ≈ τ 106yr. (The outgoing wind observed in res pp user =1.53kpcinEqs.(13,8).Themeasuredradiospectral ∼ ≃ s NGC1068 does not emanate from the SB region, but from index implies q = 2.70, and a 0.08; assuming q = 2.7, ≃ p closetothecentralAGN,seeKrolik&Begelman1986.)As- weget κ 20. FromEqs.(6)and(5),andthevalueofn ≃ e,th sumingall theobserved far-IR emission originates from the reported in Table1, we derive γ1 = 754. From Eq.(8) we SBregion,yieldsν =0.39yr−1there(seeTable1).Insert- obtain B 4µG and U 0.39eVcm−3 (radio method). SN The SMC≈has a (galaxy-pwi≈de) SN rate of νSN =10−3yr−1. ainngdtUhe rel6e5vaenVtcqmu−a3nt(iStiNesminettohoEdq)..(13) we get B ≈ 52µG p There is no mass outflow from the SMC, so τ τ ≈ res pp 1.4 107yr. (It is n 1.4cm−3.) From Eq.(13)∼we the≃n p obta×in U 1eVcm−3≃(SN method). p ≈ 5.1 Uncertainties NGC4945. This almost edge-on galaxy hosts a Seyfert- ThevaluesofU listedinTable2donotincludesubstantial 2 nucleus (deduced from its X-ray variability, Iwasawa et p observationalandmodelinguncertainties.Inthissectionwe al. 1993). However, essentially all its IR radiation arises from acentral 33′′ 19′′ (r =0.22kpc)molecular complex attempttoestimatethelevelofprecisionwithwhichUpwas s × determinedbased on only limited information on theerrors whose IR colors are typical of SB activity (see Moorwood in the various observational parameters. & Oliva 1994). The measured nuclear radio emission implies q = 2.14, and a 0.10; assuming q = 2.2, we get p ≃ κ 15.7. From Eqs.(6) and (5), and the value of n e,th ≃ 5.1.1 Radio Method reported in Table1, we derive γ = 5689. Assuming the 1 measured radio flux to be only related to the SB, from ThequantitiesinEq.(8)areusuallywelldeterminedforour Eq.(8)wethengetB 94µGandUp 201eVcm−3 (radio samplegalaxies,exceptforthep/eenergydensityratioκ,for mU1o9fpe9at≈7hg)oa2dtl2ah)0c.atetIiVtcτfrcwoemslilno−∼dw3swτ(oSifutrNh≈tom≃vmoeuν4ttS.hN6∼o×d∼1)2;1000.042ykyrmr−≈;1sE,−q1a.n((1dC3ht)hetneh&eexniHsytuieeanlndcges uiwpnnohscSisceBihrbtrlaaeeignCvitaoRylnupose,nsspadtnehicdsetcrqCuapsRls≃eipndd2sip.en1xe−tc,htqr2epa.,A2lmipfnoupdrseetqnxudb,iieδexqsap(csies.≃neu.tm,0gq.e1apd,la≃.txGria2ein.vs1s)e−l,nat2tihe.t2ess NGC1068. This galaxy hosts a prototypical Seyfert-2 nu- toafactorof 2uncertaintyonκ[seeEq.(24)],i.e.typically ∼ cleus(e.g.,Wilson&Ulvestad1982).ThecircumnuclearSB an uncertainty of 50% on U as deduced from Eq.(8). p ∼ Measures of cosmic-ray energy densities in galaxies 7 Weemphasizethattheuseofκhereisslightlydifferent independent of the γ-ray method either, because both de- from that of Persic & Rephaeli (2010), where we assumed pend on the residency time of CRp in the emission region q = q = 2α+1 in all galaxies, whereas here we appro- - although, unliketheγ-ray and radio methods, it does not p e priately drop such equality and assume a physically moti- depend on the particle radiative yield but on the statistics vated index, separately for SB (q = q ) and quiescent ofcore-collapse SN.Also,theγ-ray,radio,and SNmethods p inj ≃6 (q = q +δ) galaxies. Numerically the values of q as- are not on equalfooting. By these methods thevalue of U p inj p p ≃6 sumed here are not that different from themeasured q . iseithermeasured,inferred,orestimated,respectively.This, e Anotherimprovementinthepresentradio-basedderiva- because:(i)π0-decayγ-rayemissionisthemostrobustmea- tion of U relates to the electron low-energy cutoff, γ . In sureofU whenthedistributionoftarget gas isknownand p 1 p Persic&Rephaeli(2010)weassumedγ =103,whereashere theparticlediffusionmodeandenergylosses areaccurately 1 we calculate γ self-consistently by setting it equal to the known, whereas (ii) radio emission enables deduction of U 1 p energy at which synchrotron and Coulomb losses are equal. from electron synchrotron flux and spectrum once assump- Effectively then, γ is the low-energy limit of the electron tionshavebeenmadeonthelinkbetweenenergeticelectrons 1 PL spectrum (see Eq.1). and protons, and between these particles and the magnetic field; and (iii) assuming a SN origin for CR, SN statistics for a given (region of a) galaxy leads to an estimate of U p 5.1.2 Supernova Method there. Asubstantialagreementamongestimatesbasedonthe A precise measurement of the actual rate of core-collapse three methods is reached for most of the galaxies in Ta- SNe is, of course, crucial in these estimates. This is quite ble1. The only exceptions are (a) the SMC and (b) the difficultgiventhetypicallyheavyopticalextinction(e.g.,in SB/Seyfert-2 galaxy NGC1068. Possible reasons for these SBnuclei).Forexample,fromTable2noticethatforourSB discrepancies are: nucleitheSN-basedU aresystematicallylower,byafactor p of 2, than the corresponding radio and γ estimate, whereas (a)TheSMCmeanmagneticfieldmightbesufficientlyweak there is no such discrepancy in the quiescent sample. This thatthereisonlyapartialCRconfinement,sothatmostCR mismatch doessuggest thepossibility of missing about half diffuseouttotheintergalactic space(Abdoetal.2010d). If oftheSNremnantshostedindense,dustyenvironments.In so,theradiomethodyieldsthe(lower)actualparticleenergy addition, SN rates, even when quoted for individual galax- density, whereas the SN method gives an estimate of the ies, are often only statistical in nature and based on the (higher) produced amount. morphologyandstellarmassoftherespectivegalaxies(e.g., (b) Unlike for NGC4945 (the other SB/Seyfert-2 galaxy in Mannuccietal.2005),especiallysoatlowluminositieswhere our sample), the spectral energy distribution of NGC1068 theSNrateisverylow.Finally,radiocountsofSNremnants differsmarkedlyfromthatofpurelySBgalaxies,suggesting requireinformation on their ages in ordertobeturnedinto that its γ-ray emission may be unrelated to star formation actualSNrates.Foroursamplegalaxies,publishedobserva- (Lenain et al. 2010). Indications that this may be the case tionalresultssuggest thatνSN areknowntowithin afactor arethat(i)thereisnogalacticwindemanatingfromtheSB 2. regionofNGC1068(unlikeallotherSBgalaxiesinTable1), ∼ Also from Eq.(13) we see that uncertainties on Up can and (ii) its location in the diagnostic f12/f25 vs. f60/f100 also be due to uncertainties in τres. The latter mostly arise plane1 (see Persic & Rephaeli2007 and references therein) fromtheuncertaintyinthefastwindvelocity,whichinturn suggests that NGC1068 does not behave as a typical SB is probably known to within a factor of 2. Estimates of galaxy. (Its colors suggest an ’evolved starburst phase’, in ∼ theSNenergythatischanneledtoCR, (0.5 1)1050erg, which star formation activity has decreased dramatically ∼ − i.e. 5% 10% of the total kinetic energy of the SN ejecta from the SB peak, and cirrus emission, which is unrelated (Wo∼osley−& Weaver 1995), agree within a factor < 2 (Lin- to ongoing star formation activity, apparently contributes genfelter et al. 1998; Higdon et al. 1998). (Here w∼e assume strongly to the IR emission.) Finally, NGC1068 does not that all core-collapse SN share a universal CR acceleration conform withthetrendsetbytheotherstar-forming galax- efficiency.) ies in Table1, in the L(>100MeV) vs. ν M plane SN gas Finally, for all our sample galaxies, the effective star- (Fig.3d) and the L(>100MeV) vs. ν plane×(Fig.3e; see SN forming radii rs are deduced from high-resolution optical also Lenain et al. 2010). The discrepancy is even larger if and radio data, so their values are relatively precise, with the true ν is significantly lower then the value reported SN typical uncertainties of a few 10%. in Table1 andused in Fig.3 (asit would beif derivedfrom We conclude that all the galaxy quantities in Table1 theSB-only component ofthecircumnuclear IRemission). relevant to Eq.(13) are quoted in the literature as observationally precise to within a factor of < 2, so that U can Once these considerations are weighed in, the discrep- only be estimated from Eq.(13) to with∼in a factor ∼4.p an(c1y02b)eetVwcemen−3th),edveedruycehdigfhorCSRBpnuecnleeri,gyanddetnhseitileosw(vUaplue∼s O(U (10−1)eVcm−3), deduced for very quiet environ- p ∼ O ments,appears very significant. 6 DISCUSSION Observationally, the link between HEγ-ray emission The three methods discussed here are not independent. and SNe is displayed in Fig.3 for our sample galaxies. The The γ-ray method and the radio method are coupled through the p/e ratio at injection, through the secondary- to-primary electron ratio, and through the imposed condi- 1 TheIRASfluxdensitiesofNGC1068at12,25,60and100µm tion of particle-field equipartition. The SN method is not aref12=38.7,f25=87.4,f60=190,f100=277. 8 Persic & Rephaeli Figure3.Correlationsforallthestar-forminggalaxiesdetectedbyFermi/LATandreportedinTable1(emptycircles:starburst/Seyfert- 2galaxies;filledsquares:starburstgalaxies;filledtriangles:quiescentgalaxies.ArrowsindicateHEγ-rayfluxupper limits:Arp220and M33 at, respectively, higher and lower flux limits.) The Milky Way luminosity has theoretical uncertainties stemming from the range of possible emission models matching the Galactic diffuse γ-ray background (see Strong et al. 2010). Wherever plotted, SN rates are displayed with a factor of 1.5 uncertainty (see text), except for NGC4945 and NGC1068 where the actual range of deduced values is reportedinTable1. (a)Correlationbetween γ-rayluminosity,SN ratewithintheregionofradiusrs under study, CRpresidencytime, and total gas mass. (b) Distribution of gas mass as a function of luminosity. (c) Distributionof residency time as a function of source size. To guide the reader’s eye, the dotted line drawn through the data represents the τres ∝ rs3 relationship. (d) Correlation between γ-ray luminosity, SN rate, and total gas mass. (e) Correlation between γ-ray luminosity and SN rate. For comparison, the dotted line drawnthroughthedatashowstheν1.4 slope,impliedbytheobservational L∝SFR1.4 relationshipreportedbyAbdoetal.(2010b). SN theoretical link is apparent from combining Eqs.(9,13) It can, for example, if τ r3; observationally, this latter res ∝ s L ν τ r−3 M . (14) correlation roughly holds for our sample (see panel (b)). A ∝ SN res s gas possible reason for this: if in most galaxies in the sample InderivingEq.(14)weconsideredthatthevolume-averaged the CRp energy loss is dominated by p-p interactions, so γ-ray emissivities of the sample galaxies, appearing in τ τ n−1, and M is roughly constant within the res pp gas Eq.(9), vary little from galaxy to galaxy. This is due to the samp∼le, so∝n r−3, then τ r3 follows. Indeed, in most ∝ s res ∝ s relativelyuniformGeV-TeVphotonslopes,andcorrespond- ofourgalaxies theCRpenergylosses aredominatedbyp-p ing CRp spectral slopes, observed for these galaxies (Abdo interactions (see Table2) and thegas mass varies relatively et al. 2011). Panel (a) shows the observational correlation little(adecade)withinthesample(seepanel(c)).Panel(d) betweenγ-rayluminosity,SNratewithinrs,CRpresidency shows the ‘reduced’ relationship between γ-ray luminosity, time, and total gas mass; the plot shows the relation ex- SNrate,andtotalgasmass.AfurtherstepfromEq.(14),by pressed in Eq.(14). Can it bereduced to fewer parameters? Measures of cosmic-ray energy densities in galaxies 9 taking into account that M is relatively constant across radiodataundertheassumptionofenergyequipartition,can gas thesample,isrepresentedbypanel(e)thatshowstheγ-ray beusedasproxiesoftheactualquantitiesthataremeasured luminosity - SN rate relation; note that the distribution of directlyonlyfromγ-rays.Thiscouldbeparticularlyusefulin data points is compatible with a ν1.4 slope, which follows thecase of distant galaxies, whose (unbeamed)γ-ray fluxes SN from ν SFR and the observational L SFR1.4 rela- are too faint to be measured; SN γ ∝ ∝ tion found by Abdo et al. (2010b) for this same sample of (iii) core-collapse SN, both in quiescent galaxies and in SB galaxies (except the composite SB/AGN sources). galaxies, arelikelytoshareauniversalCRacceleration effi- It should be noted that the steps leading from panel a ciency; and through panel d to panel e are based on the relative con- (iv) the Fermi-I acceleration mechanism, assumed to be at stancy of M within the sample; however, this is a clear gas play in the environment of SN remnants, leads to accel- selection effect stemming from the fact that L(>100MeV) eration timescales for CRp in galaxies such that particles is higherfor alarger M ,because starformation ishigher gas and fields attain equilibrium over typical star formation andbecausethereismoretargetgasavailableforp-pinter- timescales, in agreement with observational evidence. action. Given thelow fluxesemitted by star-forming galaxies, which are close to the sensitivities of the Fermi/LAT andCherenkovinstruments,itisclearthatonlythebright- Acknowledgements. This paper has developed out of a talk est galaxies can be observed, i.e., the most gas-rich ones, presented by MP at the ”Beamed and Unbeamed Gamma- withlogMHI 9 10(seetheHImassfunctionofgalaxies, Raysfrom Galaxies” workshop (Muonio, Finland:April11- ∼ − e.g. Zwaan et al. 2003). 15, 2011). MP acknowledges useful exchanges with Keith With the exception of (the mostly Seyfert-2 galaxy) Bechtold, Jean-Philippe Lenain, Andrew Strong, and Mas- NGC1068,currentmeasurementsofthegalaxiesinoursam- simo Turatto. pleprovideappreciableevidenceforthedirectlinkbetween SN and VHEγ-ray emission. REFERENCES 7 CONCLUSION AbdoA.A.,etal.(LATCollab.)2011,ApJ,inpreparation Activestarformation in galaxies leads toproductionofCR AbdoA.A.,etal.(LATCollab.)2010b,A&A,523,L2 AbdoA.A.,etal.(LATCollab.)2010c,A&A,512,A7 protons and electrons via the Fermi-I diffusive shock ac- AbdoA.A.,etal.(LATCollab.)2010a,ApJL,709,L152 celeration mechanism in SNremnants.Basic considerations AbdoA.A.,etal.(LATCollab.)2010d,A&A,523,A46 suggest that the timescales required for CRp to be Fermi-I AcciariV.A.,etal.(VERITASCollab.)2009,Nature,462,770 accelerated(τ )andtoloseenergyviapiondecayintopho- + AceroF.etal.(HESSCollab.)2009Science,326,1080 tonsande+e− pairsorviaadvectionbybulkoutflows(τ−), AckermannMetal.(LATCollab.)2011,ApJ,726:81 areshorterthanthetimescaleofstarburstactivityingalax- AharonianF.,etal.(HESSCollab.)2006,A&A,449,223 ies (τSB);thelatteris itself comparable with thedynamical AharonianF.,etal.(HESSCollab.)2006,Nature,439,695 timescaleofgalaxies.AconsequenceisthatinaSBregiona AlbertJ.etal.(MAGICCollab.)2007,ApJ,658,245 balance can roughly be achieved between energy gains and BaltrusaitisR.M.,etal.1984,PRL,52,1380 losses of CR during a typical burst of star formation. Un- Bastian N., Ercolano B., Gieles M., et al. 2007, MNRAS, 379, der equilibrium conditions in a galaxy, a minimum-energy 1302 BauerM.,PietschW.,TrinchieriG.,etal.2007, A&A,467,979 configurationofthefieldandtheCRmaybeattained.This Beck R. 2000, in ”The Interstellar Medium of M31 and M33”, impliesthatenergydensitiesofparticlesandmagneticfields eds. E.M.Berkhuijsen, R.Beck, R.A.M.Walterbos (Aachen: may be in approximate equipartition. Shaker),p.171(astro-ph/0009455) For 10 galaxies for which pointed GeV-TeV data are BeckR.,GräveR.1982,A&A,105,192 available (from Fermi/LAT) and from Cherenkov tele- BeckR.,KrauseM.,2005,Astr.Nacht.,326,414 scopes), we have estimated Up using the the radio, γ-ray, BellA.R.1978, MNRAS182,443 andSNmethods.Asubstantialagreementamongestimates ChenY.,&HuangJ.-H.1997,ApJ,479,L23 basedonthethreemethodsisreachedfor9ofthe11galac- ChevalierR.A.,CleggA.W.,1985,Nature,317,44 tic regions (3 SB nuclei, the Milky Way’s disk and central CorralP.,HollenbachD.J.,LordS.D.,etal.1994,ApJ,423,223 region, 4 quiescent galaxies, 2 SB/Seyfert-2 galaxies) con- CoxD.P.2005, ARA&A,43,337 sidered in this paper. The discrepancy between the very deCeaDelPozoE.,TorresD.F.,RodriguezMarreroA.Y.,2009, high values (U (102)eVcm−3) found in SB nuclei ApJ,698,1054 p ∼ O DehnenW.,BinneyJ.,1998,MNRAS,294,129 such as M82, NGC253 and NGC4945, and the low values DiehlR.,HalloinH.,KretschmerK.,etal.,2006,Nature,439,45 (U (10−1)eVcm−3) found in very quiet environments p ∼ O Domingo-Santamar´ıaE.,TorresD.F.,2005,A&A,444,403 such as the Local Group galaxies, appears to be highly sig- DruryL.O’C.,AharonianF.A.,VölkH.J.1994,A&A,287,959 nificant. Elmouttie M., Haynes R.F., Jones, K.L., et al. 1997, MNRAS, Theresultsofthisstudyextendthevalidityofourpre- 284,830 vious suggestions that: FermiE.1954,ApJ,119,1 (i)CRpenergydensitiesinstar-forminggalaxiesrangefrom GinzburgV.L.,SyrovatskiiS.I.,1964,TheOriginofCosmicRays (102)eVcm−3inveryactiveenvironments(e.g.,SBnuclei) (NewYork:Macmillan) dOown to (10−1)eVcm−3 in very quiet ones (e.g., Local GuptaM.,Webber W.R.1989,ApJ,340,1124 O HaynesR.F.,KleinU.,Wayte S.R.,etal.1991, A&A,252,475 Group galaxies); HelouG.,KhanI.R.,MalekL.,BoehmerL.1988,ApJS,68,151 (ii) CR energy densities and magnetic fields, inferred from HigdonJ.C.,LingenfelterR.E.,RamatyR.,1998,ApJ,509,L33 10 Persic & Rephaeli Hou J., Yin J., Boissier S. et al., 2009, in Proc. of ’The Galaxy APPENDIX: PROTON/ELECTRON RATIOS DiskinCosmological Context’, eds. J.Andersenetal.(Cam- Expanding on Schlickeiser (2002), let us assume that bridge: Cambridge University Press), IAU Symposium Vol. electrons and protons are accelerated out of a thermal 254,p.27 bath, characterized by a non-relativistic kinetic energy Hughes A., Staveley-Smith L., Kim S., Wolleben M., Filipovic, T 10keV, to a differential PL spectrum (in momentum) 0 IwasMaw.a20K07.,,KMoNyaRmAaS,K3.8,2A,w5a4k3iH.,etal.1993, ApJ,409,155 Nj(≃p)=N0,jp−qj where j=e,p. At injection, qe =qp. Later, differentloss anddiffusion processes forthetwoCRspecies KennicuttR.C.Jr.,1998,ARAA,36,189 willingeneralresultinq =q .Ifelectricalneutralityofpri- Kewley L.J., Heisler C.A., Dopita M.A., et al. 2000, ApJ, 530, e 6 p 704 maryCRsisconserved,thenthetotalnumberofCRparticle KleinU., Wielebinski R., Haynes R.F.,MalinD.F., 1989, A&A, of each species pervolume unit is 211,280 ∞ ∞ KrolikJ.H.,BegelmanM.C.1986,ApJ,308,L55 n = N (T)dT = N (T)dT. (15) o e p Ku¨hrH.,WitzelA.,Pauliny-TothI.I.K.,NauberU.1981,A&AS, ZT0 ZT0 45,367 Lenain J.-P., Ricci C., Tu¨rler M., Dorner D., Walter R. 2010, Theenergy-momentumrelationT= m2c4+p2c2 mc2im- − A&A,524,72L plies p= T2/c2+2Tm and dp/dTp=(T/c2 +m)(T2/c2 + LingenfelterR.E.,RamatyR.,KozlovskyB.1998,ApJ,500,L153 2Tm)−1/p2. As N(T)=N[p(T)]dp/dT, the final expression j j Longair M.S., 1994, High Energy Astrophysics (2nd ed.; Cam- is (see Schlickeiser 2002) bridge:CambridgeUniv.Press) Man8n0u7cciF.,DellaValleM.,PanagiaN.,etal.2005,A&A,433, Nj(T) = Nc02,j (T +mc2) Tc22 +2Tm −(qj+1)/2. (16) MannucciF.,MaiolinoR.,CresciG.,etal.2003, A&A,401,519 (cid:0) (cid:1) MoorwoodA.F.M.&OlivaE.1994, Apj,429,602 InsertingEq.(16)inEq.(15),weobtainthenormalizationof Paglione T.A.D., Marscher A.P., Jackson J.M., Bertsch D.L., each CR species, 1996,ApJ,460,295 PavlidouV.,FieldsB.D.2001, ApJ,558,63 N = (q 1) n T02 +2T m (qj−1)/2. (17) PersicM.,RephaeliY.,2007,A&A,463,481 0,j j− 0 c2 0 (cid:0) (cid:1) PersicM.,RephaeliY.2010,MNRAS,403,1569 Because of the assumed electrical neutrality of the primary PersicM.,RephaeliY.,ArieliY.,2008,A&A,486,143 CRs, we get Petuchowski SJ, Bennett CL, Haas MR, et al. 1994, ApJ, 427, PoinLt1s7S.D., Chu Y.-H., Snowden S.L., Smith R.C. 2001, ApJS, N0,p = qp−1 mp+(T0/2c2) (qp−1)/2 (2T0)(qp−1)/2 136,99 N0,e qe−1 (cid:2)me+(T0/2c2)(cid:3)(qe−1)/2 (2T0)(qe−1)/2 ≃ ProtheroeR.J.,ClayR.W.2004,PASA,21,1 q 1 ((cid:2)2T m )(qp−1)/2(cid:3) ReganM.W.,Vogel.S.N.1994, ApJ,434,536 p− 0 p (18) RephaeliY.,1979,ApJ,227,364 ≃ qe 1 (2T0me)(qe−1)/2 − RephaeliY.,ArieliY.,PersicM.2010,MNRAS,401,473 since T <<m c2 <<m c2. RoyA.L.,OosterlooT.,GossW.M.,AnantharamaiahK.R.2010, 0 e p A&A,517,A82 The p/enumberdensity ratio is SarazinC.L.,1999, ApJ,520,529 • Spoon H.W.W., Koornneef J., MoorwoodA.F.M.,Lutz D.,Tie- ω(T;q ,q ) = Np(T)dT . (19) lensA.G.G.M.2000,A&A,357,3000 p e N (T)dT e Tabatabaei F.S., Krause M., Fletcher A., Beck R. 2008, A&A, 490,1005 InsertingEqs.(16),(18) in Eq.(19), we obtain SScehaqlpiuc.4kis7eti2sEer.RR..,,O20d0e2g,aCrdosNm.,ic1R99a1y,AAsptrJo,p3h6y9s,ic3s2(0Berlin:Springer), ω(T;qp,qe) = ((qqpe−−11)) ((22TT00mmpecc22))qqep22−−11 × Spinoglio L., Malkan M.A., Smith H.A., et al. 2005, ApJ, 623, 123 T1−qp(T +mpc2)(T +2mpc2)−qp2+1 . (20) SSttrriocnkglaAnd.WD.,.KP.o,rHteerckTm.Aa.n,DTi.gMel.,S2.0W09.,,eAtpaJl.,2609170,,2A03p0J,722,L58 × T1−qe(T +mec2)(T +2mec2)−qe2+1 Tabatabaei F.S.,BeckR.,Kru¨gelE.,etal.2007,A&A,475,133 From Eq.(20) it is straighforward to see that at injection, Tatischeff V., 2008, in ”Supernovae: lights in the darkness” when q =q =q , it is (Schlickeiser2002) p e inj (XXIII Trobades Cientifiques de la Mediterrania), PoS(028) (arXiv:0804.1004) =1... ... T/c2<<m e TTourcrkbeersridDgW.eF,..,M,12A907:054M,,IARTpaPJd,irae6ts1iso7)n,9P66rocesses in Astrophysics (Cam- ω(T;qinj) ∝(cid:0)mTpc2q(cid:1)inqji−n2j1−1 ... me<<T/c2 <<mp (21) = mp 2 ... T >>m c2 . vVaönlkdHen.JB.,eKrglheinS.U,T.,aWmmielaenbninGsk.iAR.,.,1919918,9,AAR&AAA,,22193,,3L6132 Notice that for(cid:0)qme(cid:1) 2.2, ω(T >> 1GeVp) 102, as re- Webber W.R.1987,A&A,179,277 inj ≃ ≃ WeinbergM.D.,NikolaevS.2001,ApJ,548,712 marked by Schlickeiser (2002). WilkeK.,Stickel M.,HaasM.,etal.2003,A&A,401,873 The p/eenergy density ratio is WilsonA.S.,UlvestadJ.S.1982, ApJ,263,576 • WoosleyS.E.,Weaver T.A.,1995, ApJS,101,181 ∞N (T)TdT ZwaanM.A.,Staveley-SmithL.,KoribalskiB.S.,etal.2003,AJ, κ(q ,q ) = T0 p . (22) p e R∞ 125,2842 T0 Ne(T)TdT R