Adopting the convection-diffusion model for energetic electron and proton
propagation, and accounting for all the relevant hadronic and leptonic
processes, the steady-state energy distributions of these particles in the
starburst galaxies M82 and NGC253 can be determined with a detailed numerical
treatment. The electron distribution is directly normalized by the measured
synchrotron radio emission from the central starburst region; a commonly
expected theoretical relation is then used to normalize the proton spectrum in
this region, and a radial profile is assumed for the magnetic field. The
resulting radiative yields of electrons and protons are calculated: the
predicted >100MeV and >100GeV fluxes are in agreement with the corresponding
quantities measured with the orbiting Fermi telescope and the ground-based
VERITAS and HESS Cherenkov telescopes. The cosmic-ray energy densities in
central regions of starburst galaxies, as inferred from the radio and gamma-ray
measurements of (respectively) non-thermal synchrotron and neutral-pion-decay
emission, are U=O(100) eV/cm3, i.e. at least an order of magnitude larger than
near the Galactic center and in other non-very-actively star-forming galaxies.
These very different energy density levels reflect a similar disparity in the
respective supernova rates in the two environments. A L(gamma) ~ SFR^(1.4)
relationship is then predicted, in agreement with preliminary observational
evidence.Comment: Invited talk at SciNeGHE2010 (8th Wotkshop on Science with the New
  Generation of High Energy Gamma-ray Experiments): Gamma-ray Astrophysics in
  the Multimessenger Context (Trieste, Sept.8-10, 2010

Persic, Massimo

Rephaeli, Yoel

English

arXiv

Adopting the convection-diffusion model for energetic electron and proton propagation, and accounting for all the relevant hadronic and leptonic processes, the steady-state energy distributions of these particles in the starburst galaxies M82 and NGC253 can be determined with a detailed numerical treatment. The electron distribution is directly normalized by the measured synchrotron radio emission from the central starburst region; a commonly expected theoretical relation is then used to normalize the proton spectrum in this region, and a radial profile is assumed

for the magnetic field. The resulting radiative yields of electrons and protons are calculated: the predicted > 100 MeV and > 100 GeV fluxes are in Agreement with the corresponding quantities measured with the orbiting Fermi telescope and the ground-based VERITAS and HESS Cherenkov telescopes. The cosmic-ray energy densities in central regions of starburst galaxies, as inferred from the radio and γ-ray measurements of (respectively) non-thermal synchrotron and π0-decay emission, are Up = O(100) eV cm−3, i.e. at least an order of magnitude larger than near the Galactic center and in other non–very-actively star-forming galaxies. These very different energy density levels reflect a similar disparity in the respective supernova

rates in the two environments. A Lγ ∝ SFR1.4 relationship is then predicted, in agreement with preliminary observational evidence

Persic, M.

Rephaeli, Y.

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2011-10858-1Colloquia: Scineghe2010IL NUOVO CIMENTO Vol. 34 C, N. 3 Maggio-Giugno 2011High-energy emission from star-forming galaxiesM. Persic(1) and Y. Rephaeli(2)(3)(1) INAF and INFN - Trieste, Italy(2) Tel-Aviv University - Tel-Aviv, Israel(3) University of California - San Diego, CA, USA(ricevuto il 25 Febbraio 2011; pubblicato online il 29 Aprile 2011)Summary. — Adopting the convection-diffusion model for energetic electron andproton propagation, and accounting for all the relevant hadronic and leptonic pro-cesses, the steady-state energy distributions of these particles in the starburst galax-ies M82 and NGC253 can be determined with a detailed numerical treatment. Theelectron distribution is directly normalized by the measured synchrotron radio emis-sion from the central starburst region; a commonly expected theoretical relation isthen used to normalize the proton spectrum in this region, and a radial profile is as-sumed for the magnetic field. The resulting radiative yields of electrons and protonsare calculated: the predicted > 100MeV and > 100GeV fluxes are in agreementwith the corresponding quantities measured with the orbiting Fermi telescope andthe ground-based VERITAS and HESS Cherenkov telescopes. The cosmic-ray en-ergy densities in central regions of starburst galaxies, as inferred from the radio andγ-ray measurements of (respectively) non-thermal synchrotron and π0-decay emis-sion, are Up = O(100) eV cm−3, i.e. at least an order of magnitude larger than nearthe Galactic center and in other non–very-actively star-forming galaxies. These verydifferent energy density levels reflect a similar disparity in the respective supernovarates in the two environments. A Lγ ∝ SFR1.4 relationship is then predicted, inagreement with preliminary observational evidence.PACS 95.85.Pw – γ-ray.PACS 98.54.Ep – Starburst galaxies and infrared excess galaxies.PACS 98.56.Ne – Spiral galaxies (M31 and M33).PACS 98.56.Si – Magellanic Clouds and other irregular galaxies.1. – IntroductionIn the nuclear regions of starburst (SB) galaxies, active star formation (SF) powersemission of radiation directly by supernova (SN) explosions and indirectly by SN-shockheating of interstellar gas and dust, as well as from radiative processes involving SNR-accelerated cosmic-ray electrons (CRe) and protons (CRp).Some basic considerations suggest that the timescales required for CRp to be accel-erated (by SN shocks) and lose energy (via pion decay into photons and e+e− pairs, orc© Societa` Italiana di Fisica 217218 M. PERSIC and Y. REPHAELIvia advection) are shorter than timescales of SB activity in galaxies, that are themselvescomparable to galactic dynamical timescales. A consequence is that in a SB region abalance can roughly be achieved between energy gains and losses for galactic CRs duringa typical burst of SF [1]. Under basic hydrostatic and virial equilibrium conditions ina galaxy, a minimum-energy configuration of the field and the CRs may be attained.This implies that energy densities of particles and magnetic fields can be in approximateequipartition [2].The equipartition assumption enables deduction of the CRp energy density, Up, fromthe measured synchrotron radio emission (which can be observed relatively easily) anda theoretically motivated injection p/e ratio. Alternatively, Up can be estimated alsofrom SN rates and the fraction of SN energy that is channeled into particle acceler-ation. Knowledge of Up enables prediction of γ-ray emission (either at high energies(HE: ≥ 100MeV) or at very high energies (VHE: ≥ 100GeV)), which is mostly due toCRp interactions with ambient gas protons, via π0 decay.2. – HE emission from star-forming galaxiesIn this section we will review some basic features of SB modeling, notably appliedto the local galaxies M82 and NGC253, and the status of observations of star-forminggalaxies in the HE/VHE γ-ray domain.2.1. Modeling . – In both nearby SB galaxies, M82 and NGC253, the central SB region(which will also referred to as the source region) with a radius of ∼ 300 pc and height of300 pc is identified as the main site of particle acceleration. Here, the injection particlespectrum is assumed to have a non-relativistic strong-shock index q = 2. A theoreticalNp/Ne ratio, predicted from charge neutrality of the injected CRs, is likely to hold inthis source region—as is also the assumption of equipartition.Due to the implicit dependences in the expression for the synchrotron flux, CR/fieldequipartition is implemented iteratively to solve for Ne (primaries plus secondaries), Np,and B. For both M82 and NGC253, central values B0 ∼ 200 μG have been obtained indetailed models (M82: [3, 4]; NGC253: [5-7]).Adopting the convection-diffusion model for energetic electron and proton propaga-tion, and accounting for all the relevant hadronic and leptonic processes, the steady-stateenergy distributions of these particles in the galaxies M82 and NGC253, in both the SBnucleus and the disk, can be determined with a detailed numerical treatment. In par-ticular, to numerically follow particle energy losses and propagation outside the sourceregion, one needs to know the HI and HII densities and their profiles, as well as thespatial variation of the mean strength of the magnetic field. (E.g., assuming magneticflux freezing in the ionized gas, then B ∝ n2/3HII [8].)A measured radio index of ∼ 0.7 in the central disk implies q ∼ 2.4 there. Thisimplies a substantial steepening of the CRe spectrum from the injection value, q = 2.The steady-state electron and proton spectra in the SB region of NGC253 are shown infig. 1. At low energies both spectra are flat, whereas at E  1GeV the stronger electronlosses result in steeper electron (than proton) spectra.Electron emissions by bremsstrahlung and Compton scattering are shown in fig. 2;the γ-ray emission from π0 decay (following pp collisions) is also shown. As expected,the losses due to bremsstrahlung dominate the lower energy regime, whereas losses dueto π0 decay dominate at higher energies. (While synchrotron emission extends to theHIGH-ENERGY EMISSION FROM STAR-FORMING GALAXIES 21910−2 10−1 100 101 102 103 10410−2010−1510−1010−5E (Gev)Particle Density (GeV−1  cm−3 )Fig. 1. – Properties of the emitting particles in the central SB region of NGC253 [7]: steady-statespectra of primary (solid line) and secondary (dot-dashed line) electrons and protons (dashedline).10−3 10−2 10−1 100 101 102 10310−1810−1610−1410−1210−1010−810−610−4Eγ (Gev)Flux (GeV−1  cm−2  s−1 )Fig. 2. – Properties of the emitted radiation in the central SB region of NGC253 [7]: radia-tive yields from electron Compton scattering off the FIR radiation field (dotted line), electronbremsstrahlung off ambient protons (dashed line), π0 decay following pp collisions (dash-dottedline), and their sum (solid line).220 M. PERSIC and Y. REPHAELIX-ray region, it is negligible at much higher energies.) Our main interest here is the VHEemission, which—as anticipated—is mainly from the latter process.It is interesting to note that the numerically predicted VHE γ-ray flux is a factor ∼ 6lower than that obtained in an approximate treatment where the impact of radial energylosses and propagation mode of the CRp is ignored [3]. This simplified approach resultsin an unrealistically high contribution of the main disk (exterior to the SB region) to thetotal TeV emission: in fact even the slight steepening of the CRp spectrum, occurring inthe disk because of energy losses, significantly lowers the TeV emissivity [9] and hencethe predicted source flux.We note that the related neutrino flux (π± eventually produce e±+νe + ν¯e+νμ + ν¯μ)at energies higher than 100GeV is about a third of the corresponding photon flux [3].2.2. γ-ray detections. – The two local SB galaxies M82 and NGC253 are the onlynon-AGN extragalactic sources that, up to now, have been detected in both the GeV [10]and TeV [11, 12] domains. The measured fluxes and spectra of both galaxies in the twobands agree with predictions of recent numerical models (M82: [3, 4]; NGC253: [5-7]).The highest-SFR galaxy in the nearby universe, Arp 220, was undetected by MAGIC [13].HE γ-ray detections were obtained for a number of low SFR galaxies: the Large Mag-ellanic Cloud (LMC: [14]), the Small Magellanic Cloud (SMC: [15]), the Andromedagalaxy (M31: [16]), and the composite Sy2/SB galaxies NGC1068 and NGC4945 [17].The scenario of mostly hadronic HE γ-ray emission is generally confirmed for these galax-ies, except for NGC1068 where emission from the active nucleus may be dominant. Onlyflux upper limits exist for the Triangulum galaxy (M33: [16]).3. – CRs in star-forming galaxiesThe CRp energy density in galaxies can be either i) measured directly if the GeV-TeV spectral flux is known, or ii) evaluated indirectly if source size, distance, and radiospectral index and flux are known, and particles/field equipartition and a p/e ratio areassumed, or iii) estimated if the SN rate, the CRp residence timescale, the energy perSN going into CRs, and the size of the SF region are known.i) CRs and GeV-TeV emission. The detection of M82 and NGC253 confirmed thevalues Up = O(100) eV cm−3, resulting from accurate numerical treatments based on thesolution of the diffusion-loss equation for the accelerated particles (see refs. above). In the∼ 200 pc region of the Galactic center Up ∼ 5 eV cm−3 based on HESS observations [18].For the comparable environment of the Andromeda galaxy, the Fermi -LAT detectionimplies an average Up at a level of ≈ 0.35 the average Galactic value [16]. For the evenmore quiet environments of the LMC and the SMC), actual Fermi -LAT GeV detectionsimply, respectively, Up ∼ (0.2− 0.3) and ∼ 0.1 eV cm−3 [14, 15].ii) CRs and radio emission. Based on method ii) above, for the central SB regionsof NGC253, M82, and Arp 220, respectively, [1] evaluate Up ≈ 75, 97, and 520 eV cm−3.These radio-based estimates match, to within a factor of ≈ 2, those derived from GeV-TeV-based measurements.iii) CRs and supernova rates. The CRp residence timescale is given by τ−1res = τ−1pp +τ−1out, where the pp interaction timescale τpp is a function of the ambient gas density n,and the advection timescale τout is a function of the speed of the outflowing gas (vout)and of the size (radius) of the SB region (rs). Typically, τpp ∼ 104 y and ∼ 105 y for thecentral SB regions of Arp 220 and, respectively, the M82 and NGC253 [1]. If, however,HIGH-ENERGY EMISSION FROM STAR-FORMING GALAXIES 221a fast SB-driven wind advects the energetic particles out of the disk plane, then possiblyτout  τpp. For M82, vout ∼ 2500 km s−1 [19]. Assuming a homogeneous distribution ofSNe within the SB nucleus of radius rSB, the outflow timescale is then τout ∼ 3× 104 y.So in some SB galaxies τres ∼ τout. During τres a number νSNτres of SNs explode anddeposit the kinetic energy of their ejecta, Eej = 105 erg, into the interstellar medium.The Galactic CR energy budget and SN statistics suggest that η ∼ 0.05 of this energymay go into accelerating particles. The CRp energy density in the central SB region isthen Up = 14νSNτresηEejr−3SB . A substantial agreement with the equipartition estimates isreached for NGC253, M82, Arp 220, Milky Way, LMC: Up ∼ 75, 95, 505, 5.7, 0.2 eV cm−3,respectively [1]. Summarizing, the CR energy densities estimated in five galactic nucleiof similar size (three SB galaxies, the central Galactic region, and the LMC), appear tobe largely correlated with key features of the ongoing SF: SN rate and CRp residencetime (the latter being, in turn, a function of the local gas density and of the galacticsuperwind speed). In fact, in these environments, for same ηEej (by assumption) andsimilar rs (from observations), the CRp energy density seems to be well described justas a function of the number of SN explosions during the CRp residence timescale,(1) Up ∝ νSNτres .4. – HE/VHE γ-ray emission and SFRThe Schmidt-Kennicutt (SK) law of SF, ΣSFR ∝ ΣNgas (where gas comprises both HIand H2), states that projected SFR varies as a power law the projected gas density. Thisis true piecewise: both locally and disk-averaged, it is N ∼ 2.5 for Σgas < 10M pc−2and N ∼ 1.4 for higher densities [20]. If disk thicknesses do not vary much amonggalaxies, then the SK law can be written in deprojected units with the same index N .For a source with gas number density n, proton energy density Up, and volume V ,the integrated hadronic γ-ray photon luminosity above some photon energy  is(2) L≥ =∫Vg≥ nUp dV s−1with the integral emissivity g≥ in units of photon s−1(H-atom)−1(eV/cm3)−1 [9]. Usingvolume-averaged quantities and setting  = 100MeV, from eqs. (1), (2) we can write(3) L≥100MeV ∝Mgas νSN .This is in agreement with the observational luminosity vs. (gas mass)×(SN rate) corre-lation [16], which evidently describes the γ-ray luminosity arising from π0 decay.Owing to the SK law, the above equation transforms into L≥ ∝ SFR1+1/N : if N = 2.5as appropriate for our sample galaxies with Σgas < 10M pc−2 [20], then(4) L≥100MeV ∝ SFR1.4 .Within limited statistics, this prediction agrees with observations [16].So the observational non-linear Lγ-SFR correlation [16] stems from the GeV lumi-nosity being (mostly) hadronic in origin, from CRs being linked with SF (through SNexplosions), and from the Fermi -LAT–detected galaxies being located in the steep wing(i.e., low-Σgas regime) of the SK law of SF.222 M. PERSIC and Y. REPHAELI5. – ConclusionThe link between SF and CR particles was suggested long ago [21]. It is based on therecognition that the CRe’s, responsible for diffuse non-thermal synchrotron emission, areproduced in the sites of SN explosions. The rough agreement between the relatively shortlifetime ( 3 × 107 y) of massive stars, and the similarly short synchrotron energy losstime of high-energy electrons, led to the expectation that the non-thermal radio emissionof a galaxy is a measure of its SF activity on scales much shorter than the Hubble time.HE/VHE γ-ray detections (with, respectively, the orbiting Fermi telescope andground-based IACTs) of some nearby star-forming (SB and normal) galaxies, that spana large range of SFR, have provided direct Up measurements. These are consistent withtheoretical predictions based on radio measurements, and with estimates based on SNrates and local CRp residence times. Should the match between measured and predictedUp be confirmed, some immediate implications would be:i) star-forming galaxies can be powerful particle accelerators, able to achieve CRpenergy densities orders of magnitude higher than the Galactic value;ii) SNe, both in quietly star-forming galaxies and in very actively star-forming galax-ies, probably have a common universal CR acceleration efficiency;iii) CR energy densities and equipartition magnetic fields derived from radio mea-surements can be used as proxies for the quantities characterizing the full particle energydistributions (derived from accurate spectral fits of the GeV-TeV emission): this couldbe particularly useful in the case of galaxies that are too far away for their (umbeamed)γ-ray emission to be measured.REFERENCES[1] Persic M. and Rephaeli Y., Mon. Not. R. Astron. Soc., 403 (2010) 1569.[2] Longair M. 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(LAT Collaboration), Astron. Astrophys., 523 (2010) A46.[16] Abdo A. A. et al. (LAT Collaboration), Astron. Astrophys., 523 (2010) L2.[17] Lenain J.-P. et al., Astron. Astrophys., 524 (2010) A72.[18] Aharonian F. et al. (HESS Collaboration), Nature, 439 (2006) 695.[19] Strickland D. K. and Heckman T. M., Astrophys. J., 697 (2009) 2030.[20] Bigiel F. et al., Astron. J., 136 (2008) 2846.[21] Ginzburg V. L. and Syrovatskii S. I., The Origin of Cosmic Rays (Macmillan, NewYork) 1964.

High-energy emission from star-forming galaxies

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