A multifrequency view of starburst galaxies
aa r X i v : . [ a s t r o - ph . H E ] J u l Mem. S.A.It. Vol. 75, 282 c (cid:13) SAIt 2008
Memorie della
A multifrequency view of starburst galaxies
J. K. Becker , F. Schuppan , and S. Sch¨oneberg Institut f¨ur Theoretische Physik, Fakult¨at f¨ur Physik & Astronomie, Ruhr-Universit¨atBochum, 44780 Bochum e-mail: [email protected]
Abstract.
During the past few years, first observations of starburst galaxies at > GeV ener-gies could be made with the Fermi Gamma-ray Space Telescope (GeV range) and ImagingAir Cherenkov Telescopes (TeV range). The two nearest starbursts, M82 and NGC253 weredetected, and most recently, the detection of two starburst-Seyfert composites (NGC1068and NGC4945) were reported. The emission for the two starbursts is best explained byhadronic interactions, and thus providing a first, unique opportunity to study the role ofcosmic rays in galaxies. In this paper, the role of cosmic rays for the non-thermal com-ponent of galaxies is reviewed by discussing the entire non-thermal frequency range fromradio emission to TeV energies. In particular, the interpretation of radio emission arisingfrom electron synchrotron radiation is predicted to be correlated to TeV emission comingfrom interactions of accelerated hadrons. This is observed for the few objects known at TeVenergies, but the correlation needs to be established with significantly higher statistics. Anoutlook of the possibility of tracing cosmic rays with molecular ions is given.
Key words. starburst galaxies – high-energy photons –cosmic rays – molecular ions
1. Introduction
Galaxies with a high star formation rate pro-vide the opportunity to study the influence ofmassive stars on the large-scale behavior ofgalaxies in detail. In particular, the role of gasheating by star formation can be studied bythe observation of far-infrared emission andthe role of supernova remnants can be inves-tigated by looking at non-thermal radio emis-sion from electron synchrotron radiation. Mostrecently, first gamma-ray detections using theFermi Gamma-ray Space Telescope (FGST)and Imaging Air Cherenkov Telescopes likeH.E.S.S. and VERITAS were made. The near-est starburst galaxies M82 and NGC253 weredetected above GeV energies, tracing the inter-
Send o ff print requests to : J. K. Becker action of hadronic cosmic rays with the gas inthe galaxy.In this paper, the multifrequency spec-trum of starburst galaxies will be reviewed.In Section 2, the correlation between the farinfrared and radio emission is discussed. InSection 3, hadronic interactions at energies E > GeV are discussed in the context of neu-tral secondary production. In Section 4, cos-mic ray-induced ionization is mentioned as afuture method of tracing hadronic cosmic raysin galactic environments. In particular, a su-pernova remnant interacting with a molecularcloud provides an optimal environment for theproduction of H + , at a level which should bedetectable in the future with instruments likeHerschel and ALMA. ecker: Starburst galaxies 283
2. The Radio-FIR correlation
The correlation between the total radio and far-infrared emission in starburst galaxies is ex-perimentally well established. As an example,a sample of local starburst galaxies with red-shifts below z = .
03 is shown in Figure 1.Far-infrared emission arises when newly born,massive stars heat the surrounding gas. Radioemission, on the other hand, is directly cor-related to the death of massive stars: elec-trons are accelerated at supernova remnantshock fronts and lose their energy via syn-chrotron radiation at radio wavelengths. Thus,from this very general statement, a correla-tion between radio and far-infrared emissionis expected. A detailed modeling of the cor-relation, however, remains di ffi cult when try-ing to explain all observations. While a calori-metric model, in which all electrons lose theirentire energy to synchrotron radiation seemsfeasible in the theoretical framework as pre-sented by V¨olk (1989), observations of the ra-dio spectral index in starburst galaxies showrelatively flat spectra: On average, radio spec-tra in the GHz range behave as ∼ ν − . . Thesynchrotron spectral index α radio and primaryparticle spectral index α p are directly con-nected as (Rybicki & Lightman 1979) α p = · α radio + . (1)Thus, a synchrotron spectral index of α radio ∼ . α p ∼ .
6. In the calorimet-ric model, however, higher energy electronsshould lose all their energy, resulting in spec-tra as steep as E − . An alternative model, basedon a cosmic ray driven wind model for star-burst galaxies, is discussed by Becker et al.(2009). Here, the non-thermal radio flux, in-duced by electron synchrotron losses, turns outto be only weakly dependent on the magneticfield of the starburst ( F ν ∝ B . ), even withoutthe assumption of a calorimeter. The questionremains whether or not electrons can partly es-cape the starburst galaxies and more detailedcalculations have to be performed in order tomatch all observational features.An additional complication in the interpre-tation of electromagnetic radiation from star- burst galaxies is the apparent co-existence be-tween starburst galaxies and active Seyfertcores. Figure 1 shows those galaxies that re-veal an active core in a starburst galaxy as filledtriangles. Thus, when the emission cannot beresolved spatially, ambiguities can arise con-cerning the electromagnetic contribution fromthe central activity and the starburst part of thegalaxy.
3. Hadronic interactions at E > GeV
A significant part of the total energy budgetof a galaxy goes into the acceleration of cos-mic rays. It is known from the observation ofthe charged cosmic ray flux at Earth, that thetotal energy carried by Galactic cosmic rayswith energies above 100 GeV corresponds toa total luminosity of ∼ erg / s. The shockfronts of supernova remnants are one of theprimary candidates for the acceleration of cos-mic rays up to 10 eV or higher (Stanev et al.1993; Biermann et al. 2009, 2010a,b). Wheninteracting with the local gas of the consid-ered galaxy, a significant amount of the pri-mary cosmic rays’ energy is put into the pro-duction of high-energy photons and neutrinos.While neutrino telescopes have not yet reachedthe sensitivity to detect di ff use emission fromthe Milky Way, gamma-ray emission is de-tected at a level of 10 erg / s. Thus, the trans-port of cosmic rays in a galaxy is expected toplay a significant role considering the dynam-ics of the galaxy itself. The di ffi culty in pin-pointing the sources of cosmic rays themselveslies in the complexity of the transport of thecharged particles through the galactic magneticfield. For the Milky Way, the observed flux ofcosmic rays contains information about the to-tal energy budget and the spectral behavior af-ter transport. However, no direct informationon the direction of the sources of cosmic raysor about the primary spectra at injection can bededuced from observations. Concerning star-burst galaxies, compared to the high cosmicray flux from the Milky Way, any possible sig-nal in charged cosmic rays would be negligi-ble. So, in general, in order to understand therole of cosmic rays in a galaxy, the search forneutral secondaries like photons and neutrinos
84 Becker: Starburst galaxies (cid:1) (cid:2) (cid:3) z (cid:5) I (cid:9) (cid:10) (cid:11) ) R(cid:14),86F6F,86I6I,86R6R,86666,867 (cid:1)(cid:2)(cid:3)z(cid:5) (cid:19)(cid:20)(cid:21) )
67 67,8 68 68,8 6(cid:22) 6(cid:22),8 6(cid:23) 6(cid:23),8 6(cid:24) 6(cid:24),8 6(cid:14)
Fig. 1.
FIR-radio correlation for a sample of local starburst galaxies at z ≤ .
03, showing a linear correlationbetween the two wavelengths. Luminosities are given in units of erg / s. The sample contains a significantfraction of sources which, apart from the starburst behavior of the galaxy, reveal Seyfert-like properties ofthe galaxy core. While those galaxies with no Seyfert core identification are shown as open triangles, thesupposed Seyfert-starburst composites are shown as filled triangles. from hadronic interactions is one of the mostinteresting approaches.High-energy photons and neutrinos areproduced in hadronic interactions, in environ-ments with a high flux of high-energy cos-mic rays j p ( E p ) and a large target density n H (Becker et al. 2009): p p → N ( π + /π − /π ) + X . (2)Here, N ( π + /π − /π ) denotes that multiple pi-ons N are created in the process. Charged pi-ons contribute to the production of high-energyneutrinos, π + → µ + ν µ → e + ν e ν µ ν µ (3) π − → µ − ν µ → e − ν e ν µ ν µ . (4)Neutral pions produce high-energy photons, π → γ γ .Assuming that the dominant part ofcharged cosmic rays below 10 eV is accel-erated in supernova remnants, the target den-sity directly at the acceleration site is im-portant as a local e ff ect. At high hydrogendensities, cosmic rays interact directly at thesource and the neutral interaction products re-veal the spectral shape at injection. For sourcesthat have proton-proton optically thin environ-ments, most protons will escape the acceler-ation region and change their energy spec-trum due to transport e ff ects. Then, interactionswith the di ff use gas in the galaxy serve as a tracer of the cosmic ray spectrum after trans-port. Measurements concerning the transportof cosmic rays through the Milky Way’s mag-netic field indicate that di ff usion steepens theinjection spectrum by a factor of ∼ E − . − E − . (Gupta & Webber 1989). With the ob-served spectrum being close to E − . , the ex-pected cosmic ray energy spectrum at injec-tion is expected to be close to E − . − E − . .At gamma-ray energies above ∼
300 MeV, thephoton spectrum roughly follows the chargedcosmic ray spectrum in the case of hadronicinteractions. Thus, the observation of the spec-tral behavior of gamma-rays from a galaxy canhelp to identify if the interactions on averagetake place close to the remnant, at injection, orrather in the interstellar medium, after trans-port. While observations of our own Galaxyindicate that propagation steepens the cosmicray spectrum before interactions take place, thetwo starburst galaxies with observed gamma-ray spectra, M82 and NGC253, reveal a quiteflat spectral behavior of around E − . . Thus, itis expected that a large fraction of the cosmicray interactions happen in the vicinity of thesources. ecker: Starburst galaxies 285 As of today, there are six objects observed atgamma-ray energies, where the emission ap-pears to arise from hadronic interactions: – M82 (Starburst galaxy)– NGC253 (Starburst galaxy)– The Milky Way– Star-forming region 30 Doradus (LargeMagellanic Cloud)– NGC1068 (Starburst-Seyfert composite)– NGC4945 (Starburst-Seyfert composite)
Although the statistics with only six objects re-vealing hadronic interactions is still low, it isworth to have a first look at what kind of cor-relations to expect and to investigate if thoseshow up in this still very small sample. It isclear that there are many caveats when lookingfor correlations in this small sample: the onlytrue starburst galaxies are M82 and NGC253.The star-forming region 30 Doradus is only apart of the dwarf galaxy. The Milky Way isa regular galaxy with contributions to the FIRemission from stars that do not explode as su-pernovae. Thus, the Milky Way is not expectedto lie on the FIR-radio correlation curve. Thetwo starburst-Seyfert composites could havecontributions from the active core in all wave-length ranges. Thus, future observations of alarger sample of pure starburst galaxies willhave to confirm or reject the results presentedbelow.
From Fermi- and IACT-observations, thegamma-ray flux from M82, NGC253, theMilky Way and the star-forming region 30Doradus in the LMC are known (Abdo et al.2010a). The measurements give a unique op- portunity to draw conclusions about the pri-mary cosmic ray flux.First of all, the gamma-ray spectra forM82 and NGC253 appear to be very flat, i.e. E − . and flatter. In the observed energy region( > GeV), the hadronic gamma-ray flux followsthe spectral behavior of the primary cosmicrays.Since the gamma-ray spectrum reproducesthe same spectral shape as the interactingprimary particles, most of the interactionsmust happen close to the acceleration re-gion: while the injection spectrum is expectedto be close to E − . − E − . (Stanev et al.1993; Biermann et al. 2009, 2010a,b), trans-port through the galactic magnetic field steep-ens the charged primaries’ spectrum to E − . .Interaction after transport into the ISM wouldtherefore lead to a steep gamma-ray spectrumof close to E − . , j γ = dN γ dE γ dt dA Earth , (5)in units of GeV − s − cm − .The number of pion-decay inducedgamma-rays of a single SNR in a starburstper unit time, volume and energy is given(Kelner et al. 2006), Φ γ ( E γ ) = n H ·· Z ∞ E γ σ inel ( E p ) · j p ( E p ) · F γ E γ E p , E p ! dE p E p . (6) Here, n H is the density of the ambient mediumand σ inel ( E p ) is the cross section of inelas-tic proton-proton interactions . The function F γ ( x , E p ) implies the number of photons in theenergy interval ( x , x + dx ) per collision andis a dimensionless probability density distribu-tion function. The flux of relativistic protons atthe source is given as j p ( E p ) = a p · Φ ( E p ) . (7) Here, j p is given per energy, time and areainterval. The spectral shape of the interactingproton flux is contained in the function Φ ( E P )and can be expected to follow a power-law, Kelner et al. (2006) use the cosmic ray density,while here the cosmic ray flux is used.86 Becker: Starburst galaxies Φ ∼ E − p , while a p is defined as the normal-ization factor, i.e. how many protons there areper energy, time and area interval. This normal-ization can be done at an arbitrary energy, wechose E p = V of a single SNR and the number of SNRs N SNR ,which scales directly with the SN rate R SN ofthe galaxy. Further, assuming isotropic emis-sion, the detected flux scales with 1 / (4 π d ).The observed flux is then directly connected tothe produced density as Φ | ⊕ = Φ γ ( E γ ) · V · N SNR · (cid:16) π d (cid:17) − (8) = n H · V π d · (9) · Z ∞ E γ σ inel ( E p ) · j p ( E p ) · F γ E γ E p , E p ! dE p E p . Assuming a proton flux at the source follow-ing a power-law with normalization a p and aspectral shape Φ ( E p ) yields Φ | ⊕ = a γ · (10) · Z ∞ E γ σ inel ( E p ) · Φ p ( E p ) · F γ E γ E p , E p ! dE p E p , with a γ = a p · n H · V · N SNR π d . (11)This factor needs to be fixed to a certain valueto match the observations, and conclusionsabout the parameters on the right-hand side canbe drawn.The proton spectral normalization, a p canbe calculated using the conservation of energy: Z ∞ E min j p E p dE p = a p · Z ∞ E min Φ ( E p ) E p dE p = W p · cV . (12) where W p is the total proton energy budgetof protons with a minimum energy of E min ,assuming the protons travel approximately at the speed of light. Solving the equation for a p gives: a p = W p · cV · R ∞ E min Φ ( E p ) E p . dE p , (13)Thus, the normalization of the photon spec-trum can be written as a γ = W p · c · n H · N SNR π d · R ∞ E min Φ ( E p ) E p dE p . (14)Given the distance to the source and determin-ing the average shape of the primary particlespectrum from the shape of the gamma-rayspectrum, the product of the total cosmic rayenergy budget, the target density and the num-ber of SNRs, W p · n H · N SNR determines thegamma-ray flux normalization. Alternatively,the cosmic ray energy density ρ CR = W p / V canbe used, and in this case, it is the product withthe total interacting mass, ρ CR · M · N SNR = ρ CR · n H · V · N SNR (15)is the determining factor. Thus, assuming aconstant cosmic ray energy density and a di-rect scaling of the number of SNRs with thesupernova rate R SN would result in a direct pro-portionality between the observed gamma-rayemission and the total interacting gas mass.First Fermi results seem to suggest thata correlation between the gamma-ray lumi-nosity and the product of the supernova rateand the total gas mass is present (Abdo et al.2010a). However, the calculation has severalcaveats: For once, it is not likely that the cos-mic ray energy density is constant for all star-burst galaxies. In addition, it is assumed herethat all SNRs have the same cosmic ray energyspectrum, although it is known that the spec-trum actually strongly depends on their age andthe local environment of the sources, see e.g.Blasi et al. (2005) and references therein. Onemight consider to rather search for a correla-tion between the product of the SN rate andthe gas density with the total gamma-ray flux.However, even in this case, the above calcu-lations rely on the fact that the energy budgetfor each SNR is the same. However, it is ex-pected that it depends on the total mass of the ecker: Starburst galaxies 287 stars and the energy put into cosmic rays mightnot even be a constant for the same progeni-tor star mass, but depend on the local environ-ment. Further, the spectral behavior of the cos-mic rays might vary depending on the local en-vironment. And, finally, the average observeddensity of the galaxy might not represent theaverage density in which the secondary pho-tons are produced. The non-thermal radio emission at GHz fre-quencies is expected to come from synchrotronradiation of electrons accelerated at supernovashock fronts. The gamma-ray emission, on theother hand, is believed to have the same ori-gin, following the interpretation of the signalas the interaction of cosmic rays with the am-bient medium. Thus, a correlation between theradio and gamma-ray luminosities is expectedto be present. Figure 2 shows the gamma-rayluminosity for the six objects versus their radioluminosity. A clear trend of increased gamma-ray emission at enhanced radio emission is ob-served. While the performed power-law fit iscompatible with a linear correlation of the twoemission features, the lack of statistics doesnot allow for the formulation of a quantitativestatement on this correlation. This might stillbe a first hint that there is a connection betweenthe two wavelengths, which could further beused to study acceleration processes.
Due to the co-production of high-energy pho-tons and neutrinos, hadronically producedgamma-rays are always accompanied by aneutrino flux. Due to their low interactionprobability, the detection of neutrinos requiresthe use of kilometer-scale natural water orice reservoirs, see e.g. Becker (2008). As ofDecember 18, 2010, the first cubic-kilometerscale neutrino detector IceCube was completedat the geographic South Pole. The detectiontechnique allows for the observation of the en-tire northern hemisphere at a duty cycle of γ (cid:2) (cid:3) γ (cid:4) (cid:5)8 (cid:7)(cid:8) γ (cid:9) (cid:10) (cid:11) z (cid:13) (cid:14) (cid:1)(cid:2) (cid:3)(cid:4) (cid:1)(cid:2) (cid:3)(cid:1) (cid:1)(cid:2) (cid:2) (cid:1)(cid:2) (cid:1) (cid:1)(cid:2) (cid:4) (cid:1)(cid:2) (cid:5) (cid:2) (cid:15)(cid:16)(cid:17)(cid:18) γ(cid:4)(cid:5)8 (cid:7)(cid:19) γ(cid:9)(cid:10)(cid:11)z(cid:13)(cid:14) (cid:1)(cid:2) (cid:3)(cid:4) (cid:1)(cid:2) (cid:3)(cid:1) (cid:1)(cid:2) (cid:2) (cid:1)(cid:2) (cid:1) (cid:1)(cid:2) (cid:4) Fig. 2.
Luminosities at gamma-ray energies asmeasured by Fermi versus radio luminosities at5 GHz. Shown are the LMC, the Milky Way, M82,NGC253, NGC1068 and NGC4945, using the dataas summarized by Lenain et al. (2011). The linerepresents a power-law fit to the data. Due to thesmall number of sources, the error of the correlationis still too large to make a quantitative statement.Qualitatively, the result is compatible with a linearcorrelation. more than 99%. The main background areneutrinos produced in the Earth’s atmosphere.Point source searches can be performed forsingle sources as well as by the stacking ofa source list. If a contribution from unresolv-able sources is expected, which is the casefor instance for several classes of active galac-tic nuclei, a search for a di ff use flux can beperformed. Since astrophysical sources are ex-pected to produce relatively flat neutrino en-ergy spectra for interactions at the source ( ∼ E − − E − . ), the explicit search for enhancedemission at the highest energies reduces thebackground of the very steep atmospheric neu-trino flux ( ∼ E − . ).Concerning the case of starburst galaxies,the gamma-ray detection from M82 gives afirst concrete test case of the expected neu-trino flux from a point source. It turns outthat the flux of M82 as a single source is rel-atively low and it is not expected to be de-
88 Becker: Starburst galaxies tected within the first years of operation withIceCube. It may still be possible to observeM82 after a longer period of measurement,as the lifetime of IceCube is expected to belonger than 10 years. On the other hand, thestacking of a source catalog of nearby starburstgalaxies strongly improves the detection sig-nificance. As the significance roughly scaleswith the signal over the square root of the back-ground, adding more signal to the search helpsto reveal the signal over background. A firststacking search for starburst galaxies has beenperformed with partially completed configura-tions of the IceCube detector, see Dreyer et al.(2010); Abbasi et al. (2010). It is expected thatwithin the next few years, the limits can be im-proved using a detector of more than twice thesize. The detection of a di ff use flux from star-burst galaxies is rather challenging, since themaximum neutrino energy may be as low as10 eV.
4. Molecular ions as cosmic raytracers
While protons with GeV energies and abovecontribute to the neutrino- and photon flux ofa galaxy, low-energy cosmic rays in the keV-GeV range ionize the interstellar medium. Inthe Milky Way, the average ionization levelis observed to be of the order of ζ ≈ · − s − (Gerin et al. 2010; Neufeld et al.2010). Hydrogen ionization immediately leadsto the formation of H + , which in turn initi-ates the formation of larger molecules like H + , OH + , H O + etc., see e.g. (Black 1998) andreferences therein. Those molecules can be ob-served by detectors like Herschel and ALMAand can be used as direct tracers of cosmicray ionization. The search for molecular ionsat potential cosmic ray acceleration sites withsuitable targets might help to trace the sourcesof cosmic rays and by that improve the under-standing of the role of cosmic rays in the dy-namical processes of galaxies.In the Milky Way, several systems of su-pernova remnants and molecular clouds (SNR-MC systems) have been detected at gamma-ray energies in the past years. In partic-ular, the detections of the sources W51C (Abdo et al. 2009), W44 (Abdo et al. 2010c),W28 (Abdo et al. 2010b), IC443 (Abdo et al.2010d) and W49B (Abdo et al. 2010e) withthe Fermi Gamma-ray Space Telescope arebest-fit with a hadronic interaction model. Theobserved gamma-ray spectra can be used to es-timate the primary cosmic ray spectra at thesource above GeV energies. Extrapolating thespectrum down to below GeV energies thengives the opportunity to perform calculationsconcerning interaction of the low-energy partof the cosmic ray spectrum leading to the ion-ization of the local medium. Details of the cal-culation are presented in Becker et al. (2011).Due to the enhanced flux of cosmic rays, theionization level is expected to be enhanced by afew orders of magnitude at the discussed SNR-MC systems. In such an environment, the de-tection of line emission spectra from H + andH + would be the most direct tracer for cosmicray ionization.Line emission from H + has been dis-cussed previously in the context of cosmicray ionization, and it represents one of themolecules observed in astrophysical contexts,see e.g. (Black 1998) and references therein.With the launch of the Herschel telescope, de-tailed observations of the abundance of H + isnow possible in astrophysical environments. InIndriolo et al. (2010), for instance, an H + abun-dance corresponding to an ionization rate of ∼ · − / s was observed.Although H + is the first product of cos-mic ray ionization, it is usually destroyed tooquickly to produce significant line emission.However, in an environment of extreme ioniza-tion level as it seems to be the case for SNR-MC systems, the detection of H + seems to bepossible and would provide a unique method totrace the sources of cosmic rays.Due to their high star formation rate, star-burst galaxies are bound to host a larger num-ber of SNR-MC systems. In the future, itwould therefore be interesting to try to com-bine gamma-ray measurements with the searchfor molecular line emission in order to be ableto pin-point the cosmic ray component of thegalaxies. Acknowledgements.
The authors would like tothank S. Aalto, P. L. Biermann, J. H. Black, S.ecker: Starburst galaxies 289Casanova, J. S. Gallagher, E. J¨utte, M. Olivo and R.Schlickeiser for helpful and inspiring discussions.
References
Abbasi, R. et al. (IceCube Coll.), 2010, ApJ,732, 18Abdo, A.A. et al. (Fermi Coll.), 2009, ApJ,706, L1Abdo, A.A. et al. (Fermi Coll.), 2010, ApJ,709, L152Abdo, A.A. et al. (Fermi Coll.), 2010, ApJ,718, 348Abdo, A.A. et al. (Fermi Coll.), 2010, Science,327, 1103Abdo, A.A. et al. (Fermi Coll.), 2010, ApJ,722, 1303Abdo, A.A. et al. (Fermi Coll.), 2010, ApJ,712, 459Becker, J.K. 2008, Phys. Rep. 458, 173Becker, J.K. et al. 2011, arXiv:1106.4740, sub-mittedBecker, J.K. et al. 2009, arXiv:0901.1775Biermann, P.L. et al. 2009, Phys. Rev. Lett.,103, 061101Biermann, P.L. et al. 2010, ApJ, 710, L53Biermann, P.L. et al. 2010, ApJ, 725, 184Black, J.H. 1998, Chem. & Phys. of Molecules& Grains in Space, 109, 257Blasi, P. et al. 2005, MNRAS, 361, 907Dreyer, J. et al. (IceCube Coll.) 2010, ASTRA,7,7Gerin, M. et al. 2010, A&A, 518, L110Gupta and Webber 1989, ApJ, 340, 1124N. Indriolo et al. 2010, ApJ, 724, 1357Kelner, S.R. et al. 2006, Phys. Rev. D, 74,034018Lenain, J.-P. et al. 2011, A&A, 524, 72LNeufeld, D.A. et al. 2010, A&A, 521, L10Stanev, T. et al. 1993, A&A, 274, 902Rybicki and Lightman, 1979, “Radiative pro-cesses in astrophysics”V¨olk 1989, A&A, 218, 67
DISCUSSIONARNON DAR:
Theoretical arguments ratherpoint to a correlation between the gamma-ray flux and the density of the galaxy, and not to ascaling with the total gas mass.
JULIA BECKER:
Assuming a constant totalenergy budget for all SNRs, this is correct, thescaling should be with the target density of theinteraction. However, assuming a constant cos-mic ray energy density gives a scaling with thetotal gas mass. The di ffi culty with both argu-ments is that there still are a lot of assumptionsin both statements: For instance, in both calcu-lations, all SNRs are assumed to have the samecosmic ray injection spectrum. This is not thecase in reality. In addition, the average densityof the galaxy does not necessarily represent theactual density relevant for the interactions. WOLFGANG KUNDT:
How do you avoidthe production of hard electrons from ioniza-tion?