Cosmic Rays VI - Starburst galaxies at multiwavelengths

0.56 MB·English

by  Julia K. Becker

Astronomy&Astrophysicsmanuscriptno.starburst˙astroph c ESO2009
(cid:13)
January23,2009
Cosmic Rays VI
Starburst Galaxies at multiwavelengths
JuliaK.Becker1,2,⋆,PeterL.Biermann3,4,5,6,7,JensDreyer2,andTanjaM.Kneiske2,8
9
0 1 Go¨teborgsUniversitet,Institutionenfo¨rFysik,41296Go¨teborg,Sweden
0 2 TechnischeUniversita¨tDortmund,Institutfu¨rPhysik,D-44221Dortmund,Germany
2 3 MPIforRadioastronomy,AufdemHu¨gel69,D-53121Bonn,Germany
4 Dept.ofPhys.&Astron.,Univ.ofBonn,Germany
n
5 Dept.ofPhys.&Astron.,Univ.ofAlabama,Tuscaloosa,AL,USA
a
J 6 Dept.ofPhys.&Astron.,Univ.ofAlabama,Huntsville,AL,USA
7 Inst.Nucl.Phys.FZ,KarlsruheInst.ofTechn.(KIT),Karlsruhe,Germany
3
8 UniversityofHamburg,Institutfu¨rExperimentalphysik,Hamburg,Germany
1
January23,2009
]
E
ABSTRACT
H
. Context.Starburstgalaxiesshowadirectcorrelationbetweenradioandfar-infraredemission.Hightargetdensitiesandahighrate
h
of supernova explosions imply the possibility of accelerating hadronic cosmic rays and producing decay products from hadronic
p
interactions,likehigh-energyneutrinosandphotons.
-
o Aims.Weproposeanexplanationforthefar-infrared/radiocorrelationofgalaxiesintermsoftheenergybalanceoftheinterstellar
r mediumanddeterminethefluxfromhigh-energyphotonsandneutrinosfromstarburstgalaxies.
t Methods.Wepresentacatalogofthe127brighteststarburstgalaxieswithredshiftsofz<0.03.Inordertoinvestigatethecorrelation
s
between radio- and far-infraredemission, we apply theleaky box approximation. Further, wederive photon- and neutrino spectra
a
[ fromproton-protoninteractionsinsupernovaremnants(SNRs).Here,weassumethatafractionoftheSNR’senergyistransferredto
theaccelerationofcosmicrays.WealsoinvestigatethepossibilityofdetectingGammaRayBurstsfromnearbystarburstgalaxies,

1 usingthecatalogdefinedhere.
v Results.Weshowthattheradioemissionisonlyweaklydependentonthemagneticfield.Itturnsoutthattheintensityoftheradio
5 signal is directly proportional to the number of supernova explosions, which scales with the far-infrared luminosity. In addition,
7 wefindthathigh-energyphotons fromproton-proton interactionsinSNRsinstarburstscanmakeupseveral percentofthediffuse
7 gamma-raybackground.Theneutrinofluxfromthesamesourceshasamaximumenergyof 105 GeV.Neutrinoscan,ontheother
1 hand,canbeobservedifaGammaRayBursthappensinanearbystarburst.About0.03GRB∼speryearareexpectedtooccurinthe
. entirecatalog.Thetruenumberisexpectedtobeevenhigher,sinceweonlyincludethebrightestsources.Thenumberofeventsper
1
burstinIceCubevariesbetweenaboutoneeventandmorethan1000events.ThisprovidesgoodprospectsforIceCubetodetecta
0
significantevent,sincethebackgroundforaGRBsearchisclosetozero.
9
0 Keywords.Galaxies:starburst–Infrared:galaxies–Radiocontinuum:galaxies–Catalogs–cosmicrays–Neutrinos
:
v
i
X
1. Introduction Galaxiesalsohaveabundantfar-infrared(FIR)emission,which
r is dueto dust. Thisdustis heatedby stars, oftenmostly young
a
Radio emission from galaxies is usually dominated by syn- stars. As was noted from the mid-eighties, this thermal dust
chrotron emission from a population of non-thermal, energetic emissioncorrelatesratherwellwiththenon-thermalradioemis-
electrons in a magnetic field which permeates most of the in- sion. The correlation in its most simple form is just a propor-
terstellar medium. This radio emission is often spatially struc- tionalitybetweenfar-infraredandnon-thermalemission.Asref-
tured, such as in the starburst galaxy M82, showing individual erence wavelengths, 60µm and 100µm are used for the far-
compact sources, which can be interpreted as fairly young su- infrared. Frequencies between 1.4GHz and 5GHz are used as
pernova remnants (Kronbergetal., 1985; Kronberg&Sramek, typicalfortheradioregime.
1985; Barteletal., 1987). The origin of these energetic elec-
Manyattemptshavebeenmadetounderstandtheproportional-
trons,apartofthecosmicrays,isthusexpectedtobetheyoung
itybetweenradioandfar-infrared.Onthebasisofrathersimple
supernova remnants, see Baade&Zwicky (1934); Shklovskii
modeling of galactic evolution, a strong correlation is actually
(1953)andforaextensivereviewBerezinskyetal.(1990).Thus
expected,sincebothsupernovaremnantsandthedominantheat-
the radio emission is a key to interpret the physics of cosmic
ingbyultravioletlightfrommassivestarsderivesfromthesame
rays, and conversely, any attempt to understand cosmic rays
stellarpopulation(Biermann,1976;Biermann&Fricke,1977).
should also try to understand the properties of the radio emis-
Using such models the far-infrared luminosity of NGC2146
sion.
had been predicted by Kronberg&Biermann (1981) and veri-
fied subsequentlyby IRAS observations(Moshiretal., 1990a).
⋆ Correspondingauthor.Contact:[email protected],phone: The correlation as seen in the data was first clearly stated by
[phone] deJongetal.(1985),andsubsequentlydiscussedatsomelength
2 JuliaK.Beckeretal.:CosmicRaysVI
by many authors (Bicayetal., 1989; Wunderlichetal., 1987; FIR luminosity vs. distance
Wunderlich&Klein, 1988, 1991; Condonetal., 1991). It still ] 34
s
defiesaclearexplanation. g/
An extensive attempt to interpret the correlation was made er 33
[
bLyiseVnfo¨ellkdeatnadl.,c1o9ll9a6b)o.rTathoersele(Vctor¨olkn,sa1r9e8b9e;liXevueedttaol.l,os1e9a9l4lbe,na-; )micron32
0
ergy in this model and therefore, the correlation is calorimet- L6
ric.However,thiswouldpredictanactualsteepeningofthera- g( 31
o
dioemissionbetweenthereferencefrequencies,aneffectwhich L
is not seen in the data. The solution of a spatial mixture of 30 No cuts
cutoffs would still allow for a locally loss-dominated scenario. z<0.03, S >= 4 Jy ,S >= 20 mJy
However,first spatially resolvedobservationsof M 33 indicate 29 60 micron 1.4 GHz
4 Jy flux
that the local star-forming regions typically have flat spectra,
too (Tabatabaeietal., 2007a,b). It is therefore likely that star 2-08.05 0 0.05 0.1 0.15 0.2 0.25 0.3
formingregionsaregenerallyinjectiondominated. Luminosity distance [Gpc]
Here, we proposea simple model,basedupona particularpic-
tureoftheenergybalanceintheinterstellarmedium.Thismodel
Fig.1. 60µ luminosity - distance diagram. Crosses indicate all
alsousessomesimple assumptions,aswewillemphasize.The
309pre-selectedstarburstgalaxies,squaresshowthoseremain-
model is local, and so automatically allows for starbursts and
ingafterthecutsS >20mJyandS >4Jyandz<0.03.
1.4GHz 60µ
gradientsindiskgalaxies,whileupholdingthecorrelation.The
ThedashedlineshowsthesensitivityforS >4Jy.
60µ
modelleadstosomespecificpredictionswhichcanbechecked
withfurtherdata.Acatalogofstarburstgalaxiesispresentedto
performfirstchecks. Onlylocalsourcesareconsidered,sinceouraimistoinvestigate
Theoutlineofthispaperisasfollows:Wefirstdefinevariables, theclosestsources.Thecatalogpresentedhereconsistsofatotal
used throughout the paper, in Section 2. In Section 3, a cata- of127starburstgalaxies.Thisisasub-samplefromalargersam-
logof127nearby,brightstarburstgalaxiesispresented,includ- pleof309starburstgalaxies,applyingcutsatbothFIRandradio
ing far-infrared,radioand X-ray data. The correlationbetween wavelengthstoensureacomplete,localsample.Thesecutsare
FIR and radio emission is outlined together with the difficulty discussedinthefollowingparagraphs.Differenttestswereper-
ofexplainingit.InSection4,wepresentamodelexplainingthe formedinordertoverifythattheconsideredgalaxiesareindeed
FIR-radiocorrelation.Thepossibleemissionofcosmicraysand starbursts,aspresentedinthefollowingparagraphs.Inorderto
secondariesproducedinproton-protonandproton-photoninter- removecontaminationfromSeyfertgalaxies,we onlyuse high
actionsis discussedin Section5. In particular,we examinethe ratiosofFIRtoradiofluxdensity,i.e.S /S >30.Totest
60µ 1.4GHz
possibilityofdetectingsecondariesfromsupernovaremnants,as ifthesampleconsistsofstarburstgalaxiesasopposedtoregular
wellascosmicraysandsecondariesfromGammaRayBurstsin galaxies,wecheckthatthecorrelationbetweenradiopowerand
starbursts.Finally,implicationsarediscussedinSection6. FIR luminosityis a direct proportionality.Apartfrom that, our
maincriterionforthecatalogisthatthesourcesarecloserthan
z < 0.03, i.e. located in the supergalactic plane, and that they
2. Definitions
havebothradio andIRdetections.The latter givesusinforma-
Inthefollowingsections,theelectromagneticspectraatdifferent tionabouttheratiooftheIRtoradiosignal,whichwerequireto
wavelengthsareusedinordertoinvestigatethestarburstnature belargerthan30.Thisensuresa highIRcomponentcompared
ofthecatalogsources.Table1givesasummaryofthedifferent to the radio part, i.e. that the sources are indeed starbursts and
parametersused.Concerningspectralpower-lawfitsbetweenthe notSeyfertgalaxies.Further,weapplysensitivitycuts,weonly
wavelengths,weusetheconvention includesourceswithafluxdensity> 4Jyat60µmandaradio
fluxdensityat1.4GHzlargerthan20mJy.Figures1and2show
ν α the60µmresp.1.4GHzluminosityofstarburstgalaxiesversus
S =S , (1)
0· ν ! their luminosity distance. The dotted lines represent the sensi-
0
tivity for 4 Jy, resp. 20 mJy. Crosses represent all 309 sources
with S as the flux per area and frequency interval, in units of we selected in the beginning, squares show those 127 sources
Jy=10−26W/m2/Hz. Here, S0 is the flux at a reference fre- remainingafter the cuts at S1.4GHz > 20 mJy and S60µ > 4 Jy,
quencyν0. as well as z < 0.03. We apply those cuts in order to ensure a
complete,localsampleinbothFIRandradiowavelengths.
Since the sources are closer than z = 0.03, many of the star-
3. Localstarbursts:asample
bursts are located in the supergalactic plane. Their spatial dis-
Inthissection,wepresentasampleoflocalstarburstgalaxies1. tributionshouldthereforebeaflatcylinderwithafurthermore
ThedataoftheindividualsourcesarepresentedinappendixA. sphericalcomponent,forthose sourcesnotin the supergalactic
plane. We therefore expect that the number of sources with a
1 The data have been collected from the references
(Heeschen&Wade, 1964; Whiteoak, 1970; Sramek, Douglasetal., 1996; Condonetal., 1996, 1998; Whiteetal., 2000;
1975; Sramek&Tovmassian, 1976; Disney&Wall, 1977; Condonetal., 2002; Sandersetal., 2003; Stricklandetal., 2004;
Dressel&Condon, 1978; Ku¨hretal., 1981; Condonetal., 1983; Vollmeretal., 2004; Suraceetal., 2004; Bravo-Alfaroetal., 2004;
Wright&Otrupcek, 1990; Condon, 1983; Beichmanetal., 1988; Leroyetal., 2005a; Nagaretal., 2005; Ottetal., 2005; Leroyetal.,
Soiferetal., 1989; Moshiretal., 1990b; Beckeretal., 1991; 2005b; Ionoetal., 2005; Tajeretal., 2005; Tengetal., 2005;
Fabbianoetal., 1992; White&Becker, 1992; Brinkmannetal., Guainazzietal.,2005;Baan&Klo¨ckner,2006;Tu¨llmannetal.,2006;
1994; Knapp, 1994; Wrightetal., 1994; Griffithetal., 1994, 1995; Gallimoreetal., 2006; Lisenfeldetal., 2007; Rosa-Gonza´lezetal.,
Beckeretal., 1995; Rigopoulouetal., 1996; Wrightetal., 1996; 2007;Shuetal.,2007)
JuliaK.Beckeretal.:CosmicRaysVI 3
parameter symbol units
Electronspectrum
––psericmonadryary ddNNee//ddEEee ∝∝EEee−−ααpeseercim GGeeVV−−11ss−−11ssrr−−11ccmm−−22
Electronenergy E keV
e
espectralindex
–primary αprim
e
–secondary αsec
e
Protonspectrum
dNp/dEp =Ap·(Ep/Emax)−αp· GeV−1s−1sr−1cm−2
exp( E /E )
· − p max
Protonenergy E GeV
p
pspectralindex α
p
pcutoffenergy E GeV
max
Neutrinospectrum dNν/dEν =Aν·(Eν/GeV)−αν GeV−1s−1sr−1cm−2
Neutrinoenergy E GeV
ν
νspectralindex α
ν
normalizationfactor A GeV 1s 1sr 1cm 2
ν − − − −
Radiofluxdensity
–at1.4GHz,2.4GHz, 2.7GHz&5GHz S ,S , S , S mJy
1.4GHz 2.4GHz 2.7GHz 5GHz
IRfluxdensity,IRAS
–at12µm, 25µm, 60µm&100µm S ,S ,S &S Jy
12µ 25µ 60µ 100µ
IRfluxdensity,2MASS Jy
–at1.25µm,1.65µm&2.17µm S , S ,S Jy
1.25µm 1.65µm 2.17µm
X-rayfluxdensity,ROSAT
–btw.[0.1-4.5],[0.1-2.3]or[0.2-2.0]keV S nJy
ROSAT
spectralindex
–btw1.4GHz&5GHz α
–btw1.4GHz&60µm α
rir
–btw60µm& 1keV α
∼ xir
Table1.Summaryofparametersusedinthispaper.
Radio luminosity (cid:10) 1.4GHz vs. distance NN>(S> Sv)s .v IsR. IfRlu fxl u(cid:10) 6x0 (cid:10) 6m0i croµnm w withit hc uctust sa papplpielided
s] 32 S)
erg/ 31 N(>102 fit N(>S)=N0(S+S0)-β
[
)
Hz 30
G
4
L1. 29
g( 10
o 28
L
No cuts
27
z<0.03, S >= 4 Jy ,S >= 20 mJy
60 micron 1.4 GHz 1
26
20 mJy flux
25
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
Luminosity distance [Gpc] Log(S )[Jy]
60µm
Fig.2. 1.4 GHz luminosity - distance diagram. Same notation Fig.3.logN logS representationofthecatalog.AnS 1.2 fit
−
− −
as Fig. 1. The dashed line shows the sensitivity for S > matchesthedatanicely,withaturnoveratS =10.56Jy.
1.4GHz 0
20mJy.
Here,N , S andβarefitparameters.Usinganerrorof √N,the
0 0
parametersaredeterminedto
fluxdensitylargerthanS, N(> S),shouldfollowabehaviorof N0 = 3155 1297.9
±
Sde−r1,−whSi−le1.5a.sAphpeurirceaSld−1is−trbiebhuativoinorreissuelxtspeinctaendSfor1.a5 flbaethcayvliionr-. S0 = (10.56±3.78)Jy
− β = 1.2 0.2.
−
Figure3showsthelogarithmicnumberofsourcesaboveanFIR ±
fluxdensityS60µ.Wefitthedatawiththefollowingfunction: The behavior N(>S) S 1.2 0.2 matches the expectation that
− ±
thefunctionshouldlie∼betweenS 1.0andS 1.5.Inthefollowing
− −
paragraphs,wewillinvestigatefurtherwhethertheclassification
N(>S)= N (S +S ) β (2) ofthe127sourcesasstarburstsisjustified.
0 0 −
·
4 JuliaK.Beckeretal.:CosmicRaysVI
Radio Luminosity vs. FIR Luminosity (z>0.03, S60µm/SRadio>30, S60µm>=4Jy, SRadio>=20mJy) radiofluxdensityat1.4GHz,S1.4GHz:
) 32
]
z
H
S
s/ 31 s := 60µ . (6)
g/ 60µ/1.4GHz S
r 1.4GHz
e 30
[
z
H
G
1.4 29 For Seyfert galaxies, this ratio is about s60µ/1.4GHz ∼10, while
P it is significantly higher in the case of starburst galaxies,
(
og 28 s60µ/1.4GHz 300. The histogram of the ratio between the FIR
L flux density∼at 60µm and the radio flux density at 1.4GHz is
27 showninFig.5.All127sourceshavearatioofs60µ/1.4GHz >30,
whichconfirmsthatthesourcesarenotlikelytobeSeyferts.
26
41 42 43 44 45 46 47
Log(L [erg/s])
FIR
Flux ratios 60µm and Radio(1.4 GHz-5 GHz)(z>=0.03, fraction>=30, S60µm>=4 Jy, S1.4GHz>=20mJy)
Fig.4.RadiopowerP1.4GHzatν=1.4GHzversusFIRluminos- nt
ityL .Adirectproportionality,P L isfound. u 16
FIR 1.4GHz FIR o
∝ C
14
3.1.FIRluminosityversusRadiopower 12
10
Lookingatawelldefinedsampleofgalaxies,itturnsoutthatthe
correlationbetweenradioandfar-infrared(FIR)emissionisnot 8
linear, i.e., that the radio luminosity is proportional to the far- 6
infraredluminositytothepower1.30 0.03(Xuetal.,1994b).
± 4
AsXuandcollaboratorsnote,thefar-infraredemissionhastwo
heating sources, stars that do explode later as supernova rem- 2
nants,andalsostars,thatwillneverexplodeassupernovae.This 0
0.5 1 1.5 2 2.5 3 3.5
second population of stars needs to be corrected for, and their Log(S / S )
contribution to the dust heating needs to be eliminated. This 60µm 1.4GHz
then leads to a corrected far-infrared luminosity, which is di-
Fig.5. Ratio of the flux density at 60µm and at 1.4 GHz. All
rectlyproportionaltotheradioluminosity(Xuetal.,1994b).
sources in the sample have ratios larger than 30, which indi-
Theproportionalityholdsalongadiskinagalaxy,evenforfairly
catesahighstarformationrate.Themedianisaround100.This
shortlivedphaseslikeastarburst,suchasinM82,andthusre-
matches previous investigations, e.g. Biermannetal. (1985),
quiresclearlylocalphysics,withashortreadjustmenttimescale.
who find a mean value of 250 at higher radio frequencies,
Thisposesaseveredifficultyforanyproposaltoexplainthera-
ν=5GHz.
dio/FIRcorrelation.
The FIRluminosityin the rangeof 60µmand100µmis given
as(Xuetal.,1994b):
L :=4πd2 F . (3)
FIR l · FIR 3.3.RadiotoInfraredandX-raytoInfraredspectralindices
Here,d istheluminositydistanceoftheindividualsourcesand
l
A further criterion of distinguishing regular galaxies and
F :=1.26 10 14 2.58 S60µ + S100µ Wm 2 (4) Seyferts is their spectral index from X-ray to IR (XIR)
FIR · − ·" · Jy ! Jy !# − and from radio to IR (RIR). The diagram of the XIR
(1 keV to 60 µm) versus RIR (5 GHz to 60 µm) index of
istheFIRfluxdensityatEarthasdefinedinHelouetal.(1988). the sources in shown in Fig. 6. Derived from figure 3 in
Thenormalizationfactorcomesfromthe frequencyintegration (Rodriguez-Pascualetal., 1993), starburst galaxies have spec-
andfromthe conversionofJy to W/m2/Hz.InFig.4, theloga- tral indices scattering around (RIR,XIR) (0.6, 1.9),
starburst
rithmoftheradiopowerat1.4GHz,P1.4GHzversusthelogarithm Seyfert-Igalaxiesshow(RIR,XIR)Sy I (0.48, ∼1.2),Se−yfert-
oftheFIRluminosityLFIR isshownforourcatalog.Thecircles II galaxies have (RIR,XIR)Sy II −(0.∼47, 1.6−) and quasars
show the single sources and the solid line is a fit through the are located at (RIR,XIR) − (∼0.28, 1.−1). The values for
quasar
data.Thefityieldsacorrelationof the RIR and XIR indices of∼starburs−t galaxies given by
Chinietal. (1989) are slightly higher, which matches the sam-
P L 1.0. (5)
1.4GHz ∝ FIR ple examined here: Chinietal. (1989) give a RIR index of
This demonstratesthat short stellar lifetimes dominatethe cor- 0.82 and a XIR index of 1.66. We find average values of
−
relationinoursample,andsothisisstronglysupportingourhy- (RIR, XIR)=(0.82, 1.77) which is compatible with the ex-
−
pothesis,thatthemajorityofoursamplegalaxiesarestarbursts. pectedresult.
Still, we do not have X-ray data for all the sources, so there
may still be some contamination from both Seyferts and regu-
3.2.Infraredtoradiofluxdensityratio
lar galaxiesinthe sample.As we onlyused catalogswherethe
Generally,regulargalaxiesaredistinguishedfromactivegalax- sources have previously been identified as starbursts, this con-
iesbytheirratiooftheFIRfluxdensityat60µm,S ,andthe taminationshouldbesmall.
60µ
JuliaK.Beckeretal.:CosmicRaysVI 5
RIR Index vs. XIR Index Ithadbeenobservedearlythatthethreemaincomponentsofthe
x1.2 interstellarmedium,thegas,thecosmicrays,andthemagnetic
e field have very similar energy densities, or pressures. Since all
d Seyfert I Galaxies
R In 1 SQeSyOfesrt II Galaxies tahtraepepdreorxivimeafrteomeqvueipryardtiitffioenreinmtpplhiyessitchaaltptrhoectehsrseees,titmoekesecpaltehseomf
RI0.8 Mean of this sample changeare also all threethe same. Thisisthe basic premiseof
This sample
the following argument, and it will lead naturally to an under-
0.6 standingofthefar-infraredradiocorrelation.Sointhisspecific
sense it is a calorimetric argument similar to Vo¨lk (1989), al-
0.4 thoughweapproachtheproblemisasomewhatdifferentway.
The following line of reasoning is visibly influenced by
0.2 earlier papers, like Biermann (1950); Biermann&Schlu¨ter
(1951); Cox (1972); Cox&Smith (1974); McKee&Ostriker
-02.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 (1977); Beuermannetal. (1985); Kronbergetal. (1985);
XIR Index Kronberg&Sramek (1985); Snowdenetal. (1997);
Hunteretal. (1997); Becketal. (2003); Hanaszetal. (2004,
2006),andofcourseothersmentionedinduecourse.
Fig.6.Radio-to-IRspectralindexversusX-ray-to-IRspectralin-
First we wish to establish the concepts which we use, for easy
dex.Thecrossesrepresentthose48sourcesinourcatalogwith
reference,andthenapplythemtotheproblemhere.
radio, FIR and X-ray measurements. The blue triangle shows
theaverageofthevalues.Theopencircleshowstheaveragelo-
cationofSeyfert-Igalaxies,theopensquarerepresentsaverage
4.1.Thethreemaincomponentsoftheinterstellarmedium
Seyfert-II galaxies and the star indicates QSOs. The last three
valuesaretakenfromRodriguez-Pascualetal.(1993).Notethat Thethreemaincomponentsarethegas,thecosmicraysandthe
individualgalaxiesscatteraroundthegivenvalues(Chinietal., magneticfield.Atleastthegasandthemagneticfieldisclearly
1989). spatiallyhighlyinhomogeneous(Becketal.,2003):
The gas has a number of components, molecular clouds, neu-
tralHydrogenclouds,diffuseneutralHydrogen,diffuseionized
4. TheinterstellarmediumandtheFIR/radio Hydrogen, HII regions, stellar wind bubbles, supernova rem-
nantswithX-rayemittingshells,atunnelnetworkofconnected
correlation
oldersupernovaremnants(Cox&Smith,1974),athickhotdisk
The interstellar medium connects the formation of stars, the (Beuermannetal., 1985; Snowdenetal., 1997; Kronbergetal.,
explosion of supernova remnants, the regularization and en- 2007), and a wind (Breitschwerdt, 2008; Everettetal., 2008).
hancement of the magnetic field, and the transport of cosmic Thetunnelnetworkprobablyconnectstothehotthickdisk.The
rays. In order to understand the observation that the thermal windisprobablyfedfromthehottestregionsofthetunnelnet-
hot dust emission from a galaxy is simply proportional to the work, in a fashion perhaps similar to the Solar wind being fed
non-thermal radio emission from relativistic cosmic ray elec- fromcoronalholes(Stepanianetal.,2008,e.g.).
trons,weneedtounderstandtheinterstellarmedium,oratleast Themagneticfieldispermeatingalmosteverything,andalsohas
get close enough to a comprehension, that we can understand a thick disk. The field permeates the clouds, and is often con-
thisamazingcorrelation(deJongetal.,1985;Wunderlichetal., finedvisiblybytheclouds(Appenzeller,1974,e.g.).Themag-
1987;Wunderlich&Klein,1988,1991;Condonetal.,1991). netic field is strongly perturbed by HII regions, and supernova
Obviously, since the very massive stars power the far-infrared explosions.Themagneticfieldistransportedoutofthediskby
emission through a large fraction of the ultra-violet emission, thewind.
whichisabsorbedbydust,andtheninsupernovaexplosionspro- The cosmic rays, produced by supernova explosions in shock-
ducetheenergeticcosmicrayelectrons,whichemittheobserved waves (Baade&Zwicky, 1934; Fermi, 1949; Drury, 1983;
radioemission,thereshouldbeacorrelation.Usingsimpleini- Berezinskyetal., 1990) cannot easily be repelled by anything,
tial models for stellar population evolution, this rather naive andsogothroughallclouds,andalltheneutralandionizedgas.
earlypicturesuccessfullypredictedtheapproximatefar-infrared In bulk they cannot travel faster then the Alfve´n speed, since
emissionalreadyin1977(Biermann,1976;Biermann&Fricke, otherwisetheywouldexcitewavesintheplasma,scatteringthe
1977; Kronberg&Biermann, 1981). However, the tightness of particles,effectivelyreducingtheirbulkvelocity.
the correlation was neither anticipated nor predicted. The cor- Themagneticfieldisinstrumentaltoallowcosmicrayaccelera-
relation was finally discovered by deJongetal. (1985). Since tioninshocks,andperhapsthroughoutthemedium.
the dust emission just measures the total output in ultra-violet The cosmic rays in turn drive the dynamo mechanism to en-
by youngstars, it seems obvious, that in the limit of much ab- hance an existing magnetic field and give it spatial coherence
sorption,thefar-infraredemissionwouldjustbeproportionalto (Parker, 1969, 1992; Ferrie`re, 1996; Ferrie`re&Schmitt, 2000;
the star formation rate, given a general initial mass function. Hanaszetal.,2004,2006;Otmianowska-Mazuretal.,2008).In
However, the radio emission is approximately proportional to the classical Biermann-battery mechanism (Biermann, 1950;
theproductofthecosmicrayelectrondensityandthemagnetic Biermann&Schlu¨ter, 1951), only a rotating star with surfaces
fieldenergydensity,andthereforeitisnotreallyobviousatall, of density and pressure in non-coincidence is required to pro-
that integrating along a vertical column through the disk of a duceaseedfield,which,however,isgenerallyweak;thedynamo
galaxythesetwoemissioncomponentsshouldbebasicallypro- mechanism in stars can strongly enhance magnetic fields, and
portional. throughwindsejectthem (Bisnovatyi-Koganetal., 1973, e.g.):
Modern descriptions of starburst galaxies such as M82 or Thiswouldconstituteaveryirregular,butpotentiallyrelatively
NGC2146 are in Dopitaetal. (2005, 2006a,b); Grovesetal. strong source of magnetic fields in galaxies;in such a case the
(2008). dynamomechanismonaGalacticscaleisrequiredmoretoreg-
6 JuliaK.Beckeretal.:CosmicRaysVI
ularizethefieldratherthantostrengthenit.Inthemechanismof 4.2.Supernovaexplosions
Lucek&Bell(2000);Bell(2004,2005)theshockwavescandi-
FordidacticsimplicitywebasicallyadopttheapproachofSedov
rectlyenhancethemagneticfield,usinganexistingpopulationof
(1958); Cox (1972), but use more modern cooling approxima-
cosmicrays.Asnotedalready,thecosmicrayscoupleeffectively
tions, and allow for much lower environmental densities, but
tothegas.Anisotropiesinthephasespacedistributionofparti-
otherwiserescaletheirequations.
cles,alwayspresentinshockwaves,alsocanproducenewmag-
Anexplosionrunsintotheinterstellarmedium,andexpandsinto
netic fields on small scales (Weibel, 1959; Bykov&Toptygin,
the tenuous gas, which surrounds the clouds, and extends far
2005). Galactic magnetic fields have also been reviewed by
above and below the central layer of cool clouds. We consider
Becketal.(1996);Kulsrud(1999);Kulsrud&Zweibel(2008).
theexpansionintothesurroundinglowdensitymediumandask,
Thermodynamicallyboththecosmicraysandthemagneticfield whentheexpansionrunsintothecoolinglimit:
canbethoughtofasarelativisticgas,withalmostzeronetmass The first question is what density should be used:
density. The galaxy has a wind (Westmeieretal., 2005;
Breitschwerdt, 2008; Everettetal., 2008; Gresseletal.,
Thereforetheensembleofcosmicraysandmagneticfieldcon-
2008; Otmianowska-Mazuretal., 2008) and it is getting fed
stitutealightfluidpushingagainsttheheavyfluidofthenormal
fromthetunnelnetworkofCox&Smith(1974)probably.This
gas,andgivenenoughenergydensity,thesetwocomponentses-
implies thatthe Alfve´nspeed mustapproachthe escape speed,
capeviaaninstability(Parker,1965;Kowaletal.,2003,2006).
for a cosmic ray driven magnetic wind. Other galaxies also
Therefore all three components are strongly coupled, and the showevidenceforwinds(Chyz˙yetal.,2000a,b;Chyz˙y&Beck,
dataconfirmanapproximateenergyequipartitionbetweencos- 2004;Chyz˙yetal.,2006,2007):
micraysandthemagneticfield,andthesumofthesetwocom-
ponentsequalinenergydensitytothegas. B
V = 400km/s. (7)
A 4πρ ≃
The one given parameter is the total energy input, integrated
across all spatial inhomogeneities, since the energy supply is
With B 3µGauss, this implies a density of about
given by the stars, in the form of winds, explosions, and radi- n = 3 10≈4cm 3.
− −
ation. Since the inhomogeneitiesare extreme,especially in the ·
Thetimetostartcoolingis
density,itis importantto use spatiallyintegratedenergydensi-
tiesforreferenceasmuchaspossible.Sowenotethattheenergy E 2/11
density of the magnetic irregularitiesintegratedoverall spatial τc = 5 106yrs 51 (rΛ 21n 3.5)−5/11, (8)
scalesisalsoinapproximateequipartition(Becketal.,1996). · n 3.5! − −
−
The energy input can be estimated from the explosions of su- where E is the energy of the explosion in units of 1051erg,
51
pernovaeto about1 supernovaof 1051 erg,every100years, so n is the tenuous density in units of 3 10 4cm 3, Λ is
3.5 − − 21
atL = 3 1041erg/s;theuncertaintyinthisisaboutafactor th−e cooling coefficient in units of 10 21erg· cm3s 1, and−r is a
kin − −
·
of 3. Some fraction of this energy goes into cosmic rays. This compaction parameter of order unity. This low density reflects
fractioncouldbelarge(Drury,1983). thefindingthatthetenuousmediumisofverylowdensity,and
due to substructure may on volume average be of even lower
Other energy input can be estimated from the infrared emis-
densitythansuggestedbytheX-raydata(Snowdenetal.,1997;
sion (Cox&Mezger, 1989): About 1/3 to 1/4 of the total stel-
Everettetal., 2008), of order 3 10 3 cm 3; but we do use the
lar radiationis absorbedby dust and reradiatedin the infrared, temperatureof105 K,nearthem·ax−imum−,andalso closetothe
beyond a wavelength of 25 µ, about 1010 L . Of this, about
stable region(Field, 1965). However,the coolingsuggestedby
2 109L =8 1042 erg/siscomingfromyoun⊙gstarformingre-
gi·ons. ⊙ · the X-rayspectrumisan integralovertheentire evolution,and
so only sensitive to the earliest part of the evolution. As soon
The energy density of magnetic fields can be estimated to as two or more supernovaremnantsoverlap,and start building
be about 1.6 10 12dyn/cm2 (Becketal., 1996; Everettetal., anetwork(Cox&Smith,1974),thenthetemperatureevolution
−
·
2008),theenergydensityofcosmicraysisaboutthesame,and will be different, giving again higher temperatures, consistent
theirsumisaboutequaltothegaspressure,of4 10 12dyn/cm2. withobservations.
−
·
Using a scale height of full width of 3 kpc, and a radius of 10 Theradiusatthatstageis
kpc,we obtaina crudeestimate of the energycontent.Thisre-
quires for magnetic fields and cosmic rays together an average E 3/11
supplyofenergyofabout4·1041erg/s,usingthetimescaleob- Rc = 8·102pc n 531.5! (rΛ−21n−3.5)−2/11 (9)
tained from cosmic rays (see below). Such numbersare uncer- −
tainbyprobablyafactorof2.Everettetal.(2008)alsoestimate andthetemperaturethenisinitially
therequiredwind-powertoabout4 1041erg/s,aGalacticwind
drivenbycosmicrays;theydiscuss·otherestimates. E 2/11
Td = 1.7 105K 51 (rΛ n )6/11. (10)
21 3.5
Itis interestingtonote thatto withinthe uncertaintiesall these · n 3.5! − −
−
power estimates (supernovae, wind power, magnetic field and
This corresponds to an injection scale of turbulence.
cosmicrayreplenishment)agreebetterthantheirrespectiveer-
Interestingly, the time scale is of the same order of magni-
rorestimates.
tude to what we derive from cosmic ray transport, and the
Thereforethetimescalestoreplenishanyoneofthecomponents length scale is not far from the scale height of the hot disk
must also be approximately be the same. We do have the real (Snowdenetal., 1997), demonstrating qualitative consistency.
numberfromradioactiveisotopesofcosmicraysinteracting,and WenotethatSnowdenetal.(1997)gaveamuchhighertemper-
thenumberisabout10millionyears(Brunetti&Codino,2000, ature,ofabout4 106K, with a densityof 3 10 3 cm 3. Also,
− −
· ·
e.g.).Thisisthenthetimescaleforallkeyprocesses. Everettetal.(2008)suggestahighertemperature.However,the
JuliaK.Beckeretal.:CosmicRaysVI 7
luminosity of that phase is a very small fraction of the entire Using the approachof Cox (1972) with the environmentof the
dissipationintheISM. tenuous hot phase of the interstellar medium (Snowdenetal.,
As Field (1965) shows the cooling is stable if the temperature 1997; Everettetal., 2008) the cooling stage of an expanding
dependenceofthecoolingfunctionΛis sufficientlystrongand shellofasupernovaremnantmightleadtosuchaconfiguration,
its doublelogarithmicderivativepositive,or in the presence of ofaverythinshellatlargedistances,withstrongmagneticfields.
heating larger than 2. This is the cooling phase we are inter- Insuchapicturethisstagewouldencompassmostofthesuper-
ested in. This is the case attemperaturesbelow andnear about nova’senergydissipation,andsosimilarconsiderationsmayap-
105K. plytotheinterpretationoftheX-raydata(Snowdenetal.,1997;
∼
Datasuggestthatthebreak-upofsupernovaremnantshellshas Everettetal.,2008).
beenobservedinthestarburstgalaxyM82(Barteletal.,1987).
However, in that case it is not clear whether we are observing
4.4.Turbulence
thebreak-upofawind-shellproducedinasnow-ploweffectby
the stellar wind prior to the supernovaexplosion,or the break- Turbulence is an ubiquitous phenomenon, and also is a key
upofthesnow-plowofthenormalsupernovaexplodingintothe ingredient in the interstellar medium (see reviews by Rickett
interstellarmedium. (1977);Goldsteinetal.(1995)).Keyconceptstoturbulencethe-
oryhavebeenintroducedbyPrandtl(1925);Karman&Howarth
(1938); Kolmogorov(1941a,b,c); Obukhov(1941); Heisenberg
4.3.Magneticinhomogeneities
(1948);Kraichnan(1965), andhavebeenreviewedbySagdeev
Inthemagneticfielddatainourgalaxy(Becketal.,2003)there (1979).Onekeyargumentwhichwewishtouse,istheconcept
isalreadystrongevidenceforsmallscalesubstructure,sincedif- oftheturbulentcascade.Theretheenergyoftheturbulenceisin-
ferentmeasuresofthe magneticfield yieldverydifferentnum- jectedintothegasatsomelargewavelength,andcascadesdown
bers: linear measures such as Faraday Rotation Measures indi- throughwavenumberspace,tothesmallwavelengthswherethe
cate much lower strengths of the magnetic field than quadratic energy is dissipated. In many examples this leads in a three-
measuressuchassynchrotronemission.Thisistypicalforsmall dimensionalisotropicmodeltotheKolmogorovcascade,which
scalesubstructure(Leeetal.,2003;deAvillez&Breitschwerdt, canbedescribedinalocalapproximationbythefollowingdiffu-
2004,2007), whereforagiventotalenergycontenthighinten- sionequationinwavenumberspace(McIvor,1977;Achterberg,
sitysheetscanholdalltheenergyforasmallvolumefraction.In 1979):
suchapicturelinearmeasuresgiveamuchsmallernumberthan
quadraticmeasures,asiswellknownfrommathematicallyiso-
d I(k) 1 ∂ k4 ∂ I(k)
morphicargumentsinthermalemission.Ofcourseweshouldbe = Aδ(k k ) (14)
comparingtheproperintegrals,alsoinvolvingthespatialdistri- dt 4πk2 − k2 ∂k 3τk ∂k 4πk2!! − o
butionofthermalelectrondensityandcosmicrayelectronden-
HereI(k)istheenergydensityoftheturbulenceperwavenumber
sity (see, e.g., Bowyeretal. (1995)). We ignore all this in our
k,andpervolumeelement,andτ isthetimescaleofdiffusion,
simpleexercise. k
whichcanbewrittenas
Wecanquantifythisbyintegratingalongalongthincylinderof
unitlength.We refertothemagneticfieldas B ,whenitisho-
0 1
mogeneous,andfortheinhomogeneouscasethemagneticfield τ = . (15)
k 1/2
is B overmost of the length, and enhancedby a factor 1/x in k γ I(k)k/ρ
1 eff
a region of length x: This then gives for the integrated energy (cid:16) (cid:17)
density Here ρ is the matter density, and γeff is an effective adiabatic
constantfor the turbulentenergy.The turbulence has a source-
1 term,herelimitedtoasinglewavenumberk .Theturbulencedif-
B2 +B2 (1 x) = B2. (11) o
1· x 1· − 0 fusionequationbasicallysaysthattheturbulencemovesthrough
wavenumberspace with noadditionalsourceor sink,as a con-
Keeping the integrated energy content B2 constant, the linear
0 stantenergycurrentin wavenumberphasespace (Kolmogorov,
measureofthemagneticfieldisgivenby
1941a,b,c).Thesolutionstothisdiffusionequationcanbewrit-
1 tenas
B x+B (1 x) = B (2 x). (12)
1 1 1
· x · · − · −
Combiningthetwoexpressionsgives I(k) k2 for k k and (16)
o
∼ ≤
I(k) k 5/3 for k k .
x ∼ − ≥ o
(2 x) (13)
r1 x · − ThislatterbehavioriscommonlyreferredtoastheKolmogorov
−
fortheratioof linearmeasureversusquadraticmeasure.Inthe cascade,andisfoundubiquitouslyinnature.
limitofsmallxthisisjust √x.Theobservationssuggestthatthis
ratioisoforder1/5(Becketal.,2003),andsox=0.04byorder
4.5.Thecoolingoftheinterstellarmedium
ofmagnitude.Thisimpliesthatmostofthemagneticenergyis
containedinshellsofavolumeafewpercent,possiblyaslowas The interstellarmediumhasa numberof phases, whichappear
1percent.Sincethelinearmeasureisproportionaltothebending tobeinapproximatepressureequilibrium.Concentratingonthe
of ultra high energy cosmic rays, this implies that the bending phaseofthehighesttemperature,thehighestspeedofsignalling
is reduced by a factor between 5 and 10 over what we might (beitsoundwaves,orAlfve´nwaves,orotherwavemodes),we
reasonably expect otherwise. Obviously, in realistic situations notethatitstemperatureisintherangewherethetypicalgaseous
much of this effect will be smoothed out, and so perhaps even emission is detectedin the X-rayregime.The coolingcurveof
moreextremesituationsmayberequired. suchagashasbeenextensivelydiscussedbymany(Cox,1972;
8 JuliaK.Beckeretal.:CosmicRaysVI
Sutherland&Dopita,1993;Dopita&Sutherland,2003,e.g.).It the ratio Boron to Carbon already give information as to the
shows the following features, starting at low temperature, and energy dependence of the leakage time, and such an analy-
considering the cooling coefficient Λ(T) with n the interstellar sis gives an energy dependence as E 0.6 0.1 (Engelmannetal.,
− ±
densityinparticlescm 3 1990,e.g).Wehavearguedelsewherealready(Biermann,1995;
−
Wiebel-Soothetal.,1995,1998),thatthisreflectstheenergyde-
n2Λ(T)erg/cm3/sec. (17)
pendence of the amount of target material seen for spallation.
Mostofthetargetinteractionwithheavynucleiamongthecos-
This cooling curve Λ(T) rises from near 104K to a lo-
mic rays happens near the most massive stars, the Wolf-Rayet
cal peak near 3 105K. The level of cooling along this
local peak is g≈iven· by Λ 10 21ergs/cm 3/s, dropping to stars,withtheturbulenceexcitedbythecosmicraysthemselves,
Λ 10 22ergs/cm 3/s nea≈r 1−06K, and−towards a mini- giving an energy dependence of the spallation secondaries of
mu≈m ne−ar Λ 3 −10 23erg/c≈m 3/s in the range 3 106K E−5/9(Biermann,1998;Biermannetal.,2001;Biermann,2006),
to 108K. T≈he ·peak− is due t−o many edges an≈d li·nes in consistentwith the data,which give E−0.54 (Ptuskin, 1999). On
≈ theotherhand,mostofthegammaemissionfromπ-zerodecay
the soft X-ray range. At higher temperatures the continuum
arisesfromtheinteractionamongthemorenumeroussupergiant
emission begins to dominate and that emission is then given
stars, the red supergiants, for which we suggest that the turbu-
by Λ 1.4 10 27T1/2erg/cm 3/s. The sharp cutoff to low
temper≃atures·nea−r 104K is du−e to beginning recombination lencearisesfrominstabilities.
and thus a smaller density of free electrons to interact with.
A contemporary discussion including the effects of strong 4.7.Theradioemission
departures from ionization equilibrium has been given by
In order to calculate the radio emission from the total number
Schmutzler&Tscharnuter(1993);Breitschwerdt&Schmutzler
of relativistic electronsin a columnwe first have to proceedto
(1994).
workoutthecosmicraylosstimeforelectrons,secondthecool-
ingtimeforthetenuoushotmedium,putthemequal,andthird
4.6.Theleakyboxapproximation calculatetheradioemissionpersupernovaeventfromacolumn
inthedisk.
ConsideracolumnperpendiculartoagalacticdiskofheightH,
Themaximumenergyintheelementaldistributionandspectrum
andthenumberofcosmicrayparticlesinitasafunctionofpar-
ofthecosmicraysisinprotonsneartheirrestmassenergy,since
ticleenergyandtimeN(E,t);thenwehavethebalanceequation
their spectrum is steeper than 2 in energy.This means that the
d N(E,t) energy which has to be used in the expression for the leakage
N(E,t) + = Q(E). (18) timeisfixed.So,theleakagetimeisgivenby
dt τ(E)
whereτ(E)istheescapetimescale.Thesignofthesecondterm H2I k
τ o o . (24)
ispositive,since theprocessdescribedisa loss.Ina stationary CR ∼ B5/3r2/3E1/3
statewethenobtainreadily o
The maximum energy content of the population in the protron
N(E) = Q(E)τ(E). (19)
spectrumisherenearE =1GeV,sothat
Thecharacteristictimeoflosscanbewrittenas
H2I k
τ (E =1GeV) o o . (25)
H2 CR ∼ B5/3r2/3
τ(E) . (20) o
∼ κ
inthiscase.
Here,κisthediffusioncoefficientofcosmicrayparticles,which
Thecoolingtimeisgivenby
canbewrittenapproximatelyinthequasi-linearapproximation
as nk T B2/8π 1
κ ∼ 13rgc BI2(k/)8kπ, (21) τcool ∼ n2ΛB(T) ∼ B2/8π/2kBT⋆ 2 Λ(T⋆) (26)
T2 1 (cid:0) 1 (cid:1)
wherewewritefortheturbulentenergydensity ⋆
∼ Λ(T ) B2 ∼ B2
⋆
I(k)k I k (k/k ) 2/3 I k B 2/3r 2/3E2/3, (22)
∼ o o o − ∼ o o − o− intheapproximationthatΛ(T⋆)/T⋆2 isaconstant,andassuming
usingheretheassumptionofaKolmogorovspectrum.Here,r equipartitionagain.Thisisreasonableinthedissipationstageof
g
1/k E/BistheLarmorradiusofaparticleofenergyE unde∼r supernova remnants when Λ approaches a double-logarithmic
cons∼ideration, which gyrates in a magnetic field of strength B. derivativeof2,belowatemperatureof105K.Also,inthattem-
Thebasicradiusr 1/k correspondstotheinjectionscaleof peraturerangethecoolingtimeisaminimum,foragivenenergy
o o
theturbulence.This∼thenleadstoadependenceofthediffusion density.Wenotedabovethatthedissipationstagereachesthose
coefficientonthevariousparameters temperatures.
Puttingthetwotimescalesequalthenyieldstherelation
κ E1/3B5/3r2/3I 1k 1. (23)
∼ o o− o− H2I k 1
o o . (27)
Therefore,weadoptthepointofviewthattheleakagetimescale B5/3r2/3 ∼ B2
τ(E)isproportionalto(relativistic)energyE 1/3,andsothatthe o
−
equilibrium density of energetic particles N(E) is proportional Now,wewishtoconsiderelectrons,whichemitradioemission
toE−1/3aswell. atacertainfrequencyν,whichgivestheconditionthat
There is a difficulty with this argument, which can be solved:
The secondary to primary ratio of cosmic ray nuclei such as E ν1/2B 1/2 (28)
−
∼
JuliaK.Beckeretal.:CosmicRaysVI 9
andso,makinguseofthe frequencyandmagneticfielddepen- 4.8.Whereisthelimittothediffusionlimit?
denceofEqu.(26)andEqu.(28),thediffusiontimeforelectrons
Thelineofreasoningseemstobeadeusexmachinainthesense
whichemitatνisgivenby
thatweseemtobealwaysinthediffusionlimit,independentof
τCR,e ∼ H2E−1/3B−5/3ro−2/3Ioko ∼ B−11/6ν−1/6 (29) whether we have starburst galaxieswith relatively strong mag-
TheemissionisfromaspectrumofelectronsofE 2.42 0.04atin- neticfields,ornormalgalaxieslikeourown.
− ±
jection(Biermann&Strom, 1993),andso the totalradioemis- Theequationsaboveimplythat
sionS persupernovaeventinacolumninadiskcanbewritten
ν
as (2k T)28π 6πm c
τ = B < e = τ . (31)
Sν B1.71±0.02ESN,CR,eν−0.71±0.02B−11/6ν−1/6 (30) diff Λ B2 σTγeB2 syn
∼
B 0.12 0.02ν 0.88 0.02
∼ − ± − ± We note first that both sides depend on the magnetic field
forthecasethatallsupernovaremnantsproducethesamenum- strength squared, so the argument is independent on the mag-
berofrelativisticelectrons.Here,weuseanintegrationalonga neticfield:Insertingnumberswefind
verticalcolumntoobtainthetotalnumberofenergeticelectrons
per supernovaexplosion.Thisis reasonablesince we are using (T )2 4 107
the adiabatic phase of supernovaremnant evolution, where the 5 < · , (32)
Λ γ
energyisconserved.Thisargumentleadstosuchaweakdepen- 21 e
−
dence on the strength of the magnetic field, that the resulting whereγ istheLorentzfactorofthemainlyemittingelectrons.
e
offsetissmallerthantheerrorsinthedata. This time, however, we need to ask what density contrast the
Thereforetheradioemissionisonlyveryweaklydependenton mainradioemittingsubstructureshave,sincethelefthandside
the magnetic field, independent of all other parameters, and is ofthe equationusesgrandtotalvolumeaverages,andthe right
directly proportionalto the number of supernovae per time in- hand samples just those regions, where B2 is especially high.
terval,andsoalsototheluminosityofmassivestars. Alreadysimplearguments,asshownabove,demonstratethatthe
Thecosmicrayelectrondatashowthataboveafew10ofGeV averageofB2isquiteabithigherthantheaverageofBsquared.
the spectrum is already in the loss limit, so steeper by unity Wecanassumehere,thatsuchafactormightbeoforder30,or
(Kardashev, 1962). Below that energythe direct data are com- evenhigher,bringingthelimitingenergyoftheelectronsdown
promisedbytheSolarwindmodulation,butfromtheradioemis- toγ <106,orpossiblyevenmuchless.Wehavealreadyargued
e
sionofnormalgalaxieswedoknowthattheelectronspectrumis earlierthatforthecoolingtobemaximal,thetemperaturehasto
closelyinagreementwithwhatweobtainforprotons,atsome- beclosetoorbelow105K.
what higher energy, allowing us to conclude that the electron
Thisallowsustounderstandperhaps,whygalaxiesare usually
spectrum corresponds to the diffusion limit, when the leakage inthediffusionlimit,sometimesofcourse,inastarburst,inthe
outof theGalaxyis faster thanthesynchrotronloss. Using the
injectionlimit:Inthatcasetheoverallspectrumcorrespondsto
expressionsforthetwotimescaleswecancheck: injection. There was just not enough time to achieve diffusive
Radioemissionat5GHzcorrespondstoanelectronenergyof8
approximateequilibrium.
GeV,andasynchrotronlosstimeof4 107yr.
·
Aswenoteelsewhere,galaxiesandstarburstgalaxiesaresome-
timessoyoungastobeintheinjectionlimit,orsooldastobe 4.9.Implications
in the loss limit, rather than the leakage or diffusion limit that
Firstofall,thistheorydoesjustwhatonewouldnaivelyexpect,
we consider here. For any reasonably young age of a starburst
relatethemassivestarswhichheatthedustthroughtheirultravi-
there is always some low radio frequency ν , below which we
1
oletlightdirectlywiththesubsequentsupernovae.Allthetheory
are still in the injection stage, below which the age of the star-
does,isworkoutthenon-linearityinherentinsynchrotronemis-
burst is longer than the diffusion time scale. So below that the
sion, and shows them to introduce negligible dependencies on
radiofluxdensityislowerthanthediffusionlimitderivedabove,
variousparameters.
andtheradiofluxdensityhasthespectrumofinjection,follow-
ingBiermann&Strom(1993)S ν 0.71,andsorelativetothe Starburst galaxies as well as quiescent galaxies equally obey
ν −
diffusionlimittheradioemissiona∼tfrequencyν < ν isweaker thecorrelationbetweentheradioandthefar-infraredemission.
1
by the factor (ν/ν )1/6; this is typically not far below unity. At Thereforethetheoryimpliesbynecessitythatthemagneticfield
1
thetheotherextreme,consideredbyVo¨lk(1989)thereisalsoa inastarburstregionriseswiththeoverallenergydensity.
radio frequency ν , beyond which the synchrotron and inverse Galaxieswhicharesubjecttosubstantialcompressionbyanen-
2
Compton losses cut in, and become faster then the diffusion. counterwithanothergalaxy,clearlyhaveamagneticfieldwhich
Thisisdirectlyvisibleintheobservedcosmicrayelectronspec- is higher than corresponds to the energy density derived from
tra (Wiebel-Sooth&Biermann, 1999). So, at radio frequencies starformation,andsomaybeexpectedtohavemoreradioemis-
ν>ν theradioemissionisagainweaker,thistimeby(ν/ν ) 1/3. sionthanindicatedbythegeneralradio-far-infraredcorrelation.
2 2 −
Soagaintheradioemissionisslightlydown.Bothvariantsshow, This is borne out by at least one example (Hummel&Beck,
thattheradioemissionisnotfarfromthediffusiveequilibrium. 1995).
This concludes the demonstration of the argument. There are Furthermore,itisclearthatforveryshorttimescales,nearorder
many checks on these ideas, which one can make, such as the 107years,thecorrelationcannothold,sincewethenrunintothe
pressure of the interstellar medium, the X-ray luminosity, the lifetimesofthemassivestars,whichdrivetheenergybalancein
possibilitytoaccountforextremegalaxiessuchasM82,thera- theinterstellarmedium.
dial gradientof the far-infrared/radioratio (Bicayetal., 1989), There is likely also a lowest level of star formation activity,
the thickness of the hot gaseous disk and the associated diffu- where the assumption that the hot medium is fully connected,
sioncoefficientofcosmicrays,andmanyothers.Wewilldiscuss fails.Thereonemayexpectalsosubstantialdeparturesfromthe
thesepointselsewhere. correlation.
10 JuliaK.Beckeretal.:CosmicRaysVI
5. Cosmicraysandtheirsecondaries Spectral indices 5 GHz < ν < 1.4 GHz (z<=0.03, S60µm/S >=30, S60µm>=4 Jy, S >=20mJy)
Radio 1.4GHz
As stated above,the cosmic ray intensity from starburst galax- nt
ies scales with the radio and infrared emission of the sources. u16
o
In this section, we discuss the emission scenarios for charged C14
cosmic rays and hadronic interactions leading to high-energy
12
pwhitohtionnsatanrdbunresutstritnhoatecmanissaicocne.leTrhateerecoasrme itcwroayssoutrocehicglhasesens- 10 loss leakage injection
ergies, namely shock fronts of supernova remnants and long
8
Gamma Ray Bursts (GRBs), the latter being connected to su-
pernovaIc explosions.In the first case, maximum energiesare 6
limitedtolessthan1015eVandthus,thecosmicraysfromstar- 4
bursts cannot be observed directly due to the high cosmic ray
2
backgroundinourownGalaxy.GammaRayBursts,ontheother
hand,wereproposedastheoriginofcosmicraysabovethean- 0
-2 -1.5 -1 -0.5 0 0.5
kle, i.e. ECR >3 1018eV, see Vietri (1995); Waxman (1995). α
·
Sinceahighstarformationrateasitispresentinstarburstgalax-
ies,leadstoahighratesupernovaexplosions,anenhancedrate
Fig.7. Histogram of the radio spectral indices of 105 sources
oflongGRBsisexpected.Thus,forclosebysources,thedistri-
between1.4GHzand5GHz.Theareasbetweenthedashedlines
butionofstarburstgalaxiescanbeusedtotestthehypothesisof
indicatesourcesintheloss,leakageandinjectionlimit(fromthe
cosmicraysfromstarbursts,asalsodiscussedinBiermannetal.
left).Asaconservativeestimate,weincludethosethreesources
(2008).
withextremelysteepspectraaslosslimitsources.Thosesources
Thedominantsourceofsecondarycosmicrayslikehigh-energy
withextremelyflatspectra,totherightoftheinjectionlimitarea,
photonsandneutrinosisproton-protoninteractionsindensehy-
aredominatedbyabsorptionorfree-freeradiation.
drogen regions and proton-photoninteractions in Gamma Ray
Bursts.Proton-protoninteractionsproducepionsvia
canreachdifferentvalues.Shockaccelerationofchargedparti-
pp π+π π0. (33)
− clesusuallyresultsinprimaryelectronspectraof
→
PthheoDtoehlatadrroensoicnainntceer,actions, on the other hand, yield pions via ddNEe ∝ Ee−αperim, (36)
e
pγ ∆+ nπ+/pπ0. (34) withαprim 2.0 2.4.Iftheelectronsescapebeforeinteracting
→ → e ≈ −
with the ambient medium, the primary spectrum stays unmod-
High-energyphotonsandneutrinosaresubsequentlyemittedin ified, αprim =αsec, referredto as the injection limit. If the elec-
π resp.π0 decays: e e
± tronsare partlyscattered downto lowerenergies,the spectrum
− −
ofsecondariessteepenstoαsec 2.5 2.8fora primaryspec-
π+ → µ+νµ →e+νeνµνµ trumwithαprim 2.0 2.4.eTh≈isisca−lledtheleakagelimit.In
π− → µ−νµ →e−νeνµνµ the case of ecalor≈imetri−c sources, basically the entire energy is
π0 γγ. (35) lostinthesourceandthespectrumofsecondaryelectronsisas
→ steepasαsec 3.2 3.4.Thisscenarioisreferredtoastheloss
e ≈ −
limit.
5.1.Supernovaremnants
AsdiscussedinRybicki&Lightman(1979),theelectronspec-
Cosmic Rays are believed to be produced in young super- tralindexαseeccorrelateswiththeindexofsynchrotronradiation
nova remnants (SNRs), reaching maximum energies of around as
αsec 1
1015 eVorabove,dependingontheirlocalenvironmentandon α= e − . (37)
thecosmicraycomposition.Theproductionofsecondariesfrom − 2
hadronicinteractionsdependsontheproton-protonopticaldepth Thus,theobservedsynchrotronspectralindicesare
intheSNRenvironment.Inthissection,wepresentamodelof
0.5 0.75 inthe injectionlimit
whichsourcesareopticallythinandwhich,incontrast,aregood − →−
ctrainndoisd.atesfor the productionof high-energyphotonsand neu- α=−−10..075→→−−1.12.0 iinntthhee lleoasskaligmeilti.mit (38)
Thesynchrotronspectralindicesinthissamplescatterbetween
1.7<α<0.7 with a peak at α 0.7. We exclude sources
5.1.1. Opticaldepth − ∼−
that may include contributions other than synchrotron radia-
We use the observation of synchrotron radiation from shock- tion, i.e. those sources that have spectral indices α> 0.5.
−
accelerated electrons, assuming that electrons and hadrons are Here, absorption is likely to have modified the spectrum.
accelerated in the same shock environment. Figure 7 shows Alternatively, spectral indices around -0.1 point to free-free
the distribution of spectral indices at radio wavelengths be- radiation (Mezger&Henderson, 1967). Of the remaining 85
tween 1.4GHz and 5GHz for 105 sources in the sample with sources, 37 sources (44%) starbursts are in the injection limit,
givenspectralindicesattherequiredwavelengths.Thespectrum 36sources(42%)areintheleakagelimitand12sources(14%)
at these energies is produced by electron synchrotron losses. areinthelosslimit.
Depending on the shape of the primary electron spectrum and The observation of a synchrotron spectrum following the in-
scattering effects, the spectral index of the electron population jectedelectronspectrumhassevereimplicationsforhadronsin