Extreme Cosmic-Ray-Dominated-Regions: a new paradigm for high star formation density events in the Universe

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by  Padeli P. Papadopoulos

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed14January2011 (MNLATEXstylefilev2.2)
Extreme Cosmic-Ray-Dominated-Regions: a new paradigm for high
star formation density events in the Universe
1
Padeli P. Papadopoulos,1 Wing-Fai Thi,2,3 Francesco Miniati,4 Serena Viti,5
1
0 1Argelander-Institutfu¨rAstronomie,AufdemHu¨gel71,D-53121Bonn,Germany
2 2UJF-Grenoble1/CNRS-INSU,InstitutdePlane´tologieetd’AstrophysiquedeGrenoble(IPAG)UMR5274,Grenoble,F-38041,France
3SUPA,InstituteforAstronomy,RoyalObservatoryofEdinburgh,UniversityofEdinburgh,BlackfordHill,EdinburghEH93HJ,UK
n
4Institutfu¨rAstronomie,ETHZu¨rich,8093Zurich,Switzerland
a
J 5DepartmentofPhysicsandAstronomy,UniversityCollegeLondon,LondonWC1E6BT,UK

3
1
Accepted...;Received...;inoriginalform...

]
O
C ABSTRACT
WeexamineindetailtherecentproposalthatextremeCosmic-Ray-Dominated-Regions(CR-
.
h DRs) characterize the ISM of galaxies during events of high-density star formation, funda-
p mentally altering its initial conditions (Papadopoulos 2010). Solving the coupled chemical
-
o and thermalstate equationsfor dense UV-shieldedgasrevealsthatthe largecosmic ray en-
r ergydensitiesin suchsystems (UCR∼ few×(103–104)UCR,Gal) will indeedraise themini-
t mum temperatureof this phase (where the initial conditionsof star formationare set) from
s
a ∼10K(asintheMilkyWay)to∼50–100K.MoreoverinsuchextremeCRDRsthegastem-
[ peratureremainsfullydecoupledfromthatofthedust,withTkin≫Tdust,evenathighdensi-
2 ties(n(H2)∼105–106cm−3),quiteunlikeCRDRsintheMilkyWaywhereTk∼Tdust when
v n(H2)&105cm−3.Thesedramaticallydifferentstarformationinitialconditionswill:a)boost
6 the Jeans mass of UV-shielded gas regions by factors of ∼10–100 with respect to those in
9 quiescentor lessextremestar formingsystems,andb)“erase” theso-calledinflectionpoint
4 oftheeffectiveequationofstate(EOS)ofmoleculargas.Boththeseeffectsoccuracrossthe
2 entire density rangeof typicalmolecularclouds,and may representa newparadigmfor all
9. high-densitystarformationintheUniverse,withcosmicraysasthekeydrivingmechanism,
0 operatingefficientlyeveninthehighdustextinctionenvironmentsofcompactextremestar-
0 bursts.Thecharacteristicmassofyoungstarswillbeboostedasaresult,naturallyyieldinga
1 top-heavystellarinitialmassfunction(IMF)andabimodalstarformationmode(withtheoc-
: curanceofextremeCRDRssettingthebranchingpoint).SuchCRDRswillbepresentinlocal
v
UltraLuminousInfraredGalaxies(ULIRGs)andmerger-drivengas-richstarburstsacrossthe
i
X Universewherelargeamountsofmoleculargasrapidlydissipatetowardscompactdiskcon-
r figurationswhere they fuel intense starbursts. In hierarchicalgalaxy formation models CR-
a controlledSFinitialconditionslendaphysicalbasisforthecurrentlypostulatedbimodalIMF
inmerger/starburstversusquiescent/diskstarformingenvironments,whilenaturallymaking
theintegratedgalacticIMFs(IGIMFs)afunctionoftheSFhistoryofgalaxies.
Keywords: cosmicrays–dust,extinction–galaxies:starburst–galaxies:starformation –
galaxies:interaction–ISM:molecules–ISM:supernovaeremants.
1 INTRODUCTION galaxies(SMGs),similarlymerger-drivenstarburstsinthedistant
Universe,SFRscanevenreachthousandsofsolarmassesperyear
Muchof thestellarmassintheUniverseformsinstarbursts(e.g.
(Smail et al. 1997; Hughes et al. 1998; Ealeset al. 1999). While
Blainetal.1999; Genzel etal.2001; Smailetal.2002), spectac-
starsforminvariablyoutofmoleculargasthroughouttheUniverse
ulareventsduringwhichthestarformationrate(SFR)ofagalaxy
(e.g. Solomon et al. 1997; Frayer et al. 1998, 1999; Greve et al.
risesfromfewsolarmassesperyear,typicalofspiralssuchasthe
2005, Tacconi et al. 2006), it is in its densest, UV-shielded, and
Milky-Way (Mckee & Williams 1997), to several hundred solar
Cosmic-Ray-Dominatedphasewherethestarformationinitialcon-
masses per year as in the local Ultra Luminous Infrared Galax-
ditions, and the characteristic mass of the emergent young stars
ies (ULIRGs) (e.g. Sanders & Mirabel 1996; Genzel et al. 1998; M(∗)aretrulyset(Bergin&Tafalla2007;Elmegreenetal.2008).
Sanders&Ishida2004)wheremerger-drivenstarburststakeplace ch
Indeed,whilePhoton-Dominated-Regions(PDRs)containthebulk
inverycompact(D 100–300pc)densegasdisks(e.g.Downes&
∼ ofthemoleculargasmassingalaxies(Hollenbach&Tielens1999;
Solomon 1998; Sakamoto et al. 2008). In the so called sub-mm
2 Papadopouloset al.
Ossenkopf et al. 2007), their widely varying physical conditions
remain always far removed from those prevailing inUV-shielded
CR=10,000
CR-dominateddensegascores.Thelocationofthelatterdeepin-
sidemolecularclouds,astrongtemperatureregulationviatheon-
setofgas-dustthermalequillibriumatdensitiesn(H )>104cm−3, )
2 K 100
andthenearlycompletedissipationofsupersonicturbulence(Lar- e ( CR=1000
son2005;Bergin&Tafalla2007;Jappsenetal.2005),allhelpto r
u
keep the thermal state of typical CRDRs a near invariant over a at CR=100
r
widerangeofISMenvironments. e
p CR=10
m
Cosmicrays(CRs),acceleratedinshocksaroundsupernovae e 10 CR=1
remnants(SNRs)orwindsassociatedwithO,Bstarclusters(e.g. s t CR=0.2
Binnsetal.2008),areresponsiblefortheheating,ionizationlevel, a
G T =8K
dust
andchemical stateofsuchdenseUV-shieldedregionsinmolecu-
larclouds(e.g.Goldmith&Langer1978;Goldsmith2001).More-
over,whiletheirheatingcontributionrelativetothatfromthe(far- 1
UV)-inducedphotoelectriceffectinPDRs,orturbulence,canvary 103 104 105 106
withina galaxy and individual molecular clouds, CRs remain re- Gas density (cm-3)
sponsible for setting the minimum temperature attainable in the
gaseous ISM (e.g. Goldmith & Langer 1978; Bergin & Tafalla
Figure1.ThetemperatureofUV-shieldeddensegascorescomputedfrom
2007; Elmegreen et al. 2008). For the Galaxy T (min) 10K,
reachedinUV-shieldedcoreswithn(H ) (104–106k)cm−3∼. Equation 2 for the range of densities typical in molecular clouds. The
2 ∼ CRenergydensities rangefromthequiescentenvironment oftheGalaxy
A recent study has shown that the average CR energy den- (UCR=(0.2–1)×UCR,Gal) to those in extreme CRDRs (UCR∼(103–
sities (UCR) in compact starbursts typical in ULIRGs (recently 104)×UCR,Gal,Papadopoulos2010).AdusttemperatureTdust=8Kand
found also in an SMG at z 2.3, Swinbank et al. 2010), will aGalacticCRionizationrateofζCR=5×10−17s−1havebeenassumed.
∼
be boosted by the tremendeous factors of U (few) (103–
CR
104)U , potentially transforming their ISM∼into e×xtreme
CR,Gal 2 THEMINIMUMGASTEMPERATUREINCRDR
Cosmic-Ray-DominatedRegions(CRDRs).Thiswilldramatically S
alter the thermal and ionization state of UV-shielded cores, and In this section we compute the equillibrium gas temperatures for
thustheinitialconditionsofstar-formation,throughout theircon- theUV-shieldedregionsofmolecularcloudsimmersedinthelarge
siderablemoleculargasreservoirs( 109-1010M⊙).Higherchar- cosmicrayenergydensitiesoftheextremeCRDRsexpectedinstar-
acteristicmass M(∗) for theyoung∼starsformed in such ISMen- burstswithhighSFRdensities.
ch
vironments,andlongerambipolardiffusiontimescalesfortheCR-
heated UV-shieled cores could thus be a new paradigm for high-
2.1 Asimplemethod
densitystarformationintheUniverse(seePapadopoulos2010for
details).ItisworthmentioningthatrecentlysuchlargeUCRboosts Wefirstconsider thesimplecasewhere thechemical stateof the
( 103.5 UCR,Gal)havebeenfoundintheOrionAbar,andwhile UV-shielded dense gas cores remains unaltered and the only ef-
∼ ×
not representing the average SF initial conditions in the Galaxy, fectoflargeU valuesistoheatthemmuchmorethaninquies-
CR
theydoallowlocalstudiesoftheeffectsoflargeCRenergyden- centISMenvironments.Followingstandardpractice(e.g.Goldmith
sities on the ISM (Pellegrini et al 2009). Finally CRs have been 2001) thetemperature of such regions can be estimated from the
showntoeffectthethermalstateofprimordialgas,catalyzingH2 thermalbalanceequation
formationintheabsenceofdust(Jasche,Ciardi,&Ensslin2007).
Inthisworkwesolvethecoupledchemicalandthermalstate
Γ =Λ +Λ , (1)
equationsforUV-shieldedgasanditsconcomitantdustinextreme CR line gd
CRDRs without the approximations employed by Papadopoulos whereΓ ζ n(H )istheCRheatingwithζ U being
CR CR 2 CR CR
∝ ∝
(2010). We then use the thermal states computed for such a gas thecosmicrayionizationrate.ThecoolingtermΛ isdominated
line
phasetoexaminetheeffectson M(∗) andtheso-calledinflection byCOandothermolecularlines,whileΛ accountsforgascool-
ch gd
pointoftheEffectiveEquationofState(EOS),setatgasdensities ingduetothegas-dustinteraction.
abovewhichT T (e.g.Spaans&Silk2000;Larson2005 Asignificantpointofdeparturefromthepreviousanalysisby
kin dust
∼
andreferencestherein).Bothoftheseplayacrucialroleindeter- Papadopoulos (2010) isthe inclusion of the atomic fine structure
mining the stellar initial mass function (IMF) in galaxies, which lines OI (at 63µm) and CII (at 158µm) in Λ . Indeed for the
line
couldthusturnouttobeverydifferentintheCRDRsofextreme CR-boosted temperatures expected in the UV-shielded dense gas
starbursts. Throughout this work we make the standard assump- ofextremeCRDRs,andunlikethecorrespondinggasphaseinthe
tionofU ρ˙ (SFRdensity)asinPapadopoulos2010,though quiescent ISM of the Galaxy, the cooling from the fine structure
CR sfr
∝
wenowdiscusspossiblecaveats(section4.4).Finally,thedifferent atomic line of OI (63µm) can also become important and along
IMFsexpectedinextremeCRDRswillmodifythetotalSFRand withthegas-dustinteractionovertaketheCOlinesfortypicalcore
ρ˙ valuescomputedingalaxies(frome.g.cmnon-thermalorIR densities of n(H )>105cm−3 when T >50K . FinallyISM-CR
sfr 2 k
thermalcontinuum).Inthisnewcontextandthroughoutthiswork interactionscangenerateinternalUVradiationwhichdestroysCO,
SFR and ρ˙ will now denote these quantities only for the mas- producing traces of CII, thus cooling via itsfine structure line at
sfr
sivestars(whichdefineU andpower theIR/cmcontinuum of 158µm must also beincluded. The thermal balance equation en-
CR
theISM), withtheir total values necessarily remaining uncertain, compassingallphysicalprocessesthatcanbeimportantintheUV-
dependingontheexactIMF,whichwillnolongerbeaninvariant. shieldedISMofextremeCRDRsthusis:
Starformationin extremeCRDRs 3
units (expected to be even lower for the dense pre-stellar cores
deepinsideH clouds)andaresidualmicro-turbulentlinewidthof
Λ (T )+Λ (T ,T )+Λ (T )+Λ (T )=Γ , (2) 2
CO k gd k dust OI63 k CII k CR ∆Vm−turb=5kms−1(whichenterstheexpressionsoflineoptical
(for the expressions used see the Appendix). The solutions are depths).Inallcaseschemicalandthermalequillibriumisreached
shown in Figure1 fromwhere itbecomes obvious that the mini- fast,withinT 6 104yrs,andisalwaysshorterthanthelo-
chem,th
mumtemperaturesattainableindensegascoresintheISMofsuch cal dynamical timescale which drives the ambient star formation
starburstsaremuchhigherthanintheGalaxyorgalaxieswithmod- eventsandthusthetemporalevolutionofU .Theresults,shown
CR
erateρ˙ values.Turbulentgasheatingwasnotconsideredsincewe inFigure2,corroboratethehighgastemperaturesobtainedusing
sfr
wanttocomputetheminimumtemperaturevaluesforUV-shielded thesimplermethod. Thisreveals thecosmicraysasthemost im-
gasandsince supersonic turbulence(and thusshock-heating) has portantfeedbackaspectofstarformationcapableofsignificantly
usually dissipated in dense pre-stellar gas cores where the initial alteringitsinitial conditions during events of high star formation
conditionsofSFareset. density via the strong heating of the deeply embedded and UV-
FromFigure1itcanbeseenthattheminimumgastempera- shielded dense gasregions of molecular clouds. It canthus oper-
turespossibleinextremeCRDRsarelowerthanthosecomputedby ateunhinderedinthehighdustextinctionenvironmentsofextreme
Papadopoulos(2010),aresultoftheextracoolingpoweremanating starburstssuchaslocalULIRGsorhighredshiftSMGs.
fromthenowincludedatomictransitionsthatbecomeexcitedatthe
hightemperaturesnowpossibleinanISMpermeatedbylargeCR
energydensities.Neverthelesstheseminimumpossiblegastemper- 2.2.1 Testingtheresultsforstrongerradiationfields
aturesremain 5–10timeshigherinextremeCRDRsthanthosein
∼ Wealsoranthesamegridofmodelswiththeincidentfar-UVra-
theMilkyWayorgalaxieswithmoderateρ˙ values.AnyIRra-
sfr
diationfieldscalingexactlyastheCRenergydensitieswhichcor-
diation“leaking”deepinthecloudandwarmingtheconcomitant
responds tothe maximum incident radiation fieldthat can be ex-
dustabove (8–10)K,oranyremnantturbulentgasheating(Pan&
∼ pectedfordensegascores(inpracticepre-stellarcoresarealways
Padoan2010)canonlyraisetheseminimumtemperaturesfurther.
UV-shieldeddeepinsidemolecularclouds).Thedusttemperatureis
nowmoreimportantthaninthepreviouscaseofG◦=1,andiscom-
2.2 Solvingforthecoupledchemicalandthermalstateof putedaspartofthecode.Itsvalueinsidethecloudcaninfluence:
UV-shieldedgascoresinextremeCRDRS thecoolingbyemittingIRphotonswhichinteractwithlineradia-
tivetransfer,theH formationbychangingthestickingprobability,
The thermal balance equation for UV-shielded, CR-heated gas 2
theevaporation/condensation of molecules, and most importantly
(Equation 2) and its solutions (Figure 1), while physically trans-
thegas-grainheating/cooling.TheUCL-PDRcodeusesamodified
parent, they do not account for the fact that ISM chemistry (and
versionoftheformulaofHollenbach,Takahashi,&Tielens(1991)
thus the abundance of coolants) is also strongly CR-regulated in
(hereafterHTT)correctedforthevariousmeangrainsizes.
such regions. This makes the problems of thermal and chemical
TheHTTformulahasbeenfurthermodifiedtoincludeatten-
balanceofCR-dominatedgasstronglycoupledthatmustbesolved
uation of the far-IR radiation. The incident FUV radiation is ab-
together,especiallygiventheverylargeCRenergydensitiespos-
sorbedandre-emittedintheinfraredbydustatthesurfaceofthe
sible in the CRDRs of compact starbursts. We do so by utilizing
cloud (up to A 1mag). In the HTT derivation, this FIR radia-
the advanced time-dependant UCL-PDR code (the latest version v∼
tion then serves as a second heat source for dust deeper into the
describedinBelletal.2007)tocomputegastemperaturesofCR-
cloud.Howeverintheirmodelthissecondaryradiationcomponent
heated molecular cloud interiors self-consistently with their CR-
isnotattenuatedwithdistanceintothecloud,remainingundimin-
regulatedchemistryforawiderangeofCRenergydensities.This
ishedwithdepthandleadingtohigherdusttemperaturesdeepinto
model has already been successfully used several timesto model
thecloud,whichinturnheatsthegastounrealistictemperatures.
PDRsintheGalaxy(e.g.Thietal.2009).
AttenuationoftheFIRradiationhasbeenintroduced byusingan
The heating mechanisms included are: (i) photoelectric ef-
approximationfortheinfrared-onlydusttemperaturefromRowan-
fect from silicate grains and Polycyclic Aromatic Hydrocarbons
(PAHs), (ii) H formation on gain surfaces, (iii) H photodisso- Robinson(1980),hisEquation30b:T=T◦(r/r◦)−0.4 wherer◦ is
2 2 theclouddepthcorresponding toA =1magouter’slab’thatpro-
ciation, (iv) H UV fluorescence, (v) CII recombination, (vi) in- v
2 cessestheincidentFUVradiationandthenre-emitsitintheFIR.
teractionoflow-energycosmicrayswiththegas.Thelatterdom-
From Figure 3 it can be readily seen that the gas tempera-
inategasheatingdeepinsideH clouds(A >5)wheredensegas
2 v turesremaininvariant beyond A 5evenwithwithincident far-
coresresideandtheinitialconditionsforstarformationareset.At v∼
UVfieldsasenhancedastheCRenergydensities.Thisessentially
cloudsurfaceshotgasemitsLyαandOI63µmlineswhiledeeper
leavesCRsastheonlystrongfeedbackfactorofstarformationop-
in (A >0.1), gas cooling occurs via fine-structure line emission
v eratingefficientlydeepinsidemolecularclouds.Moreover,intense
ofoxygen andneutral andsinglyionizedcarbon. Vibrational and
CR heating of UV-shielded gas strongly decouples gas and dust
ro-vibrationallinesofH andCOalsocoolthegaswhileCOrota-
2 temperatureevenathighdensities(Figures1,2,3)withimportant
tionallinesareexcellentcoolantsforthecoldinnerregionsasthe
implications on the gas fragmentation properties and thus on the
firstrotationally-excitedlevelreachesdownto5.5K.Theinterac-
emergentstellarIMF(section3.2).
tionbetweenthegasandthedustgrainsactsascoolingorheating
agentforthegasdependingonthedifferencebetweenthegasand
dusttemperature.H andCOself-shieldingaretakenintoaccount.
2
Thecodecalculatesthegaschemicalabundances, emergentcool-
3 NEWINITIALCONDITIONSFORSTARFORMATION,
inglinefluxes,andtemperaturesself-consistentlyateachdepthin
ANDTHESTELLARIMFINEXTREMECRDR
thecloud, andithasbeenbenchmarked againstother state-of-the S
artphotodissociationregioncodesinRo¨llig,M.etal.(2007). Thenewdetailedthermo-chemicalcalculationspresentedheresup-
We set a nominal incident far-UV field of G◦=1 in Habing porttheresultsfromthepreviousstudyofCRDRsandtheeffects
4 Papadopouloset al.
n =5 103 cm-3 n =104 cm-3
H H
CR=10,000 CR=10,000
100
) 100 CR=1000 ) CR=1000
K K
( CR=100 ( CR=100
T T
CR=10 CR=10
CR=1
CR=0.2
10 10 CR=0.2 CR=1
T T
dust dust
0.1 1.0 10.0 0.1 1.0 10.0
A A
V V
n =105 cm-3 n =106 cm-3
H H
CR=10,000
CR=10,000
100 100
CR=1000
CR=1000
) )
K K
( CR=100 (

T T
CR=100
CR=10
CR=10
10 CR=0.2 CR=1 10
CR=0.2 CR=1
T T
dust dust
0.1 1.0 10.0 0.1 1.0 10.0
A A
V V
Figure2.Thegastemperature profilesversusopticalextinction insidemolecularcloudsimmersedinarangeofCRenergydensities,estimatedusingthe
time-dependantUCL-PDRcodesolvingbothforthermalandchemicalequillibriumateachpointofthecloud.TheCRenergydensitiesrangefromGalactic
values∼(0.2–1)×UCR,Gal,tolow-levelstarformingsystems∼10×UCR,Gal,andextremestarbursts∼(103–104)×UCR,Gal.Thedensitiesencompassthe
rangetypicalforstar-formingmolecularclouds,andtheincidentfar-UVfieldassumedisG◦=1(inHabingunits).ThedusttemperatureTdust(Av)profile
isindicatedbythedashedblackline.Strongerradiationfieldsreachingthedensepre-stellarcoresdeepinsidemolecularclouds(e.g.becauseof“leaking”
far-UVradiationfromO,BstarsinsidethetypicallyclumpymolecularISM),canfurtherraisethegastemperaturesforAv65,whiledeeperthanthatgas
temperaturesremainalwaysCR-controlled.Thesmall∼10%riseofTk(Av)atthehighestdensitiesandUCRvaluesforAv&5islikelyanartifactofthe
highopticaldepthsofCandCOatsuchlargeclouddepths(seeBayetetal.2010).
ofhighU valuesontheinitialconditionsofstarformation(Pa- wellaboveT (8–10)KexpectedintheirCRDRs.Usinginap-
CR dust
∼
padopoulos 2010). Thethermal stateofUV-shieldeddensegasis propriatePDR-typeinitialconditionsofstarformationinnumerical
indeed dramatically altered in the CRDRs of extreme starbursts, models:a)wouldmakethemhard-pressedtoaccountevenforthe
and this will affect its Jeans mass, gas fragmentation properties, near-invariantIMFfoundintheGalaxy(asthewiderangeofphys-
and thecharecteristic massM(∗) of young stars. Thiscontradicts ical conditions initsmassive PDR gasphase would yield awide
ch
theresultsbyElemgreenetal.(2008)which,whilecorrectlycon- rangeofIMFs),b)omitsthesignificant,CR-induced,thermalde-
sideringtheUV-shieldedgasphaseastheonewheretheSFinitial couplingbetweengasanddust(Figures2,3).Thelatterfundamen-
conditionsareset,itomittedCRsfromitsthermalbalance. tallyimpactstheso-calledinflectionpointofeffectiveequationof
state(EOS)usedinallrealistic(i.enonisothermal)numericalsim-
Itmustbepointedoutthatwhileseveralotherstudiesinvesti- ulationsofmolecularcloudfragmentation(e.g.Jappsenetal.2005;
gatedtheeffectsofstarburstenvironmentsontheIMF,all(besides Bonnelletal.2006),andthisisfurtherdiscussedinsection3.2.
theonebyElmegreenetal.2008)failedtoconsidertheISMphase
wheretheinitialconditionsofSFareactuallyset(theCRDRs).In-
steadtheyused physicalpropertiestypical ofPDRs(e.g.Klessen
etal.2007)which,whiledominatingtheobserveddustSEDsand
3.1 ThecharacteristicmassofyoungstarsinCRDRs
molecularlineSpectralEnergyDistributions(SLEDs)ofgalaxies,
theyarehardlyrepresentativeofthephysicalconditionsexpected Thethermalstateofthesedensepre-stellargascoresisnolongera
intheirCRDRs.EvenformildlySFIR-luminousgalaxiesthedust near-invariantbutisinsteadstronglyalteredbythehighCRenergy
temperaturetypicaloftheirglobalSEDsis (30–40)K,whichis densitybackgroundsofextremestarbursts,inevitablyaffectingthe
∼
Starformationin extremeCRDRs 5
n =5 103 cm-3 n =104 cm-3
H H
100
100
) )
K K
( (

T T
10 10
0.1 1.0 10.0 0.1 1.0 10.0
A Go=CR=10,000 A
V Go=CR=1000 V
Go=CR=100
dust
gas n =105 cm-3 Go=CR=10 n =106 cm-3
H Go=CR=1 H
100 100
) )
K K
( (

T T
10 10
0.1 1.0 10.0 0.1 1.0 10.0
A A
V V
Figure3.ThecomputedgasanddusttemperatureprofilesversusopticalextinctioninsidemolecularcloudsasinFigure2,butnowwiththeincidentfar-UV
radiationfieldalsoscalingastheCRenergydensity.Thenowstronglyvaryingdusttemperaturesareshownalongwiththegastemperaturesasdashedlines
withthesamecolor.ThegastemperaturesatAv=5–10remainalmostinvariant(comparewithFigure2)demonstratingthenear-invarianceofthethermalstate
ofthegas(andthusofthestarformationinitialconditions)deepinsidemolecularcloudswhenitcomestoitsdependenceontheradiationfield.Theabrupt
Tkdropathighdensities(∼(105−106)cm−3)andG◦valuesisduetoalackofatomic/ioncoolantsintheH-richregion:asHisconvertedintoH2,theH2
formationheating(whichwasthemajorheatingagent)dropswhileatthesametimeCIcooling(CIIisconvertedtoCIduetoH2/Cmutualshielding)andH2
coolingsharplyincreases.ForhighUCRthegasremainmuchwarmerthanthedust,markingaCR-inducedthermaldecouplingofgasanddust(section3.2).
fragmentationofthosegasregionstowardsprotostars.Indeed,the a higher M(∗) and thus a top-heavy IMF (Larson et al. 2005;
ch
JeansmassforsuchCR-heatedcores Elmegreenetal.2008).Thewiderangeofdensitiesoverwhichthis
occurs makes this conclusion independent of the specific details
ofmolecular cloudfragmentationaslongasM [n(˜r,t),T (˜r,t)]
J k
M(c) = kBTk 3/2ρ−1/2 = drivesthefragmentationprocessoutcomeateachspatialandtem-
J (cid:18)GµmH2(cid:19) c poralpoint(˜r,t).Thelatteristhecurrentconsensusontheroleof
T 3/2 n (H ) −1/2 theJeansmassinmolecularcloudfragmentationtowardsastellar
= 0.9 10Kk 10c4cm2−3 M⊙, (3) IMF, though the views regarding the particular gas phase whose
(cid:18) (cid:19) (cid:20) (cid:21) M setstheM(∗)vary(e.g.Klessen2004;Bonnelletal.2006).
J ch
rises from M(Jc)∼0.3M⊙ when nc(H2)=105cm−3 and Tk=10K IfM∗ch)∝hMJiattheonsetofmolecularcloudfragmentation
(typicalfortheGalaxy),toM(Jc)∼(3–10)M⊙ forTk∼(50–110)K (Klessen 2004), the CR-boost of M(c∗h) in extreme CRDRs is ob-
expectedforsamedensityH gasimmersedintheverylargeCR vious from the large vertical displacement of the M values in
2 J
energydensitiesofextremestarbursts.Thenear-invarianceofM(c) Figure4.Inanon-isothermalgravoturbulentmolecularcloudfrag-
J
in galaxies (Elmegreen et al. 2008) is thus upended in starbursts mentationscheme(e.g.Jappsenetal.2005)itisM(∗) M (n )ata
ch ∼ J c
withhighSFRdensities.InFigure4theM valuescomputedfor characteristicgasdensityn abovewhichefficientgas-dustthermal
J c
molecular gas immersed in the CRDRsof compact extreme star- couplinglowersthegastemperatureinCRDRstowardsaminimum
bursts are shown for a gas density range typical for star-forming valueofT (min) T (Larson2005).FortheGalaxythisoccurs
k dust
molecularclouds.ForU /U >103,M increasesbyafac- atn 105cm−3,∼adensitythatmarksalsothetransitiontonear-
CR CR,Gal J c
∼
tor of 10 across the entire range, which will invariably lead to isothermalcloudregionswherethermalmotionsdominateoversu-
∼
6 Papadopouloset al.
exactshapeandmassscaleofthenewstellarIMFcanonlybedeter-
mined with dedicated molecular cloud fragmentation simulations
thatmakeuseofthenewSFinitialconditionsinextremeCRDRs,
100.0
alongwithanEOSappropriate fortheverydifferentthermaland
ionizationstateoftheirmoleculargas.
) 10.0
MSun CR=10,000 3.2 CRDRs:SFinitialconditions,theEOSinflectionpoint
(
M Jeans 1.0 CR=1000 TpahreamiemtrpiozertdanacseapooflytthroepeEPff=eKctiρveγ,iEnqtuhaetifornagmofentSattaiotenp(EroOpSer)-,
tiesandemergent massspectrumof turbulentself-gravitatinggas
CR=100
hasbeenwell-documentedinafewseminalpapers(Lietal.2003;
Jappsen et al. 2005; Bonnell et al. 2006; Klessen et al. 2007) re-
CR=10
0.1 vealingacrucialroleforγ indefiningtheshapeof thecollapsed
CR=1
CR=0.2 gascoremassdistribution(andhencethestellarIMF).TheEOS,
103 104 105 106 its polytropic index γ as a function of density, and their depen-
Gas density (cm-3) dance on ISM properties such as metallicity, and physical condi-
tions such as the elevated CMB at high redshifts have also been
well-documented (Spaans & Silk2000, 2005), with the so-called
Figure 4. The Jeans mass estimated from Equation 3, and gas tempera-
turesinsideCRDRs,computedforthecorrespondingdensities (usingthe EOS inflection point emerging as a general characteristic. In an
fullUCL-PDRcode)andaveragedovertheinnerAv=5–10cloudregions EOSthatseemswell-approximatedbyapiecewisepolytropewith
(Figure2).Lowmassstarformationwillbeclearlysurpressedinextreme twodistinctγ values,thelatterissimplythecharacteristicdensity
CRDRsforaMJ-drivengasfragmentationtowardsastellarIMF(seetext). ncforwhichγ<1whenn<nc,andγ&1forn&nc.Itscrucialrole
indeterminingtheIMFmassscale,discussedbrieflyin3.1,isdocu-
mentedthroughouttheliterature(Larson2005;Jappsenetal.2005;
personic turbulence (Larson2005; Bergin& Tafalla2007). From
Elmegreen2008).Instarburstenvironmentsa“sharpening”ofthat
Figures2,3itisobviousthatthehighCRenergydensitiesinex-
inflection point is thought to occur because of warm dust. There
tremeCRDRswillkeepthegasanddustthermallydecoupled,with
γ reachesupto 1.4andstaysaboveunityfor densitiespast the
mTka(rmkeind)b≫yTthdeuostn,saentdofthtuhseramcahlaeraqcutiellriibstriicumdenbseittwyeceanngnaoslaonndgedrubste. inflectionpointn∼c∼(104–105)cm−3(Spaans&Silk2005),which
surpressesmolecularcloudfragmentationwhile“tilting”ittowards
Such CR-induced effects have been long suspected for the dense
topheavyIMFs(e.g.Lietal.2003;Klessenetal.2007).
moleculargasintheGalacticCenter(Yusef-Zadehetal.2007).
Unfortunately PDR-like ISM has been used to set the SF
In the CR-innudated molecular clouds of extreme starbursts
initialconditionsforstarburstsinalloftheaforementionedmodels,
a characteristic density in the ISM can now remain only as the
eventhoughthedustinCRDRs(wheretheseconditionsarereally
onewherethesupersonicturbulencehasfullydissipatedandover-
set)remainscool,muchlowerthanthegas,especiallyinextreme
taken by thermal motions in pre-stellar cores, a prerequisite for
CRDRs.Thisinsensitivity of the CRDRdust temperatures to the
their efficient gravitational collapse (e.g. Krumholz & McKee
ambient far-UV radiation field can be demonstrated analytically
2005).Theaveragedensityofsuchtransitionregionscanbeesti-
bysimplyconsideringthelocationofCRDRsdeepinsidefar-UV
matedfromtwowell-knownscalingrelationsinmolecularclouds:
illuminatedmolecularcloudsatA & 5(e.g.McKee1989).Then
σsiVze()r)a=fσte◦r(sre/tpticn)ghσ(lin(emwinid)t=h(-3sikze)Tan/dµhmni=n)1◦/(2r/apsct)h−e1m(dineinmsiutym- Tdust,SB/Tdust,Gal∼[exp(−Av/v1.086)×G◦,SB/G◦,Gal]1/(4+a)
V B k H2 will be the radiation induced boost of the CRDR dust tempera-
linewidth possible, and solving for the corresponding mean vol-
ture in starbursts T with respect to that in the quiescent
umedensity, dust,SB
Galactic environments T 8K. For a dust emissivity
dust,Gal
∼
law of α=2, a large enhancement of the far-UV radiation field
hntri=n◦(cid:18)µ3mkBHT2σk◦2(cid:19)1/2h ∼11n◦(cid:16)kmσs◦−1(cid:17)2(cid:18)1T0Kk (cid:19)−1(4.) ytGeime◦l,SdpBienr/agGtuT◦r,edGupaslrt=o∼1fi10le74s,Kp,aanisdnt AgAovod=55asgihrtoeewismneTinndtuFwsitgi,tSuhBre/thT3e.dudItsetti,asGilaaelcd=tu2da.1ull5syt,
v
∼
For h=1/2 (expected for gas clouds virialiazed under ex- this robustness of dust temperatures inside CRDRs, along with a
ternal pressure, Elemgreen 1989), σ◦=1.1kms−1, and for strong gas-dust coupling at high densities (when UCR values are
n◦=few 103cm−3, it is ntr few 104cm−3. For the CR- modest) that helps retain: thethermal statesof thepre-stellar gas
× h i∼ ×
boosted gas temperatures in extreme starbursts where typically cores,theM(∗)values,andtheIMF,asnearinvariantsoverawide
Tk(min) 100K(Figures1,2,3): ntr few 103cm−3,andthe rangeofambcihentPDRconditions(Elmegreenetal.2008)
∼ h i∼ ×
(turbulentgas) (thermalcore)transitionwilloccuratlowerdensi- ThusPDRconditions,whilealwaysdominatingtheobserved
→
tiesaswellashigher(CR-boosted)gastemperaturesthaninquies- dust SEDsand molecular SLEDs of even mildly SF galaxies (as
centCRDRs.ThiswillthenshifttheexpectedM(∗)bothvertically PDRsarewarmandcontainthebulkoftheISMmass)theyarenot
ch
(highertemperatures),aswellastotheleft(lowerdensities)ofFig- representativeoftheSFinitialconditionsingalaxies,whichareset
ure4,yieldingevenhigherM(∗) valuesthanthoseresultingfrom inCRDRs.Thisleavesthepre-stellargasphaseinthem,amount-
ch
onlyaverticalshiftofM becauseofCR-boostedgastemperatures. ingtoafew%ofthemassper GiantMolecular Cloud( SFeffi-
J
∼
Thusirrespectiveofmolecularcloudfragmentationdetails,a ciency per typical GMC), yet tobe explored interms of itsEOS
muchlargercharacteristicmassofyoung starsisexpectedinthe and fragmentation properties. A detailed exploration of those in
CR-innudatedmolecularcloudsofextremestarbursts.Howeverthe CRDRs will be the subject of a future paper, but Figures 2 and
Starformationin extremeCRDRs 7
4.1 Asequenceofρ˙sfr-dependentstellarIMFs
Thedependanceofthethermo-chemicalandionizationstateofpre-
stellar dense gas in CRDRs on the average U permeating the
CR
1000.0 CR=10,000 ISMofagalaxynaturallylinkstheSFinitialconditionsandthere-
sultingIMFtotheaverageSFRdensityρ˙ ,providedU ρ˙ .
CR=1000 sfr CR ∝ sfr
The details of CR transport/escape mechanisms in quiescent SF
100.0 CR=100 disksandstarburstswilldefinetheproportionalityfactor(seeSuck-
ol
co hovetal.1993fordetailes).Thus,oncesimulationsofmolecular
/tn CR=10 gasfragmentationinCRDRsproducelibrariesofthecorresponding
y
td 10.0 IMFs,thesewillbenaturallyparametrizedbyρ˙sfr,andhenceac-
tualobservables(especiallyintheupcomingeraofhigh-resolution
CR=1.0
imagingatsubmmwavelengthswithALMA).
1.0
CR=0.2
4.2 Implicationsforhierarchicalgalaxyformationmodels:a
0.1
physically-motivatedIMFbimodality
103 104 105 106
Gas density (cm-3) In hierarchical galaxy formation models a bimodal IMF, top-
heavy for mergers/starbursts and regular for disk/regular-SF sys-
tems, has been postulated to explain the populations of the
Figure5.Theratioofdynamical/coolingtimescalesinUV-shieldedmolec-
starbursting/merger-drivensubmillimetergalaxies(SMGs)andreg-
ulargasofCRDRs(Av=5-10)estimatedusingtheUCL-PDRcodeandcos-
ularSFdisksliketheLy-breakgalaxies(LBGs)athighredshiftsin
micrayenergydensitiesrangingfromthoseexpectedinquiescentGalactic
tocompactextremestarbursts. ΛCDMcosmology(Baughetal.2005).TheCR-controlledSFini-
tialconditionsingalaxies,unhinderedbydustextinction,cannow
set this on a firm physical basis. From Figures 2 and 4 is obvi-
ous that for typical SF disks (U (0.2–10) U ) no sub-
CR CR,Gal
∼ ×
stantial effects on the gas temperatures and Jeans masses in CR-
3 already show that CRs, by inducing astrong decoupling of the
DRs are expected while in the extreme CDRDs of compact star-
gtiavseaEnOdSduinsfltetecmtiopnerpaotuinretsfowritghasTdke≫nsTitideusstu,pthtoeyn“=e1r0as6ec”ma−ny3.pTuhtais- bursts(UCR∼(103–104)×UCR,Gal)verywarmgasandlargeJeans
masseswillleadtoaneffectivesurpressionoflow-massstarforma-
will maintain efficient molecular gas cooling, with cooling times
tionandhenceatop-heavyIMF.Formerger-drivenstarformation
alwaysmuchshorterthandynamicaltimes(Figure5),andγ<1in
the latter may characterize entire star-formingepisodes (i.e. until
CRDRs over the entire gas density range explored here. In such
the in-situmolecular gas reservoir isnearly exausted) as dissipa-
regions gas gravoturbulent fragmentation will then occur equally
tioncancontinously“funnel”thelargemoleculargasmassesofthe
efficientlyfromn 5 103cm−3upto 106cm−3yieldingapure
∼ × ∼ progenitorstowardsverycompact( (100–500)pc)regionswhere
powerlawIMF(Spaans&Silk2000;Lietal.2003). ∼
extreme, Eddington-limited SF, takes place with tremendeous IR
Thelatterresult,alongwithourdiscussionin3.1makesclear brightness of σIR (few) 1013L⊙kpc−2 (e.g. Thompson 2009).
that the stellar IMF will be very different in extreme CRDRs, ∼ ×
Suchhigh IR brightness, and thus high SFRdensities, havebeen
thoughonlydetailedgravoturbulentsimulationswiththeappropri-
recentlydeducedalsoinadistantSMG(Swinbanketal.2010).
ateinitialconditions,andperformedwithanewsuitableEOScan
ThusCR-controlledSFinitialconditionsnaturallyyieldabi-
decideitsexactshapeandmassscale.Itmustbealsonotedthatthe
modalSFprocessingalaxies,withhighρ˙ valuesprovidingthe
sfr
veryhighionizationfractionsinextremeCRDRscannow“anchor”
branchingpoint,asfollows:
the magnetic field for much longer periods, and at much higher
(merger-drivenSF) (highρ˙ ) (highU ) (topheavyIMF),
sfr CR
densities,asambipolardiffusioninsuchregionsisnowmuchpro- → → →
(regulardiskSF) (lowρ˙ ) (lowU ) (GalacticIMF).
sfr CR
longed(Papadopoulos2010).Magneticfieldsmaythusremainim- → → →
This proposed ρ˙ -IMF link can then parametrize such an SF
sfr
portant during much later stages of gas fragmentation, even in a
bimodality in hierarchical galaxy formation, once IMF=F(ρ˙ )
sfr
highlyturbulentmedium,andmaythushavetobeincludedinthe
“libraries” are obtained from e.g. gravoturbulent simulations of
simulationsofthisprocessinextremeCRDRs.
molecularcloudfragmentationforarangeofρ˙ values.
sfr
A top-heavy IMF in high-ρ˙ systems will have very seri-
sfr
ous implications on the actual SFRs deduced from the IR lumi-
nositiesofthesetypicallyverydust-enshroudedsystems(whereall
thefar-UVlightfrommassivestarsisreprocessedintoIR).Their
CR-inducedtop-heavyIMFswillnowcorrespondtoseveraltimes
4 CONSEQUENCES,OBSERVATIONALPROSPECTS higherenergyoutputsperstellarmass,andtheSFRsinsuchsys-
temswillhavetobereviseddownwardsbyidenticalfactors.
ThecurrentstudysupportstherecentlysuggestedroleofCRsasa
decisiveSFfeedbackfactor,capableofalteringtheSFinitialcon-
ditionsandtheIMFinextremeCRDRs.Inthissectionwediscuss
4.3 Aρ˙ -dependentIMF:integratedgalacticIMFs
someoftheconsequencesbeyondtheimmediateissuesoftheISM sfr
dependentonstarformationhistory?
andthestellarIMFinsuchenviornments,andoutlinecurrentand
futureobservationsthatcanshedlightonthesenewSFinitialcon- A ρ˙ -dependent IMF as the natural outcome of CR-controlled
sfr
ditionsthatwillbetypicalinhighSFRdensityeventsintheUni- SFinitialconditionsingalaxiescanalsonaturalyyieldintegrated
verse. galacticIMFs(IGIMFs)thatdependonthestarformationhistory
8 Papadopouloset al.
(SFH) of galaxies. This is because ρ˙sfr can be a strong function yields M(c∗h)(M82)>2M⊙ (Fig.4). However the Galactic Center
of the evolution of a galaxy, especially during its early and pre- does offer an example of regions with locally boosted U val-
CR
sumably gas-rich state even when no mergers are involved. Such uesthatdonotnecessarilycorrespondtotop-heavyIMFsintheir
a SFH-dependance of the IGIMFshas been considered before as vicinity,possiblybecausesuchboostsaretooshortandtransientto
thecause of thewell-knownmass-metallicityrelationof galaxies systematicallybiasthelocalemergentIMF.
(Ko¨ppen,Weidner,&Kroupa2007). Stronger evidence for top-heavy IMFs exists in UCDs,
small stellar systems with r (10–30)pc (half-light radius)
e
where (106–107)M⊙ of gas ∼have been converted into stars
4.4 CRpropagationindensemoleculargas:adynamicview at SFR∼ (10–100)M⊙yr−1 (see Dabringhausen et al. 2009
h i∼
isneeded and references therein). Unlike the GC where IMF studies are
hindered by high extinction and tidal disruption of clusters,
Setting U ρ˙ in CRDRsassumes that CRs can freely pene-
CR∝ sfr and where any high-ρ˙ SF episodes may have been short-
trate and warm the entire volume of a GMC down to its densest sfr
lived (and thus could not significantly bias its average IMF to-
UV-shieldedregions.Recentgamma-rayobservationshavedirectly
wards a top-heavy one), the IMFs in UCDs are much more
measuredCRenergydensitiesinthenucleusofanearbygalaxyon
amenabletosystematicstudies,whiletheirSFepisodes havehad
parwiththosecomputedforextremeCRDRsandexpectedfromits
ρ˙ (UCDs) & ρ˙ (ULIRGs) ! They are thus ideal targets for
SFRdensity, whileindicatingonlymildlycalorimetricconditions h sfr i h sfr i
studyingtheIMFresultingfromcompletedhigh-ρ˙ SFevents.
fortheCR/ISMp-pinteractions(Aceroetel.2009).Thelattersup- sfr
Thenext bestthingbesidesstudiesoftheIMFitselfisstud-
portsanunhinteredCRpenetrationthroughthemolecularclouds.
iesoftheISMinCRDRsfromwhichtheIMFemerges,especially
NeverthelessAlfve´nwavesgeneratedoutsidesuchcloudsbyanet
those in compact extreme starburstswhere ρ˙ isvery high (e.g.
flux of CRs in their environments could be effective in keeping sfr
ULIRGs)versussystemswithmoredistributedSFandmuchlower
low energyCRsbelow afew hundred MeV (thosemost effective
ρ˙ values.Theuniqueobservationalsignaturesoftheverywarm
in heating the gas) outside their high density regions (Skilling& sfr
densegaswithhighionizationfractionsexpectedinextremeCR-
Strong 1976), which in turn would affect their thermal balance,
DRshavealreadybeendiscussedinsomedetailbyPapadopoulos
theirfragmentationproperties,andtheemergentstellarIMF.Thus
(2010), and the interested reader is refered to this work. In sum-
the coupled problems of CR transport, magnetic field dynamics,
mary, intheeraofHerschel and theupcoming eraofALMA the
and gravoturbulent evolution of non-isothermal dense molecular
sole main obstacle is the degeneracy of extreme CRDR diagnos-
gaswithhighdegreesofionizationlikethoseexpectedincompact
tic with that of X-ray Dominated regions (XDRs) induced in the
extremestarburstssuchasArp220(e.g.Greveetal.2009)mustbe
ISMbyanX-rayluminousAGN.Indeed,unlessanX-rayluminous
investigatedwithdedicatedMHDsimulations.
AGNcanbeexcludedbyotherindependentmeans(e.g.deepX-ray
observations),itcanbedifficulttotellextremeCRDRsandXRDs
apartinasimplefashionasevenexotichighexcitationspeciessuch
4.5 Observationalprospects
asOH+ andH O+,recentlydetectedbyHerschelinthearchety-
2
Thedetectionsofγ-rayemissionfromtwonearbygalaxies,namely pal ULIRG/QSO Mrk231 and attributed to XDRs (van der Werf
M82 and the starburst nucleus of NGC253 (Acciari et al. 2009, et al. 2010), could be partlydue to CRDRs.Inrecent work Mei-
Aceroetal.2009),aretwoveryimportantrecentdevelopmentsin jerinketal.2010provideadetaileddiscussionofdiagnosticslines
γ-rayastronomy,giventhatγ-rayemissionresultsfromCRproton inextremeCRDRsversusXDRsandthekeyobservationsthatcan
interactionswiththemolecularISM.Thisallowssuchobservations separatethem.
todirectlymeasuretheaverageCRenergydensitiesinSFenviron- FinallyitisworthnotingthatX-raysandXDRswillhavesim-
ments, and thus sensitivesuch measurements inULIRGssuch as ilareffectsasCRsontheJeansmassandtheIMFofUV-shielded
thenearbyULIRGArp220willbeveryimportantinrevealingex- densegasregionsasbothcanvolumetricallywarmsuchregionsto
tremeCRDRsinsuchsystems. hightemperatures.ThiswaspointedoutrecentlybyBradfordetal.
Ontheotherhand,directmeasurementsoftheexpectedtop- (2009) for the ISM of a distant QSO, and constitutes an omitted
heavy IMFs in the heavily dust-enshrouded compact starbursts aspectofAGNfeedbackonstarformation.Thishasbeenstudied
whereextremeCRDRswouldresideareimpossible.Howeverany recentlyandshowntoleadtoatop-heavyIMF(Hocuk&Spaans
caseswherethe“end”products,i.e.thestellarpopulations,ofhigh- 2010).XDRsbesideselevatingT (min)tomuchhighervaluesthan
k
ρ˙sfr SFeventscanbeobservedandtheirIMFdeterminedsuchas intheGalaxytheyalsoyieldTkin Tdust (andthustheycanalso
theGalacticCenter(GC)andlocalUltraCompactDwarfs(UCDs) “erase”theEOSinflectionpoint),th≫oughunlikeCRDRstheirinflu-
allow such direct observational tests. There is indeed strong evi- enceontheISMisnecessarilylimitedbythe 1/R2 geometric
∼ AGN
denceofCRheatingofthedensemoleculargasintheGC,setting factor(R thedistanceoftheirradiatedgasfromtheAGN).
AGN
T >T ,andexpectedstrongeffectsonthelocalJeansmass
kin dust
andambipolardiffusiontimescales(Yusef-Zadehetal.2007).Un-
5 CONCLUSIONS
fortunately,initialassertionsaboutatop-heavyIMFintheGC(e.g.
Nayakshin&Sunyaev2005) andthemassiveArchesclusternear Wehaveconducted new,detailedcalculationsonthethermalbal-
it (Figer et al. 1999; Stolte et al. 2002, 2005) have not been cor- anceofUV-shieldeddensegasinCosmic-Ray-Dominated-Regions
roboratedbylaterstudies(Kimetal.2006; Espinozaetal.2009; (CRDRs),theISMphasewheretheinitialconditionsofstarforma-
Lo¨ckmannetal.2010).Ontheotherhandsomeevidenceexistsfor tionaresetingalaxies,inordertoexamineindetailtheeffectsof
atop-heavyIMFinthenuclearstarburstofM82(e.g.Riekeetal. extremeCRDRsonthemassscaleofyoungstarsandtheIMFre-
1980; 1993), and asignificantly enhanced UCR iscertainly there centlysuggestedbyPapadopoulos(2010).Ourresultscanbesum-
( 500 UCR,Gal, directly measured via γ-ray observations; Ac- marizedasfollows:
c∼iariet×al.2009)toachievethisviaaCR-boostedM(∗) IMFmass 1.Weconfirmthehightemperaturesofdensegascoresinthe
ch
scale.IndeedforsuchU values,settingM(∗) M (105cm−3) extreme CRDRs expected in ULIRGs and all systems with large
CR ch ∼ J
Starformationin extremeCRDRs 9
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