A New Star-Formation Rate Calibration from Polycyclic Aromatic Hydrocarbon Emission Features and Application to High Redshift Galaxies

0.69 MB·

by  Heath V. Shipley

ACCEPTEDFORPUBLICATIONINAPJ
PreprinttypesetusingLATEXstyleemulateapjv.01/23/15
ANEWSTAR-FORMATIONRATECALIBRATIONFROMPOLYCYCLICAROMATICHYDROCARBONEMISSION
FEATURESANDAPPLICATIONTOHIGHREDSHIFTGALAXIES
HEATHV.SHIPLEY1,2,CASEYPAPOVICH1,GEORGEH.RIEKE3,MICHAELJ.I.BROWN4,JOHNMOUSTAKAS5
AcceptedforpublicationinApJ
ABSTRACT
We calibrate the integrated luminosity from the polycyclic aromatic hydrocarbon(PAH) features at 6.2µm,
6
7.7µmand11.3µmingalaxiesasameasureofthestar-formationrate(SFR).Thesefeaturesarestrong(con-
1
tainingasmuchas5-10%ofthetotalinfraredluminosity)andsufferminimalextinction. Ourcalibrationuses
0
Spitzer InfraredSpectrograph(IRS) measurementsof 105galaxiesat0<z<0.4, infrared(IR) luminosities
2
of 109- 1012L⊙, combined with other well-calibrated SFR indicators. The PAH luminosity correlates lin-
n
early with the SFR as measuredby the extinction-correctedHα luminosityover the range of luminositiesin
a
our calibration sample. The scatter is 0.14 dex comparableto that between SFRs derived from the Paα and
J
extinction-correctedHαemissionlines,implyingthePAHfeaturesmaybeasaccurateaSFRindicatorashy-
7 drogen recombination lines. The PAH SFR relation depends on gas-phase metallicity, for which we supply
anempiricalcorrectionforgalaxieswith0.2<Z<∼0.7Z⊙. WepresentacasestudyinadvanceoftheJames
]
A Webb Space Telescope (JWST), which will be capable of measuring SFRs from PAHs in distant galaxies at
the peakof the SFRdensity inthe universe(z∼2)with SFRs aslow as∼ 10 M yr- 1. We use Spitzer/IRS
G ⊙
observationsofthePAHfeaturesandPaαemissionplusHαmeasurementsinlensedstar-forminggalaxiesat
. 1<z<3todemonstratetheabilityofthePAHs toderiveaccurateSFRs. We also demonstratethatbecause
h
thePAHfeaturesdominatethemid-IRfluxes,broad-bandmid-IRphotometricmeasurementsfromJWST will
p
- traceboththeSFRandprovideawaytoexcludegalaxiesdominatedbyanAGN.
o
Keywords:galaxies:active—galaxies:evolution—galaxies:high-redshift—infrared:galaxies
r
t
s
a 1. INTRODUCTION their spectra generally show no [OII] emission beyond that
[
Star-formationisafundamentalpropertyofgalaxyforma- expectedfromtheAGN(Ho2005),i.e.,thequasardominates

1 tion and evolution. Understanding the exact rate of star- the excitation and the line cannot be used to probe the host
v formation and how it evolves with time and galaxy mass galaxies. UV continuum emission is a more general probe,
8 have deep implications for how galaxies form. Measuring but is also subject to extinction and to ambiguities of inter-
9 pretationingalaxieswithAGN.Restframeopticallines(e.g.,
accurate star-formation rates (SFRs) through cosmic time is
6 Hα)shiftedintothenear-IRareobservationallyexpensiveand
therefore paramount for understanding galaxy evolution it-
1 alsosufferfromambiguitiesifthereisanAGN.
self. Much work has been applied to calibrating emission
0 Deep IR surveys with the ISO, Spitzer and Herschel
from the UV, nebular emission lines, far-IR, X-ray and ra-
. Space Telescopes have proven to be a powerful tool to
1 dioastracersoftheSFRindistantgalaxies(seethereviewby
0 Kennicutt&Evans2012). explore SFRs across this range, and have revealed that
6 The epoch 1<z<3 is particularly interesting as it cor- the majority of star-formation at redshifts of z ∼ 1 -
1 responds to the peak cosmic SFR density in the Universe 3 occurs in dust enshrouded galaxies (e.g., Elbazetal.
v: (Madau&Dickinson 2014, and references therein). There i2e0s11(L;IMRGursp,hLyeta=l.12001111- );10a12ndLth)atanludmuilntroaulsumIRinoguaslaIxR-
i are different measures of the instantaneous SFR (see, e.g., IR ⊙
X Kennicutt1998), which are usefulfor probingthe SFR den- galaxies (ULIRGs, LIR > 1012 L⊙) are much more preva-
r sity evolution,buttheirutilitydependsontheredshiftofthe lent during these earlier epochs than today (Chary&Elbaz
a sourceandobservationalwavelengthsavailable. Atlowred- 2001; LeFloc’hetal. 2005; Pérez-Gonzálezetal. 2005;
Magnellietal. 2009; Murphyetal. 2011; Elbazetal. 2011;
shiftsinthisrange,[OII]λ3727Åisfrequentlyusedtomea-
Lutz2014, andreferencestherein). Notonlydofar-IRmea-
sure SFRs, but it is subject to large extinction corrections
surementsrevealdust-obscuredstar-formation,buteveninlu-
(Kennicutt 1998), and hence large uncertainties. Although
minousquasars,thisemissionappearstobedominatedbythe
the[OII]lineshouldbeexcitedbystar-formation,forgalax-
powerfromstar-formationinthehostgalaxies(Rosarioetal.
ieswithstrongactivegalacticnuclei(AGN)suchasquasars,
2013;Xuetal.2015). TheAtacamaLargeMillimeterArray
1George P. and Cynthia Woods Mitchell Institute for Fundamental (ALMA)canmeasurerestframefar-IRoutputsforz>∼2,butat
PhysicsandAstronomy,andDepartmentofPhysics&Astronomy,Texas lowerredshiftsitbecomesinefficientinthisapplication. Fur-
A&MUniversity,CollegeStation,TX77843-4242,USA thermore, no far-IR missions are planned for the immediate
2current address: Department of Physics & Astronomy, Tufts Uni- future, making it difficult to extend this method past the re-
versity, 574 Boston Avenue Suites 304, Medford, MA 02155, USA;
sultsfromSpitzerandHerschel.TheJamesWebbSpaceTele-
[email protected]
3Steward Observatory, University ofArizona, 933North Cherry Av- scope (JWST) is a promising approach for z<∼2 if accurate
enue,Tucson,AZ85719,USA SFRscanbederivedfromobservationsatrestwavelengthsof
4SchoolofPhysics&Astronomy,MonashUniversity,Clayton,Victo- ∼8µm(e.g.,Rujopakarnetal.2013).
ria3800,Australia It has been argued that estimation of SFRs using the aro-
5DepartmentofPhysics&Astronomy,SienaCollege,Loudonville,NY
12211,USA
2
maticemissionfeatures6 thatdominatethe8µmemissionof ieswereferencethroughoutthisworkpredominantlyusethis
star forming galaxies is subject to substantial scatter (e.g., cosmologyandwe adoptit as well to be consistentas much
Smithetal. 2007; Bendoetal. 2008). However, these fea- aspossible). We adoptaKroupainitialmassfunction(IMF)
turesdotrackthetotalSFRatsomelevel,andiftheycouldbe throughoutthis work, where the IMF has the slope α= 2.3
calibratedaccurately,theywouldhavenumerousadvantages. forstellarmasses0.5- 100M⊙andashallowerslopeα=1.3
For example, Spitzer 24 µm measurements provide perhaps forthemassrange0.1- 0.5M⊙ TheKroupaIMFisconsis-
thedeepestprobeavailableofSFRsfor1<z<3(Elbazetal. tentwithobservationsoftheGalacticfieldIMF(e.g.,Chabrier
2011). The luminosity in the mid-IR PAH emission bands 2003;Kroupa&Weidner2003).
is very high for galaxies with ongoing star-formation. The
totalPAHemissioncancontributeasmuchas20%oftheto- 2. SAMPLEANDDATA
tal IR luminosity and the 7.7 µm PAH band may contribute
2.1. CalibrationSample
asmuchas50%ofthetotalPAH emission(e.g.,Smithetal.
2007; Wuetal. 2010; Shipleyetal. 2013). In addition, for For proper calibration of the PAH features as a SFR indi-
galaxieswith anAGN thePAH featureshavebeenshownto cator,wecarefullyselectedgalaxiesthathadfullcoverageof
trace the SFR from the integrated light of the galaxy (if the the Spitzer/IRS spectrum and Spitzer/MIPS 24 µm observa-
AGNisnotthedominantsourceoftheintegratedlight; e.g., tions. We required the galaxies in our sample to have com-
Shipleyetal. 2013). Furthermore, the 11.3µm PAH feature pleteopticalcoverageoftheimportantemissionlinesneeded
evenintheimmediatevicinityofanAGNisnotsignificantly (specifically Hβ, [OIII]λ5007Å, Hα and [NII]λ6583Å)
suppressed(Diamond-Stanic&Rieke2010). tomeasureextinction-correctedSFRs fromthe Hα emission
Interpreting existing deep Spitzer and future JWST mea- line luminosity (Kennicuttetal. 2009), and to estimate the
surements of embedded star-formation depends upon de- ionization state (Kewleyetal. 2001; Kauffmannetal. 2003)
veloping confidence in the use of the PAH features for and the gas-phase metallicity (Pettini&Pagel 2004). We
this purpose. In this paper, we therefore discuss the util- also requiredthatthe galaxiesbe sufficientlydistantthatthe
ity of using the PAH emission to study the SFR in galax- Spitzer/IRS contains the majority of the integrated light in
ies over a large range of total IR luminosity and metal- the spectroscopicslit. In effect, this limits us to z>0.01 or
licity to determine a robust calibration of the relation be- whererobustaperturecorrectionsareavailable.Aperturecor-
tweenPAHemissionandtheSFR.Therearepreviousefforts rectionsforeachsamplewereperformedinthesamegeneral
that calibrate the PAH emission as a SFR indicator. Some way. Photometry for the integrated light of the galaxy was
of these works focus on high-luminosity objects and cali- obtainedandusedtoestimatethecorrectionfactorsappliedto
brateagainstthetotalIRluminosity,whereforthese objects theopticalandIRspectrafromthesmalleraperturesizesused
there may be unknown contributions to the emission from forthespectralslits(seebelowformoredetail).
AGNand/orunknownopticaldeptheffects(Popeetal.2008; We identifiedthreegalaxysamplesfromtheliteraturethat
Lutzetal.2008;Fu&Stockton2009). Otherstudieshavefo- fulfill our selection criteria. We use these three samples as
cused on the broadband emission in the mid-IR which con- ourcalibrationsampletoestablishthePAHluminosityasa
tains contributionsboth from the continuumand PAH emis- SFRindicator.Thecalibrationsampleincludesabroadrange
sion(Calzettietal.2007;Fumagallietal.2014;Battistietal. ofgalaxiesallowingforarobustcalibrationofthePAHlumi-
2015). There is a need for a PAH SFR indicator calibrated nosityforvastlydifferentsystems.Thefullcalibrationsample
overarangeofbolometricluminosityusingtheluminosityin includes 286 galaxies with data from O’Dowdetal. (2009),
the PAH emission features themselves. Once this has been Shipleyetal. (2013) and Brownetal. (2014) samples (spe-
accomplished, it is also possible to understand and improve cificstepstakenfordatareductionofthespectracanbefound
measurementsofSFRsbasedonphotometryinthe8µmre- therein).Wediscusseachsamplebrieflyinthefollowingsec-
gion. tions. OpticalandIRaperturecorrectionswereperformedby
This paper presents one of the first efforts to calibrate the both O’Dowdetal. (2009) and Brownetal. (2014) and can
PAH emission itself against robust SFR measures of the in- be found therein. For Shipleyetal. (2013), IR aperture cor-
tegrated light for distant galaxies over a large range of total rections were performed and can be found in the reference.
IR luminosity (Section 5). To do so, we take advantage of Optical aperture corrections were on average ∼10% for the
PAHemissionfeaturemeasurementsusingasampleofgalax- Shipleyetal.(2013)samplefortheopticallinefluxesshown
ieswithSpitzer/IRSspectroscopyouttoz<0.4. Theoutline inTable1. AfewsourcesfromBrownetal.(2014)arebelow
forthepaperisasfollows.In§2,wedefineourmaincalibra- our redshift requirement of z>0.01. We keep these galax-
tionsampleanddescribeahigh-redshiftdemonstrationsam- iesinourprimaryandsecondarycalibrationsamplesbecause
ple. In§3,wedescribeouranalysisofthederivedquantities. Brownetal. (2014) achieved very accurate aperture correc-
In§4,wepresentourSFRrelationsintermsofthePAH lu- tions to constructtheir spectral energy distributions (SEDs),
minosity. In§5,wediscusspreviouscalibrationsofthePAH but this may introduce some bias for a few galaxies as the
luminosity as a SFR indicator. In § 6, we demonstrate our aperture corrections may not apply equally between the nu-
PAH SFR relations with the demonstration sample of high- clearregionsusedforspectroscopyandthegalaxyoutskirts.
redshiftlensed galaxies. In § 7, we presentourconclusions. Weexcludedfromourfullcalibrationsamplethoseobjects
TheΛCDMcosmologyweassumeisH =70kms- 1Mpc- 1, withpoordataquality,wheremeasuredline/featurefluxesare
0
Ωm=0.3,andΩλ=0.7throughoutthiswork(previousstud- upper limits in one or more of the required emission fea-
tures: Hα, the three brightest PAH features (6.2µm, 7.7µm
and11.3µmfeatures)or the MIPS 24µm band. Also, other
6Lyingintherange3-19µm,attributedtopolycyclicaromatichydrocar- reasons made it necessary to exclude galaxies from the full
bonsandtermed“PAH"hereafter.CertainPAHbandsaremadeupofseveral
calibration sample: not all galaxies in Brownetal. (2014)
emissionfeatures(e.g.,7.7µm,8.6µm,11.3µm,12.7µm,and17.0µmPAH
bands)andsowewill usethe general term “feature” todescribe thePAH have Spitzer IRS coverage (resulting from passive galaxies
emissionbands. withoutsignificantmid-IRdustemission);thesourcesinthe
3
SpitzerFirstLookSurvey(FLS)fromShipleyetal.(2013)do TheBrownetal.(2014)samplealsoincludesclearlymerging
nothaveopticalspectroscopycoveringHα. Wediscussthese systems.ThisextendsthestudyofthePAHemissionasaSFR
reasons in detail in the following sections for each sample. indicator over a range of activity and metallicity. This sam-
Thisreducedourcalibrationsampleto227galaxies. plehascompleteopticalspectraandMIPS24µmphotometry
Finally,werestrictedourcalibrationsampletoincludeonly coverageandincludesIRSspectrafor111ofthegalaxiesthat
star-forming galaxies with no indications of AGN (which comefromseveralsurveys(seeBrownetal.2014,andrefer-
can contribute both to the Hα and 24 µm emission) and we encestherein;galaxieswithoutIRSspectraarepassive). We
required all galaxies to have approximately solar gas-phase use these for our calibration sample. 30 galaxies from this
metallicity(see§ 3.4below). Theserestrictionsreducedour samplefitourprimarycalibrationsamplecriteria.23galaxies
calibrationsampleto105galaxiesfittingalltherequirements. fitthesecondarycalibrationsamplecriteria.
This constitutes our primary calibration sample. In what BecausetheredshiftdistributionoftheBrownetal.(2014)
follows, we focus the PAH SFR calibration on this primary sampleislowercomparedtotheotherdatasetsusedinthecal-
calibrationsampleof105galaxies,whichspanredshift0.0< ibrationsample,theaperturecorrectionsforlightlostoutside
z<0.4andIRluminosityof109<LIR/L⊙ <1012. Wealso theslit can be higher. Brownetal. (2014) providedaperture
consider a secondary calibration sample of 25 galaxies that corrections at 8µm and 12µm, and caution must be applied
satisfyallourselectioncriteria,buthavesub-solarmetallicity when these differ significantly. For the Brownetal. (2014)
(see§3.4and§4.3). galaxiesinourprimarycalibrationsample,most(23/30galax-
ies)have8µmand12µmaperturecorrectionsconsistentwith
2.1.1. O’Dowdetal.(2009)Sample the overall sample (the aperture corrections are ∼1.37 and
The O’Dowdetal. (2009) sample consists of 92 galax- ∼1.34for8µmand12µm,respectively).Theremainingseven
ies that cover a range in total IR luminosity of L galaxieshave largerdifferences(the aperturecorrectionsare
IR
= 109- 1011 L that complements the lower luminosity ∼2.52and∼2.35for8µmand12µm,respectively),butavi-
⊙
sual inspection of the spectra show no obvious discontinu-
galaxies in Brownetal. (2014) with a redshift of 0.03 <
itiesandnoneofourresultswouldchangeifweexcludethese
z < 0.22 and varying AGN activity (from starbursts to
galaxies.
AGN). Compared to the solar oxygen abundance, 12 +
log(O/H) = 8.69 (Asplundetal. 2009), the galaxies in the
O’Dowdetal.(2009)samplespananarrowrangearoundso- 2.2. DemonstrationSampleofHighRedshiftGalaxies
lar(12+log(O/H)N2=8.6to8.8withonegalaxyat9.0).This To demonstrate the PAH SFR calibration, we use
sample has complete coverage of the optical spectra (using Spitzer/IRS data for a sample of high-redshift (1 < z < 3)
the emission line fluxes from the SDSS DR7), IRS spectra galaxiesthathave been gravitationallylensed by foreground
andMIPS24µmphotometrytakenfromthepublisheddata. massive galaxies and/or galaxy clusters. In many cases the
63galaxiesfromthissamplefitourprimarycalibrationsam- gravitationallensingissubstantial,boostingthefluxfromthe
plecriteria.Zerogalaxiesfitthesecondarycalibrationsample backgroundgalaxiesbyfactorsofµ≃3- 30. Becauseofthe
criteria. lensingfactorsthesensitivityiswhatcanbeexpectedfor“typ-
ical”distantgalaxiesobservedwiththeJWST Mid-IRInstru-
2.1.2. Shipleyetal.(2013)Sample
ment(MIRI).JWST/MIRIwillbeabletoobservethe6.2µm
The Shipleyetal. (2013) sample consists of 65 galaxies and 7.7µm PAH features for galaxies with SFRs as low as
covering a range in total IR luminosity of LIR = 1010- ∼10M⊙ yr- 1 to z<∼2by coveringa wavelengthrangefrom
1012 L with mostly higher IR luminosity compared to the 4.9µm to 28.8µm with greater sensitivity than any previous
⊙
Brownetal. (2014) and O’Dowdetal. (2009) samples. The IRmission7.
samplehasaredshiftof0.02<z<0.6withvaryingAGNac- WeusethesampleandresultsreportedinRujopakarnetal.
tivity(fromdominationbystarburststoAGN).Comparedto (2012), whichinclude line flux measurements(orlimits) for
the solaroxygenabundancethe galaxiesin theShipleyetal. Hα, Paα or Brα and the PAH features. The Paα and Brα
(2013)samplespanarangearoundsolar(12+log(O/H) = emission lines are “gold standard" SFR indicators as they
N2
8.4to8.8)buthavemetallicitiesthatbridgetheothertwosam- trace the ionization from the same star-forming populations
ples. This sample has complete IR coverageof the IRS and as Hα, but Paα and Brα suffer substantially less extinction
MIPS24µmphotometryandcompleteopticalspectroscopic owingto their longerwavelengthsin the rest-framenear-IR.
data for 26 of the galaxies in the sample. 12 galaxies from Anotherexcellentextinction-freeSFRindicatorisHα+24µm
this sample fit our primary calibration sample criteria. Two (Kennicuttetal.2009);Rujopakarnetal.(2012)providethis
galaxiesfitthesecondarycalibrationsamplecriteria. metricbasedonrest-frame24µmfluxesestimatedfromspec-
tral energy distribution (SED) template fitting. In addition,
2.1.3. Brownetal.(2014)Sample we reprocess the Spitzer/IRS data for the 8 o’clock arc as
TheBrownetal. (2014)studyincluded129galaxies, cov- Rujopakarnetal.(2012)didnotreportmeasurementsforthe
eringalargerangeintotalIRluminosity(L =109- 1012L ) PAHfeaturesinthemid-IRspectroscopyforthisgalaxy. We
IR ⊙
usedtheirvaluesfortheredshiftandlensingmagnificationfor
and a diverse range in morphology (from dwarf irregulars
eachgalaxy(andreferencestherein),includingthe8o’clock
to ellipticals) with a redshift of 0.0 < z < 0.06 and vary-
arc to be consistent for the sample8. We define these seven
ing AGN activity (from starbursts to AGN), and is largely
drawn from the integrated optical spectroscopic samples of
Moustakas&Kennicutt (2006) and Moustakasetal. (2010). 7see:http://ircamera.as.arizona.edu/MIRI/performance.htm
Because of the lower redshiftand mostly lower IR luminos- 8Theapproximatemagnificationofalensedgalaxyintroducesalargeun-
certainty intheestimated SFRastheactual magnification maydifferbya
ityrangeoftheBrownetal.(2014)sample,itcontainslower
factorofafewtothatofthemeasured. Asaresult,otherstudiesmayusea
metallicitygalaxies(7.8<12+log(O/H)N2<8.8)compared differentmagnification; whichcancausetheestimatedSFRstobeover-or
totheO’Dowdetal.(2009)andShipleyetal.(2013)samples. underestimatedincomparisontoours.
4
high-redshiftlensedgalaxiesfromRujopakarnetal.(2012)as 3. DERIVEDQUANTITIES
ourdemonstrationsample.
3.1. IRSSpectralFitting
We focus our comparison of the estimated PAH SFRs to
the estimated Paα and Hα+24µm SFRs in our demonstra- To determine flux estimates for the PAH features in the
tion of the PAH SFR calibration (see § 6.2). Depending IRS spectra of our calibration sample, we used the PAHFIT
on the redshiftand Spitzer/IRS channelsobserved, only one spectraldecompositioncode(Smithetal.2007),designedfor
of these SFR indicators was available for each galaxy. In SpitzerIRSdata. PAHFITusesaχ2 minimizationroutineto
general, Hα+24µm is available for the entire sample and fit a non-negativecombinationof multiple emission features
Paα is available for z > 2 galaxies, where the rest-frame and continua to the one-dimensionalspectra of our sources.
24 µm fluxes come from longer wavelength MIPS (and in The features included in PAHFIT are the dust emission fea-
some cases Herschel) data, or extrapolationsfrom observed tures from PAHs (modeled as Drude profiles), thermal dust
24 µm data. The galaxies with measured Hα+24µm fluxes continuum, continuum from starlight, atomic and molecular
onlyareA2218b(Rigbyetal.2008,atz=1.034andµ=6.1) emission lines (modeled as Gaussians), and dust extinction.
and A2667a (Rigbyetal. 2008, at z = 1.035 and µ = 17). The PAH emission features at (e.g. 7.7µm, 11.3µm, and
The galaxies with measured Hα+24µm and Paα fluxes are 17µm)areblendsofmultiplecomponents,butPAHFITtreats
the Clone (Hainlineetal. 2009; Linetal. 2009, at z=2.003 themasindividualcomplexes.
and µ=27±1), A2218a (Rigbyetal. 2008; Papovichetal. We take the published PAH fluxes from O’Dowdetal.
2009; Finkelsteinetal. 2011, at z= 2.520 and µ = 22±2), (2009) and Shipleyetal. (2013), whichused the same PAH-
A1835a(Smailetal.2005;Rigbyetal.2008,atz=2.566and FIT input parameters as we use here for the Brownetal.
µ=3.5±0.5),cB58(Seitzetal.1998;Teplitzetal.2000, at (2014) sample (see referencesfor specific parametersused).
z = 2.729 and µ ∼ 30), and the 8 o’clock arc (Allametal. We fit the features in the IRS spectrum for each galaxy in
2007;Finkelsteinetal.2009,atz=2.731andµ∼8). Brownetal.(2014)thathadanIRSspectrum(111/129galax-
For the 8 o’clock arc, we reprocessed Spitzer data taken ies).
fromprogram40443(PI:C.Papovich).Wereducedthespec- Forthedemonstrationsample,thepublishedvaluesforthe
troscopic data for this galaxy using the S17.2.0 version of Spitzer/IRSspectrawerefitusingPAHFITwiththesamepa-
theprocessingsoftwarefromthebasiccalibrateddata(BCD) rameters as our calibration sample. We use these flux mea-
for the IRS SL2 and LL1 modules by following the Spitzer surements of Paα, Hα+24µm and the PAH features to esti-
DataAnalysisCookbook,Recipe179.AsinRujopakarnetal. matetheSFRs.
(2012),wewereabletode-blendthefluxbyperformingPSF We fit the 8 o’clock arc spectra with the same procedure.
photometry to measure the flux of the arc. We reduced the It was important to have the flux measurement fit the same
IRACandMIPS24µmdatausingS16.1.0versionofthepro- wayforeachsampletohaveanaccuratecomparisonbetween
cessingsoftwarefromtheBCDimagesbyfollowingthedata ourPAH SFRs andthe SFRindicators(PaαandHα+24µm)
reduction steps outlined in Papovichetal. (2009). We used availableinRujopakarnetal.(2012). Ourmeasuredfluxval-
threeaperturesof1.8′′eachcenteredonthethreecomponents uesforthe8o’clockarcareLPaα =7.4±0.8×10- 16ergs- 1
identifiedbyFinkelsteinetal.(2009)usingtheSpitzerAPEX cm- 2 and L6.2µm = 21.1±1.4×10- 15erg s- 1 cm- 2, L7.7µm
sourceextractionsoftwaretoextractthe IRACfluxfromthe = 80.0±11.2×10- 15 erg s- 1 cm- 2. But as suggested in
5.8µm band. We estimate that the aperture corrections are Rujopakarnetal.(2012),theresultingspectrum(fortheLL1)
30- 50%10withthecontaminationfromanearbyLIRGatthe hassignal-to-noise(S/N)toolowforPAHFITtofitaccurately
30- 50%levelandthecorrectionsroughlycanceleachother. the continuum and emission features due to the contamina-
To calibrate the absolute flux density of the IRS spectra tionofthenearbysources. We doseethisto someextentas
for the 8 o’clock arc, we integrated the spectrum from the PAHFIT failed to converge and yield a more accurate fit to
SL2modulewiththeIRAC5.8µmtransmissionfunctionand thePAHfeaturesintheSpitzer/IRSLL1spectrum(Figure1).
the spectrum from the LL1 module with the MIPS 24 µm Becauseofthegalaxy’shighredshift,z=2.731,notallPAH
transmission function. We took the ratio of the observed featuresareaccessible,butthe6.2µmfeatureindicatesaSFR
fluxdensitiesasmeasureddirectlyfromtheIRACandMIPS =302±20.0M⊙ yr- 1andthe7.7µmfeatureindicatesaSFR
observations to the flux densities synthesized from the IRS =262±36.7M yr- 1. Incontrast,theSpitzer/IRSSL2spec-
⊙
spectraas an aperturecorrection. We did thisto accountfor
trum gives a consistent SFR from Paα, SFR = 265 ± 29.6
contamination from a foreground LIRG or light that is lost M yr- 1.
outsidethespectroscopicslits. Figure1showstheextracted, ⊙
flux calibrated IRS SL2 and LL1 spectra for the 8 o’clock
3.2. OpticalSpectralFitting
arc. We use these flux-corrected spectra to measure the
For the O’Dowdetal. (2009) sample, we used the up-
Paα emission line from the IRS/SL2 spectrum and the PAH
featuresfromtheIRS/LL1spectrum.Weextractedlinefluxes dated line flux measurements (Hβ, [OIII]λ5007Å, Hα
from the IRS data for the 8 o’clock arc and the galaxies in and [NII]λ6583Å) from SDSS DR7 (MPA/JHU value-
ourcalibrationsampleusingthemethodsdescribedin§ 3.1. addedgalaxycatalog,Brinchmannetal.2004;Tremontietal.
2004).11 ForShipleyetal.(2013),weusedthelinefluxmea-
surements from the AGN Galaxy Evolution Survey (AGES;
Kochaneketal. 2012), reported in Table 1 and described
in Moustakasetal. (2011) based on the continuum and
emission-line fitting technique of Moustakasetal. (2010).
For Brownetal. (2014), we fit the emission lines as simple
9see:http://irsa.ipac.caltech.edu/data/SPITZER/docs/
dataanalysistools/cookbook/23/ Gaussiansusinga leastsquaresroutinetoobtainthebestfit.
10see:http://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/
iracinstrumenthandbook/ 11seehttp://www.mpa-garching.mpg.de/SDSS/DR7/
5
0.4
Paα λ1.875µm [N II] + Hα Data
2.5 Fit
)
0.3 1 NGC 6052 (SF)
−
y) SL2 spectrum Å
mJ 2 −2.0
(0.2 m

x
u c
Fl 1−1.5
0.1 s

g
r
e

0.0 13 1.0
1.4 1.6 1.8 2.0 2.2 − [N II]
0
Rest Wavelength (µm) 1
(

λ0.5
F
2.0
6.2µm 7.7µm 8.6µm
6400 6500 6600 6700 6800
1.5
y) LL1 spectrum Rest Wavelength (Å)
mJ
(1.0
ux 8 [N II] + Hα Data
Fl Fit
)
0.5 1− 7 NGC 5256 (AGN)
Å

2
−6 [N II]
0.0 m
5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
c
Rest Wavelength (µm)
1 5
−
s
Figure1. IRSspectraofthestronglygravitationally lensedgalaxy, the“8
g
oÕclockarc".TheToppanelshowstheSL2spectrum,andtheBottompanel r4
e
showstheLL1spectrum. Ineachpanel,thedatapointsanderrorbarsshow
themeasurementsfromthedata,andthegreencurveshowsthespectralde- 14−3
compositionfromthebestfitPAHFITmodeltothedata. 0
We fit the Hα and [NII] doubletsimultaneously using three 1
(
Gaussians, with the ratio of the central wavelengths fixed. λ2
F
Figure 2 shows representativespectra and our fits for a star-
forminggalaxyandAGNintheBrownetal.(2014)sample. 1
The relationship between the [NII]λ6583Å/Hα and 6400 6500 6600 6700 6800
[OIII]λ5007Å/Hβ emission line ratios provide a test for Rest Wavelength (Å)
ionization from a central AGN using an optical Baldwin,
Figure2. Examplesofourfits(greendot-dashedline)totheopticalspectra
Phillips and Terlevich (BPT) classification (Kewleyetal.
(solidblackline)forBrownetal.(2014)fortheHαand[NII]emissionlines
2001; Kauffmannetal. 2003). We adopted the SDSS DR7 (see§3.2forfittingprocedure). Here,weshowNGC6052(star-forming)
measured emission line fluxes for the O’Dowdetal. (2009) andNGC5256(AGN)thatisrepresentativeoftheentireBrownetal.(2014)
sample. We note that a few of the galaxy classifications are sampleforeachclassification(see§3.2forclassification).
changed from those in O’Dowdetal. (2009), that used the
the rest-frame for each galaxy and again estimated the rest
SDSSDR4fluxmeasurements. FortheShipleyetal. (2013)
sample, we used the measured fluxes in Table 1 for classifi- 24 µm flux densities from the SEDs for each galaxy. This
was necessary for these two samples to be consistent with
cation. For the Brownetal. (2014) sample, we use their re-
eachotherasasignificantamountofthegalaxies’IRSspec-
portedopticalBPTclassifications.
tra at rest-frame 24 µm are shifted out of the observed IRS
3.3. Extinction-correctedHαEmissionUsingRest-Frame spectrum or dominated by noise due to the redshift of the
MIPS24µmFlux galaxies(49/142galaxiesforthecombinedsamples). Forthe
O’Dowdetal. (2009) and Shipleyetal. (2013) samples, we
We estimate extinction-correctedHα line luminosities us-
synthesized MIPS 24 µm broadband flux densities by com-
ingthesumofthe observedHαemissionlineanda fraction
putingthe(rest-frame)MIPSbandpass-weightedaverageflux
of the rest 24 µm monochromatic luminosity as defined by
densityfromtheIRSEDthatbestfitthelong-wavelengthpho-
Kennicuttetal.(2009),
tometry12.
LcHorαr (ergs- 1)=LHα+0.020L24µm(ergs- 1) (1) InmostcasestheHαextinctioncorrectionsaresubstantial.
Figure 3 showsthe relation between the correctedHα lumi-
For the Brownetal. (2014) subsample this was straightfor- nosityandthe ratio of observedHα luminosity(uncorrected
wardconsideringtheSEDsfortheirgalaxiesweregiveninthe
rest-frame. For the O’Dowdetal. (2009) and Shipleyetal. 12seehttp://irsa.ipac.caltech.edu/data/SPITZER/docs/
(2013) subsamples we used the best fit SEDs (see § 3.5) in dataanalysistools/cookbook/14/
6
Table1
OpticalFluxesandBPTClassificationforShipleyetal.(2013)Sample
ID Hβ [OIII]λ5007Å Hα [NII]λ6583Å BPT
(10- 16) (10- 16) (10- 16) (10- 16) Class
1 22.4±0.33 41.8±0.32 89.6±0.44 16.0±0.27 SF
2 ... ... ... ... ...
3 0.99±0.34 ... ... ... ...
4 9.88±0.30 1.22±0.20 63.2±0.37 21.9±0.28 SF
5 60.5±1.18 18.6±1.00 414.±2.29 155.±1.79 SF
6 1.70±0.30 1.49±0.32 11.9±0.51 7.40±0.47 SF/AGN
7 51.7±0.43 10.7±0.33 258.±1.56 98.9±0.62 SF
8 1.83±0.30 1.78±0.26 13.8±0.39 13.8±0.35 AGN
9 0.56±0.12 0.49±0.10 4.32±0.20 3.32±0.19 SF/AGN
10 2.92±0.24 2.38±0.22 22.4±0.51 12.7±0.50 SF/AGN
11 0.36±0.09 0.24±0.12 1.32±0.24 ... ...
12 6.93±0.26 7.52±0.28 40.9±0.75 17.0±0.64 SF/AGN
13 ... ... ... ... ...
14 0.82±0.28 ... 4.33±0.76 2.64±0.49 ...
15 10.0±0.26 5.75±0.25 65.6±1.00 29.4±0.77 SF
16 ... 1.36±0.27 ... ... ...
17 4.52±0.17 3.37±0.16 38.0±0.50 17.5±0.39 SF/AGN
18 21.7±0.35 12.4±0.34 120.±0.72 42.6±0.59 SF
19 2.14±0.13 3.42±0.09 11.0±0.36 2.57±0.27 SF
20 2.42±0.20 0.69±0.18 14.4±0.41 7.04±0.44 SF
21 1.51±0.24 8.42±0.25 7.22±0.62 5.65±0.60 AGN
22 7.71±0.35 13.9±0.37 39.3±1.65 25.4±1.16 SF/AGN
23 10.4±0.75 4.74±0.65 75.6±2.34 30.5±2.04 SF
24 0.94±0.26 12.3±0.24 ... ... ...
25 5.66±0.38 4.95±0.40 28.1±1.10 18.1±1.19 SF/AGN
26 ... 4.77±0.42 ... ... ...
27 1.46±0.25 4.45±0.27 7.11±1.15 6.72±0.95 AGN
28 3.43±0.13 1.66±0.15 22.5±0.82 6.31±0.71 SF
29 2.01±0.28 5.83±0.31 ... ... ...
30 2.42±0.24 2.01±0.18 ... ... ...
31 4.92±0.21 1.83±0.16 ... ... ...
32 1.76±0.10 0.58±0.10 ... ... ...
33 1.21±0.29 ... 7.17±0.64 2.78±0.44 ...
34 1.81±0.14 0.92±0.11 ... ... ...
35 2.00±0.47 ... ... ... ...
36 1.01±0.16 ... ... ... ...
37 0.47±0.08 1.53±0.09 2.97±0.29 1.67±0.19 AGN
38 ... 0.81±0.13 ... ... ...
39 ... ... ... ... ...
40 0.51±0.14 ... 6.08±0.62 5.79±0.54 ...
41 ... 0.71±0.20 3.08±0.33 5.53±0.36 ...
42 1.16±0.19 1.27±0.21 10.3±0.81 9.67±0.73 AGN
43 ... ... ... ... ...
44 1.58±0.27 9.40±0.34 ... ... ...
45 1.22±0.22 2.93±0.26 ... ... ...
46 2.75±0.26 3.15±0.20 12.1±0.32 2.55±0.21 SF
47 7.01±0.29 3.68±0.22 40.5±0.51 14.9±0.55 SF
48 5.45±0.17 1.62±0.19 59.2±2.79 26.0±2.99 SF
49 4.16±0.71 18.0±1.29 20.9±4.05 13.4±4.39 AGN
50 ... ... ... ... ...
Note. — Column 1is the galaxy identification defined in Shipleyetal. (2013).
Columns2- 5arethemeasuredfluxesfortheemissionlinesHβ,[OIII]λ5007Å,Hα
and[NII]λ6583Å, respectively (in units oferg s- 1 cm- 2). Column 6is the BPT
classificationfromthemeasuredfluxes.
fordustextinction)totheextinction-correctedHαluminosity. the results are consistent. But, there is a sample of highly
Mostofthegalaxiesinourprimaryandafewinthesecondary attenuated objects, AHα >1 mag, where we see big devia-
calibrationsampleshavecorrectionsofmorethanafactorof tions (at the higherextinction-correctedHα luminositiesthe
2 to the Hα luminosity. The median correctionfactor is 4.2 Balmer decrementcorrectionssaturate). Thelikely explana-
andtheinterquartilerange(25- 75percentiles)is2.5- 5.9. tionforthisattenuationisthattheinterstellarmedium(ISM)
InFigure4,wecompareourextinctioncorrectionsfromthe atHβisopticallythick,soweareonlyseeingthe“skin"ofthe
monochromatic24µmluminositytoextinction-correctedHα star-formingregion(down to where τ ∼1 for Hβ), whereas
luminositiesfromtheBalmer decrement,measuredfromthe wecanseedeeperintothestar-formingregionforHα.Balmer
ratiooftheHαandHβ emissionlines. Mostofourprimary absorption could be another issue. Figure 4 suggests it is a
calibrationsampleconsistsofdustystar-forminggalaxies(i.e. significant contributor, since there are many galaxies where
LIRGs) thatheavily attenuate the Hβ emission line and to a correctingwiththeBalmerdecrementovercorrectsHα. Only
lesserextenttheHαemissionline. Weindicategalaxieswith about half the sources in the primary calibration sample for
AHα>1magthat,inessence,resultsinanattenuationfactor AHα>1magallowustoextinctioncorrectusingtheBalmer
of>∼2.5forHαandafactor>∼3.6forHβ. Formanysources decrementand ∼10%of the samplehave unreliablecorrec-
7
30
25% of SF galaxies
60 low metallicity cutoff
50% of SF galaxies
solar metallicity
75% of SF galaxies
O'Dowd et al. (2009)
O'Dowd et al. (2009) 25
α30 Brown et al. (2014) Brown et al. (2014)
H Shipley et al. (2013)
L Shipley et al. (2013)

/
) 20
4
2
L
* 10
20 gal15
0 N
.
0

+
10
α 3
H
L
(
5
1
0
40 41 42 43 7.8 8.0 8.2 8.4 8.6 8.8 9.0
log L + 0.020*L (erg/s) 12 + log(O/H)
Hα 24 N2
Figure3. Therelationbetweentheextinction-correctedHαluminosityand Figure5. Histogramofthemetallicities forallthestar-forminggalaxiesin
thedustcorrectionfactor,definedastheratiooftheextinction-correctedHα thecalibrationsample,wherethemetallicitiesare12+log(O/H)N2. Forthe
toobserved(uncorrected)Hα.Thefilledsymbolsshowtheprimarycalibra- calibrationoftheSFRrelationsusingPAHluminosityweusedgalaxieswith
tionsample. Thehorizontallinesshowthe25,50,and75percentilesofthe 12+log(O/H)N2≥8.5(reddashedline)forourprimarycalibrationsample.
distribution. Themediancorrectionfactoris4.2andtheinterquartilerange Theresultingcutbeing0.65ofthesolarabundance(12+log(O/H)=8.69,
(25- 75percentiles) is2.5- 5.9. Theopenorange symbols show thesec- Asplundetal.2009,orangedashedline).
ondarycalibrationsampleoflowmetallicitygalaxiesasdefinedin§3.4.The
bluepointenclosedbyablackcircledenotesIIZw096,see§4.4. stratedthisdependenceusing8µm-to-24µmratiosofgalax-
ies above and below a metallicity of 12 + log(O/H) = 8.2,
1045 wheretheyattributedthesmallerratiosforgalaxieswithlow
unity metallicity to a decrease in the mid-IR emission bands (at-
linear, AHα ≤ 1 mag tributedtoPAHs). Calzettietal.(2007)showedstar-forming
1044 AHα > 1 mag galaxieswith low metallicities have less than expected mid-
Brown
IRdustemission(presumablyfromPAHemission)basedon
O'Dowd
)⊙ Shipley a linear fit to their calibrationof extinctioncorrectedPaα to
(L 1043 the8µmdustemission.Thistrendisnotseenintheircalibra-
m tionofextinctioncorrectedPaαtoHα+24µmluminosities,
µ
L24 illustratingthePAHemissiondependenceonmetallicity.
0 1042 We calibrate the relation between metallicity, PAH emis-
2
0 sion,andSFRsusingthedatainoursamples. Forallgalaxies
0.
+ α1041 ianbuthnedacnaclieburastiinognthsaemNp2lei,nwdeex,esNti2m≡atelotghe[NgaIIs]-pλh6a5s8e3oÅxy/Hgeαn,
H
L usingtherelationfromPettini&Pagel(2004),
1040 12+log(O/H)=8.90+0.57×N2 (2)
We use 12+log(O/H) because the N2 index is available
N2
1039 forallgalaxiesinourcalibrationsample. Figure5showsthe
1039 1040 1041 1042 1043 1044 1045 distributionofoxygenabundanceforthe galaxiesin ourpri-
Extinction-Corrected Hα (L )
mary and secondary calibration samples. Most sources fall
⊙
Figure4. Extinction-corrected HαluminositiescorrectedfromtheBalmer inatightdistribution(±0.2dex)aroundthesolarabundance
decrement(ratioofHα/Hβ)comparedtotheextinction-correctedHαlumi- (12+log(O/H)=8.69,Asplundetal.2009)withalongtailto
nositiescorrectedfromthe24µmluminosityfortheprimarycalibrationsam- lowerabundances. This is unsurprisingbecauseof the well-
ple. WedenotegalaxieswithAHα>1mag(opencircles). Weperformed knownmass-metallicityrelation(Tremontietal. 2004).Most
unity(blackdashed-line) andlinear(greendashed-line) fitstothegalaxies
withAHα≤1mag. Formanysourcestheresultsareconsistent. But,there sources in the calibration samples have LIR >1010 L⊙, and
isasampleofhighlyattenuatedobjects, AHα>1mag,whereweseebig likely have higher stellar mass, and therefore higher abun-
deviations (see§3.3forfurtherexplanation). Threegalaxies fromthepri- dance(e.g.,basedonTremontietal.2004,galaxieswithstel-
marycalibrationsampledonotappearinthefigureduetounreliableHβflux
measurements. larmass>109M⊙haveabundances>0.5Z⊙). Weusestar-
tionsduetoHβ beingheavilyattenuated. Forthisreason,we forminggalaxieswith12+log(O/H)N2≥8.5fortheprimary
adopttheLHα+0.020×L24µm methodasthebestestimator calibrationsample.
forthetotalHαemissionforourprimarycalibrationsample.
3.5. TotalIRluminosity
3.4. Gas-PhaseMetallicities
WeestimatethetotalIRluminosity(LIR =L8- 1000µm)us-
The PAH emission from a galaxy is known to depend on ingtheMIPS24µmfluxdensities(also70µmand160µm,
the gas-phase metallicity. Engelbrachtetal. (2005) demon- where available in Shipleyetal. 2013) and the method in
8
Shipleyetal.(2013). WeusetheRiekeetal.(2009)IRSEDs fortheunityrelationand
becauseforstar-forminggalaxiesthetotalIRluminositiesde-
rivedfromthesetemplatesusingthe24µmfluxdensityonly logLPAH =(1.30±0.03)+
areclosesttotheIRluminositiesderivedwhenmoreIRpho- (1.00±0.03)log(LHα+0.020×L24µm) (6)
tometricbandsareavailable.Theseresultshelpusunderstand
forthelinearrelation. WenotethattheformsofEquations5
therangeoftotalIRluminosityoverwhichourPAHSFRsare
and 6 are essentially identical, and this is because the linear
calibrated;ourcalibrationmaynotextendtohigherIRlumi-
fityieldsaslopeconsistentwithunitytofivesignificantdigits
nosities, where the PAH featurestend to be suppressed. We
were able to determine the contributing total IR luminosity (1.0003±0.03). Using Equation3, thisyieldsthefollowing
calibrationsforthetotalPAHluminosityasaSFRindicator,
rangefortheBrownetal.(2014)samplebyusingthevalues
reportedinHaanetal.(2013)forthemajorityofthegalaxies.
logSFR(M yr- 1)=
⊙
4. THEPAHSFRCALIBRATION (- 42.56±0.03)+logL (ergs- 1) (7)
PAH
Previous studies have shown that the Hα luminosity is a andusingthelinearfitwefind,
robust indicator of the SFR once corrected for dust extinc-
tion but this correction is non-trivial (e.g., Kennicutt 1998). logSFR(M yr- 1)=(- 42.56±0.03)+
⊙
MorerecentworkhasshownthattheHαluminositysummed
with a fraction of the monochromatic 24 µm light provides (1.00±0.03)logLPAH(ergs- 1) (8)
alinearfitagainstextinctioncorrectedHαandPaαemission
showingthereisstatisticaluncertaintyof≈0.03dexandscat-
(Calzettietal.2007;Kennicuttetal.2007,2009;Treyeretal.
ter of ≈0.135 dex on the total PAH luminosity unity SFR
2010). Here we use the extinction-corrected Hα from the
relationship (where we remind the reader that this applies
24µmmonochromaticemissionasourSFRcalibrator,using
for galaxies of roughly solar metallicity and luminosities of
Kennicuttetal.(2009),
109<LIR/L⊙<1012).
SFR(M yr- 1)= Weobservesmalloffsetsfromtheextinction-correctedLHα
⊙ and L calibration between the different calibration sub-
PAH
5.5×10- 42[L(Hα)+0.020L(24µm)](ergs- 1) (3) samples. We measure average offsets of LPAH/Lfit = 0.06,
0.06,-0.10fortheO’Dowdetal.(2009),Shipleyetal.(2013)
where the constant of proportionality is appropriate for the and Brownetal. (2014) subsamples, respectively. This may
KroupaIMFwehaveadopted. implythereisanadditionalsystematicuncertaintyof0.1dex
(i.e., 20%) on the PAH SFR calibration from differences in
aperturecorrectionsordataprocessingandanalysis.
4.1. PAHSFRRelations
The scatter about this relation for the primary calibration
WecomparetherelationbetweentheluminosityinthePAH sample is very small, 0.14 dex, at least over the luminosity
features to the extinction-correctedHα luminosity. Because rangeofoursample.ThisimpliesthatthetotalPAHemission
differentPAHfeaturesareaccessibleatdifferentwavelengths
correlateslinearlywiththeSFR.Thescatterissimilartothat
dependingontheredshiftofthesourceandwavelengthcapa- measuredforotherstar-formationindicatorsmeasuredagainst
bilitiesofthetelescope/instrument,wecalibrateboththeindi- each other (Kennicuttetal. 2009), indicating that the total
vidualfeaturesat6.2µm,7.7µmand11.3µm,aswellassums PAHemissionisofsimilaraccuracyindeterminingSFRs.
ofthesefeatures. ItisalsoworthnotingthatHαprobesvery Figure 6 shows that it was necessary to remove the low
youngstar-formationfromOBstars, whereasitislikelythat metallicity(andlowS/N;S/N<5)galaxiesfromourprimary
thePAH featurescovera broaderrangeof ages(presumably calibrationsample. Thelowmetallicity(andlowS/N)galax-
includingcontributionsfromAandearlyFstars)andthatdif- ieshavelowL /L ratios(Figure6, bottom),whereL is
PAH fit fit
ferentSFRindicatorsaresensitivetoslightlydifferenteffects definedastheunityrelationfittotheprimarycalibrationsam-
fromthestar-formationagerangemeasured. ple for the expected luminosity of the PAH luminosity for a
noFsiitgyu1r3e6showsthecorrelationbetweenthetotalPAHlumi- givenLHα+0.020×L24µm luminosity. We markthegalaxy
IIZw096asitisanoutlierinthefigures(Figures6,7and9)
butdonotomititasitdoesnotsignificantlyaffectourcalibra-
LPAH=L6.2µm +L7.7µm +L11.3µm (4) tionofthePAHfeatures(wediscussthisinterestinggalaxyin
§4.4).
andtheextinction-correctedHαluminosityforthe227galax-
We also calibrate the luminosity from the individualPAH
iesinourcalibrationsample. Forstar-forminggalaxieswith
features and combinations of them as SFR indicators as in
high metallicity (primary calibration sample), the total PAH
somecasesonlyoneortwoPAH featuresmaybeuseableto
luminosity correlates linearly with the extinction-corrected
getaSFR,suchasforhighredshiftgalaxies(see§6.2). Fig-
Hαluminosity. Ourderivedrelationsbetweentheextinction-
ure7showstherelationsbetweentheextinction-correctedHα
correctedHαluminosityandthetotalPAHluminosityare
luminosityandtheindividualPAHfeaturesandthetotalPAH
luminosityfortheprimarycalibrationsample.Figure8shows
logL =
PAH thedistributionofresidualsbetweenthePAHluminosityand
(1.30±0.03)+log(LHα+0.020×L24µm) (5) thefit,andshowsboththescattercomputedfromthemedian
absolute deviation(MAD, Beersetal. 1990) and a Gaussian
fit,bothofwhichareconsistent.Thescatterissmallest,σ
13LPAHweusetodenotethePAHluminosityforthetotalluminosityofthe =0.14dex(i.e.,40%)wheneverthe7.7µmfeatureisinvolMvAeDd
6.2µm,7.7µmand11.3µmfeatures. AllotherinstancesofPAHluminosity
willbedenoted bytheincluded PAHfeatures (e.g. L6.2µm). Howeverin in the fit. This implies this feature may provide the most
figures,welabelexplicitlywhichfeaturesareused. robust measure of the SFR. The relation against the 6.2µm
9
1
SFR (M yr )
−
Hα
0.1 1 ⊙ 10 100
45
PAH 6.2µm + 7.7µm + 11.3µm 100
low Z or S/N
)
44 unclassified
) 1
s AGN −
/ 10 r
g composite
y
r 43 star-forming
e ⊙
( 1 M

3
. (
1 42
1 3
+ .
0.1 1
7 1
. +
7
+ 41 7
.
2 7
. 0.01 +
6
L Brown et al. (2014) 2
g 40 O'Dowd et al. (2009) R6.
o Shipley et al. (2013) F
l S
unity fit SF only
39
linear fit SF only
it 10
Lf 1040 1041 1042 1043
/
3 1.0
.
1
1
+
0.1
7
.
7
+
0.01
2
.
6
L
40 41 42 43
log L + 0.020 L (erg/s)
Hα 24
×
Figure6. Thetoppanelistheextinction-corrected Hαluminosity(LHα+0.020×L24µm)versustotalPAHluminosity(L6.2µm +L7.7µm +L11.3µm PAH
features).Wefitaunityrelation(dashedblackline)totheprimarycalibrationsample(filledbluepoints)andusethisline(thatwedefineasLfit)toshowtheratio
ofthetotalPAHluminosity,foreachgalaxy,totheunityrelationshipasafunctionofextinction-correctedHαluminosity(bottompanel). Weclassifygalaxies
asstar-forming(filledbluepoints),composite(unfilledgreenpoints)oranAGN(unfilledredpoints)basedonthelocationoftheiremissionlineratiosonaBPT
diagram. Unclassifiedgalaxies(unfilledpurplepoints)didnothavealllinesrequiredforBPTclassificationandthestar-forminggalaxieswithlowmetallicity
orS/N(unfilledorangepoints)arenotusedforthePAHSFRcalibration(filledbluepoints;seetextformoredetail). Thebluepointenclosedbyablackcircle
denotesIIZw096,see§4.4.
feature has the highest scatter, σ = 0.21 dex (i.e., 60%), fortheunityrelationsandthelinearrelationsare
MAD
which may indicate more variation in galaxies between the
luminosityinthisfeatureandtheSFR. logL6.2µm=(- 1.20±0.09)+
Ourderivedrelationsbetweentheextinction-correctedHα (1.04±0.04)log(LHα+0.020×L24µm)
luminosityandtheindividualPAHluminositiesare
logL7.7µm=(1.12±0.06)+
(10)
logL6.2µm= (1.00±0.03)log(LHα+0.020×L24µm)
(0.47±0.08)+log(LHα+0.020×L24µm) logL11.3µm=(2.87±0.08)+
logL7.7µm= (0.94±0.03)log(LHα+0.020×L24µm)
(9)
(1.11±0.05)+log(LHα+0.020×L24µm) In every instance, the linear relations are consistent with
logL11.3µm= a unity slope between the PAH luminosities and the SFR
(within 2σ of unity). Again, using the relation from
(0.54±0.07)+log(LHα+0.020×L24µm)
10
SFR (M yr 1) SFR (M yr 1)
Hα − Hα −
0.1 1 ⊙ 10 100 0.1 1 ⊙ 10 100
45 45
PAH 6.2µm + 7.7µm + 11.3µm 100 PAH 6.2µm
)
s) 44 1− 44
g/ 10 yr 100)
er 43 ⊙ s) 43 1−
( M g/ yr
g L6.2+7.7+11.3444012 BOr'Dowown de te at la. l(.2 (021040)9) 01.1 R (6.2+7.7+11.3 log L (er6.2444012 BOr'Dowown de te at la. l(.2 (021040)9) 011.01 SFR (M 6.2⊙
o Shipley et al. (2013) F Shipley et al. (2013)
l unity fit SF only S unity fit SF only
39 39
linear fit SF only linear fit SF only
Lfit 10 1040 1041 1042 1043 10 1040 1041 1042 1043
/
11.31.0 Lfit 1.0
+7.7+ L/6.20.00.11
20.1
6.
L 40 41 42 43 40 41 42 43
log L + 0.020 L (erg/s) log L + 0.020 L (erg/s)
Hα × 24 Hα × 24
SFR (M yr 1) SFR (M yr 1)
Hα − Hα −
0.1 1 ⊙ 10 100 0.1 1 ⊙ 10 100
45 45
PAH 7.7µm PAH 11.3µm
100
44 44
100
) )
s) 43 10 1− s) 43 1−
g L (erg/7.74412 01.1 R (M yr7.7⊙ g L (erg/11.34412 110 R (M yr11.3⊙
lo 40 BOr'Dowown de te at la. l(.2 (021040)9) SF lo 40 BOr'Dowown de te at la. l(.2 (021040)9) 0.1 SF
Shipley et al. (2013) Shipley et al. (2013)
unity fit SF only unity fit SF only
39 39
linear fit SF only linear fit SF only
10 10
1040 1041 1042 1043 1040 1041 1042 1043
L/L7.7fit1.0 L/L11.3fit1.0
0.1 0.1
40 41 42 43 40 41 42 43
log L + 0.020 L (erg/s) log L + 0.020 L (erg/s)
Hα × 24 Hα × 24
Figure7. Theextinction-corrected Hαluminosity(LHα+0.020×L24µm,Kennicuttetal.2009)versusLPAH(topleft)andforthe6.2µm(topright),7.7µm
(bottomleft)and11.3µm(bottomright)PAHfeaturesseparately.ThisillustratesthatthesmallscatterpersistsfortheindividualPAHfeatures(σMAD<∼0.2dex).
Wefitaunityrelationtotheprimarycalibrationsample(solidblackline)andusethislineasLfittodetermineresidualsofexpectedLPAHvalues(bottomforeach
panel). WeusedthisfittodetermineaSFRrelationforLPAHandeachPAHfeatureshownindividually(see§4.1). Thebluepointenclosedbyablackcircle
denotesIIZw096,see§4.4.
Kennicuttetal. (2009) given in Equation 3, this yields the
followingcalibrationsfortheindividualPAHluminositiesas
SFRindicators,
logSFR(M yr- 1)=
⊙
(- 41.73±0.08)+logL6.2µm (ergs- 1)
logSFR(M yr- 1)=
⊙
(11)
(- 42.37±0.05)+logL7.7µm (ergs- 1)
logSFR(M yr- 1)=
⊙
(- 41.80±0.07)+logL11.3µm (ergs- 1)