A Turnover in the Galaxy Main Sequence of Star Formation at $M_{*} \sim 10^{10} M_{\odot}$ for Redshifts $z < 1.3$

5.7 MB·English

by  Nicholas Lee

Draft version January 7, 2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
A TURNOVER IN THE GALAXY MAIN SEQUENCE OF STAR FORMATION AT M ∼1010M FOR
∗ (cid:12)
REDSHIFTS Z <1.3
Nicholas Lee1, D. B. Sanders1, Caitlin M. Casey1,2, Sune Toft3, N.Z. Scoville4, Chao-Ling Hung1,5, Emeric Le
Floc’h6, Olivier Ilbert7, H. Jabran Zahid 1,5, Herve´ Aussel6, Peter Capak4,8, Jeyhan S. Kartaltepe9,10, Lisa J.
Kewley11, Yanxia Li1, Kevin Schawinski12, Kartik Sheth13, Quanbao Xiao1,14
Draft version January 7, 2015
ABSTRACT
Therelationshipbetweengalaxystarformationrates(SFR)andstellarmasses(M )isre-examined
∗
5 usingamass-selectedsampleof∼62,000star-forminggalaxiesatz ≤1.3intheCOSMOS2-deg2 field.
1
Usingnewfar-infraredphotometryfromHerschel-PACSandSPIREandSpitzer-MIPS24µm,along
0
withderivedinfraredluminositiesfromtheNRKmethodbasedongalaxies’locationsintherestframe
2
color-color diagram (NUV −r) vs. (r−K), we are able to more accurately determine total SFRs for

n ourcompletesample. Atallredshifts,therelationshipbetweenmedianSFRandM followsapower-
∗
a law at low stellar masses, and flattens to nearly constant SFR at high stellar masses. We describe a
J new parameterization that provides the best fit to the main sequence and characterizes the low mass

6 power-law slope, turnover mass, and overall scaling. The turnover in the main sequence occurs at a
characteristic mass of about M ∼ 1010M at all redshifts. The low mass power-law slope ranges
0 (cid:12)
] from 0.9-1.3 and the overall scaling rises in SFR as a function of (1+z)4.12±0.10. A broken power-law
A
fit below and above the turnover mass gives relationships of SFR ∝ M0.88±0.06 below the turnover
∗
G mass and SFR ∝ M0.27±0.04 above the turnover mass. Galaxies more massive than M (cid:38) 1010 M
∗ ∗ (cid:12)
. have on average, a much lower specific star formation rate (sSFR) than would be expected by simply
h
extrapolating the traditional linear fit to the main sequence found for less massive galaxies.
p
- Subject headings: galaxies: evolution - galaxies: high-redshift
o
r
st 1. INTRODUCTION ing to higher values at increasing redshift (Noeske et al.
a 2007).
Over the last decade, a tight correlation between a
[ A common interpretation of the existence and tight-
galaxy’s star formation rate (SFR) and its stellar mass
ness of the main-sequence is that the majority of star-
1 (M ) has been discovered (Noeske et al. 2007; Daddi
∗ forminggalaxiesarepoweredbysimilarquasi-steadypro-
v et al. 2007; Elbaz et al. 2007). Commonly referred to as
cesses, with only a small fraction of galaxies undergoing
0 thegalaxy “main-sequence”(MS)ofstarformation, this
8 relationship has important implications for the physical morechaoticprocessessuchasmajormergereventsthat
0 natureofstarformationingalaxies. TheMSisgenerally might be expected to produce strong bursts of star for-
1 described as a single power law of the form SFR∝Mβ, mation (e.g. Elbaz et al. 2011; Rodighiero et al. 2011;
0 ∗ Sargent et al. 2012). These starburst galaxies are gener-
withβ =0.7–1.0andthenormalizationoftheMSevolv-
. ally thought to lie significantly above the MS and repre-
1
sent a minority of galaxies.
0
1InstituteforAstronomy,2680WoodlawnDr.,Honolulu,HI, A key uncertainty in measuring galaxy SFRs is the
5
96822,USA effect of dust obscuration. The most direct method of
1 2Department of Physics and Astronomy, University of Cali-
determiningdustobscurationisfromobservationsinthe
: fornia,Irvine,CA,92697,USA
v 3DarkCosmologyCentre,NielsBohrInstitute,Universityof far-infrared, where the absorbed starlight is thermally
i Copenhagen,JulianaMariesvej30,2100Copenhagen,Denmark reradiated. In the absence of far-infrared data, various
X 4California Institute of Technology, MS 105-24, 1200 East
extrapolations from shorter wavelength have been used
ar Ca5liHfoarrnviaarBd-oSumleivtahrsdo,niPaansaCdeenntae,rCfAor9A11st2r5ophysics, Cambridge, to study the main sequence, such as using emission lines
MA02138,USA combined with reddening corrections to infer the dust-
6UMR AIM (CEA-UP7-CNRS), CEA-Saclay, Orme des corrected SFR (Brusa et al. 2010; Sobral et al. 2012; Za-
Merisiers,bˆat. 709,F-91191Gif-sur-YvetteCedex,France
hid et al. 2012; Kashino et al. 2013) or measuring the
7Aix Marseille Universit´e, CNRS, LAM (Laboratoire
d’AstrophysiquedeMarseille)UMR7326,13388,Marseille UV or optical emission from young massive stars and
8Spitzer Science Center, 314-6 Caltech, 1201 East California correctingfortheradiationlosttodustobscuration(Lee
Boulevard,Pasadena,CA91125 etal.2011;Rodighieroetal.2011;Steinhardtetal.2014).
9HubbleFellow Observationsinthemid-infrared(e.g. 24µm)havebeen
10National Optical Astronomy Observatory, 950 North
used to estimate far-infrared luminosities (e.g. Noeske
CherryAve.,Tucson,AZ,85719,USA
11Research School of Astrophysics, Australian National Uni- et al. 2007; Daddi et al. 2007; Elbaz et al. 2007), al-
versity,CanberraACT0200,Australia thoughtheaccuracyoftheseestimatesdecreasesathigh
12Institute for Astronomy, Department of Physics, ETH
redshifts and bright infrared luminosities (e.g. Papovich
Zurich,Wolfgang-Pauli-Strasse27,CH-8093Zurich,Switzerland
13National Radio Astronomy Observatory, 520 Edgemont et al. 2007; Lee et al. 2010; Elbaz et al. 2011). Stud-
Road,Charlottesville,VA22903,USA ies of radio emission take advantage of the well-known
14TheShanghaiKeyLabforAstrophysics,100GuilinRoad, radio-FIR correlation (Helou et al. 1985; Condon 1992;
Shanghai,200234,People’sRepublicofChina
2 LEE ET AL.
Yunetal.2001)toestimatetheinfraredluminosities,but tion5andwelistourconclusionsinSection6. Whencal-
many of these studies rely on stacking to overcome high culating rest-frame quantities, we use a cosmology with
sensitivitylimits(Dunneetal.2009;Pannellaetal.2009; Ω = 0.28, Λ = 0.72, and H = 70 km s−1 Mpc−1
m 0
Karim et al. 2011). The consensus from these studies is (Hinshaw et al. 2013). A Chabrier (2003) Initial Mass
thattheMSfollowsasinglepowerlawSFR∝M∗β,with Function (IMF) truncated at 0.1 and 100 M(cid:12) is used
theslopegenerallybetweenβ =0.7–1.0andthenormal- when deriving SFRs and stellar masses.
ization varying based on the study’s redshift, SFR in-
2. DATA
dicator, sample selection, and IMF (for a summary, see
Our analysis of the MS is made possible by the large
Speagle et al. 2014).
area multi-wavelength coverage of the COSMOS field, a
However, a few studies have found indications of a
2 deg2 area of the sky with observations from the ul-
more complex main-sequence relationship. Some stud-
traviolet through far-infrared and radio (Scoville et al.
ies suggest that the MS slope varies with stellar mass
2007). We construct a mass-complete sample of galax-
so that a single power-law cannot explain the MS and
ies with K < 24 from the deep K -band catalog of Il-
a stellar mass-dependent slope is a better fit (Karim s s
bert et al. (2013), based on data from the first Ultra-
et al. 2011; Whitaker et al. 2012; Magnelli et al. 2014).
VISTA DR1 data release, covering ∼75% of the COS-
Recent studies based on far-infrared selected samples
MOS field (McCracken et al. 2012). 20 bands of opti-
fromHerschelshowthatfar-infraredselectedgalaxieslie
cal and near-infrared photometry were extracted using
mostly above the MS, with a much shallower slope in
matched apertures in dual-image mode from the vari-
log(SFR)/log(M ) (Lee et al. 2013; Oteo et al. 2013a,b;
∗ ous available COSMOS images and was combined with
Lemaux et al. 2013). However, this discrepancy is due
GALEX magnitudes from the multi-wavelength catalog
to the flux limited selection of far-infrared samples that
of Capak et al. (2007). We use updated Spitzer IRAC
introduce a SFR-based selection bias, as compared to
photometry from the Spitzer Large Area Survey with
studies based on stellar mass-selected galaxy samples.
Hyper-Suprime-CAM (SPLASH, Capak et al. in prep).
This has been demonstrated by stacking analyses that
We cross-match this catalog with the Spitzer MIPS 24
explore the far-infrared emission as a function of stellar
µm catalog of Le Floc’h et al. (2009) and the Herschel
mass and find generally good agreement between dust-
catalog of Lee et al. (2013) using a matching radius of
corrected UV-derived SFRs and Herschel-derived SFRs
2(cid:48)(cid:48).
(e.g. Rodighiero et al. 2014).
Stackingisacommonlyusedtechniquetomeasurelow-
2.1. Source Selection
level emission from galaxies that would be undetected
Weinterpolatethe90%stellarmasscompletenesslim-
individually. Stacking analyses require a number of as-
its from Ilbert et al. (2013) to determine approximate
sumptions and can miss vital information about indi-
mass completeness thresholds at all redshifts, and se-
vidual galaxies and their distributions. Unless the par-
lect only galaxies with stellar masses above their red-
ent population is identical (a key assumption in stack-
shift dependent mass completeness limit. When study-
ing),interpretationofstackingresultscanbedifficultbe-
ing star-forming galaxy populations, we separate “star-
cause the underlying distribution is unknown (although
forming” and “quiescent” galaxies using a two-color se-
see Schreiber et al. 2014, for a possible method to de-
lection technique: NUV−r+ versus r+−J (as described
termine the underlying distribution). In addition, these
in Ilbert et al. 2013). Specifically, galaxies with absolute
stacking analyses do not explain why the dust-corrected
magnitude colors M −M > 3(M −M )+1 and
SFRs cannot accurately recover the SFRs seen in high NUV r r J
M −M >3.1areconsidered“quiescent”(∼15%of
luminosity galaxies, which have an elevated contribution NUV r
the sample) while the remaining galaxies are considered
totheintegratedbuildupofstellarmassintheuniverse.
actively star-forming galaxies.
Direct Herschel FIR measurements remain a unique
Star-forminggalaxiesthatalsocontainluminousAGN
tooltoproperlyestimatetheongoingstarformationrate
are a concern because the luminosity from the AGN is
in the most active dusty galaxies. Analysis of the rest-
extremely difficult to separate from emission from star-
frameUVemissionindustygalaxiessuggeststhatapply-
formation, and thus these sources may have erroneously
ingthenominalattenuationlaws(e.g.Meureretal.1999;
high SFRs (although this concern is lessened for FIR
Calzetti et al. 2000) will dramatically underestimate to-
sources because AGN generally heat dust to tempera-
tal star formation rate in galaxies exceeding ∼50M /yr
(cid:12)
tures too hot to radiate in the far-infrared). On the
(Smail et al. 2004; Casey et al. 2014; Rodighiero et al.
other hand, many of the galaxies that host AGN also
2014).
contain significant star-formation, and removing these
Inthefollowingpaper, weattempttoaddresstheseis-
sources introduces a bias to our study. We find that the
suesbyusingadust-correctedSFRindicatorthatisaccu-
overall results of our study are not significantly affected
rateforgalaxiesatallluminosities. Byanalyzingalarge
by either the inclusion or exclusion of these sources, so
sampleofindividualgalaxies,wedonotloseinformation
we do not remove galaxies that have been detected in
about the distribution of sources from stacking and can
the X-ray (∼ 0.5% of sample) by XMM-Newton (Brusa
re-examine the shape of the star-forming MS in a stellar
etal.2010)orChandra(Civanoetal.2011),orthathave
mass-selected sample. The data are described in Sec-
IRACpower-lawcolors(Donleyetal.2008)thatsuggest
tion 2 and SFRs computed by several different methods
AGN activity (∼25% of sample).
are measured and compared in Section 3. In Section 4
we analyze our mass-selected sample of galaxies in the
2.2. Infrared Data
SFR/M plane and find the best fits to the data. The
∗
implications of the main-sequence are discussed in Sec- The Herschel-selected sample of galaxies is described
in detail in Lee et al. (2013, hereafter L13) and is briefly
MAIN SEQUENCE 3
summarized here. L13 use Spitzer 24 µm and VLA SFR to derive the total SFR as in Arnouts et al. (2013):
1.4 GHz priors to find 4,218 sources in COSMOS that
were each detected in at least two of the five available SFRTotal =(8.6×10−11)×(LIR+2.3×νLν(2300˚A)) (1)
Herschel PACS (100 µm or 160 µm) and SPIRE (250
where L ≡L(8–1000µm) and all luminosities are mea-
µm, 350 µm, or 500 µm) bands. These sources span suredinIuRnitsofL . ForsourceswithSFR(cid:38)50M /yr,
log(L /L ) = 9.4–13.6 and z = 0.02–3.54. Dust prop- (cid:12) (cid:12)
IR (cid:12) the infrared contribution dominates the total SFR, con-
erties of each source (e.g. L , T , M ) were mea-
IR dust dust tributing as much as ∼90% of the total SFR.
suredbyfittingthefullinfraredphotometrytoacoupled
WhilewehaveexcellentHerschelcoverageofthefull2-
modified blackbody plus mid-infrared power law using deg2 COSMOS field that yields 4,218 sources, the detec-
the prescription given in Casey (2012) and assuming an
tion limits of Herschel introduce a selection bias against
opacity model where τ =1 at 200 µm.
all but the most luminous infrared sources. A common
There is a population of galaxies that are classified as
method of determining the L of less luminous galax-
“quiescent” from their NUV−r+ versus r+ −J colors, IR
ies is to use deep Spitzer 24 µm data to estimate the
but have been detected in the infrared by Herschel or
far-infrared luminosity (e.g. Kennicutt et al. 2009; Rieke
Spitzer, suggesting that these galaxies are actually un-
et al. 2009; Rujopakarn et al. 2013). COSMOS has ex-
dergoing a significant amount of star-formation (∼ 7%
tremely deep coverage at 24 µm and Le Floc’h et al.
of the “quiescent” population). These galaxies are more
(2009) provide SFR estimates for 36,635 galaxies, which
consistent with being very dusty objects that have ex-
weusetoextendoursampleofinfrareddetectedgalaxies
tremely red colors due to obscuration, not lack of active
to more moderate luminosities.
star-formation,soweincludethesegalaxiesinoursample
of star-forming galaxies (see Section 4.3).
3.1.2. Optical & UV based SFR Indicators
For galaxies without direct measurements from far-
2.3. Photometric Redshifts and Physical Parameters
or mid-infrared wavelengths of the obscured SFR, the
Ilbert et al. (2013) measure accurate 30-band pho- amountofradiationobscuredbydustmustbeestimated
tometric redshifts of the full K -band COSMOS cata- indirectly. A common method for estimating total SFR
s
log. We find a median ∆z/(1+z) = 0.02 in our sam- is to fit libraries of model SEDs (that include prescrip-
ple of star-forming galaxies, with a catastrophic failure tions for dust obscuration) to optical & UV photometry.
(|∆z|/(1+z) > 0.15) in 5.6% of sources. In addition, Ilbertetal.(2013)usethefullopticalCOSMOSphotom-
physical parameterssuchas stellarmassand starforma- etryandfittoalibraryofsyntheticspectrafromBruzual
tionratehavebeencalculatedbyfittingtheSpectralEn- & Charlot (2003), and estimate the total SFR for each
ergyDistributions(SEDs)tosyntheticspectragenerated of the galaxies in our sample from the best fit SEDs.
using the Stellar Population Synthesis (SPS) models of Another method of estimating dust-corrected SFRs is
Bruzual&Charlot(2003). Wealsorecalculatethephys- by using rest-frame UV observations to measure the un-
ical parameters using different templates and extraction obscured SFR and inferring the appropriate dust correc-
parameters, and find that our final results are not af- tion factor from observed colors. Two examples of this
fected by the specific choice of template. Thus, we use are the BzK method from Daddi et al. (2004) and the
the same set of parameters used to create the catalog in NRKmethodfromArnoutsetal.(2013). BzKSFRsare
Ilbert et al. (2013), but with updated near-IR photome- determinedbyusingtheobserved-frameB-bandphotom-
try from SPLASH. etry to measure the rest-frame UV luminosity, and then
estimating the extinction as E(B −V) = 0.25(B −z+
3. ANALYSIS 0.1)AB (Daddi et al. 2007). BzK SFRs are only valid for
redshifts 1.4 < z < 2.5, as these are the only redshifts
3.1. Star Formation Rate Calculations
where the desired portions of the SED are redshifted
Therearemanymethodsforestimatingagalaxy’sSFR to the correct wavelengths, and we limit our selection
based on observations at various wavelengths (for a re- to the good-sBzK with errors δlog[SFR(UV)]< 0.3 dex
view, see Kennicutt 1998; Murphy et al. 2011). Here we (Rodighiero et al. 2014).
compare a few commonly used SFR indicators using a NRKSFRsarecalculatedbyusingtheirlocationinthe
subset of COSMOS galaxies to determine how much the rest-frame color-color diagram (NUV −r) vs. (r−K)
differentSFRmethodsdisagree. Inallcases,wemeasure toestimateextinction. Arnoutsetal.(2013)findthatat
the total SFR as SFRTot =SFRIR+SFRUV. z ≤ 1.3, the infrared excess IRX ≡ LIR/LNUV in star-
forming galaxies can be parameterized as a function of
3.1.1. Infrared derived SFR redshiftandthevectorNRK=0.31×(NUV−r)+0.95×
(r−K). This allows us to estimate the L and calcu-
As discussed in Section 2.2, the infrared properties of IR
late total SFR using Equation 1. When measuring NRK
theHerschel-selectedgalaxieshavebeenmeasuredbyfit-
SFRs, we use the small “sSFR correction” as described
ting the infrared SEDs to a coupled modified blackbody
in Arnouts et al. (2013).
plus mid-infrared power law model (Casey 2012). It has
been shown that measuring the L from fitting the far-
IR 3.2. Comparison of SFR indicators
infrared data to libraries of SED (e.g. Chary & Elbaz
2001; Dale & Helou 2002) gives roughly the same results We compare commonly used SFR indicators using a
as the modified blackbody plus power-law model (Casey common subset of COSMOS galaxies to determine how
2012; U et al. 2012; Lee et al. 2013). The infrared ob- much agreement there is between the different measures
servations give us an estimate of the obscured SFR, and of SFR. We have a large set of Herschel detected galax-
wecombinethiswithUVobservationsoftheunobscured ies from Lee et al. (2013) where, for the first time, we
4 LEE ET AL.
have direct measurements of both the obscured and un- SFR shows essentially no correlation (ρ =
Total BzK
obscured SFR (from UV observations) at a wide range −0.11). It should be noted that the redshift range of
of redshifts. We compare the other SFR indicators dis- the BzK indicator (1.4 < z < 2.5) limits us to a small
cussed previously (24 µm, SED fits, BzK, and NRK) to sample size containing only the brightest galaxies. As
this sample of 4,218 Herschel detected galaxies. seen in Figure 2, this selection limits our comparison
Figure1displaysthecomparisonofSFR fromthe to galaxies at SFRs where all indicators begin to devi-
Total
four different indicators discussed above to SFR as ate significantly from SFR . Stacking analyses sug-
Total Total
measured by Herschel. Density contours show the loca- gestastrongercorrelationbetweenaverageSFR and
BzK
tion and concentration of the majority of the sources, average SFR at fainter luminosities (Rodighiero
Herschel
with outliers shown in gray circles. Median values et al. 2014), but the tightness of the distribution is not
in 20 equally populated bins of SFR are well determined. The BzK galaxies that are Herschel
Total,Herschel
over-plotted to show average trends. To determine the detected show no correlation between the SFR derived
strength of the correlation between each SFR indicator fromtheBzKmethodandfromHerschelmeasurements.
and SFR , we measure the Pearson correla-
Total,Herschel
3.2.1. Selection Effects of SFR Indicators
tion coefficient (ρ) and provide these values at the top
of each sub-panel. The Pearson correlation coefficient The comparisons of the various SFR indicators shown
can vary between +1 and -1, with +1 indicating total inFigure1spandifferentdynamicrangesinSFR,mostly
positive correlation, 0 indicating no correlation, and -1 due to the redshift limitations of the NRK and BzK
indicating total negative correlation. We also measure indicators. In Figure 2, we plot the typical difference
the median difference between each SFR indicator and between SFR indicators and SFR as a function of
Total
Herschel SFR (<∆log(SFR)>) and list these values at SFR . We see that all of the SFR indicators pro-
Total
the top of each sub-panel. vide poor estimates of the infrared measured SFR
Total
The 24 µm-determined SFR correlates with the Her- above log(SFR) (cid:38) 1.5 (∼ 30M /yr). These common
(cid:12)
schel SFR very well (ρ = 0.88, < ∆log(SFR ) > SFR indicators fail to accurately estimate the true SFR
24 24
=0.12),exceptatthehighestIRluminosities. Thistrend of luminous infrared galaxies. This highlights the need
has been previously explored in many studies which find fordirectinfraredobservationstoaccuratelymeasurethe
that at moderate redshifts and IR luminosities, 24 µm SFR of highly star forming galaxies.
observations are a good proxy for L , but at high red- Throughout this analysis we have assumed the
IR
shiftsandinfraredluminosities,the24µmestimatestend Herschel-determinedSFRisthemostaccuratebecauseit
tooverpredictthetrueL ,possiblyduetoredshiftingof directly probes far-infrared wavelengths, where the bulk
IR
the observed 24 µm-band to wavelengths contaminated of the re-radiated radiation from dust is emitted. How-
by PAH features (e.g. Papovich et al. 2007; Lee et al. ever, it is possible that the high detection threshold of
2010; Elbaz et al. 2011). As we are using the 24 µm Herschellimitsustoabiasedsamplethatdoesnotaccu-
SFRs to fill in the low and moderate luminosity galaxies rately reflect the emission properties of lower luminosity
that are not detected with Herschel, this discrepancy is galaxies. To test this possibility, we re-run our analyses
not a major issue for our work. usingthemuchdeepersampleofSpitzer24µm-detected
The NRK SFRs also show strong correlation with galaxies (which showed excellent agreement with Her-
the Herschel-derived SFRs (ρ = 0.79, < schel SFRs) as the comparison sample. We find very
NRK
∆log(SFR ) > = 0.17). This is not completely un- similar results as the Herschel comparison, with NRK
NRK
expected since the NRK method was developed using 24 providingboththestrongestcorrelationandthetightest
µm-derived SFRs as a baseline, but the NRK measured distribution.
SFRs match very well with those derived from Herschel.
3.2.2. A Ladder of SFR Indicators
Like with SFR , the correlation shows signs of break-
24
ingdownatthehighestSFRs,butaslongastheNRKis While all three non-infrared based SFR indicators fail
used mainly for low SFR galaxies, it provides a reliable toaccuratelyestimatetheSFRinhighluminositygalax-
estimate of the SFR. ies, the NRK method provides the most accurate and
By contrast, the agreement between SFR and consistent estimates across the full dynamical range of
SED
SFR is quite poor, showing much weaker correla- Herschel SFRs. At high SFRs (SFR (cid:38) 30M /yr), 70%
Total (cid:12)
tion between the two indicators (ρ = 0.56). The ofoursampleisdirectlydetectedintheinfraredbyeither
SED
tightness of the correlation is also much broader (< Herschel or Spitzer. Thus, we can study the full popula-
∆log(SFR ) > = 0.43), even at low SFRs where tion of star forming galaxies by constructing a “ladder”
SED
the median points lie closer to the unity line. Again, of SFR indicators (as in Wuyts et al. 2011) based on
at high SFRs the median points show a clear deviation the Herschel, Spitzer 24 µm, and NRK SFR indicators.
from unity. Wuyts et al. (2011) are able to find a bet- All sources have SFR calculated using Equation 1,
Total
termatchbetweenSFR andSFR iftheytunekey with different methods of determining L . For sources
SED 24 IR
parameters of the SED fit, such as τ , the e-folding detected by Herschel, we measure L from fitting the
min IR
time of the exponentially declining star formation his- far-infrared photometry to the Casey (2012) greybody
tory. The exact tuning needed varies based on several plus power-law models. We use the L estimated from
IR
other assumptions in the SED fitting procedure, such 24 µm (Le Floc’h et al. 2009) for sources that are not
as different stellar population synthesis codes, and even detected by Herschel but are detected at Spitzer 24 µm.
whenthetuningisdone,thecomputedSFR stillsys- And for the remaining sources, we estimate the L us-
SED IR
tematicallyunderestimatesthetrueSFRforasignificant ingtheNRK-derivedIRX(asdiscussedinSection3.1.2).
fraction of sources. Although we include NRK-derived IRX for all galax-
Finally, the comparison between SFR and ies above our mass-completeness limits, the method has
BzK
MAIN SEQUENCE 5
only been well-calibrated for M > 109.3M . Infrared affectthefollowingresults,althoughwemustbalancebe-
∗ (cid:12)
stacking suggests that any systematic offsets should be tweenhavingredshiftbinsthataretoowideandcombine
small, but when calculating main sequence relationships galaxy samples at different epochs with having redshift
we only include galaxies with M >109.3M . bins that are too narrow and are affected by small num-
∗ (cid:12)
The relative fraction of sources with SFRs measured ber statistics. The same is true for the number of stellar
from each indicator is plotted in Figure 3 as a function mass bins, although having at least 30 bins is prefer-
of both stellar mass and redshift. Below M (cid:46)109.5M , ableforaccuratelydeterminingthegoodnessoffittothe
∗ (cid:12)
SFRsarealmostalldeterminedfromNRK,butathigher models. The median SFRs for every bin are plotted in
stellarmasses,thefractionofsourceswithdirectinfrared Figure 5, colored by redshift, with bootstrapped errors
measurementsincreasesuntilabout25%(60%)ofsources on the median represented by vertical bars.
at M (cid:38) 1010.5M have SFRs determined from Herschel UsingtheMPFITpackageimplementedinIDL(Mark-
(cid:12)
(Spitzer 24 µm). Because of the redshift limitations of wardt2009),wefitthemedianlog(M∗)andlog(SFR)in
theNRKmethod(seeArnoutsetal.2013)andthelarger eachredshiftbinwithmanymodelsincludinglinear, 2nd
errors associated with the SFR and SFR indi- order polynomial, and broken linear, and find the best
SED BzK
cators, we restrict the rest of our analysis to redshifts fit is provided by the following model:
0<z <1.3, where we can more accurately measure the
SFR of our full sample. (cid:34) (cid:18) 10M (cid:19)−γ(cid:35)
S =S −log 1+ (2)
4. SHAPEOFTHEMAINSEQUENCEOFSTAR 0 10M0
FORMATION
whereS =log(SFR)andM=log(M /M ). Wechoose
WithreliableandconsistentSFRestimatesforalarge, ∗ (cid:12)
this model because (1) at all redshifts, it provides the
mass-completesampleofgalaxiesinCOSMOS,weexam-
ine the star-forming main sequence for a large, unbiased best reduced χ2 fit to the data, and (2) unlike polyno-
sample of 62,521 galaxies. Figure 4 displays the stellar mial fits, the parameters of the model allow us to quan-
mass and SFR of our full sample, split into four redshift tifytheinterestingcharacteristicsoftherelationbetween
bins spanning 0.2 ≤ z ≤ 1.3. Black contours display stellarmassandSFR:γ,thepower-lawslopeatlowstel-
the density of sources at each location in SFR and M∗ larmasses,M0,theturnovermass(inlog(M∗/M(cid:12))),and
parameter space, and colored bars represent the median S0, the maximum value of S (or the maximum value of
SFR in stellar mass bins of width ∆log(M ) = 0.3, with log(SFR)) that the function asymptotically approaches
∗
vertical error bars displaying the standard deviation of at high stellar mass. The best-fit parameters for each
theSFRsinthatbin. Thesesamebinsareusedtocreate redshift bin are listed in Table 1.
thefractionalhistogramsplottedonthesideofeachred-
shift bin, which display the distribution of SFRs within 4.2. Evolution of Model Parameters
eachmassbinwiththecorrespondingcolor. Thederived
In the top panels of Figure 6, we plot the evolution
main sequence relationships from star-forming galaxies
of S , M , and γ as functions of log(1+z). The bot-
0 0
in Karim et al. (2011) and Whitaker et al. (2014) are
tom panels of Figure 6 examine the covariance between
also plotted for comparison.
these parameters by displaying the 95% confidence error
Figure 4 shows that the galaxies in our sample do
ellipses.
not follow a simple linear main sequence relationship
We see clear and strong evolution of S with redshift,
0
between log(SFR) and log(M ) (or a single power-law
∗ andthebestfitlinesuggestsanevolutionofS ∝(4.12±
0
relationship between SFR and M ). Instead, the me-
∗ 0.10)×log(1+z),orequivalently,SFR ∝(1+z)4.12±0.10.
dianSFRrelationshipappearstoflattenatmassesabove 0
The covariance between S and M (Figure 6D) and
M ∼ 1010M . This can be seen in the histograms, 0 0
∗ (cid:12) between S and γ (Figure 6E) is relatively minor, so we
which show that the peak of each SFR distribution in- 0
infer that the evolution in S is true evolution and not
creases with increasing M at low masses, but at high 0
∗ due to variation in the other parameters.
masses, the histogram peaks all lie at approximately the
Both M and γ show some evidence for weak evolu-
same SFR. The standard deviation of the SFR in each 0
tion to more massive M and steeper γ with redshift,
stellar mass bin remains mostly constant at all masses 0
although much of the perceived evolution may be due
and at all redshifts, with σ ∼ 0.36 dex in all bins. The
to the covariance seen in Figure 6F. The best (linear)
shape of this relationship appears roughly constant with
fit to the evolution in the turnover mass is given by
redshift,withtheentirerelationshipincreasingtohigher
M ∝(1.41±0.20)×log(1+z). Wetestthepossiblered-
SFRs at higher redshifts. 0
shiftevolutionofturnovermassbycalculatingwherethe
data deviates by 0.2 dex from a single power-law fit to
4.1. Parameterizing the Star-Forming Main Sequence
the low mass data and find similar evolution, suggesting
From Figure 4, it is clear that a single power-law does that the turnover mass does indeed change with cosmic
not accurately describe the relationship between stellar time. Thelow-masspower-lawslope,γ,hasabest-fitline
mass and star formation rate. We split our sample of that suggests evolution of γ ∝(1.17±0.13)×log(1+z).
star-forming galaxies into 6 equally populated redshift Redshiftevolutioninγ tosteeperslopesatearliercosmic
bins, each of which are then split into 30 equally popu- times would suggest that the SFR in the lowest stellar
lated stellar mass bins (with ∼350 sources in each bin), massgalaxiesdoesnotincreaseasmuchasinmoremas-
and calculate the median SFR in each bin. We limit our sive systems.
sample to stellar masses above a conservative mass limit
(see Table 1) to ensure that we are not affected by sys-
4.3. Separating Quiescent Galaxies
tematics. The specific number of redshift bins does not
6 LEE ET AL.
We have described the main sequence relationship be- misclassifiedasquiescent. Manetal. (inprep)stackthe
tween SFR and M for star-forming galaxies. How- infrared emission from quiescent galaxies and find up-
∗
ever,possiblemisclassificationofgalaxiesaseither“star- per limits of SFR < 0.1–1 M /yr. The SFRs of the
IR (cid:12)
forming” or “quiescent” could drastically affect the IR-Q galaxies in our sample tend to lie below the main-
trends we observe. sequence,butareallatleast×2–3higherthantheupper
As described in Section 4, we remove galaxies that are limitfromManetal.,whichsuggeststhattheyareindeed
consideredquiescentfromoursampleusingtheselection stillactivelystar-forming. Inaddition,theinfraredemis-
M −M >3(M −M )+1 and M −M >3.1 sion from IR-Qs is brighter than expected from a “post-
NUV r r J NUV r
(Ilbert et al. 2013). This selection is shown in Figure 7, starburst” glow (Hayward et al. 2014). It is unlikely
with the full mass-selected sample of COSMOS galaxies that catastrophic photo-z errors or low signal-to-noise
at 0.2 < z < 1.3 generally separated into two distinct photometry are causing these misidentifications, as the
“star-forming” and “quiescent” regions. Improper clas- sources have excellent photometry and well-constrained
sification of the “in-between” galaxies that are not obvi- photometric redshifts (only 0.1% of the IR-Q galaxies
ously star-forming or quiescent could lead to changes in have σ > 0.15). Thus, the likely explanation
∆z/(1+z)
themainsequenceshape. Totestthispossibility,weshift for these sources is that they are actively star-forming
the entire separating line (both horizontal and diagonal galaxies that have been misclassified as “quiescent”, and
segments) between quiescent and star-forming galaxies we include them in our analysis of the main-sequence.
by ±0.4 mag in M −M , and in either case there is We note, however, that the shape of the main-sequence
NUV r
no appreciable change to the main-sequence. does not change significantly based on the inclusion or
GalaxiesdetectedintheinfraredbyHerschelorSpitzer exclusion of these sources.
24µmarehighlightedinFigure7,andwhilethemajority
fallonthestar-formingsequence,weseeanumberofob- 5. DISCUSSION
jects that lie in the quiescent region. This population of Weseethattheslopeofthemainsequencerelationship
infrared-detected quiescent (IR-Q) galaxies is relatively between SFR and M changes with stellar mass. While
∗
small, with only ∼7% of the galaxies classified as quies- most previous studies found a constant main sequence
cent having detectable infrared emission, but these mis- slope (for a summary see Speagle et al. 2014), some re-
classifiedgalaxiesarepredominantlyfoundathighstellar cent studies found a curved relationship might provide a
mass. The fraction of quiescent galaxies detected in the better fit to the data (Karim et al. 2011; Whitaker et al.
infrared increases rapidly from ≤ 1% at M∗ ∼ 109.5M(cid:12) 2012). However, the mass completeness limit in both
to 15-20% at M∗ ≥ 1011M(cid:12), and this trend holds at all studies coincided with the turnover mass, leaving doubt
redshifts. These massive galaxies could heavily influence astowhethertheturnoverwasarealtrendoranartifact
the shape of the main-sequence we observe, so it is vital of completeness. With our new COSMOS observations,
to understand what is driving their infrared emission. we are able to study star-forming galaxies considerably
There could be several reasons why galaxies with qui- less massive than the turnover mass, and we find that a
escentcolorshavesignificantemissionintheinfrared,in- singlepower-lawdoesnotprovidethebestdescriptionof
cluding (i) improper classification of star-forming galax- the star-forming main-sequence.
ies possibly due to extreme dust obscuration, (ii) el-
evated infrared luminosity from an AGN, (iii) inaccu- 5.1. The Turnover in the Star-Forming Main Sequence
rate absolute magnitudes due to catastrophic failures
TherelationshipbetweenSFRandM varieswithstel-
in photo-z’s or low signal-to-noise photometry, or (iv) ∗
lar mass, with two distinct regions below and above
“post-starburst” infrared glow due to dust heating from
the characteristic turnover mass, M . What causes
youngstars(thatisnotrelatedtotheinstantaneousstar 0
this change, and why does the turnover occur at about
formation).
M ≈1010M at all redshifts?
AGN typically heat dust to very hot temperatures, so ∗ (cid:12)
we expect any AGN contribution to infrared radiation
5.1.1. The slope of the main-sequence
to be predominantly in near- and mid-IR wavelengths,
whilefar-infraredemissionislikelyduetostarformation Theparameterizationofthemainsequenceweemploy
alone. Only about 10% of the IR-Q galaxies have been inSection4.1includesaparameterγ thatwedescribeas
detectedbyHerschel,andtherestare24µm-onlydetec- the low stellar mass power-law slope. However, we note
tions, where AGN may heavily influence the emission. thatthisslopeisnotderivedfromanactualpower-lawfit
However, only ∼1–5% of the IR-Q galaxies are detected to the data, but instead represents the power-law slope
in the X-ray by Chandra, and only ∼ 2–8% of the IR-Q that the relationship approaches in the very low-mass
galaxies have IRAC power-law colors indicative of AGN, regime, based on Equation 2. This slope is significantly
with significant overlap in those two populations, and steeper than power-law slopes commonly quoted in the
the percentages are even lower when looking only at the literature, and should not be compared to slopes from
24 µm-only sources. This suggests that radiation from power-law fits to data.
an AGN is not fueling the infrared emission. The aver- For an easier comparison to the existing literature, we
age SFR of the IR-Q galaxies with AGN is 0.2–0.5 dex derive best-fit power-law relationships, fitting the low
higher than the average SFR of all the IR-Q galaxies, mass regime and high mass regime separately. Galax-
so the presence of AGN in these galaxies is likely just ies less massive than the turnover mass follow a fairly
a reflection of the well-studied trend that AGN fraction tight power-law relationship of SFR ∝ Mβ, with β =
increases with SFR or L (e.g. Kartaltepe et al. 2010). 0.88±0.06. This slope is shallower than γ because it in-
IR
TheratherhighSFRsoftheIR-Qgalaxiessuggestthat cludesgalaxiesinthe “turnoverregion”, wheretheslope
they are indeed driven by star-formation, and have been isalreadystartingtoflatten. Galaxiesmoremassivethan
MAIN SEQUENCE 7
the turnover mass follow a drastically different relation- with mass. If this is the case, the turnover in the main-
ship, withβ =0.27±0.04forM >1010M . Agalaxy’s sequence could be simply due to growing bulges in the
∗ (cid:12)
specific star formation rate (SSFR ≡SFR/M ) can be highest mass systems. However, one might expect the
∗
interpreted as a measure of the efficiency of current star turnovertodisappear(orbecomelesssevere)athighred-
formation as compared to its past average star forma- shifts as galaxies become more disk-dominated, but this
tionhistory. TheSSFR ofmassivegalaxiesissystemat- isnotseeninthedata. Schawinskietal.(2014)findthat
ically lower than would be expected from an extrapola- disk galaxies and elliptical galaxies likely quench their
tion of low mass galaxies, suggesting that there may be starformationratesthroughdifferentprocesseswithvery
decreased star formation efficiency in high stellar mass different timescales. A galaxy’s physical size may also
galaxies. play a role in quenching, as the surface mass density
hasbeenshowntocorrelatestronglywithSSFR(Kauff-
5.1.2. Quenching in High Mass Galaxies mann et al. 2003; Franx et al. 2008), and compact star
forminggalaxiesmaybeontheevolutionarypathtoward
The turnover in the main sequence to lower star for-
quiescent galaxies (Barro et al. 2014).
mation efficiencies in massive galaxies suggests there is
Our data suggest that galaxies with high stellar mass
a fundamental change that occurs as galaxies become
(M > 1010M ) are forming stars at a lower rate than
more massive, as has been predicted in some studies. ∗ (cid:12)
would be expected from extrapolating the trends of low
Galaxy luminosity and mass functions, which measure
stellar mass galaxies. Finding the possible causes of this
the brightness and mass distribution of galaxies at vari-
“quenching” of star formation is one of the key hurdles
ous lookback times, show a steep, exponential decline at
for understanding galaxy evolution. The existence of a
high stellar masses and high luminosities while retaining
“turnover mass” hint that the stellar mass of a galaxy
a remarkably consistent shape at all redshifts (e.g. Bell
plays a crucial role in quenching, possibly related to the
et al. 2003; Pozzetti et al. 2010; Ilbert et al. 2013). The
“mass quenching” discussed in Peng et al. (2010). Fur-
lack of large, bright galaxies throughout cosmic time ar-
ther study is needed to determine the physical mecha-
guesforthepresenceofacharacteristicmassabovewhich
nism(s) behind quenching.
agalaxyislikelytohaveitsstarformationstronglysup-
pressed or quenched.
In contrast, the dark matter halo mass function from 5.2. Increasing SFR with Redshift
semi-analytic models does not show the same exponen- From our fits, we find strong evolution in S , which
0
tial decline, and instead has a much shallower power- parameterizes the overall scaling of the SFR/M main-
∗
lawcutoffatmuchhighermasses(Somerville&Primack sequence with redshift.15 The scaling of the main se-
1999; Benson et al. 2003), leading to a “pivot mass” quence has been found in the literature to evolve as
above which the ratio of dark matter to light matter in- (1+z)n, with the exponent n varying from 2.2<n<5
creases rapidly (e.g. Leauthaud et al. 2012). At low stel- (Erb et al. 2006; Daddi et al. 2007; Damen et al. 2009;
larmasses,thestellartohalomassrelation(M ∝M0.46; Dunne et al. 2009; Pannella et al. 2009; Karim et al.
h ∗
Leauthaud et al. 2012) and the dark matter halo growth 2011). Thevalueofn=4.12±0.10wemeasureisamong
rates from N-body simulations (M˙ ∝ (M )1.1; the steeper slopes seen in the literature.
halo halo
Wechsler et al. 2002; McBride et al. 2009; Fakhouri It’s thought that the redshift evolution of the main-
& Ma 2010) suggest a main sequence relationship of sequence normalization is due, at least in part, to in-
SFR ∝ M1.04, similar to the slope seen in the main- creasing gas content in galaxies at earlier cosmic times.
sequence. T∗he “pivot mass”, above which the stellar- However, measuring the gas content in galaxies can be
to-halo mass relation deviates from the low stellar mass difficult, especially in high redshift systems. Molecu-
relationship, appears to evolve to higher M at higher lar hydrogen is notoriously difficult to detect, so many
∗
redshifts(Leauthaudetal.2012),ataratesimilartothe surveys instead probe the rotational transitions of CO
possible evolution seen in the main sequence turnover and use locally calibrated CO-to-H2 conversion factors,
mass, M . In galaxies more massive than the “pivot although this conversion factor may differ in starburst
0
mass,” the halo mass rises sharply in comparison with galaxies (Tacconi et al. 2008; Magdis et al. 2011; Mag-
stellar mass, suggesting that while massive dark matter nelli et al. 2012). Another method to estimate gas con-
haloes appear to continue growing, the galaxies residing tent is to measure the dust mass from far-infrared or
in them quench their star formation. submillimeter photometry and convert to gas masses us-
Possible mechanisms for this quenching include struc- inganassumedgas-to-dustratio(e.g.Magdisetal.2012;
tural disruptions or galaxy mergers (Sanders & Mirabel Santini et al. 2014; Scoville et al. 2014). Magdis et al.
1996; Hopkins et al. 2006), feedback from accretion onto (2012) find gas fraction evolves as (1+z)2.8, while re-
a supermassive black hole (Springel et al. 2005), gravi- cent ALMA observations suggest a steeper evolution of
tational heating of the surrounding intracluster medium (1+z)5.9 (Scovilleetal.2014). Zahidetal.(2014)study
(Khochfar & Ostriker 2008), changes in the mode of gas the mass metallicity relationship and infer a much shal-
accretionontogalaxies(Kereˇsetal.2005;Birnboimetal. lower evolution of gas mass Mg ∝ (1+z)1.35. Future
2007;Nelsonetal.2013),orgasremovalorstrangulation studies will be needed to determine if the evolving nor-
in dense environments (Peng et al. 2010, 2012). malizationofthemain-sequencecanbeexplainedsimply
Morphological studies may be key for understanding byanincreasinggassupplyingalaxies,orifotherexpla-
the star-formation in massive galaxies. Abramson et al. nations such as increased merger rates or increased star
(2014) find that galaxy SFRs are more strongly corre-
lated to disk stellar mass (as opposed to total stellar 15 Alternatively,measuringtheredshiftevolutionoftheSFRat
mass), and that SSFR is approximately constant aconstantcharacteristicmassprovidessimilarresults
disk
8 LEE ET AL.
formationefficiencyarenecessarytofullyexplaintheob- the Space Telescope Science Institute, which is operated
served evolution. by AURA Inc, under NASA contract NAS 5-26555; also
based on data collected at: the Subaru Telescope, which
6. CONCLUSIONS is operated by the National Astronomical Observatory
Using new far-infrared data from Herschel, we com- of Japan; the XMM-Newton, an ESA science mission
pare direct measurements of unobscured and obscured with instruments and contributions directly funded by
SFR with various SFR indicators that estimate the ob- ESAMemberStatesandNASA;theEuropeanSouthern
scured SFR from data at shorter wavelengths (usually Observatory, Chile; Kitt Peak National Observatory,
in optical or UV), and find that the NRK method of Cerro Tololo Inter-American Observatory, and the
Arnouts et al. (2013) provides the most consistent esti- National Optical Astronomy Observatory, which are
mate of the far-infrared derived SFR. By combining the operated by the Association of Universities for Re-
SFRs from Herschel, Spitzer, and NRK, we analyze the search in Astronomy, Inc. (AURA) under cooperative
relationship between SFR and M (commonly referred agreement with the National Science Foundation; the
∗
to as the “star-forming main-sequence”) in 62,521 star- National Radio Astronomy Observatory which is a
forming galaxies at z ≤1.3 in the COSMOS field. From facility of the National Science Foundation operated
our new analysis we find: undercooperativeagreementbyAssociatedUniversities,
Inc; and the Canada-France-Hawaii Telescope operated
• The relationship between SFR and stellar mass bytheNationalResearchCouncilofCanada, theCentre
does not follow a simple power-law, but flattens National de la Recherche Scientifique de France and the
to near-constant SFRs at high stellar masses. The University of Hawaii.
shape of the main sequence is roughly constant for The Dark Cosmology Centre is funded by the Danish
all redshifts z ≤1.3. National Research Foundation.
• The scaling of the entire star-forming main se-
quence rises with redshift as (1+z)4.12±0.10.
• The characteristic turnover mass lies at M ≈
0
1010M , with possible evolution toward higher
(cid:12)
turnover masses at high redshift.
• The slope of the low-mass power-law lies between
γ = 0.9–1.3, with possible weak evolution toward
steeper slopes at higher redshift.
• Abrokenpower-lawfittogalaxiesbelowandabove
the turnover mass results in SFR ∝ M0.88±0.06
∗
below the turnover mass and SFR ∝ M0.27±0.04
∗
above the turnover mass.
Our analysis suggests that star-forming galaxies cannot
be described by a single power-law relationship between
SFR and M , as had been suggested in many previous
∗
studies. Because of the strong effects of dust, direct ob-
servations in the FIR are crucial for studying the entire
population of star-forming galaxies. In future work we
will explore possible causes of the turnover in the main
sequence by studying detailed morphology and examin-
ing possible feedback mechanisms, and we will extend
our analysis to higher redshifts.
7. ACKNOWLEDGEMENTS
D. B. Sanders and C. M. Casey acknowledge the hos-
pitality of the Aspen Center for Physics, which is sup-
ported by the National Science Foundation Grant No.
PHY-1066293. C. M. Casey would like to acknowledge
generous support from a McCue Fellowship through the
University of California, Irvine’s Center for Cosmology.
KSgratefullyacknowledgessupportfromSwissNational
Science Foundation Grant PP00P2 138979/1. KS ac-
knowledges support from the National Radio Astron-
omy Observatory, which is a facility of the National Sci-
ence Foundation operated under cooperative agreement
by Associated Universities, Inc.
COSMOS is based on observations with the
NASA/ESA Hubble Space Telescope, obtained at
MAIN SEQUENCE 9
Table 1
RedshiftRange <z> log(Mlimit) S0 M0 γ Reducedχ2
log(M(cid:12)) log(M(cid:12)/yr) log(M(cid:12))
0.25–0.46 0.36 8.50 0.80±0.019 10.03±0.042 0.92±0.017 1.74
0.46–0.63 0.55 9.00 0.99±0.015 9.82±0.031 1.13±0.033 1.52
0.63–0.78 0.70 9.00 1.23±0.016 9.93±0.031 1.11±0.025 1.48
0.78–0.93 0.85 9.30 1.35±0.014 9.96±0.025 1.28±0.034 1.84
0.93–1.11 0.99 9.30 1.53±0.017 10.10±0.029 1.26±0.032 0.62
1.11–1.30 1.19 9.30 1.72±0.024 10.31±0.043 1.07±0.028 1.24
Note. — Parameters of the best fit model to the star-forming main sequence. The full sample of 62,521 star-forming
galaxies is split into six equally populated bins, with each bin containing ∼ 17745 galaxies. Within each redshift bin, the
galaxies are split into 30 equally populated bins of stellar mass. The median SFR in each mass bin is calculated and then
fittoS =S0−log(cid:20)1+(cid:16)1100MM0(cid:17)−γ(cid:21), whereS =log(SFR)andM=log(M∗). Tablecolumnsareasfollows: (1)Redshift
range of bin; (2) Median Redshift; (3) Stellar Mass Limit of redshift bin; (4) S0, the maximum value of S; (5) Turnover
Mass;(6)Low-masspower-lawslope;(7)Reducedχ2 offit.
10 LEE ET AL.
4 4
ρ = 0.88; <∆log(SFR)> = 0.12 ρ = 0.56; <∆log(SFR)> = 0.43
3 3
R)24 2 2 R)SED
log(SF 1 1 log(SF
0 0
-1 -1

ρ = 0.79; <∆lo g(SFR)> = 0.17 ρ = -0.11; <∆lo g(SFR)> = 0.60
3 3
R)NRK 2 2 R)BzK
SF SF
g( g(
lo 1 1 lo
0 0
-1 -1
-1 0 1 2 3 4 0 1 2 3 4
log(SFR +SFR ) log(SFR +SFR )
UV Herschel UV Herschel
Figure 1. ComparisonoftotalSFRdeterminedfromcombiningdirectmeasurementsofFIR(Herschel,Leeetal.2013)andUV(GALEX,
Zamojski et al. 2007) with various SFR indicators using observations at shorter wavelengths. The different SFR indicators are: [top left]
Spitzer24µm(LeFloc’hetal.2009)+GALEX;[topright]multi-wavelengthSEDfits(Ilbertetal.2013);[bottomleft]NRK(0<z<1.3,
Arnouts et al. 2013); and [bottom right] BzK (1.4 < z < 2.5, Daddi et al. 2007). In each panel, black contours give the density and
concentration of sources, with extreme outliers plotted as gray circles. We bin the data in 20 equally populated bins (except BzK, which
has8bins)andfindthemedianSFR ineachbin. Errorsonthemedianpointsaremeasuredusingabootstrappingtechniqueand
indicator
are plotted when larger than the size of the symbol. At the top of each panel is the Pearson correlation coefficient (with a value of +1
indicatingstrongpositivecorrelationand0indicatingnocorrelation)andthetypicaldifferencebetweeneachparticularSFRindicatorand
theHerschel-derivedSFR.