Astronomy&
Astrophysics
A & A 6 3 1 , A 109 (2019)
https://doi.org/10.1051/0004-6361/201935913
© E S O 2019
A LOFAR-IRAS cross-match study: the far-infrared radio correlation and the 150 MHz luminosity as a star-formation rate
tracer
L. Wang12, F. Gao12, K. J. Duncan3, W. L. Williams3, M. Rowan-Robinson4, J. Sabater5, T. W. Shimwell3, M. Bonato6,7, G. Calistro-Rivera3, K. T. Chyży8, D. Farrah9,10, G. Gurkan11, M. J. Hardcastle12,1. McCheyne13,
I. Prandoni6, S. C. Read12, H. J. A. Rottgering3, and D. J. B. Smith 12
1 SRON Netherlands Institute for Space Research, Landleven 12, 9747 AD Groningen, The Netherlands e-mail: l.w an g @ sro n .n l
2 Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 AV Groningen, The Netherlands 3 Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
4 Astrophysics Group, Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK 5 SUPA, Institute for Astronomy, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
6 INAF - Istituto di Radioastronomia, and Italian ALMA Regional Centre, Via Gobetti 101, 40129 Bologna, Italy 7 INAF - Osservatorio Astronomico di Padova, Vicolo Osservatorio 5, 35122 Padova, Italy
8 Astronomical Observatory of the Jagiellonian University, ul. Orla 171, 30-244 Kraków, Poland
9 Department of Physics and Astronomy, University of Hawaii, 2505 Correa Road, Honolulu, HI 96822, USA 10 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
11 CSIRO Astronomy and Space Science, PO Box 1130, Bentley, Perth, WA 6102, Australia
12 Centre for Astrophysics Research, School of Physics, Astronomy and Mathematics, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK
13 Astronomy Centre, Dept. of Physics & Astronomy, University of Sussex, Brighton BN1 9QH, UK Received 17 May 2019 / Accepted 10 September 2019
ABSTRACT
Aims. We aim to study the far-infrared radio correlation (FIRC) at 150 MHz in the local Universe (at a median redshift (z) ~ 0.05) and improve the use of the rest-frame 150 MHz luminosity, L150, as a star-formation rate (SFR) tracer, which is unaffected by dust extinction.
Methods. We cross-match the 60 yum selected Revised IRAS Faint Source Survey Redshift (RIFSCz) catalogue and the 150 MHz selected LOFAR value-added source catalogue in the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) Spring Field.
We estimate L150 for the cross-matched sources and compare it with the total infrared (IR) luminosity, LIR, and various SFR tracers.
Results. We find a tight linear correlation between log L150 and log LiR for star-forming galaxies, with a slope of 1.37. The median qIR value (defined as the logarithm of the LIR to L150 ratio) and its rms scatter of our main sample are 2.14 and 0.34, respectively.
We also find that log L150 correlates tightly with the logarithm of SFR derived from three different tracers, i.e., SFRHa based on the H a line luminosity, SFR60 based on the rest-frame 60yum luminosity and SFRir based on LIR, with a scatter of 0.3 dex. Our best-fit relations between L150 and these SFR tracers are, log L150 (L0) = 1.35(±0.06) x log SFRHa (M0 yr-1) + 3.20(±0.06), log L150 (L0) = 1.31(±0.05) x log SFR60 (M0 yr-1) + 3.14(±0.06), and log L150 (L0) = 1.37(±0.05) x log SFRir (M0 yr-1) + 3.09(±0.05), which show excellent agreement with each other.
Key words. radio continuum: galaxies - infrared: galaxies - galaxies: general - methods: observational - methods: statistical - galaxies: star formation
10u m b y van der K ruit ( 1971, 1973) , at 100u m b y R ickard &
H arvey ( 1984), and at 60 u m using early-release IRA S data by D ickey & S alpeter ( 1984) and de Jong et al. ( 1985) . M oreover, the F IR to radio correlation (FIR C ) also seem s to b e m ore o r less independent o f red sh ift (e.g. G arrett 2 0 0 2 ; A ppleton e t al. 2 0 0 4 ; Ibar e ta l. 2 0 0 8 ; Jarvis e ta l. 2 0 1 0 ; S argent e ta l. 2 0 1 0 ; B ourne etal.
2011) , although this is still an issue o f intense debate as som e stud
ies do show evidence fo r red sh ift evolution (e.g. S eym our et al.
2 0 0 9 ; Ivison et al. 2 0 1 0 a; M ichałow ski et al. 2 0 1 0 a,b ; M agnelli et al. 2 0 1 5 ; B asu et al. 2 0 1 5 ; D elhaize e t al. 2017) .
H arw it & P acini ( 1975) had p roposed th at the radio em ission from star-form ing galaxies could arise from supernova rem nants (SN R) b ut H elou et al. ( 1985) show ed th at SN R cou ld account for less than 10% o f the rad io em ission. Instead H elou et al. ( 1985) 1. Introduction
T he correlation betw een far-infrared (FIR ) and rad io lu m i
nosities in n orm al star-form ing galaxies, i.e. w ith o u t signifi
cant active galaxy nuclei (AGN) activity, w as discovered by H elou e t al. ( 1985) using d ata from the Infrared A stronom ical S atellite (IR A S). It has b een confirm ed in m any subsequent stud
ies w ith facilities like the S pitzer S pace Telescope, th e B alloon- B orne L arge A perture S ubm illim eter T elescope (B L A ST ) and the H erschel S pace O bservatory (C ondon 1992; Yun et al. 2 0 0 1 ; Sargent e t al. 2 0 1 0 ; B ourne e t al. 2 0 1 1 ; Ivison et al. 2 0 1 0 a,b ) and has continued to intrigue for its tightness and extent over m any orders o f m agnitude in lum inosity. This relationship betw een F IR and radio lum inosity had been prefigured in earlier studies at
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A&A 631, A109 (2019)
red sh ift z ~ 2 , b u t there is still ongoing debate over w hether this correlation evolves w ith redshift.
W ith th e advent o f the L O w F requency A R ray (LOFAR;
R ottgering et al. 2 0 1 1 ; van H aarlem et al. 2013) w hich co m bines a large field o f view w ith high sensitivity on b oth sm all and large angular scales, w e can now study th e F IR C a t low er frequencies w here the contribution from therm al free-free em is
sion is even less im portant than a t 1.4 G H z. O perating betw een 30 and 230 M H z, LO FA R offers com plem entary inform ation to the w ealth o f d ata collected a t higher frequencies. U sing deep L O FA R 150 M H z observations in the 7 deg2 B ootes field (W illiam s e t al. 2016) , C alistro R ivera et al. (2017) studied the F IR C a t 150 M H z from z ~ 0.05 o u t to z ~ 2.5. T hey found fairly m ild red sh ift evolution in the logarithm ic IR to radio lu m i
n osity ratio in th e form o f qIR ~ (1 + z) -0 '22±0 05. H owever, if the F IR C is non-linear (i.e. the logarithm ic slope is different from one), then it im plies th at th e qIR p aram eter w ould depend on lum inosity. T herefore the rep o rted red sh ift dependence o f q IR m ay sim ply be a consequence o f the n on-linearity o f the FIR C (B asu et al. 2015) as th e m ean SFR o f galaxies is gener
ally larger at higher redshifts (e.g., H opkins & B eacom 2 0 0 6 ; M adau & D ickinson 2 0 1 4 ; P earson et al. 2 0 1 8 ; L iu et al.
2 0 1 8 ; W ang e t al. 20 1 9 ). B ased on LO FA R observations o f the H erschel A strophysical Terahertz L arge A rea S urvey (H- ATLAS; Eales et al. 2010) 1 4 2 d eg 2 N orth G alactic P ole (NG P) field (H ardcastle et al. 2016), G urkan et al. (2018) found that a broken pow er-law (w ith a b rea k around SFR ~ 1 M 0 y r-1) co m pared to a single pow er law is a b etter calibrator for the re la tionship betw een RC lum inosity and SFR, possibly im plying additional m echanism s for generating cosm ic rays and/or m a g netic fields. A lso using LO FA R d ata in the n G p field, R ead et al. (2018) found evidence for red sh ift evolution o f the FIR C at 1 50M H z. H eesen et al. (2019) studied th e relation betw een radio em ission and SFR surface density using spatially resolved LO FA R data o f a few n earby spiral galaxies. They fo u n d a sub- linear relation betw een the resolved RC em ission an d th e SFR surface densities b ased on G A L E X U V an d Spitzer 24 p m data.
T he LO FA R Tw o-m etre Sky S urvey (LoTSS) is currently conducting a survey o f the w hole northern sky w ith a nom inal central frequency o f 150 M H z. T he LoTSS F irst D ata R elease (DR 1; S him w ell e t al. 2019) contains a catalogue o f over 325 000 sources detected over 425 deg2 o f th e H obby-E berly T elescope D ark E nergy E xperim ent (H E T D E X ) Spring Field, w ith a m edian sensitivity o f 71 p J y b ea m -1 and a resolution o f
~ 6 " . In this paper, w e cross-m atch the LO FA R catalogue in the H E T D E X Spring F ield w ith the 60 p m selected R evised IRA S F ain t S ource Survey R edshift (R IFSC z; W ang & Row an- R obinson 2 0 0 9 ; W ang e t al. 2014) C atalogue, w hich is co n structed from the all-sky IR A S F ain t Source C atalog (FSC ), in order to study the FIR C in the local U niverse and the use o f the rest-fram e 150 M H z lum inosity, L 150, as a SFR tracer.
T here are several key differences betw een this study and the previous studies o f C alistro R ivera e t al. (2017) , G urkan et al. (2018) and R ead et al. (2018) w hich w ere b ased solely on H erschel observations from either the H erschel M u lti-tiered E xtragalactic Survey (H erM ES; O liver et al. 2012) or H-ATLAS.
First, the sky coverage o f this study is a t least three tim es larger than any previous studies, w hich m eans w e can detect m ore rare sources such as ultra-lum inous infrared galaxies (U LIR G s) w ith total IR lum inosity (LIR) greater than 1012 L0 and SFR m o re than several hundred solar m asses p er year. Secondly, the previous L O FA R studies relied on H erschel observations to determ ine LIR o f the LO FA R sources. T he intrinsic 90% co m pleteness lim it o f the IRA S F aint Source S urvey at 60 p m is suggested that relativistic electrons m u st leak o u t from SN R into
the general m agnetic field o f the galaxy. This picture w as later refined by H elou & B icay ( 1993). In an idealized calorim eter m odel first p roposed by Voelk ( 1989) , the cosm ic ray electrons lose all o f their energy b efore escaping th e galaxy, w hich is o p ti
cally th ick to ultraviolet (U V ) photons. A ssum ing calorim etry, the logarithm ic slope o f th e F IR C is equal to one (i.e. the F IR C is linear) as both the non-therm al synchrotron radiation and IR ra d i
ation (due to d u st heated b y U V photons) depend on the sam e star-form ation rate (SFR ). T he calorim eter m odel, w hich m ay hold for starburst galaxies, was able to reproduce the tightness o f the FIR C b u t also h ad several shortcom ings. A lternative, m ore com plex n on-calorim etric m odels have also been pro p o sed to explain the tight FIR C for n orm al star-form ing galaxies (e.g. B ell 2 0 0 3 ; M urgia et al. 2 0 0 5 ; T hom pson e t al. 2 0 0 6 ; L acki e t al. 2 0 1 0 ; S chleicher & B eck 2013) . F or exam ple, the “equipartition m o d el”
by N iklas & B eck ( 1997) was the first to p red ict th at th e lo g a
rithm ic slope o f th e F IR C is different from one (i.e. th e F IR C is non-linear) for n orm al star-form ing galaxies. A lthough a detailed picture o f the physical origin o f the FIR C is still lacking, the basic understanding is that m assive star form ation is the d river o f this correlation as U V photons from young stars h eat d u st grains w hich then rad iate in th e IR, and th e sam e short-lived m assive stars explode as supernovae w hich accelerate cosm ic rays thereby co n tributing to n on-therm al synchrotron em ission in the radio.
A n im portant application o f the F IR C is th e use o f th e radio continuum (RC) em ission as a S FR tracer w hich (like the F IR - based SFR tracer) is n o t affected by d u st extinction, as opposed to the often heavily obscured em ission at U V or optical w ave
lengths. A nother advantage o f using R C em ission as a SFR tracer is th at rad io observations using interferom eters from th e ground can achieve m uch h igher angular resolutions (arcsec o r even sub- arcsec resolution) com pared to single aperture IR telescopes in space. T he H erschel space observatory w as the largest IR te le
scope ever launched w ith a 3 .5 m prim ary m irror. T he full w idth at h a lf m axim um (FW H M ) o f th e H erschel-P A C S beam s are (for the m o st com m on observing m ode) 5 .6 ", 6 .8 " and 10.7"
at 70, 100, and 160 p m , respectively 1 and th e F W H M o f the H erschel-SP IR E beam s are 18.1", 2 5 .2 " and 3 6 .6 " at 250, 350, and 5 0 0 p m , respectively (S w inyard e t al. 2010) .
T he F IR C has been investigated m o stly a t G H z freq u en cies in the past, particularly a t 1.4 G H z. F or exam ple, Yun et al.
(2001) studied the N R A O Very L arge A rray (V LA ) Sky Survey (N V SS) 1.4 G H z rad io counterparts o f IR galaxies selected from the IRA S R edshift survey o u t to z ~ 0.15 and found the FIR C is w ell described b y a linear relation over five orders o f m a g n i
tude w ith a scatter o f only 0.26 dex. U sing 24 and 70 p m IR data from S pitzer an d 1.4 G H z radio d ata from V LA , A ppleton et al.
(2004) found strong evidence for th e universality o f the FIR C out to z ~ 1. Ivison e t al. (2010b) studied the FIR C over the re d shift range 0 < z < 2 using m ulti-band IR d ata including obser
vations from Spitzer, H erschel, an d SCU BA , and 1.4 G H z data from the V L A . T hey found n o evidence for significant evolu
tion o f the FIR C w ith redshift. U sing deep IR observations from H erschel and deep 1.4 G H z V L A observations and G ian t M etre- w ave R adio Telescope (GM RT) 6 1 0 M H z observations in som e o f the m o st studied blank extragalactic fields, M agnelli e t al.
(2015) rep o rted a m o derate but statistically significant redshift evolution o f th e F IR C out to z ~ 2.3. Thus, the overall co n clu sions are that there is a tight correlation betw een the F IR and radio lum inosity at 1.4 G H z in the local U niverse out to at least
1 These values are taken from HERSCHEL-HSC-DOC-2151, version 1.0, February 28, 2017.
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L. Wang et al.: The far-infrared radio correlation
derived b y applying the tem plate-fitting m ethod used to construct the S W IR E P hotom etric R edshift C atalogue (R ow an-R obinson e ta l. 20 0 8 , and references therein). Six galaxy tem plates and three Q S O tem plates are used. F o r sources w ith at least 8 photom etric bands and w ith re d u c e d ^ 2 < 3, the percentage o f catastrophic o u t
liers, i.e. (1 + zphot) differs from (1 + zspec) b y m o re than 15%, is 0.17% and th e rm s accuracy is 3.5% after exclusion o f these o u t
liers. IR SED tem plates are fitted to th e m id- and far-IR data, fo l
low ing the m ethodology o f R ow an-R obinson e t al. (2 0 0 5 , 2008) and as in W ang & R ow an-R obinson (2009), w ith a com bination o f tw o cirrus tem plates, three starburst tem plates and an A G N dust torus tem plate. T he total IR lum inosity LIR (integrated betw een 8 and 1 0 0 0 u m ) is estim ated b ased on the fitted tem plates.
T he m ethodology o f R ow an-R obinson et al. (2008) is fo l
low ed to calculate stellar m asses and SFR. Briefly, the rest-fram e 3 .6 u m lum inosity is estim ated and converted to stellar m ass using the m ass-to -lig h t ratio derived from stellar synthesis m o d els. To estim ate SFR, th e conversion recipes o f R ow an-R obinson et al. ( 1997) and R ow an-R obinson (2001) are used
S FR 60 (M 0 y r-1) = 2 .2 n- 1 10-10L6 0 (L0 ) ( 1) w here n is th e fraction o f U V light absorbed by dust, taken as 2/3. T he SFRs are calculated for a S alpeter ( 1955) IM F betw een 0.1 and 100 M 0 . To convert to K roupa (2001) IMF, w e divide the values b y 1.5. W e can also estim ate SFR b ased on the total IR lum inosity LIR follow ing th e w idely used recipe of K ennicutt ( 1998) after converting to K roupa IMF,
S F R ir (M0 y r-1) = 10-10 L ir (L0 ). (2)
In principle, the form ula o f Eq. (2 ) is only suitable fo r dusty starburst galaxies in w hich all o f the radiation from young stars is assum ed to b e absorbed by dust an d subsequently re-em itted in the IR. In practice, Eq. (2 ) has been found to also apply to norm al galaxies (e.g. R osa-G onzdlez et al. 2 0 0 2 ; C harlot et al.
2002) . T he explanation is th at there are tw o com peting effects, w hich are overestim ation in SFR caused b y assum ing all o f the IR lum inosity arises from rec en t star form ation (as opposed to old stellar populations) and underestim ation in SFR caused by neglecting the p o ssibility th at som e o f the young stellar radiation is n o t absorbed b y dust. It is a coincidence th at these tw o effects cancel o u t (e.g. Inoue 2 0 0 2 ; H irashita e t al. 2003) .
F or sources in th e R IF S C z w hich have been cross-m atched to SDSS D R 10, w e also have SFR estim ates b ased on the H a line lum inosity, S F R Ha, co rrected for d u st attenuation an d aperture effects provided in th e M PA -JPU database (B rinchm ann et al.
2004) .
2.2. The LOFAR survey
E xploiting the unique capabilities o f LO FA R (van H aarlem e t al.
2013) , L oT SS is an ongoing sensitive, high-resolution, low- frequency ( 1 2 0 -1 6 8 M H z) radio survey o f the northern sky and is d escribed in S him w ell e t al. (2017) . L oT SS provides the astro m etric p recision n eed ed for accurate and ro b u st identification of optical an d N IR counterparts (e.g. M cA lpine et al. 2012) and a sensitivity that, for typical radio sources, is superior to previous w ide area surveys at h igher frequencies such as the NrAo V L A Sky S urvey (N V SS; C ondon e t al. 1998) and F ain t Im ages o f the R adio Sky at T w enty-C entim eters (FIRST; B ecker et al. 1995) and is sim ilar to forthcom ing h igher frequency surveys such as the E volutionary M ap o f th e U niverse (EM U ; N orris e t al. 2011) , and the A P E R ture Tile In Focus survey (e.g. R ottgering e t al. 2011) . T he prim ary observational objectives o f L oT SS are to reach a S 60 = 0.36 Jy (W ang & R ow an-R obinson 2010) . A t the m edian
red sh ift o f our m ain sam ple z ~ 0.05 (see Sect. 3.3), this flux lim it corresponds to a 60 u m lum inosity o f L60 ~ 1010 27 L0 , or equivalently LIR ~ 1010 5 L0 , b ased on th e m edian ratio o f L60 to Lir using the IR spectral energy distribution (SED ) tem plates from C hary & E lbaz (2 001) . In com parison, the H-A TLAS 5 a lim it, including b o th confusion and instrum ental noise, is 37 m Jy (V aliante e t al. 2016) at 250 u m w hich is the m o st sensitive band.
A t z ~ 0.05, this flux lim it corresponds to a 250 u m lum in o s
ity o f L25o ~ 108 84 L0 , o r equivalently LIR ~ 1010 2 L0 , b ased on the m edian ratio of L250 to LIR using the C hary & E lbaz (2 001) tem plates. Therefore, the IR A S observations are only a factor o f ~ 2 shallow er than the H-ATLAS survey. Finally, the IRA S p h otom etric bands sam ple th e p ea k o f the d u st SED for the IR lum inous galaxies in the local U niverse. In com parison, the H erschel-S P IR E bands sam ple the R ayleigh-Jeans regim e o f the SED. D ue to the lack o f p hotom etric bands covering the peak o f the IR SED , b oth G urkan et al. (2018) and R ead et al. (2018) focused on the relation betw een the L250 and L 150, rath er than betw een LIR and L 150. M o st o f the sources in the R IF S C z lie at red sh ift below 0.1 and thus provide an excellent local b en c h m ark. T he m edian red sh ift o f our m ain sam ple is z ~ 0.05. In com parison, th e low est red sh ift b in in the C alistro R ivera e t al.
(2 017) study has a m edian red sh ift o f 0.16. T he sam ple used in G urkan e t al. (2018) and R ead e t al. (2018) covers the redshift range a t z < 0.25, w ith a m edian red sh ift o f 0.1.
T he p ap e r is structured as follow s. In Sect. 2 , w e introduce the tw o m ain datasets (and th eir associated m ulti-w avelength data) in ou r analysis, nam ely the R IF SC z catalogue and the L O FA R value-added catalogue (VAC) in the H E T D E X Spring F ield. T he construction o f the L O FA R -R IFS C z cross-m atched sam ple an d its basic properties such as its w avelength co v erage and red sh ift distribution are sum m arised in Sect. 3 . In Sect. 4 , w e presen t the m ain results o f our study, the F IR C at b oth 1.4 G H z and 150 M H z an d the correlation b etw een the rest- fram e 150 M H z lum inosity an d various S FR tracers. Finally, w e give ou r conclusions in Sect. 5 . T hroughout the paper, w e assum e a flat A C D M universe w ith Q m = 0.3, Q a = 0.7, and H 0 = 7 0 k m s - 1 M p c- 1. W e ad o p t a K roupa (2 001) initial m ass function (IM F) unless stated otherw ise.
2. Data
2.1. The RIFSCz catalogue
T he R evised IRA S F ain t S ource Survey R edshift (R IFSC z) C ata
logue (W ang & R ow an-R obinson 2 0 0 9 ; W ang et al. 2 0 1 4 ; Rowan- R obinson & W ang 2015) is com posed o f galaxies selected from the IRA S F ain t S ource C atalog (FSC) over the w hole sky at G alactic latitude |b| > 20°. R IF SC z incorporates d ata from G A LEX , th e S loan D igital Sky S urvey (S D sS ; York e t al. 2000), the Two M icron A ll Sky S urvey (2 m A sS ; Skrutskie et al. 2006), the W ide-field Infrared S urvey E x p lo rer (W ISE; W rig h t e t al.
2010), an d P lanck all-sky surveys (P lanck C ollaboration 1 2013) to give w avelength coverage from 0 .3 6 -1 3 8 0 u m . A t a 60 g m flux density o f S 60 > 0.36 Jy, w hich is the 90% com pleteness lim it of the FSC , 93% o f R IF SC z sources have o ptical or near-IR (N IR) counterparts w ith spectroscopic o r photom etric redshifts (W ang e t al. 2014) . S pectroscopic redshifts are com piled from the SDSS spectroscopic D R 10 survey (A hn e t al. 2014), the 2M A SS R edshift S urvey (2M R S; H uchra e t al. 2012), the N ASA /IPAC E xtragalactic D atabase (N ED ), the PSC R edshift Survey (PSCz;
Saunders e t al. 2000) , the 6 dF G alaxy Survey, and the FSS re d shift survey (FSSz; Oliver, PhD thesis). P hotom etric redshifts are
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from LO FA R (based on the SDSS D R 14). 71 sources th at have n o spec-
z
from LO FA R b u t have a spec-z
from R IF S C z 3. The origin for these new spec-z
are N E D (54 out o f 71), SDSS (2 3 In the RIFSCz, the recommended spec-z and flags are 1 = SDSS DR10, 2 = PSCz, 3 = FSSz, 4 = 6dF, 5 = NED and 6 = 2MRS, prioritised as NED > SDSS > 2MRS > PSCz > FSSz > 6dF. These spectro
scopic surveys (except SDSS) are not used in the construction of the LOFAR VAC.
sensitivity o f less than 100u J y b e a m -1 at an angular resolution, defined as the F W H M o f the synthesised beam , o f ~ 6 " across the w hole northern hem isphere.
T he LoTSS F irst D ata R elease (D R 1) presents 424 deg2 o f RC observations over the H E T D E X Spring F ield (10h4 5 m00 s <
right ascension < 15h30m0 0 s and 4 5 °0 0 '0 0 " < declination <
5 7 °0 0 '0 0 ") w ith a m edian sensitivity o f 71 u J y b e a m -1 and a resolution o f 6 " , resulting in a catalogue w ith over 3 2 5 0 0 0 sources. S him w ell et al. (2019) estim ated th at the positional accuracy o f the catalogued sources is b etter than 0 .2 " . T he VAC includes optical cross m atches and p hotom etric redshifts for the L O FA R sources. T he p rocedure o f cross-m atching to currently available o ptical and m id-IR photom etric surveys is p resented in W illiam s et al. (2019) . P hotom etric redshifts (phot-
z
) are estim ated using a com bination o f tem plate fitting m ethods and em pirical training b ased m ethods (D uncan et al. 2019) . The overall scatter an d outlier fraction in the p h o t-z is 3.9% and 7.9% , respectively. F ollow ing R ead e t al. (2018), w e calculate the K -corrected 150 M H z lum inosity assum ing a spectral shape o fS
v k v a , w here the spectral index a = 0.71 (C ondon 1992;M a u c h e ta l. 2013) .
3. The RIFSCz-LOFAR cross-matched sample In order to cross-m atch th e IRA S sources in the R IF SC z c a t
alogue and L O FA R sources in the H E T D E X Spring F ield, w e take a com bined approach o f the closest m atch m eth o d an d the likelihood ratio (LR ) m eth o d as d etailed below .
3.1. The closest match m ethod
F or IRA S sources in the R IF SC z w hich are m atch ed to sources detected at other w avelengths (e.g., the SDSS optical b an d s or the W IS E IR bands), w e choose the closest LO FA R m atch w ithin a 5 " searching radius w hich results in a cross-m atched sam ple o f 771 sources2. T he conservative choice o f 5 " for the searching radius is m ainly m otivated b y the F W H M o f the LO FA R beam , although w e no te th at the p ositional uncertainty is m uch sm aller than that (S him w ell e t al. 2019). O nly one source has tw o p o s
sible m atches (one located a t 1.8" aw ay and the o ther at 4 .4 "
aw ay). T he top pan el o f F ig. 1 show s th at th e m ajority o f the m atches have positional differences w ell w ithin 1", consistent w ith w hat w e expect from the positional accuracies o f LO FA R, SDSS and W IS E (Y ork et al. 2 0 0 0 ; W rig h t et al. 2 0 1 0 ; Shim w ell e ta l. 2019).
T he m iddle panel o f F ig. 1 com pares the W IS E W 1 fluxes at 3 .4 u m pro v id ed b y the cross-id in b oth th e R IF SC z and LO FA R catalogues. T he excellent agreem ent for th e vast m ajority o f sources dem onstrates th at w e have th e sam e id for m o st o f the R IF SC z-LO F A R m atch ed sources. S om e sources have fairly d if
ferent W IS E fluxes w hich indicate p otential problem s w ith the cross-ids (betw een R IF S C z an d LO FA R, b etw een R IF S C z and W IS E, o r b etw e en L O FA R an d W IS E ). T herefore, w e exclude a total o f 22 sources for w hich the W IS E flux ratio from the tw o catalogues differs b y m ore than a factor o f 1.5.
T he b o tto m panel o f Fig. 1 com pares redshifts provided for the R IF SC z-LO F A R m atched sources from b o th catalogues, after excluding the 22 sources th at could b e erroneous m atches.
T he spectroscopic redshifts (spec-z ) show excellent agreem ent.
15 sources that have no spec-
z
in the R IF S C z now have a spec-z
2 The positions given in the RIFSCz catalogue correspond to the posi
tions of the multi-wavelength cross-id matched to the IRAS sources, prioritised in the order of SDSS, 2MASS, WISE, NED and IRAS FSC.
A109, page 4 o f 12
Fig. 1. Top: distribution of positional separations of sources matched between RIFSCz and LOFAR. Middle: comparison of WISE W1 flux for sources listed in RIFSCz and in LOFAR. Sources inside the two horizontal red lines have good WISE flux agreement (i.e., the difference is within a factor of 1.5). Bottom: comparison of redshifts compiled in the RIFSCz and LOFAR VAC.
The far-infrared radio correlation L. Wang et
S eparation (arcsec)
Fig. 2. Distribution of radial offsets between the RIFSCz sources (which only have IRAS observations) and LOFAR sources by selecting all matches within 3'. The radial distribution of the random associations is plotted as the red dashed line, while the radial distribution of the true counterparts is shown as the green dot dashed line. The black solid line is the sum of the two.
assum ing a co nstant surface density o f b ackground LO FA R sources uncorrelated w ith IRAS sources.
In Fig. 2 , w e p lo t the distribution o f radial offsets betw een the IR A S-only R IF S C z sources and L O FA R sources by selecting all m atches w ithin 3 ', w hich contains both the true counterparts and the random associations. W e fit ou r m odel
N (r )d r = E x f (r)d r + p x b (r)d r, (6 ) to the observed histogram to determ ine th e best-fit p aram e
ters to b e E = 251.2¾ ± 34.28, T r = 4 0 .9 2 " ± 3 .5 9 " and p = 0.0111 ± 0.0005. This is consistent w ith w hat w e expect b ased on the p ositional accuracy o f IRAS sources. T he a n g u lar resolution o f IRA S varied betw een about 0 .5 ' a t 12 g m to about 2 ' at 100 g m . T he p ositional accuracy o f the IR A S sources depends on their size, brightness and SED b u t is usually b etter than 2 0 '' (1 -t). A histogram o f th e angular separations betw een IRA S positions and the N E D positions can b e found in W ang &
R ow an-R obinson (2009) .
In Fig. 3 , w e p lo t the 6 0 g m - 150 M H z colour distribution o f all m atches w ithin 3' betw een the R IF SC z sources (w hich only have IRAS observations) and L O FA R sources. T hese m atches contain b oth true and ran d o m associations. W e assum e that this colour distribution can b e fit by tw o G aussian distributions. W e also p lo t the colour distribution o f the R IF SC z-LO F A R m atches from the m ain sam ple discussed in Sect. 3 .1 . It is clear that there are system atic differences in m edian values an d w idths betw een the green dot-dashed line and th e blue histogram . This is caused by the difference in the red sh ift ranges (see discussions in Sect. 3.3) .
H aving derived th e positional and colour probability distri
butions o f the true and random associations, w e can now cal
culate th e L R for every possible m atch b ased on its positional separation and IR -to-radio colour. So, for every R IF SC z object w ith m o re than one LO FA R co unterpart w ithin 3' , w e select the m atch w ith the highest L R 5. W e also im pose a m inim al L R threshold to ensure th e false identification rate is no m ore than
10%. T he L R threshold is derived as follow s:
5 A total of 9 IRAS sources only have one LOFAR match within 3' . For these sources, we simply select the only LOFAR match.
out o f 71), PSC z (3 out o f 71), F SS z (12 out o f 71). A g en erally go o d agreem ent can b e found betw een the phot-z e sti
m ates from both catalogues. In som e cases, th e LO FA R phot- z tend to be higher than the phot-z from the R IFSC z. W e have studied 39 cases w here th e phot-z estim ates differ b y m o re than 0.2 and fo u n d th at the higher LO FA R phot-z are likely to be erroneous b ecause they w ould im ply unrealistically high optical lum inosity. T herefore, w e ado p t a p riority o rder o f red sh ift e sti
m ates as follow s: spec-z from R IF S C z (652 sources), follow ed by spec-z from th e L O FA R VAC (15 sources), follow ed b y phot- z from R IF SC z (76 sources), and finally phot-z from LO FA R (6 sources).
To sum m arise, w e select the sources w ith go o d W IS E flux agreem ent (749 o u t o f 771) and call this ou r “m ain sam ple” . A ll o f the sources in th e m ain sam ple have red sh ift estim ates. O u t o f 749 sources, 581 sources (78% ) have spec-z from both R IFSC z and the L O FA R VAC. As discussed in the paragraph above, the tw o spec-z values are in p erfect agreem ent w ith each other. W e refer to this subset o f th e m ain sam ple as the “m ain spec-z sam p le” w hich is ou r m o st ro b u st sam ple w ith n o am biguity in the m ulti-w avelength cross-id. I f w e include the 15 new spec-z from L O FA R and the new 71 spec-z from R IF SC z, then w e increase the sam ple size to 667 galaxies (89% ) an d w e refer to this sub
set as the “m ain jo in t spec-z sam ple” . Finally, 82 sources (11% ) have phot-z. W e refer to this subset o f the m ain sam ple as the
“m ain phot-z sam ple” .
3.2. The likelihood ratio m ethod (LR)
F or IRA S sources in the R IF S C z w hich have n o t been m atched to sources at o ther w avelengths and therefore only have IRA S posi- tions4, w e ad o p t an L R m ethod (S utherland & Saunders 1992;
B rusa e t al. 2 0 0 7 ; W ang & R ow an-R obinson 2 0 1 0 ; C hapin e t al.
2 0 1 1 ; W ang e t al. 2014) in o rder to m atch them w ith LO FA R sources. T he accurate L O FA R positions w ould then allow these IRA S only sources to b e m atch ed w ith optical or N IR sources.
T he L R technique com pares th e p robability o f a true counter
p art w ith the p robability o f a chance association, as a function o f 60 g m to 150 M H z flux ratio S 60/S 150 an d radial offset r. A ssu m ing the p robability o f true counterpart and random association is separable in lo g 10( S 60/ S 150) (or C60-150 as a shorthand) and r, w e can w rite
L R = Probtrue(C60-150, r) = q(C 60-150)E f (r)d C d r (3 ) Probrandom(C60-150, r) p ( C6 0-1 5 0) p b (r )d C d r ,
w here q(C 60-150) and p (C 60-150) are the colour distributions o f the true counterparts and ran d o m m atches respectively, an d f ( r ) and b(r) are the positional distributions o f the true counterparts and random associations respectively.
To derive the positional distribution o f the true counterparts f ( r ) , w e assum e a sym m etric G aussian distribution as a fu n c
tion o f orthogonal p ositional coordinates. T herefore, f (r) can b e w ritten as a R ayleigh radial distribution,
f ( r) d r = - rJ e x p ( - r 2/2 ^ 2 )d r, (4) (T2
w here the scale param eter, T r , is w here f ( r ) peaks and f ( r ) d r = 1. T he positional distribution o f random asso cia
tions can be w ritten as,
b (r)d r = 2 n rd r, (5)
4 These IRAS only sources can be selected by applying FLAG posi
tion = 5 in the RIFSCz catalogue. Around 19% of the sources in the RIFSCz catalogue have only IRAS observations.
A109, page 5 of 12
A&A 631, A109 (2019)
Fig. 5. Top: redshift distribution of the RIFSCz-LOFAR cross-matched sample. Bottom: normalised distributions (i.e. the integral of the distri
bution is 1). The median redshifts of the main sample and the second sample are 0.05 (indicated by the dashed line) and 0.12 (the dot-dashed line), respectively.
3.3. Sum m ary o f the cross-matched sample
Figure 4 shows a schem atic view o f our R IF SC z-LO F A R m atched sam ple. T he com bined sam ple o f 861 sources is a com bination o f the m ain sam ple (generated using the closest m atch m ethod) and the second sam ple (g enerated using the like
lihood ratio m ethod). B oth sam ples are divided into subsam ples depending on w hether the sources have spec-z or phot-z . In the m ain sam ple, there are a total o f 581 sources w ith spec-z from both R IF S C z and L O FA R w hich w e refer to as the m ain spec-z sam ple. A n additional 86 sources have spec-z from either L O FA R or R IF SC z w hich form the m ain jo in t spec-z sam ple after com bining w ith the m ain spec-z sam ple. T he top panel in Fig. 5 shows the red sh ift distribution o f the cross-m atched R IF SC z-L O F A R sam ple. M o st galaxies have spec-z . T he m ajor
ity o f our sources lie at z < 0.1. T he b ottom p anel shows the norm alised distribution to bring o u t the co n trast in the redshift distribution. T he m edian red sh ift o f the m ain sam ple and the sec
ond sam ple is 0.05 and 0.12, respectively.
T able 1 shows the num ber o f sources in the m ain sam ple b y IR w avelength coverage (i.e. the num ber o f sources detected at a given IR w avelength). M o st sources have been m atched to W ISE. F or the IR A S fluxes, the flux quality is classified as high (N Q = 3), m oderate (N Q = 2) o r upper lim it (N Q = 1). W e require flux quality flag N Q > 1 to avoid upper lim its. T he exception is the 6 0 g m band. A ll sources in the R IF S C z have high-quality flux m easurem ent in the 6 0 g m band. A sm all fraction also have
lo g S60/S150
Fig. 3. 60 g m - 150 MHz colour distribution of all matches within 3' between the RIFSCz sources (which only have IRAS observations) and LOFAR sources (yellow histogram). The dot-dashed Gaussian repre
sents the inferred colour distribution of the true counterparts and the dashed Gaussian represents that of the random associations. The black solid line is the sum of the two. The colour distribution of the main sample is shown as the blue histogram.
Fig. 4. Schematic view of our RIFSCz-LOFAR matched sample.
- First, w e calculate the L R distribution o f m atches betw een a random ised R IF SC z and a random ised L O FA R VAC.
T he random ised catalogues are generated by random ly re arranging the flux m easurem ents o f the sources, w hile k ee p ing the positions unchanged.
- Then, w e com pare the L R distribution o f the m atches betw een the random ised catalogues w ith th a t o f the m atches betw een the original catalogues (i.e. before random isation).
- Finally, w e set the m inim al L R threshold to th a t above w hich the num ber o f random m atches is 10% o f the num ber o f m atches betw een the original catalogues.
In total, 141 galaxies are m atched betw een R IF SC z and L O FA R using the L R m ethod. O ut o f the 141 galaxies, 112 galaxies have m ulti-w avelength optical and N IR d ata in the L O FA R VAC w hich are then used in the p h o t-z estim ation procedure discussed in Sect. 2 .1 . W e refer to this subset o f 112 galaxies m atched b etw een R IF SC z and L O FA R using the L R m ethod as the “ sec
ond sam ple” . 79 galaxies in the second sam ple have spec-z from the VAC. W e refer this as the second spec-z sam ple and the rest o f the galaxies as the second phot-z sam ple.
A109, page 6 of 12
The far-infrared radio correlation L. Wang et
Table 1. Number of sources in the main sample of the cross-matched RIFSCz-LOFAR sample (749 sources in total) by wavelength coverage.
Wavelength (pm) Survey Number of sources
Fig. 6. Normalised distribution of the radio spectral index between 150 MHz and 1.4 GHz.
4.1. The FIR-radio correlation at 1.4 GHz
W e obtained the 1.4 G H z F IR S T survey catalogue (14 D ec. 17 version) w hich contains 946 432 sources observed from th e 1993 through 2011 observations6. T he F IR S T detection lim it is 1 m Jy over m o st o f th e survey area. T he angular resolution o f F IR S T is
~ 5 " , sim ilar to LO FaR. W e cross-m atched F IR S T w ith LO FA R b y selecting the clo sest m atch w ithin 3 ". 412 m atches w ere found w ith the m ain sam ple and 79 m atches w ere found w ith the second sam ple. W e derive the rad io spectral index b y follow ing
_ log (SV1 / SV 2)
V1 log(V2/V1) ( )
w here v1 _ 150 M H z and v2 _ 1400 M H z. F igure 6 shows the h is
togram o f the derived spectral index values. W e do n o t find a significant d if ference betw een the m ain sam ple and the second sam ple. T he m edian value o f th e spectral index and scatter for the m ain sam ple are 0.58 and 0.22, respectively. T he m edian value and scatter for the second sam ple are 0.64 and 0.35, resp e c
tively. T hese values are very sim ilar to the spectral index found in Sabater et al. (2019) using the galaxies overlapping betw een the SDSS D R 7 and L oT SS . S abater e ta l. (2 0 1 9 ) also show ed that their spectral index value (m edian value 0.63) is p robably b iased to low er values for low lum inosity galaxies d ue to selection biases in the shallow er 1.4 G H z sam ple com pared to the low -frequency LO FA R data (w hich m isses sources w ith steeper rad io spectra).
T he spectral index values found in our sam ples are also likely to b e b ia sed to low er values com pared to the canonical value o f 0.71 (see Sect. 2.2) b ecause o f the shallow er 1.4 G H z data.
In th e top panel o f Fig. 7 , w e p lo t th e 1.4 G H z radio lu m i
nosity against th e IR A S 60 p m lum inosity. T he vertical dashed line indicates the 90% com pleteness lim it L 60 ~ 1010 27 L0 a t the m edian red sh ift z ~ 0.05 o f the m ain sam ple. T he vertical d o t
ted line indicates th e 90% com pleteness lim it L 60 ~ 101108 L0 at th e m edian red sh ift z ~ 0.12 o f the second sam ple. In co m parison, the detection lim it o f F IR S T o f around 1 m Jy co rre
sponds to a 1.4 G H z lum inosity L 14 ~ 104 34 L0 at z ~ 0.05 and L 14 ~ 10514 L 0 at z ~ 0.12. Yun et al. (2001) studied a sam ple o f IR A S sources w ith S 60 > 2 Jy an d found th at over 98% o f their sam ple follow a linear FIR C over five orders o f m agnitude in lum inosity w ith a scatter o f only 0.26 dex. W e overplot their best-fit relation (w ith a slope o f 0.99) in the top panel in F ig. 7 . M o st o f our sources seem to follow the Yun et al. (2001) re la tion. S om e sources in our second sam ple show deviations from 748
748 748 59 748 135 749 194 205 452 196 171 56 54 50 36 WISE WISE WISE IRAS WISE IRAS IRAS AKARI AKARI IRAS AKARI AKARI Planck Planck Planck Planck 3.4
4.6 12 12 22 25 60 65 90 100 140 160 350 550 850 1380
Notes. For the IRAS fluxes, we require moderate- or high-quality flux measurement. The exception is the IRAS 60 pm band where all sources have high-quality flux measurement.
Table 2. Number of sources in the second sample of the cross-matched RIFSCz-LOFAR sample (112 sources in total) by wavelength coverage.
Wavelength (pm) Survey Number of sources 107
106 94 1 83 12 112 2 2 51 1 2 3 3 2 2 WISE WISE WISE IRAS WISE IRAS IRAS AKARI AKARI IRAS AKARI AKARI Planck Planck Planck Planck 3.4
4.6 12 12 22 25 60 65 90 100 140 160 350 550 850 1380
http://sundog.stsci.edu/first/catalogs.html A K A R I flux m easurem ent o u t to 160 p m . A very sm all num ber
o f sources also have P lanck m easurem ents at 250, 550, 850 and 1380p m . Table 2 shows the nu m b er o f sources in the second sam p le by IR w avelength coverage. A gain, m o st sources have been m atched to W IS E. As the second sam ple is generally a t higher red sh ift than the m ain sam ple, th e IR SED coverage is p oorer especially at the longer w avelengths from A K A R I and P la n ck.
4. Results
G iven that th e FIR C has been very w ell studied at 1.4 G H z (see Sect. 1) , in this section w e first study th e FIR C at 1.4 G H z and com pare w ith previous studies. T hen w e focus on th e F IR C at 150 M H z and possible variations w ith resp ect to redshift. A fter that, w e investigate th e use o f th e 150 M H z lum inosity density as a SFR tracer.
A109, page 7 o f 12
A&A 631, A109 (2019)
Fig. 8. Histogram of qIR values at 1.4GHz, derived using Eq. (10). The dashed line is a Gaussian with its mean and standard deviation set to 2.64 and 0.26 respectively, which are values found by Bell (2003).
w hich N Q > 1 at 100jum. This indicates th at there is n o signifi
cant red sh ift evolution in the q (1.4 G H z) value although the red- shift ran g e p ro b ed b y ou r sam ple is probably too sm all to detect this. W e over-plot a G aussian distribution w ith m ean an d stan
dard deviation set to the values in Yun et al. (2001) . T he distri
butions o f q (1.4 G H z) o f ou r sam ples agree w ell w ith th e Yun et al. (2 0 0 1 ) distribution.
B ell (2003) p ro p o sed an alternative definition o f q using the total IR to radio lum inosity ratio,
w here L 14 is the 1.4 G H z lum inosity. In F ig. 8, w e p lo t the distribution o f the q IR (1.4 G H z) values o f o ur sam ple. Bell (2003) found a m edian value o f 2.64 and a scatter o f 0.26 w hich are over-plotted in F ig. 8 . A gain, the distribution o f our q IR (1.4 G H z) values (w ith m edian = 2.61 and scatter = 0.30 for the m ain sam ple) has excellent agreem ent w ith that o f B ell (2003). It is also w orth noting th at B ell (2003) found perfect agreem ent w ith the Yun et al. (2001) study, after correcting for the difference in the definitions o f q and qIR. O ur results for the F IR C at 1.4 G H z are fully consistent w ith Yun e t al. (2001) and B ell (2003) . In the subsequent analysis, w e adopt the B ell (2003) definition o f q IR given in Eq. ( 10), b ased on th e total IR to radio lum inosity ratio. To calculate qIR at 150 M H z, q IR (150 M H z), w e can sim ply replace the 1.4 G H z lum inosity L 14 w ith the
150 M H z lum inosity L 150.
4.2. The FIR-radio correlation at 150 MHz
N ow w e have show n th at ou r results o f the F IR C a t 1.4 G H z are consistent w ith previous m easurem ents, w e can study the FIR C at 150 M H z. F irst, to identify A G Ns from ou r sam ple, w e use the A G N classifications from th e LO FA R VAC. As d etailed in D uncan et al. (2 018a,b ), A G N candidates have been identified using a variety o f selection m ethods. O ptical A G N are identified p rim arily through cross-m atching w ith the M illion Q uasar C a t
alogue com pilation o f optical A G N, prim arily b ased on SDSS (A lam et al. 2015) and other literature catalogues (F lesch 2015) . Sources w hich have been spectroscopically classified as A G N are also flagged. B rig h t X -ray sources w ere identified b ased on the Second ROSAT all-sky survey (B oller et al. 2016) and the XMM- N ew ton slew survey. Finally, IR A G Ns are selected using the A ssef et al. (2013) criteria b ased on m agnitude an d colour at the W IS E W 1 and W 2 bands. W e select sources w ith IR C lass > 4 from the Fig. 7. Top: 1.4 GHz radio luminosity plotted against the IRAS 60gm
luminosity. The vertical dashed line indicates the 90% completeness limit at the median redshift of the main sample. The vertical dotted line indicates the 90% completeness limit of the second sample. The solid line is the Yun et al. (2001) relation. Bottom: histogram of q(1.4G Hz) values, derived using Eq. (8), using only sources with NQ > 1 at 100 gm.
The dashed line is a Gaussian distribution with mean and standard devi
ation set to 2.34 and 0.26 respectively, which are values found by Yun etal. (2 0 0 1).
the Yun et al. (2001) relation. H ow ever, the second sam ple is m uch sm aller and less reliable.
B ecause the F IR C has a slope o f unity, it can also be ex am ined w ith the “q ” param eter, w hich is the logarithm ic F IR to radio flux ratio and is com m only defined as (e.g., H elou et al.
1985; C ondon e t al. 1991; Yun et al. 2001) ,
(
8
)q(L4GHz) = log ( ) - log<S 1‘>
w here S 14 is the observed 1.4 G H z flux density in units o f W m -2 H z-1 and
Sf i r = 1.26 x 10-1 4(2.586 x S6 0 + S1 0 0) W m - (9)
w here S 60 and S 100 are the IR A S 60 and 100 g m flux densities in Jy (H elou et al. 1988) . In the bo tto m p an el Fig. 7 , w e p lo t the q (1.4 G H z) values derived for our sam ple, using only sources for w hich N Q > 1 at 100 g m . This requirem ent on m oderate- or high-quality flux m easurem ent at 100 g m reduces the sizes o f the m ain an d second sam ple to 45 2 an d 51, respectively (see Tables 1 and 2 ) . W e do n o t see a significant difference betw een the m ain sam ple and the second sam ple. T he m edian q (1.4 G H z) value and rm s scatter for the m ain sam ple are 2.35 and 0.25 resp e c
tively, w hile th e m edian q (1.4 G H z) value and scatter for the second sam ple are 2.34 an d 0.35 respectively, using sources for A109, page 8 o f 12
q IR (,.4 G H z ) = log ( LIR/ ( 3 7 L * 101;H z>) (10)
The far-infrared radio correlation L. Wang et
Fig. 9. Top: correlation between the IR luminosity and the rest-frame 150 MHz luminosity for the main spec-z sample, including AGNs iden
tified in the X-ray, IR, the Million Quasar Catalog and in optical spec
troscopy. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ~ 0.05) of the main sample. Bottom: same as top panel but for the second sample. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ~ 0.12) of the second sample.
T he best-fit relation derived for all galaxies is p lotted as the red dashed line. W e also test the significance o f the correlation by calculating th e P earson correlation coefficient p w hich is found to b e 0.79 and the p -v alu e w hich is 1.40 x 10-69. T he b o t
tom panel in F ig. 10 shows the correlation betw een log LIR and log L 150 for star-form ing galaxies in th e second sam ple. A gain w e do n o t fit the second sam ple but sim ply over-plot the best- fit linear relation for the m ain sam ple. T he P earson correlation coefficient p an d p -value fo r galaxies above the 90% com plete
ness lim it in the second sam ple are 0.36 and 0.05, respectively.
F igure 11 shows the distribution o f q IR (150 M H z) values o f our sam ple derived using Eq. ( 10) and replacing th e 1.4 G H z lum inosity w ith the 150 M H z lum inosity. T he m edian value and scatter o f qIR (150 M H z) are 2.14 an d 0.34, respectively, for the m ain sam ple. T he m edian value and scatter are 1.93 and 0.61, respectively, for th e second sam ple. C alistro R ivera e t al. (2017) found a m edian q IR (150 M H z) value o f 1.544. This is incon
sistent w ith o ur result. T he m ain cause o f this inconsistency is the large difference in the distributions o f LIR in the tw o stud
ies. T he m ean LIR o f the galaxy sam ple in C alistro R ivera et al.
(2017) is roughly 1.3 dex higher than this study. U sing Eq. ( 12), w e can derive that an increase in LIR by 1.3 dex w ould reduce q IR (150 M H z) by - 0 .5 .
In F ig. 12, w e p lo t the q IR (150 M H z) values against redshift. A m ild red sh ift evolution has been rep o rt by Table 3. Numbers of AGNs identified by various methods in our main
sample and second sample.
A G N identification m ethod N u m b er of sources M ain sam ple
X -ray AG N 13
IR AGN 84
M Q C A GN 71
S pectroscopy AGN 16
S econd sam ple
X -ray AG N 4
IR AGN 18
M Q C A GN 17
S pectroscopy AG N
6
VAC w hich corresponds to the “75% reliab ility ” selection criteria.
Table 3 lists the n um ber of identified A G N s in ou r sam ples.
T he top p anel in Fig. 9 shows the correlation betw een log LI R
a n d th e re st-fra m e 150 M H z lum inosity log L1 5 0fo rth e m a in spec- z sam ple and A G Ns (predom inantly lum inous system s) identified using X -ray, optical and IR data. T he vertical dashed line indicates the 90% com pleteness lim it a t the m edian red sh ift (z - 0.05) o f the m ain sam ple, a t LI R - 101 0 5 L0 . This value is derived from m u l
tiplying the 90% com pleteness lim it at 60 u m , L6 0- 101 02 7L0 , by the m edian ratio of LI R to L6 0 using the IR SED tem plates from C hary & E lbaz (2001) . T he C hary & E lbaz (2001) te m plates are show n to b e able to reproduce the observed lum inosity- lum inosity correlations a t various IR w avelengths for local galaxies. In com parison, th e selection effect due to the m edian sensitivity (71 u J y b ea m -1) o f the L O FA R 150 M H z observations is negligible (i.e., LO FA R is m u ch d eeper than IRA S for typical galaxy SED s). A t z - 0.05, this m edian sensitivity corresponds to L 15o = 1029 2L0 a t 5 a . W e perfo rm a linear regression w hich is based on a fitting m eth o d called th e bivariate correlated errors and intrinsic scatter (B C ES) d escribed in A kritas & B ershady ( 1996) . We use th e p u b lic code developed in N em m en e t al. (2012) . The red solid line show s ou r best-fit linear relation using galaxies above the 90% com pleteness lim it,
lo g L1 5 o(L0) = 1.306(±0.057)x lo g Li r(L0) -9 .9 0 0 (± 0 .6 2 3 ), (11) w hile the red dashed line show s th e best-fit relation using all galaxies. W hile som e optically-identified A G N s clearly show an excess rad io em ission and therefore do n o t lie on the FIR C , m ost o f the optical A G Ns still obey the F IR C . M o st o f th e IR and X -ray identified A G N also lie on the FIR C .
T he b ottom panel in Fig. 9 shows the correlation betw een log Lir and log L1 5 0 for the second sam ple. T he vertical dashed line indicates th e 90% com pleteness lim it a t the m edian redshift (z - 0.12) o f th e second sam ple, a t LI R - 101 1 3 L0 . B y co m parison, the LO FA R sensitivity lim it at z - 0.12 is at around L 15o = 10371 L0 at 5 a . W e do n o t attem pt to fit the second sam ple (due to th e sm all sam ple size) b u t sim ply over-plot th e best-fit linear relation for the m ain sam ple w hich seem s to describe the second sam ple reasonably w ell.
T he top panel in Fig. 10 show s th e correlation betw een log L 15o and log LI R for ou r star-form ing galaxies from the m ain sam ple, after rem oving A G N s. U sing the B C ES m ethod, our best-fit linear relation betw een the log o f L1 5 0 and the log o f
LI R for galaxies above the 90% com pleteness lim it (plotted as
the red solid line) is,
log L15o(L0) = 1.372 (±0.045) x log Lir(Lo) - 10.625(±0.490). (12)
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A&A 631, A109 (2019)
Fig. 11. Histogram of the qIR values at 150 MHz using the definition in Eq. (10) and replacing the 1.4 GHz luminosity with the 150 MHz luminosity.
Fig. 12. qIR (150 MHz) values as a function of redshift for the RIFSCz- LOFAR matched sources.
and the logarithm o f SFR b ased on LI R for galaxies above the 90% com pleteness lim it is,
log L1 5 0 (Lq) = 1.372 (± 0.045) x log S FRi r (M 0 y r-1)
+ 3.092 (± 0.047). (14)
T he P earson correlation coefficient p is equal to 0.79 and th e p - value is 1.40 x 10-6 9. O ur best-fit linear relation b etw een log L1 5 o
and the logarithm o f SFR b ased on H a line lum inosity for g alax ies above the 90% com pleteness lim it is,
log L1 5 0 (Lq) = 1.351 (± 0.064) x log S F R ^ (MQ y r-1)
+ 3.202 (± 0.061). (15)
T he P earson correlation coefficient p is equal to 0.67 and th e p - value is 2.99 x 10-3 2. Thus, the relation betw een the logarithm o f the 150 M H z lum inosity an d the logarithm o f SFR is linear w ith a slope o f 1.3 over a dynam ic ran g e o f four orders o f m a g n itude in SFR. W e also show the b est-fit relations derived using all galaxies, i.e., including the fainter galaxies b elo w the co m pleteness lim it. T hese relations (plotted as dashed lines) show shallow er slopes.
T he b o tto m p anel in Fig. 13 com pares L1 5 0 w ith several SFR tracers for star-form ing galaxies from the second sam ple. D ue to the sm all sam ple size, w e do n o t attem pt to fit th e second sam ple b u t sim ply over-plot th e best-fit linear relations for the m ain sam ple. In the plot, w e also show the Pearson correlation coefficient p and p -value derived fo r th e galaxies above the 90%
com pleteness lim it in th e second sam ple.
Fig. 10. Top: correlation between the IR luminosity and the 150 MHz luminosity for the main sample, after excluding AGNs. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ~ 0.05) of the main sample. Bottom: same as top panel but for the second sample. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ~ 0 .12) of the second sample.
C alistro R ivera et al. (2017) and R ead et al. (2018) . W e do n o t see significant evidence for any red sh ift evolution although o ur sam p le is perhaps too low red sh ift to see any evolutionary effects.
W hen L oT SS is com pleted, th e areal overlap b etw e en IR A S and L oTSS w ill reach ~ 2 0 0 0 0 d e g 2. B y then, w e w ill have a m uch larger cross-m atched sam ple w hich w ill b e m ore adequate for detecting m ild red sh ift evolution effect, if it exists.
4.3. The rest-frame 150 MHz lum inosity as a SFR tracer In the top panel in Fig. 13, w e com pare th e rest-fram e 150M H z lum inosity L 150 w ith several SFR tracers fo r star-form ing g alax ies from the m ain sam ple. T he b lu e sym bols correspond to SFRs derived b ased on the total IR lum inosity Li r . T he re d sym bols correspond to SFRs provided in the R IF SC z b ased on L60 (see Sect. 2.1) . T he green sym bols correspond to S FR derived from the H a line lum inosity. G o o d agreem ent b etw een the various S FR estim ates are found. O ur best-fit linear relation b etw een log L 15o and the logarithm ic value o f SFR b ased on L60 for g alax ies above th e 90% com pleteness lim it is,
(13) lo g L1 5o (Lq) = 1 .3 1 2 (± 0 .0 5 0 ) x lo g S F R6 0(Mq y r-1)
+ 3.141 (± 0.055).
T he P earson correlation coefficient p is equal to 0.68 and the p - value is 2.38 x 10-43. O ur best-fit linear relation betw een log L 15o A109, page 10 of 12
L. Wang et al.: The far-infrared radio correlation
Fig. 13. Top: correlation between the rest-frame 150 MHz luminosity and various SFR tracers for the main sample, after excluding AGNs. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ~ 0.05) of the main sample. The solid lines are best-fit relations derived using only galaxies above the completeness limit. The dashed lines are best-fit relations derived using all galaxies.
Bottom: same as top panel but for the second sam
ple. The vertical dashed line indicates the 90% com
pleteness limit at the median redshift (z ~ 0.12) of the second sample.
- A linear and tig h t correlation betw een log LI R an d log L1 5 0
holds w ith a slope o f 1.37. O ur m edian qI R value is higher than the n um ber reported in C alistro R ivera e t al. (2017) . This is m ainly due to a large difference in the d istributions o f
LI R o f our sam ples.
- T he logarithm o f L1 5 0 correlates tightly w ith th e logarithm o f SFR derived from three tracers, including SFR derived from Ha line lum inosity, the rest-fram e 6 0p m lum inosity and LI R. B est-fit form ulae for the correlation betw een L1 5 0 and the three SFR tracers are provided, w hich are in excellent ag ree
m e n t w ith each other. T he logarithm ic slope ( ~ 1.3) o f the correlation betw een L1 5 0 and SFR suggests that the co rrela
tion is non-linear.
T he L oT SS S econd D ata R elease w ill include im ages and cat
alogues for 2500 deg2 o f the northern sky an d w ill be released b y 2020. T he all-sky IRA S survey allow s the m axim um areal overlap w ith LO FA R. A t the eventual com pletion o f L oT SS , the areal overlap betw een IRA S an d L oT SS w ill reach ~ 2 0 0 0 0 d e g2. Therefore, w e w ill b e able to n o t only rep e at the sam e analysis 5. Conclusions
In this paper, w e set o u t to study the FIR C in both the 1.4 G H z and the 150 M H z bands in the local U niverse as the m edian re d shift o f ou r m ain sam ple is a t z ~ 0.05, w ith the aim o f testing the use o f the rest-fram e 150 M H z lum inosity L1 5 0 as a SFR tracer.
W e cross-m atch the 60 p m selected R IF SC z catalogue and the 150 M H z selected LO FA R VAC in the H E T D E X spring field, using a com bination o f th e clo sest m atch m ethod an d the lik eli
hood ratio technique. W e also cross-m atch o ur sam ple w ith the 1.4 G H z selected F IR S T survey catalogue. W e estim ate L1 5 0 for the L O FA R sources and com pare it w ith the IR lum inosity, LI R, and several S FR tracers, after rem oving A G Ns. O ur m ain co n clusions are:
- A linear and tight correlation w ith a slope o f unity betw een log Li r an d log L1 4 holds. O ur m edian q value and scatter at 1.4 G H z for the m ain sam ple, w hich are 2.37 and 0.26, respectively, are consistent w ith previous studies such as Yun e ta l. (2001) .
A109, page 11 of 12
