The H-alpha luminosity function at redshift 2.2: A new determination using VLT/HAWK-I
aa r X i v : . [ a s t r o - ph . C O ] D ec Astronomy&Astrophysicsmanuscript no. half c (cid:13)
ESO 2018October 31, 2018 L etter to the E ditor The H-alpha luminosity function at redshift 2.2 ⋆ A new determination using VLT/HAWK-I
Matthew Hayes , Daniel Schaerer , , and G ¨oran ¨Ostlin Geneva Observatory, University of Geneva, 51 chemin des Maillettes, 1290 Sauverny, Switzerlande-mail: [email protected] Laboratoire d’Astrophysique de Toulouse-Tarbes, Universit´e de Toulouse, CNRS, 14 Avenue E. Belin, 31400 Toulouse, France Oskar Klein Center for Cosmoparticle physics, Department of Astronomy, Stockholm University, 10691 Stockholm, SwedenReceived September 01, 2009; accepted December 07, 2009
ABSTRACT
We aim to place new, strengthened constraints on the luminosity function ( LF ) of H-alpha (H α ) emitting galaxies at redshift z ≈ . ρ ⋆ ). We have used the new HAWK-I instrumentat
ESO-VLT to obtain extremely deep narrow-band (line;
NB2090 ) and broad-band (continuum; K s ) imaging observations. The targetfield is in the GOODS-South, providing us with a rich multi-wavelength auxiliary data set, which we utilise for redshift confirmationand to estimate dust content. We use this new data to measure the faint-end slope ( α ) of LF (H α ) with unprecedented precision. Thedata are well fit by a Schechter function and also a single power-law, yielding α = ( − . ± .
20) and ( − . ± . α from low- to high- z predicted by a number of authors and observed at other wavelengths.We combine our LF data-points with those from a much shallower but wider survey at z ∼ . LF spanning a factor of 50 in luminosity. Re-fitting the Schechter parameters, we obtain log L ⋆ = (43 . ± .
22) erg s − ; log φ ⋆ = ( − . ± .
52) Mpc − ; α = ( − . ± . LF (H α ) and apply a correction for dust attenuation to determine theinstantaneous cosmic star-formation rate density at z ∼ α or extrapolating it from lower- z . Our measurement of˙ ρ ⋆ is (0 . ± . M ⊙ yr − Mpc − , integrated over a range of 37 ≤ log( L H α / erg s − ) ≤ Key words.
Galaxies: evolution – Galaxies: high-redshift – Galaxies: starburst
1. Introduction
Since the evolution in the rate of cosmic star-formation was firstplotted (Lilly et al. 1996; Madau et al. 1996), the literature hasbeen awash with studies adding further points to the diagram.To estimate this quantity, one typically needs to find a num-ber of galaxies by a given method and estimate their densityin both space and luminosity (i.e. the luminosity function, LF ).Integration of LF · L · dL thus provides the volume-averaged lu-minosity density ( ρ L ) and, if L is a suitably calibrated measureof star-formation rate (SFR), ρ L converts directly into the volu-metric rate of star-formation ( ˙ ρ ⋆ ).A favourite tracer among low- z observers for estimating star-formation is the H α emission line due to its simple physics, highintrinsic brightness, and convenient rest-wavelength at 6563Å.At z & .
5, however, the H α line shifts out of the K − band, mak-ing it highly ine ffi cient for galaxy evolution studies. Fortunatelyat this z , selection by either the Ly α line or continuum ( BM / BX , BzK ) criteria becomes possible, but unfortunately a di ff erentpopulation of galaxies may be recovered, introducing biasesin selected star-formation rate / history, dust content, etc. Morespecifically with regard to SFR, continuum luminosities cometo equilibrium (and are therefore calibrated) over very di ff erenttime-scales to nebular lines: &
100 and ∼
10 Myr respectively,implying that lines are more sensitive to the instantaneous SFR(e.g. Kennicutt 1998). Ly α enables surveys to go much further in ⋆ Based on observations made with ESO Telescopes at the ParanalObservatory under programme ID 081.A-0932 redshift and has identical production physics, but is a resonanceline and undergoes a complex radiation transport, which rendersit an unreliable tracer of intrinsic properties. From a purely phys-ical perspective, H α is a far preferable tool.Luminosity functions are typically parameterised and com-pared using the Schechter function in which the luminositydistribution below (above) the characteristic luminosity, L ⋆ , isdominated by a power-law (exponential). When fitting, the threeSchechter parameters are degenerate, and strong constraints areonly obtained by sampling above and significantly below L ⋆ .Many attempts have been made to pin down LF (H α ) and itsevolution with redshift from z ≈ z (Yan et al. 1999; Hopkins et al. 2000;Tresse et al. 2002; Sobral et al. 2009; Shim et al. 2009), with thefirst z = z = L ⋆ , but does not permitan estimate of the faint-end slope.With the wide-field (7 . ′ × . ′ HAWK-I instrument(Pirard et al. 2004; Casali et al. 2006) at
ESO-VLT we have ob-tained the deepest narrowband H α observations to date as partof a programme to study H α and Ly α emitting galaxies froma single volume at z ∼ . α data alone enable us to study the faint-end of LF (H α ) at unprece- Φ ( L ) · d L = φ ⋆ · ( L / L ⋆ ) α · exp( L / L ⋆ ) · d L / L ⋆ Matthew Hayes et al.: The H-alpha luminosity function at redshift 2.2 dented depths, tightening constraints on the overall LF (H α ), andproviding the content of this Letter . In Sect. 2 we briefly de-scribe the data, reduction, and selection; in Sect. 3 we presentthe z ∼ α luminosity functions we derive and the constraintson ˙ ρ ⋆ ; and in Sect. 4 we briefly summarise. Throughout we adopta cosmology of ( H , Ω M , Ω Λ ) = (70 km s − Mpc − , . , . α ) calibration of Kennicutt (1998), derived for aSalpeter initial mass function in the mass range ( M lo , M hi ) = (0 . , M ⊙ and solar abundances, and the AB magnitude sys-tem (Oke & Gunn 1983).
2. The data
A field in the GOODS South (Giavalisco et al. 2004) was se-lected to maximise the depth and quality of the auxiliary data.The central pointing was α = δ = –27:47:16; p.a. = −
44 deg. The field was observed in service mode between 08September and 21 August 2008 on a single dithered pointing.The
NB2090 filter ( λ c = . µ m; ∆ λ = . µ m) was usedto isolate emission line candidates, using a total integration timeof 60 000 seconds. For the continuum we obtained 7 500 s in HAWK-I K s band, which we combined with the publicly avail-able ISAAC K s data from the GOODS / ESO Imaging Survey.Full details of the reduction process are beyond the scope ofthis
Letter and will be presented in a forthcoming article (Hayeset al. 2010). For brevity, the
EsoRex HAWK-I pipeline was usedon the individual frames for bias-subtraction, flat-fielding, andsubtraction of the sky with temporally adjacent image pairs.Custom scripts were then used to mask cross-talk artifacts, reg-ister and co-add the individual frames. We modelled the pointspread function (PSF) in the final image and determined a see-ing of 0.89 ′′ . To estimate the limiting magnitude we added arti-ficial point-sources (full width at half maximum set to the mea-sured seeing) to the images with the addstar task in noao/iraf and tested their recovery using SExtractor (Bertin & Arnouts1996; see Sect. 2.2). It should be noted that the limiting magni-tude for extended objects will be somewhat shallower, but alsothat at z = .
2, one seeing disc corresponds to a physical scaleof 7.4 kpc. Using
SExtractor mag auto magnitudes we de-termined a 5 σ limiting magnitude of 24.6 in NB2090 . By com-puting the product of this flux density and ∆ λ NB , this corre-sponds to a line flux of 6 . × − erg s − , if all the NB2090 fluxcomes from H α and falls at the peak of the filter throughput. Thisassumption, valid for perfect top-hat bandpasses, holds well forour bandpass, which has steep edges by narrowband standards:the full width at 80% transmission is over 80% the FWHM. Thislimiting flux corresponds to SFR = . M ⊙ yr − . The K s σ limitis 25.4. Source detection was performed in the on-line image using
SExtractor , where we required a minimum of 12 contiguouspixels (plate-scale = . ′′
106 px − ) to reside above the backgroundnoise by a signal–to–noise ( S / N = K s photometry was performed using “double image” mode. We se-lected emission line candidates based upon two criteria, the firstof which was a minimum rest-frame equivalent width, EW H α = K s -faint objects scattering into the colour-selection region, werequired the narrowband flux to be a factor of Σ =
Fig. 1.
The selection function for candidate H α emitters. Blackdots represent all the objects detected in the NB2090 image. Thered dashed line shows the colour cut of EW H α =
20 Å, and thegreen solid line the limit of
Σ =
5. The blue points show theselected candidate galaxies. The inset histogram shows the nar-rowband magnitude distribution of all candidate emission linegalaxies in blue, and confirmed z ≈ . α emitters after therejection of interlopers (see text) in magenta.magnitude selection diagram, including the cuts in EW H α and Σ . After inspecting each candidate by eye, we found 152 objectsthat could potentially be emitters of any emission line betweenPa α at z ≈ .
11 and Ly α at z ≈
16. We then cross-correlated ourcandidates with the merged z − and K s -selected GOODS-MUSIC catalogue of Santini et al. (2009), finding 143 matches. The ob-jects for which counterparts were not detected all appear to begenuine narrowband-excess objects, but with equivalent widthlower limits so high that their stellar continua are too faint tobe detected in the
ISAAC K s or ACS z − band images. GOODS-MUSIC provided us with spectral energy distributions (SEDs)between the U − band and Sptizer -MIPS 24 µ m. To assemble thefinal catalogue we first examined the spectroscopic redshift mea-surements in the GOODS-MUSIC catalogue. If the spec- z had aquality flag of “very good” or “good” and was consistent with theredshift interval defined by the NB2090 bandpass (2 . < z < . z range(26 galaxies). This ratio of 26 galaxies excluded versus one in-cluded may superficially appear to show the selection method ina rather negative light, but the bias can easily be explained byconsidering the selection methods of the many studies that fol-lowed up the GOODS imaging spectroscopically. We searchedthe spectroscopic catalogues for all galaxies in GOODS-MUSIC with spec- z in the range covered by FWHM NB and spec- z flags of good or better, finding only a single object that could bedetected by our survey: the one we do find, followed up from BzK selection. In contrast the catalogue is rife with spectra tar-geting the z = − z > . z = − z ∼ . iii ]; low- z Pa α ,Pa β and lines in the higher order Brackett series; and z ∼ . ii ] emitters, although a handful of more unknown or inter-esting lines are also recovered. The number of emission linecandidates is of su ffi cient interest to warrant further examina-tion, which will be the topic of a forthcoming paper. For ob-jects with no spec- z or an uncertain flag, we used the Hyper- atthew Hayes et al.: The H-alpha luminosity function at redshift 2.2 3
Fig. 2.
Left : H α luminosity functions. The black points show the bins created from HAWK-I data obtained for our programmewith error-bars derived from Poisson statistics and Monte Carlo incompleteness simulations. The best-fit Schechter function isshown by the black solid line, while the black dotted line represents the best fitting simple power-law. Other lines show variousluminosity functions from the literature, scaled to our cosmology. H00 = (Hopkins et al. 2000, all points), G08 = Geach et al. (2008),G95 = Gallego et al. (1995), T02 = Tresse et al. (2002), So09 = Sobral et al. (2009). Sh09 = Shim et al. (2009). Dashed vs. solid repre-sentation shows the 3 σ limiting survey depth. Right : The complete luminosity function combining these
HAWK-I data with thepoints from G08. The shaded cyan area shows the LF (H α ) derived by Reddy et al. (2008) from the modelling of < z > = . z photometric-redshift code (Bolzonella et al. 2000), modifiedto include nebular continuum and lines (Schaerer & de Barros2009). Here we selected objects that had 1 σ errors on their phot- z consistent with z = .
19. Combined with the spectroscopicallyconfirmed objects this gave us 55 z ≈ . α -emitters. For se-curity, we tested our galaxies against the BzK colour criterion of( B − z ) − ( z − K ) ≥ − . z ≥ .
4. Onlyfour of our 55 objects do not satisfy this criterion, but when ex-amining the
BzK colours of the entire narrowband-excess sam-ple (143) we found an additional 7 objects that do. We note alsothat the
BzK criteria neglect the fact that the B and K photometrymay be contaminated by the Ly α and H α emission lines, respec-tively. Since the number of objects that are classified / declassifiedby BzK colours are ( i. ) so similar, ( ii. ) only a small ( ∼ iii. ) possibly contaminated by lines, weopt to leave our phot- z selected sample unchanged. Finally, wecross-correlated our sample against the 1 Mega-second Chandra
Catalogue (Giacconi et al. 2002; Rosati et al. 2002), but no ob-jects in which the H α production is obviously dominated byan active nucleus were found, including the objects missed bybroadband cross-correlation. Our final catalogue comprises 55objects.
3. Results and Discussion
All H α photometry is corrected for the contribution of[N ii ] λλ , ii ] / H α ra-tio varies strongly with metallicity ( Z ) between ∼ ii ] / H α may plausibly be estimated from L H α through theluminosity–metallicity relationship. However a significant o ff set Table 1.
Luminosity function parameters
Param. Unit HAWK-I all a HAWK-I α b Combined c log L ⋆ erg s − . ± .
56 ... 43 . ± . φ ⋆ Mpc − − . ± .
94 ... − . ± . α ... − . ± . − . ± . − . ± . a HAWK-I data only. b α only: HAWK-I data only. c HAWK-I data + G08 points. in the L − Z relationship is found at z ∼ z ≈ ii ] / H α = . LF (H α ) is created by binning all selected objects by lumi-nosity, with errors derived from the standard Poisson statistic andMonte Carlo simulations of incompleteness. We fit the Schechterfunction using a standard χ minimiser, determining errors from1 000 re-drawn Monte Carlo realisations. The best-fit Schechterparameters are presented in Table 1 and are shown graphicallywith other determinations from the literature in Fig. 2.The brightest galaxy in our sample has a luminosity of3 . × erg s − , which is a factor of 4.5 fainter than the value of L ⋆ we derive, and even allowing for the error on L ⋆ , we clearlyare not probing this luminosity domain. This galaxy is a factorof 2 fainter than the L ⋆ = . × erg s − derived by G08and demonstrates the inadequacy of such a small survey to con- Matthew Hayes et al.: The H-alpha luminosity function at redshift 2.2
Fig. 3.
The cosmic star-formation rate density. Open grey pen-tagons show all of the dust-corrected points compiled byHopkins (2004) that were derived from anything other than H α .Filled red squares show dust-corrected points from Shim et al.(2009), all of which are H α -based. The black point is the mea-surement from this study and the open blue point is the resultfrom G08, artificially shifted to higher- z to allow it to be distin-guished from our own.strain all Schechter parameters. Indeed, the statistical error onthe degenerate parameter φ ⋆ spans an entire dex and it is appar-ent that the only parameter we can reliably constrain is α , sinceall our H α emitters have luminosities that place them firmly inthe power-law region of the LF . For security, we proceed to ex-amine the faint-end only by fitting of a simple power-law, usingexactly the same Monte Carlo realisation data as previously. Ourderived faint-end slope is found to be − . ± .
21, also presentedin Table 1, and exhibits a near-identical mean and errorbar.Some authors find a steepening in the faint end slope of LF (H α ) moving from z = z & z = z = α for H α emitters at z ∼ . HST / NICMOS , with α = − .
60 or 1.86depending on the selection criteria. However, Trenti & Stiavelli(2008) note that for such small field–of–view studies, an arti-ficial steepening of the faint-end slope may manifest itself ifunder-dense regions are targeted. Examining the redshift distri-bution of galaxies in the whole GOODS field using both spec- z and phot- z reveals z = . α = − . ± . σ level with respectto Gallego et al. (1995) ( z = α = − .
35, and ourresults are consistent with no evolution within 1 σ to z = . α = − .
65; Sobral et al. 2009) and 0 . . z . . α = − . LF ( H α ) and thestar-formationrate density As stated above, our data are not su ffi cient to constrain thebrighter end of LF (H α ). To address this we take the LF (H α )data-points from G08 and combine them with our own. We ex-tract the LF data-points, which have been corrected for the [N ii ] using the z ∼ z ∼ LF can be seen in the right panelof Fig. 2 with the best-fitting Schechter parameters, derived fol-lowing exactly the same method as in Sect. 3.1 in Table 1. Wealso show an estimate of the observed (i.e. dust-uncorrected) LF (H α ) at < z > = . α ) and re-applying the e ff ects of dust attenuation toH α . The observed and inferred LF (H α ) agree well in general,particularly around L ⋆ , with only a mild deviation at the faintand (unsampled) bright ends.In order to estimate the cosmic star-formation rate density,we need to correct our H α fluxes for dust attenuation. To do thiswe re-fit the SEDs of all the H α -emitters, fixing their redshift to2.19. Ideally we would correct our luminosity function bin bybin, but no obvious correlation is observed between L H α and A V .Thus we adopt the average A V for the sample of 1 . ± . ff ects of di ff erential at-tenuation of stellar and nebular light, since at z ∼ α ) without this fac-tor. A V = .
19 equates to A = .
977 for the fainter bins in LF (H α ), identical to the assumption of 1 mag used by G08 at thebrighter end, and we correct for 1 mag of attenuation through-out. It is noteworthy that Reddy et al. (2008) find a maximumlikelihood E B − V of 0.12 ( A = .
4, Calzetti dust) for BX –selected galaxies at < z > = .
3. The significantly di ff erent ex-tinction determined from H α selection may be due to the verydi ff erent selection functions: indeed EW H α is independent ofdust extinction, whereas BX selection cuts the multi-broadbandsample based on U − G colours, and thus it is not unreason-able to infer that galaxies with very di ff erent extinctions sur-vive the respective cuts. The errors derived on the Schechterparameters are strongly correlated, and thus we compute ˙ ρ ⋆ from each of the raw Monte Carlo realisations previously de-scribed. For consistency with Hopkins (2004) we integrate overthe luminosity range 37 ≤ log( L H α / erg s − ) ≤
47, where wefind a value of ρ L = (2 . ± . × erg s − Mpc − and˙ ρ ⋆ = (0 . ± . M ⊙ yr − Mpc − . This however repre-sents a significant extrapolation over luminosity, and we alsopresent the same integration performed over the range coveredby our bins in total LF (H α ): 41 . ≤ log( L H α / erg s − ) ≤ . ρ L = (1 . ± . × erg s − Mpc − and˙ ρ ⋆ = (0 . ± . M ⊙ yr − Mpc − . We show the resultin Fig. 3, along with two compilations of ˙ ρ ⋆ from the litera-ture. We include the dust-corrected H α survey data compiled byShim et al. (2009), and points from the Hopkins (2004) compi-lation based upon many di ff erent observations where we haveexcluded all determinations based upon H α . We also indicateseparately the point of G08, which has been artificially movedin redshift to separate it from our own. Our point agrees wellwith that of G08, which is initially surprising, given that we ob-tain a significantly steeper faint-end slope and marginally higher L ⋆ . The culprit behind the similar ˙ ρ ⋆ yet di ff ering ( L ⋆ , α ) is nat-urally the overall normalisation of the luminosity function, φ ⋆ ,which we calculate to be a factor of 4 lower. Furthermore the er-rorbar produced by our analysis is actually larger than that pub-lished by G08, despite our LF extending an order of magnitudefainter in luminosity. These errorbars, however, are statistical er-rors that result from averaging over many Monte Carlo realisa-tions, and our fitting engine includes an additional parameter ( α )– fixing one parameter introduces a systematic error that is not atthew Hayes et al.: The H-alpha luminosity function at redshift 2.2 5 accounted for by Monte Carlo. Had we locked α to its best-fitvalue and fitted L ⋆ and φ ⋆ as usual, our statistical errorbar on˙ ρ ⋆ would be a factor of 3 smaller. Finally it is possible that ourselection criterion of EW H α >
20Å could cause us to underes-timate the total luminosity density. To assess the impact of thiswe examine the EW H α distribution of our sample and fit an expo-nential of the form N ∝ exp( EW / EW ), finding EW H α, = EW H α to be independent of L H α and also of the continuum luminosity, we find that our selectioncriterion misses between 1.3 and 16% of the integrated luminos-ity. We also examine the EW H α distribution of nearby galaxiesin the Sloan Digital Sky Survey , selecting the complete spectro-scopic sample at z < .
1, and find that removal of galaxies with EW H α <
20Å cuts 19% of the H α luminosity density.
4. Summary
We have used the new
HAWK-I instrument mounted at
ESO-VLT to carry out a blind, narrowband survey for H α emitting galaxiesat a redshift of 2.2. This is the deepest unbiased survey carriedout at this redshift to date and enables us to estimate the faint-end of the H α luminosity function, a parameter hitherto merelyassumed at this cosmic epoch. The target is the GOODS-Southfield, o ff ering us a rich, deep multi-wavelength ancillary data-set, in which we find 55 H α emitters.1. We construct a luminosity function from the HAWK-I datawhich we find is well fit by a Schechter function with pa-rameters of log L ⋆ = (43 . ± .
56) erg s − , log φ ⋆ = ( − . ± .
94) Mpc − , α = ( − . ± . α = ( − . ± . z =
2, which is predicted and observed at other wave-lengths.2. We combine our luminosity function bins with those fromthe much wider but shallower survey of G08, which yieldsthe best-sampled H α luminosity function at this redshift.This is also well described by a Schechter function with theparameters of log L ⋆ = (43 . ± .
22) erg s − , log φ ⋆ = ( − . ± .
52) Mpc − , α = ( − . ± . . ± . M ⊙ yr − Mpc − . This provides the most robustemission-line estimate to date at this redshift. Acknowledgements.
M.H. & D.S. are supported by the Swiss National ScienceFoundation. G¨.O. is Royal Swedish academy of Sciences Research Fellow, sup-ported by a grant from the Knut and Alice Wallenberg Foundation and acknowl-edges support from the Swedish Research Council. We thank Naveen Reddyfor making specific LF (H α ) realisations available, Hyunjin Shim for sharing thecompilation of literature ˙ ρ ⋆ values. We thank Claudia Scarlata for useful dis-cussions. Finally we thank the anonymous referee for thoroughly dissecting themanuscript and suggesting numerous improvements. References
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