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A 1200 micron MAMBO Survey of ELAIS N2 and the Lockman Hole I. Maps, sources and number cou

A 1200 micron MAMBO Survey of ELAIS N2 and the Lockman Hole I. Maps, sources and number cou
A 1200 micron MAMBO Survey of ELAIS N2 and the Lockman Hole I. Maps, sources and number cou

a r X i v :a s t r o -p h /0405361v 1 18 M a y 2004

Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 2February 2008

(MN L A T E X style ?le v2.2)

A 1200μm MAMBO survey of ELAIS N2and the Lockman Hole:I.

Maps,sources and number counts

T.R.Greve 1,R.J.Ivison 1,2,F.Bertoldi 3,J.A.Stevens 2,J.S.Dunlop 1,D.Lutz 4&C.L.Carilli 5

1Institute for Astronomy,University of Edinburgh,Blackford Hill,Edinburgh EH93HJ,UK 2Astronomy Technology Centre,Royal Observatory,Blackford Hill,Edinburgh EH93HJ,UK 3Max-Planck-Institut f¨u r Radioastronomie(MPIfR),Auf dem H¨u gel 69,53121Bonn,Germany 4Max-Planck-Institut f¨u r extraterrestrische Physik,Postfach 1312,85741,Garching,Germany 5

National Radio Astronomy Observatory,P .O.Box O,Socorro,NM 87801,USA

2February 2008

ABSTRACT

We present a deep,new 1200μm survey of the ELAIS N2and Lockman Hole ?elds using the Max Planck Millimeter Bolometer array (MAMBO).The areas surveyed are 160arcmin 2in ELAIS N2and 197arcmin 2in the Lockman Hole,covering the entire SCUBA ‘8mJy Sur-vey’.In total,27(44)sources have been detected at a signi?cance ≥4.0σ(≥3.5σ).The pri-mary goals of the survey were to investigate the reliability of (sub)millimetre galaxy (SMG)samples,to analyse SMGs using ?ux ratios sensitive to redshift at z >3,and to search for ‘SCUBA drop-outs’,i.e.galaxies at z >>3.We present the 1200μm number counts and ?nd evidence of a fall at bright ?ux levels.Employing parametric models for the evolution of the local 60μm IRAS luminosity function (LF),we are able to account simultaneously for the 1200and 850μm counts,suggesting that the MAMBO and SCUBA sources trace the same underlying population of high-redshift,dust-enshrouded galaxies.From a nearest-neighbour clustering analysis we ?nd tentative evidence that the most signi?cant MAMBO sources come in pairs,typically separated by ~23′′.Our MAMBO observations unambiguously con?rm around half of the SCUBA sources.In a robust sub-sample of 13SMGs detected by both MAMBO and SCUBA at a signi?cance ≥3.5σ,only one has no radio counterpart.Further-more,the distribution of 850/1200μm ?ux density ratios for this sub-sample is consistent with the spectroscopic redshift distribution of radio-detected SMGs (Chapman et al.2003).Finally,we have searched for evidence of a high-redshift tail of SMGs amongst the 18MAMBO sources which are not detected by SCUBA.While we cannot rule out that some of them are SCUBA drop-outs at z >>3,their overall 850-to-1200μm ?ux distribution is statistically indistinguishable from that of the 13SMGS which were robustly identi?ed by both MAMBO and SCUBA.

Key words:cosmology:early Universe –cosmology:observations –galaxies:evolution –galaxies:formation –galaxies:starburst

1INTRODUCTION

In a time of ‘high-precision cosmology’one of the fundamental questions about which we remain largely ignorant is the forma-tion and evolution of galaxies and clusters of galaxies.One of the most important breakthroughs in this ?eld was the discovery of a signi?cant population of far-IR-luminous,high-redshift sources in surveys at submillimetre (submm)and millimetre (mm)wave-lengths using SCUBA and MAMBO (Smail,Ivison &Blain 1997;Hughes et al.1998;Barger et al.1999;Eales et al.2000;Bertoldi et al.2000),resolving at least half of the far-IR/submm background detected by the DIRBE and FIRAS experiments (e.g.Hauser et al.1998).

It is widely believed that the large far-IR luminosities (>~10

12

L ⊙)of these sources is caused by intense UV light from starbursts and/or active galactic nuclei (AGN)being absorbed

by dust and re-radiated longwards of 100μm .The negative k -correction at λ≥400μm allows submm/mm observations to select

star-forming galaxies at z >1in an almost distance-independent manner,providing an ef?cient method of ?nding obscured,star-forming galaxies at 1

The large star-formation rates (~1000M ⊙yr ?1)found for (sub)mm galaxies (hereafter SMGs)are suf?cient to construct a gi-ant elliptical (~1011M ⊙)in less than a Gyr,providing that the starburst is continuously fueled.This has led people to speculate that SMGs could be the progenitors of such galaxies (e.g.Dunlop 2001),a scenario which is further strengthened by the fact that the co-moving number density of SMGs appears to be consistent with that of today’s massive ellipticals (Scott et al.2002;Dunne,Eales &Edmunds 2003).However,the nature of SMGs,and in particu-lar their relationship with possible present-day counterparts,is not

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known,just as their relation to other high-redshift populations such as Lyman-break galaxies(LBGs)and extremely red objects(EROs) is not well understood.

Progress has been hampered by the large positional uncertain-ties of the SMGs.The relatively large beams of(sub)mm telescopes (11–14′′,FWHM)makes it impossible to reliably tie an SMG to an optical or near-IR counterpart,unless additional data at a com-plementary wavelength are available.Since a characteristic feature of both starburst galaxies and AGN is radio emission,deep radio imaging has proven to be a highly ef?cient way of accurately iden-tifying optical/near-IR counterparts to SMGs(Ivison et al.1998, 2000,2002;Smail et al.2000).

Use of the radio-to-submm spectral index as an redshift indi-cator(Hughes et al.1998;Carilli&Yun1999,2000)has shown that the SMGs lie at high redshift,with an estimated median red-shift of≥2(Ivison et al.2002).Recently,Chapman et al.(2003, 2004)have obtained spectroscopic redshifts for~90SMGs and found they span0.8

In a very deep radio survey of the Lockman Hole and ELAIS N2?elds,Ivison et al.(2002)found that about one third of SMGs did not have radio counterparts.One plausible explana-tion was that some of these radio-blank SMGs lie at very high red-shifts.Such a population of SMGs—the so-called‘high-redshift tail’—would ask dif?cult questions of popular hierarchical mod-els.The high-redshift SMGs would have low S850μm/S1200μm?ux ratios(see Eales et al.2003)and would be readily detectable with MAMBO.

Blain,Barnard&Chapman(2003),amongst others,have pointed out the limitations of photometric redshift techniques:the redshift is degenerate with the far-IR luminosity as parametrised by the dust temperature,T d.In principle,however,a comparison be-tween the850,1200μm and1.4-GHz?ux densities allows us,in some cases at least,to break this degeneracy,assuming that SMGs follow the radio/far-IR correlation.For example,an SMG which has a’warm’S850μm/S1200μm ratio but has no radio counterpart is likely to be at high redshift.The S850μm/S1200μm redshift es-timator is particular sensitive at z>3and is currently the most effective way to assess whether there is a signi?cant high-redshift tail of SMGs.

The primary advantage of a mapping survey,rather than pointed photometry(on–off)observations of known sources (e.g.Eales et al.2003),is that one obtains an unbiased view of the sky.Data are not skewed by the choice of targets,by possible errors in coordinates,or by potentially spurious assumptions about how the sky is expected to appear.A key goal of our new survey was to determine unbiased?ux densities for the radio-blank SCUBA sources using MAMBO,and to search for new populations of mm-bright sources,in particular a sign of a dusty,star-forming z>>5 population—‘SCUBA drop-outs’—that would be expected to be below the typical SCUBA detection threshold at850μm but de-tectable by MAMBO at1200μm.

In this paper we present a new,unbiased1200μm survey, using MAMBO on the IRAM30m telescope,of the Lockman Hole and ELAIS N2,the two regions observed by the SCUBA 8mJy survey(Scott et al.2002;Fox et al.2002).A plethora of multi-wavelength observations exist for both?elds,including very deep X-ray,optical,near-IR,mid-IR and radio imaging(Hasinger et al.2001;Manners et al.2002;Ivison et al.2002;Almaini et al.2002).Our observations,data reduction and maps are described in§2and3.The source extraction technique and the source cata-logues for each?eld are presented in§4,as are the results of Monte Carlo simulations to assess completeness,positional accuracy,?ux boosting,etc.In§5and6we present our measurements of the source counts and the clustering properties of MAMBO sources. Finally,§7describes our joint analysis of the850and1200μm sam-ples,and implications for ongoing(sub)mm surveys and for the redshift distribution of SMGs.

Throughout,we have adopted a?at cosmology,with?m= 0.3,?Λ=0.7and H0=70km s?1Mpc?1.

2OBSERV ATIONS

The survey was carried out with the37-and117-channel MPIfR Max Planck Millimeter Bolometer arrays(MAMBO-I and MAMBO-II;Kreysa et al.1998)at the IRAM30m telescope on Pico Veleta near Granada in Spain.Both MAMBO-I and MAMBO-II are He3-cooled arrays operating at an effective frequency of 250GHz or1200μm with a half-power spectral bandwidth of 80GHz.At1200μm,the30m telescope has an effective beam of 10.7′′(FWHM).The arrays are background limited and the perfor-mance of the array routinely gives noise equivalent?ux densities (NEFDs)of30–45mJy Hz?1/2.The bolometer feedhorns are ar-ranged in a compact hexagonal pattern each with a diameter of2Fλwhich ensures an optimal coupling to the incoming radiation from a point source.MAMBO-II is amongst the largest(sub)mm bolome-ter arrays currently in use.In combination with the IRAM30m dish which has a surface accuracy of75μm rms,it is the most powerful tool for large blank-?eld surveys at(sub)mm wavelengths,and will remain so until the advent of APEX/LABOCA,JCMT/SCUBA2 and LMT/Bolocam.

Scan-mapping along the azimuthal direction is the only method available at the30m to map large areas of the sky.The signal from the sky is modulated by the secondary mirror(the wobbler)which is wobbling in the the scan direction(azimuth). The wobbler frequency is2Hz which re?ects a compromise be-tween wanting to eliminate changes in the atmosphere on as short a timescale as possible and the challenges involved in moving a 2m secondary at this frequency and keeping it mechanically sta-ble.We used a standard on-the-?y MAMBO scan-map,typically 300′′×320′′in size,scanned at a velocity of5′′s?1,and with an elevation spacing between each subscan of8′′.Hence,a map con-sists of41subscans of60s each.This results in a fully-sampled map over a300′′×320′′region in~43min(this includes~3s of overhead per subscan).In order to obtain uniform coverage,a reg-ular grid with a grid-spacing of2′was de?ned across each of the two?elds.Each grid position was observed once which in prac-tice means that,in the?nal map,each point on the sky has been observed at least two times.In principle,this ensures that an rms of~0.8mJy beam?1is reached across most of the?eld.In prac-tice,however,scans were taken in slightly different weather condi-tions which means that the noise is not entirely uniform.In order to eliminate any possible systematics and any residual effects from the double beam pro?le,wobbler throws in the range36′′?45′′were used.Furthermore,maps were taken with different scan-directions, just as care was taken to map each grid position once while the ?eld was rising and once while it was setting.All this served the purpose of minimising any systematic effects from the atmosphere and/or instrument which may otherwise had arisen from observ-ing the same grid-position in two consecutive maps using identical wobbler-and scan-con?guration.

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A1200μm MAMBO Survey of the ELAIS N2and Lockman Hole:I

3

Figure1.The MAMBO survey regions(outlined in black)of the ELAIS N2and Lockman Hole?elds.The mapped areas are160and197sq.arcmin in ELAIS N2and Lockman Hole,respectively.For comparison,the coverage of the SCUBA UK8mJy Survey(Scott et al.2002)is also shown(grey curve).The boxes are21′.7×21′.7.

The two?elds were only observed when above30o and below 70o in elevation.The latter constraint,which avoids distorted scan-maps,was particularly troublesome for the ELAIS N2?eld which reaches a maximum elevation of85o at Pico Veleta.

Since observations were pooled,they were done only under good weather conditions,i.e.when the atmospheric zenith opacity at1200μm was less than0.3,with low sky-background variations. After each map,i.e.every hour,the telescope was pointed and fo-cused.The opacity of the atmosphere was measured every other hour by doing a skydip but was also continuously monitored with a radiometer located next to the telescope.Variations in the sky-background were monitored from the pointings by on-line mea-surements of the correlation of the horns across the array.Also quick on-offs of the pointing sources were done throughout the night in order to check the sky noise and calibration.In order to tie down the absolute?ux calibration,primary?ux calibrators(in-cluding planets when available)were observed at the beginning and end of each run,and resulted in an absolute?ux calibration of better than20per cent.

In total,34scan-maps,corresponding to26hrs,went into the ?nal map of ELAIS N2,all of which were obtained with MAMBO-II as part of the pooled observing mode during the winter period of the2001-2002and2002-2003seasons.The bulk of the obser-vations of the Lockman Hole were also obtained during that time using MAMBO-II,although,early observations of the Lockman Hole during the winter of2000–01,and to some extent also2001–02,were obtained with the37-channel MAMBO-I array.For the Lockman Hole,19and51scan-maps taken with MAMBO-I and MAMBO-II,respectively,were used for the?nal map,equivalent to a total integration time of53hr.

The areas surveyed were160arcmin2in the ELAIS N2?eld and197arcmin2in the Lockman Hole.In the case of ELAIS N2 the MAMBO observations were designed to cover the region ob-served at850μm as part of the SCUBA UK8mJy Survey(Scott et al.2002).The small fraction of the SCUBA map which is not covered by our observations(Fig.1)is also the most noisy,and no 850μm sources were detected in that region.However,in the Lock-man Hole the overlap between MAMBO and SCUBA observations is complete,as is seen from Fig.1.The Lockman Hole MAMBO data presented in this paper are part of the larger area MAMBO Deep Field Survey(Bertoldi et al.2000;Dannerbauer et al.2002; Bertoldi et al.2004,in prep.).In addition,the Lockman Hole is being targeted by SCUBA as part of the SCUBA Half Degree Ex-tragalactic Survey(SHADES—https://www.wendangku.net/doc/087746564.html,/ifa/shades/), and the data presented here constitute only a small part of the area surveyed at(sub)mm wavelengths in that part of the sky.

3DATA REDUCTION

The data were reduced using the MOPSI software package(Zylka 1998).Bolometers which were either dead or very noisy were ?agged from the data reduction,and the remaining data streams were de-spiked,?at-?elded and corrected for atmospheric opacity.

Since all bolometers look through the same region of the at-mosphere at any given time,there will be a correlated signal across the array which will have to be removed in order to recover the (uncorrelated)astronomical signal.In MOPSI the removal of this correlated sky background is done in an iterative way.For each bolometer an inner and outer radius from the channel is speci?ed, and the correlation with every bolometer lying within this annulus is computed.In our case,we chose an inner and outer radius of1′′and60′′,respectively,which is suitable for compact weak sources. The correlated signals of the surrounding6channels with the best correlation were then chosen and the average correlated noise sub-tracted from the bolometer in question.This procedure is then re-peated until the sky background has been removed satisfactorily across the array.

Up until this point in the data reduction,the signal from each chopping position(called the on and off phase)was processed sep-

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4Greve et al.

arately,the reason being that in a single phase the bolometers cor-relate much better which results in a much more reliable subtrac-

tion of the background.MOPSI then calculated the phase difference,

thereby effectively removing any electronic systematics between the data obtained in one wobbler position and the other.Additional

de-spiking and baseline-?tting was then done on the phase differ-

ences,from which the weights for each bolometer were calculated.

Finally,the data were restored and rebinned using a shift-and-

add technique which for each map produces a positive image brack-

eted by two negative images of half the intensity located one wob-bler throw away.The rebinning was done onto a grid of1square

arcsec pixels,with the?ux in each pixel being a noise-weighted

average of the bolometers hitting that position.MOPSI also out-

puts a weight image,W,which at pixel position(i,j)is given by W(i,j)= k1/σ2k,i.e.the error on the noise-weighted aver-age,where k denotes summing over the bolometers’seen’by pixel

(i,j).

The noise maps are shown in Figure2.The rms noise in the

deepest parts of the maps is~0.6mJy beam?1,increasing towards

the edges.The Lockman Hole received more integration time than the ELAIS N2?eld and as a result it is slightly deeper and has more uniform noise properties than the latter.

4SOURCE EXTRACTION AND MONTE CARLO SIMULATIONS

4.1Source extraction

Scan-mapping is the only option for large area mapping at the IRAM30m telescope,and as a result the chopping direction is not ?xed on the sky but varies with time which means that the chops are smeared out in the?nal map.Hence,unlike SCUBA jiggle maps, one cannot utilise the extra information contained in the position of the negative side-lobes for source extraction.Instead,a simple matched-?ltering technique was adopted,using a Gaussian as the ?lter.However,as is seen from the noise images shown in Figure 2,the noise is not entirely uniform across the two?elds and any attempt at extracting sources has to take this into account.This was done by adopting a noise-weighted convolution technique similar to that of Serjeant et al.(2003).In order to account for the10.7′′beam and the typical pointing error of3′′rms,a Gaussian PSF, P(x,y),with a FWHM of

x,y W(i?x,j?y)P(x,y)2.(2) The error on the?ux can then be shown to be:

?F(i,j)=

1

x,y W(i?x,y?j)P(x,y)2.(3)

The signal-to-noise images,F/?F,obtained in this way are shown in Figure3and4for the ELAIS N2?eld and Lockman Hole,re-spectively.The?nal source catalogues for ELAIS N2and the Lock-man Hole are listed in Table1and2.We?nd a total of13sources at signi?cance≥4.0σ,and21sources with≥3.5σin the ELAIS N2 region while the number of sources in the Lockman Hole are14 and23at≥4.0σand≥3.5σ,respectively.

4.2Monte Carlo Simulations

Extensive Monte Carlo simulations were performed in order to de-termine the reliability of the source extraction technique,i.e.how large a fraction of the extracted sources are due to spurious noise peaks,and how well does the extraction reproduce?uxes and posi-tions as a function of signal-to-noise?Due to the slight difference in survey depth and also geometry between the ELAIS N2and Lock-man Hole maps,we decided to perform separate Monte Carlo sim-ulations for each of the two?elds.

In order to assess the contamination from spurious noise peaks to the source catalogues,we produced maps based on the real data but with the astrometry corrupted.This was done by randomising the array parameters of each scan and then producing?nal maps using the same MOPSI data reduction pipeline as for the real map. The advantage of this method is that the correlated noise in the raw data is preserved,and is taken out during the data reduction process in the same manner as for the real map.As a result,this method should give a realistic picture of the number of spurious noise peaks expected in our maps.We produced100such astromet-rically corrupted maps and counted the number of positive spurious sources as a function of detection threshold.The results are shown in Figure5with empty and?lled circles referring to the ELAIS N2 and Lockman Hole maps,respectively.As expected,the number of spurious detections drops off exponentially as a function of signal-to-noise threshold.From Figure5we?nd that a threshold of4.0σresults in less than one spurious source expected at random,while a cut-off at3.5σyields less than2spurious sources per?eld.We adopt3.5σas the detection cut-off for sources in both?elds since it provides a good compromise between catalogue size and source reliability.

Monte Carlo simulations were also used to test the complete-ness and reliability of the?ux and position estimates.Sources in the?ux range1–12mJy were added to the map in steps of0.5mJy, one at a time and each at a random position,with50sources in each ?ux bin.We used a scaled beam pattern as the template for the arti-?cial sources.However,due to sky-rotation,the double-beam pro-?le varies across the map and as a result a separate multi-beam PSF had to be constructed for each source,depending on its position in the map.To accomplish this,the source—with its correct intensity and position—was added to the data stream and then the data were reduced in the same manner as the real data.Thus,each arti?cial source added to the map had exactly the right multi-beam pro?le corresponding to its position in the map.Finally,sources were ex-tracted using the same detection threshold as used for the real map. If a simulated source happened to fall within half a beam width of a real source in the map,it was discarded from the analysis.The results from these Monte Carlo simulations are shown in Figure6, again with open and?lled circles representing results based on the ELAIS N2and Lockman Hole?elds,respectively.

Figures6a and b show the completeness of the survey,i.e.the percentage of recovered sources in our Monte Carlo simulations as a function of input?ux density.As expected the source extraction does well in extracting all of the brighter sources,but fares less well for sources close to the detection threshold.In both?elds the completeness is seen to be~50per cent at a?ux level of?2.5mJy, increasing to about95per cent at3mJy.The solid curves are best ?ts of the function f(S in)=1?exp(A(S in?B)C).

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A 1200μm MAMBO Survey of the ELAIS N2and Lockman Hole:I 5

Figure 2.Noise maps of the ELAIS N2and Lockman Hole East ?elds.Contours are at 0.7,0.8...1.5mJy beam ?1.The axes denote the offset (arcsec)from the map centre,and the intensity scale is in units of mJy beam ?1.

Table 1.1200μm MAMBO source catalogue in the ELAIS N2?eld.The rms noise in the centre of the map is ~0.65mJy beam ?1and increases towards the edges.The area surveyed in the ELAIS N2?eld is 160arcmin 2.

ID MAMBO ID RA (J2000)Dec (J2000)S 1200μm ±σ1200μm S/N

MM J163647+4054N21200.116:36:47.9+40:54:464.0±0.8 5.00MM J163639+4053N21200.216:36:39.1+40:53:265.0±1.0 5.00MM J163635+4055N21200.316:36:35.7+40:55:593.9±0.8 4.87MM J163639+4056N21200.416:36:39.1+40:56:363.4±0.7 4.85MM J163632+4059N21200.516:36:32.1+40:59:465.7±1.2 4.75MM J163708+4054N21200.616:37:08.3+40:54:184.2±0.9 4.66MM J163640+4056N21200.716:36:40.7+40:56:463.2±0.7 4.57MM J163710+4055N21200.816:37:10.5+40:55:024.0±0.9 4.44MM J163705+4054N21200.916:37:05.8+40:54:264.0±0.9 4.44MM J163650+4057N21200.1016:36:50.3+40:57:363.1±0.7 4.42MM J163656+4058N21200.1116:36:56.3+40:58:142.5±0.6 4.16MM J163713+4054N21200.1216:37:13.8+40:54:034.9±1.2 4.08MM J163619+4054N21200.1316:36:19.5+40:54:005.7±1.4 4.07

MM J163640+4058N21200.1416:36:40.4+40:58:443.1±0.8 3.87MM J163636+4057N21200.1516:36:36.2+40:57:193.1±0.8 3.87MM J163644+4102N21200.1616:36:44.8+41:02:012.7±0.7 3.85MM J163706+4053N21200.1716:37:06.7+40:53:154.2±1.1 3.81MM J163655+4059N21200.1816:36:55.9+40:59:122.2±0.6 3.66MM J163658+4104N21200.1916:36:58.3+41:04:372.9±0.8 3.62MM J163647+4055N21200.2016:36:47.9+40:55:392.5±0.7 3.57MM J163715+4055N21200.2116:37:15.6+40:55:403.9±1.1 3.54

6Greve et al.

Table2.1200μm MAMBO source catalogue in the Lockman Hole?eld.The rms noise is~0.6mJy beam?1at the centre where the map is deepest,and increases towards the edges.The total area surveyed is197arcmin2.

ID MAMBO ID RA(J2000)Dec(J2000)S1200μm±σ1200μm S/N

MM J105238+5724LE1200.110:52:38.3+57:24:374.8±0.68.00

MM J105238+5723LE1200.210:52:38.8+57:23:224.1±0.6 6.83

MM J105204+5726LE1200.310:52:04.1+57:26:583.6±0.6 6.00

MM J105257+5721LE1200.410:52:57.0+57:21:075.7±1.0 5.70

MM J105201+5724LE1200.510:52:01.3+57:24:483.4±0.6 5.66

MM J105227+5725LE1200.610:52:27.5+57:25:152.8±0.5 5.60

MM J105204+5718LE1200.710:52:04.7+57:18:123.2±0.7 4.57

MM J105142+5719LE1200.810:51:42.0+57:19:514.1±0.9 4.55

MM J105227+5722LE1200.910:52:27.6+57:22:203.1±0.7 4.42

MM J105229+5722LE1200.1010:52:29.9+57:22:052.9±0.7 4.14

MM J105158+5717LE1200.1110:51:58.3+57:17:532.9±0.7 4.14

MM J105155+5723LE1200.1210:51:55.5+57:23:103.3±0.8 4.12

MM J105246+5724LE1200.1310:52:46.9+57:24:472.4±0.6 4.00

MM J105200+5724LE1200.1410:52:00.0+57:24:252.4±0.6 4.00

MM J105245+5716LE1200.1510:52:45.1+57:16:053.1±0.8 3.87

MM J105244+5728LE1200.1610:52:44.8+57:28:125.0±1.3 3.84

MM J105121+5718LE1200.1710:51:21.5+57:18:404.8±1.3 3.69

MM J105157+5728LE1200.1810:51:57.7+57:28:002.2±0.6 3.66

MM J105128+5719LE1200.1910:51:28.4+57:19:474.0±1.1 3.63

MM J105224+5724LE1200.2010:52:24.4+57:24:201.8±0.5 3.60

MM J105131+5720LE1200.2110:51:31.3+57:20:063.6±1.0 3.60

MM J105203+5715LE1200.2210:52:03.0+57:15:462.8±0.8 3.50

MM J105223+5715LE1200.2310:52:23.4+57:15:272.8±0.8 3.50

A1200μm MAMBO Survey of the ELAIS N2and Lockman Hole:I

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Figure3.1200μm MAMBO signal-to-noise map of the ELAIS N2?eld.Sources detected at≥3.5σare circled in white,and are numbered in order of signi?cance.The axes denote the offset(arcsec)from the map centre.

The boost-corrected number counts obtained in this way were then corrected for completeness using the?tted completeness curves in Figures6a and b.

The?nal integrated number counts in?ux bins2.75,3.25, 3.75,4.25,4.75,and5.25mJy are given in Table3along with the raw number counts.The table shows the counts derived for the ELAIS N2and Lockman Hole separately,as well as the com-bined number counts.The quoted errors correspond to the95per cent two-sided con?dence level of a Poissonian distribution.The number counts derived from the two?elds separately are seen to agree well within the error.In Figure7we have plotted the cor-rected accumulative1200μm number counts as derived from the MAMBO survey presented in this paper.While the surface density of SCUBA sources detected at850μm has been fairly well con-strained over a large range in?ux density thanks to a number of large submm surveys(Smail et al.1997;Scott et al.2002),only one other published MAMBO survey has so far attempted to con-strain the1200μm number counts(Bertoldi et al.2000).

For comparison we have also plotted the850μm source counts as derived from a number of SCUBA surveys.It is seen that the1200μm counts are lower than those at850μm.This is ex-pected if one assumes that the MAMBO and SCUBA sources trace the same population of dust-enshrouded galaxies:the lower MAMBO counts are due to the fact that one is sampling further down the Rayleigh-Jeans tail than at850μm.Thus,if one scales the MAMBO?uxes by a factor of~2.5,which roughly corresponds to the850/1200μm?ux ratio for a starburst at z~2.5,the MAMBO counts are found to coincide with the SCUBA counts.The over-all similarity between the shape of the1200and850μm number counts lends support to the view that the MAMBO and SCUBA sources are the same population viewed at slightly different wave-lengths.

c 0000RAS,MNRAS000,000–000

8Greve et

al.

Figure 4.1200μm MAMBO signal-to-noise map of the Lockman Hole ?eld.Sources detected at ≥3.5σare circled in white,and are numbered in order of signi?cance.The axes denote the offset (arcsec)from the map centre.

At ?ux levels fainter than ~4mJy the MAMBO counts dis-play a power-law slope of α??2.2,similar to that of the SCUBA counts in the ?ux range 2–9mJy.The 1200μm source counts ap-pears to show a break at ~4mJy beyond which the slope of the counts steepens to α~?4.7.The dot-dashed curve in Figure 7represents a Schechter-type function of the form dN/dS ∝(S/4mJy)?2.3exp(?S /4mJy).The Schechter function has a nat-ural break at 4mJy and appears to provide a somewhat better match than a power law,although the data do not allow for a statisti-cally signi?cant distinction between a power law and a Schechter function.At the bright end of the 850μm counts there is some dis-agreement between the SCUBA surveys,with the Scott et al.(2002)counts dropping off more steeply than found by Borys et al.(2003).The 1200μm counts show tentative evidence for a break at a ?ux level which corresponds to the 850μm ?ux at which the SCUBA counts by Scott et al.(2002)appear to turn over,suggesting that this

feature is real.In order to better constrain the bright end of the num-ber counts,larger surveys such as the one square degree MAMBO Deep Field Survey (Bertoldi et al.,in preparation)and SHADES are needed.Con?rmation of our tentative ?ndings would be impor-tant —the bright (and very faint)ends of the number counts hold the biggest potential in terms of discriminating between models.

At 1200μm the extragalactic background amounts to I νν~0.16nW m 2sr ?1(Fixsen et al,1998).By integrating up SdN/dS over the ?ux range 2.25–5.75mJy using the above Schechter func-tion,we estimate that our survey has resolved about 10per cent of the background light at 1200μm.This is comparable to the UK 8mJy Survey which also resolved ~10per cent of the extragalac-tic background at 850μm.

If indeed MAMBO and SCUBA sources are the same,then it should be possible to construct models which can simultaneously reproduce the 850and 1200μm counts.

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0000RAS,MNRAS 000,000–000

A 1200μm MAMBO Survey of the ELAIS N2and Lockman Hole:I 9

C o m p l e t e n e s s [%]

S o u t /S i n

S in [mJy]

P o s i t i o n a l O f f s e t ["]

S in [mJy]

Figure 6.Results from Monte Carlo simulations.The solid lines in all three panels represent best ?ts to the points,see text for details.As in Figure 5,empty and ?lled circles refer to results from the ELAIS N2and Lockman Hole maps.Top:Percentage of added sources recovered against input ?ux in the range 1to 12mJy.Middle:The ’boosting’factor,i.e.the factor by which the input ?ux is scattered upwards due to instrumental and confusion noise (Eddington bias),plotted against input ?ux.Bottom:Deviations between true (input)positions and the positions derived from the source extraction technique as a function of input ?ux.

In order to do so,we considered a simple parametric model which is based on the local 60μm LF,Φo (L 60),as derived from IRAS data (Saunders et al.1990).The latter provides the best esti-mate of the far-IR LF of dusty galaxies in the local Universe to date,and is thus a useful template to try and model the number counts of dusty high-redshift galaxies.While a local 850μm LF has been

established by Dunne et al.(2000),who used SCUBA to observe a

large number of galaxies from the IRAS Bright Galaxy Sample,the bright end of this function is still highly uncertain.Furthermore,if the majority of the MAMBO sources are at redshifts z >2and have similar dust temperatures to the IRAS galaxies (30–40K ),then the 60μm LF will be a better approximation to the rest-frame

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Table3.1200μm source counts as derived from the ELAIS N2?eld(columns2–4),Lockman Hole(columns5–7),and the combined?elds(columns8–10). Only the≥3.5σcatalogue is used.The area surveyed in the three cases are160,197,and357arcmin2,respectively.The errors corresponds to95per cent two-sided con?dence levels of a Poissonian distribution.

ELAIS N2LOCKMAN TOTAL S N raw(>S)N(>S)N(>S)N raw(>S)N(>S)N(>S)N raw(>S)N(>S)N(>S) corrected corrected corrected corrected corrected corrected [mJy][deg?2][deg?2][deg?2]

Figure7.Cumulative number counts at1200μm(solid circles)based on the≥3.5σMAMBO source catalogue presented in this paper.The error bars represent 95per cent two-sided con?dence levels on a Poissonian distribution.Also shown are850μm cumulative number counts from a number of recent SCUBA surveys.The dashed black and grey lines show the number counts at1200and850μm,respectively,as predicted by a pure luminosity scenario in which g(z)=(1+z)3out to z=2,beyond which no further evolution occurs.The solid black and grey curves represent predicted number counts at1200and 850μm,respectively,based on the galaxy evolution model by Jameson et al.(1999),see text for details.The thin dotted line corresponds to a simple power law with slopeα=?2.2,while the dark solid curve represents the Schechter function dN/dS∝(S/S o)?αexp(?S/S o),whereα=2.3and S o=4mJy. Finally,the thick dotted line represent a no-evolution scenario.

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11

S/N threshold

# s p u r i o u s d e t e c t i o n s

Figure 5.Expected average number of spurious positive sources in ELAIS N2(empty circles)and the Lockman Hole (?lled circles)as a func-tion of signal-to-noise ratio.The solid and dashed lines are the expected number of positive spurious sources in the ELAIS N2and Lockman Hole,assuming the noise is purely Gaussian and the MAMBO beam is a Gaussian with a FWHM of 10.7′′.

far-IR LF of the MAMBO sources.We have therefore adopted the 60μm LF as the reference LF at z =0.In order to assess the evo-lution in the far-IR LF,we used a simple approach in which the LF at redshift z is given by a simple scaling and/or translation of the local LF,i.e.Φ(L,z )=f (z )Φo (L/g (z )),where f (z )and g (z )are parametric models of the evolution in number density and luminosity,respectively.It is then straightforward to compute the cumulative source counts per unit solid angle brighter than a given ?ux density,S ν,as N (≥S ν)=

z max

L min (S ν,z )

f (z )Φo

L

dz

dz,(4)

where dV C /dz is the co-moving volume element per redshift in-crement,and L min (S ν,z )=4πD 2

L S ν(1+z )?1L ν/L ν(1+z )is the minimum luminosity observable for a source at redshift z and a survey ?ux limit of S ν.The evolution functions f (z )and g (z )are constrained by the fact that their predictions of the extragalactic background,the observed number counts and redshift distribution has to be consistent with observations.

In Figure 7we have plotted the predicted 1200and 850μm number counts from a model with a luminosity evolution of g (z )=(1+z )3out to z =2,beyond which the evolution is un-changed out to z =10,which marks the high-redshift cut-off of the model.The model assumes the same SED for all sources —here we have adopted T d =44K ,β=+1.2,and a critical frequency of νc =2THz.While this pure-luminosity evolution model does an excellent job at reproducing the number counts at 1200μm it fares less well at 850μm,where it tends to slightly underpredict the number counts at bright ?ux levels.

Another parametric model is that of Jameson (1999)which employs a pure luminosity evolution of the form

g (z )=(1+z )3/2sech 2(b ln(1+z )?c )cosh 2c,

(5)

where b =2.2±0.1and c =1.84±0.1,see also Smail et al.(2002).This model is arguably the most realistic of the parametric models,since it is motivated by semi-analytical models,i.e.mod-els based on dark matter halo merging trees and assumptions about the astrophysics of the gas in halos.Furthermore,the model is not only in agreement with predictions of the chemical enrichment as a function of cosmic time but it also naturally includes a peak in the evolution at z ?2which is in agreement with the recently de-termined redshift distribution of radio-identi?ed SMGs (Chapman et al.2003).In Figure 7we have plotted the predicted 1200and 850μm number counts for this model,under the assumption that the SEDs of all MAMBO and SCUBA sources are well matched by modi?ed blackbody law with T d =37K ,β=+1.5,and a crit-ical frequency of νc =2THz.It is seen that this physically more realistic model is able to reproduce both the MAMBO and SCUBA number counts extremely well,suggesting that the MAMBO and SCUBA sources trace the same population of high-redshift,far-IR-luminous,starburst galaxies.

While the mm number counts at faint as well as bright ?ux levels is still too poorly determined to warrant a detailed test of models of galaxy evolution,it is clear from the comparison with simple analytical model made above,that a scenario in which no evolution takes place at all,as illustrated by the thick dotted line in Figure 7,can be ruled out.

6CLUSTERING OF MAMBO SOURCES

The next big step forward in our understanding of SMGs is likely to come from determining how they are clustered.Their clustering properties may then provide a link to a present-day population of galaxies.If SMGs are the progenitors of massive elliptical galax-ies,as suggested by their star-formation rates,molecular/dynamical masses and co-moving space densities,then they are expected to be strongly clustered.This follows from the way peaks in the den-sity ?eld in the early Universe are biased in mass (e.g.Benson et al.2001).Giant ellipticals,being the most luminous objects in the local Universe,are often found residing in the centres of galaxy clusters;as such they pin-point the most overdense and therefore mass-biased regions in the Universe.

Submm surveys of various depths and sizes have searched for clustering among SMGs and have all failed to detect a signi?cant signal (Scott et al.2002;Webb et al.2003;Borys et al.2003).This has been due largely to the limited size of the survey regions,though efforts are further hampered by the fact the (sub)mm pop-ulation spans a broad range in redshift —the quartile range is z =1.9–2.8(Chapman et al.2003,2004)with a possible high-redshift tail extending to z >~4—and any clustering signal will thus,when projected onto the sky,become heavily diluted.Any detection of angular clustering will therefore be a lower limit on the real 3D clustering.One lesson learned from these surveys was that very large (~1square degree)areas containing several hundred sources with strong redshift constraints are required in order to determine the clustering properties of SMGs.Here,we present the results for the the MAMBO population using two independent clustering statistics.

The ?rst test calculates the angular two-point correlation func-tion,w (θ),which quanti?es the excess probability of ?nding a source within an angle,θ,of a randomly selected source,over that of a random distribution,i.e.

c

0000RAS,MNRAS 000,000–000

12Greve et al.

δP(θ)=N2(1+w(θ))δ?1δ?2,(6)

whereδP(θ)is the probability of?nding a source within a solid

angleδ?1,and another source in another solid angleδ?2within a

angular distanceθof each other(see e.g.Coles&Lucchin2002).

N is the mean surface density of objects on the sky.

Several estimators of w(θ)have been suggested in the liter-

ature,and here we shall use the one?rst proposed by Landy&

Szalay(1993):

DD ?2 DR + RR

w(θ)=

DD 1/2.

structure.A more detailed analysis of this will be presented in a

future paper(Greve et al.,in preparation).

An alternative test for clustering is the so-called nearest-

neighbour analysis(Scott&Tout1989).This considers the distri-

bution of nearest neighbour separations,θ,of sources on a sphere.

For a random distribution of sources,the probability density func-

tion can be shown to be:

N?1

P(θ)dθ=

A1200μm MAMBO Survey of the ELAIS N2and Lockman Hole:I

13 Figure9.Distributions of nearest-neighbours in the ELAIS N2(left col-

umn)and the Lockman Hole(right column).The black curves represent the

actual data(the≥4.0σsource catalogues),while the red curves are the en-

semble averaged distributions obtained from500simulated maps of the two

?elds.

distributions being drawn from the same underlying distribution is

about10per cent.In other words,there is a10per cent chance

of a random distribution yielding a more paired distribution than

that observed for the MAMBO sources.A similar analysis on the

≥3.5σsample shows a similar signi?cant peak at~15–30′′.

Thus,while we haven’t found a signi?cant clustering signal

from the two-point correlation function,there is tentative evidence

from the nearest-neighbour analysis that MAMBO sources are not

randomly distributed but tend to come in pairs.This is qualitatively

in agreement with a recent study which utilises the results from

the spectroscopic survey of radio-bright SMGs to search for pairs

and/or triplets of sources in redshift space.This has yielded a sig-

ni?cant detection of the clustering of SMGs and has constrained

the correlation length to r0?6.1±2.1h?1Mpc(Blain et al.2004;

Smail et al.2003).

7COMPARISON WITH THE SCUBA UK8MJY SURVEY

While a detailed analysis of the properties of the MAMBO sources

at radio and optical/near-IR wavelengths shall be presented in Paper

II(Greve et al.,in preparation),it is appropriate here to compare

the MAMBO and SCUBA maps.Such a comparison is meaningful

since as we saw in section5both surveys reach very similar integral

counts,and a’typical’z~2.5starburst SED will hit the?ux limit

in both surveys almost simultaneously.

7.1The reliability of(sub)mm surveys

First of all,such a cross-check between the MAMBO and SCUBA

catalogues will allow us to assess the reliability of(sub)mm sur-

veys.As already mentioned,(sub)mm surveys in general have

adopted detection thresholds at low signal-to-noise ratios(typically

3.0–3.5σ-see e.g.Eales et al.2000;Scott et al.2002;Webb et

al.2003;this work),and confusion has been a major issue for these

surveys.In addition,different surveys have used different data-

reduction software,and widely differing source extraction tech-

niques have been adopted.

The comparison between the MAMBO and SCUBA≥3.5σ

source catalogues is shown in Figure10,which shows the outline

of the MAMBO and SCUBA maps with the≥3.5σ850μm sample

as given by Scott et al.(2002)and the≥3.5σ1200μm sources

presented in this paper overplotted.It is seen immediately that

four SCUBA sources in ELAIS N2are unambiguously detected at

1200μm,while in the Lockman Hole eight SCUBA sources have

been con?rmed with MAMBO.

It is interesting to see how these MAMBO identi?cations are

distributed in terms of signal-to-noise and whether the identi?-

cation rate increases if we lower the source detection threshold

to3.0σ.In order to do so,we have compared the4.0,3.5,and

3.0σSCUBA source lists of Scott et al.with our corresponding

MAMBO source catalogues,and for each SCUBA source we com-

puted the distance to the nearest MAMBO source.The resulting

distributions are shown in Figure11.For both?elds the distribution

is seen to peak at offsets smaller than10′′.In fact,both distributions

seem to show that a cutoff in positional offset of<10′′is a natu-

ral selection criterion as to whether a MAMBO source is a genuine

counterpart to a SCUBA source or not.This is in line with what

we would expect given the FWHM s of the MAMBO and SCUBA

beams.Adopting this criterion and using the≥3.0/3.5/4.0σcata-

logues from both surveys,we con?rm6/4/3out of36/17/7SCUBA

sources in the ELAIS N2?eld and9/8/5out of36/21/12SCUBA

sources in the Lockman Hole,respectively.Thus,the identi?cation

rate clearly increases with signal-to-noise,from17–25per cent for

the3.0σ-catalogues to43per cent in ELAIS N2and42per cent

in the Lockman Hole for the4.0σ-catalogues.At face value,our

MAMBO survey thus con?rms about half of the most signi?cant

SCUBA sources.

An additional24hr of850μm data—not used in the original

8mJy Survey—resulted in a slightly different source catalogue

than that given in Scott et al.(2002).With the inclusion of the new

data,the signi?cance of N2850.17drops from3.5σto3.3σ,with a

new?ux density of5.3±1.7mJy,while N2850.16disappears(see

Ivison et al.2002).At the position of N2850.17in the MAMBO

map,we detect a source at the2.7σsigni?cance level,suggesting

that N2850.17is a real source,even though it is just below the

formal3.5σdetection threshold of the8mJy Survey.N2850.16,

however,is not detected at1200μm at greater than1σsigni?cance,

con?rming that this was a spurious source in the original Scott et

al.map.

Based on extremely deep radio imaging of the8mJy?elds,

Ivison et al.(2002)concluded that six of the original SCUBA

sources in the ELAIS N2and Lockman Hole?elds were likely

to be fake sources.Not only were they extracted from extremely

noisy regions,but they also lacked a radio counterpart despite be-

ing amongst the brightest SMGs in the sample.The sources in ques-

tion were LE850.9,LE850.10,LE850.11,LE850.15,LE850.20,

and N2850.14.From Figure10it is seen that none of these

sources,which are denoted by grey crosses,coincide with a≥3.5σ

MAMBO source.In fact,the highest signi?cance1200μm de-

tection of the above sources was at the1.6-σlevel.Hence,our

MAMBO maps strengthen the conclusion of Ivison et al.(2002)

that these sources are spurious.If we compare the MAMBO

catalogue with the re?ned SCUBA source catalogue,in which c 0000RAS,MNRAS000,000–000

14Greve et

al.

Figure 10.Distribution of MAMBO and SCUBA sources detected at ≥3.5σin the ELAIS N2and Lockman Hole ?elds (this paper;Scott et al.2002).The black circles are sources detected by MAMBO while grey triangles are SCUBA detections.The crosses denote the seven SCUBA sources which were deemed spurious and therefore rejected by Ivison et al.(2002)due to their lack of radio identi?cations and high associated noise levels.The MAMBO and SCUBA

survey regions are outlined in black and grey,respectively,see also Figure 1.The boxes are 21′.

7×21′.7.the above mentioned SCUBA sources (including N2850.16and

N2850.17)have been omitted,we ?nd that at the ≥3.0/3.5/4.0σlevel,we con?rm 6/4/3out of 33/14/7SCUBA sources in the ELAIS N2?eld and 9/8/5out of 31/16/9SCUBA sources in the Lockman Hole,respectively.Hence,the MAMBO identi?cation rate of SCUBA sources in the Lockman Hole increases to 56per cent,which is becoming comparable to fraction of SMGs detected in deep radio maps (Smail et al.2000;Ivison et al.2002).

An important point to make in this context is that Figure 10clearly shows that while not all SCUBA sources are detected by MAMBO,there is a good overall spatial correspondence between SCUBA and MAMBO sources,as was also pointed out in section 6.One way to interpret this result is that the two surveys represent two different realisations of the same large-scale structure.From two independent but similar (sub)mm surveys of the same region,we would expect to ?nd the most signi?cant sources in both sur-veys,but this is not necessarily true of the fainter sources near the detection threshold.

Deep radio observations provide an alternative route to reli-ably identify SMGs.About two thirds of SMGs are detected in the radio where the ratio of submm to radio ?ux detection thresholds is above ~400(Smail et al.2000;Ivison et al.2002).However,it remains an open question whether the third of the population which are radio-blank are SMGs at very high redshifts (z >>3),or cooler,less-far-IR-luminous objects at similar redshifts as the bulk of the population,or simply spurious sources.All three scenarios would explain the lack of radio counterparts.

In Table 4we list all the ≥3.5σSCUBA sources with a MAMBO counterpart detected at ≥3.0σsigni?cance within 10′′,along with their positional offsets and ?ux densities at 1200and 850μm.Of the 12≥3.5σSCUBA sources in the ELAIS N2?eld which were not detected by MAMBO,only four had a radio iden-ti?cation.Of the eight radio-blank SCUBA sources,only one —N2850.3—was con?rmed by MAMBO,indicating that it could

be cool,or lie at z >>3.In the Lockman Hole,none of the radio-blank SCUBA sources were detected at 1200μm,and only three of the 11radio-identi?ed SCUBA sources were not detected by MAMBO.

Since the depth of the MAMBO maps at 1200μm is compara-ble to that of the SCUBA maps at 850μm it is hard to conceive of a way in which an 850μm source with no radio counterpart could fail to be detected at 1200μm .The only plausible explanations require that the sources are spurious or confused.

In Table 5we have summarised the above ?ndings.They suggest strongly that the fraction of robust SCUBA sources,i.e.sources con?rmed by MAMBO,which are not detected in the radio is low:20per cent (1/5)in ELAIS N2and 0per cent in the Lockman Hole.These ?ndings suffer from small number statistics and we await a comparison between the much larger map of the Lockman Hole being obtained with MAMBO (Bertoldi et al.in prep.)and the SCUBA map of that region which is being obtained as part of SHADES (see https://www.wendangku.net/doc/087746564.html,/ifa/shades/).

In the light of current and future (sub)mm surveys,our ?nd-ings underline the importance of multi-wavelength follow-up in or-der to establish the reality of (sub)mm sources,and the dependence only on the most robust samples to draw meaningful statistical con-clusions (cf.Dannerbauer et al.2004).7.2The 850/1200μm ?ux density ratio

Another valuable piece of information which can be gleaned from a comparison of the MAMBO and SCUBA maps is the 850/1200μm ?ux ratios for a large sample of (sub)mm galaxies.Beyond z ≥3this ?ux ratio becomes a strong function of red-shift,and can thus be used as a crude discriminator between low-and high-redshift sources (Eales et al.2003),much in the same way that the radio-to-submm spectral index acts as a redshift estimator for sources at z <~3(Carilli &Yun 1999,2000).Thus,the two

c

0000RAS,MNRAS 000,000–000

A1200μm MAMBO Survey of the ELAIS N2and Lockman Hole:I15 Table4.MAMBO and VLA radio identi?cations of the SCUBA8mJy Survey≥3.5σsource catalogue(Scott et al.2002).The850μm and1.4GHz radio

?ux densities are from Scott et al.(2002)and Ivison et al.(2002),respectively.

SCUBA ID S850μm±σ850μm MAMBO ID S1200μm±σ1200μm SCUBA/MAMBO Offset RADIO S1.4GHz±σ1.4GHz mJy mJy′′μJy

N2850.111.2±1.6yes45±16

N2850.210.7±2.0N21200.393.4±1.18.4yes92±16

N2850.38.5±1.6N21200.192.9±0.8 5.1no<44

N2850.48.2±1.7N21200.103.1±0.7 4.5yes221±17

N2850.58.5±2.2N21200.33.9±0.8 1.0yes77±31

N2850.69.2±2.4no38±19

N2850.79.0±2.4N21200.43.4±0.7 4.0yes159±27

N2850.85.1±1.4yes74±29

N2850.99.0±2.5yes33±12

N2850.105.4±1.5no58±24

N2850.117.1±2.0no<44

N2850.125.5±1.6no32±17

N2850.13?6.3±1.9yes99±23

N2850.14?11.2±3.3no<44

N2850.155.0±1.5no31±20

N2850.16?12.9±3.9no<44

N2850.17??5.3±1.7no<44σ≥4.0Detections

4.0>σ≥3.5Detections

?Detected with MAMBO at the2.8σlevel.

?Excluded from the re?ned8mJy sample of Ivison et al.(2002).

?This source vanished with the inclusion of an additional24hr of SCUBA data.

??This source dropped from3.5to3.3σwith the inclusion of additional SCUBA data.It is detected with MAMBO at2.7σ.

c 0000RAS,MNRAS000,000–000

16

Greve et al.

01234

5

N

ELAIS N2

4.0 sigma 3.5 sigma 3.0 sigma

5

1015

20

25

Offset ["]

1234

5

N

LOCKMAN

4.0 sigma 3.5 sigma 3.0 sigma

Figure 11.Distribution of offsets between SCUBA sources and their near-est MAMBO counterpart in the ELAIS N2(top panel)and Lockman Hole ?elds (bottom panel).The 4.0,3.5,and 3.0σMAMBO samples are com-pared with the 4.0,3.5,and 3.0σSCUBA samples of Scott et al.(2002),and the corresponding distributions are shown as solid,dashed and dotted curves,respectively.

redshift estimators complement each other,and if used in combi-nation can potentially be used to probe the redshift distribution of (sub)mm sources.However,both of these redshift estimators suffer from the T d ?z degeneracy ?rst pointed out by Blain (1999),which implies that a low-redshift source with a cold dust temperature is indistinguishable from a warm source at high redshift.

The distribution of 850/1200μm ?ux ratios for the 13≥3.5σSCUBA sources which

were robustly identi?ed by our MAMBO survey are plotted in Figure 12a,along with the ratios for a sample of SCUBA-observed MAMBO sources by Eales et al.(2003).Us-ing SCUBA in its photometry mode,they observed 21MAMBO-

Figure 12.a)The distribution of 850/1200μm ?ux ratios for the 13≥3.5σSCUBA sources identi?ed with MAMBO in this paper (light-grey shaded area),and for the sample presented by Eales et al.(2003)(dashed line).b)The dotted histogram is the ?ux ratio distribution for all the ≥3.5σMAMBO sources within the SCUBA regions,including the ones which were not detected by SCUBA.In the latter case upper ?ux limits were es-timated as the peak ?ux within an aperture of radius 10′′centered on the MAMBO position in the SCUBA map.The distribution of ?ux ratios for all the ≥3.5σSCUBA sources (dashed histogram)were obtained in a similar manner by measuring the peak ?ux in the MAMBO map within a 10′′radius of the SCUBA position.The light-grey shaded histogram represents the dis-tribution for the subset of MAMBO sources which were robustly identi?ed in the radio.c)The same as b)except more conservative upper ?ux limits (2σ+F )were adopted,see text for details.

c

0000RAS,MNRAS 000,000–000

A 1200μm MAMBO Survey of the ELAIS N2and Lockman Hole:I

17

Figure 13.The 850/1200μm ?ux density ratio for SCUBA sources de-tected by MAMBO in the ELAIS N2(crosses)and Lockman Hole (tri-angles).Six of the sources have spectroscopic redshifts (see Chapman et

al.2003,2004),while the remainder have been placed at z =0.5.The two encircled sources have no radio counterpart.Shown as diamonds are the 850/1200μm ?ux ratios for the sample of Eales et al.(2003).The thick solid curve represents the expected ?ux ratio for an optically thin modi?ed blackbody with T d =45K and β=+1.5,typical for a local ULIRG.This curve is enveloped by two thin solid curves which correspond to changes in the dust temperature and spectral index of ?T d =±5K and ?β=±0.2.The light-grey shaded area corresponds to a modi?ed black-body with T d =(35.6±5.0)K and β=(+1.3±0.2).The dot-dashed curves corresponds to SEDs with β=1.0and T d =20...70K in step if 10K.

Table 5.The number (and percentage)of SCUBA sources identi?ed by MAMBO divided into radio and non-radio ID categories.Note,that all the number in this table are based on the comparison with the ≥3.5σ8mJy Sample of Scott et al.(2002)and the ≥3.0σMAMBO sample presented in this paper.

MAMBO ID

No MAMBO ID

Field

Radio ID

No Radio ID

Total Radio ID

No Radio ID

Total ELAIS N24154812Lockman 80831013Total

12(92%)

1(8%)

13

7(28%)

18(72%)

25

selected sources from the MAMBO Deep Field Survey (Bertoldi et al.,in preparation).While there is a considerable overlap between the two distributions,the latter has a signi?cant over-density at low values which is not reproduced by our sample.From our sample we ?nd a median value of S 850/S 1200=2.6±0.6,marginally higher than the median value of 2.1±0.7found by Eales et al.(2003),although within the scatter.

In Figure 13we have plotted the measured 850/1200μm ?ux ratios of our sample and the Eales et al.sample along with curves showing the predicted 850/1200μm ?ux density ratios against red-shift for an SED with T d =45K and β=+1.5,and an SED with

T d =35.6K and β=+1.3.The former SED provides a good match to the local ULIRG,Arp 220,while the latter is based on the average T d and βvalues derived from the SCUBA Local Uni-verse Galaxy Survey (Dunne et al.2000).In addition,we have also plotted the S 850μm /S 1200μm –z relationship for a set of SEDs with β=1and T d =20,30...70K,i.e.SEDs which have very different dust properties from local ULIRGs.Note,the above dust tempera-tures are at a redshift of zero.In order to account for the increas-ing cosmic microwave background radiation (CMBR)temperature with redshift and its thermal coupling with the dust we have used

T d (z )= T 4+βd,z =0+T 4+βCMBR (1+z )

4+β

?1 1/(4+β)

,(9)

where T CMBR is the present epoch CMBR temperature,(see

e.g.Eales &Edmunds 1996).The effect is only signi?cant when the dust is cold relative to the CMBR temperature,and therefore be-comes more important at very high redshifts.The slight downward trend in the S 850μm /S 1200μm curves at low redshifts is due to the negative spectral slope (α=?0.7)of the radio continuum emis-sion which boosts the 1200μm ?ux relative to the ?ux at 850μm .However,this effect is completely negligible at redshifts beyond z ~0.5.

The low ?ux ratios found by Eales et al.(2003)led them to conclude that a signi?cant fraction of SMGs must lie at very high redshifts (z >>3)or possess dust properties different from low-redshift starburst galaxies.In contrast,we ?nd no con?ict between our measured S 850μm /S 1200μm ratios and SEDs based on local ULIRGs.From a subset of ?ve sources which have been targeted spectroscopically by Chapman et al.(2003,2004),and thus are placed at their correct redshift in Figure 13,we can conclude that the observed ?ux ratios for at least four of the ?ve sources are con-sistent with the range of SEDs expected from local ULIRGs.The one exception is the outlying point at S 850μm /S 1200μm =3.8This data point corresponds to the source LE 850.6/LE 1200.10which has another source (LE 1200.9)close to it.This source was detected by MAMBO but not by SCUBA,and it is likely that LE 1200.9contributes to the 850μm ?ux of LE 850.6,leading to an arti?cially high ?ux ratio for this source.

Our sample is taken from two unbiased surveys at slightly dif-ferent (sub)mm wavelengths and is thus independent of any radio selection bias.Furthermore,it is clear from Figure 13that the SMG without a radio counterpart (circled symbol)does not have a lower 850/1200μm ?ux ratio than the rest of the sample.This suggest that the source is blank in the radio because it is a cooler,less-far-IR-luminous object at similar redshifts to the bulk of the popula-tion,not because it lies at a very high redshift.

Candidates for very-high-redshift sources,i.e.850μm dropouts,should be sought amongst sources de-tected by MAMBO but not SCUBA.From Figure 10it is seen that 9MAMBO sources in the ELAIS N2?eld and 9in the Lockman Hole fall within the regions observed by SCUBA,yet are not detected at ≥3.5σsigni?cance at 850μm.Upper limits on the ?ux densities at 850μm of these sources were measured,taking the peak ?ux in a 10′′radius aperture region of the SCUBA map coincident with the MAMBO position.These limits were then merged with the 850μm ?uxes of the robust sample,resulting in 850μm ?ux estimates (or upper limits)for all the 9+9+13=31MAMBO sources which lie within the SCUBA regions.The resulting distribution of 850-to-1200μm ?ux ratios is shown as the dotted curve in Figure 12b.The distribution appears to have two peaks,one at S 850μm /S 1200μm ~1which reproduces the low-end tail of Eales et al.(2003)rather well and is almost entirely due to the MAMBO sources not detected by SCUBA,and another at

c

0000RAS,MNRAS 000,000–000

18Greve et al.

~2.5which stems from the13sources robustly identi?ed at both 1200μm and850μm.

In order to make a fair comparison with the?ux ratios of the SCUBA sample,we estimated1200μm?uxes for all the SCUBA sources.This was done in an identical fashion as above,i.e.upper 1200μm?ux limits were derived for the SCUBA sources not de-tected with MAMBO using the peak?ux within a10′′radius aper-ture region of the MAMBO map centered on the SCUBA position, and concatenated with the robust sample.This distribution is shown as the dashed histogram in12b.

The dotted and dashed distributions appear to be distinct, and in order to determine the probability of the two samples be-ing drawn from the same parent distribution,we have employed the standard’survival analysis’tests(Feigelson&Nelson1985), which are appropriate in the case where the samples contain up-per or lower limits(censored data).This included the Gehan,log rank,Peto-Peto,and Peto-Prentice tests,the latter being perhaps the most conservative and least sensitive to differences in the censoring patterns.However,common to all the tests is that they are unable to compare samples with mixed censor indicators,i.e.one cannot compare a sample containing upper limits with a sample containing lower limits.As a result we ran the tests where only one of the sam-ples contained censored data,assuming that the limits in the other sample were not limits but measured values,and vice versa.In both cases the tests yielded probabilities less than0.01,thereby strongly suggesting that the two distributions are signi?cantly different.This argues in favour of there being a low-end tail consisting of galaxies at either high redshifts or with cool dust temperatures.Consistent with these?ndings is the distribution of MAMBO sources with ra-dio counterparts(shaded histogram in Figure12b)which shows that few of the sources with?ux ratios<~1.5are identi?ed in the radio.This is what one would expect if they were at high redshifts or cool,not very far-IR luminous systems.

In addition to the two astrophysical explanations(i.e.cold dust or high redshift)Eales et al.also suggest more mundane reasons for their low?ux ratios,the most important of which is astromet-ric errors(see discussion in Eales et al.2003).For all but?ve of their21sources,they used positions derived from radio observa-tions or mm-wave interferometry.For the remaining sources they used the MAMBO positions.With our dataset,in conjunction with the8mJy Survey images,we can reproduce the Eales et al.exper-iment in the case where only MAMBO positions are available.In order to do this we consider the sample of13sources which were detected by both MAMBO and SCUBA.However,instead of using the850μm?uxes reported by Scott et al.(2002),we measure the 850μm?ux at the MAMBO position in the SCUBA map using the peak?ux within a10′′aperture.In general,we?nd that the effects of positional errors are small,and the?ux ratios are not skewed towards lower values.

Finally,it is possible that contamination by spurious or?ux-boosted MAMBO sources is responsible for at least some of the low?ux ratios observed.However,based the Monte Carlo simula-tions in section4.2we expect no more than2sources to be spurious in each of the MAMBO maps.This is an upper limit,given that the overlap between the SCUBA and MAMBO regions is only about 68per cent of the areas covered by MAMBO.

While the above analysis suggests that astrometrical errors and spurious/?ux-boosted sources are unable to account for the12 MAMBO sources with S850μm/S1200μm<~1.5,we caution that the low?ux ratio could be due to the way we have estimated the up-per?ux limits.Simply adopting the peak?ux within a10′′aperture might in some cases result in too low?ux estimates and would tend to bias the MAMBO and SCUBA distributions towards lower and higher?ux ratios,respectively.In Figure12c we have adopted a more conservative approach in which the upper limits on the?uxes were estimated by adding2×σto the peak?ux,whereσis the local rms noise.Clearly,the overlap between the two distributions is now much greater,and the two distributions appear to be indistinguish-able.This is con?rmed by the’survival analysis’tests which yield probabilities in the range0.22(log rank)to0.11(Peto-Prentice)and similar for the reverse comparison,https://www.wendangku.net/doc/087746564.html,paring the SCUBA dis-tribution with the uncensored MAMBO distribution.Thus,adopt-ing what is arguably more realistic upper?ux limits we?nd no ev-idence for SMGs with unusually low850-to-1200μm?ux ratios as reported by Eales et al.(2003).If this is the case,the major impli-cation is that,beyond the few completely unrepresentative submm-loud AGN at z>4,there is no signi?cant population of SMGs at very high redshifts.The redshift distribution of radio-identi?ed SCUBA sources,as determined by Chapman et al.(2003,2004), would be applicable to virtually all of the(sub)mm population.

However,while we?nd no conclusive evidence for’850μm-dropouts’a handful of MAMBO sources do seem to be good can-didates for SMGs at z>>5.In particular,LE1200.2is one of the brightest sources in our survey,yet it is not detected by SCUBA nor is it seen in the radio.Pointed SCUBA photometry observa-tions of this source would provide an accurate accurate estimate of its850μm?ux and con?rm or dismiss its status as a’850μm-dropout’.

Furthermore,with the completion of the MAMBO Deep Field Survey and the SCUBA Half Degree Extragalactic Survey,which will not only provide us with much larger samples but also a mul-titude of observations at complementary wavelengths,we should be able to obtain a much better census of the high-redshift tail of (sub)mm sources.

8CONCLUSIONS

In this paper we have presented results from a MAMBO 1200μm blank-?eld survey of the ELAIS N2and Lockman Hole?elds,covering a total of357arcmin2to a rms level of ~0.8mJy beam?1.We detect27sources at≥4.0σsigni?cance, and more than40sources at≥3.5σ.

From the≥3.5σcatalogue we have derived accurate num-ber counts over the?ux range3–5.5mJy,and?nd evidence for a break at S1200μm?4mJy.This corresponds to a far-IR lumi-nosity of~1013L⊙for a modi?ed blackbody with T d=40K andβ=+1.5at z=2.5.The observed1200μm source counts can be successfully reproduced by a simple parametric model for the evolution the local ULIRG population.Furthermore,this model also?ts the850μm source counts which suggests that the MAMBO and SCUBA sources are drawn from the same population of dust-enshrouded starburst at high redshift.

Two independent tests were carried out with the aim of de-tecting clustering in the MAMBO population.Although,the an-gular two-point correlation function showed no evidence of clus-tering,a nearest neighbour analysis suggests that the most signif-icant MAMBO sources are not randomly distributed but come in pairs,typically separated by23′′.Furthermore,the spatial distri-bution of sources appears to be non-random,with sources tend-ing to reside in clusters surrounding large voids.The reality of these structures is strengthened by the good overall spatial corre-lation between the SCUBA,MAMBO andμJy-level radio sources. This suggests that co-spatial surveys at the two slightly different

c 0000RAS,MNRAS000,000–000

A1200μm MAMBO Survey of the ELAIS N2and Lockman Hole:I19

(sub)mm wavelengths skim the brightest members of a numerous but faint population,yielding two similar but low-signal-to-noise visualisations of the true(sub)mm sky.

Our MAMBO survey con?rms roughly half of the re?ned ≥3.5σSCUBA8mJy Survey sample(Scott et al.2002;Ivison et al.2002).This is comparable to the radio identi?cation rate of SCUBA and MAMBO sources.As a by-product of this analysis,we have produced a extremely robust sub-sample of13SMGs detected at≥3.5σby both SCUBA and MAMBO.We?nd that only one (~8per cent)has no radio counterpart,a signi?cantly lower frac-tion than the third which the radio-blank SMGs have generally been believed to constitute.Our results thus suggest that the population of SMGs which are detected by both SCUBA and MAMBO has no signi?cant tail at z>>3.This conclusion is further strengthened by the observed distribution of850/1200μm?ux density ratios for the13sources in our sample.We?nd their?ux density ratios to be consistent with the SEDs found for local ULIRGs and in agreement with the spectroscopic redshift distribution of SMGs as determined by Chapman et al.(2003,2004).

Finally,we have identi?ed18MAMBO sources within the SCUBA UK8-mJy regions which are not detected at850μm at greater than3.0σsigni?cance.Any high-redshift SMGs should be sought amongst this population of’850μm-dropouts’.However, using conservative upper?ux limits we?nd that the distribution of850-to-1200μm?ux ratios for these sources is statistically in-distinguishable from that of the sources identi?ed robustly in both wavelengths.

ACKNOWLEDGEMENTS

TRG acknowledges support from the Danish Research Council and from the European Union RTN Network,POE.We are grateful to Robert Zylka for providing us with the MOPSI package and for use-ful discussions concerning MOPSI.We are also grateful to Ian Smail for helpful comments on the paper.Finally,we thank Ernst Kreysa and his team for providing MAMBO.

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