arXiv:astro-ph/0002081v2 24 Oct 2000
o.Nt .Ato.Soc. Astron. R. Not. Mon. trus/G tz28adtecretstaini that is situation massive current a 850 the is complete and which the 1998), z=2.8 al. at et starburst/AGN (Ivison J02399-0136 SMM early and galaxies. very formation of to the into evolution back insight way unprecedented the gain and can all times we Universe route, our in this By study results sub-mm. therefore which the emission FIR, in dust the k-correction negative thermal into a the galaxies starbursting of in redshifting Th peak the Universe. by the aided of history view star-formation invaluable the an into give by insight can hidden observations sub-mm is that star-formation means much dust that of possibility amounts The has large dust. IRAS It containing to galaxies, 1998). t starbursting/AGN similar al appear be be which et may galaxies) infra- infra-red galaxies Ivison the (ultra-luminous dusty, these ULIRGs 1997; of that luminous, al. result proposed of et been a (Smail population as galaxies new Universe red a James distant of the the discovery on of in knowledge 1999) galaxies our al. transformed dusty has et Telescope Maxwell (Holland Clerk camera SCUBA The INTRODUCTION 1 ta.19;Sale l 97.Otcladna infra- near and Optical Barger 1997). et third 1998; a al. Eales about al. for et 1999; identified et been Smail have al. Holland counterparts red(NIR) 1998; et 1998; al. (Blain al. et sources et Hughes 50 1999; over al. well of sists 1Otbr2018 October 31 Labs, Science Durham, of University Physics, Shanks of Tom Department Busswell, S. Geoff Sub-mm the to Background Galaxies and Blue Counts Faint of Contribution The c 00RAS 0000 h rtsbm aayt edtce ySUAwas SCUBA by detected be to galaxy sub-mm first The µ apefo l h aiu ruscon- groups various the all from sample m 000 0–0 00)Pitd3 coe 08(NL (MN 2018 October 31 Printed (0000) 000–000 , enpeiul noe notclglx on oeswihassume which models count prese reds galaxy The high optical obscuration. at dust in lie intrinsic invoked to high previously proposed their been to are due These faint sources. a optically revealed sub-mm recently luminous, have waveband of submillimetre the in Observations ABSTRACT e words: Key esnbefi otebih 60 bright the to 850 at fit background reasonable extra-galactic a the of proportion significant ,paigat peaking 3, otiuint h an,sbm ubrcut si h esitr redshift the in is counts find number We sub-mm ULIRGs). faint, QSOs, fluxes(e.g. the brighter to at contribution apply may counts mm hs oescnacutfralo h ‘faint’( the of ’bright’( all fit for fa to the account into 1/ fail can data radiation a UV count models either galaxy the spiral these using evolved fit by the these that re-distributing and and show spirals now for We evolution K. Charlot & Bruzual z aais prl-eouin-ifae:glxe lrvoe:galaxies ultraviolet: - galaxies infrared: - evolution - spiral galaxies: ≈ ≥ 1 . my ore,idctn htaohrepaainfrtesub- the for explanation another that indicating sources, 2mJy) .Teaoemdl sn ihrds a,cnas xli a explain also can law, dust either using model, above The 8. ot od uhmD13E UK 3LE, DH1 Durham Road, South is o atta h nytosbm ore SMJ02399-0136 (SMM sources sub-mm two only the by that further strengthened fact is the hypothesis are in This luminous far-infra-red. discovered sta extremely far massive, are ie which so ULIRG’s, galaxies IRAS sources bursting/AGN local the to similar ( of are ‘bright’ ‘bright’) most popula- the (since the at fluxes with that contributing mm associated confirm sources are to of sources seems tion the interactions of or all mergers almost that fact The r ossetwt enrdhf nterne1 range the in tha results redshift derive mean all Lilly a they 1999a; and with al. 2000) consistent al. et are et Barger Smail 1998; 1999; al. al. sub et et of (Hughes distributions samples redshift mm obtained redshifts have photometric groups accurate Various reasonably and cases) some rvdn uhmr cuaeaglrpstos( positions 2000) al. angular et accurate Ivison 2000: more al. many much et for providing (Smail identified sources sub-mm been the now of have 1.4GHz at counterparts sources. sub-mm for searches hav al. optical therefore et and in 2000) (Dey found al. objects been the et Ivison red not of 1999: very many al. be et example, Smail detected to for 1999; shown be as, been will limit have source flux sources optical true chance Also the the reasonable errors. to that these down a guarantee within no is lie is there there could so candidates source, several sub-mm that a on rors WMo h CB emrslsin results beam SCUBA the of FWHM aisgety hspolmi u otefc htthe that fact the to due is identifica problem these This greatly. of varies reliability the although sources, the of µm hthspoe xrml niheigi htradio that is enlightening extremely proved has What RScounts. IRAS λ A rClet bopinlwfrtedust the for law absorption Calzetti or T E tl l v1.4) file style X ≤ my 850 1mJy) µ µ swl sproducing as well as m aaycut,but counts, galaxy m − + infra-red(FIR), r ne0 ange 3 e population new c fds has dust of nce elfo to U from well itadt be to and hift ′′ httemain the that > oiinler- positional τ my sub- 2mJy) Gyr 9 = . 5 < z < < < z < ≈ 1 tions ′′ 15 the in 3. r- ′′ e t - . , 2 Busswell et al. and SMM J14011+0252) with reliable redshifts have been Metcalfe et al (1996) included a 1/λ internal dust ab- followed up with millimeter wave observations (Frayer et al. sorption law with AB = 0.3 for spirals to prevent the τ = 9 1998, 1999), resulting in CO emission being detected at the Gyr SFR from over-predicting the numbers of high redshift redshifts of both sources (z=2.8 and z=2.6), a characteris- galaxies detected in faint B< 24 redshift surveys (Cowie et tic indicator of large quantities of molecular gas present in al 1995). This 1/λ dust law differs from the Calzetti(1997) IRAS galaxies. dust law derived for starburst galaxies, in that for a given The nature of the fainter (≤ 1mJy) sub-mm popula- AB, more radiation is absorbed in the UV. The Calzetti dust tion is, however, the focus of this paper. It has been claimed law is used by Steidel et al(1999) to model their ‘Lyman by Peacock et al. (2000) and Adelberger et al. (2000) that Break’ galaxies; they find an average E(B-V)=0.15 which the Lyman Break Galaxy(LBG) population could not only gives AB = 0.87mag and A1500 = 1.7mag. This compares to contribute significantly to the faint sub-mm number counts, our A1500 = 0.9mag with AB = 0.3mag. Both models also but could also account for a substantial proportion of the fail to predict as red colours as observed for the U-B colours background at 850µm. This may indicate that ULIRG’s of spirals in the Herschel Deep Field (Metcalfe et al 1996). cannot explain all of the sub-mm population and that the However, if we assumed E(B-V)=0.15 for our z=0 spirals, UV-selected galaxy population, which are predicted to be as compared to our E(B-V)=0.05, then the rest colours of evolved spirals by the Bruzual & Charlot models, may in spirals as predicted by the Bruzual & Charlot model might fact make a substantial contribution. It is exactly this hy- start to look too red as compared to what is observed. Other- pothesis our paper addresses. wise, the main difference between these two dust laws is that In this paper we will first review the situation regard- the Calzetti law would produce more overall absorption and ing the optical galaxy counts, focusing in particular on the hence a higher FIR flux from the faint blue galaxies. Thus in models of Metcalfe et al. (1996). These simple models which some ways our first use of the 1/λ law appears conservative use a τ = 9Gyr SFR for spirals and include the effects of in terms of the predicting the faint blue galaxy FIR flux. dust give good fits to galaxy counts and colours from U Later, we shall experiment by replacing the 1/λ law with to K. The idea is then to see whether this combination of the Calzetti(1997) law in our model. exponential SFR and relatively small amounts of dust in So this pure luminosity evolution (PLE) model with 1/λ the first instance (AB = 0.3 mag. for the 1/λ law), which dust and q0 = 0.05 then slightly under-estimates the faintest would re-radiate the spiral ultra-violet (UV) radiation into optical counts but otherwise fits the data well, whereas for the FIR, could cause a significant contribution to the sub- q0 = 0.5 the underestimate (with or without dust) is far mm galaxy number counts and background at 850µm. Our more striking. An extra population of galaxies has to be in- modelling will be described in section 3 and then in sec- voked at high redshift to attempt to explain this more seri- tion 4 our predicted contribution to the 850µm and 60µm ous discrepancy for the high q0 model. This new population galaxy counts and the extra-galactic background in the sub- was postulated to have a constant SFR from their forma- mm will be shown. Also in this section we demonstrate how tion redshift until z ∼ 1 and then the Bruzual & Charlot to get a fit to the background in the 100 − 300µm range by models predict a dimming of ∼ 5m in B to form a red dwarf using warmer, optically-thicker dust in line with that typi- elliptical (dE) by the present day and therefore has the form cally seen in ULIRG’s. We will then discuss the implications of a ’disappearing dwarf’ model (Babul & Rees 1992). No of our predictions in section 5 and conclude in section 6. dust was previously assumed in the dE population but this assumption is somewhat arbitrary. The τ = 9Gyr SFR was inconsistent with the early 2 THE OPTICAL COUNTS observations at low redshift from Gallego et al.(1996) and this is partly accounted for by the high normalisation of the m It is well known that non-evolving galaxy count models, optical number counts at B ∼ 18 . There is still a problem where number density and luminosity of galaxies remain with the UV estimates from the CFRS UV data of Lilly constant with look-back time, do not fit the optical num- et al at z=0.2. More recent estimates of the global SFR at ber counts e.g. (Shanks et al. 1984), as there is always a low redshift based on the [OII] line (Gronwall et al.1998; large excess of galaxies faintwards of B ∼ 22m. One way Tresse & Maddox 1998; Hammer and Flores 1998) indicates to account for this excess of ’faint blue galaxies’ is to in- that the decline from z=1 to the present day may not be as vestigate the way galaxy evolution will influence the optical sharp as first thought and that the τ = 9Gyr SFR in fact number counts. Metcalfe et al (1996) showed that by assum- provides a better fit to this low redshift data. Metcalfe et al ing that the number density of galaxies remains constant, (2000) have further found that this model also agrees well the Bruzual and Charlot(1993) evolutionary models of spi- with recent estimates of the luminosity function of the z=3 ral galaxies with a τ = 9Gyr SFR give excellent fits to the Lyman break galaxies detected by Steidel et al.(1999). optical counts. The galaxy number counts are normalised The main question then that we will address in this at B ∼ 18m so that the non-evolving models give good fits paper is whether the small amount of internal spiral dust to the B band data and redshift distributions in the range absorption assumed in these models which give an excellent 18m c 0000 RAS, MNRAS 000, 000–000 The Contribution of Faint Blue Galaxies to the Sub-mm Counts and Background 3 3 MODELLING ∞ C(z, M ) β(λ,T )dλ = G L /L (5) B Z abs B BM⊙ Using the optical B band parameters for spiral galaxies, we −∞ attempt to predict the contribution to the sub-mm galaxy where C(z,M ) is the scaling factor, which is a function counts and background at 850µm by using a 1/λ absorption B of z and MB , β(λ,T ) is the Planck function (in this case a law for the dust and re-radiating the spiral UV radiation − sum of two Planck functions) and κ (λ) ∝ λ β , where κ (λ) into the FIR. We use the Bruzual & Charlot(1993) galaxy d d is an opacity law (we use β = 2.0 for each Planck function evolution models with H = 50kms−1Mpc−1 and a τ=9 Gyr 0 to model optically thin dust). SFR - with a galaxy age of 16 Gyr in the low q case, and 0 We then calculate the received 850µm flux, S(z,M ), 12.7 Gyr in the high q case to produce our 1M⊙ galactic B 0 from a galaxy with absolute magnitude M and redshift z spectral energy distribution(SED) as a function of redshift. B using the equation We then use the equation −β C(z, MB)λe β(λe,T ) −0.4∗AB ∗(4500/λ) S(z, MB )= 2 (6) Gabs(z)= Fλ(z)(1 − 10 )dλ (1) 4π(1 + z)d Z L where C(z,M ) is defined from (4) and λ is equal to as used by Metcalfe et al(1996), which is used to calcu- B e 850µm/(1+z). We can then obtain the number count of late the radiation absorbed by the dust, G (ergss−1), for abs galaxies with absolute magnitude between M and M + our 1M⊙ model spiral galaxy as a function of z, using our B B dM and redshift between z and z+dz for which we mea- 1/λ absorption law with A = 0.3. Since Bruzual & Charlot B B sure the same flux density S(z,M ) at 850µm (see (4)). provides us with a 1M⊙ SED at each redshift increment, we B need to calculate the factor required to scale this SED (after dV dN(z, M )= φ(M ) dM dz (7) the effect of absorption from the dust) to obtain that of a B B dz B galaxy with absolute magnitude MB at zero redshift, and dV this factor will then remain constant for MB galaxies at all where φ(MB ) is the optical Schechter function and dz other redshifts. This then provides a zero point from which is the cosmological volume element. Then the integral source to calculate scaling factors for all the other galaxies in our counts N(> Slim) are obtained, for each value of Slim, by luminosity functions. We find the scaling factor for an MB integrating (5) over the range of values of MB and z such galaxy by making use of a relation from Allen(1995) that S(z,MB ) >Slim, where S(z,MB ) is defined in (4). dV mB = −2.5log( Bλfλdλ) − 12.97 (2) N(>S )= φ(M ) dM dz (8) Z lim B B ZMB Zz dz where f is the received flux(ergs−1A˚−1cm−2) and B is λ λ It is straightforward to then obtain model predictions the B band filter function. By re-arranging, setting m =M B B of the FIR background for a given wavelength. The inten- and then multiplying by 4π(10pc)2 we obtain the total emit- −1 sity, dI, at 850µm from galaxies with absolute magnitudes ted power, LB (ergs ) in the B band from an MB galaxy between MB and MB + dMB and redshifts between z and 2 [−0.4(MB +12.97)] LB = 4π(10pc) .10 (3) z+dz is given by multiplying the number of galaxies with these z’s and MB ’s by the flux density which we would mea- sure from each The intensity emitted in the B band, after absorption by dV the dust from our 1M⊙ galaxy, LBM is then calculated by dI = S(z, M )φ(M ) dM dz (9) ⊙ 850 B B dz B integrating the SED, assuming a flat B band filter, between 4000A˚ and 5000A˚. and then we simply integrate over all absolute magnitudes and all redshifts (0 c 0000 RAS, MNRAS 000, 000–000 4 Busswell et al. Figure 1. The 60µm differential number counts. The graph shows Figure 2. The 850µm integral number counts. The filled circles the evolution and no-evolution models for a low q0 Universe(the show the results of the SCUBA Lens Survey (Blain et al. 1999); corresponding high q0 models are indistinguishable) along with the open circles are as labelled:S97 - Smail, Ivison & Blain(1997); the observed 60µm counts of IRAS galaxies down to a flux limit B98 - Barger et al.(1998); H98 - Holland et al.(1998); E99 - Eales of 0.6Jy, plotted in the format used by Oliver et al.(1992). The et al.(1999); HDF, P(D) - Hughes et al.(1998). Also shown are crosses are from Hacking & Houck(1987), the empty triangles our predictions for q = 0.05 and q = 0.5 models with and without from Rowan-Robinson et al. (1990), Saunders et al.(1990) are Bruzual & Charlot evolution, using the parameters from Fig. 1. the filled triangles and the circles are Gregorich et al.(1995) and Both the high and low q0 models, with evolution (dashed and solid Bertin et al.(1997). We use a two-component dust temperature curves), do very well with the faint counts but fail the most lumi- of 15K and 45K to model both interstellar and circumstellar dust nous sources. In the no evolution cases(dotted and dot-dashed) respectively. Other parameters used are β = 2.0, H0 = 50 and the high q0 model again predicts more galaxies then the low q0 a redshift of formation of z = 4. The dot-dashed line shows the model, but they both underpredict the faint 850µm counts by same evolution model using the Calzetti dust law with three dust about an order of magnitude and then again fall away again at temperature components of 15, 25, and 32K. This fits the IRAS the higher flux densities. The graph also shows a predicted con- counts less well at < 0.2mJy, and this is because of the lack of tribution from AGN (Gunn & Shanks 1999) and a model using a 45K dust component meaning that there is much less thermal the calzetti dust law (the two dot-dot-dot- dashed curves). The emission from the dust at 60µm AGN model (the steeper of the curves) predicts that, at most, QSO’s could contribute 30 percent of the background at 850µm, . and these models do much better in the number counts at brighter fluxes, but they fail to contribute at the 0.5mJy level where we predict that faint blue galaxies are dominant. Our Calzetti dust see that there is very little difference between the two models law uses three dust temperature components (see Fig. 1, and as and that they both fit the data reasonably well. The IRAS with our 1/λ dust law, it can account for the faint number counts counts below 0.2Jy are slightly under-predicted using both but then fails the much brighter sources. dust laws, which could possibly be due to the fact our model doesn’t include any fast-evolving AGN/ULIRG population. We use the Calzetti dust law with three dust components of fluxes, suggesting that 2 populations may be contributing to 15, 25, and 32K and this failure of the fainter IRAS counts is the counts. greater than when the 1/λ law is used because of the absence The high q0 model contains a dwarf elliptical popula- of the 45K dust component, which dominates the thermal tion in order to fit the optical counts, as already explained, emission at 60µm.. but no dust was invoked in these galaxies in the optical We then go on to show in Fig. 2 our sub-mm predic- models and so they do not contribute to our 850µm pre- tions using the Bruzual & Charlot evolution model with low dictions. Contrary to the optical number counts, the high and high q0 (q0 = 0.05, q = 0.5) and also for the corre- q0 models predict more galaxies greater than a given flux sponding no-evolution models where we use the Bruzual & limit than low q0 models. The reason for this is illustrated Charlot SED at z = 0 for all redshifts. We have used a two- in Fig. 3, which shows how the received flux density from component dust temperature, as described in the previous a MB = −22.5 galaxy would vary with redshift in the high section and a galaxy formation redshift, zf = 4. The low q0 and low q0 case, with and without τ=9Gyr. Bruzual & Char- model reproduces the faint counts well, but fails the very lot evolution. In the no-evolution cases the two factors in- bright counts. This makes sense since these very luminous volved are the cosmological dimming and the effect of the sources would require ULIRG’s, having SFR’s of order ≈ negative k-correction, since we are effectively looking up the −1 100-1000M⊙ yr , and/or AGN, in order to produce these black body curve as we look out to higher redshift. The huge FIR luminosities. Indeed, the 850µm integral log N:log high q0 model( dotted line) predicts greater flux densities S appears flat between 2-10mJy before rising again at fainter for a given redshift than with low q0, explaining why the c 0000 RAS, MNRAS 000, 000–000 The Contribution of Faint Blue Galaxies to the Sub-mm Counts and Background 5 Figure 3. If a galaxy has an absolute magnitude MB = −22.5 Figure 4. The effect of varying the interstellar dust temperature, at the present day then these graphs show how the received flux Tint The graph shows the low q0 model with Tcirc = 45K(β = from such a galaxy would vary as a function of redshift using 2.0) and zf = 4. The modest warmer dust component is included our model with the parameters described in the previous figure in each plot and the interstellar dust temperature, which is dom- (Fig. 2). The solid line is for a q0 = 0.05 Universe with Bruzual & inant for the 850µm counts, is varied from 15K(solid curve) to Charlot evolution, the dashed line for q0 = 0.5 with evolution, the 30K(dotted curve), again with β = 2.0. Our model predictions dot-dashed line for q0 = 0.05 without evolution and the dotted are sensitive to this variation and increasing the interstellar dust line for q0 = 0.5 without evolution. temperature in fact means we see less galaxies above a given flux limit. Typical interstellar dust temperatures are ≈ 15K. This trend is perhaps the opposite of what you would expect when integral number counts are higher for a given flux density. varying dust temperatures and the reasons are explained in sec- When the Bruzual & Charlot evolution is invoked (solid and tion 5. dashed lines), we predict more flux than in the correspond- ing no-evolution cases at high redshift, because a galaxy is significantly brighter than at the present day. The high q0 obtain much larger flux densities at 850µm, explaining why model(with evolution) is virtually flat in the redshift range our models are very sensitive to Tint. 0.5 c 0000 RAS, MNRAS 000, 000–000 6 Busswell et al. Figure 5. The predicted number-redshift distribution of sub-mm Figure 6. The predicted contribution to the FIR background selected faint blue galaxies down to flux limits, Slim of 4.0, 2.0, from our models. The latest measurements of the extragalac- 1.0 and 0.5mJy. The graph shows the low-q0 model using the 1/λ tic FIRB, compared with the COBE measurement of the cos- dust law with the parameters described in Fig. 1 As the flux limit mic microwave background (Mather et al. 1994). F98 - Fixsen is increased, the peak in the n(z) distribution shifts from around et al.(1998)(upper solid line) and P96 - Puget et al.(1996)(lower z=1.8 at Slim=0.5mJy to much lower redshifts, reaching z≈ 0.2 solid line); H98 - Hauser et al.(1998); S98 - Schlegel et al.(1998). for Slim=4.0mJy. Both the Hauser and Schlegel data each have points at 240µm and 130µm. Low and high q0 models are shown with and with- out evolution, where we have used our standard parameters of using our model is to use higher values of AB and higher Tint = 15K, Tcirc = 45K, β = 2.0 and zf = 4.0 The evolution dust temperatures, as this means dust is absorbing more en- model, in the low q0 case can account for all of the FIR back- ergy from each galaxy and so the contribution to the back- ground at 850µm, whereas the high q0 one in fact overpredicts ground in the wavelength range where warmer dust emis- by about a factor of 2. The no evolution models both underpre- sion dominates(100µm<λ< 500µm) is much greater. The dict the sub-mm background but are consistent with it to within an order of magnitude. The solid curve shows a model where we solid curve in Fig. 6 shows a prediction where we have tried have used the Calzetti dust law using AB = 1.02 (equivalent to the Calzetti dust model which gives more overall absorption E(B-V)=0.18 and close to the value 0.15 used by Steidel et al with similar amounts of reddening; this model might also be for their Lyman Break Galaxies) for the dust obscuration with a expected to fit the B optical counts. We see that its larger three-component dust temperature of 15K, 25K and 32K. It fits amount of absorbed flux allows more flexibility in terms of the background and faint number counts at 850µm, the IRAS using more dust components. By using three dust temper- 60µm counts and also does much better in the wavelength range ature components results we obtain a better (though still 100µm<λ< 500µm. not perfect) fit to Fig. 6 in the 100µm<λ< 300µm range, while still giving fits to the IRAS 60µm (Fig. 1) and faint 850µm number counts (Fig. 2). cantly colder than that used in models of starburst galaxies (typically 30-50K), means that we are able to show that the evolution of normal spiral galaxies like our own Milky 5 DISCUSSION Way, using the Bruzual model with an exponential SFR of τ = 9Gyr, could make a very significant contribution to the We have taken a different approach from the standard way sub-mm number counts in the S850 < 2mJy range. Indeed in which sub-mm flux’s are estimated using UV luminosities this sort of temperature for spirals has been given recent sup- (Meurer et al. 1999). Instead of assuming a relationship be- port from observations of ISO at 200µm (Alton et al. 1998a) tween the UV slope β and the ratio LFIR/LUV , we proceed where, for a sample of 7 spirals, a mean temperature of 20K directly from the spiral galaxy UV luminosity functions and was found, about 10K lower than previous estimates from simply re-radiate into the FIR by assuming a simple dust IRAS at shorter wavelengths. They found that 90 percent of law constrained from the optical counts. A direct result of the FIR emission came from very cold dust at temperatures this, as has already been illustrated in the previous section, of 15K. Sub-mm observations of spirals (Alton et al. 1998b; is that decreasing the interstellar dust temperature actu- Bianchi et al. 1998) and observations of dust in our own ally increases the received flux density at 850µm, firstly be- galaxy (Sodroski et al. 1994; Reach et al. 1995; Boulanger cause the peak in the Planck emission curve moves towards et al. 1996; Sodroski et al. 1997) also support the claims of longer wavelengths and secondly because (as the absorbed these sorts of dust temperatures. Of course, at z=4 our as- flux from the dust is fixed) the normalisation scaling fac- sumed interstellar dust temperature of 15K is comparable tor goes up. The fact then that we model the dust using to that of the microwave background. a dominant interstellar component of 15K, which is signifi- Our models show that normal spiral galaxies (ie those c 0000 RAS, MNRAS 000, 000–000 The Contribution of Faint Blue Galaxies to the Sub-mm Counts and Background 7 that evolve into galaxies like our own Milky Way assuming mm number counts and background as much as was first the Bruzual model) fail to provide the necessary FIR flux of thought. the most luminous sources(> 2mJy) and this is not surpris- The spectral slope of the UV continuum and the ing since the τ = 9Gyr SFR at high redshift(z > 1), which strength of the Hβ emission line in Lyman Break Galaxies is consistent with the UV data, is lower than that inferred support the fact that interstellar dust is present (Chapman by other models which fit the sub-mm counts by a factor of et al. 1999), but the physics of galactic dust and the way about 5 or so (Blain et al. 1998a). The LBG galaxies at high it obscures the optical radiation from a source is still very redshift are predicted to be evolved spirals by the Bruzual poorly understood. We started by adopting a very simplistic models and the dust we invoke (AB=0.3 implies an atten- model for the dust, treating it as a spherical screen around uation factor at 1500Aof˚ 2.3) is enough to make them low our model spiral galaxy. The dust might, in reality, be con- luminosity sub-mm sources at flux levels of around 0.5mJy. centrated in the plane of the disk for spiral galaxies and may This amount of dust, though, is not enough to account for also tend to clump around massive stars. This would make the factor of 5 discrepancy and there are several possible the extinction law effectively grayer as suggested by observa- reasons for this. tions of local starburst galaxies (Calzetti, 1997). Indeed, we have investigated the effect of the grayer Calzetti extinction The first is the possible additional contribution to the law and found that it would produce a larger sub-mm count sub-mm counts from AGN. Modelling of the obscured QSO contribution due to the higher overall absorption it would population has shown that they could contribute, at most, imply. Metcalfe et al (2000) have also suggested that there about 30% of the background at 850µm but they can get may be evidence for evolution of the extinction law from the much closer to the bright end of the sub-mm number counts U-B:B-R diagram of faint blue galaxies in the Herschel Deep (Gunn & Shanks 1999). This is shown in Fig. 2 where we Field. also show the q =0.5 model of Gunn & Shanks. Although 0 We have assumed pure luminosity evolution (PLE) the slope of the QSO count at the faintest limits is too flat, throughout this paper. The assumption that the number at brighter fluxes the QSO model fits better than the faint density of spiral galaxies remains constant might certainly blue galaxy model and the combination of the two gives a not be the case if dynamical galaxy merging is important for better fit overall. galaxy formation. However, as we have seen it is relatively It is also possible that the optical and sub-mm obser- easy to fit the sub-mm number counts with PLE models vations are sampling a completely different population of whereas it is in fact impossible to fit the counts using pure galaxies as the obscured galaxies sampled by the sub-mm density evolution models without hugely overpredicting the observations may well just be too red or too faint to be background by 50 or 100 times (Blain et al. 1998a). So, if detected in the UV at the current flux limits (Smail et al. existing sub-mm observations are correct then although den- 1999, 2000; Dey et al. 1999). That may mean that the most sity evolution may also occur, luminosity evolution may be 13 luminous sub-mm sources or ULIRG’s(> 10 L⊙) are not dominant. It is also striking how well the PLE models do in the LBG galaxies (which the Bruzual model predicts as the optical number counts and colour-magnitude diagrams evolved spirals) and so then it would not be surprising if and together with the fact that we observe highly luminous the current sub-mm and UV derived star-formation histo- objects in the sub-mm out to at least z = 3 , this could in- ries at high redshift were different. However, the evidence dicate that the biggest galaxies could have formed relatively is growing that the faint blue galaxies are significant con- quickly, on timescales of about 1Gyr or so. If this were true, tributors to the faint sub-mm counts. Chapman et al.(1999) then the PLE models may be a fair approximation to the carried out sub-mm observations of 16 LBG’s and found, galaxy number density and evolution in the Universe out to with one exception, null detections down to their flux limit z ≈ 3 in both the optical/near-IR and FIR. of 0.5mJy. But their one detection may suggest that with We have not taken into account early-type galaxies as enough SCUBA integration time it might be possible to de- no dust was invoked in these in the optical galaxy count tect LBG’s that are particularly luminous in the FIR and models. In particular, we have not included any contribu- indeed, while this paper was in preparation, work from Pea- tion from dust in the dE population which is invoked to cock et al (1999) suggests that faint blue galaxies may be fit the faint optical counts in the q0 = 0.5 model (Metcalfe detected at 850µm at around the 0.2mJy level. This is be- et al. 1996). If we were to include their possible contribu- low the SCUBA confusion limit of ≈ 2mJy (Hughes et al. tion this would increase our 850µm counts predictions at 1998; Blain et al. 1998b) and highlights the problem faced by the faint end since in our models both early-type and dE Chapman et al.(1999) in performing targetted sub-mm ob- star formation occurs at high redshift which is the region servations of LBG’s. The conclusions of Peacock et al.(1999) of greatest sensitivity for the sub-mm counts. At brighter suggest that the LBG population (the faint blue galaxies in fluxes though, where, in our models, low redshift galaxies our model) contribute at least 25 percent of the background are the only possible influence, the inclusion of early-type at 850µm and Adelberger et al.(2000) also come to similar galaxies would be negligible. conclusions, namely that the UV-selected galaxy population could account for all the 850µm background and the shape of the number counts at 850µm. However, the conclusions of 6 CONCLUSIONS Adelberger et al.(2000) are based on the fact that the SED of SMM J14011+0252 is representative of both the LBG and The aim of this paper was to investigate whether, by re- sub-mm population. At present, they are only assumptions, radiating the absorbed spiral galaxy UV flux into the FIR, but nevertheless the conclusions of all these authors seem to the dust invoked in the faint blue spirals at high z from the suggest that ULIRG’s may not contribute to the faint sub- optical galaxy count models of Metcalfe et al.(1996) could c 0000 RAS, MNRAS 000, 000–000 8 Busswell et al. have a significant contribution to the sub-mm galaxy counts Flores, H., Hammer, F. et al., 1999, ApJ, 517, 148 and also the FIR background at 850µm. We have found that, Frayer, D.T., Scoville, N.Z., 1999, conf., Science with the Ata- using a interstellar dust temperature of 15K, a modest cir- cama Large Millimeter Array (ALMA), Associated Universi- cumstellar component of 45K, a beta parameter of 2.0 and a ties, Inc. Gallego, J., Zamorano, J., Aragon-Salamanca, A., Rego, M., 1996, galaxy formation redshift of zf ≈ 4 we can account for a very significant fraction of the faint 850µm source counts, both in ApJ, 459, 43 Glazebrook, K.,Ellis, R.S., Santiago, B. & Griffiths, R.E. 1995a, the low and high q cases when we invoke Bruzual & Charlot 0 MNRAS, 275, L19 evolution (see Fig. 2). These evolutionary models give 5-10 Gregorich, D.T., Neugebauer, G., Soifer, B.T., Gunn, J.E., times more contribution to the faint sub-mm counts than Hertler, T.L., 1995, AJ, 110, 259 the corresponding no-evolution models. At brighter fluxes, Gronwall, C., Salzer, J.J., McKinstry, K., 1998, AAS, 193, 7606G we find that the SFR and dust assumed in our normal spiral Guiderdoni, B. & Rocca-Volmerange, B. 1990, A&A 227, 362 model are too low to produce the FIR fluxes of the most lu- Gunn, K.F., Shanks, T., 1999, astro-ph/9909089 minous sources. In the no-evolution cases, we underpredict Hacking, P.B., Houck, J.R., 1987, ApJS, 63, 311 the number counts, even at the faint end. Our predicted Hauser, M.G. et al., 1998, ApJ, 508, 25 redshift distribution of sub-mm selected faint blue galaxies Holland, W.S. et al., 1998 SPIE, 3357, 305H suggests that the main contribution to the faint counts is in Holland, W.S. et al., 1999, MNRAS, 303, 659 the range 0.5 c 0000 RAS, MNRAS 000, 000–000 The Contribution of Faint Blue Galaxies to the Sub-mm Counts and Background 9 Steidel, C.C., Adelberger, K.L., Giavalisco, M., Dickinson, M., Pettini, M., 1999, ApJ, 519, 1S Thronson, H., Telesco, C., 1986, ApJ, 311, 98 Tresse, L., Maddox, S.J., 1998, ApJ, 495, 691T c 0000 RAS, MNRAS 000, 000–000