Measurement of the star formation rate from Ha in eld galaxies at z ˆ 1

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1 Mon. Not. R. Astron. Soc. 306, 843±856 (1999) Measurement of the star formation rate from Ha in eld galaxies at z ˆ 1 Karl Glazebrook, 1 Chris Blake, 2 Frossie Economou, 3 Simon Lilly 4 and Matthew Colless 5 1 Anglo-Australian Observatory, PO Box 296, Epping, NSW 2121, Australia 2 Magdalen College, Oxford OX1 4AU 3 Joint Astronomy Centre, 660 North A'ohoku Place, University Park, Hilo, HI 96720, USA 4 Department of Astronomy, University of Toronto, 60 St George Street, Toronto, Ontario M5S 3H8, Canada 5 Research School of Astronomy & Astrophysics, The Australian National University, Weston Creek, ACT 2611, Australia Accepted 1999 February 16. Received 1999 February 16; in original form 1998 August 28 ABSTRACT We report the results of J-band infrared spectroscopy of a sample of 13 z ˆ 1 eld galaxies drawn from the Canada±France Redshift Survey, targeting galaxies with redshifts that place the rest-frame Ha line emission from H ii regions in between the bright night sky OH lines. As a result we detect emission down to a ux limit of erg cm 2 s 1, corresponding to a luminosity limit of erg at this redshift for an H 0 ˆ 50 km s 1 Mpc 1, q 0 ˆ 0:5 cosmology. From these luminosities we derive estimates of the star formation rates in these galaxies that are independent of previous estimates based upon their rest-frame ultraviolet (2800 AÊ ) luminosity. The mean star formation rate at z ˆ 1, from this sample, is found to be at least three times as high as the ultraviolet estimates. The dust extinction in these galaxies is inferred to be moderate, for standard extinction laws, with a typical A V ˆ 0:5±1.0 mag, comparable to that of local eld galaxies. This suggests that the bulk of star formation is not heavily obscured, unless one uses greyer extinction laws. Star-forming galaxies have the bluest colours and a preponderance of disturbed/interacting morphologies. We also investigate the effects of particular star formation histories, in particular the role of bursts versus continuous star formation in changing the detailed distribution of ultraviolet to Ha emission. Generally we nd that models dominated by short, overlapping, bursts at typically 0.2 Gyr intervals provide a better t for the data than a constant rate of star formation. The star formation history of the Universe from Balmer lines is compiled and found to be typically 2±3 times higher than that inferred from the ultraviolet waveband at all redshifts. It cannot yet be clearly established whether the star formation rate falls off or remains constant at high redshift. Key words: surveys ± stars: formation ± galaxies: evolution ± galaxies: starburst ± cosmology: observations. 1 INTRODUCTION The topic of the history of star formation in the Universe has excited much interest in recent years, stimulated by the rst observations of nearly normal star-forming galaxies at z > 3 (Steidel et al. 1996). Previously, high-redshift studies were limited to highly active galaxies that may be poor tracers of the typical star formation history of the Universe as a whole. Steidel et al. used the colour signature of the Lyman break/lyman a forest discontinuity being redshifted through optical lters to select high-redshift objects (Guhathakurta, Tyson & Majewski 1990); these were subsequently con rmed spectroscopically on the 10-m W. M. Keck telescope. Comparison of these objects with low-redshift (z < 1) samples of eld galaxies (Lilly et al. 1995a; Ellis et al. 1996) appears to show a rise in the Universal star formation rate from z ˆ 0toz ˆ 1 and a drop-off at z > 3, indicating a star formation peak at the z ˆ1±2 epoch (Madau et al. 1996). This is also inferred to be the epoch when large galaxies with classical elliptical and spiral morphologies are assembled: Hubble Space Telescope observations indicate that they are extant at z ˆ 1 (Brinchmann et al. 1998; Lilly et al. 1998a) but absent in the z > 3 sample (Giavalisco, Steidel & Macchetto 1996; Lowenthal et al. 1997). Theoretical developments using galaxy formation simulations constrained by the observed evolution in the density of neutral gas from Lya QSO absorbers show qualitative agreement with this picture (Fall, Charlot & Pei 1996). However, these measurements of star formation rate are based upon the measurement of ultraviolet continuum luminosity, at 1500±2800 AÊ in the rest frame, assumed to be from young stellar populations. If dust extinction played a signi cant role in obscuring ultraviolet (UV) radiation, they could be underestimated by large factors which may change the picture completely. q 1999 RAS

2 844 K. Glazebrook et al. A more robust way to measure the star formation rate of highredshift galaxies would be to measure their luminosities in Balmer recombination lines. This radiation come from reprocessed ionizing radiation emitted by young stars. This approach has two advantages. First, the ionizing radiation comes from more massive shortlived stars than the softer 1500±2800 AÊ UV radiation, and hence falls quickly to zero only 20 Myr after star formation stops. Thus the Balmer luminosity is a more direct measure of the instantaneous star formation rate. This contrasts with the UV luminosity, which continues to rise as the stellar populations evolve, typically doubling, for example, between 10 and 1000 Myr at 1500 AÊ.For Ha the main dependence is directly on the initial mass function, and there is negligible dependence on the temporal evolution. The second main advantage is that the Balmer radiation is emitted in the red part of the optical spectrum and is thus much less affected by any dust extinction or attenuation than the ultraviolet. For example, for typical Small Magellanic Cloud (SMC) and Milky Way extinction laws (Pei 1992), the 1500 AÊ and 2800 AÊ extinctions (in magnitudes) range from 2±7 times greater than that at Ha (6563 AÊ ). However, to observe Ha at high redshift requires infrared spectroscopy, which has not been possible until recently because of the faintness of the sources involved. Pettini et al. (1998) have secured the rst infrared (IR) spectra of ve of the z > 3 Steidel et al. galaxies, and obtained Hb luminosities. In this paper we report the results of the rst measurements of the Ha line in a sample of normal z. 1 eld galaxies drawn from the Canada±France Redshift Survey (Lilly et al. 1995a,b; Le Fevre et al. 1995; Hammer et al. 1995). This sample (hereafter `CFRS') is a highly complete redshift survey of a magnitude-selected (I AB < 22:5) sample of normal eld galaxies. The median redshift is 0.6, and galaxies extend out to z ˆ 1:3. Because the sample is magnitude-selected, the z * 1 end is dominated by luminous L, L galaxies. 2 OBSERVATIONS AND DATA REDUCTION The observations were carried out on 1996 May 10±11 and October 3±5 at the UK Infrared Telescope in Hawaii using the CGS4 spectrograph (Wright 1994). We chose galaxies in the redshift range 0.790± so that the Ha line would lie in the relatively clean part of the near-infrared J band (1.17±1.34 mm) where the atmospheric extinction is relatively low (< 15 per cent). We also selected galaxies with detectable [O ii] emission in the optical CFRS spectra, which make up 85 per cent of the CFRS sample at z, 1. As well as absorption, the J band is contaminated by numerous airglow OH emission lines, which increase the broad-band sky brightness by a factor of 30 and hinder the detection of faint objects. Our observational strategy was to observe at high resolution with CGS4, thus resolving out the OH background. The limited wavelength coverage at high resolution was not a problem, because we already knew the redshifts of the galaxies from the optical spectra. Moreover, we could exclude galaxies with redshifts that would put the Ha line on or close to an OH line. (A similar strategy was also adopted by Pettini et al.) We observed with the 150 line mm 1 grating and the 1 arcsec 1 pixel slit, giving a resolution l=dl ˆ We determined empirically that at this resolution OH lines contaminated 50 per cent of the bandpass, i.e. we had to exclude 50 per cent of the high-redshift galaxies, but in the remaining clean part of the bandpass the mean background was only 20 per cent of that of broad J. Targets were acquired using the following procedure. First we `peaked-up' on a very bright star (V ˆ 1±2 mag) within 1±28 of the target. This involves centring the star on the optical nder TV, reading the IR array in a continuous `MOVIE' mode, and then adjusting the offset between the axis of CGS4 and the TV until the IR ux is maximized. This assures the IR slit is aligned with the TV cross-hair. Then we went to a fainter star, typically 17th mag, within 1±2 arcmin of our target galaxy and measured off the same coordinate system, centred the star on the TV cross-hair and performed a blind offset on to the target galaxy. (The targets were too faint to see on the TV.) We then autoguided on either the offset star or another bright star in the region. Observations were made stepping the InSb detector array in 0.5 pixel increments to sample the instrument pro le fully and nodding the telescope 6 9 arcsec along the slit between `OBJECT' and `SKY' positions to facilitate sky subtraction (though note that the object is still on the slit in both positions). Individual exposures ranged from min. The typical seeing was 1.0 arcsec. A total of 13 objects were observed: these are listed with their total exposure times in Table 1. Standard wavelength calibration and at- eld corrections were applied. The October observing run was affected by the spectrograph slit being jammed out of position which caused the lines to be tilted on the image. The shifts were measured by cross-correlation and the tilt corrected by re-interpolation. Even with the resolved OH background, accurate sky subtraction is critical to detection of faint lines. To rst order, the sky can be removed by simply subtracting the pairs of offset frames, although this leaves a residual signal caused by temporal sky changes. To second order, the residual sky was removed by performing a polynomial interpolation along the slit, excluding the two object regions, and subtracting. This leaves no systematic residual, although the regions near the OH lines are still noisier because of the extra Poisson contribution, with the result being a 2D image with a positive spectrum in the `OBJECT' row and a negative spectrum in the `SKY' row. For each image we also made a pixel mask to exclude bad pixels on the detector and regions with noisy OH residuals. In many of the images there were strong Ha and continuum detections. We summed all the Ha lines with good detections, tted Gaussians spectrally and spatially to de ne the typical line pro le and then used this mean pro le (with the pixel mask) to extract optimally all bright, faint and possibly non-detected objects in a consistent manner. In most of our observations we found that the negative spectrum was typically weaker, or even absent, compared with the positive spectrum. This is attributed to the fact that any small errors in acquisition are magni ed when stepping 9 arcsec away from the centre along the slit, as the rotation is not precisely known. When there was a signi cant negative spectrum, it was combined in a weighted manner (to maintain consistent exposure times) into the positive spectrum. This marginally increases the signal=noise ratio, although none of the ux measurements presented below is signi cantly changed if this step is omitted. Next the spectra had atmospheric absorption removed using a smooth-spectrum standard and were ux-calibrated using ux standards. Finally we applied aperture corrections to allow for our nite 1.0- arcsec wide slit. Our objects are resolved, and our mean Gaussian spatial pro le along the slit of the Ha line has a full width at half maximum (FWHM) of 2.0 arcsec [which is consistent with the typical 3±5 arcsec isophotal optical diameters measured for the CFRS sample (Hammer et al. 1997)]. The ux calibration stars are observed through the same slit in 1.0 arcsec seeing. Assuming Gaussian pro les for both, we derive a relative correction factor of

3 Ha star formation rate at z ˆ Table 1. Observed sample and ux measurements. CFRS no. Exposure z I AB V I AB EW [O ii] F Ha J C HST morphology (s) (mag) (mag) (rest AÊ ) erg cm 2 s 1 ) (mag) :0 6 13:9 19:67 6 0:13 ± :1 6 7:8 20:19 6 0:10 ± :9 6 33:9 > 21:87 ± :0 6 6:8 > 22:87 Spiral :0 6 24:9 > 20:87 ± :9 6 23:8 20:70 6 0:23 ± :5 6 16:2 > 21:69 Peculiar (merger) :2 6 19:0 19:08 6 0:19 Peculiar (close pair) :0 6 30:5 18:74 6 0:11 ± :0 6 15:7 19:10 6 0:10 Compact :9 6 6:4 20:74 6 0:18 ± :5 6 3:6 20:36 6 0:08 Peculiar (merger) :3 6 6:2 21:24 6 0:20 Compact 1.7, by which we multiply our spectra. While this can only be a rough correction, it gives uxes consistent with the optical lines (see Section 3). It is also only of order unity, so even if it is ignored our conclusions below are not drastically altered. The continuum level was determined in each case by taking the mean of the data points mm either side of the emission line, ignoring the masked points and the emission line. The noise level of the data was determined empirically from the rms value in the same region. In most cases we found signi cant continuum emission. Note that for individual pixels the continuum is mostly below the noise; it is only by summing up that we get a signi cant detection. To check the validity of our measurements we repeated the same procedure for an off-object row in the long-slit spectra. This gave non-detections in all cases, so we are con dent in our procedure. After subtraction of the continuum level from the data we computed the line ux by summing the ux 6N pixels around the line, excluding the masked pixels, where N ˆ 7 is chosen to be the typical line FWHM. This is done regardless of whether there appears to be a detection or not (as the expected wavelength is known). The nal line uxes and continuum uxes (converted to AB mag and denoted J C ) are given in Table 1, along with the most useful CFRS parameters of our objects. Ha uxes < 1j are set equal to zero. We nd seven detections > 2j and ve detections > 3j out of our 13 objects. We convert these to luminosities using a H 0 ˆ 50 km s 1 Mpc 1 and q 0 ˆ 0:5 cosmology in Table 2. We use this cosmology for the rest of our paper. We note that in our further analysis our conclusions are based on comparing the luminosities of the same galaxies at different wavelengths. As all the galaxies in our sample lie close to z ˆ 1, our conclusions are essentially unchanged if we use a different cosmology. To complete the quantities derived from the lines, we tted Gaussian pro les (excluding masked pixels) to derive velocity line widths for all our detections. Each of the ts was checked visually by plotting on top of the line; the instrumental resolution was determined by tting to unresolved night-sky OH lines in the region of the galaxy line and the value was subtracted in quadrature from the galaxy line widths. It should be noted that all our lines except one are well resolved, as we expected given the spectral Table 2. Derived luminosities and velocity widths. CFRS no. L(Ha) i L([O ii]) i L(2800-AÊ ) i FWHM ii (10 41 erg s 1 ) (10 41 erg s 1 ) (10 27 erg s 1 Hz 1 ) rest km s :0 6 5:2 3:8 6 0:5 18:5 ± :1 6 2:8 6:5 6 1:5 10: :7 6 22:2 12:9 6 1:8 52: :0 6 2:5 2:4 6 0:4 3:6 ± :0 6 16:3 22:6 6 2:4 81:3 ± :8 6 8:6 13:2 6 1:8 42: :2 6 7:8 7:7 6 1:4 43: :5 6 12:2 36:4 6 8:3 154: :0 6 14:3 16:1 6 1:9 125:3 ± :0 6 7:4 14:9 6 1:9 60:5 ± :3 6 2:4 13:5 6 1:1 29:8 unresolved :4 6 1:4 19:5 6 2:5 70: :8 6 2:4 21:8 6 1:2 33:3 279 Notes. (i) To correct for dust using the nal extinction values derived in Section 5, multiply the above values by the following factors: L(Ha) 1:6, L([O ii]) 2:4, L(2800-AÊ ) 3:1. (ii) The instrumental resolution ranges from 70±100 km s 1 (FWHM) and has been subtracted in quadrature from these values.

4 846 K. Glazebrook et al. resolution and the typical velocity widths of galaxies. The spectral line FWHMs of the galaxies range from 3±5 pixels (one pixel ˆ 2± 3 AÊ depending on the spectrum), compared with 2.4±2.6 pixels for the sky lines. The results are presented in Table 2; we make no detailed analysis here, we just note that the typical velocity FHWMs are in the range 200±400 km s 1 expected for large L, L galaxies. 3 COMPLETENESS In eight out of 13 of the galaxy spectra Ha emission was detected; additionally nine out of 13 of the galaxies had detected continuum emission. This proves quite useful: we can check whether our line non-detections are caused by poor acquisition by comparing the continuum level of our line detections and non-detections. There are only two cases in which there is no line and no continuum detection. The general trend is that the average continuum ux is brighter for the non-detections, this translates into a median I J C AB colour 1.1 mag redder. This argues against the slit missing the object, in fact the trend towards redder colours is precisely what is expected for non-line-emitting objects. We note that at z ˆ 1 a Scd galaxy should have observed colours I J AB ˆ 1:0 and an E/SO galaxy I J AB ˆ 2:0, using template SEDs from Kennicutt (1992). We nd median colours of I J AB ˆ 1:6 for the Ha detections and I J AB ˆ 2:7 for the non-detections, which agree very well given that our actual galaxies will differ in detail from Kennicutt's templates. Fig. 1 shows the nal set of spectra, which have been continuumsubtracted and centred on the Ha line. The line is in all cases found within the error box given by the optical redshift (Dz. 0:002). Our resolution is high enough that Ha is well separated from the [N ii] lines, so we do not have to correct for blending. Also in a few cases (e.g. objects and ) we see evidence for one of the weaker [N ii] lines as well as the main Ha line. This is additional evidence for the robustness of our detections. Note in many cases the position of one or both of the [N ii] lines is occluded by a noisy OH residual. We can also test our completeness using CFRS values for the [O ii] ux (Hammer et al. 1997) to calculate a Ha/[O ii] line ratio. In the CFRS sample, in this redshift range 85 per cent of galaxies have [O ii] emission. Hammer et al. tabulate the [O ii] equivalent width and ux; the latter is aperture-corrected by comparing the spectra at,5500 AÊ with their V-band image photometry. Other than excluding galaxies with zero [O ii] emission, we made no attempt to concentrate on the objects with the strongest [O ii] emission. Thus the mean [O ii] equivalent width (32 AÊ ) and range (10±60 AÊ ) of our small subsample are consistent with random sampling from the larger sample. The CFRS galaxies at z ˆ 1 with zero [O ii] are all at the red end of the colour distributions in V I and I K. Thus the colours also indicate they are not signi cant star-forming systems and we conclude their exclusion has no signi cant impact on our conclusions below. One might also ask the question: is the lack of Ha detection in some of our objects consistent with the presence of [O ii] in our optical spectra? This is addressed in Fig. 2, where we plot the strength of the two lines against each other. It can be seen that, given the Ha error bars, all points are consistent with a reasonable linear correlation. Kennicutt (1992) estimates the line ratio Ha/[O ii] as having a median value of about 2 (with a spread from 1 to 3) for a sample of local star-forming galaxies (1.0 mag mean extinction). Our observed values at high redshift are entirely consistent with Kennicutt's median and spread, implying that we too have small amounts of extinction, which agrees with our ndings below in Section 5. The points with zero Ha are consistent with detected [O ii] given the larger error bars. Note that the line ratios are also good evidence that our aperture corrections are reasonable; if omitted we would obtain a much lower ratio Ha/[O ii] ˆ 1. 4 STAR FORMATION RATES FROM Ha AND UV Using models of population synthesis it is possible to calculate the relation between input star formation rates and output UV and Ha uxes. The basic principle is that the UV light is dominated by short-lived main-sequence stars (the Ha light is reprocessed ionizing UV) so the number of these stars in a galaxy is proportional to the star formation rate. The prescription for this calculation is simple. For reference we outline it (and the corresponding assumptions) in detail. (i) For a given time-dependent star formation rate the population synthesis code gives the UV stellar spectrum as a function of time. Note that Kennicutt (1983) in deriving his calibration uses a simple grid of stars of different masses with evolutionary tracks current at the time. (ii) For the UV continuum estimators one takes an averaged ux (e.g. through a synthetic box lter) at a speci c wavelength (e.g AÊ, 2800 AÊ ). At the longer wavelengths, with increasing stellar lifetimes, the conversion from a constant star formation rate to a UV ux is age-dependent (see for example Pettini et al., who use different factors at 1500 AÊ for 10 7 and 10 9 yr). One then also needs to apply corrections for dust attenuation and/or Lyman absorption by line-of-sight systems (e.g. Madau 1995). (iii) For Ha one calculates the number of ionizing Lyman continuum photons. This ux comes from the most short-lived stars radiating at l < 912 AÊ with lifetimes of &10 Myr. Then it is assumed that all this radiation is absorbed by intervening hydrogen gas in the galaxy in which the forming stars are embedded and that none leaks out. In practice it seems this is very close to the truth. At very high redshift, the Lyman limit can be observed in the optical (e.g. the Steidel et al. galaxies) and the ux does indeed go to zero, but as these galaxies are identi ed by the Lyman breaks, this could be a selection effect. For local galaxies there has been limited l < 912 AÊ spectroscopy, for example Leitherer et al. (1995) observed a sample of four starburst galaxies with the Hopkins Ultraviolet Telescope and concluded that < 3 per cent of the ionizing photons escaped. Constrained models of the ionizing radiation eld of the Milky Way (Bland-Hawthorn & Maloney 1997, 1999) indicate that approximately 6 per cent may escape. (iv) The ionizing photons are reprocessed into recombination lines, and the relative strengths can be calculated in detail. Hummer & Storey (1987) calculate that 0.45 Ha photons are emitted per Lyman continuum photon for case B recombination. This number is quite robust, over a range of nebulosity conditions (10 2 ±10 6 K, 10 2 ± 10 4 electron cm 3 ). As there are a number of values for these conversion factors in the literature, we thought it would be useful for reference purposes to tabulate these systematically for a set of models. This also serves to illustrate the range of variations and trends. The results of our calculations are given in Table 3 for UV 1500-AÊ, 2800-AÊ and Ha conversions. The Bruzual & Charlot (1993, 1996) models (`BC96') offer a range of metallicities (albeit using theoretical model atmospheres ± the `kl96' models). The PEGASE models (Fioc et al. 1997) offer two sets of post-main sequence evolutionary tracks but only solar metallicity. Both sets of models offer several stellar initial

5 Ha star formation rate at z ˆ Figure 1. The J-band spectra of our CFRS galaxies. The spectra have been continuum-subtracted and centred on the Ha line. The large central arrow indicates the predicted Ha position based on the optical redshift, the associated horizontal error bar denoting the 1j error on the redshift. The two smaller arrows show the predicted positions of the [N ii] 6548-AÊ and 6583-AÊ lines. The vertical dotted lines indicate the positions of strong night sky OH lines, which have been masked out. The objects where we nd a > 2j Ha detection are labelled `DET.' mass functions (IMFs); we tabulate the results using the IMFs of Salpeter (1955) and Scalo (1986) because these bracket the upper and lower limits of the variation. We also tabulate some other values given previously in the literature. For all these models Ha reaches a constant asymptote after 20 Myr, then stays constant to within a 5±10 per cent out to 10 Gyr. Thus it can be used as a tracer of the instantaneous star formation rate on time-scales of order,10 Myr. For reference we give the value at 100 Myr. The conversion is very sensitive to the IMF, as the ionizing ux comes from the most massive stars, with Salpeter giving a value 2.8±3.4 times higher than Scalo for the different models. Another important point, which has not been remarked upon in the literature discussing high-z galaxies, is the strong effect of metallicity below 912 AÊ. This occurs in stellar evolutionary models because the most luminous stars (contributing below 912 AÊ ) have a much greater dependence of effective temperature on metallicity than the less luminous stars contributing at longer wavelengths. The effect of the hotter stars at low metallicty is to raise the Ha ux about 1.7 times compared with the solar metallicity value for a given star formation rate.

6 848 K. Glazebrook et al. 1.5±2.5) as these UV bands come from less massive stars and the metallicity dependence on temperature is much smaller. However there is a stronger time dependence, with the ux increasing signi cantly between 10 7 and yr, especially at 2800 AÊ, and for the Scalo IMF which is much less rich in massive stars. For cosmological times (> 1 Gyr) the 1500 AÊ ux is relatively insensitive to time as noted by Madau, Dickinson & Pozetti (1998) (except for the extreme 0.02 Z ( case). Thus it can be used as a tracer of the star formation rate on time-scales of 1 Gyr. The 2800 AÊ ux is not as stable and changes at the 10±40 per cent level over 1±10 Gyr. There are further &50 per cent variations in the exact conversion, depending on the model and metallicity assumed. These time and metallicity effects are illustrated graphically in Fig. 3. Finally, it is worth noting that the range in the ratio of Ha to UV is less than the absolute range; as both come from high-mass stars the choice of IMF matters somewhat less. Figure 2. Comparison of line luminosities of the sample in [O ii] and Ha. Dotted lines show slopes of Ha= O iiš ˆ1; 2; 3, the spread of ratios found by Kennicutt (1992). The average UV luminosity per unit Hz is computed as the total energy integrated through a 6 10 per cent box lter divided by the total bandwidth. This gives a negligible colour term. For a 10 per cent lter the difference in the average between a constant f n spectrum (which approximates these spectra for > 912 AÊ ) and a much redder constant f l spectrum is only 1 per cent. The IMF dependence is somewhat less than for Ha (typically a factor of 5 THE STAR FORMATION RATE AT z ˆ 1 Turning back to our data we can perform a direct galaxy by galaxy comparison of the star formation rates inferred from UV and Ha. Our UV uxes are particularly robust because for redshifts near unity the rest-frame 2800 AÊ light corresponds very closely to the observed frame V-band light. To a rst approximation we can simply ignore the K-correction and derive the 2800 AÊ ux directly from the CFRS V magnitudes. We re ne this slightly by using the SED ts from Lilly et al. (1996); this corrects the uxes by 10±20 Table 3. Conversions of Ha, UV to star formation rates. Luminosities are for 1 M ( yr 1. Model Z=Z ( IMF L(Ha) L(1500 AÊ ) L(2800 AÊ ) L(2800 AÊ )/L(Ha) (10 41 erg s 1 ) (10 27 erg s 1 Hz 1 ) (10 27 erg s 1 Hz 1 ) (10 14 Hz 1 ) 0.1 Gyr 1.0 Gyr 3.0 Gyr 0.1 Gyr 1.0 Gyr 3.0 Gyr (1 Gyr) BC96 (kl96) 0.02 SC BC96 (kl96) 0.20 SC BC96 (kl96) 0.40 SC BC96 (kl96) 1.00 SC BC96 (kl96) 2.50 SC BC96 (gs95) 1.00 SC BC96 (gshr) 1.00 SC PEG (Pad) 1.00 SC PEG (Gen) 1.00 SC M SC BC96 (kl96) 0.02 SP BC96 (kl96) 0.20 SP BC96 (kl96) 0.40 SP BC96 (kl96) 1.00 SP BC96 (kl96) 2.50 SP BC96 (gs95) 1.00 SP BC96 (gshr) 1.00 SP PEG (Pad) 1.00 SP PEG (Gen) 1.00 SP K SP-like 1.12 M SP M SP Notes. (i) SC and SP are the Scalo (1986) and Salpeter (1955) IMFs. (ii) K83 is Kennicutt's (1983) conversion for a Salpeter-like IMF. (iii) M96 are the Madau et al. (1996) values for 0.1±1 Gyr, derived from Bruzual & Charlot (1993); M98 are the values from Madau et al. (1998). (iv) BC96 are values derived from Bruzual & Charlot (1996) models; multi-metallicity `kl96' stellar spectra are based on stellar model atmospheres (Lejeune et al. 1997) and `gs95' are based on observed Gunn & Stryker (1983) spectra. All use the `Padova' stellar evolutionary tracks. (v) PEG are values derived from the PEGASE models (Fioc et al. 1997) for the `Padova' and `Geneva' stellar evolutionary tracks respectively.

7 Ha star formation rate at z ˆ Figure 4. Comparison of the Ha versus UV continuum ux at 2800 AÊ for the individual galaxies. The overlaid axes show the locus of constant star formation rate for a set of ducial models covering the range of UV=Ha ratios given in the last column of Table 3. The numerical labels on the axes are the corresponding star formation rates in M ( yr 1. The dotted line shows the ratio of the mean luminosity densities derived in Section 5. Figure 3. Illustration of the dependence of the UV spectrum on metallicity and time for a constant star formation rate. These are theoretical galaxy spectra from the BC96 population synthesis models (Salpeter IMF). The position of the 1500 AÊ and 2800 AÊ 610 per cent bands are marked, along with the ionizing photons that are reprocessed into Ha. The vertical order of the labels is the same as the vertical order of the spectra. Panel (a) shows the spectrum at 1 Gyr for a decreasing metallicity sequence. Panel (b) shows the solar metallicity spectrum for an increasing time sequence. It is easily seen that, while the redder UV bands are relatively insensitive to metallicity, they are strongly time-dependent until they are 1 Gyr old. The reverse is true for the ionizing photons ± the stellar spectra below 912 AÊ are identical for times > 20 Myr at a given metallicity. Hence the resulting Ha ux is mainly dependent on metallicity. per cent. Thus the UV luminosities we use are the same as the raw data that go into the z ˆ 1 star formation rate determinations of Madau et al. (for 0:2 # z # 1 this was based on the CFRS luminosity density functions of Lilly et al. 1996). We use a formal error bar of 20 per cent for our UV uxes to give errors representative of the V photometric errors and the K-corrections. We plot the Ha versus UV luminosities in Fig. 4 and overlay lines for a set of conversions from Table 3. Note these are only valid for a continuous, constant star formation rate ± the more complex problem of bursts is considered below in Section 6. It is clear from the plot that there is an order-of-magnitude agreement in the star formation rates derived from the two methods and a reasonable correlation, i.e. strong UV systems are usually strong Ha systems. There are no galaxies with an extremely large excess of Ha relative to UV, which would occur if the star formation were highly obscured by dust. We do nd points with zero Ha ux and appreciable UV ux, which we would expect to detect within the measurement errors if there was a linear correlation. This cannot be caused by dust as the latter can only enhance the Ha/UV ratio, not diminish it. As noted in Section 3, these spectra are detected, they just do not contain signi cant Ha. One physical effect that will explain this is the relative lifetimes of stars contributing to the UV and Ha as mentioned in Section 4. When one moves away from the simple scenario of a constant star formation rate the picture changes considerably. For example, for an instantaneous starburst the Ha ux will drop to effectively zero after 30 Myr while signi cant UV ux will persist up to 1000 Myr. This will produce low Ha points such as are seen in our sample. Weak Ha should be present in all our galaxies because they are known to have [O ii] emission (see Section 3), however the Ha/UV ratio will scatter more widely and it is certainly possible for Ha to be below our detection limit despite signi cant [O ii] and UVemission. To quantify these effects requires us to develop a proper model for starburst activity in galaxies. We do this below in Section 6. Nevertheless when one averages over many galaxies the effect of bursts should cancel out in the mean ± the continuous star formation conversions of Table 3 should be applicable for an ensemble of galaxies. (This approximation is tested below using the methods developed in Section 6 and is found to be accurate to, 6 10 per cent, even for this small sample.) It can be seen that the values scatter about a mean ratio of 2±3 times as much star formation inferred from the Ha as from the UV. This is balanced to some extent by the zero-points. By summing over all the galaxies we nd the following relation between the luminosity per comoving volume in Ha and UV: L 2800 ÊA ˆ 3:1 6 0:4; L Ha with units as in the last column of Table 3. This ratio is plotted as the dotted line in Fig. 4.

8 850 K. Glazebrook et al. The ratio is somewhat lower that those predicted by the models which give values in the range 4±14 for 0.2±2.5 Z (. What can cause this discrepancy? It is too large to be encompassed by our range of metallicities; one can boost the Ha/UV ratio if we assume a lower age than,1 Gyr. However changing to 0:1 Gyr only increases the slopes of the solid lines in Fig. 4 by,30 per cent; we could achieve the observed slope if star formation is only,0:01 Gyr old in all the detected galaxies, but this would be unlikely simply because of random sampling ± the redshift range of the sample corresponds to a timespan of.1 Gyr at z ˆ 1. The most likely explanation for the discrepancy is the presence of dust attenuating the ultraviolet light. If we adopt ducial model values of (10.9, 6.3) for (Scalo, Salpeter) for Z (, which agree well between PEGASE and BC96 models (kl96 tracks), the ratios of Ha to UV inferred star formation rates are (3.5, 2.0). Using Pei (1992) extinction formulae (a standard dust-screen model) we then derive a mean sample A V of (1.0, 0.5) mag for the SMC law, (1.1, 0.6) for the Galactic law. These extinction values are entirely consistent with those found from studies of star formation from Balmer lines in local normal Sab galaxies. For example Kennicutt (1983) found A V ˆ 1:0 mag and a study of low-redshift z < 0:3 CFRS galaxies using the Hb=Ha line ratios by Tresse & Maddox (1998) found the same value. Calzetti, Kinney & Storchi-Bergmann (1994) and Calzetti (1997) have proposed an empirical dust-attenuation law for heavily reddened starbursts (A V. 2:2 mag). In this model the nebular lines have about twice the optical depth of the stellar continuum; moreover although the lines are well-described by a standard Galactic screen law, the stellar continuum is empirically described by a greyer law in which the dust and stars are intermixed. Using the Calzetti law we derive A V attenuations of (2.6, 1.4) mag (for stars, 1.4 times this for nebulae); because the attenuations of the Ha and 2800 AÊ continuum are more similar to each other than for the screen models, a much higher obscuration is required to match the observed excesses: attenuations of (2.9, 1.6) mag result for Ha and (4.2, 2.3) mag for the 2800 AÊ stellar continuum. It should be noted, however, that it is still not established that corrections derived for the Balmer lines in starburst regions of nearby galaxies are appropriate to the integrated light of the distant galaxies studied here. This question remains open. We can now examine the total correction for dust in both the Ha and UV determined star formation rates. The Milky Way law gives corrections for (Scalo, Salpeter) IMFs of (2.2, 1.5) times for Ha and (8.0, 3.1) for the UV. These numbers are the same to within 610 per cent for the SMC extinction law; this is because the two extinction curves differ most strongly in the UVat << 2800 AÊ (e.g. at the AÊ dust feature), and in the near-uvand optical they are very similar. The Calzetti law of course gives much larger values: the nal star formation rates are an additional factor of,6 times higher for the Scalo IMF and,3 times higher for the Salpeter IMF. Finally we can compare the star formation rate of our z, 1 CFRS galaxies with that of local counterparts. We adopt the Salpeter IMF as that is conventionally used for deriving the local rates. For the range of dust corrections we have derived we obtain rates of,20± 60 M ( yr 1, comparable to those for local starbursts (e.g. Calzetti 1997) and much greater than the typical 4 M ( yr 1 found for local normal spirals (Kennicutt 1983) and the Milky Way (Smith, Biermann & Mezger 1978). 6 MODELLING OF STARBURSTS As noted earlier, the interpretation of Ha and UV luminosities as star formation rates becomes more complicated if non-constant star formation histories are assumed. For this reason we developed a mathematical framework for exploring this and to see how well we could reproduce the observed distribution. 6.1 Methods The principles are based upon maximum likelihood and are a 2D generalization of the methods developed by Abraham et al for colour±colour tting. For a given star formation history we can run a spectral evolution code and calculate Ha and UV luminosity as a function of time using the methods of Section 4. We evolve the models for 5 Gyr and sample at random times (we can do this because all the galaxies are at similar redshift) to create a 2D model distribution of light in the the (Ha, UV) plane. The code then computes the likelihood of drawing the observational data from the model: L ˆ Y P h; u exp h i h 2 2Dh 2 u i u 2 i 2Du 2 i du dh; 2pDh i Du i i where the observational (Ha, UV) points are h i ; u i with errors Dh i ; Du i, and the model points have probability density P h; u. The star formation histories are parametrized and likelihood space is explored to nd the maximum likelihood. We use an adaptive algorithm where a large parameter space is explored with a coarse parameter grid to locate the peak and the region around the peak is then examined with a ner grid to give con dence limits on the tted parameters from DL. Once we have the best- tting parameters for a model, we can then create simulated observational data sets. This is done 1000 times, the maximum likelihood t being recomputed each time; this allows us to normalize our relative likelihood into an absolute probability of the observed data, given the model. 6.2 Star formation histories explored We parametrized the star formation histories as continuous star formation, with galaxy-to-galaxy scatter, plus a random distribution of bursts. Initially the total star formation rate is kept constant and normalized to the values derived in Section 5. This is a good approximation as an ensemble of galaxies undergoing bursts will approximate continuous star formation and results in one less free parameter. For our further analysis we con ne ourselves to the BC96 models (Z (, `kl96' atmospheres) and the Salpeter IMF (as the latter gives better results for tting the star formation histories, colours and mass-to-light ratios of galaxies, see for example Kennicutt (1983); Lilly et al. 1996; Calzetti 1997; Madau et al. 1998). We correct all (Ha, UV) points using the A V ˆ 0:6 mag Milky Way law derived in Section 5; the effect of adopting the Calzetti law is just a simple scaling to star formation rates that are globally 3 times higher and does not affect the details of the analysis. To start with, we modelled a simple continuous star formation model to check that our code was giving sensible results. To make it more realistic we introduced a scatter, C j, between galaxies following a normal distribution (slightly corrected to avoid negative star formation rates). The best- tting results are shown in Fig. 5 as a likelihood contour plot overlaid on the model points. For comparison we also show a simulated set of data points drawn from the model distribution. It can be seen that some scatter is introduced; this originates physically from the time variation of UV light even for constant star

9 Ha star formation rate at z ˆ Figure 5. Results of tting burst models to our extinction-corrected Ha and UV (2800 AÊ ) data. The three rows show three different models as described in the text: continuous star formation (top row), xed mass exponential bursts plus continuous star formation (middle row) and variable mass exponential bursts plus continuous star formation (bottom row). The left-hand column of panels shows the observational data (points) compared with a model distribution generated from the best- tting model (contours correspond to a factor of 10 in probability density). The middle column of panels shows the likelihood contours of the main burst parameters generated by our tting. (Contours correspond to a factor of 10 in likelihood; the lled circle marks the maximum likelihood point.) The right-hand column shows a realization of the best- tting model, i.e. 13 simulated data points generated from the model distribution with the observed errors (points < 1j are set equal to zero as in the data). Note that the continuous star formation includes a component of galaxy±galaxy scatter.

10 852 K. Glazebrook et al. Table 4. Best- tting model parameters. Description of model Best- tting parameters with errors, in the form log(l best ) Monte Carlo deviation P fitted ˆ 2j < 1j < best value < 1j < 2j of L best (percentiles) Continuous star formation C j ˆ 0:61 < 0:65 < 0:70 < < 38: rate Continuous plus constant F ˆ 0:87 < 0:90 < 1:00 < < 36: starbursts of xed mass C j not relevant because F best ˆ 1:0 M m ˆ 1:23 < 1:31 < 1:39 < 1:48 < 1: M ( t ˆ < 50:6 < 80:0 < 88:4 < 97:8 Myr Continuous plus constant F ˆ 0:93 < 0:96 < 1:00 < < 35: starbursts of variable mass C j not relevant because F best ˆ 1:0 M m ˆ 1:57 < 1:84 < 2:15 < 2:56 < 3: M ( M j ˆ 0:18 < 0:22 < 0:30 < 0:32 < 0:34 t ˆ 65:9 < 72:6 < 80:0 < 107:0 < 143:1 Myr Continuous plus exponential F ˆ 0:83 < 0:94 < 1:00 < < 36: starbursts of xed mass C j not relevant because F best ˆ 1:0 M m ˆ 4:28 < 4:71 < 5:18 < 5:54 < 5: M ( t ˆ 122:7 < 140:1 < 160:0 < 170:5 < 181:7 Myr Continuous plus exponential F ˆ 0:92 < 0:96 < 1:00 < < 36: starbursts of variable mass C j not relevant because F best ˆ 1:0 M m ˆ 2:67 < 2:91 < 3:16 < 3:37 < 3: M ( M j ˆ < < 0:10 < 0:13 < 0:17 t ˆ 65:0 < 72:1 < 80:0 < 106:3 < 141:4 Myr Notes. (i) Parameter ranges `1j' and `2j' correspond to D log L ˆ 0:5, 1:0. (ii) M j is expressed as a fraction of M m. formation. The best- tting parameter values are shown in Table 4 ± the model is a very bad t to the distribution of data. One might ask whether the scatter could be explained by variation in extinction between galaxies. While it is possible that this can explain some of the variation, it cannot explain the points with large amounts of UV emission and small amounts of Ha emission. This is because dust quenches the UV much more than the Ha ± precisely the opposite effect to that sought. We next explored the effects of starbursts to see if these could plausibly explain the observed distribution. Initially we tried xed-mass bursts, then we tried a scheme for allowing the burst masses to vary. As we could nd little information in the literature as to an appropriate mass function to adopt for bursts, we invented our own simple phenomenological scheme: bursts are parametrized by a mean mass (M m ) and standard deviation (M j ). The distribution is assumed to be normal. While this has no physical basis, it only has two parameters and at least allows us to investigate the effects of mass distributions. M m and our global star formation rate normalization x the mean interval between bursts. Finally we have F, the fraction of the star formation occurring in bursts. For the form of the bursts we consider two cases (modelled after BC96): a constant burst of length t and exponential bursts of e- folding time t: The results of this exercise is shown in Table 4. It can be seen that the burst models provide much better ts than the continuous models. The Monte Carlo realizations show that the latter generate data sets like the observed one only about 1 per cent of the time. This is because the continuous star formation cannot generate enough variation in the Ha/UV ratio. The burst models are much better and generate synthetic points which look like the data,10± 20 per cent of the time. This is because the variation in the star formation rate is the principle cause of variation in the Ha/UV ratio. Allowing the burst mass to vary improves the t only slightly; we conclude that our data do not constrain the shape of the burst mass function signi cantly. The best- tting burst fraction is.1, indicating that the burst mode is preferred. The results are illustrated graphically in the lower two rows of Fig. 5, which compares the dust-corrected observational data with model realizations for a sample of key models. The likelihood contours of the main parameters are also shown. The best- tting mass of a typical burst is 2± M (, corresponding to a time interval between bursts of typically,200± 300 Myr, and the characteristic time t is,100±200 Myr. This means that the bursts usually overlap in time. These values are similar to what one might expect intuitively based on the data: the chance of catching a galaxy in the Ha quiescent stage has to be of order 1=3 to reproduce the fraction of points seen with UV but no Ha. We note that this kind of `continuous but episodic' star formation with several bursts per Gyr is of the same form as that found in local starburst galaxies by Calzetti (1997). Our average star formation rates are of the same order too. In between bursts, the star formation rate and Ha ux does indeed drop close to zero while the UV persists (see Fig. 6, which shows a sample time dependence) because of the stellar lifetime effects mentioned in Section 4. Thus the zero Ha points in our data (given the error bars) are naturally explained. Finally, with these tools we were able to test how well an ensemble of galaxies converged to approximating a continuous star formation rate, as assumed in Section 5. To do this we reran the likelihood tting, this time tting for the total star formation rate as a free parameter. The results of this gave rates of between 19 and 23 M ( yr 1 per galaxy, which agrees well with the value of 20 M ( yr 1 calculated in Section 5 for the same Salpeter IMF. While these simple models could do with some elaboration to obtain a better t, we are near the limit of what can be inferred from

11 Ha star formation rate at z ˆ Figure 6. The star formation rate, luminosity history in Ha and UV (2800 AÊ ) typical of our best- tting models. This is for the case of exponential bursts of variable mass, with a continuous star formation component, i.e. the model shown in the lowest three panels in Fig. 5. It can be seen that for long interburst periods galaxies are indeed quiescent in Ha, but not the UV. 13 data points. It is clear that this sort of detailed approach will bene t greatly from future observations and much larger samples. 7 MORPHOLOGICAL TRENDS Six of the galaxies in our sample have morphological information from our programme of Hubble Space Telescope high-resolution imaging of CFRS and LDSS2 high-redshift galaxies (Brinchmann et al. 1998; Lilly et al. 1998a). This is obviously an even more limited sample, but we can look qualitatively at the dependence of star formation rate on galaxy type. The classi cations are listed in Table 1 and `postage stamps' of the galaxies are shown in Fig. 7. There are three galaxies classi ed as `Peculiar'. All have detected Ha emission and blue colours [ V I AB < 1], and one ( ) has the highest star formation rate in our sample. Two of these are classed as `mergers' and one as a close pair, indicating an association between star formation and interaction. There are two galaxies classed as 'Compact'. Both of these are also blue [ V I AB < 1:2] and it is interesting to note that while one has quiescent Ha and strong UV the other has a large Ha excess (3.2). The remaining galaxy is , a red spiral, [ V I AB ˆ 2:9] which is quiescent in both UV and Ha.

12 854 K. Glazebrook et al. Figure 7. `Postage stamps' (10:1 arcsec 10:1 arcsec) of the six galaxies having images from our HST morphology programme. Finally we note that galaxies with star formation, whether inferred through Ha or UV, have the bluest V I colours [ V I AB < 1:2]. This is not in contradiction with the modest extinction values derived in Section 5 ± an extinction of A V ˆ 0:6 mag would only redden the observed V I (rest-frame 2800-AÊ B) by a small 0.4 mag, whereas the difference between and old and young stellar population is of order 2±3 mag. 8 COMPARISON WITH OTHER RESULTS There are now enough measurements of Balmer line star formation rates at high and low redshift to construct the rst star formation history of the Universe in Balmer light to compare with the previous UV measurements. For consistency we use the Salpeter IMF, H 0 ˆ 50 kms 1 Mpc 1, q 0 ˆ 0:5 throughout. All points are rederived from their original luminosity densities in a consistent manner using the UV, Ha factors in Table 3 for BC96 (kl96) with solar metallicity. This is shown in Fig. 8. The point at z ˆ 0 comes from the Gallego et al. (1995) local objective prism survey and is based on Ha. Tresse & Maddox (1998) have measured the Ha luminosity function at z ˆ 0:2 from the CFRS, at which point Ha is still available in the optical CFRS spectra. They nd a value a factor of 2 higher than the UV measurements. Our Ha measurements are used to derive a new value for the star formation rate density in the CFRS at z ˆ 1. This is higher by a factor of 3.1 times than the UV point. At z ˆ 2:8 we show the point derived from the work of Pettini et al., who used CGS4 to measure the Hb line in ve of Steidel et al.'s galaxies. They infer star formation rates 0.7±7 times higher than derived from the UV at 1500 AÊ rest and typical extinctions A 1500 AÊ ˆ1±2 mag. We show this as a factor of 3 above the UV point. As well as the Balmer lines, we also plot the point of Hughes et al. based on submillimetre observations and the points of Flores et al. (1998) from farinfrared ISO observations. It should be noted, however, that the derivations of the latter are qualitatively different from the Balmer line and UV measurements: the far-ir and submillimetre bands measure UV reprocessed by dust into thermal radiation and hence they are sensitive to galaxies that might not appear at all in the optical. Moreover, the Hughes et al. points are based on assumed redshift distributions for sources that have not yet been veri ed, and they have been disputed (Richards 1999). Finally it is also worth noting that the Hughes et al., Connolly et al. and Madau et al. points are all based on the same patch of sky, the Hubble Deep Field North (Williams et al. 1996), which may not be representative. It can be seen, however, that the general trend is for the Balmer line and ISO/submillimetre measurements to nd values several times higher than the UV continuum at all redshifts. The rise to z ˆ 1 is preserved; arguably the fall-off at z > 2 is preserved, although given the random errors and the systematics in the dust correction no change for z > 1 would also be consistent with the data. Whether star formation peaks at intermediate redshifts (z ˆ 1±2) or continues to high redshifts (z > 4) is an important test of hierarchical formation scenarios (e.g. Baugh et al. 1998). From the current data the question must remain open. The agreement between the far-ir/submillimetre measurements and Balmer measurements is particularly impressive, because both attempt to compensate for dust in different ways. Flores et al. nd an upward dust correction of 2:9 6 1:3 atz ˆ 1 and extinctions of A V ˆ 0:5±0.9 mag, both consistent with our best estimates. It should be noted that independent ISO observations of the Hubble Deep Field North by Rowan-Robinson et al. (1997) give a con icting value several times higher than that of Flores et al.; however the latter is derived from a 19 times larger area of sky and so is probably better determined.