Cosmological Applications of H Surveys

The star formation rate of massive stars

The proportionality between the emission measure and the intensity of the Balmer H emission provides an estimate of the total number of ionising photons emitted, and hence on the number of massive, hot stars that produced them. This has become the standard technique to infer not only the star formation rate but also the initial mass function (IMF) of massive stars. The total number of ionising photons in a stellar population of age t, IMF and with a history of SFR given by , can be expressed as

where is the number of ionising photons emitted by stars of mass m at time , and the effective lifetime extends from the ZAMS to the terminal age main sequence (TAMS). Note that the effective cutoff mass is given by the IMF-weighted Ly-c production rate and is about 10 M. The reason for this is that the dependence of the number of emitted ionising photons with temperature (mass) is extremely steep : going from 20,000 K to 35,000 K increases the Ly-c flux density by 4 orders of magnitude. This sharp cutoff, weighted by the IMF makes sure that no stars below about 10 M contribute to the final ionising flux. This implies that estimates of the ionising flux give a direct constraint on the IMF of stars above 10 M, but says nothing on the IMF below that mass. Using the recent models from Schaerer & De Koter (1997) which incorporate for the first time stellar interiors with realistic stellar atmospheres, we obtain for a Salpeter IMF

The existence of in the equation above is only the consequence of the assumption of continuity (à la Salpeter) of the IMF below 10 solar masses. Under standard (case B) recombination conditions, the ratio is approximately 2.2, for a wide range of IMF slopes.

However, estimating the flux of ionising photons from the H emission has several problems: (1) the ionisation conditions for the opacity in the Lyman continuum [clumpy ISM, escape fraction, diffuse emission], (2) dust corrections [at wavelengths below 912 Å dust tends to absorb rather than to scatter], (3) contamination by the [NII] 6583 line [variable, and usually not resolved from H], (4) evolution of the stellar populations [which may produce an underlying absorption H line], (5) contamination of the H line by nonthermal processes [presence of AGN-like activity].

Each of these caveats would deserve a section by itself, but we will comment here only the first one that has implications for the next section. Oey & Kennicutt (1997) compared H\ fluxes with predicted Ly-c fluxes and found that a significant fraction (up to 51%) could leak from HII regions, providing a bath of ionising photons in the WIM. The origin of these Ly-c photons could either be from the leakage in HII regions or from field massive stars. The first interpretation is favoured by Ferguson et al. (1996ab), although Patel & Wilson (1996ab) argue that the number of OB stars detected in the field is more than enough to ionise the WIM. In any case, the failure of take into account the diffuse H emission underestimates the true SFR by factors between about 3 and an order of magnitude.

In the case of an ensemble of galaxies, the problems above add to the completeness of the sample, and of the temporal evolution of the emission line due to the evolving stellar populations on cosmological time scales. Despite these caveats, useful constraints can be obtained on the luminosity density at H (assuming the observations are sensitive enough to low fluxes so that the luminosity density converges). For instance, Tresse & Maddox (1997) get a luminosity density of 3.16 10 erg s Mpc at using the CFRS sample, which is substantially larger than the local value. For higher redshifts the sensitivity in the near IR is much lower, and the current limits (van der Werf, in preparation) are about 1.56 10 erg s Mpc at , much lower than the (lower) limits obtained from the HDF survey.

© Copyright Astronomical Society of Australia 1997