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Astron. Astrophys. 350, 349-367 (1999)

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5. Dependence on cosmology

Besides the standard flat [FORMULA] = 1 cosmology (SCDM) used so far, we have also studied two additional cosmologies; one open cosmology (OCDM) with [FORMULA] = 0.3 and [FORMULA] = 0, and one flat, [FORMULA]-dominated cosmology ([FORMULA]CDM) with [FORMULA] = 0.3 and [FORMULA] = 0.7. The most obvious effect of a different cosmology comes from the luminosity distance, [FORMULA] (Eq. (5)). Changing from SCDM to OCDM and [FORMULA]CDM increases the distance modulus, making the high-z SNe fainter (Eqs. (4) & (5)), as seen in Fig. 2. The increased distance modulus in the OCDM and [FORMULA]CDM cosmologies also affects the intrinsic star formation rates used. A larger distance modulus implies an increase in the absolute magnitudes of the galaxies from which the star formation rate, and hence also the supernova rates, are derived. As expected, these two effects, i.e. fainter apparent SNe and an increased SNR, almost cancel when it comes to the observed number of core collapse SNe per square angle.

The cosmology also affects the volume element, given by


where [FORMULA] is the proper motion distance, [FORMULA] = (1+[FORMULA]. The luminosity distance, [FORMULA], is given by Eq. (5). The change in volume element affects the SNRs when expressed in units number of SNe per Mpc3 per yr. It does not, however, change the estimated rates of observed core collapse SNe expressed in number of SNe per square angle. This is due to the fact that the core collapse SNR is directly proportional the observed luminosity density of galaxies, which is calculated from the number of galaxies per redshift interval for a specific angle over the sky, an observational quantity independent of cosmology.

When it comes to the Type Ia SNe, the volume element enters the calculations since the time between the formation of the progenitor star and the explosion of the SN may be a significant fraction of the Hubble time. This dependency on cosmology increases as the delay time [FORMULA] increases. The general trend is an increased SNR for the alternative cosmologies at high redshift.

Fig. 9 show the estimated number per square arcmin of core collapse and Type Ia (using [FORMULA] = 1 Gyr) SNe in the I and K´ filters down to different limiting magnitudes for the three cosmologies, using the hierarchical model for star formation.

[FIGURE] Fig. 9. Number of SNe per square arcmin that can be detected down to different limiting magnitudes in the I and K´ bands for three different cosmologies; SCDM ([FORMULA] = 1, [FORMULA] = 0), OCDM ([FORMULA] = 0.3, [FORMULA] = 0) and [FORMULA]CDM ([FORMULA] = 0.3, [FORMULA] = 0.7). For the Type Ia rates we assume a delay time [FORMULA] = 1 Gyr.

For the number of core collapse SNe the effect of changing cosmology is small for the reasons discussed above. Only at the very faintest magnitudes is there significant deviation between the models. At K´ = 31, the estimated rates increase by a factor [FORMULA] 1.5 when changing from SCDM to [FORMULA]CDM.

The estimated rates of Type Ia SNe differ at faint magnitudes by up to a factor two between the cosmologies. For [FORMULA] = 1 Gyr the intrinsic rates of the OCDM and [FORMULA]CDM models are higher than the SCDM at redshifts [FORMULA] 1. It is, however, necessary to reach faint magnitudes [FORMULA] to observe this increase in the total rates. Note, however, that a Type Ia at peak magnitude has m [FORMULA] 25 at [FORMULA] 1. This means that using SNe seen at peak allows probing of the region where the rates start to differ between the cosmological models at more moderate limiting magnitudes. Ruiz-Lapuente & Canal (1998) discuss the use of Type Ia's to distinguish between different cosmologies. In Sect. 8 we comment on their results.

The increased Type Ia rates at high z for the alternative cosmologies means that the redshift cutoff moves to higher redshifts. This cutoff is also highly dependent on the delay time [FORMULA] (see Fig. 1). It is, however, somewhat less dependent on the SFR. Therefore, if [FORMULA] is known, it should be possible to constrain the cosmology, even if the SFR is not accurately known. As an illustration, including all SFR scenarios, and using [FORMULA] = 1 Gyr ([FORMULA] = 3 Gyr), results in a cutoff in the Type Ia rates at z 2.5-3.5 (1.2-1.5) for the SCDM cosmology, while the drop is at z 2.9-4.9 (1.6-2.2) and z 3.2-5.3 (1.9-2.6) for the OCDM and [FORMULA]CDM cosmologies, respectively. The higher values in these redshift ranges correspond to the hierarchical star formation scenario.

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999