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Astron. Astrophys. 331, 815-820 (1998)

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2. Method

The procedure followed is essentially the same as that used by Tripp (1997) to investigate H0, q0, and b. That analysis used the Hamuy et al. (1996) data and six more distant ([FORMULA]) SNe Ia of Perlmutter et al. (1997). The Hubble constant H0 is calculated for each supernova using the expression


Here [FORMULA] is the apparent blue magnitude and [FORMULA] the absolute blue magnitude at maximum light, while [FORMULA] is the deceleration constant and z is the measured redshift.

Following the evidence of Phillips (1993) and Hamuy et al. (1995) that supernovae whose light curves fall more rapidly have lower peak luminosities, the absolute magnitudes [FORMULA] of the supernovae have been modified by adding a term b [FORMULA]. The measured quantity [FORMULA] is the decline in magnitude during the first 15 days beyond maximum blue light and b is a decline-rate parameter to be varied in a least squares fit of all the supernovae. To accommodate different amounts of reddening observed in the 29 supernovae of Hamuy et al. (1996), arising either from an intrinsically reddened supernova or from intervening dust in the parent galaxy, we introduce, in the same spirit as the parameter b, another phenomenological parameter R in the form R ([FORMULA]). Here [FORMULA] is the difference between the apparent B and V magnitudes at their respective maximum light as measured by Hamuy et al.(1996) and R ([FORMULA]) (called [FORMULA] ([FORMULA]) in the conventional terminology of dust absorption) incorporates both the intrinsic dependence of [FORMULA] on [FORMULA] as well as the B-band extinction due to dust. The modified value of [FORMULA] for any supernova with a measured value of [FORMULA] and [FORMULA] is then written as:


The value -19.48 is the mean absolute magnitude of seven Cepheid-calibrated supernovae 1 and 1.05 is an average decline rate as used previously (Tripp, 1997). These are preliminary values pending further study of the nearby Cepheid-calibrated supernovae in the light of this new color correction (Tripp & Branch, in preparation). Any revision will have absolutely no effect on the quality of the fits nor on the best-fit values of the two correction parameters b and R obtained in this paper. However, it will directly affect H0 through the relation [FORMULA] obtained from Eq. (1).

Fig. 1 is a plot of the [FORMULA] color vs. [FORMULA] for the 29 Cal [FORMULA] n/Tololo supernovae. Apart from the one highly reddened supernova, there appears to be only a relatively weak dependence of color on [FORMULA], so we may anticipate that the color correction is not strongly correlated with the [FORMULA] correction.

[FIGURE] Fig. 1. Plot of the [FORMULA] color vs. [FORMULA] for the 29 Cal [FORMULA] n/Tololo SNe. Previous fits (Hamuy et al., 1996, Tripp, 1997) had excluded from their analyses the three highly reddened supernovae with values of [FORMULA]

Knowing [FORMULA], [FORMULA], and z, we use Eqs. (1) and (2) to evaluate H0 for each supernova, with b, R, and q0 as parameters. The uncertainty in H0 for each supernova is obtained by combining in quadrature the quoted errors [FORMULA], [FORMULA], and [FORMULA] with an uncertainty in the luminosity distance due to a possible peculiar motion [FORMULA] km/s of the host galaxy with respect to the Hubble flow. Thus


The uncertainty in absolute magnitude calibration is common to all the supernovae so is not, at this point, included. A weighted average of the 29 values of H [FORMULA] is calculated. In this way a least-squares value for H0 along with its uncertainty and a [FORMULA] for the fit is obtained with b and R as parameters. Since it has little effect on this discussion, we fix the deceleration parameter q0 = 0.385 as determined by the previous fit (Tripp, 1997) of the Hamuy et al. (1996) data combined with six more distant cosmological SNe Ia of Perlmutter et al. (1997) that are much more sensitive to q0. (We do not include these cosmological SNe Ia in the present analysis since their [FORMULA] colors were not measured.) The parameters b and R are then varied to search for a [FORMULA] minimum.

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998