## 3. ResultsUsing tabulated data (Hamuy, 1996) from the 29 Cal
n/Tololo supernovae and keeping q
Thus, by introducing one additional parameter R, we have achieved a very substantial reduction in compared to our previous analysis. There, without a color correction, the best fit obtained when the smaller sample of 26 Cal n/Tololo SNe that passed the color cut plus the six cosmological SNe yielded a large reduced = 1.47 with a low confidence level of CL = 0.05. Since these two studies use somewhat different sets of data, a closer comparison would be to the best fit of 29 Cal n/Tololo supernovae alone which yields for R set to zero, b = 1.09 and CL = while a fit to 26 Cal n/Tololo supernovae passing the color cut, yields b = 0.80 and CL = 0.027 for R = 0. It could be argued that the low merely reflects the introduction of yet another uncertainty ) multiplied by R in Eq. (3). However a convincing argument that this is not the case can be made by arbitrarily setting both the measurement uncertainties ) and to zero. When this is done and the minimized, the reduced becomes 0.94 (CL = 0.55), i.e. a highly probable representation of the data using for measurement uncertainties only the apparent magnitude uncertainties and the assumed peculiar velocity , which is generally considered a minimal estimate of peculiar velocity. Thus the introduction of a second parameter R has indeed improved the fit and is fully justified. As an alternative (and more realistic) way to obtain a more likely confidence level of about 0.5, all measurement errors of the 29 Cal n/Tololo SNe could be scaled by a factor of 0.55. The above three fits with different treatment of errors, as well as
others with b or R or both set to zero, are tabulated in Table 1.
It is interesting to note that setting b = 0 yields an acceptable
confidence level for all 29 SNe, while setting R = 0 does not. Thus
the color correction appears to be more
effective in standardizing SNe Ia than does the presently popular
shape correction , although both appear to be
necessary as can be seen in Fig. 3. Fig. 3a,b shows the impact of
setting both b and R to zero. A best-fit value of H
Fig. 4 is a plot of confidence level (with measurement
uncertainties scaled by 0.55) as a function of b and R, showing that
there is some negative correlation between these parameters.
Consequently by setting one parameter to zero as can be noted from
Table 1, there is for the best-fit solution a compensatory
increase in the other parameter. Further consequences of these
omissions, as mentioned above and seen in Fig. 3, are
less-than-satisfactory fits of H
Table 1 also lists under the various conditions the dispersion
of the data points expressed in magnitudes. This is obtained from the
standard deviation in the calculated values of H © European Southern Observatory (ESO) 1998 Online publication: March 3, 1998 |