Re: Notes on Iband phone conference 12 Feb.

From: Andy Howell (howell@astro.utoronto.ca)
Date: Mon Mar 01 2004 - 08:11:40 PST

  • Next message: Chris Lidman: "Re: Notes on Iband phone conference 12 Feb."

    On Mon, 1 Mar 2004, Serena Nobili wrote:
    > >I can give you an example of where the chi_sq minimum value is not used.
    > >When Andy determines the SN epoch, he takes the average of the best five(?)
    > >fits. I've cc'ed this e-mail to Andy so he can explain to us why
    > >he chooses this method of analysis.
    > >
    >
    > As I said above, I think this is due to the fact that the chisq is not a
    > good indicator for the goodness of the fit of SN spectra. This depends on
    > the signal-to-noise but also on the differences in the spectral features.
    > I hope Andy agrees with me about this point.

    Hi,
    It will take me a little longer to digest all of the comments here, but I
    can reply immediately to this question of how I calculate a date from SN
    spectroscopy fits. I calculate a weighted average based on the best 5
    fits to a SN spectrum. The weights are the inverse of the square of the
    goodness-of-fit parameter. The goodness of fit parameter is like a
    chi-sq, but without the errors. So if "S" is the goodness of fit
    parameter, and "D" is the date I determined from that fit, then the
    average date is:

         5
         __ Di/Si^2
    Dav= \ _________
         /
         __ 1/Si^2
         i=1

    Thus if the best fit is much better than the rest, it dominates the date
    determination. However, allowing the other fits to have some influence
    gets around the discreteness problem. Dates are only good to +/- 1 day on
    SN spectra (if that). Since different SNe have differnt distributions of
    elements, what looks like day 15 on one SN may well be day 17 on another
    SN. By averaging you beat down some of this scatter. At the same time,
    by doing a weighted average, you ensure that the best fits drive the
    average. I have done tests on the effects of different indicators of the
    date, e.g. (a) just the best fit date, (b) the median of the top five, (c)
    the weighted average. The weighted average gave the least dispersion in
    spectroscopic day vs photometric day plots.

    -Andy

    This archive was generated by hypermail 2.1.4 : Mon Mar 01 2004 - 08:12:00 PST