Re: Color text

From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Fri May 23 2003 - 15:46:57 PDT

  • Next message: Greg Aldering: "Re: Updated color text (based on Greg's changes to my last version)"

    I don't know whether I stuck to the party line here, but I did add
    some thing that I think we should say simple to support our own
    method (not to attack Riess).

    >From robert.a.knop@vanderbilt.edu Fri May 23 13:58:23 2003
    >Date: Fri, 23 May 2003 15:58:21 -0500
    >
    >Changes
    >
    >1. The first three paragraphs of "Colors and Extinction"
    >
    > In this section, we discuss the limits on host-galaxy extinction we
    > can set based on the measured colors of our supernovae. For the
    > primary fit of our P99 analysis, extinction was estimated by comparing
    > the mean host-galaxy \ebv\ values from the low- and high-redshift
    > samples. Although the uncertainties on individual \ebv\ values for
    > high-redshift supernovae were large, the uncertainty on the mean of
    > the distribution was only 0.02 magnitudes. P99 showed that there was
    > no significant difference in the mean host-galaxy reddening between
    > the low and high-redshift samples of supernovae of the primary
    > analysis (Fit C). This tightly constrained the systematic uncertainty
    > on the cosmological results due to differences in extinction. The
    > models of \citet{hat98} suggest that most SNe~Ia should be found with
    > little or no host galaxy extinction. By making a cut to include only
    > those objects which have small \ebv\ values, we are creating a
    > subsample likely to have quite low extinction. The strength of this
    > method is that it does not depend on the exact shape of the intrinsic

      "\ebv\ distribution, only that most supernovae show very low
       extinction. Figure~3 demonstrates that most supernovae indeed have
       low-extinction, as expected from the \citet{hat98} models. Monte
       Carlo simulations of our data using the \citet{hat98} extinction
       distribution function and our low-extinction \mbox{$\ebv$} cuts
       confirm the robustness of this approach, and further, demonstrating
       that similarly low extinctions result for both low- and high-redshift
       datasets despite the larger color-errors of some of our earliest
       high-redshift SNe."

    > \citet{rie98} used the work of \citet{hat98} differently, by applying
    > a one-sided Bayesian prior to their measured \ebv\ values and
    > uncertainties; this prior had zero probability for negative values of
    > \ebv\, and sharply falls for positive values of \mbox{$\ebv>0.2$}

    Based on the HBD P(A_B)'s I've been working with, I would say the
    following. This also gives us wriggle-room in case Riess et al didn't
    exactly use HBD. That is, instead of saying what their prior *was*
    we say what it should have been if they did what they said they did:

      "uncertainties. A prior formed from the \citet{hat98} extinction
       distribution function would have zero probability for negative values
       of \ebv\, a peak at \mbox{$\ebv\sim0$} with roughly 50\% of the
       probability, and then an exponential tail to higher extinctions."

    > magnitudes. As discussed in P99 (see the ``Fit E'' discussion, where
    > P99 apply the same method to their data), when uncertainties on high-
    > and low-redshift supernova colors differ, use of an asymmetric may

                                                                   ^^^^^
                                                                   prior

    > introduce bias into the cosmological results, depending on the details
    > of the prior. While a prior with a tight enough peak at low
    > extinction values introduces little bias (especially when low- and
    > high-redshift supernovae have comparable uncertainties), it does
    > reduce the apparent \ebv\ error bars on all but the most reddened
    > supernovae. As we will show in Figure~ref{fig:ebvcosmofits}
    > (\S~\ref{sec:cosmoparam}) the use of this prior almost completely
    > eliminates the contribution of color uncertainties to size of the the

                                                           ^^^ ^^^
                                                           the xxx

    > cosmological confidence regions, meaning that an extinction correction
    > using a sharp enough prior is much more akin to simply selecting a
    > low-extinction subset than to fully performing an assumption-free
                                     ^^^^^
                                     xxxxx

    > extinction correction using the \ebv\ measurement uncertainties

    > The high precision measurements of the $R$-$I$ color afforded by the
    > \wfpc\ lightcurves for the new supernovae in this work allow a direct
    > estimation of the host-galaxy \ebv\ color excess without any need to
    > resort to a prior assumption concerning the intrinsic color-excess

                                   ^^
                                   s
    > distribution.
    >
    >2. Change the text on the left side, middle row of Figure 9 to
    > "(Contours depend on prior used; see text)". Edit (and cut down)
    > that caption so that it now reads:
    >
    > 68.3\%, 95.4\%, and 99.7\% confidence regions for \om\ and \ol\
    > using different data subsets and methods for treating host-galaxy
    > extinction corrections. The top row represents our fits to the
    > low-extinction primary subset, where significantly reddened
    > supernovae have been omitted and host-galaxy extinction corrections
    > are not applied. The second row shows fits where extinction
    > corrections have been applied using a one-sided color-excess prior.
    > Note that the published contours from \citet{rie98} in this row are
    > the non-dashed contours from their Fig. 6, and result from fits
    > that included not only well-observed supernovae, but also
    > supernovae without lightcurve color measurements (the equivalents
    > to which have been omitted from the SCP sets plotted in the other
    > panels), one supernova at $z=0.97$ without a spectral confirmation,
    > as well as two supernovae from the P99 set. The third row shows
    > fits with unbiased extinction corrections applied to our primary
    > subset. The HST SNe presented in this paper show a marked
    > improvement in the precision of the color measurements, and hence
    > in the precision of the \om\ and \ol\ measurements when a full
    > extinction correction is applied. With full and unbiased
    > extinction corrections, dark energy is still required with
    > \mbox{$P(\ol>0)=0.99$}.
    >
    > The text in the section discussing this figure didn't really go on
    > about the bias, so didn't need any editing, except to remove the
    > phrase "but at the expense of biasing the results" after "...hence
    > apparently tightens the constraints of the cosmological confidence
    > regions" (page 21). The last sentence of this paragraph no longer
    > says that we do host galaxy extinction corrections in an unbiased
    > manner, but just that "when host-galaxy extinction is directly and
    > fully accounted for..."



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