From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Thu May 22 2003 - 18:20:20 PDT
I have simulated the behavior of our low-extinction method. I started
with the models of Hatano, Branch and Deaton, which provide the
probability distribution function of B-band extinction, A_B, for SNe
observed through spiral and elliptical galaxies viewed at various
orientations. I generated random values of A_B following this
distribution function, but adding a flux-limit bias which depresses the
probability of finding extincted SNe in proportion to the volume of
space in which they would be accessible in a flux-limited sample. I
next "observed" them by randomly chosing an E(B-V) error bar and then
generating a Gaussian deviate with this error bar, and adding the
result to the generated value of A_B. I then applied the cuts a SNe
currently must pass to be included in the low-extinction subset in the
HST paper:
sigma R-I < 0.25
E(B-V) < 0.1 or E(B-V) < 2*(sigma E(B-V))
I also added a too-faint cut, requiring that SN not be fainter than N
times its magnitude uncertainty (including an intrinsic error of
0.17). In Rob's last fits, all the residuals were within 3-sigma for
the low-extinction subset, even though no cut on deviation was
applied. Thus, my cut considers the likelihood that if there were a
significantly dim outlier we might have chosed to reject it even
without a well-measured color to prove that it is reddened.
I find that our method does have a bias, but that the bias is small
compared to our other systematics. However, it might not be small
relative to the Riess prior (that has to be checked).
Here is what I get:
N-sigma <A_B> <A_B> Bias
dim cut low-z high-z low-high
-------------------------------------
2.0 0.068 0.081 0.013
2.5 0.075 0.094 0.019
3.0 0.080 0.104 0.024
All mean A_B values are in magnitudes. Basically what happens is that
the requirement that E(B-V) < 2*(sigma E(B-V)) lets in SNe which are
more reddened than E(B-V) < 0.1. This effect is larger at high redshift
because the errors are larger. Note also that the average is not zero,
and in fact the mode is not zero either. For our current method, I
estimate that the bias is about 0.024 magnitudes in the sense that the
high-redshift SNe are dimmer. This depresses Omega_M by a comparable
amount.
Note that if I do not include the flux-limit suppression, our bias is
worse. So, we would expect the low-extinction technique to perform
worse in a volume-limited sample.
- Greg
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