From: Ariel Goobar (ariel@physto.se)
Date: Fri May 23 2003 - 00:28:26 PDT
Hi Greg,
that sounds interesting. Have you tried what happens when
adding a Gaussian intrinsic spred in B-V around 0.05 mag?
As you point out the effect will be highly dependent on the
the flux limit you use in your simulations. I am not sure
there is a perfect 1-to-1 correspondence with the
parameter you used (dim-cut). There are a few steps between
candidate discovery (a different stages in the I-band LC,
stretches, spectroscopy screening, K-corrs, LC fit, etc) and
the residual showing up in Rob's Hubble diagram.
Ariel
On Thu, 22 May 2003, Greg Aldering wrote:
>
> 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
>
>
-- ___________________________________________________________________ Ariel Goobar (www.physto.se/~ariel) Department of Physics, Stockholm University AlbaNova University Center, SE-106 91 Stockholm, SWEDEN tel: +46 8 55378659 fax: +46 8 55378601
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