From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Sun Apr 13 2003 - 03:50:50 PDT
On Sat, Apr 12, 2003 at 11:03:51PM -0700, Greg Aldering wrote:
> Sorry if I was unclear -- I meant that we could use the magnitude
> dispersion about the Hubble line for those few high-redshift SNe, after
> they are extinction corrected using whatever extinction determination
> you choose. This simply addresses whether the assigned magnitude
> uncertainty is appropriate. After extinction correction, the color
> error dominates the magnitude error, so scaling the color error up or
> down to get chi-square/DOF ~ 1 gives an estimate of the correct color
> error to use.
Ah. The problem I'd have with this, aside from what you note, is that
the rest of the supernovae don't really give evidence that
chi-square/DOF~1 would be exactly the right intrinsic error to
use... unless you believe that they, took, don't have enough intrinsic
uncertainty, since we're getting too high chisquares. On the other
hand, what you suggest is the conservative thing to do, since it will
*overestimate* the intrinsic U-B dispersion compared to the chisquare
one is getting from the rest. (There are statistics of small numbers
issues, though; with that few supernovae, the chisquare distribution has
a fair dispersion itself, though off of the top of my head the "within
factor of two" limit you quote below sounds plausible.)
> I realize there are few points to do this with; in Table 3 the 5
> highest redshift SNe have large quoted errors in E(B-V), which I assume
> has something to do with the assigned intrinsic uncertainty in U-B at
> max.
That's not it; the current table uses *no* intrinsic uncertainty in U-B.
It has to do with two things. First, the higher redshift are dimmer, so
the R-I colors at max tend to have higher uncertainties anyway. Second,
R-I at different redshifts has different leverage on E(B-V). Considered
to zeroth order, E(U-B)/E(B-V) is something like 0.75, so for supernovae
where R predominantly measures U and I predominantly measures V, you'd
expect 1.33 times the E(B-V) error for a given uncertainty in R-I. (The
way I in practice work it out is figure out what E(B-V) I need to
reproduce the color, figure out what E(B-V) I need to reproduce a
slightly different color, and then scale dE(B-V) as dR-I times the
difference in calculated E(B-V)'s divided by the offset in color I
used-- i.e., just a numerical implemetnation of the whole derivative
error propogation formula.)
> Since this is very simple, it is at least worth finding out what can
> be learned from this approach. I would do this myself if I had the
> residuals for your extinction-corrected OM-OL fit, and knew what intrinsic
> color uncertainty had been assigned to each SN.
I will post this later today; intrinsic already errors already are 0 as
noted above, which makes this calculation a bit easier.
> Since your cosmology fits (I did find the attachment after you pointed
> it out) show that the assigned U-B color dispersion is not all that
> important for OM-OL, I think the main remaining question then is whether
> or not we think we have good extinction measurements for those 5
> highest-redshift SNe. (There may also be a question of the role the
> assigned color uncertainty plays in the OM-w plots.)
I will try in the next two days to get the dependence of these issues on
OM-w too. (I probably won't get them out Sunday, but Monday.)
-Rob
-- --Prof. Robert Knop Department of Physics & Astronomy, Vanderbilt University robert.a.knop@vanderbilt.edu
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