From: Michael Wood-Vasey (wmwood-vasey@lbl.gov)
Date: Tue Apr 15 2003 - 09:07:05 PDT
On Tue, Apr 15, 2003 at 10:01:03AM -0500, Robert A. Knop Jr. wrote:
> >From Kolb & Turner p. 41:
>
>
> d_L^2 = R^2(t_0) r_1^2 (1+z)^2
>
> where R(t_0) is the scale factor at the time of detection, r_1 is the
> coordinate distance to the object, and z is the redshift. In this case,
> r_1 can be figured out as r_1(z). Equivalently, work out the proper
> distance to the object at time of detection, and that is R(t_0)r_1(z) ;
> this gives us (most of) our standard luminosity distance integral
> (missing one factor of (1_z)).
>
> r_1(z) should clearly just use that z that comes from cosmological
> redshift, since this is giving you the radius of the sphere surrounding
> the emitting object, and as such you want the real distance.
>
> The other z, in the (1+z)^2 above, however, should use your observed
> (geocentric) redshift, as those terms are to take care of (1) the
> redshifting of the photons (and corresponding energy loss) and (2) time
> dilation. Energy loss and time dilation will happen if it's a doppler
> shift or a cosmological redshift, so the total redshift is appropriate
> here.
>
> Probably what this means is that to do it *right*, we need to use *both*
> heliocentric and CMB-based redshifts, putting the right one in the right
> place.
>
> Does anybody agree with this, or can anybody point out a flaw in my
> reasoning?
This is fine. Alex and I agree.
- Michael
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