From: Don Groom (deg@panisse.lbl.gov)
Date: Wed Apr 16 2003 - 08:55:36 PDT
Rob,
Not sure whether Eric Linder is on deepnews or has commented on this or
not...
He argues that it is perfectly valid to threat the cosmological redshift
as a relativistic Doppler shift in "adding" velocities. Several of us had
an extended discussion of this at teatime a week or two ago.
While it is easy to construct examples (with pathological R(t)) in which
the redshift cannot be construed as an expansion velocity, we still behave
schizophrenically and talk about "the expanding Universe." Eric can object
when he reads this, but he argues that this is OK when combining proper
motion with cosmological expansion.
D
On Tue, 15 Apr 2003, 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?
>
> -Rob
>
> --
> --Prof. Robert Knop
> Department of Physics & Astronomy, Vanderbilt University
> robert.a.knop@vanderbilt.edu
>
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Don Groom (Particle Data Group, Supernova Cosmology Project)
DEGroom(at)lbl.gov www-ccd.lbl.gov Voice: 510/486-6788 FAX: 510/486-4799
Analog: 50-308//Berkeley Lab//Berkeley, CA 94720
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