# [AstroPy] Cosmology Recession Velocity

Michael Seifert michaelseifert04 at yahoo.de
Tue Feb 23 20:05:00 EST 2016

```Many thanks, your explanation is very good and the notebook even better.

But I have another question because I think the problem arose because I misunderstood something fundamental here. They quoted in their paper that "present day recession velocities are shown" (defining it in a later paper as "a(z) = a(0)"). So is present day recession velocity the "current" recession velocity (62c) or the currently measurable recession velocity of light that reaches us (3.3c)?
If that's beyond the scope of the mailing list, I apologize.

Thanks again,Michael

Thøger Emil Rivera-Thorsen <trive at astro.su.se> schrieb am 1:35 Mittwoch, 24.Februar 2016:

Sorry, that did not come out very clear.

The two different values you find are the recession velocity at the time of emission and the recession velocity now. Since the Universe has expanded by a lot since then, a current value of 62 c seems reasonable.

I have a notebook demonstrating some key Astropy features for students at our department, including this very calculation, here: http://nbviewer.jupyter.org/urls/ttt.astro.su.se/~trive/teaching/tools-package/Astropy-intro.ipynb (Scroll to the bottom)

On 02/24/2016 01:14 AM, Thøger Emil Rivera-Thorsen wrote:

62 c at z=1000 does not sound completely off for the *current value*. I suppose the values between 2 and 4 c you get gggfrom Davis & Lineweaver is velocities at the time of emission? These two differ *strongly*.

On 02/24/2016 12:25 AM, Michael Seifert wrote:

Hi,

today I tried to determine cosmological recession velocities based on the paper of Davis, Lineweaver, 2001 (http://arxiv.org/pdf/astro- ph/0011070v2.pdf) with astropy.cosmology.

But I'm not sure what I'm doing wrong (or if I just misunderstood their reasoning). But they said the recession velocity is just "v_rec = da(z)/dt * comoving distance(z)" and "da/dt = H(z)*a(z)" so the recession velocity should be with "cosmo = astropy.cosmology.WMAP9" and redshift "z=1000":

v_rec = cosmo.H(z) * cosmo.scale_factor(z) * cosmo.comoving_distance(z)

but this gives me 62 times the speed of light where it should only be between 2 and 4 (based on the paper). But just using

v_rec = cosmo.H0 * cosmo.comoving_distance(z)

gives me 3.25 * c which seems to fit their calculations. Is my formula or reasoning wrong or is there something strange in the comoving distance calculation of WMAP9?

I hope this question is not too basic but I'm not very deep into cosmology and it just seemed strange to me.

Many thanks in advance,
Michael

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