# Temperature of a molecule in a galaxy

1. Nov 24, 2007

### randa177

Given the redshift z of a galaxy, how can one measure the temperature of a molecule in that Galaxy? ( Assuming it is heated only by the CBR) ?

2. Nov 24, 2007

### Wallace

You don't get a measure of the temperature of the gas in a galaxy from the redshift. Temperature changes the relative 'strengths' and widths of spectral lines and also changes the nature of continuum emmission, but doesn't shift the frequency of spectral lines, which is what redshift is defined as. So you do get temperature information from the spectra of galaxies, but the information is not encoded in the observed redshift.

The assumption that gas in galaxies in heated by the CMBR is not a good one. Any contribution that the CMB makes to heating gas in galaxies is negligible at best. Radiation from stars, shock fronts from colliding gas clouds etc are the sources of heating of gas in galaxies, not the CMBR.

3. Nov 25, 2007

### malawi_glenn

one molecule can't have temperature. Temperature is the mean kinetic energy of a large bunch of particles.

4. Nov 25, 2007

### Wallace

Oh yeah, good point malawi, I think my mind simply converted 'molecule' to 'gas' when I read the OP, since as you say, a single molecule can't have a temperature!

5. Nov 25, 2007

### malawi_glenn

I just pointed that out scince the OP seems to be quite confused.

To the OP:
Is this homework?
If this is a exercise about CBR, then your assumption has nothing do with the real physics, as Wallace pointed out.
The "real" question is then "Given z, what is the temperature of CBR?"

And there are many ways to work it out, depending on what equations and relations you know of etc, so there is no point for me to give you some formulas, it depends of you back ground knowledge and so on. I am very sure that if you consult your textbook the equation you need is trivially given or you can just create it from other equations.

6. Dec 6, 2007

I agree with two of the points in this thread, that the question really is asking for a calculation of the peak temperature of the CMBR, and that a temperature can't be defined for a single molecule, only for an ensemble of molecules.

However, it is incorrect to say that the CMBR's effect on interstellar gas temperatures in galaxies is negligible, especially at high redshift as the temperature of the CMBR increases. In fact, a critical test for the existence of the CMBR, and of current cosmological theories is in the measurement of molecular temperatures as a function of redshift.

The research I'm referring to measures the relative strengths of UV/optical absorption lines of CN to derive a rotational temperature for the CN molecule in interstellar gas. In the Galaxy, such measurements yield 2.7 K (consistent with the CMBR), but in redshifted galaxies, higher temperatures have been observed, consistent with the expected peak CMBR temperature at those earlier epochs.

For a strongly dipolar molecule such as CN, theory predicts that it relaxes to the temperature of the CMB due to its strong radiative rotational transitions at very low (radio) energies. This can only happen in relatively diffuse gas though (densities of ~ 10^3 per cc) where collisional excitation of the molecule is not significant.

7. Dec 6, 2007

### malawi_glenn

Sounds exciting :)

Do you have references?

8. Dec 6, 2007

Interstellar CN rotational temperature measurements go back to the observations of McKellar in 1941. Ironically, Hoyle used McKellar's temperature of 2.3 K to refute the big bang model in favour of steady state - apparently he thought the CMB temperature should be 11 K, so 2.3 was far too small!

Here's a paper on some more modern Milky Way CMB temperature measurements using CN:

Unfortunately, I can't find the article I was thinking about that described measurements of redshifted CN. It's just possible that I dreamt it! Sorry about that, I really thought we already had some high redshift CMB temperatures from molecules but this may in fact be work for the future. Keep your eyes peeled.

Last edited by a moderator: May 3, 2017
9. Dec 6, 2007

### malawi_glenn

Cool, never knew about these aspects.

10. Dec 7, 2007

### Nereid

Staff Emeritus
http://www.eso.org/public/outreach/press-rel/pr-2000/pr-27-00.html":
http://babbage.sissa.it/abs/astro-ph/0012222" [Broken]:
The tracer used was not CN rotational lines but fine structure in neutral C atoms (and 'an isolated cloud' rather than the ISM), but the principle is essentially the same as mentioned in cadnr's post.

Since 2000 I think several other high-z objects have been (spectroscopically) studied, with similar results.

More exciting, perhaps, is the prospect that the next generation of leading telescopes will greatly expand the scope of such tests, by using many more tracers, different wavebands, many more objects, and greater ranges of z (not to mention tighter constraints) - http://adsabs.harvard.edu/doi/10.1007/s10509-007-9632-3" [Broken].

Last edited by a moderator: May 3, 2017
11. Dec 18, 2007