Temperature of a molecule in a galaxy

[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) ?

 

[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.

 

[malawi_glenn]

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

 

[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!

 

[malawi_glenn]

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!

I just pointed that out science 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.

 

[cadnr]

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.

 

[malawi_glenn]

Sounds exciting :)

Do you have references?

 

[cadnr]

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:
http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1985ApJ...297..119M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

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.

 

[malawi_glenn]

Cool, never knew about these aspects.

 

[Nereid]

http://www.eso.org/public/outreach/press-rel/pr-2000/pr-27-00.html":

VLT Observations Confirm that the Universe Was Hotter in the Past
UVES Measures the Cosmic Temperature 12 Billion Years Ago

Summary

A fundamental prediction of the Big Bang theory has finally been verified .

For the first time, an actual measurement has been made of the temperature of the cosmic microwave background radiation, at a time when the Universe was only about 2.5 billion years old . This fundamental and very difficult observation was achieved by a team of astronomers from India, France and ESO [1]. They obtained a detailed spectrum of a quasar in the distant Universe, using the UV-Visual Echelle Spectrograph (UVES) instrument at the ESO 8.2-m VLT KUEYEN telescope at the Paranal Observatory.

If the Universe was indeed formed in a Big Bang, as most astrophysicists believe, the glow of this primeval fireball should have been warmer in the past. This is exactly what is found by the new measurements.

The analysis of the VLT spectrum of the distant quasar not only gives the definitive proof of the presence of the relict radiation in the early Universe, it also shows that it was indeed significantly warmer than it is today, as predicted by the theory.

PR Photo 35/00 : VLT spectrum of the distant quasar PKS 1232+0815 , displaying lines of carbon atoms from an intervening cloud in which the cosmic temperature was measured.

http://babbage.sissa.it/abs/astro-ph/0012222" :

The microwave background temperature at the redshift of 2.33771
Authors: R. Srianand (IUCAA, Pune), Patrick Petitjean (IAP, Paris), Cedric Ledoux (ESO, Munich)
(Submitted on 11 Dec 2000)

Abstract: The Cosmic Microwave Background radiation is a fundamental prediction of Hot Big Bang cosmology. The temperature of its black-body spectrum has been measured at the present time, $T_{\rm CMBR,0}$ = 2.726$\pm$ 0.010 K, and is predicted to have been higher in the past. At earlier time, the temperature can be measured, in principle, using the excitation of atomic fine structure levels by the radiation field. All previous measurements however give only upper limits as they assume that no other significant source of excitation is present. Here we report the detection of absorption from the first {\sl and} second fine-structure levels of neutral carbon atoms in an isolated remote cloud at a redshift of 2.33771. In addition, the unusual detection of molecular hydrogen in several rotational levels and the presence of ionized carbon in its excited fine structure level make the absorption system unique to constrain, directly from observation, the different excitation processes at play. It is shown for the first time that the cosmic radiation was warmer in the past. We find 6.0 < T_{\rm CMBR} < 14 K at z = 2.33771 when 9.1 K is expected in the Hot Big Bang cosmology.

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" .

 

[cadnr]

Thanks for the link Nereid, this carbon excitation analysis was in fact the article I was thinking about.

PS. Don't I know you from myspace?