What's going on with the CMB spectrum?

[tayga]

I've been browsing some of the papers listed in the excellent resource mnemeth1 posted in the Resources conference.

Something caught my attention in the Physics today paper "COBE Satellite Finds No Hint of Excess in the Cosmic Microwave Spectrum " http://public.lanl.gov/alp/plasma/downl ... ay1990.pdf

In the figure at the top of the article, the horizontal axis is labeled "FREQUENCY (cm-1)". The proper units of frequency are s-1 whereas cm-1 denotes wavenumber. The discrepancy led me to investigate further.

While it's true that frequency is directly proportional to wavenumber, there is a difference between a conventional black body spectrum and the spectrum of the CMB as it is presented. In a black body spectrum (cf. http://en.wikipedia.org/wiki/File:Blackbody-lg.png) intensity is more often shown as a function of wavelength whereas it seems that the CMB spectrum (cf. http://en.wikipedia.org/wiki/File:Firas_spectrum.jpg) generally shows intensity as a function of frequency.

Usually, when a black body spectrum is shown as a function of frequency it has a different appearance, cf.http://quantumrelativity.calsci.com/Phy ... ckbody.jpg.

This raises two points. Firstly, that there is, to my thinking, some sloppy labeling in the paper; even if this is a convention it’s a sloppy one. Secondly, and more importantly, although the shape of the CMB spectrum, as a function of frequency, is similar to a conventional black body spectrum, as a function of wavelength, this is entirely coincidental or due to factors beyond my puny intellect.

I can't be the first person to have noticed this. Does anyone know of a reasonable explanation or is this some sleight of hand?

I’d appreciate your comments.

tayga

[StevenO]

The labelling seems to be common among spectroscopists as Wikipedia states:

Furthermore, spectroscopists often express a quantity proportional to the wavenumber, such as frequency or energy, in cm−1 and leave the appropriate conversion factor as implied.

If you plot against wavelenght instead of frequency, the X-axis will be inverted and hyperbolically stretched since (wavelenght = c/frequency) so the shape will definitely look different.

The interesting thing about the CMB is that is has a near perfect BlackBody spectrum, while the radiation does not come from a 'body'. It comes from all directions equally. There is a mainstream explanation for it but that makes as much sense as the Big Bang, so I'm not going to defend it. I have a theory that provides a simpler explanation but I cannot post that in the 'Electric Universe' section.

[tayga]

Thanks, Steve. I'm familiar with wavenumber from infrared spectroscopy. It's just that we chemists never call it frequency.

[Lloyd]

Since the article talks about wavelengths, I'd say it's very likely that they just put Frequency on the bottom of the graph by mistake, and meant to say waves per cm, which is the inverse of wavelength.