The AstroStat Slog » Angstrom http://hea-www.harvard.edu/AstroStat/slog Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 09 Sep 2011 17:05:33 +0000 en-US hourly 1 http://wordpress.org/?v=3.4 keV vs keV [Eqn] http://hea-www.harvard.edu/AstroStat/slog/2008/eotw-kev-kev/ http://hea-www.harvard.edu/AstroStat/slog/2008/eotw-kev-kev/#comments Wed, 30 Jul 2008 17:00:20 +0000 vlk http://hea-www.harvard.edu/AstroStat/slog/?p=360 I have noticed that our statistician collaborators are often confused by our units. (Not a surprise; I, too, am constantly confused by our units.) One of the biggest culprits is the unit of energy, [keV], which is 1000 electron Volts, for the energy acquired by an electron when it falls through an electric potential of 1 Volt:

1 [eV] ≡ 1.6021892 · 10-19 [Joule] ≡ 1.6021892 · 10-12 [erg] .

The confusion is because the same units are used to denote two separate quantities which happen to have similar magnitudes for a commonly encountered spectral model, Bremsstrahlung emission.

  1. the frequency ν, or wavelength λ, of a photon: As Planck discovered, the energy of a photon is directly related to the frequency ν,

    E = h · ν ≡ h · c / λ ,

    where h=6.6261760 · 10-27 [erg s] is Planck’s constant and c=2.9979246 · 1010 [cm s-1] is the speed of light in vaccum. When λ is given in [Ångström] ≡ 10-8 [cm], we can convert it as

    [keV] = 12.398521 / [Å] ,

    which is an extraordinarily useful thing to know in high-energy astrophysics.

  2. the temperature T of a gas or plasma: Here we look to thermodynamics, which relates the kinetic energy of random motion of particles in a gas to a gross property, the temperature of the gas,

    E = kB · T ,

    where kB = 1.3806620 · 10-16 [erg K-1] is Boltzmann’s constant. Then, a temperature in degrees Kelvin can be written in units of keV by converting it with the formula

    [keV] = 8.6173468 · 10-8 · [K] ≡ 0.086173468 · [MK] .

It is tempting to put the two together and interpret a temperature as a photon energy. This is possible for the aforementioned Bremsstrahlung radiation, where plasma at a temperature T produces a spectrum of photons distributed as e-h ν / kB T and it is possible to tie the temperature to the photon energy at the point where the numerator and denominator have the same numerical value. For example, a 1 keV (temperature) Bremsstrahlung spectrum extends out to 1 keV (photon energy). X-ray Astronomers use this as shorthand all the time, and it confuses the hell out of everybody else.

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