Wednesday, March 12, 2014

astronomy units in cosmology

can you express the flux density of the cosmic microwave background in Jansky per squared arcminute?

1 comment:

  1. the Planck-spectrum in CMB science is usually written down using the dimensionless frequency $x=h\nu/(k_BT)$,
    \begin{equation}
    S(x) = 2\frac{(k_BT)^3}{(ch)^2}\frac{x^3}{\exp(x)-1},
    \end{equation}
    and the prefactor $S_0$ has units of power per unit area, unit frequency and unit solid angle. converting the unit solid angle $pi$ into squared arcminutes yields a conversion factor $(180 \times60 /\pi)^2$. the unit Jansky is defined as $10^{-26}$ Watts per unit area, unit frequency and solid angle, so one obtains:
    \begin{equation}
    S_0 = 2\frac{(k_BT)^3}{(ch)^2}\times\left(\frac{180\times60}{\pi}\right)^2\times10^26 = 22.99527 \mathrm{Janksy}/\mathrm{arcmin}^2
    \end{equation}
    for a CMB temperature of $T=2.726$ Kelvin.

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