ARlogo Annu. Rev. Astron. Astrophys. 1994. 32: 319-70
Copyright © 1994 by Annual Reviews. All rights reserved

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A. Some Useful Numbers

Converting from multipole space ell to angles theta is accomplished via the approximate formula

Equation 37 (37)

It is this equality that is used to make statements that certain measurements are on a scale of theta. This correspondence, theta appeq ell-1 radians, seems most natural for large ell [cf the window function, Equation (28)]; for small ell, it may be better to think of theta appeq pi / ell radians, but in any case the correspondence is not exact. At any z >> 1, an angle theta degrees subtends a comoving distance of 105 theta(Omega0 h)-1 Mpc.

To convert from ell to comoving wavenumber k we have ell ~ (6, 000h-1 Mpc)k. Additionally we have the physical scales (at horizon crossing)

Equation 38 (38)

The redshifts of equality, recombination, and decoupling (Compton cooling) for standard recombination are

Equation 39 (39)

and for reionization with constant ionized fraction xe

Equation 40 (40)

The following angles are also useful:

Equation 41 (41)

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