Numerical solutions (Green's functions) for intermediate-type distortions and Mathematica code

Spectrum created by energy release in the early Universe, before recombination, creates distortions which are a superposition of μ-type, y-type and intermediate-type distortions, shown in the above figure. The final spectrum can thus be constructed from the templates, once energy injection rate as a function of redshift is known. This package contains the spectral distortions (Green's functions) spaced at dy=0.001 for y<1 and dy=0.01 for y>1 covering a range 0.001 < y < 10. Also included is a mathematica code which can combine these numerical solutions of Kompaneets equation (Green's functions) for user-defined rate of energy injection as a function of redshift. Silk damping, particle decay and annihilation examples are also included. More details can be found in the README file and the companion paper arXiv:1207.6654 See also Appendix of arXiv:1303.7212 for the algorithm and how to use the Green's functions provided to write your own code.

Package can be downloaded here (size 34.7 MB)

NEW: Mathematica notebook including code for Fisher matrix calculation
If you use the Fisher matrix code you can additionally cite arXiv:1303.7212

*** Note for arbitrary primordial power spectrum ***
Arbitrary input power spectrum can be specified by replacing the dQdz with an integral over the power spectrum. See the "frun[]" function in the new mathematica notebook with Fisher matrix calculation (idistort_fisher_beta.nb). Replace the integrand in frun with your ( power spectrum * Exp[-2 k^2 /(mparsec*kd[z])^2] ) and copy the next few lines until dQdz[z_]=... into the main code replacing the dQdz for silk damping. The definition of power spectrum in the integrand is such that the standard power spectrum is (k/k0)^ns, with k0 the pivot point and ns=0.96 the Planck value. This routine numerically integrates the modes dissipating in different redshift bins to calculate the power injected into the CMB at those redshifts.

Typical runtime for a spectrum calculation is < 30 seconds

Last modified: Mon May 29 13:52:10 CET 2017