Wilkinson Microwave Anisotropy Probe

Product Name
MCMC Foreground Maps
Coord. System
Projection Type
HEALPix, nested, res 6 (Nside=64)
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These maps were generated from the MCMC fit described in Gold, et.al.. The inputs are the one degree smoothed maps per frequency band, binned to Nside=64. There is an MCMC chain for each pixel which is used to estimate the likelihood for all the parameters. The maps provided for each parameter are:

  • The best-fit parameter (i.e. peak likelihood) from each chain.
  • The mean parameter over the chain.
  • The marginalized variance.

Four sets of maps are provided: MCMC Models c, e, f and g as described in Bennett et. al (2013). Each model has a slightly different set of parameters that are allowed to vary.

Model c ('base') assumes a power-law dependence for synchrotron, free-free, and dust, where the synchrotron and dust spectral indices are free parameters.

Model e ('sd070') includes synchrotron, free-free, thermal dust emission, and a spinning dust component. The synchrotron spectral index is fixed to -3. The spinning dust spectrum is fixed to the Cold Neutral Medium spectral form from Silsbee, etal, 2011 with a peak frequency shift parameter of 0.7.

Model f ('bsfree sd084') is similar to Model e, but allows the synchrotron spectral index to vary per pixel (a pure power law is assumed). The spinning dust spectrum uses a fixed shift parameter of 0.84.

Model g ('bsfree Strong sd084') is similar to Model f, but constrains the synchrotron spectral index behavior with frequency to follow that specified in Strong, etal, 2011 instead of a pure power law.

The following parameters are reported:

Parameter Notes
CMB temperature All four models.
CMB Stokes Q All four models.
CMB Stokes U All four models.
Free-free temperature at K-band All four models.
Synchrotron temperature at K-band All four models.
Synchrotron Stokes Q at K-band All four models.
Synchrotron Stokes U at K-band All four models. Not an independent parameter.
Synchrotron spectral index Not present in Model e.
Dust temperature at W-band All four models.
Dust Stokes Q at W-band All four models.
Dust Stokes U at W-band All four models. Not an independent parameter.
Dust spectral index All four models.
Spinning Dust Temperature at K-band Not present in Model c.
Error flags. All three models. Each pixel is bit-coded:
  • 0 - no error
  • 1 - did not find a good adaptive stepsize in the "prechain" for that pixel, but the chain was run anyway
  • 2 - the chain for that pixel failed the convergence test
  • 4 - not used
  • 8 - not used
  • 16 - pixel was masked before processing, no fit was done
Best fit reduced χ2 All four models.

Temperatures in mK are in antenna units except for the CMB maps, which are provided in thermodymanic units.

The reduced χ2 are the best-fit χ2 divided by the number of degrees of freedom determined from the chain using the "effective complexity".

Additional Information

  • Silsbee, K., et.al., 2011, MNRAS, 411, 2750
  • Strong, A.W., et.al., 2011, A&A, 534, A54

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Goddard Space Flight Center, National Aeronautics and Space Administration
HEASARC Director: Dr. Alan P. Smale
LAMBDA Director: Dr. Eric R. Switzer
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