31 May 2006 - Foreground plot for BUD proposal II

This is a re-work of my previous entry.

We wish to predict the level of polarized foreground structure in l range of grav BB experiment - presumbly l of 50-100. We have limited data to do this from - there is high resolution and low noise IRAS100 map but it is total intensity only. Also there is WMAP K band (23GHz) map which is polarized, but the signal is below the noise floor in some regions of the sky.

The l range of interest to a grav BB experiment implies that only a modest area of sky is required - a patch 25x25 deg should be sufficient. Our aim is to investigate which areas of sky might be preferred, and how much lower in foreground they actually are.

I follow the this procedure for dust:

• Take FDS (model 8) dust map as extrapolated to 150GHz by "predict_thermal" program (thermodynamic units).
• Pull out a square 30x30deg (sine projection) map around each of 192 equally spaced points on the sky (healpix ring nside=4 pixel centers).
• Multiply this by 0.05 on the basis that "dust may be about 5% polarized".
• Subtract out the mean level (this is important!).
• Apodize with a sin^2 edge taper to central 25x25 deg.
• Take the power spectrum.

And this procedure for synchrotron:

• Take the WMAP K band Q,U maps as provided on their webbsite in file "wmap_band_iqumap_r9_3yr_K_v2.fits".
• Pull out square 30x30deg (sine projection) map as above.
• Extrapolate to 150GHz using scale factor (1/1.01)*(150/23)^-3*1.72. (The factors of 1.01 and 1.72 are thermo to RJ conversions.)
• Subtract out the mean level (not important).
• Apodize as above.
• Gen pseudo EE,BB power spectra. (Pseudo because square grids and celestial coords and WMAP maps are galactic and proper rotation not done.)
• Take the mean of EE,BB.

Here are the resulting power spectra. The thick black line shows the result for the BICEP field centered on RA,Dec 0,-57.5. The dust spectra in left panel show modest up and down slopes. (In previous posting I had a bump at low l. This was due to mean level in map interacting with apodization mask. I am now subtracting out mean level.) The worst regions of the sky have 10^6 times more power than the best. The sync spectra in right panel show l^2 noise at high l. Over some of the sky signal is visible above the noise floor at low l - when it is it is either flat spectrum or falling. However over some regions of the sky signal is not visible over noise right down to the lowest l. I played with fitting these spectra to a sum of two power laws, signal plus noise. For the cleanest regions the signal component is completely un-constrained and crazy fit values result. The BICEP field spectrum does flatten below l=30 indicating that in this region real sync structure has been measured. This implies that the BICEP field is not amongst the very lowest sync regions - there are regions nearly an order of magnitude cleaner. Note that the gap between the BICEP field and the lowest noise regions can increase with increasing sensitivity of the WMAP measurements, but the fraction probably better cannot increase much. It looks like the range of sync across the sky is about factor 10^3 best to worst.

Here are plots for the proposal. The top left panel shows the WMAP K band P map where P=sqrt(Q^2+U^2). This is the low res map provided in file wmap_band_iqusmap_map_r4_3yr_K_v2.fits. The map has been extrapolated to 150GHz assuming spectral index of -3. The lower left shows the FDS 150GHz dust map multiplied by 0.05. The red box is the BICEP field. The right panels show integral distributions of power spectrum value at the given l for the 192 trial fields. Since the dust spectra are rather flat it doesn't matter much what l one picks. For sync the noise floor forces you to as low an l as possible to get an unbiased estimate. I choose 36 as above this value the the BICEP field spectrum starts to rise. Again the underlying sync spectra look rather flat so these results should apply over a range of l's. It has to be realized when looking at these plots that the noise floor artificially compresses the range of values for sync - I have tried to indicate this with the "noise floor" line. The black outlines in the maps at left are the aggregate outline of all trial fields better than the BICEP field according to the integral distributions at right.