Discrete Source Polarization Foregrounds to the CMB


  • To measure the CMB power spectrum to a given accuracy in L(L+1)C_L, to what limiting flux density must we know the source counts?
  • To measure the CMB power spectrum to a given accuracy in L(L+1)C_L, what density of missed sources of a given flux density is acceptable?
  • What is the relevant CMB observation baseline case?
  • What are the observational capabilities as a function of wavelength, and how can they best be deployed to address the challenege? What new capabilities do we need?
  • What is the current state of our knowledge about source counts from 1.4 to 300 GHz? What about their polarization?
  • How will we be helped by lower- or higher- frequency observations?
  • How much do nasties like variability matter?
  • How much do very extended radio sources (such as are seen, e.g., in COSMOS) matter, and how do we deal with them?

Baseline CMB Observation Case

  • Large-scale expt -- 10 deg (L~20) is largest scale of interest. Cover from 100deg x 100deg to whole sky
  • Small scale expt -- do 100 deg2 and aim to get high quality lensed B mode spectrum (out to L=2000)
  • Weakest signal of interest: about 0.01 microKelvin (sqrt(L(L+1)CL/2pi)) r~0.01

Current Knowledge of Source Counts

1.4 GHz

15 GHz

9C survey:

20 GHz

AT20G -- ongoing survey of all dec < -15 deg down to 40 mJy (complete to 60 mJy)

30 Ghz

Mason et al. 2003 (CBI, 100 deg2 to 20 mJy at 30 GHz) -- N(>S_{30}) = 2.8 \pm 0.8 \, \left(\frac{S_{30}}{10 \, mJy}\right)^{-1.0}

Large scale (2400 sources) GBT 30 GHz survey (will get counts down to ~ 1 mJy in stokes I); Large scale (6000 sources) Bonn 5 - 12 GHz survey in the same field. Both surveys completed & in preparation.

mm & submm

needs filling in

Current Knowledge of Polarization


Pol Measurements: 1.4 GHz

Pol Measurements: 20 Ghz

18 GHz ATCA -- Ricci et al. 2004 -- targets Kuhr sample.

20 GHz ATCA Sadler et al 2006 bigger sample

Most of the ones with useful pol information here are quite bright (>100 mJy at 20 Ghz)

Pol Measurements: 30 Ghz

GBT survey of several 100 sources, probably 40 mJyish 9C sources, will detect all with > 1% linear poln.

Pol Measurements mm/submm

needs filling in


It is straightforward do show that the angular power spectrum of polarized anisotropies in a single stokes parameter, for isotropic, uncorrelated point sources with a power-law distribution in flux density, due to the sources below S_c, is:

C_L = \frac{1}{2} <p^2> N(>S_c) \frac{\lambda}{2-\lambda} S_c^2 \left( \frac{\lambda^2}{2 k T_0 g(\nu)} \right)^2

where we have assumed a flux density distribution of the form N(>S)=N_0 \left(\frac{S}{S_C}\right)^{-\lambda} and expressed the result in terms of an equivalent temperature fluctuation using g(x)=\frac{x^2 e^x}{(e^x-1)^2} and x=h \nu/kT

Apply this using CBI 30 GHz counts; <p^2>=(0.02)^2; and a range of flux density cutoffs:

Scut ell sqrt(L(L+1)CL/2pi) [microK]
40 100 0.014
10 100 7.3e-3
25 1000 0.11
1 2000 0.04

One should probably aim for < 0.01 uK on large scales in able to reach smaller T/S (0.01 say), and 0.05 uK or so at L=2000 to get all of the lensing modes.

Figure 1: Power spectra from polarized point sources at 30 GHz, calculated with the CBI 30 GHz counts and assuming <p^2>=0.02^2, for Scut values of 2.8 Jy and 5 mJy. The Scut=5 mJy line shows the expected residual point source power spectrum if all sources brighter than 5 mJy can be identified and perfectly subtracted. The total source variance in a 100 \, deg^2 map is represented by the S_{cut}=2.8 \, Jy line -- this is approximately the brightest source you would expect to occur at random in such a patch. Also shown is 5% of the total source variance, meant as an indicator of what level of precision is needed (which would be set by confounding factors such as source variability and instrumental systematics). It is comparable to but slightly greater than the 5 mJy residual. Scut values are quoted in stokes I. cmbpolnPtsrcs30ghz.png

Figure 2: CMB polarization power spectra and one estimate of the polarized source power spectrum, this time at 90 GHz. The CBI 30 GHz counts were used directly and no contribution for dusty galaxies is included. This time only the total source variance is shown. The effect which reduces the contribution of the sources here, in comparison to 30 GHz, is simply the increase in the specific intensity of the CMB relative to the point sources. cmbpolnPtsrcs90ghz.png

For 30 GHz B-mode measurements, one needs a ~5 mJy (detection limit) stokes I survey with (possibly followup) QU photometry accurate to ~5%. The requirements are similar for large scale (primordial, 100x100 deg2) and small scale (lensed E-modes, say, 10x10 deg). At 90 GHz it's likely that only a very shallow survey is needed (say 100-200 mJy detection limit) but this needs closer looking into.

What We Need To Do

  • 30-50 GHz counts down to 1 mJy
  • Fractional polarizations of sources from submJy to 10s of mJy, from 30 to 250 GHz
  • Blind surveys of the fields actually to be observed

Observational Capabilities

What can we do with each in reference to the baseline CMB experiments? What specific new instruments do we need?

  • GBT: sensitive large area stokes I surveys (possibly also Q&U) at 30 & 90 GHz; targetted IQU photometry. 125 feed 30 GHz system would get to 1 mJy RMS on 1e4 deg2 in 125 hours or so.
  • EVLA: deep and wide IQU surveys. There are about 6 sources per square degree above 5 mJy at 30 GHz ; 60,000 in 1/4 of the sky; EVLA Ka band snapshots will give 0.1 mJy or better RMS which is sufficient to characterize source poln to 2% (better than needed at the survey limit). 60 sec for each source w/slew time gives a 1,000 hour survey. Could do the 1 mJy blind survey in around 600 hours.
  • ALMA: 90 and 150 GHz surveys, targetted IQU photometry.
  • IRAM/PdB: nearer term 90 GHz targetted IQU photometry.
  • ATCA: shallow, large area I (QU?) surveys -- 20G and followup polarimetry

-- BrianMason - 29 Aug 2007

Topic revision: r8 - 2007-09-12, BrianMason
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