Point source contamination in CMB non-Gaussianity analyses

In this paper we analyze the biasing effect of point sources, either thermal Sunyaev-Zeldovich clusters or standard radio sources, on the estimated strength of the non-Gaussianity in the cosmic microwave background (CMB). We show that the biggest contribution comes from the cross correlation of the CMB with the matter density rather than from the Poisson term which is conventionally assumed in these calculations. For the three year WMAP data, we estimate that point sources could produce a non-Gaussian signature equivalent to a bias in $f_{NL}$ of 0.35, 0.24, $-0.097$, $-0.13$ in the Ka, Q, V, and W bands, respectively. The level of bias we find is largely insufficient to explain the very high $f_{NL}$ values recently detected by Yadav and Wandelt. For Planck, we estimate the point source bispectra to contaminate the $f_{NL}$ estimator with a bias of 1.3, 0.34, $-0.25$, $-0.48$ at 30, 44, 70, 100 GHz, respectively. These results depend on the assumed redshift distribution of the point sources. However, given the projected Planck sensitivity of $\Delta f_{NL}\simeq 5$ (95% C.L.), a good estimate of point sources’ properties including their number density and redshift distribution is essential before deriving strong conclusions on primordial non-Gaussianity.

Figure 1

Redshift weight functions for the ISW effect (green, dot-dashed line); radio point sources—model 1 (red, dashed line) and model 2 (blue, long-dashed line); and thermal SZ effect (solid, black line).

Figure 2

Density-ISW cross correlation spectrum for thermal SZ (solid, black line); radio point sources—model 1 (red, dashed line) and model 2 (blue, long-dashed line).

Figure 3

Number density modulation equilateral bispectra for thermal SZ (solid, black line); radio point sources—model 1 (red, dashed line) and model 2 (blue, long-dashed line). The local model ($f_{NL}=1$) (green, dot-dashed line) is also shown for reference. The equilateral shape corresponds to (${\ell }_1={\ell }_2={\ell }_3=\ell$).

Figure 4

Number density modulation collapsed bispectra for thermal SZ (solid, black line); radio point sources—model 1 (red, dashed line) and model 2 (blue, long-dashed line). The local model ($f_{NL}=1$) (green, dot-dashed line) is also shown for reference. We show representative collapsed bispectra with ${\ell }_1=5$, ${\ell }_2={\ell }_3=\ell$.

Figure 5

Convergence-ISW cross correlation spectrum for thermal SZ (solid, black line); radio point sources—model 1 (red, dashed line) and model 2 (blue, long-dashed line).

Figure 6

Magnification modulation equilateral bispectra for thermal SZ effect (solid, black line); radio point sources—model 1 (red, dashed line) and model 2 (blue, long-dashed line). The local model bispectrum ($f_{NL}=1$) (green, dot-dashed line) is also shown for reference.

Figure 7

Magnification modulation collapsed bispectra for thermal SZ (solid, black line); radio point sources—model 1 (red, dashed line) and model 2 (blue, long-dashed line). The local model ($f_{NL}=1$) (green, dot-dashed line) is also shown for reference. We show representative collapsed bispectra with ${\ell }_1=5$, ${\ell }_2={\ell }_3=\ell$.

Figure 8

The WMAP estimator bias terms $\Delta f_{NL}^{\alpha }$ as a function of ${\ell }_{\max }$ for radio point source density modulation (solid, black line); SZ number density modulation (dotted, red line); radio point source gravitational lensing magnification modulation (dashed, blue line); and SZ gravitational lensing magnification modulation (long-dashed, green line) in $\mathrm{Ka}-33\mathrm{GHz}$ (upper left); $\mathrm{Q}-40\mathrm{GHz}$ (upper right); $\mathrm{V}-61\mathrm{GHz}$; and $\mathrm{W}-94\mathrm{GHz}$. The density modulation terms produce a negative bias, while the magnification bias produce a positive bias.

Figure 9

The Planck estimator bias terms $\Delta f_{NL}^{\alpha }$ for 30 GHz (upper left); 44 GHz (upper right); 70 GHz (lower left), and 100 GHz (lower right). The curves are the same as Fig. 8. The density modulation terms produce a negative bias, while the magnification bias produce a positive bias.