Statistical simulations of the dust foreground to cosmic microwave background polarization

¹ Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay Cedex, France
² California Institute of Technology, Pasadena, California CA 91125, USA
³ Sorbonne Universités, UPMC Univ Paris 6 et CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98bis bd Arago, 75014 Paris, France
⁴ Sorbonne Universités, Institut Lagrange de Paris (ILP), 98bis Boulevard Arago, 75014 Paris, France
⁵ Laboratoire AIM, IRFU/Service d’Astrophysique, CEA/DSM, CNRS, Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁶ LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, École normale supérieure, 75005 Paris, France
⁷ CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
⁸ CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France

Received: 1 November 2016
Accepted: 24 March 2017

Abstract

The characterization of the dust polarization foreground to the cosmic microwave background (CMB) is a necessary step toward the detection of the B-mode signal associated with primordial gravitational waves. We present a method to simulate maps of polarized dust emission on the sphere that is similar to the approach used for CMB anisotropies. This method builds on the understanding of Galactic polarization stemming from the analysis of Planck data. It relates the dust polarization sky to the structure of the Galactic magnetic field and its coupling with interstellar matter and turbulence. The Galactic magnetic field is modeled as a superposition of a mean uniform field and a Gaussian random (turbulent) component with a power-law power spectrum of exponent α_M. The integration along the line of sight carried out to compute Stokes maps is approximated by a sum over a small number of emitting layers with different realizations of the random component of the magnetic field. The model parameters are constrained to fit the power spectra of dust polarization EE, BB, and TE measured using Planck data. We find that the slopes of the E and B power spectra of dust polarization are matched for α_M = −2.5, an exponent close to that measured for total dust intensity but larger than the Kolmogorov exponent − 11/3. The model allows us to compute multiple realizations of the Stokes Q and U maps for different realizations of the random component of the magnetic field, and to quantify the variance of dust polarization spectra for any given sky area outside of the Galactic plane. The simulations reproduce the scaling relation between the dust polarization power and the mean total dust intensity including the observed dispersion around the mean relation. We also propose a method to carry out multifrequency simulations, including the decorrelation measured recently by Planck, using a given covariance matrix of the polarization maps. These simulations are well suited to optimize component separation methods and to quantify the confidence with which the dust and CMB B-modes can be separated in present and future experiments. We also provide an astrophysical perspective on our phenomenological modeling of the dust polarization spectra.