One of the main challenges in detecting the CMB polarization power spectra is the presence of confounding signals from polarized foregrounds. It is necessary to understand these foregrounds in order to separate them from the primordial signal. Polarized foregrounds are not under the same symmetry constraints as the primordial perturbations, and so there is no reason they cannot generate both E- and B-modes. We expect the main sources of SPIDER’s polarized foregrounds to be from dust and synchrotron radiation.
Both of these foregrounds are the result of galactic magnetic fields. The galactic mag- netic field, which was originally proposed by Enrico Fermi, is not well understood. Our current knowledge of the galactic magnetic field is that it is aligned with the disk and arms of our spiral galaxy on large scales and is turbulent on small scales. It is sustained by an unknown dynamo mechanism, and magnetic fields can vary widely from galaxy to galaxy.
Models of the galactic magnetic field feed directly into SPIDER simulations of synchrotron and thermal dust emission.
1.5.1 Synchrotron Radiation
Synchrotron radiation is generated by electrons forced to travel on a curved path by a mag- netic field. It can be highly polarized at microwave frequencies in the direction orthogonal to the magnetic field. We use the WMAP 23 GHz data to estimate the amplitude of polar- ized synchrotron radiation at frequencies in SPIDER’s bands. We extrapolate using a power law and find that it should be negligible at 150GHz in SPIDER’s sky region (synchrotron radiation is quite bright in the galactic plane). At 90GHz it is estimated to be a factor of two higher than a B-mode signal equivalent tor = 0.03 at large scales (10< ` <30), but still a factor of five smaller than the foreground contribution from polarized dust. We find that the multipole dependence of the polarized synchrotron emission to be well-described by a power law , C` ∝ `−2.5, which brings the signal to less than the r = 0.03 B-mode spectrum by ` ∼ 30. At the peak of BB spectrum, ` ∼ 80, the polarized emission from synchrotron radiation is estimated to be an order of magnitude fainter than the signal at r= 0.03 [36].
1.5.2 Dust
Polarized emission from galactic dust is expected to be the dominant foreground for SPIDER. Although we still do not have a complete theoretical understanding of the physical process by which dust grains radiate polarized emission, it was first proposed as a way to explain the polarization of starlight by Albert Hiltner and independently by John Hall in 1949 [46, 43].
The essential idea is that radiation from galactic and intergalactic objects is absorbed by dust grains in the interstellar medium and then reradiated in the infrared. To get polarized emission, Hiltner and Hall proposed that non-spherical dust grains aligned with the galactic magnetic field. With the long axis of the dust grain aligned perpendicular to the field, a grain of dust will absorb more incident radiation in the direction perpendicular to the local magnetic field than the direction parallel to it. This differential absorption results in a net polarization of the incident radiation in a direction parallel to the magnetic field and, therefore, a net polarization of the emission of radiation from the dust grain. So the polarization of thermal dust emission is expected to be perpendicular to the sky-projected direction of the magnetic field. There are several proposed alignment mechanisms, including the Davis-Greenstein mechanism [26] (paramagnetic alignment of thermally rotating grains) and radiative torques (which models dust grains as helical and then assumes that geometric optics apply).
Dust is typically composed of both carbonaceous material and silicate minerals. There is no single power law emissivity model that fits the known dust spectrum, likely because of the multiple components. The most frequently used thermal (non-polarized) emission model (FDS model 8) assumes there are two dust components and fits four parameters [34]. Polarized dust models include randomly oriented polycyclic aromatic hydrocarbons (PAHs), oblate spheroidal silicate grains, and graphite grains assumed to be spheres or oblate spheroids.
SPIDER simulations of polarized thermal dust emission use a 3-dimensional model of the galactic magnetic field and dust distribution. Since the overall normalization of the polarized emission in SPIDER dust model is a free parameter, we set this parameter to 3.6% to match the average value derived by WMAP [70] for areas outside the Galactic plane. We extrapolate polarized intensity maps to the SPIDER bands by using FDS model 8 to account for the frequency dependence [34].
Figure 1.9: Left: A comparison of statistical noise, astrophysical and cosmological signals in each SPIDER band, assuming two SPIDER flights. Right: Galactic foreground emission for the nominal SPIDERfield (fsky = 10%) and constituent trial fields withfsky = 2%. The optimal 2% of the sky has polarized dust emission that it an order of magnitude smaller than that of the nominal field. Figure from [36].
Large-scale (` ≤ 10) polarized dust emission is expected to be at least an order of magnitude brighter than ther= 0.03 primordial B-mode spectrum at 90GHz. However, at the scales of most interest to SPIDER, the power spectrum of the dust is compatible with a power-law C` ∝ `−2.6, which results in the amplitude being comparable to the B-mode signal at r = 0.03 at ` = 40 [24]. The dust signal at 150GHz is an order of magnitude higher than at 90GHz.
One of the ways SPIDERwill deal with this foreground is to select fields of view that are exceptionally clean of galactic emission. Our field of view will include the cleanest 2% of the sky accessible from a McMurdo flight, where the polarized dust emission is expected to be an order of magnitude less than the levels shown in the left panel of Fig. 1.9. Additionally, we expect that the next release of results from the Planck satellite will include maps of polarized dust emission, which we can then use in our data analyses to subtract this foreground.
1.5.3 Honorable Mentions
Spinning and magnetic dust have also been proposed as possible sources of polarized dust emission. The theoretical expectation for spinning dust is that its emission will be unpolar- ized [58]. However, the polarization of magneto-dipole emission from magnetic dust can be
quite high, even if the intensity of the magnetic dust is subdominant to that from rotating grains. One of the characteristics of magnetic dust is that its polarization direction will vary with frequency, and so should be able to be separated from the CMB signal [58]. We have not included spinning or magnetic dust in the SPIDERforegrounds model.
Other possible sources of polarized radiation are free-free emission and galactic carbon monoxide (CO). Free-free emission (caused by free electrons scattering off charged particles without being captured) is intrinsically unpolarized. It may become polarized by Thomson scattering at the edge of HII clouds. As the Galactic plane will be masked during the analysis of SPIDERdata, we do not include polarized emission from free-free emission in our models.
Galactic CO has an emission line at 230GHz from the J 2-1 transition. Although we don’t know much about CO at high galactic latitudes, this line is well above the current SPIDER bands.