Simulating the Interferometer

1. Simulating Performance for CMB Polarization Interferometers E.D. Lopeza, P.T. Timbieb, S. Malub aUniversity of California-Berkeley, Berkeley, CA 94720 USA bUniversityof Wisconsin-Madison, Madison, WI 53706 USA Abstract The next step in CMB cosmology is to map the polarization of the CMB, and in particular the B-modes of the polarization. The space based polarization Interferometer EPIC is a proposed mission to do this. We present a possible horn configuration for EPIC, with simulated power spectra produced by this configuration on a simulated CMB sky. We examine the results of varying several effects such as the frequency bandwidth and the instrument beam. This work was supported by the REU and ASSURE programs through NSF award AST-0453442. The Einstein Polarization Interferometer for Cosmology EPIC . • EPIC is a space based interferometer proposed to map the B-mode polarization anisotropy of the CMB. • It consists of many interferometer arrays tuned to several microwave frequencies. The main science arrays are at 90GHZ and 120GHZ with arrays at other frequencies to remove galactic foregrounds. • Each array has 64 corrugating horns each with their own set of filters. • Primary and secondary mirrors are used to interfere the signal from the horns and focus it onto the detector. • The detector is an array of 1000s of ultra sensitive bolometers. • Transition-Edge Hot-Electron Micro-BolometersTHMs will be used, read out by Superconducting Quantum Interference Devices SQUIDs. • Currently a 4 horn prototype array the Microwave Bolometric Interferometer MBI is under going tests at UW Madison Scientific Motivation: Polarization of the CMB In addition to the well studied temperature anisotropy there is a polarization anisotropy in the CMB. This is usually divided into a curl-less component (E-modes) and a divergence-less component (B-modes). B-Mode • A B-mode polarization anisotropy in the CMB is predicted at a 0.1uK scale, however this is extremely difficult to detect. • The B-mode anisotropy is believed to be caused by gravitational waves from inflation. • Detecting the B-modes would provide observational evidence for both gravitational waves and inflation and provide a link to the inflationary epoch between 10-33 and 10-32 seconds after the big bang. Temperature Temperature/E-mode Correlation E-Mode Diagram of a single EPIC array with horns, primary mirror, and detector array9. Predicted power spectra along with results from WMAP3. Simulating the Interferometer In order to simulate the performance of an interferometer, 20 by 20 degree sections were extracted from the simulated CMB map. For each array configuration tested a map of uv plane coverage was created and then applied to the Fourier transform of the CMB section. The power spectra were then extracted by computing the variance in an annulus with a radius given by the multipole moment l and a width defined by the frequency bandwidth. The effect of the instrument beam was applied by approximating it as a 2D Gaussian. . Simulating the CMB Sky In order to simulate performance for an EPIC interferometer array, simulated CMB maps were created. To do this the online tool CMBFAST1 was used, which when given an input cosmology provides predicted temperature and polarization power spectra. This was used along with the JPL software package HEALPix2, which given these spectra creates simulated CMB maps. • For a 64 horn array there are n*(n-1)/2 = 2016 possible baselines. • An ideal array needs all 2016 baselines to be distinct and smoothly distributed, while at the same time being sufficiently compact for space and allowing room for the secondary mirror. • The array configuration shown here has the horns distributed at points along an Archimedes spiral with the angular separation slowly varying. • No baselines are repeated, it is compact and excepting the necessary decline at long baselines and the dip at just over one horn width, it is relatively smooth. • For the main frequency at 90 GHz this array is 30.2 cm wide, with the secondary mirror 7.5 cm wide, and the horns each 2.5 cm wide. This array covers a range of multipole moments from 10 to 120. • For other multipole moment ranges or frequencies of interest the array dimensions are scaled accordingly 30.2 cm Proposed EPIC horn array configuration. Simulated CMB Map created with HEALPix2. and CMBFAST1 using a standard cosmology2. Results The recovered temperature power spectrum is shown below using a 10% frequency bandwidth and a 15 degree instrument beam. To create this spectrum, the interferometer simulation was performed on 4 separate 20 by 20 degree sections and the results were then averaged . The temperature power spectrum was used because it best illustrates the efficacy of this array configuration, and so the array dimension were scaled up by a factor of 10 to cover the multipole moment range from 100 to 1200. Histogram of array baseline lengths. Conclusions A spiral horn configuration provides excellent uv coverage while at the same time maintaining the compactness required of a space based mission. For reasonable estimates of the bandwidth and instrument beam the expected power spectrum is easily recovered. When combined with high sensitivity THM bolometric detectors, and low noise SQUID readouts this should allow EPIC to detect the B-modes of the polarization anisotropy in the CMB. References 1.NASA Legacy Archive for Microwave Background Data Analysis CMBFAST http://lambda.gsfc.nasa.gov/toolbox/tb_cmbfast_ov.cfm. 2.Jet Propulsion LabratoryHealpix http://healpix.jpl.nasa.gov/ (2007). 3.Page, L. et al., astro-ph/0603450, (2006). 4.Heiles, C. "Discretely Finicky Times with Discrete Fourier Transforms" (2002). 5.Tristram, M., Ganga, K., Rept.Prog.Phys.70:899, (2007). 6.Malu, S. "E-B Decomposition" (2005). 7.Guyon, O., Roddier, F., Astronomical Society of the Pacific, 113:-104, (2001). 8.Timbie, P.T. (2007). 9. Ryden, B., Introduction to Cosmology, 1st Ed., Addison Wesley (2002) • At 10% bandwidth all three peaks are clearly visible. • The power loss due to the instrument beam is small. • The coverage is effective and near uniform over an order of magnitude in multipole moments. Acknowledgements I would like to thank Peter Timbie and SiddharthMalu REU research advisors and along with the Observational Cosmology Group at UW Madison. I would also like to thank Edwin Mierkiewicz for his excellent job managing the summer REU program at UW Madison. Finally I would like thank the National Science foundation and the University of Wisconsin Madison for support. Resulting power spectrum with 10 % bandwidth and 15̊ beam.