Simulating the Interferometer In order to simulate the performance of an interferometer, 20 by 20...
If you can't read please download the document
Simulating the Interferometer In order to simulate the performance of an interferometer, 20 by 20 degree sections were extracted from the simulated CMB
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 CMBFAST
1 was used, which when given an input cosmology provides predicted
temperature and polarization power spectra. This was used along
with the JPL software package HEALPix 2, which given these spectra
creates simulated CMB maps. 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.
Simulating Performance for CMB Polarization Interferometers E.D.
Lopez a, P.T. Timbie b, S. Malu b a University of
California-Berkeley, Berkeley, CA 94720 USA b University of
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. 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). Predicted power spectra along with results from WMAP 3.
Temperature Temperature/E-mode Correlation E-Mode B-Mode The
Einstein Polarization Interferometer for Cosmology EPIC. References
1.NASA Legacy Archive for Microwave Background Data Analysis
CMBFAST http://lambda.gsfc.nasa.gov/toolbox/tb_cmbfast_ov.cfm.
2.Jet Propulsion Labratory Healpix 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) Acknowledgements I would like to thank Peter
Timbie and Siddharth Malu 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. 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. 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. 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- Bolometers THMs 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 Diagram of a single EPIC array with
horns, primary mirror, and detector array 9. Simulated CMB Map
created with HEALPix 2. and CMBFAST 1 using a standard cosmology 2.
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. Histogram of array
baseline lengths. 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. Resulting power spectrum with 10 % bandwidth
and 15 beam.