Visibilitybased angular power spectrum estimation in lowfrequency radio interferometric observations
Abstract
We present two estimators to quantify the angular power spectrum of the sky signal directly from the visibilities measured in radio interferometric observations. This is relevant for both the foregrounds and the cosmological 21cm signal buried therein. The discussion here is restricted to the Galactic synchrotron radiation, the most dominant foreground component after point source removal. Our theoretical analysis is validated using simulations at 150 MHz, mainly for GMRT and also briefly for LowFrequency Array. The Bare Estimator uses pairwise correlations of the measured visibilities, while the Tapered Gridded Estimator uses the visibilities after gridding in the uv plane. The former is very precise, but computationally expensive for large data. The latter has a lower precision, but takes less computation time which is proportional to the data volume. The latter also allows tapering of the sky response leading to sidelobe suppression, an useful ingredient for foreground removal. Both estimators avoid the positive bias that arises due to the system noise. We consider amplitude and phase errors of the gain, and the wterm as possible sources of errors. We find that the estimated angular power spectrum is exponentially sensitive to the variance of the phase errors but insensitive to amplitude errors. The statistical uncertainties of the estimators are affected by both amplitude and phase errors. The wterm does not have a significant effect at the angular scales of our interest. We propose the Tapered Gridded Estimator as an effective tool to observationally quantify both foregrounds and the cosmological 21cm signal.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 December 2014
 DOI:
 10.1093/mnras/stu2027
 arXiv:
 arXiv:1409.7789
 Bibcode:
 2014MNRAS.445.4351C
 Keywords:

 methods: data analysis;
 methods: statistical;
 techniques: interferometric;
 diffuse radiation;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 20 pages, 15 figures, 1 table.One typo corrected in Fig.13. Accepted for publication in MNRAS