SLIDE 1 Angular Power Spectrum Estimation in Radio Interferometric Observations
Samir Choudhuri Indian Institute Technology Kharagpur, India
Collaborators:
- Prof. Somnath Bharadwaj
- SK. Saiyad Ali
Abhik Ghosh
2014MNRAS.445.4351C
SLIDE 2
2 . 2
) ( ) ( ) , ( d e I A v U V
iU
Direction to the source
Correlator
d
T1 T2
Radio Interferometers: Visibilities
Field of view of the antenna – Small – Plane parallel approx.
Antenna beam pattern Intensity distribution
d U
SLIDE 3 Giant Metrewave Radio Telescope, Pune,India 30 fixed antennas x 45m diameter
It is currently operating at several frequency band in
the frequency range 150 -1420 MHz
SLIDE 4 Point Sources Diffuse
Foregrounds
Ghosh et al. 2012
GMRT 150MHz Observation
SLIDE 5
How to quantify these fluctuations ?
Motivation
SLIDE 6 Angular Power Spectrum
Any brightness temperature fluctuation on the sky are usually described by an expansion in spherical harmonics. The Angular Power Spectrum defined as :
*
( ) ( )
l lm lm
C a a
SLIDE 7 How they are related? Two Visibility Correlation:
Entire Sky Signal Noise bias can be avoided by excluding self-correlation term.
SLIDE 8 Simulation Estimators
Bare Estimator Tapered Gridded Estimator
Results
SLIDE 9
Simulation
SLIDE 10 We generate the ,
Ghosh et al. 2012
Then we use FFT to generate in the image plane.
Simulation
Simulations has been done considering GMRT 150 MHz Observations.
SLIDE 11
Diffuse Emission (sky plane)
SLIDE 12
GMRT Baseline Distribution
U V
SLIDE 13
Estimators
SLIDE 14 Bare Estimator
The Bare Estimator is defined as Correlation length,
0.76
FWHM
For GMRT, σ0=16.6
SLIDE 15
Bare Estimator
SLIDE 16 The Bare Estimator deals directly with the visibilities and the computational time for the pairwise correlation scales proportional to N2, where N is the total number of visibilities in the data.
Disadvantage:
SLIDE 17 We define tapered Gridded Estimator as, Tapered Gridded Estimator
θ in arc-min
SLIDE 18
Tapered Gridded Estimator
SLIDE 19
Why Overestimate?
SLIDE 20
Random UV Distribution
U V
SLIDE 21
Tapered Gridded Estimator
SLIDE 22
Instrumental Effect
(a) Gain Error (b) W-term Effect
SLIDE 23
Gain Error
SLIDE 24
The W-term Effect
SLIDE 25
1.We have introduced two estimators for quantifying the angular power spectrum of the sky brightness temperature. We find that the Bare Estimator is able to recover the input model to a good level of precision. For the GMRT estimated angular power spectrum from the Tapered Gridded Estimator is largely within the 1σ errors from the input model. 2.We studied the effect of gain error and find that expectation value of the estimators only depends on the phase error. 3.We find that the w-term does not cause a very big change in the estimated Cℓ at the scales of our interest.
SUMMARY
SLIDE 26
THANK YOU
