1. Sanjay K. Pandey L.B.S.P.G.College, Gonda (India). Statistical Analysis of Redshifted Neutral Hydrogen

2. Basic Problem: “To quantify neutral hydrogen distribution using visibility based techniques.”

3. “To quantify statistical properties of visibilities measured at different baselines and frequencies and their relation to statistical properties of HI distribution.”

4. Primary beam pattern Intensity distribution Visibility: d T1 T2 Direction to the source

5. Visibility correlations: Two visibility correlation function (S 2 ) probes the power spectrum of HI density fluctuation,whereas three visibility correlation function (S 3 ) probes the bispectrum of HI density fluctuation at the redshift where the radiation originated. Power spectrum and bispectrum both are real quantities. While power spectrum is necessarily positive, bispectrum need not to do so. S 3 (or bispectrum) is the lowest order statistics sensitive to non-Gaussian features.

6. HI Fluctuations: S 3 = 0 S 3 is non-zero we considcer only those combinations of baselines for which they form a closed triangle. We suppose HI fluctuations homogenous and isotropic. Homoginity Isotropy implies that only shape and size of the triangles are important not their orientation (in the plane of the sky)

7. We assume HI traces dark matter with a possible bias

8. Problem Restated: Using analytical form of Bispectrum, we estimate the magnitude and the nature of the HI signal. We investigate the feasibility of using such observations to probe the structure formation at high redshifts ( in particular post reionization epoch). We have used GMRT parameters but scaling the results for other telescope could be done.

9. Results and Discussion:

10. Frequency dependence of S 3 : Correlations decay rapidly as frequency separation is increased. For a given central frequency the signal is large for small baselines.

11. U dependence of Ratio of S 3 and S 2 Magnitude S 3 and S 2 are comparable. The signal corresponding to S 3 falls faster than that for S 2 with increasing U. Because bispectrum is quadratic in power spectrum whereby it grows faster with time.

12. Dependence of S 3 on shape of triangles and bias parameters : There is shape dependence for larger baselines U > 1000. S 3 decreases faster for equilateral triangle than for bilateral. The ratio has distinct dependence on bias parameter. The shape dependence of S 3 can be used to determine bias parameters

13. Issues still to be resolved: Errors in the estimates are to be evaluated. Extraction of HI signal from various contaminants which are dominants at low frequencies. Contribution from continuum sources is expected to be correlated at large frequency differences. HI signal becomes uncorrelated beyond 1.3 MHz. System noise. For GMRT 200 – 1000 hrs of observations are needed to detect the HI signal. Man made interference: cell phone etc. Difficult to remove ?

14. Thanks !