Matched Filter Search for Ionized Bubbles in 21-cm Maps Kanan K. Datta Dept. of Astronomy Stockholm University Oskar Klein Centre

Collaborators Somnath Bharadwaj Tirthankar Roy Choudhury Suman Majumdar

21 cm observations of the reionization : Major Approaches 1)Global evolution of average redshifted 21 cm differential brightness temperature with redshift. (Ravi Subramanian’s talk) 2)The rms, skewness measurement as a function of redshift. (Garrelt Mellema’s talk) 3)Measuring HI power spectrum. (Abhik Ghosh, Somnath Bharadwaj, Stuart Wyithe’s talk) 4)Cross – Correlation (Brigs, T. Guha Sarkar’s talk) 5) Detecting Individual Ionized Bubbles

HI

Can we detect individual ionized bubbles in 21-cm observations?

Motivation for Individual Bubble detection Direct probe of reionization. Interpretation is easier. IGM properties (HI fraction surrounding the HII regions) Source properties (age, photon emission rate ) This will compliment the study through power spectrum measurements

A Visibility based method Direct measured quantity is Visibility Noise in the image is correlated, where as in visibility it is uncorrelated. Advantages over the image base method

To optimally combine the signal from an ionized bubble of radius R_b at redshift z_c we introduce an estimator A Visibility based method

To optimally combine the signal from an ionized bubble of radius R_b at redshift z_c we introduce an estimator Total Observed visibility A Visibility based method

To optimally combine the signal from an ionized bubble of radius R_b at redshift z_c we introduce an estimator Filter A Visibility based method

To optimally combine the signal from an ionized bubble of radius R_b at redshift z_c we introduce an estimator Summation over all baselines and frequency channels A Visibility based method

To optimally combine the signal from an ionized bubble of radius R_b at redshift z_c we introduce an estimator Analytically the mean also can be calculated using A Visibility based method

To optimally combine the signal from an ionized bubble of radius R_b at redshift z_c we introduce an estimator Analytically the mean also can be calculated using A Visibility based method Baseline Distribution function

Simulate dark matter distribution at redshift 6 Grid size=2 Mpc, Box size=256 Mpc (GMRT), 512 Mpc (MWA) Simulating Signal Dark Matter map

Simulate dark matter distribution at redshift 6 Grid size=2 Mpc, Box size=256 Mpc (GMRT), 512 Mpc (MWA) Assume HI traces Dark matter with bias 1 HI map Simulating Signal

Simulate dark matter distribution at redshift 6 Grid size=2 Mpc, Box size=256 Mpc (GMRT), 512 Mpc (MWA) Assume HI traces Dark matter with bias 1 We put spherical ionized bubbles by hand with one at the centre. Simulating Signal

Simulate dark matter distribution at redshift 6 Grid size=2 Mpc, Box size=256 Mpc (GMRT), 512 Mpc (MWA) Assume HI traces Dark matter with bias 1 We put spherical ionized bubbles by hand with one at the centre. Simulating Signal

Simulate dark matter distribution at redshift 6 Grid size=2 Mpc, Box size=256 Mpc (GMRT), 512 Mpc (MWA) Assume HI traces Dark matter with bias 1 We put spherical ionized bubbles by hand with one at the centre. Simulating Signal

Simulate dark matter distribution at redshift 6 Grid size=2 Mpc, Box size=256 Mpc (GMRT), 512 Mpc (MWA) Assume HI traces Dark matter with bias 1 We put spherical ionized bubbles by hand with one at the centre. Simulating Signal

SB PR1 PR2 Simulated maps

Simulating visibilities

Effect of the HI fluctuations

Baseline distribution

Matched Filter The signal to noise ratio (SNR) is maximum if we use the filter exactly matched with the signal from the bubble that we are trying to detect ie.,

Matched Filter The signal to noise ratio (SNR) is maximum if we use the filter exactly matched with the signal from the bubble that we are trying to detect ie., The filter subtracts out any frequency independent component from the frequency range the frequency range To remove the foreground contribution we modify the filter as,

Results Restriction on bubble detection: Detection of bubbles of radius >8 Mpc for GMRT is possible. HI fluctuations will affect Small bubble detection (<8 Mpc). SB

Bubble detection in Patchy reionization PR1 We get almost similar results for PR1 scenario.

Bubble detection in Patchy reionization PR1 We get almost similar results for PR1 scenario. In the PR2 scenario HI fluctuations will dominate over the bubble signal.

Size determination of ionized bubbles In reality bubble size and position not known. We have to find out size and positions (4 unknown parameters) We expect signal to noise ratio (SNR) to peak when the filter is exactly matched to the signal. We propose this can be used to measure bubble size.

Bubble Filter SNR If we know the source position

Bubble Filter SNR !PEAK !

Bubble Filter SNR Credit: Suman Majumdar

Size determination With 1000 h of observations, SNR ~ 3 We calculate the SNR for the filters for various sizes and find out peak SNR and calculate bubble size. Datta, Majumdar, Bharadwaj, Choudhury, MNRAS,2008

Size determination is not limited by the HI fluctuations but limited by the resolution of the experiments This can be done more accurately for larger bubbles hrs, SNR~ 9

Filter Bubble SNR If we don’t know where the source is

FilterBubble SNR !PEAK !

SNR Filter Bubble Credit: Suman Majumdar

Searching bubbles (Position determination) The bubble is placed at the center of the field of view (FoV) We move the center of the filter to different positions and search for a peak in the SNR. Datta, Majumdar, Bharadwaj, Choudhury, MNRAS,2008

Scaling Relations Instrument Reionization history Background Cosmology Source properties

ERLR that redshift range and We find that redshift range and are the most appropriate for the GMRT and the MWA respectively. A 3 sigma detection is possible with the GMRT for bubbles > 50 Mpc or >30 Mpc for 1000 hrs of integration time for ER or LR models. The same figure is >40 Mpc and >30 Mpc for the MWA. Optimal Redshift Datta, Bharadwaj, Choudhury, MNRAS, 2009

Conclusions We developed a technique for detecting individual ionized bubbles in 21-cm maps. The technique maximizes the SNR and subtracts out foregrounds. A 3 sigma detection is possible with instruments like GMRT, LOFAR, MWA for bubbles > 50 Mpc or >30 Mpc for ~1000 hrs of integration time for ER or LR models. Bubble size can be determined which will give crucial information about reionizing source properties Blind search for bubbles is, in principle possible. Detailed study with simulated signal, foregrounds, noise etc needs to be done.

Thank You