Mr
Rajesh Mondal
(Indian Institute of Technology Kharagpur)
Observations of the redshifted 21-cm signal from neutral hydrogen (HI) are a very promising probe of the Epoch of Reionization (EoR), and there is a considerable observational effort underway to detect the EoR 21-cm power spectrum e.g. [GMRT][1], LOFAR, MWA, and PAPER. Observing the EoR 21-cm signal is one of the key scientific goals of the future telescope SKA. It is important to have quantitative predictions of both, the expected EoR 21-cm power spectrum and the sensitivity of the different instruments to measure the expected signal.
On the theoretical and computational front, a considerable amount of effort has been devoted to simulate the expected EoR 21-cm signal. There also have been several works to quantify the sensitivity to the EoR signal for different instruments. Many people have recently made quantitative predictions for detecting the EoR 21-cm power spectrum with the MWA, LOFAR, SKA and PAPER respectively.
The sensitivity of any instrument to the EoR 21-cm power spectrum is constrained by the errors, a part of which arises from the system noise of the instrument and another component which is inherent to the signal that is being detected (cosmic variance). It is commonly assumed, as in all the sensitivity estimates mentioned earlier, that the system noise and the EoR 21-cm signal are both independent Gaussian random variables. This is a reasonably good assumption at large scales in the early stages of reionization when the HI is expected to trace the dark matter. Ionized bubbles, however, introduce non-Gaussianity and the 21-cm signal is expected to become highly non-Gaussian as the reionization proceeds.
We use semi-numerical simulations of the EoR 21-cm signal to study the effect of non-Gaussianities on the error estimates for the 21-cm power spectrum. Not only is this important for correctly predicting the sensitivity of the different instruments, it is also important for correctly interpreting the observation once an actual
detection has been made. The entire analysis here focuses on the errors which are intrinsic to the 21-cm signal, and we do not consider the system noise corresponding to any particular instrument.
[1]: http://www.gmrt.ncra.tifr.res.in
[2]: http://www.lofar.org/
[3]: http://www.haystack.mit.edu/ast/arrays/mwa/
[4]: http://eor.berkeley.edu/
[5]: http://www.skatelescope.org
Summary
The EoR 21-cm signal is expected to become increasingly non-Gaussian as reionization proceeds. We have used semi-numerical simulations to study how this affects the error predictions for the EoR 21-cm power spectrum. We expect $SNR=\sqrt{N_k}$ for a Gaussian random field where $N_k$ is the number of Fourier modes in each $k$ bin. We find that the effect of non-Gaussianity on the $SNR$ does not depend on $k$. Non-Gaussianity is important at high $SNR$ where it imposes an upper limit $\lfloor SNR \rfloor_l$. It is not possible to achieve $SNR > \lfloor SNR \rfloor_l$ even if $N_k$ is increased. The value of $\lfloor SNR \rfloor_l$ falls as reionization proceeds, dropping from $\sim 500$ at $x_{HI} = 0.8 - 0.9$ to $\sim 10$ at $x_{HI} = 0.15$. For $SNR \ll \lfloor SNR \rfloor_l$ we find $SNR = \sqrt{N_k}/A$ with $A \sim 1.5 - 2.5$, roughly consistent with the Gaussian prediction. We present a fitting formula for the $SNR$ as a function of $N_k$, with two parameters $A$ and $\lfloor SNR \rfloor_l$ that have to be determined using simulations. Our results are relevant for predicting the sensitivity of different instruments to measure the EoR 21-cm power spectrum, which till date have been largely based on the Gaussian assumption.
Mr
Rajesh Mondal
(Indian Institute of Technology Kharagpur)
Prof.
Somnath Bharadwaj
(Indian Institute of Technology Kharagpur)
Dr
Suman Majumdar
(Stockholm University)
