Multiphase turbulent interstellar medium: some recent results from radio astronomy

The radio frequency 1.4 GHz transition of the atomic hydrogen is one of the important tracers of the diffuse neutral interstellar medium. Radio astronomical observations of this transition, using either a single dish telescope or an array interferometer, reveal different properties of the interstellar medium. Such observations are particularly useful to study the multiphase nature and turbulence in the interstellar gas. Observations with multiple radio telescopes have recently been used to study these two closely related aspects in greater detail. Using various observational techniques, the density and the velocity fluctuations in the Galactic interstellar medium was found to have a Kolmogorov-like power law power spectra. The observed power law scaling of the turbulent velocity dispersion with the length scale can be used to derive the true temperature distribution of the medium. Observations from a large ongoing atomic hydrogen absorption line survey have also been used to study the distribution of gas at different temperature. The thermal steady state model predicts that the multiphase neutral gas will exist in cold and warm phase with temperature below 200 K and above 5000 K respectively. However, these observations clearly show the presence of a large fraction of gas in the intermediate unstable phase. These results raise serious doubt about the validity of the standard model, and highlight the necessity of alternative theoretical models. Interestingly, numerical simulations suggest that some of the observational results can be explained consistently by including the effects of turbulence in the models of the multiphase medium. This review article presents a brief outline of some of the basic ideas of radio astronomical observations and data analysis, summarizes the results from recent observations, and discusses possible implications of the results.Comment: 20 pages, 10 figures. Invited review accepted for publication in the Proceedings of the Indian National Science Academy. The definitive version will be available at http://insaindia.org/journals/proceedings.ph

Turbulent power spectrum in warm and cold neutral medium using the Galactic HI 21 cm emission

Small-scale fluctuations of different tracers of the interstellar the medium can be used to study the nature of turbulence in astrophysical scales. Of these, the `continuum' emission traces the fluctuations integrated along the line of sight whereas, the spectral line tracers give the information along different velocity channels as well. Recently, Miville-Desch\^enes et al. (2016) have measured the intensity fluctuation power spectrum of the continuum dust emission, and found a power law behaviour with a power law index of $-2.9 \pm 0.1$ for a region of our Galaxy. Here, we study the same region using high-velocity resolution 21-cm emission from the diffuse neutral medium, and estimate the power spectrum at different spectral channels. The measured 21-cm power spectrum also follows a power law, however, we see a significant variation in the power law index with velocity. The value of the power-law index estimated from the integrated map for different components are quite different which is indicative of the different nature of turbulence depending on temperature, density and ionization fraction. We also measure the power spectra after smoothing the 21 cm emission to velocity resolution ranging from $1.03$ to $13.39~{\rm km~s^{-1}}$, but the power spectrum remains unchanged within the error bar. This indicates that the observed fluctuations are dominantly due to density fluctuations, and we can only constrain the power-law index of velocity structure function of $0.0 \pm 1.1$ which is consistent with the predicted Kolmogorov turbulence $(\gamma=2/3)$ and also with a shock-dominated medium $(\gamma=1.0)$.Comment: 8 pages, 7 figures. Accepted for publication in MNRAS. The definitive version will be available at http://mnrasl.oxfordjournals.org

Accurate measurement of the HI column density from HI 21cm absorption-emission spectroscopy

We present a detailed study of an estimator of the HI column density, based on a combination of HI 21cm absorption and HI 21cm emission spectroscopy. This "isothermal" estimate is given by $N_{\rm HI,ISO} = 1.823 \times 10^{18} \int \left[ \tau_{\rm tot} \times {\rm T_B} \right] / \left[ 1 - e^{-\tau_{\rm tot}} \right] {\rm dV}$, where $\tau_{\rm tot}$ is the total HI 21cm optical depth along the sightline and ${\rm T_B}$ is the measured brightness temperature. We have used a Monte Carlo simulation to quantify the accuracy of the isothermal estimate by comparing the derived $N_{\rm HI,ISO}$ with the true HI column density $N_{\rm HI}$. The simulation was carried out for a wide range of sightlines, including gas in different temperature phases and random locations along the path. We find that the results are statistically insensitive to the assumed gas temperature distribution and the positions of different phases along the line of sight. The median value of the ratio of the true H{\sc i} column density to the isothermal estimate, $N_{\rm HI}/{N_{\rm HI, ISO}}$, is within a factor of 2 of unity while the 68.2% confidence intervals are within a factor of $\approx 3$ of unity, out to high HI column densities, $\le 5 \times 10^{23}$\,cm$^{-2}$ per 1 km s$^{-1}$ channel, and high total optical depths, $\le 1000$. The isothermal estimator thus provides a significantly better measure of the HI column density than other methods, within a factor of a few of the true value even at the highest columns, and should allow us to directly probe the existence of high HI column density gas in the Milky Way.Comment: 6 pages, 4 figure; accepted for publication as a Letter in MNRA

The prospects of measuring the angular power spectrum of the diffuse Galactic synchrotron emission with SKA1 Low

The diffuse Galactic synchrotron emission (DGSE) is the most important diffuse foreground component for future cosmological 21-cm observations. The DGSE is also an important probe of the cosmic ray electron and magnetic field distributions in the turbulent interstellar medium (ISM) of our Galaxy. In this paper we briefly review the Tapered Gridded Estimator (TGE) which can be used to quantify the angular power spectrum of the sky signal directly from the visibilities measured in radio-interferometric observations. The salient features of the TGE are (1.) it deals with the gridded data which makes it computationally very fast (2.) it avoids a positive noise bias which normally arises from the system noise inherent to the visibility data, and (3.) it allows us to taper the sky response and thereby suppresses the contribution from unsubtracted point sources in the outer parts and the sidelobes of the antenna beam pattern. We also summarize earlier work where the TGE was used to measure the C_l of the DGSE using 150 MHz GMRT data. Earlier measurements of the angular power spectrum are restricted to smaller angular multipole l ~ 10^3 for the DGSE, the signal at the larger l values is dominated by the residual point sources after source subtraction. The higher sensitivity of the upcoming SKA1 Low will allow the point sources to be subtracted to a fainter level than possible with existing telescopes. We predict that it will be possible to measure the angular power spectrum of the DGSE to larger values of l with SKA1 Low. Our results show that it should be possible to achieve l_{max} ~ 10^4 and ~ 10^5 with 2 minutes and 10 hours of observations respectively.Comment: 10 pages, 3 figures; Accepted for publication in Journal of Astrophysics and Astronomy (JOAA) special issue on "Science with the SKA: an Indian perspective

The visibility based Tapered Gridded Estimator (TGE) for the redshifted 21-cm power spectrum

We present the improved visibility based Tapered Gridded Estimator (TGE) for the power spectrum of the diffuse sky signal. The visibilities are gridded to reduce the computation, and tapered through a convolution to suppress the contribution from the outer regions of the telescope's field of view. The TGE also internally estimates the noise bias, and subtracts this out to give an unbiased estimate of the power spectrum. An earlier version of the 2D TGE for the angular power spectrum $C_{\ell}$ is improved and then extended to obtain the 3D TGE for the power spectrum $P({\bf k})$ of the 21-cm brightness temperature fluctuations. Analytic formulas are also presented for predicting the variance of the binned power spectrum. The estimator and its variance predictions are validated using simulations of $150 \, {\rm MHz}$ GMRT observations. We find that the estimator accurately recovers the input model for the 1D Spherical Power Spectrum $P(k)$ and the 2D Cylindrical Power Spectrum $P(k_\perp,k_\parallel)$, and the predicted variance is also in reasonably good agreement with the simulations.Comment: 19 pages, 13 figures. Accepted for publication in MNRAS. The definitive version will be available at http://mnrasl.oxfordjournals.org

Validating a novel angular power spectrum estimator using simulated low frequency radio-interferometric data

The "Tapered Gridded Estimator" (TGE) is a novel way to directly estimate the angular power spectrum from radio-interferometric visibility data that reduces the computation by efficiently gridding the data, consistently removes the noise bias, and suppresses the foreground contamination to a large extent by tapering the primary beam response through an appropriate convolution in the visibility domain. Here we demonstrate the effectiveness of TGE in recovering the diffuse emission power spectrum through numerical simulations. We present details of the simulation used to generate low frequency visibility data for sky model with extragalactic compact radio sources and diffuse Galactic synchrotron emission. We then use different imaging strategies to identify the most effective option of point source subtraction and to study the underlying diffuse emission. Finally, we apply TGE to the residual data to measure the angular power spectrum, and assess the impact of incomplete point source subtraction in recovering the input power spectrum $C_{\ell}$ of the synchrotron emission. This estimator is found to successfully recovers the $C_{\ell}$ of input model from the residual visibility data. These results are relevant for measuring the diffuse emission like the Galactic synchrotron emission. It is also an important step towards characterizing and removing both diffuse and compact foreground emission in order to detect the redshifted $21\, {\rm cm}$ signal from the Epoch of Reionization.Comment: 18 pages, 1 table, 9 figures, Accepted for publication in New Astronom