Day 3 (May 8, 2021)

The Nobel Prize in physics in 2017 was awarded for the development of the LIGO detectors and for the observation of gravitational waves (GW). Several ground-based detectors around the world are in various stages of development including LIGO-India. However, there are astrophysically interesting GW sources, such as supermassive black-holes, which emit GW below 10 mHz. These lie below the band-width of ground-based detectors because it is impossible to screen off noise (for instance, gravity-gradient noise) below few Hz. The solution is to build a detector in space.

The Laser Interferometric Space Antenna (LISA) - a ESA-NASA project is an instrument for observing low frequency GW. LISA and the ground based detectors complement each other in an essential way, just as various astronomies such as the optical, radio, etc. complement each other. The LISA configuration forms an unequal arm interferometer in the shape of a giant triangle which is almost equilateral.

A major noise source is the laser frequency noise which arises due to phase fluctuations in the laser. Amongst the important noise sources, laser phase noise is expected to be several orders of magnitude larger than other noises in the instrument. Thus, cancelling the laser frequency noise is vital for LISA to reach the requisite sensitivity. Thereare six elementary data streams which are formed by going clockwise and anti-clockwise around the LISA triangle. In time-delay interferometry the data streams are combined with appropriate time delays in order to cancel the laser frequency noise. This scheme can be interestingly translated to an algebraic-geometric problem posed by David Hilbert in 1890. The laser noise cancelling data combinations can be expressed as six-tuple polynomial vectors which form a module over a polynomial ring, well known in the literature, as the first module of syzygies. Gr¨obner basis methods are used to find the generators of the module and which generate all the noise cancelling data combinations. The talk will briefly mention the salient features of this approach and also the recent approaches involving matrix representation theory.

Abstract: Asymptotically flat spacetimes are known to possess an infinite number of symmetries known as the Bondi-Metzner-Sachs (BMS) supertranslations. These BMS symmetries were shown to be related, both, to the gravitational memory effect and Weinberg’s soft theorems, the significance of which was recently realised by Hawking et. al. who conjectured that applying these relations to an asymptotically flat spacetime with a black hole in the interior would imply the existence of an infinite number of soft hairs for the black hole. We discuss the effect of BMS symmetries on quantum entanglement and its implications in the context of the black hole information paradox.

We illustrate the gravitational memory effect for linear uniformly accelerated observers in a physical process involving a BMS shock-wave without planar/spherical symmetry. This classical memory is accompanied by a quantum memory that modulates the quantum entanglement between the opposing accelerated wedges in a flat spacetime. A corresponding phenomenon across the Schwarzschild black hole horizon suggests that the Negativity measure of entanglement between infalling and outgoing Hawking pair should be degraded due to an infalling BMS shockwave while there should be linear order generation of Negativity between two outgoing Hawking particles.

There has been clear observational evidence that jet activity in active galactic nuclei (AGN), which is believed to be due to accretion onto a supermassive black hole, could be episodic over a wide range of time scales. The most striking examples of such episodic or recurrent nuclear activity are the double-double or triple-double radio galaxies with distinct pairs of radio lobes on opposite sides of the nucleus of the parent optical object, reflecting the different cycles of nuclear jet activity. Estimates of the ages of the different pairs of lobes may be used to constrain the time scales of recurrent jet activity. Episodic nuclear activity may also be probed via multiwavelength studies. This includes radio sources in clusters of galaxies as well as an old electron population revealed via inverse-Compton scattering of cosmic microwave background photons with low-energy electrons. We present an overview of recurrent jet activity in AGN, possible models to understand this phenomenon, and suggestions for further work.

Abstract: Multiply-imaged quasar images reveal the mass of the lensing galaxy, and often the geometry of the images indicates that contribution of the galaxy group to which the lens belongs. This technique can be used to find galaxy groups at high/intermediate redshift.

Abstract: Pulsars can act as an excellent probe of the Milky Way magnetic field. The average strength of the Galactic magnetic field component parallel to the line of sight can be estimated as 1.232 RM/DM, where RM and DM are the rotation and dispersion measure of the pulsar. However, this assumes that the thermal electron density and magnetic field of the interstellar medium are uncorrelated. Using numerical simulations and observations, we test the validity of this assumption. Based on magneto-hydro-dynamical simulations of driven turbulence, we show that the correlation between the thermal electron density and the small-scale magnetic field increases with increasing Mach number of the turbulence. We find that the assumption of uncorrelated thermal electron density and magnetic fields is valid only for subsonic and transonic flows, but for supersonic turbulence, the field strength can be severely overestimated by using 1.232 RM/DM. We then correlate existing pulsar observations from the Australia Telescope National Facility with regions of enhanced thermal electron density and magnetic fields probed by CO data of molecular clouds, magnetic fields from the Zeeman splitting of the 21 cm line, neutral hydrogen column density, and Halpha observations. Using these observational data, we show that the thermal electron density and magnetic fields are largely uncorrelated over kpc scales. Thus, we conclude that the relation 1.232 RM/DM provides a good estimate of the magnetic field on Galactic scales, but might break down on sub-kpc scales.

Abstract: The Sun is a laboratory to understand the plasma processes in a stellar environment. In the Sun, the outermost layer, the corona, shows a vast range of magnetic field and plasma density structures. Such variation provides contrasting plasma environments residing in the magnetic field topology, rooted in the photosphere. The coronal magnetic configuration is dynamic due to the changing photospheric magnetic flux, presence of MHD waves and interaction with neighbouring magnetic loops, some resulting in many transient phenomena like solar flares and coronal mass ejection. These phenomena lead to particle acceleration and heating of ambient plasma, i.e. significant w.r.t space weather. We capture them in various electromagnetic bands. In particular, at radio wavelengths from a few cm to few meters, the coronal plasma is optically thin, i.e. captures the detail of these process. With new generation instruments in radio wavelengths, we observe unprecedented and fine observations of the solar flares. In this presentation, I will review the new results, challenges and talk about future missions to understand the solar corona using radio wavelengths as a probe in conjunction with other wavebands.

I will begin with examples of binary- and ternary-fluid flows and of turbulence in such flows. I will then introduce the Cahn-Hilliard-Navier-Stokes (CHNS) equations for such binary and ternary fluids. I will then give some illustrative results from (a) our direct numerical simulations of such flows and (b) a regularity criterion for the solutions of the three-dimensional CHNS equations.

This talk is based on studies that I have carried out with: Nadia Bihari Padhan, Department of Physics, I.I.Sc., Bangalore; Nairita Pal, Los Alamos National Laboratory, USA; Prasad Perlekar, TIFR, Hyderabad; John D. Gibbon, Department of Mathematics, Imperial College, London; Anupam Gupta, IIT, Hyderabad. I would like to acknowledge support from CSIR, DST, UGC (India) and SERC (IISc).

Abstract: One of the spectacular sights in a lake is a wake formed past a moving duck or a boat. Owing to the mathematical analogy between shallow water waves and ion-acoustic waves, we discover the analogue of Kelvin wakes created as an object moves past a plasma. Although not universal as the Kelvin wake, there still is a range of Mach numbers where they occur.

The existence of magnetic field dependent ambipolar diffusion inside a weakly ionized plasma was first proposed in 1955-1956 by Piddington, Cowling, Mestel and Spitzer [1-3]. Today this process is widely accepted to be of crucial importance in galactic molecular clouds and interstellar medium. We will revisit the potential role played by the ambipolar diffusion in the atmospheres of cool stars such as our Sun. In particular, we will explore its influence on the surface dynamo and magnetic reconnection process in the photosphere and lower chromosphere.

[1] J. H. Piddington, Mon. Not. R. Astron. Soc. 114, 638 and 651 (1955).

[2] T. G. Cowling Mon. Not. R. Astron. Soc. 116, 114 (1956).

[3] L. Mestel and L. Spitzer, Mon. Not. R. Astron. Soc. 116, 503 (1956).

Abstract: Cosmological simulations of galaxy formation solve for fluid mechanics at the largest possible scales. They have come a long way in their development and are now able to produce galaxy populations broadly consistent with observations. My talk will cover the basic physical principles that are involved in these simulations, including their numerical implementation which typically involves powerful supercomputing facilities. I'll highlight the successes of current state of the art simulations in explaining various aspects of observed galaxies. Finally, I'll also talk about inevitable limitations of these simulations in their current form and discuss possible directions for current and future endeavours.

Abstract: The origin and maintenance of coherent magnetic fields in galaxies is reviewed. We begin with an interesting baroclynic battery which can generate seed magnetic fields, worked out in collaboration with Prof. Chitre. These seed fields need to be further amplified and maintained by a dynamo to explain observed magnetic fields in galaxies. Basic ideas behind large-scale turbulent dynamos are discussed with particular emphasis on current theoretical challenges and their possible resolution.

Abstract: Internal dynamo-generated magnetic fields in the stars are inaccessible to direct observations, thus deterring our understanding of their origin and evolution in time. A tool that has proved very useful in analyzing the stellar interiors, called asteroseismology, however, has not yet been able to provide details of internal stellar magnetic fields. Here, we investigate the signatures of subsurface magnetic fields in the dispersion relations of acoustic waves (trapped near the stellar surface).

We first begin with an isothermal, stratified atmosphere, permeated by a non-uniform (exponential function of the vertical coordinate) horizontal magnetic field (arXiv:1812.06947). We solve the problem exactly. Next we consider a more realistic polytropic atmosphere. We calculate the dispersion relation numerically and perturbatively. We show that the presence of a horizontal magnetic field breaks the symmetry of rings of constant frequencies over the horizontal wavenumbers. Such asymmetry arising from the magnetic fields eludes the standard helioseismologywith its present resolution. Our results hint that internal stellar magnetic fields might be possible to infer based upon stellar surface oscillations.

Convection in the Sun is a topic that interested Professor Chitre for many years. This convection occurs under extreme conditions of Rayleigh number, Prandtl number, stratification, etc., and the nature of turbulence and the entire flow structure in the Sun is different as a consequence. This talk will present some related considerations.