# General research Interests

**Observational Astronomy:**I have spent lots of time on analysing the systematic characteristics of the FORS2 instrument on the UT1 of the VLT and how they affect exoplanet observations.**Data Reductin:**I am very much interested in astronomical data reduction techniques and optimising them for application to exoplanet transmission spectroscopy. I have written my own reduction and analysis pipeline for spectroscopic time-series observations with the FORS2 instrument.**Transmission Spectroscopy:**This is the technique through which we detect atmospheres of transiting exoplanets.**Exoplanet Atmospheres:**Detection of exoplanetary atmospheres will provide us with an avenue for detecting possible biological processes on those exoplanets capable of harbouring life.**PLATO 2.0:**This is an M-class ESA space telescope mission dedicated to detection of transiting exoplanets, for which my PhD advisor, Prof. Heike Rauer, is the PI. (read more here)

# Exoplanet atmosphere observations

Since the discovery of the first exoplanet, merely a couple of decades ago, the field of exoplanetary science has moved far beyond just the dicovery. We have now started to characterise these alien worlds and the most exciting aspect is the study of their *atmospheres*. Understanding the atmosphere not only gives us clues about the place and how a planet is formed, but one day it will provide us with a tool for discovering biological processes present there. This is due to the fact that life, as we know it, produces very specific set of by-product gases. When we can detect these, we will know that we are not alone in the unievrse.

One method for detection of exoplanetary atmospheres is what is known as **Transmission Spectroscopy**. This is essentially observing the imprint that a planet's atmosphere leaves on the light of its host star, and it passes through the upper layers of the atmosphere, as demonstrated below.

I have been working on detection of exoplanetary atmospheres through this technique of transmission spectrosopcy, using instruments on ground-based facilities, such as the FORS2 instrument on ESO's VLT. I have been compiling a survey of hot Jupiter atmospheres using this instrument, which include detection of *Potassium* in the atmosphere of the exoplanet WASP-17b;

as well as possible detection of the same species in the atmosphere of WASP-80b, a rare hot Jupiter exoplanet, orbiting a cool dwarf star;

# First detection of TiO in an exo-atmosphere

The presence of metal oxides in the atmospheres of highly irradiated, hot Jupiter exoplanets has long been hypothsised by Fortney et al. (2008). However, all the subsequent searches for potential signatures of such molecules have thus far proved elusive. It was only until very recently that marginal evidence for presence of Vanadium Oxide (VO) was reported by Evans et al. (2017) in the secondary eclipse of the hot Jupter WASP-121b. I designed and executed an observational campaign to observe the hot Jupiter WASP-19b with multiple grisms of the FORS2 instrument, covering the entire visible wavelength domain, while the planet passed **in front** of its host star (i.e. the primary transit). This comprehensive wavenlength coverage, coupled with a sophisticated and thourough atmospheric model retrieval search, performed by the exoplanetary atmosphere reseach group at the University of Cambridge, we were able to detect, for the first time Titanium Oxide (TiO), as well as water (H_{2}O), a strongly scattering haze and Sodium (Na) in the atmosphere of an exoplanet. The complete transmission spectrum of this planet is shown in Figure 4 below.

A complete description of this work has been presented in the journal *Nature*, and you can read the entire paper here.

# FORS2 reduction pipeline

The sort of signals that we are trying to detect with transmission spectroscopy are rather below what the current instrumation, such as FORS2, were designed to do. Therefore, great care needs to be given to both astrophysical *data reduction* and *analysis techniques* (next section). Subsequently, as part of my previous studies, I have developed a unified reduction and analysis pipeline for FORS2 data, with the needs of transmission spectroscopy science case in mind. This pipeline, written in PyRAF (essentially a python interface for IRAF), includes detailed tests at every step of reduction to ensure the optimization of that particular step. Additionally, it includes corrections to the wavelength solution of the spectra determined from the calibration frames, through a cross correlation method;

or a detailed analysis of the dispersion in the transit light curves and how it depends on the width of integration bins, across the entire wavelength domain;

# Correlated noise analysis

A major issue plaguing astrphysical time-series data, is the presence of *systematic* or *correlated* noise. These can be of astrophysical, telluric or instrumental origin, which manifest thmeselves in the final observations in either an additive multiplicative manner, producing high frequency, non-Gaussian distributed noise. Whatever its origin, the presence this so-called *red noise* has significant impact upon the determination of final parameter solutions, as well as biasing the estimation of the uncertainties for those parameters.

A novel approach to the inclusion of this correlated noise in modelling of transit light curves is the use of the non-parameteric **Gaussian Process** method, whose use to exoplanet transit light curve modelling was initially introduced recently. In a nutshell, a *GP* involves writing the likelihood function in the Bayesian relation as a full matrix equation, where the full covariance matrix is included, via a covariance funcation, or a *kernel*.

In this framework, possible physical variants that could be introducing the correlated noise are used as inputs for calucaltion of the covariance matrix, in a non-parametric and a stochastic manner. For instance, in Fig. 6, two physical variants (atmospheric seeing and the transmission variations in the optics), plotted on top the figure, are used to model the transit light curve and reproduce the deviations from the expected transit morphology.

# MCMC simulations in a Bayesian framework

In solving the complex, multi-variate problem of an exoplanet transit, we run multiple, simulatanous Monte Carlo Markov Chains, solving the Bayesian relation at every step. Generally, flat and uninformative prior probabilities are set on most parameters, which allows for an unbaised search for best-fitting solutions. The posterior probability is updated at every step, through the solution of the Bayesian relation that involves the inversion of the covariance matrix. Once the chains have converged, via the Gelman & Ruben's statistics test, posterior probability distributions are drawn from those chains and the final solutions, as well as their uncertainties, are estimated based on those pdf's. Additionally, one looks at the parameter-parameter distribution spaces to check for any possible correlations among those variables, that could bias the final solutions. An example of such correlation plots, as well as the parameter posterior distributions drawn from samples of the MCMC simulations, is shown in Fig. 7 below for a select set of variable.