We present X-ray spectral and timing behavior of Cyg X-3 as observed by AstroSat during the onset of a giant radio flare on 01-02 April 2017. Within a time-scale of few hours, the source shows a transition from the hypersoft state (HPS) to a more luminous state (we termed as the very high state) which coincides with the time of the steep rise in radio flux density by an order of magnitude. Modeling the SXT and LAXPC spectra jointly in 0.5-70.0 keV, we found that the first few hours of the observation is dominated by the HPS with no significant counts above 17 keV. Later, an additional flat powerlaw component suddenly appeared in the spectra which extends to very high energies with the powerlaw photon index of 1.49 +/- 0.04. Such a flat powerlaw component has never been reported from Cyg X-3. Interestingly the fitted powerlaw model in 25-70 keV, when extrapolated to the radio frequency, predicts the radio flux density consistent with the trend measured from RATAN-600 telescope at 11.2 GHz. This provides a direct evidence of the synchrotron origin of flat X-ray powerlaw component and the most extensive monitoring of the broadband X-ray behavior at the moment of decoupling the giant radio jet base from the compact object in Cyg X-3. Using SXT and LAXPC observations, we determine the giant flare ejection time as MJD 57845.34 +/- 0.08 when 11.2 GHz radio flux density increases from ~100 to ~478 mJy.

Mayukh Pahari J S Yadav Jai Verdhan Chauhan Divya Rawat Ranjeev Misra P C Agrawal Sunil Chandra Kalyani Bagri Pankaj Jain R K Manchanda Varsha Chitnis Sudip Bhattacharyya

We report the detection ($>4\sigma$) of a Quasi-Periodic Oscillation (QPO) in the $\gamma$-ray light curve of 3C 454.3 along with a simultaneous marginal QPO detection ($>2.4\sigma$) in the optical light curves. Periodic flux modulations were detected in both of these wavebands with a dominant period of $\sim 47$ days. The $\gamma$-ray QPO lasted for over 450 days (from MJD 56800 to 57250) resulting in over nine observed cycles which is among the highest number of periods ever detected in a blazar light curve. The optical light curve was not well sampled for almost half of the $\gamma$-ray QPO span due to the daytime transit of the source, which could explain the lower significance of the optical QPO. Autoregressive Integrated Moving Average (ARIMA) modelling of the light curve revealed a significant, exponentially decaying, trend in the light curve during the QPO, along with the $47$ days periodicity. We explore several physical models to explain the origin of this transient quasi-periodic modulation and the overall trend in the observed flux with a month-like period. These scenarios include a binary black hole system, a hotspot orbiting close to the innermost stable circular orbit of the supermassive black hole, and precessing jets. We conclude that the most likely scenario involves a region of enhanced emission moving helically inside a curved jet. The helical motion gives rise to the QPO and the curvature ($\sim 0.05^{\circ}$ pc$^{-1}$) of the jet is responsible for the observed trend in the light curve.

Arkadipta Sarkar Alok C. Gupta Varsha R. Chitnis Paul J. Wiita

Quasi-periodic fluctuations in the light curves of blazars can provide insight into the underlying emission process. This type of flux modulation hints at periodic physical processes that result in emission. CTA 102, a flat spectrum radio quasar at $z=1.032$, has displayed significant activity since 2016. The multi-waveband light curve of CTA 102 shows signs of quasi-periodic oscillations during the 2016-2017 flare. Our goal is to quantify the presence of any periodicity in the emitted flux during the mentioned period and to explore the causes that can give rise to it. Techniques such as the Lomb-Scargle periodogram and weighted wavelet z-transform were employed to observe the power emitted at different frequencies. To quantify the significance of the dominant period, Monte-Carlo techniques were employed considering an underlying smooth bending power-law model for the power spectrum. In addition, the light curve was modeled using an autoregressive process to analytically obtain the significance of the dominant period. Lastly, the light curve was modeled using a generalized autoregressive integrated moving average process to check whether introducing a periodic component results in a statistically preferable model. Significant, simultaneous quasi-periodic oscillations (QPOs) were observed in the $\gamma$-ray and optical fluxes of blazar CTA 102 during its 2016-2017 flare. The periodic flux modulation had a dominant period of $\sim$ 7.6 days and lasted for $\sim$ 8 cycles (MJD 57710-57770). All of the methods used point toward significant ($>4\sigma$) quasi-periodic modulation in both $\gamma$-ray and optical fluxes. Several possible models were explored while probing the origin of the periodicity, and by extension, the 2016--2017 optical flare. The best explanation for the detected QPO appears to be a region of enhanced emission, moving helically inside the jet.

Arkadipta Sarkar Pankaj Kushwaha Alok C. Gupta Varsha R. Chitnis Paul J. Wiita

The regular monitoring of flat-spectrum radio quasars (FSRQs) in $\gamma$-rays by Fermi-LAT since past 12 years indicated six sources who exhibited extreme $\gamma$-ray outbursts crossing daily flux of $10^{-5}$ photons/cm$^{2}$/s. We obtained nearly-simultaneous multi-wavelength data of these sources in radio to $\gamma$-ray waveband from OVRO, Steward Observatory, SMARTS, Swift-UVOT, Swift-XRT, and Fermi-LAT. The time-averaged broadband Spectral Energy Distributions (SEDs) of these sources in quiescent states were studied to get an idea about the underlying baseline radiation processes. We modeled the SEDs using one-zone leptonic synchrotron and inverse-Compton emission scenario from broken power-law electron energy distribution inside a spherical plasma blob, relativistically moving down a conical jet. The model takes into account inverse-Compton scattering of externally and locally originated seed photons in the jet. The big blue bumps visible in quiescent state SEDs helped to estimate the accretion disk luminosities and central black hole masses. We found a correlation between the magnetic field inside the emission region and the ratio of emission region distance to disk luminosity, which implies that the magnetic field decreases with an increase in emission region distance and decrease in disk luminosity, suggesting a disk-jet connection. The high-energy index of the electron distribution was also found to be correlated with observed $\gamma$-ray luminosity as $\gamma$-rays are produced by high-energy particles. In most cases, kinetic power carried by electrons can account for jet radiation power as jets become radiatively inefficient during quiescent states.

Abhradeep Roy Sonal R. Patel Arkadipta Sarkar Anshu Chatterjee Varsha R. Chitnis

We present a long-term and intraday variability study on optical multiwaveband ($U\!BV\!RI$) data from the blazar AO 0235+164 collected by various telescopes for $\sim$44 years (1975--2019). The blazar was found to be significantly variable over the years in all wavebands with a variation of about six magnitudes between its low and active states. The variations in the different wavebands are highly correlated without any time lag. We did not observe any significant trend in color variation with time, but we observed a bluer-when-brighter trend between the $B-I$ color index and the $R$-magnitude. Optical $BV\!R$-band spectral energy distributions always show a convex shape. Significant intraday variability was frequently seen in the quasi-simultaneous observations of AO\,0235+164 made on 22 nights in $R$ and $V$-bands by the CASLEO and CAHA telescopes during 1999--2019. We also estimated the central supermassive black-hole mass of $7.9\times10^7 M_{\odot}$ by analyzing the broad Mg II emission line in AO 0235+164's spectrum. We briefly explore the probable physical scenarios responsible for the observed variability.

Abhradeep Roy Alok C. Gupta Varsha R. Chitnis Sergio A. Cellone Claudia M. Raiteri Gustavo E. Romero Paul J. Wiita Anshu Chatterjee Jorge A. Combi Mai Liao Arkadipta Sarkar Massimo Villata

We prove new lower bounds on the likely size of a maximum independent set in a random graph with a given average degree. Our method is a weighted version of the second moment method, where we give each independent set a weight based on the total degree of its vertices.

Varsha Dani Cristopher Moore

In this paper invariant subspace method has been employed for solving linear and non-linear fractional partial differential equations involving Caputo derivative. A variety of illustrative examples are solved to demonstrate the effectiveness and applicability of the method.

Sangita Choudhary Varsha Daftardar-Gejji

In the present paper invariant subspace method has been extended for solving systems of multi-term fractional partial differential equations (FPDEs) involving both time and space fractional derivatives. Further the method has also been employed for solving multi-term fractional PDEs in $(1+n)$ dimensions. A diverse set of examples is solved to illustrate the method.

Sangita Choudhary Varsha Daftardar-Gejji

Developing analytical methods for solving fractional partial differential equations (FPDEs) is an active area of research. Especially finding exact solutions of FPDEs is a challenging task. In the present paper we extend Sumudu transform iterative method (STIM) to solve a variety of time and space FPDEs as well as systems of them. We demonstrate the utility of the method by finding exact solutions to a large number of FPDEs.

Manoj Kumar Varsha Daftardar-Gejji

Optical networks play a crucial role in todays digital topography, enabling the high-speed and reliable transmission of vast amounts of data over optical fibre for long distances. This paper provides an overview of optical networks, especially emphasising on their evolution with time.

Varsha Lohani Anjali Sharma Yatindra Nath Singh Kumari Akansha Baljinder Singh Heera Pallavi Athe