arXiv subjects

Brajesh Kumar

Publications and source records attributed to Brajesh Kumar.

At least 55 records · Page 3Linked to original sources

arXiv2023

A study of the propagation of magnetoacoustic waves in small-scale magnetic fields using solar photospheric and chromospheric Dopplergrams: HMI/SDO and MAST observations

In this work, we present a study of the propagation of low-frequency magneto-acoustic waves into the solar chromosphere within small-scale inclined magnetic fields over a quiet-magnetic network region utilizing near-simultaneous photospheric and chromospheric Dopplergrams obtained from the HMI instrument onboard SDO spacecraft and the Multi-Application Solar Telescope (MAST) operational at the Udaipur Solar Observatory, respectively. Acoustic waves are stochastically excited inside the convection zone of the Sun and intermittently interact with the background magnetic fields resulting into episodic signals. In order to detect these episodic signals, we apply the wavelet transform technique to the photospheric and chromospheric velocity oscillations in magnetic network regions. The wavelet power spectrum over photospheric and chromospheric velocity signals show a one-to-one correspondence between the presence of power in the 2.5-4 mHz band. Further, we notice that power in the 2.5-4 mHz band is not consistently present in the chromospheric wavelet power spectrum despite its presence in the photospheric wavelet power spectrum. This indicates that leakage of photospheric oscillations (2.5-4 mHz band) into the higher atmosphere is not a continuous process. The average phase and coherence spectra estimated from these photospheric and chromospheric velocity oscillations illustrate the propagation of photospheric oscillations (2.5-4 mHz) into the solar chromosphere along the inclined magnetic fields. Additionally, chromospheric power maps estimated from the MAST Dopplergrams also show the presence of high-frequency acoustic halos around relatively high magnetic concentrations, depicting the refraction of high-frequency fast mode waves around vA ~ vs layer in the solar atmosphere.

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arXiv2022

First light preparations of the 4m ILMT

The 4m International Liquid Mirror Telescope (ILMT) is a zenith-pointing optical observing facility at ARIES Devasthal observatory (Uttarakhand, India). The first light preparatory activities of the ILMT were accomplished in April 2022 followed by on-sky tests that were carried out at the beginning of May 2022. This telescope will perform a multi-band optical (SDSS $g'$, $r'$ and $i'$) imaging of a narrow strip (~$22'$) of sky utilizing the time-delayed integration technique. Single-scan ILMT images have an integration time of 102 sec and consecutive-night images can be co-added to further improve the signal-to-noise ratio. An image subtraction technique will also be applied to the nightly recorded observations in order to detect transients, objects exhibiting variations in flux or position. Presently, the facility is in the commissioning phase and regular operation will commence in October 2022, after the monsoon. This paper presents a discussion of the main preparation activities before first light, along with preliminary results obtained.

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arXiv2022

First Lunar Occultation Results with the TIRCAM2 Near-Infrared Imager at the Devasthal 3.6-m Telescope

TIRCAM2 is the facility near-infrared Imager at the Devasthal 3.6-m telescope in northern India, equipped with an Aladdin III InSb array detector. We have pioneered the use of TIRCAM2 for very fast photometry, with the aim of recording Lunar Occultations (LO). This mode is now operational and publicly offered. In this paper we describe the relevant instrumental details, we provide references to the LO method and the underlying data analysis procedures, and we list the LO events recorded so far. Among the results, we highlight a few which have led to the measurement of one small-separation binary star and of two stellar angular diameters. We conclude with a brief outlook on further possible instrumental developments and an estimate of the scientific return. In particular, we find that the LO technique can detect sources down to K~ 9 mag with SNR=1 on the DOT telescope. Angular diameters larger than ~ 1 milliarcsecond (mas) could be measured with SNR above 10, or K~6 mag. These numbers are only an indication and will depend strongly on observing conditions such as lunar phase and rate of lunar limb motion. Based on statistics alone, there are several thousands LO events observable in principle with the given telescope and instrument every year.

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arXiv2022

Astrometric and photometric standard candidates for the upcoming 4-m ILMT survey

The International Liquid Mirror Telescope (ILMT) is a 4-meter class survey telescope that has recently achieved first light and is expected to swing into full operations by 1st January 2023. It scans the sky in a fixed 22' wide strip centered at the declination of $+29^o21'41''$ and works in Time Delay Integration (TDI) mode. We present a full catalog of sources in the ILMT strip that can serve as astrometric calibrators. The characteristics of the sources for astrometric calibration are extracted from Gaia EDR3 as it provides a very precise measurement of astrometric properties such as RA ($α$), Dec ($δ$), parallax ($π$), and proper motions ($μ_{α^{*}}$ & $μ_δ$). We have crossmatched the Gaia EDR3 with SDSS DR17 and PanSTARRS-1 (PS1) and supplemented the catalog with apparent magnitudes of these sources in g, r, and i filters. We also present a catalog of spectroscopically confirmed white dwarfs with SDSS magnitudes that may serve as photometric calibrators. The catalogs generated are stored in a SQLite database for query-based access. We also report the offsets in equatorial positions compared to Gaia for an astrometrically calibrated TDI frame observed with the ILMT.

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arXiv2022

Optical spectroscopic characterization of Fermi blazar candidates of uncertain type with TNG and DOT: First Results

The classification of gamma-ray-detected blazar candidates of uncertain type (BCU) is a relevant problem in extragalactic gamma-ray astronomy. Here we report the optical spectroscopic characterization, using two 3-4~m class telescopes, Telescopio Nazionale Galileo and Devasthal Optical Telescope, of 27 BCUs detected with the Fermi Large Area Telescope. Since the identification of emission lines is easier in broad-line blazars, which usually exhibit low frequency peaked (synchrotron peak frequency $\leqslant10^{14}$ Hz) spectral energy distribution, we primarily target such BCUs. We found that 8 out of 27 sources exhibit broad emission lines in their optical spectra, 3 of them have redshifts $>$1 and the farthest one is at $z=2.55$. The optical spectra of 2 of the 19 remaining objects are dominated by the absorption spectra of the host galaxy, and there is a tentative detection of the Lyman-$α$ absorption feature in one source. The spectra of the remaining 16 objects, on the other hand, are found to be featureless.

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arXiv2022

GROWTH on S190426c II: GROWTH-India Telescope search for an optical counterpart with a custom image reduction and candidate vetting pipeline

S190426c / GW190426_152155 was the first probable neutron star - black hole merger candidate detected by the LIGO-Virgo Collaboration. We undertook a tiled search for optical counterparts of this event using the 0.7m GROWTH-India Telescope. Over a period of two weeks, we obtained multiple observations over a 22.1 deg^2 area, with a 17.5% probability of containing the source location. Initial efforts included obtaining photometry of sources reported by various groups, and a visual search for sources in all galaxies contained in the region. Subsequently, we have developed an image subtraction and candidate vetting pipeline with ~ 94% efficiency for transient detection. Processing the data with this pipeline, we find several transients, but none that are compatible with kilonova models. We present the details of our observations, working of our pipeline, results from the search, and our interpretations of the non-detections that will work as a pathfinder during the O4 run of LVK.

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arXiv2022

MUSSES2020J: The Earliest Discovery of a Fast Blue Ultraluminous Transient at Redshift 1.063

In this Letter, we report the discovery of an ultraluminous fast-evolving transient in rest-frame UV wavelengths, MUSSES2020J, soon after its occurrence by using the Hyper Suprime-Cam (HSC) mounted on the 8.2 m Subaru telescope. The rise time of about 5 days with an extremely high UV peak luminosity shares similarities to a handful of fast blue optical transients whose peak luminosities are comparable with the most luminous supernovae while their timescales are significantly shorter (hereafter "fast blue ultraluminous transient," FBUT). In addition, MUSSES2020J is located near the center of a normal low-mass galaxy at a redshift of 1.063, suggesting a possible connection between the energy source of MUSSES2020J and the central part of the host galaxy. Possible physical mechanisms powering this extreme transient such as a wind-driven tidal disruption event and an interaction between supernova and circumstellar material are qualitatively discussed based on the first multiband early-phase light curve of FBUTs, although whether the scenarios can quantitatively explain the early photometric behavior of MUSSES2020J requires systematical theoretical investigations. Thanks to the ultrahigh luminosity in UV and blue optical wavelengths of these extreme transients, a promising number of FBUTs from the local to the high-z universe can be discovered through deep wide-field optical surveys in the near future.

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arXiv2022

SN 2020jfo: A short plateau Type II supernova from a low mass progenitor

We present spectroscopic and photometric observations of the Type IIP supernova, SN 2020jfo, in ultraviolet and optical wavelengths. SN 2020jfo occurred in the spiral galaxy M61 (NGC 4303), with eight observed supernovae in the past 100 years. SN 2020jfo exhibited a short plateau lasting < 65 d, and achieved a maximum brightness in V-band of $M_V$ = -17.4 $\pm$ 0.4 mag at about 8.0 $\pm$ 0.5 d since explosion. From the bolometric light curve, we have estimated the mass of $^{56}$Ni synthesised in the explosion to be 0.033 $\pm$ 0.006 $M_\odot$. The observed spectral features are typical for a type IIP supernova except for shallow H$α$ absorption throughout the evolution and the presence of stable $^{58}$Ni feature at 7378 Å, in the nebular phase. Using hydrodynamical modelling in the MESA + STELLA framework, an ejecta mass of ~ 5 $M_\odot$ is estimated. Models also indicate SN 2020jfo could be the result of a Red Super Giant progenitor with $M_{ZAMS}$ ~ 12 $M_\odot$. Bolometric light curve modelling revealed the presence of a secondary radiation source for initial ~ 20 d, which has been attributed to interaction with a circumstellar material of mass ~ 0.2 $M_\odot$, which most likely was ejected due to enhanced mass loss about 20 years prior to the supernova explosion.

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arXiv2022

Investigating the observational properties of Type Ib supernova SN 2017iro

We report results of optical imaging and low-resolution spectroscopic monitoring of supernova (SN) 2017iro that occurred in the nearby ($\sim$\,31 Mpc) galaxy NGC 5480. The \ion{He}{1} 5876 Å\, feature present in the earliest spectrum (--\,7 d) classified it as a Type Ib SN. The follow-up observations span from --\,7 to +\,266 d with respect to the $B$-band maximum. With a peak absolute magnitude in $V$-band, ($M_{V}$)\,=\,$-17.76\pm0.15$ mag and bolometric luminosity (log$_{10}$\,L)\,=\,42.39\,$\pm$\, 0.09 erg s$^{-1}$, SN 2017iro is a moderately luminous Type Ib SN. The overall light curve evolution of SN 2017iro is similar to SN 2012au and SN 2009jf during the early (up to $\sim$100 d) and late phases ($>$150 d), respectively. The line velocities of both \ion{Fe}{2} 5169 Å\, and \ion{He}{1} 5876 Å\, are $\sim$\,9000 km s$^{-1}$ near the peak. The analysis of the nebular phase spectrum ($\sim$\,+209 d) indicates an oxygen mass of $\sim$\,0.35 M$_{\odot}$. The smaller [\ion{O}{1}]/[\ion{Ca}{2}] flux ratio of $\sim$\,1 favours a progenitor with a zero-age main-sequence mass in the range $\sim$\,13--15 M$_{\odot}$, most likely in a binary system, similar to the case of iPTF13bvn. The explosion parameters are estimated by applying different analytical models to the quasi-bolometric light curve of SN 2017iro. $^{56}$Ni mass synthesized in the explosion has a range of $\sim$\,0.05\,--\,0.10 M$_{\odot}$, the ejecta mass $\sim$1.4\,--\,4.3 M$_{\odot}$ and the kinetic energy $\sim$\,0.8\,--\,1.9\,$\times$ 10$^{51}$ erg.

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arXiv2021

The upcoming 4m ILMT facility and data reduction pipeline testing

The 4m International Liquid Mirror Telescope (ILMT) installation activities have recently been completed at the Devasthal observatory (Uttarakhand, India). The ILMT will perform continuous observation of a narrow strip of the sky ($\sim$27$'$) passing over the zenith in the SDSS $g'$, $r'$ and $i'$ bands. In combination with a highly efficient 4k $\times$ 4k CCD camera and an optical corrector, the images will be secured at the prime focus of the telescope using the Time Delayed Integration technique. The ILMT will reach $\sim$22.5 mag ($g'$-band) in a single scan and this limiting magnitude can be further improved by co-adding the nightly images. The uniqueness of the one-day cadence and deeper imaging with the ILMT will make it possible to discover and study various galactic and extra-galactic sources, especially variable ones. Here, we present the latest updates of the ILMT facility and discuss the preparation for the first light, which is expected during early 2022. We also briefly explain different steps involved in the ILMT data reduction pipeline.

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arXiv2021

Revealing nature of GRB 210205A, ZTF21aaeyldq (AT2021any), and follow-up observations with the 4K$\times$4K CCD Imager+3.6m DOT

Optical follow-up observations of optical afterglows of gamma-ray bursts are crucial to probe the geometry of outflows, emission mechanisms, energetics, and burst environments. We performed the follow-up observations of GRB 210205A and ZTF21aaeyldq (AT2021any) using the 3.6m Devasthal Optical Telescope (DOT) around one day after the burst to deeper limits due to the longitudinal advantage of the place. This paper presents our analysis of the two objects using data from other collaborative facilities, i.e., 2.2m Calar Alto Astronomical Observatory (CAHA) and other archival data. Our analysis suggests that GRB 210205A is a potential dark burst once compared with the X-ray afterglow data. Also, comparing results with other known and well-studied dark GRBs samples indicate that the reason for the optical darkness of GRB 210205A could either be intrinsic faintness or a high redshift event. Based on our analysis, we also found that ZTF21aaeyldq is the third known orphan afterglow with a measured redshift except for ZTF20aajnksq (AT2020blt) and ZTF19abvizsw (AT2019pim). The multiwavelength afterglow modelling of ZTF21aaeyldq using the afterglowpy package demands a forward shock model for an ISM-like ambient medium with a rather wider jet opening angle. We determine circumburst density of $n_{0}$ = 0.87 cm$^{-3}$, kinetic energy $E_{k}$ = 3.80 $\times 10^{52}$ erg and the afterglow modelling also indicates that ZTF21aaeyldq is observed on-axis ($θ_{obs} < θ_{core}$) and a gamma-ray counterpart was missed by GRBs satellites. Our results emphasize that the 3.6m DOT has a unique capability for deep follow-up observations of similar and other new transients for deeper observations as a part of time-domain astronomy in the future.

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arXiv2021

SN 2020sck: deflagration in a carbon-oxygen white dwarf

We present optical UBVRI photometry and low-to-medium resolution spectroscopic observations of type Iax SN 2020sck spanning -5.5 d to +67 d from maximum light in the B-band. From the photometric analysis we find $Δm_{\rm{B}}$(15) = 2.03$\pm$0.05 mag and $M_{\rm{B}}$=-17.81$\pm$0.22 mag. Radiation diffusion model fit to the quasi-bolometric light curve indicates 0.13$\pm$0.02 $M_{\odot}$ of $^{56}$Ni and 0.34 $M_{\rm \odot}$ of ejecta are synthesized in the explosion. Comparing the observed quasi-bolometric light curve with angle-averaged bolometric light curve of three-dimensional pure deflagration explosion of $M_{\rm{ch}}$ carbon-oxygen white dwarf, we find agreement with a model in which 0.16 $M_{\odot}$ of $^{56}$Ni and 0.37 $M_{\odot}$ of ejecta is formed. By comparing the +1.4 day spectrum of SN 2020sck with synthetic spectrum generated using SYN++, we find absorption features due to C II, C III and O I. These are unburned materials in the explosion and indicate a C-O white dwarf. One dimensional radiative transfer modeling of the spectra with TARDIS shows higher density in the ejecta near the photosphere and a steep decrease in the outer layers with an ejecta composition dominated mostly by C, O, Si, Fe, and Ni. The star formation rate of the host galaxy computed from the luminosity of the H$α$ ($λ$6563) line is 0.09 $M_{\odot}$ yr$^{-1}$ indicating a relatively young stellar environment.

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arXiv2021

Photometric, polarimetric, and spectroscopic studies of the luminous, slow-decaying Type Ib SN 2012au

Optical, near-infrared (NIR) photometric and spectroscopic studies, along with the optical imaging polarimetric results for SN 2012au, are presented in this article to constrain the nature of the progenitor and other properties. Well-calibrated multiband optical photometric data (from $-$0.2 to +413 d since $B$-band maximum) were used to compute the bolometric light curve and to perform semi-analytical light-curve modelling using the $\texttt{MINIM}$ code. A spin-down millisecond magnetar-powered model explains the observed photometric evolution of SN 2012au reasonably. Early-time imaging polarimetric follow-up observations ($-$2 to +31 d) and comparison with other similar cases indicate signatures of asphericity in the ejecta. Good spectral coverage of SN 2012au (from $-$5 to +391 d) allows us to trace the evolution of layers of SN ejecta in detail. SN 2012au exhibits higher line velocities in comparison with other SNe Ib. Late nebular phase spectra of SN 2012au indicate a Wolf$-$Rayet star as the possible progenitor for SN 2012au, with oxygen, He-core, and main-sequence masses of $\sim$1.62 $\pm$ 0.15 M$_\odot$, $\sim$4$-$8 M$_\odot$, and $\sim$17$-$25 M$_\odot$, respectively. There is a clear absence of a first overtone of carbon monoxide (CO) features up to +319 d in the $K$-band region of the NIR spectra. Overall analysis suggests that SN 2012au is one of the most luminous slow-decaying Type Ib SNe, having comparatively higher ejecta mass ($\sim$4.7$-$8.3 M$_\odot$) and kinetic energy ($\sim$[4.8 $-$ 5.4] $\times$ 10$^{51}$ erg). Detailed modelling using $\texttt{MESA}$ and the results obtained through $\texttt{STELLA}$ and $\texttt{SNEC}$ explosions also strongly support spin-down of a magnetar with mass of around 20 M$_\odot$ and metallicity Z = 0.04 as a possible powering source of SN 2012au.

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arXiv2021

Differential rotation of the solar transition region from STEREO/EUVI 30.4 nm images

The solar photosphere, chromosphere and corona are known to rotate differentially as a function of latitude. To date, it is unclear if the solar transition region also rotates differentially. In this paper, we investigate differential rotational profile of solar transition region as a function of latitude, using solar full disk (SFD) images at 30.4 nm wavelength recorded by Extreme Ultraviolet Imager (EUVI) onboard Solar Terrestrial Relations Observatory (STEREO) space mission for the period from 2008 to 2018 (Solar Cycle 24). Our investigations show that solar transition region rotates differentially. The sidereal rotation rate obtained at +/- 5 degree equatorial band is quite high (~ 14.7 degree/day), which drops to ~ 13.6 degree/day towards both polar regions. We also obtain that the rotational differentiality is low during the period of high solar activity (rotation rate varies from 14.86 to 14.27 degree/day) while it increases during the ascending and the descending phases of the 24th solar cycle (rotation rate varies from 14.56 to 13.56 degree/day in 2008 and 14.6 to 13.1 degree/day in 2018). Average sidereal rotation rate (over SFD) follows the trend of solar activity (maximum ~ 14.97 degree/day during the peak phase of the solar activity, which slowly decreases to minimum ~ 13.9 degree/day during ascending and the descending phases of the 24th solar cycle). We also observe that solar transition region rotates less differentially than the corona.

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arXiv2021

Intermediate Luminosity Type Iax SN 2019muj With Narrow Absorption Lines: Long-Lasting Radiation Associated With a Possible Bound Remnant Predicted by the Weak Deflagration Model

We present comprehensive spectroscopic and photometric analyses of the intermediate luminosity Type Iax supernova (SN Iax) 2019muj based on multi-band datasets observed through the framework of the OISTER target-of-opportunity program. SN 2019muj exhibits almost identical characteristics with the subluminous SNe Iax 2008ha and 2010ae in terms of the observed spectral features and the light curve evolution at the early phase, except for the peak luminosity. The long-term observations unveil the flattening light curves at the late time as seen in a luminous SN Iax 2014dt. This can be explained by the existence of an inner dense and optically-thick component possibly associated with a bound white dwarf remnant left behind the explosion. We demonstrate that the weak deflagration model with a wide range of the explosion parameters can reproduce the late-phase light curves of other SNe Iax. Therefore, we conclude that a common explosion mechanism operates for different subclass SNe Iax.

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arXiv2021

SN 2017hpa: A carbon-rich type Ia supernova

We present the optical (UBVRI) and ultraviolet (Swift-UVOT) photometry, and optical spectroscopy of Type Ia supernova SN 2017hpa. We study broadband UV+optical light curves and low resolution spectroscopy spanning from $-13.8$ to $+108$~d from the maximum light in $B$-band. The photometric analysis indicates that SN 2017hpa is a normal type Ia with $Δm_{B}(15) = 0.98\pm0.16$ mag and $M_{B}=-19.45\pm0.15$ mag at a distance modulus of $μ= 34.08\pm0.09$ mag. The $(uvw1-uvv)$ colour evolution shows that SN 2017hpa falls in the NUV-blue group. The $(B-V)$ colour at maximum is bluer in comparison to normal type Ia supernovae. Spectroscopic analysis shows that the Si II 6355 absorption feature evolves rapidly with a velocity gradient, $\dot{v}=128\pm 7$ km s$^{-1}$ d$^{-1}$. The pre-maximum phase spectra show prominent C II 6580 Å absorption feature. The C II 6580 Å line velocity measured from the observed spectra is lower than the velocity of Si II 6355 Å, which could be due to a line of sight effect. The synthetic spectral fits to the pre-maximum spectra using syn++ indicate the presence of a high velocity component in the Si II absorption, in addition to a photospheric component. Fitting the observed spectrum with the spectral synthesis code TARDIS, the mass of unburned C in the ejecta is estimated to be $\sim 0.019$~$M_{\odot}$. The peak bolometric luminosity is $L^{bol}_{peak} = 1.43\times10^{43}$ erg s$^{-1}$. The radiation diffusion model fit to the bolometric light curve indicates $0.61\pm0.02$ $M_\odot$ of $^{56}$Ni is synthesized in the explosion.

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arXiv2021

SN 2020ank: a bright and fast-evolving H-deficient superluminous supernova

We investigate the observational properties of a hydrogen-deficient superluminous supernova (SLSN) SN 2020ank (at z = 0.2485), with the help of early phase observations carried out between $-$21 and +52 d since $g$-band maximum. Photometrically, SN 2020ank is one of the brightest SLSN ($M_{g,peak}$ $\sim$ $-$21.84 $\pm$ 0.10 mag), having fast pre-peak rising and post-peak decaying rates. The bolometric light curve of SN 2020ank exhibits a higher peak luminosity ($L_{max}$) of $\sim$(3.9 $\pm$ 0.7) $\times$ 10$^{44}$ erg s$^{-1}$ and appears to be symmetric around the peak with $L^{rise}_{max}$/e $\approx$ $L^{fall}_{max}$/e $\approx$ 15 d. The semi-analytical light-curve modelling using the MINIM code suggests a spin down millisecond magnetar with $P_i$ $\sim$2.2 $\pm$ 0.5 ms and $B$ $\sim$(2.9 $\pm$ 0.1) $\times$ $10^{14}$ G as a possible powering source for SN 2020ank. The possible magnetar origin and excess ultraviolet flux at early epochs indicate a central-engine based powering source for SN 2020ank. Near-peak spectra of SN 2020ank are enriched with the W-shaped O II features but with the weaker signatures of C II and Fe III. Using the estimated rise time of $\sim$27.9 d and the photospheric velocity of $\sim$12050 km s$^{-1}$, we constrain the ejecta mass to $\sim$7.2 $M_{\odot}$ and the kinetic energy of $\sim$6.3 $\times$ 10$^{51}$ erg. The near-peak spectrum of SN 2020ank exhibits a close spectral resemblance with that of fast-evolving SN 2010gx. The absorption features of SN 2020ank are blueshifted compared to Gaia16apd, suggesting a higher expansion velocity. The spectral similarity with SN 2010gx and comparatively faster spectral evolution than PTF12dam (a slow-evolving SLSN) indicate the fast-evolving behavior of SN 2020ank.

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arXiv2020

Evidence of strong relationship between hemispheric asymmetry in solar coronal rotation and solar activity during solar cycle 24

In this article, we report an evidence of very high and statistically significant relationship between hemispheric asymmetry in solar coronal rotation rate and solar activity. Our approach is based on cross correlation of hemispheric asymmetry index (AI) in rotation rate with annual solar activity indicators. To obtain hemispheric asymmetry in solar rotation rate, we use solar full disc (SFD) images at 30.4 nm, 19.5 nm, and 28.4 nm wavelengths for 24th Solar Cycle i.e., for the period from 2008 to 2018, as recorded by the Solar Terrestrial Relations Observatory (STEREO) space mission. Our analysis shows that hemispheric asymmetry in rotation rate is high during the solar maxima from 2011 to 2014. On the other hand, hemispheric asymmetry drops gradually on both sides (i.e., from 2008 to 2011 and from 2014 to 2018). The results show that asymmetry index (AI) leads sunspot numbers by ~1.56 years. This gives a clear indication that hemispheric asymmetry triggers the formation of sunspots working together with the differential rotation of the Sun.

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