IntroductionSupernovae (SNe) are one of the most energetic events occurring in the Universe, which outshine anentire galaxy and emit enormous amount of energy.

They can be understood in terms of two mechanismsof explosion, one is a complete disruption of white dwarf accreting mass from its companion known asthermonuclear SNe, other is the collapse of a massive star (? 8 M ) under its own gravity giving riseto core collapse SNe. Based on the spectral features they are classified as type I and II dependingupon absence or presence of hydrogen respectively in their early time spectra. Further classification ismade on the basis of Si 6150  ?A feature. Type Ib SNe contains He 5876  ?A features in their maximumlight spectra and type Ic SNe do not have He features. A wide range exist for progenitors for differentsubtypes of SNe.

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Progenitors of thermonuclear SNe (type Ia) are carbon-oxygen white dwarf whereascore collapse SNe are associated with massive progenitors having mass range between 8 M to 20 M (Podsiadlowski et al. 1992). The work in this thesis will focus on the hydrogen deficient SNe namelythe type Ia, Ib and Ic.1.11.

1.1Thermonuclear SNeType Ia SNeType Ia SNe which are hydrogen deficient are the result of complete disruption of a carbon oxygen whitedwarf accreting matter from its companion and are commonly known as thermonuclear SNe. When awhite dwarf touches Chandrasekhar mass limit of 1.4 M , nuclear burning reactions are initiated dueto high temperature. Due to these nuclear burning reactions star explodes and produces type Ia SNleaving behind no remnant. Type Ia SNe have secondary peaks in their I band light curves 30-35 daysafter maximum in B band. Type Ia SNe exhibit a wide range of similarities and can be parameterizedwith a few parameters.

These parameters are the decline rate ?m 15 which is the difference in magnitudeduring 15 days since maximum in B band and R(Si II) which is ratio of the depth of two absorptionfeatures usually attributed to Si II 5972 and Si II 6355 lines (Nugent et al. 1995). A tight correlationis seen between their peak luminosity and light curve shape ?m 15 (Phillips 1993; Hamuy et al. 1996).In spite of the similarities that were seen for type Ia SNe at both low and high redshifts (Riess et al.1998, 2000; Coil et al. 2000), there exist several proofs of differences in the properties of type Ia SNeat different redshifts (Riess et al. 1999; Falco et al.

1999; Aldering et al. 2000; Howell et al. 2000; Liet al. 2001b).

1.1.2A peculiar subclass of type Ia SNeWith the discovery of two SNe 1991T and 1991bg, diversity in the class of type Ia SNe was noted. SN1991T was lacking secondary peak and was an over luminous event. SN 1991bg was a sub luminousevent with a very short peak phase and no secondary maxima. Due to the peculiarities seen in SN1991T and SN 1991bg, any SN discovered after that was termed as SN 1991T type or SN 1991bg typeon the basis of similarity of spectral features at maximum. Generally it is believed that type Ia SNeoriginate from complete eruption of carbon oxygen white dwarf. But there is a subclass of type Ia SNewhich supports a different mechanism of explosion because of their peculiar features.

Members of thissubclass are low luminous and less energetic as compared to normal type Ia SNe. The discovery of SN2000cx (Li et al. 2001a) hinted towards a peculiar SN in terms of light curve, colour curves and spectralevolution. A broadening in the light curve, point of inflection in colour curves and presence of Si featureat 6150  ?A three weeks after maximum were the key features highlighting the differences between type3Ia SNe. With the discovery of SN 2002cx a new era began in the study of type Ia SNe. SN 2002cxshowed a broad peak in R band, a unique plateau around 20 days after B band maximum, peculiarcolour evolution, mysterious emission lines around 7000  ?A and reaching the nebular phase quite early(60 days) in the evolution.

The pre-maximum spectral features of SN 2002cx were similar to SN 1991Tbut the luminosity was comparable to SN 1991bg (Li et al. 2003) which confirms the need of defining anew subclass of peculiar type Ia SNe thereafter termed as type Iax. After the discovery of SN 2002cxa few more SNe are added in the class of type Iax SNe namely SN 2005hk (Sahu et al. 2008; Phillipset al. 2007), SN 2008ha (Foley et al.

2009), 2010ae (Stritzinger et al. 2014), SN 2011ay (Szalai et al.2015), SN 2012Z (Stritzinger et al. 2015), (Yamanaka et al. 2015), SN 2013en (Liu et al.

2015a), SN2015H (Magee et al. 2016) and SN 2014dt (Foley et al. 2015; Fox et al. 2016; Singh et al. 2016). Adetailed study of the individual SNe reveals several peculiar features.Core collapse SNe – Type Ib/IcType Ib/Ic SNe belong to the class of core collapse SNe which are hydrogen deficient. Their progenitorsare very massive like Wolf-Rayet (WR) stars which have stripped off their outer hydrogen envelope (insome cases also the Helium envelope) through very high stellar winds or with interaction of a binarycompanion (Podsiadlowski et al.

1992). These SNe are also called as stripped-envelope SNe. Type IbSNe are associated with He I absorption lines at maximum light whereas type Ic SNe maximum lightspectra has no association of helium lines. Prominent feature in the spectra of type Ic SNe is the PCygni profile of the Ca II NIR triplet, O I absorption and Ca II H&K absorption. Progenitors of typeIb/Ic SNe are not detected in pre explosion images. SNe 2000ds, 2000ew, SN 2001B and 2004gt are afew cases in which upper limits on the flux of the progenitors have been detected (Maund & Smartt,2005; Maund, Smartt & Schweizer 2005; Eldridge et al. 2013). Detection of progenitors of type Ic SNe ismore difficult as compared to type Ib SNe.

Detailed monitoring of these SNe is very crucial for havinga deep insight into the post-explosion phenomenon and pre-explosion properties of the progenitors.Study of late nebular phase of these SNe gives important signature about nature of progenitor starand explosion mechanism. This study has immense importance because these phases can probe deeperinto the core of the expanding envelope. Also asphericity of the explosion of stripped-envelope SNe isconfirmed through spectropolarimetric studies of these SNe during early phase. These indications ofasphericity arise from the asymmetric profile of the OI 6300  ?A – 6400 ?A (Mazzali et al. 2005) or from ? ?the narrower width of the OI 6300 A – 6400 A line as compared to Fe II features at ?5200  ?A (Mazzaliet al.

2001; Maeda et al. 2002). The nature of evolution of late time spectra of type Ib/Ic SNe aredifferent in comparison to spectra of type Ia SNe. Nebular phase spectra of type Ia SNe are enrichedwith broad emission lines of several forbidden features of Fe and Co which are singly or doubly ionized.On the other hand late nebular phase spectra of type Ib/Ic SNe are associated with a few emission linesof neutral oxygen and singly ionized calcium along with different intermediate mass elements. Theseemission features are broad, strong and relatively unblended.

A brief review of the work already done in the fieldType Ia SNe have excellent cosmological applications and they are widely used as distance indicators.Henne et al. (2016) studied the environment of type Ia SNe and the impact of the host galaxy nature onthe Hubble diagram fitting. They confirmed from their study that stretch parameter of type Ia SNe iscorrelated with the type of the host galaxy.

The explosion is believed to be caused by thermal runawayof degenerate WD (Nomoto et al. 1984). No significant correlation is found between colour of typeIa SNe and host morphology. Since there is no clear picture still for the nature of progenitor system4and explosion mechanism, Maoz et al. (2014) proposed different progenitor scenarios and explosionmechanisms for explaining the observed diversity. Zheng et al. (2016) investigated a new empiricalfitting method for the optical light curves of type Ia SNe for estimating the time of first-light and foundthat the rise time is correlated with the decline rate parameter ?m 15 but with a larger scatter. Blacket al.

(2016) examined the time evolution of late nebular phase spectra in optical domain for 27 normaltype Ia SNe and concluded that the universal redshift of spectral features of late time spectra of typeIa SNe is not due to the decrease in the velocity of forbidden iron emission lines, in fact they are theresults of decreasing line velocities and opacity of iron absorption lines which are permitted.Since the discovery of the first member of type Iax SNe class (SN 2002cx), there are 35-40 typeIax SNe discovered so far. Foley et al. (2013) did a statistical analysis on a sample of 30–35 type IaxSNe and inferred that type Iax SNe exhibit a wide range of around five magnitudes in peak absolutebrightness (M B = -14 to -18 mag), their expansion velocities are (4000 to 9000 km s ?1 ) half of that oftype Ia SNe (10,000 to 15,000 km s ?1 ). Type Iax SNe exhibit a correlation between light curve shapeand luminosity but have a large scatter. A weak correlation was also seen between peak luminosityand ejecta velocity (Foley et al. 2013), also the estimated range of ejecta mass for type Iax SNe variesbetween 0.

2 to 1.4 M . There are some open questions to be addressed like the progenitor scenario,low expansion velocity and energy etc. Foley et al. (2016) studied the late time spectra of type Iax SNeand emphasized the similarities and differences of late time spectra of type Iax SNe. Spectra of typeIax SNe at late times are similar with a similar continuum shape and strong forbidden line emission.Type Iax SNe possess diversity in terms of narrow P-Cygni features from permitted lines, a continuumwhich is indicative of photosphere at late-times, both strong and weak narrow forbidden lines and strongbroad forbidden lines. The two component model proposed by Foley et al.

(2016) discusses the origin ofbroad emission lines from the ejecta and narrow forbidden lines originating from a wind. This wind isassociated with the remnant of the progenitor white dwarf and driving force for the wind is radioactivedecay of the material which is left in the remnant and is newly synthesized.Shape of the light curves of type Ib/Ic SNe put constraints on 56 Ni mass, mass of ejecta and kineticenergy by two parameters, one is diffusion time for a given opacity and other is observed expansionvelocity. Principal light curves for hydrogen deficient Ib/Ic SNe are often similar near maximum, butlate time light curves show a great dispersion, indicating a wide range in ejecta masses and kineticenergies. Wheeler et al.

(2015) studied and analysed a sample of single band and quasi bolometriclight curves of these core collapse SNe. They conclude with heterogeneous behaviour of late time lightcurves of stripped-envelope SNe. They also conclude that properties which are derived from peak maybe inconsistent with the tail properties. Events those have spectral differences can have tail similarities.Evolution scenario of type Ib/Ic SNe gives signature about the mass loss through winds, metallicitydependence, binary interactions and stellar rotation. Yoon et al.

(2015) reviewed the prime resultsof evolutionary models proposed for type Ib/Ic progenitors. They argued the difference of SNe Ib/Icprogenitors from single and binary systems. They also support the binary evolution model for theejecta masses derived from SNe Ib/Ic light curves. Branch et al. (2002) used parameterized supernovasynthetic-spectrum code SYNOW for comparison of synthetic spectra with photospheric-phase spectraof type Ib SNe. They found a tight relation between the velocity at the photosphere, which is determinedfrom the Fe II features and the maximum light time. They inferred the similarity of ejecta masses andkinetic energy within their sample. Late nebular phase spectrum of these SNe are enriched with Caand O lines, with the ratio of flux of these lines probable progenitor mass are estimated for variouscore collapse SNe.

Oxygen mass is also calculated for several core collapse SNe from late nebular phasespectra. A subclass of type Ic SNe which are highly energetic and have broad spectral features areassociated with Gamma Ray Bursts are known as hypernovae. There are examples of several corecollapse SNe for which hydrodynamical modelling is used for constraining the progenitor mass.ObjectivesThe rigorous follow up of hydrogen deficient SNe will be done by 104 cm Sampurnanand Telescope (ST),130 cm Devasthal Fast Optical Telescope (DFOT) and 360 cm Devasthal Optical Telescope (DOT) inARIES, Nainital.

Spectroscopic observations will be done by 200 cm Himalayan Chandra Telescope(HCT), IAO Hanle. We use a pair of grisms Gr7 and Gr8, which covers a wavelength range 3500  ?A to 9500 A. Main objectives of this thesis are as follows.(1) To study the temporal evolution of light curves and spectral features of type I SNe.(2) Estimation of the ejected mass, kinetic energy and 56 Ni mass synthesized during explosion.

(3) To throw light on progenitor system of type Iax SNe and the applicability of bound remnanttheory.(4) To understand the nature of expanding ejecta with spectral modelling.(5) A statistical analysis to be done for a sample of type Iax SNe.

(6) With the study of this sample a group characterization can be done for type Iax SNe.Methodology UsedReduction of photometric data is done under IRAF and DAOPHOT environment. Preprocessing whichincludes bias subtraction for removing zero time integration noise, flat fielding for removing pixel topixel non uniformity followed by cosmic ray removal are done with IRAF packages. After preprocessing,instrumental magnitudes are derived using DAOPHOT II packages. Calibration of these magnitudesare done by using Landolt standard fields. Zero points and colour terms are estimated for convertinginstrumental magnitudes of secondary standards into standard magnitudes.Spectroscopic reduction is done with IRAF packages. Preprocessing includes same steps as discussedabove for photometry.

For wavelength calibration arc lamps such as FeAr and FeNe are observed eachnight and for flux calibration standard stars such as Feige 34, Feige 110 and HZ 44 are observed.Aperture extraction, identification of lines using lamps and dispersion correction are done by tasksAPALL, IDENTIFY and DISPCOR respectively. STANDARD, SENSFUNC and CALIBRATE tasksare used for flux calibration.We carry out parameterized spectrum synthesis code SYN++ which is considered as a rewrite andimprovised version of SYNOW code written in C++ (Thomas et al. 2011). The basic assumptions ofthis code are spherical symmetry and homologous expansion of ejecta, considering ejecta as a gas whichis flowing rapidly and assuming Sobolev approximation (Sobolev 1957) for line formation by ignoringthe effects of continuous opacity and dealing local thermodynamic equilibrium (LTE) for maintainingpopulations at different levels. SYN++ code uses input files which are well structured known as YAMLfiles consisting of different input parameters such as photospheric velocity, outer velocity of line form-ing regions, blackbody photosphere temperature, line opacity, lower and upper cut off velocity, auxparameter for deciding the form of opacity which is needed (also known as e-folding length for opacityprofile) including Boltzmann excitation temperature for line strength parameterization.

With spectralmodelling various parameters of ejecta configuration can be estimated as velocity of different lines, theirexcitation temperature, photospheric temperate etc. These informations are beneficial to understandthe nature of expansion of photosphere and distribution of various layers of elements synthesized duringexplosion.We will also use other spectrum synthesis codes such as SYNAPPS and TARDIS for our study.Noteworthy contribution in the field of proposed workand current statusDuring previous observing seasons from October 2014 to June 2016 we have done a rigorous follow upof a few type I SNe – SN 2014dt, MASTER OT J120451.50+265946.

6 and PS15bgt. Out of these SN2014dt is a type Iax SN and rest two are type Ib SNe. We have done a detailed analysis of SN 2014dtin galaxy M61 with photometric span of 410 days and 235 days span for spectroscopy.

SN 2014dt is oneof the brightest (peak magnitude ?13.6 in V filter) and closest discovered type Iax SN (D < 20 Mpc).The broad band light curves follow a linear decline upto ?100 days after which a significant flatteningis seen in the late-time (beyond 150 days) light curves of SN 2014dt. SN 2014dt best matches the lightcurve evolution of SN 2005hk and reaches a peak magnitude of M B ?-18.11 and with ?m 15 ?1.

69±0.17mag. In Figure 1 we have compared evolution of absolute magnitude of SN 2014dt in V band (M V= -18.2) with other well studied type Iax SNe. By inspecting the absolute magnitude evolution of SN2014dt with other type Iax SNe, we conclude that SN 2014dt is comparatively brighter than severalother type Iax discovered so far and falls in the category of bright type Iax SNe like SN 2005hk (M V= -18.02 mag) and SN 2012Z (M V = -18.50 mag).

Using the peak bolometric luminosity we estimate56 Ni mass of 0.15 M in the case of SN 2005hk and the striking similarity between SN 2014dt andSN 2005hk implies that a comparable amount of 56 Ni would have been synthesized in the explosion ofSN 2014dt. The earliest spectrum at ?23 days (Figure 2) is dominated by Fe II and Co II lines withthe absence of Si II 6150  ?A line.

The spectral evolution upto ?100 days matches best with SN 2002cx,SN 2005hk and SN 2015H with narrow absorption features. The nebular phase spectrum is dominatedby a few noticeable emission features around 4800  ?A due to Fe III which are absent in the nebularspectra of SN 2002cx, SN 2005hk and SN 2012Z. Narrow late nebular phase spectral features of SN2014dt indicate that there could be a bound remnant associated with explosion of SN 2014dt. Theexpansion velocities of different lines estimated from absorption lines are comparable to those obtainedfrom SYN++ modeling of the early epoch spectra. The ejecta velocities are between 5000 to 1000 kmsec ?1 which also confirms the low energy budget of type Iax SN 2014dt as compared to normal typeIa SNe. Being one of the brightest and closest discovered SN, deep imaging of SN 2014dt in futurewill be very useful for detecting possible bound remnant and putting constraints on the progenitor.

Inmany cases, the chances of a late-time detection are rare mainly because they could be distant objectsor relatively faint or the location of the SN is close to a bright host galaxy nucleus. The proximity ofSN 2014dt and its location in the host galaxy is ideal for a late-time detection and makes this objectas an excellent candidate for long term monitoring. This work has been submitted for publication in areferred journal. Also we plan to do a group characterization of a sample of around 30 type Iax SNe.

MASTER OT J120451.50+265946.6 and PS15bgt are type two type Ib SNe. We have good photo-metric and spectroscopic data coverage for both of them. Data reduction and analysis are in progressfor these two events.Expected outcome of the proposed workIn this thesis we propose to study hydrogen deficient type I SNe in optical domain. Prime outcome ofthis study will be:1.

Thorough analysis of temporal evolution of type I SNe.2. To get an idea about chemical enrichment through spectral evolution.

3. To examine the validation of bound remnant theory associated with incomplete eruption of whitedwarf for type Iax SNe.4.

To have an idea about explosion scenario for several type I SNe by estimating various physicalparameters associated with the explosion.List of published papers of the candidate7.1Publication related to thesis1.”SN 2014dt : A new chapter in the series of type Iax Supernovae”, Singh Mridweeka et al., 2016,submitted in MNRAS7.2Other Publications1.SN 2013ej : A type IIL supernova with weak signs of interactionBose Subhash, et al., including Singh Mridweeka, 2015, ApJ, 806, 160B2.Photometric and polarimetric observations of fast declining Type II supernovae 2013hj and 2014GBose Subhash, et al., including Singh Mridweeka, 2015, MNRAS, 455, 2712B


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