The solar wind, magnetosphere and ionosphere are coupled by magnetohydrodynamic waves, and this gives rise to new and often unexpected behaviours that cannot be produced by a single, isolated part of the system. This thesis examines two broad instances of coupling: field-line resonance (FLR) which couples fast and Alfvén waves, and magnetosphere-ionosphere (MI-) coupling via Alfvén waves. The first part of this thesis investigates field-line resonance for equilibria that vary in two dimensions perpendicular to the background magnetic field. This research confirms that our intuitive understanding of FLR from 1D is a good guide to events in 2D, and places 2D FLR onto a firm mathematical basis by systematic solution of the governing equations. It also reveals the new concept of ‘imprinting’ of spatial forms: spatial variations of the resonant Alfvén wave correlate strongly with the spatial form of the fast wave that drives the resonance. MI-coupling gives rise to ionosphere-magnetosphere (IM-) waves, and we have made a detailed analysis of these waves for a 1D sheet E-region. IM-waves are characterised by two quantities: a speed v_{IM} and an angular frequency ω_{IM} , for which we have obtained analytic expressions. For an ideal magnetosphere, IM-waves are advective and move in the direction of the electric field with speed v_{IM}. The advection speed is a non-linear expression that decreases with height-integrated E-region plasma-density, hence, wavepackets steepen on their trailing edge, rapidly accessing small length-scales through wavebreaking. Inclusion of electron inertial effects in the magnetosphere introduces dispersion to IM-waves. In the strongly inertial limit (wavelength λ << λ_{e} , where λ_{e} is the electron inertial length at the base of the magnetosphere), the group velocity of linear waves goes to zero, and the waves oscillate at ω_{IM} which is an upper limit on the angular frequency of IM-waves for any wavelength. Estimates of v_{IM} show that this speed can be a significant fraction (perhaps half) of the E_{⊥} × B_{0} drift in the E-region, producing speeds of up to several hundred metres per second. The upper limit on angular frequency, ωIM , is estimated to give periods from a few hundredths of a second to several minutes. IM-waves are damped by recombination and background ionisation, giving an e-folding decay time that can vary from tens of seconds to tens of minutes. We have also investigated the dynamics and steady-states that occur when the magnetosphere-ionosphere system is driven by large-scale Alfvénic field-aligned currents. Steady-states are dominated by two approximate solutions: an ‘upper’ solution that is valid in places where the E-region is a near perfect conductor, and a ‘lower’ solution that is valid where E-region depletion makes recombination negligible. These analytic solutions are extremely useful tools and the global steady-state can be constructed by matching these solutions across suitable boundary-layers. Furthermore, the upper solution reveals that E-region density cavities form and widen (with associated broadening of the magnetospheric downward current channel) if the downward current density exceeds the maximum current density that can be supplied by background E-region ionisation. We also supply expressions for the minimum E-region plasma-density and shortest length-scale in the steady-state. IM-waves and steady-states are extremely powerful tools for interpreting MI-dynamics. When an E-region density cavity widens through coupling to an ideal, single-fluid MHD magnetosphere, it does so by forming a discontinuity that steps between the upper and lower steady-states. This discontinuity acts as part of an ideal IM-wave and moves in the direction of the electric field at a speed U = \sqrt{v_{IM} {+} v_{IM} {-}}, which is the geometric mean of v_{IM} evaluated immediately to the left and right of the discontinuity. This widening speed is typically several hundreds of metres per second. If electron inertial effects are included in the magnetosphere, then the discontinuity is smoothed, and a series of undershoots and overshoots develops behind it. These undershoots and overshoots evolve as inertial IM-waves. Initially they are weakly inertial, with a wavelength of about λ_{e}, however, strong gradients of ω_{IM} cause IM-waves to phase-mix, making their wavelength inversely proportional to time. Therefore, the waves rapidly become strongly inertial and oscillate at ω_{IM}. The inertial IM-waves drive upgoing Alfvén waves in the magnetosphere, which populate a region over the downward current channel, close to its edge. In this manner, the E-region depletion mechanism, that we have detailed, creates small-scale Alfvén waves in large-scale current systems, with properties determined by MI-coupling.

De nos jours, il est bien accepté que le cycle magnétique de 11 ans du Soleil est l'oeuvre d'une dynamo interne présente dans la zone convective. Bien qu'avec la puissance de calculs des ordinateurs actuels il soit possible, à l'aide de véritables simulations magnétohydrodynamiques, de résoudre le champ magnétique et la vitessse dans toutes les directions spatiales, il n'en reste pas moins que pour étudier l'évolution temporelle et spatiale de la dynamo solaire à grande échelle, il reste avantageux de travailler avec des modèles plus simples. Ainsi, nous avons utilisé un modèle simplifié de la dynamo solaire, nommé modèle de champ moyen, pour mieux comprendre les mécanismes importants à l'origine et au maintien de la dynamo solaire. L'insertion d'un tenseur-alpha complet dans un modèle dynamo de champ moyen, provenant d'un modèle global-MHD [Ghizaru et al., 2010] de la convection solaire, nous a permis d'approfondir le rôle que peut jouer la force électromotrice dans les cycles magnétiques produits par ce modèle global. De cette façon, nous avons pu reproduire certaines caractéristiques observées dans les cycles magnétiques provenant de la simulation de Ghizaru et al., 2010. Tout d'abord, le champ magnétique produit par le modèle de champ moyen présente deux modes dynamo distincts. Ces modes, de périodes similaires, sont présents et localisés sensiblement aux mêmes rayons et latitudes que ceux produits par le modèle global. Le fait que l'on puisse reproduire ces deux modes dynamo est dû à la complexité spatiale du tenseur-alpha. Par contre, le rapport entre les périodes des deux modes présents dans le modèle de champ moyen diffère significativement de celui trouvé dans le modèle global. Par ailleurs, on perd l'accumulation d'un fort champ magnétique sous la zone convective dans un modèle où la rotation différentielle n'est plus présente. Ceci suggère que la présence de rotation différentielle joue un rôle non négligeable dans l'accumulation du champ magnétique à cet endroit. Par ailleurs, le champ magnétique produit dans un modèle de champ moyen incluant un tenseur-alpha sans pompage turbulent global est très différent de celui produit par le tenseur original. Le pompage turbulent joue donc un rôle fondamental au sein de la distribution spatiale du champ magnétique. Il est important de souligner que les modèles dépourvus d'une rotation différentielle, utilisant le tenseur-alpha original ou n'utilisant pas de pompage turbulent, parviennent tous deux à produire une dynamo oscillatoire. Produire une telle dynamo à l'aide d'un modèle de ce type n'est pas évident, a priori. Finalement, l'intensité ainsi que le type de profil de circulation méridienne utilisés sont des facteurs affectant significativement la distribution spatiale de la dynamo produite. / It is generally agreed upon that the 11-year magnetic cycle of the Sun arises through the action of an internal dynamo operating in the convective zone, and perhaps also immediately beneath it. Although the computing power of current supercomputers is sufficient to allow fairly realistic magnetohydrodynamical simulations of this dynamo process, to study the temporal and spatial evolution of the large-scale solar magnetic field over long timescales, it remains advantageous to work with simpler models. Thus, to better understand the physical mechanisms at the origin and maintenance of the solar dynamo, we used a simplified formulation, known as a mean-field model. By using a complete alpha-tensor extracted from a global MHD model of solar convection [Ghizaru et al., 2010] as input to a kinematic axisymmetric mean-field dynamo model [Charbonneau & MacGregor, 1997], it becomes possible to study the effect of the electromotive force on the magnetic cycles produced by the global model. In this way, we are able to reproduce some of the observed characteristics of the Ghizaru et al., 2010 simulation, in particular magnetic cycles. The axisymmetric magnetic field produced by the mean-field dynamo model exhibits two distincts dynamo modes. These modes, with similar periods, are present and peak at substantially at the same radii and latitudes as the sonlly-averaged magnetic fields extracted from the global model. Thanks to the spatial complexity of the alpha-tensor, we can reproduce these two dynamo modes. In contrast, the ratio of the periods of the two modes present in the mean field model differs significantly from that found in the global model. In addition, the accumulation of strong magnetic fields at the base of the convective zone disappears in a model where differential rotation has been removed. This suggests that differential rotation plays a significant role in the accumulation of magnetic fields in this region. Furthermore, removing the turbulent pumping component of the alpha-tensor produces a very different magnetic field cycle. Therefore, turbulent pumping plays a crucial role in the spatial distribution of the magnetic field. It is important to underline that the models without differential rotation, with or without turbulent pumping, both succeed in producing an oscillatory dynamo using only the turbulent electromotive force. However, the dynamos materializing in these modified models are significantly different from that using the full alpha-tensor. Finally, both the intensity and form of meridional circulation profiles are significant factors affecting the dynamo modes.

No description available.

De nos jours, il est bien accepté que le cycle magnétique de 11 ans du Soleil est l'oeuvre d'une dynamo interne présente dans la zone convective. Bien qu'avec la puissance de calculs des ordinateurs actuels il soit possible, à l'aide de véritables simulations magnétohydrodynamiques, de résoudre le champ magnétique et la vitessse dans toutes les directions spatiales, il n'en reste pas moins que pour étudier l'évolution temporelle et spatiale de la dynamo solaire à grande échelle, il reste avantageux de travailler avec des modèles plus simples. Ainsi, nous avons utilisé un modèle simplifié de la dynamo solaire, nommé modèle de champ moyen, pour mieux comprendre les mécanismes importants à l'origine et au maintien de la dynamo solaire. L'insertion d'un tenseur-alpha complet dans un modèle dynamo de champ moyen, provenant d'un modèle global-MHD [Ghizaru et al., 2010] de la convection solaire, nous a permis d'approfondir le rôle que peut jouer la force électromotrice dans les cycles magnétiques produits par ce modèle global. De cette façon, nous avons pu reproduire certaines caractéristiques observées dans les cycles magnétiques provenant de la simulation de Ghizaru et al., 2010. Tout d'abord, le champ magnétique produit par le modèle de champ moyen présente deux modes dynamo distincts. Ces modes, de périodes similaires, sont présents et localisés sensiblement aux mêmes rayons et latitudes que ceux produits par le modèle global. Le fait que l'on puisse reproduire ces deux modes dynamo est dû à la complexité spatiale du tenseur-alpha. Par contre, le rapport entre les périodes des deux modes présents dans le modèle de champ moyen diffère significativement de celui trouvé dans le modèle global. Par ailleurs, on perd l'accumulation d'un fort champ magnétique sous la zone convective dans un modèle où la rotation différentielle n'est plus présente. Ceci suggère que la présence de rotation différentielle joue un rôle non négligeable dans l'accumulation du champ magnétique à cet endroit. Par ailleurs, le champ magnétique produit dans un modèle de champ moyen incluant un tenseur-alpha sans pompage turbulent global est très différent de celui produit par le tenseur original. Le pompage turbulent joue donc un rôle fondamental au sein de la distribution spatiale du champ magnétique. Il est important de souligner que les modèles dépourvus d'une rotation différentielle, utilisant le tenseur-alpha original ou n'utilisant pas de pompage turbulent, parviennent tous deux à produire une dynamo oscillatoire. Produire une telle dynamo à l'aide d'un modèle de ce type n'est pas évident, a priori. Finalement, l'intensité ainsi que le type de profil de circulation méridienne utilisés sont des facteurs affectant significativement la distribution spatiale de la dynamo produite. / It is generally agreed upon that the 11-year magnetic cycle of the Sun arises through the action of an internal dynamo operating in the convective zone, and perhaps also immediately beneath it. Although the computing power of current supercomputers is sufficient to allow fairly realistic magnetohydrodynamical simulations of this dynamo process, to study the temporal and spatial evolution of the large-scale solar magnetic field over long timescales, it remains advantageous to work with simpler models. Thus, to better understand the physical mechanisms at the origin and maintenance of the solar dynamo, we used a simplified formulation, known as a mean-field model. By using a complete alpha-tensor extracted from a global MHD model of solar convection [Ghizaru et al., 2010] as input to a kinematic axisymmetric mean-field dynamo model [Charbonneau & MacGregor, 1997], it becomes possible to study the effect of the electromotive force on the magnetic cycles produced by the global model. In this way, we are able to reproduce some of the observed characteristics of the Ghizaru et al., 2010 simulation, in particular magnetic cycles. The axisymmetric magnetic field produced by the mean-field dynamo model exhibits two distincts dynamo modes. These modes, with similar periods, are present and peak at substantially at the same radii and latitudes as the sonlly-averaged magnetic fields extracted from the global model. Thanks to the spatial complexity of the alpha-tensor, we can reproduce these two dynamo modes. In contrast, the ratio of the periods of the two modes present in the mean field model differs significantly from that found in the global model. In addition, the accumulation of strong magnetic fields at the base of the convective zone disappears in a model where differential rotation has been removed. This suggests that differential rotation plays a significant role in the accumulation of magnetic fields in this region. Furthermore, removing the turbulent pumping component of the alpha-tensor produces a very different magnetic field cycle. Therefore, turbulent pumping plays a crucial role in the spatial distribution of the magnetic field. It is important to underline that the models without differential rotation, with or without turbulent pumping, both succeed in producing an oscillatory dynamo using only the turbulent electromotive force. However, the dynamos materializing in these modified models are significantly different from that using the full alpha-tensor. Finally, both the intensity and form of meridional circulation profiles are significant factors affecting the dynamo modes.

Dans les réacteurs industriels ou dans la nature, l'écoulement de fluides peut être couplé à des réactions chimiques. Dans de nombreux cas, il en résulte l'apparition de structures complexes dont les propriétés dépendent entre autres de la géométrie du système.<p><p>Dans ce contexte, le but de notre thèse a été d'étudier de manière théorique et sur des modèles réaction-diffusion-convection simples les propriétés de dynamiques spatio-temporelles résultant du couplage chimie-hydrodynamique. <p>Nous nous sommes focalisés sur les instabilités hydrodynamiques de digitation visqueuse et de densité qui apparaissent respectivement lorsqu'un fluide dense est placé au-dessus d'un fluide moins dense dans le champ de gravité et lorsqu'un fluide visqueux est déplacé par un fluide moins visqueux dans un milieu poreux.<p><p>En particulier, nous avons étudié les problèmes suivants:<p>- L'influence d'une réaction chimique de type A + B → C sur la digitation visqueuse. Nous avons montré que les structures formées lors de cette instabilité varient selon que le réactif A est injecté dans le réactif B ou vice-versa si ces réactifs n'ont pas un coefficient de diffusion ou une concentration initiale identiques.<p>- Le rôle de pertes de chaleur par les parois du réacteur dans le cadre de la digitation de densité de fronts autocatalytiques exothermiques. Nous avons caractérisé les conditions de stabilité de fronts en fonction des pertes de chaleur et expliqué l'apparition de zones anormalement chaudes lors de cette instabilité.<p>- L'influence de l'inhomogénéité du milieu sur la digitation de densité de solutions réactives ou non. Nous avons montré que les variations spatiales de perméabilité d'un milieu poreux peuvent figer ou faire osciller la structure de digitation dans certaines conditions.<p>- L'influence d'un champ électrique transverse sur l'instabilité diffusive et la digitation de densité de fronts autocatalytiques. Il a été montré que cette interaction peut donner lieu à des nouvelles structures et changer les propriétés du front.<p><p>En conclusion, nous avons montré que le couplage entre réactions chimiques et mouvements hydrodynamiques est capable de générer de nouvelles structures spatio-temporelles dont les propriétés dépendent entre autres des conditions imposées au système.<p>/<p>In industrial reactors or in nature, fluid flows can be coupled to chemical reactions. In many cases, the result is the emergence of complex structures whose properties depend among others on the geometry of the system.<p>In this context, the purpose of our thesis was to study theoretically using simple models of reaction-diffusion-convection, the properties of dynamics resulting from the coupling between chemistry and hydrodynamics.<p><p>We focused on the hydrodynamic instabilities of viscous and density fingering that occur respectively when a dense fluid is placed above a less dense one in the gravity field and when a viscous fluid is displaced by a less viscous fluid in a porous medium.<p><p>In particular, we studied the following issues:<p>- The influence of a chemical reaction type A + B → C on viscous fingering. We have shown that the fingering patterns observed during this instability depends on whether the reactant A is injected into the reactant B or vice versa if they do not have identical diffusion coefficients or initial concentrations.<p>- The role of heat losses through the reactor walls on the density fingering of exothermic autocatalytic fronts. We have characterized the conditions of stability of fronts depending on heat losses and explained the appearance of unusually hot areas during this instability.<p>- The influence of the inhomogeneity of the medium on the density fingering of reactive solutions or not. We have shown that spatial variations of permeability of a porous medium may freeze or generate oscillating fingering pattern under certain conditions.<p>- The influence of a transverse electric field on the Rayleigh-Taylor and diffusive instabilities of autocatalytic fronts. It was shown that this interaction may lead to new structures and may change the properties of the front.<p><p>In conclusion, we showed that the coupling between chemical reactions and hydrodynamic motions can generate new space-time structures whose properties depend among others, on the conditions imposed on the system. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Magnetohydrodynamic instabilities are responsible for geo- and astrophysical phenomena such as reversals of the geomagnetic field, sunspots, solar flares, and accretion disk dynamics. Two particular types of these instabilities were experimentally investigated in rotating spherical and cylindrical apparatus using the eutectic alloy GaInSn as a working fluid. The spherical apparatus, Hydromagnetic Experiment with Differentially Gyrating sphEres HOlding GaInSn (HEDGEHOG), was used to investigate the magnetised spherical Couette (MSC) flow for a range of the imposed axial magnetic field corresponding to Hartmann numbers of 0 to 40 and for a Reynolds number of 1000. A wave with an azimuthal wavenumber of 2 was observed at a Hartmann number of 0, which changed its azimuthal wavenumber to 3 at Hartmann numbers of 5 and 10. For Hartmann numbers between 10 and 22.5, the experimental flow displayed no temporal dependence, since the MSC flow was in its base state. In the remainder of the investigated range of Hartmann numbers, rotating waves with azimuthal wavenumbers of 2, 3, and 4 manifested, with some dependence on whether the Hartmann numbers were fixed or continuously varied. For the magnetised Taylor-Couette (MTC) flow investigated using the Potsdam ROssendorf Magnetic InStability Experiment (PROMISE), thermal convection was found to influence the azimuthal magnetorotational instability (AMRI) in two major ways. Firstly, it reduced the critical Hartmann number required for the onset of AMRI. Secondly, it broke the symmetry of the AMRI travelling waves so that they either travelled upwards or downwards depending on the direction of the radial heat flux.

Thesis: M.S., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1978 / Includes bibliographical references. / M.S. / M.S. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science

A white dwarf is most likely the end stage of a low mass star like our Sun, which results when the parent star consumes all the hydrogen in its core, thus bringing fusion to a halt. It is a dense and compact object, where the inward gravitational pull is balanced by the outward pressure arising due to the motion of its constituent degenerate electrons. The theory of non-magnetized and non-rotating white dwarfs was formulated extensively by S. Chandrasekhar in the 1930s, who also proposed a maximum possible mass for this objects, known as the Chandrasekhar limit (Chandrasekhar 1935)1. White dwarfs are believed to be the progenitors of extremely bright explosions called type Ia supernovae (SNeIa). SNeIa are extremely important and popular astronomical events, which are hypothesized to be triggered in white dwarfs having mass close to the famous Chandrasekhar limit ∼ 1.44M⊙. The characteristic nature of the variation of luminosity with time of SNeIa is believed to be powered by the decay of 56Ni to 56Co and, finally, to 56Fe. This feature, along with the consistent mass of the exploding white dwarf, is deeply linked with their utilization as “standard candles” for cosmic distance measurement. In fact, SNeIa measurements were instrumental in establishing the accelerated nature of the current expansion of the universe (Perlmutter et al. 1999). However, several recently observed peculiar SNeIa do not conform to this traditional explanation. Some of these SNeIa are highly over-luminous, e.g. SN 2003fg, SN 2006gz, SN 2007if, SN 2009dc (Howell et al. 2006; Scalzo et al. 2010), and some others are highly under-luminous, e.g. SN 1991bg, SN 1997cn, SN 1998de, SN 1999by, SN 2005bl (Filippenko et al. 1992; Taubenberger et al. 2008). The luminosity of the former group of SNeIa implies a huge Ni-mass (often itself super-Chandrasekhar), invoking highly super-Chandrasekhar white dwarfs, having mass 2.1 − 2.8M⊙, as their most plausible progenitors (Howell et al. 2006; Scalzo et al. 2010). On the other hand, the latter group produces as low as ∼ 0.1M⊙ of Ni (Stritzinger et al. 2006), which rather seem to favor sub-Chandrasekhar explosion scenarios. In this thesis, as the title suggests, we have endeavored to establish the existence of exotic, super- and sub-Chandrasekhar limiting mass white dwarfs, in order to explain the aforementioned peculiar SNeIa. This is an extremely important puzzle to solve in order to comprehensively understand the phenomena of SNeIa, which in turn is essential for the correct interpretation of the evolutionary history of the universe. Effects of magnetic field: White dwarfs have been observed to be magnetized, having surface fields as high as 105 − 109 G (Vanlandingham et al. 2005). The interior field of a white dwarf cannot be probed directly but it is quite likely that it is several orders of magnitude higher than the surface field. The theory of weakly magnetized white dwarfs has been investigated by a few authors, however, their properties do not starkly contrast with that of the non-magnetized cases (Ostriker & Hartwick 1968). In our venture to find a fundamental basis behind the formation of super-Chandrasekhar white dwarfs, we have explored in this thesis the impact of stronger magnetic fields on the properties of white dwarfs, which has so far been overlooked. We have progressed from a simplistic to a more rigorous, self-consistent model, by adding complexities step by step, as follows: • spherically symmetric Newtonian model with constant (central) magnetic field • spherically symmetric general relativistic model with varying magnetic field • model with self-consistent departure from spherical symmetry by general relativis-tic magnetohydrodynamic (GRMHD) numerical modeling. We have started by exploiting the quantum mechanical effect of Landau quanti-zation due to a maximum allowed equipartition central field greater than a critical value Bc = 4.414 × 1013 G. To begin with, we have carried out the calculations in a Newtonian framework assuming spherically symmetric white dwarfs. The primary ef-fect of Landau quantization is to stiffen the equation of state (EoS) of the underlying electron degenerate matter in the high density regime, and, hence, yield significantly super-Chandrasekhar white dwarfs having mass much & 2M⊙ (Das & Mukhopadhyay 2012a,b). Consequently, we have proposed a new mass limit for magnetized white dwarfs which may establish the aforementioned peculiar, over-luminous SNeIa as new standard candles (Das & Mukhopadhyay 2013a,b). We have furthermore predicted possible evo-lutionary scenarios by which super-Chandrasekhar white dwarfs could form by accretion on to a commonly observed magnetized white dwarf, by invoking the phenomenon of flux freezing, subsequently ending in over-luminous, super-Chandrasekhar SNeIa (Das et al. 2013). Before moving on to a more complex model, we have justified the assumptions in our simplistic model, in the light of various related physics issues (Das & Mukhopad-hyay 2014b), and have also clarified, and, hence, removed some serious misconceptions regarding our work (Das & Mukhopadhyay 2015c). Next, we have considered a more self-consistent general relativistic framework. We have obtained stable solutions of magnetostatic equilibrium models for white dwarfs pertaining to various magnetic field profiles, however, still in spherical symmetry. We have showed that in this framework, a maximum stable mass as high as ∼ 3.3M⊙ can be realized (Das & Mukhopadhyay 2014a). However, it is likely that the anisotropic effect due to a strong magnetic field may cause a deformation in the spherical structure of the white dwarfs. Hence, in order to most self-consistently take into account this departure from spherical symmetry, we have constructed equilibrium models of strongly magnetized, static, white dwarfs in a general relativistic framework, first time in the literature to the best of our knowledge. In order to achieve this, we have modified the GRMHD code XNS (Pili et al. 2014), to apply it in the context of white dwarfs. Interestingly, we have found that signifi-cantly super-Chandrasekhar white dwarfs, in the range ∼ 1.7 − 3.4M⊙, are obtained for many possible field configurations, namely, poloidal, toroidal and mixed (Das & Mukhopadhyay 2015a). Furthermore, due to the inclusion of deformation caused by a strong magnetic field, super-Chandrasekhar white dwarfs are obtained for relatively lower central magnetic field strengths (∼ 1014 G) compared to that in the simplistic model — as correctly speculated in our first work of this series (Das & Mukhopadhyay 2012a). We have also found that although the characteristic deformation induced by a purely toroidal field is prolate, the overall shape remains quasi-spherical — justifying our earlier spherically symmetric assumption while constructing at least some models of strongly magnetized white dwarfs (Das & Mukhopadhyay 2014a). Indeed more accurate and extensive numerical analysis seems to have validated our analytical findings. Thus, very interestingly, our investigation has established that magnetized white dwarfs can indeed have mass that significantly exceeds the Chandrasekhar limit, irre-spective of the origin of the underlying magnetic effect — a discovery which is not only of theoretical importance, but also has a direct astrophysical implication in explaining the progenitors of the peculiar, over-luminous, super-Chandrasekhar SNeIa. Effects of modified Einstein’s gravity: A large array of models has been required to explain the peculiar, over- and under- luminous SNeIa. However, it is unlikely that nature would seek mutually antagonistic scenarios to exhibit sub-classes of apparently the same phenomena, i.e., triggering of thermonuclear explosions in white dwarfs. Hence, driven by the aim to establish a unification theory of SNeIa, we have invoked in the last part of this thesis a modification to Einstein’s theory of general relativity in white dwarfs. The validity of general relativity has been tested mainly in the weak field regime, for example, through laboratory experiments and solar system tests. However, the question remains, whether general relativity requires modification in the strong gravity regime, such as, the expanding universe, the region close to a black hole and neutron star. For instance, there is evidence from observational cosmology that the universe has undergone two epochs of cosmic acceleration, the theory behind which is not yet well understood. The period of acceleration in the early universe is known as inflation, while the current accelerated expansion is often explained by invoking a mysterious dark energy. An alternative approach to explain the mysteries of inflation and dark energy is to modify the underlying gravitational theory itself, as it conveniently avoids involving any exotic form of matter. Several modified gravity theories have been proposed which are extensions of Einstein’s theory of general relativity. A popular class of such theories is known as f (R) gravity (e.g. see de Felice & Tsujikawa 2010), where the Lagrangian density f of the gravitational field is an arbitrary function of the Ricci scalar R. In the context of astrophysical compact objects, so far, modified gravity theories have been applied only to neutron stars, which are much more compact than white dwarfs, in order to test the validity of such theories in the strong field regime (e.g. Cooney et al. 2010; Arapoˇglu et al. 2011). Moreover, a general relativistic correction itself does not seem to modify the properties of a white dwarf appreciably when compared to Newtonian calculations. Our venture of exploring modified gravity in white dwarfs in this thesis, is a first in the literature to the best of our knowledge. We have exploited the advantage that white dwarfs have over neutron stars, i.e., their EoS is well established. Hence, any change in the properties of white dwarfs can be solely attributed to the modification of the underlying gravity, unlike in neutron stars, where similar effects could be produced by invoking a different EoS. We have explored a popular, yet simple, model of f (R) gravity, known as the Starobinsky model (Starobinsky 1980) or R−squared model, which was originally pro-posed to explain inflation. Based on this model, we have first shown that modified gravity reproduces those results which are already explained in the paradigm of general relativity (and Newtonian framework), namely, low density white dwarfs in this context. This is a very important test of the modified gravity model and is furthermore necessary to constrain the underlying model parameter. Next, depending on the magnitude and sign of a single model parameter, we have not only obtained both highly super-Chandrasekhar and highly sub-Chandrasekhar limiting mass white dwarfs, but we have also established them as progenitors of the peculiar, over- and under-luminous SNeIa, respectively (Das & Mukhopadhyay 2015b). Thus, an effectively single underlying the-ory unifies the two apparently disjoint sub-classes of SNeIa, which have so far hugely puzzled astronomers. To summarize, in the first part of the thesis, we have established the enormous significance of magnetic fields in white dwarfs in revealing the existence of significantly super-Chandrasekhar white dwarfs. These super-Chandrasekhar white dwarfs could be ideal progenitors of the peculiar, over-luminous SNeIa, which can, hence, be used as new standard candles of cosmic distance measurements. In the latter part of the thesis, we have established the importance of a modified theory of Einstein’s gravity in revealing both highly super- and highly sub-Chandrasekhar limiting mass white dwarfs. We have furthermore demonstrated how such a theory can serve as a missing link between the peculiar, super- and sub-Chandrasekhar SNeIa. Thus, the significance of the current thesis lies in the fact that it not only questions the uniqueness of the Chandrasekhar mass-limit for white dwarfs, but it also argues for the need of a modified theory of Einstein’s gravity to explain astrophysical observations.