1,721,029 research outputs found
Circumstellar Interaction Of Young Supernovae : With inputs From Radio And X-ray Wavebands
Get PDFThis thesis deals with the radiative emission arising out of the interaction of several core collapse supernovae (SNe) with their dense circumstellar medium (CSM) and uses the radiative properties as diagnostics of the ionized plasma in and around the interaction region. These supernovae include: SN 1993J, SN 1995N, SN 2002ap & SN 2003bg. In a SN explosion, the outer layers of the star are set in motion with high velocities and the collision of the ejecta with the CSM leads to a less dense and hot blast wave forward shock with velocities ~ 20,000 km/s and T ~ 109K. When the external layers of the expanding ejecta decelerate upon interaction with the CSM, a reverse shock develops that starts propagating into the stellar envelope, with velocity few times 1000 km/s relative to the expanding stellar ejecta, heating it to T ~ 107K. Forward shock velocities are typically 1000 times the speed of the wind that was being lost from the progenitor prior to the SN explosion. Consequently, evolution of the shock and the radiative properties of the SN few years after the explosion probes the history of the environment of the progenitor star thousands of years before the explosion. Interaction of the shocked ejecta with the CSM gives rise to emission in radio and X-ray bands. The emission in various wavebands arising due to this interaction usually has a slower decay rate than the initial photospheric emission arising from ionic recombination and radioactive decay. Hence, one is usually able to track the supernovae for longer time.
Radio emission is generated from the forward shocked shell due to the synchrotron emission by relativistic electrons in the presence of the strong magnetic fields. The strong magnetic field in the shocked shell is believed to be generated by Rayleigh Taylor instability, which enhances any seed magnetic field present initially. Relativistic electrons are produced, most likely, by shock mediated acceleration processes. The early rapid rise in the radio flux density results from the shock overtaking progressively further into the progenitor’s stellar wind and therefore in the regions of decreasing optical depth. Since optical depth is larger at lower frequencies lower frequencies turn on later in time. The emission from the shocked region decreases slowly with time as the shock expands, so even when the radio absorption has become negligible, the radio light curve would show this decline. Radio emission is absorbed initially by different mechanisms depending upon the mass loss rate in the progenitor wind, shock velocity, electron temperature etc. If the emission is absorbed by an electron moving in the field of an ion (free-free absorption), then one can infer the mass loss of the progenitor. If on the other hand, the radio emission is absorbed by synchrotron self absorption in which the photon interacts with an electron in a magnetic field, then it gives information about the size of the emitting region.
In contrast, X-ray emission initially comes from the forward shock and is non-thermal in nature. The X-rays could be either due to synchrotron emission or due to inverse Compton scattering in which the photospheric optical photons can be boosted to X-ray energies due to multiple scattering with the electrons. Late time X-rays, which are thermal in nature, arise from the reverse shock and probe the CSM interaction of the SN ejecta and provide information of the plasma and surroundings. However, in an alternate model due to Chugai (1993, Astron. Rep., 41, 672), X-rays can also emerge from the radiative cooling of the shocked, dense clumps (clouds) embedded in the circumstellar wind overtaken by the blast-wave shock and crushed by the pressure of the strongly shocked wind. Line-widths, elemental yields and luminosity curves are the observational signatures to distinguish between the two models. X-ray spectra of SNe can be used to determine what elements are there in the shock heated ejecta, the supernova’s nucleosynthetic yield and thence the (helium) core mass of the progenitor at the explosion stage. Nucleosynthetic studies of SNe and constraints on their progenitor masses are of vital interest to the origin and distribution of elements in the galaxy and its chemical evolution.
Chapter 1 gives a general overview of supernova types, explosion scenarios and essentials of shock dynamics in the CSM. Chapter 2 gives an overview of the radiative processes relevant to radio and X-ray emission. I describe the radio and X-ray data analysis procedures in Chapter 3.
I discuss synchrotron aging in young supernovae in Chapter 4. Synchrotron aging has been seen in many old sources, such as radio galaxies, Compact Steep Spectrum sources etc., where the age of the source is not known. Synchrotron aging was used to determine the age of such sources using magnetic field under equipartition (between magnetic energy density and relativistic energy density) as an input parameter. However in young supernovae (whose ages are known), the magnetic fields are generated due to the instabilities (Rayleigh Taylor) created in the plasma and hence it is difficult to estimate the field correctly. Here synchrotron aging can be used to derive the magnetic field independent of any assumption of equipartition. I discuss the synchrotron aging in detail and derive a significant conclusion about the plasma energetics from the combined GMRT and Very Large Array (VLA) spectrum of a 10 year old type IIb SN 1993J around day 3200 after explosion. I found a steepening of its spectrum caused by synchrotron aging. After taking into account the adiabatic losses and Fermi acceleration of electrons, I estimate from the synchrotron break, the magnetic field in the plasma and derive that the magnetic energy density is 10,000 times larger than the relativistic energy density. In Chapter 4, I also underscore the importance of wide band radio spectrum in dealing with issues of the physics of shocked plasma.
In Chapter 5, I describe further studies of SN 1993J with the GMRT at frequencies 1420, 610, 325 and 235 MHz, from 7.5 years to 10 years since explosion. SN 1993J is a unique supernova for which magnetic field and sizes are determined from model independent measurements; the former from the synchrotron cooling break and the latter from VLBI measurements. Using GMRT spectra and earlier published spectra of SN 1993J, I compare the VLBI sizes of the SN 1993J with that of obtained from the peak of the spectra using synchrotron self absorption (SSA) model. I find that the SSA sizes are roughly equal to the VLBI sizes of the SN. This suggests that the synchrotron self absorption is responsible for the turn over in the spectra of SN 1993J at all the epochs. The size evolution shows that the ejecta expands freely initially and then show a small deceleration in the later epochs. I also plot the magnetic field evolution, which goes as Spectral index initially lies between 0.8 - 1.0 and later seems to flatten with time and lies within the range of 0.5 - 0.7. The mass loss rate roughly remains constant ( ~ 5 x 10−5M yr−1) in two years of GMRT observations, i.e., 8000-10,000 years before explosion. Light curves based on high frequency existing models extrapolated to low frequencies overpredict the flux densities at low frequencies. Some extra opacity is needed to incorporate the difference. This suggests that the low frequency opacity in SN 1993J is not a simple extrapolation of high frequency opacity and a hitherto unaccounted for absorption may be at work at low frequencies.
I describe the Chandra X-ray observatory work on SN 1995N, which we observed on March 28, 2004, in Chapter 6. I detected the X-ray emission from the SN with most of the emission found to be below 2 keV. SN 1995N had also been observed by ROSAT and ASCA earlier on three occasions. Our reanalysis of ASCA 1998 spectra revealed certain line features which were not reported in the published work of Fox et al. (2000, MNRAS, 319, 1154). I detect a Ne X line in both ASCA and Chandra observations, and while I detect a Ne IX line in the Chandra observation this was absent in the ASCA one. At the same time I detect a 1.3 keV line in the ASCA observation, absent in the Chandra spectrum of SN 1995N. No Fe line was detected in either spectrum. The light curves of SN 1995N suggested a non-linear profile due to high ASCA flux. We re-analyzed the ASCA data in view of the high-resolution imaging data obtained by Chandra and found at least ten more sources contributing to the SN flux due to the large ASCA PSF. After taking out the contribution from the contaminating sources, the light curve appears to be consistent with a linear decline. This indicates that the X-ray emission is due to the reverse shock going through a shallow ejecta profile. I also find that the absorption column density is at least 2.5 times more than that calculated from the galactic extinction maps. This suggests that the moderate, extra absorption is likely to be due to the formation of a thin cool ejecta-shell between reverse-shock and the contact discontinuity. About 0.01 M of Ne is estimated to be present in SN 1995N from the Chandra line detection. This, most likely, arises in the partially burnt He core at velocities > 5000 km s−1 . I also observed SN 1995N with the GMRT in radio bands. I describe these results in Chapter 7. The spectrum is seen to be peaking towards lower frequencies with the time. The radio light curve suggests that the SN is already in the optically thin part of the light curve.
Some but not all type Ic supernovae have shown association with Gamma Ray Burst (GRB) sources. This seems to divide the type Ic SNe in two subclasses -the ones associated with GRBs and the ones without the GRB connection. The observations of these two classes of type Ic SNe and their comparison (the ”afterglows”) are likely to be useful in determining the physical conditions inside the progenitor star which leads some of the type Ic supernovae to have GRB associations. Since these SNe are bare core SNe with no hydrogen and little or no helium envelope, their prompt emission in the radio and high energy bands provide the most promising probes of their interior at early times. In Chapter 8, I investigate the origin of prompt X-ray emission in a type Ic supernova SN 2002ap, a non-GRB supernova. An analysis of SN 2002ap, observed with XMM-Newton on Feb 3, 2002 as a Target Of Opportunity is presented and spectral model fits to the prompt X-ray emission are obtained. I model the early X-ray emission with inputs from optical photometry and light curve and find that multiple inverse Compton scattering of optical photons from the supernova photosphere by electrons in the medium can account for the observed early X-ray flux and its spectrum for modest electron temperatures and optical depths. I compare the X-ray image with the GMRT 610 MHz radio image obtained three days apart. While I find no radio counterpart of the SN at such low frequencies, several sources in the field have radio and X-ray counterparts. I compare the radio data obtained from three different supernovae in their early phases and model these using the synchrotron self absorption model. GRB associated SN 1998bw was found to be most rapidly expanding with fastest transition from optically thick to optically thin part in the spectrum.
Radio studies of SN 2003bg, another type Ic supernova is discussed in Chapter 9. I observed SN 2003bg with the GMRT from day 43 till day 600 since explosion. On one occasion (day ~ 350), I combined the GMRT data with the VLA data to get a composite spectrum. From the optically thick part of the spectrum, I find that the dominant absorption mechanism in the SN is synchrotron self absorption. I deduced magnetic field and size of the supernova under the assumption of equipartition.
I discuss the overall results in Chapter 10. In this thesis, I have investigated four supernovae in detail and few more have been observed with lesser sampling frequency (see Chapter 10 and P. Chandra et al 2002, BASI 30, 755). Although they all belong to the ejecta dominated free expansion phase, the core-collapse supernovae are of widely different subclasses and I have observed them at very young ages (few days) to more than 10 years of age, with multiple probes, going through a variety of emission mechanisms and absorption processes. I provide comparison between different supernovae observed by us and others. In cases, where I am able to obtain X-ray spectra, nucleosynthesis arguments lead me to constrain the mass of the progenitor star and the composition of its layers
Prolate Shaped Dark Matter Halo And The Galactic Warp
Get PDFThe physical explanation for the existence of the galactic warp is one of the major research areas in Astronomy. People have proposed various theories but nobody has yet given a convincing explanation. Most of the spiral galaxies are observed to be warped which reveals that the galactic warp is a stable characteristic. In the theory of kinematic bending wave, warp is considered as a wave that is propagated through the galactic disk with a speed called pattern speed.
If the pattern initially had straight line of nodes, according to bending wave theory, the warp would tend to wind up rapidly in the gravitational field of galactic disk. But still we observe warped galaxies in the sky. In the literature, it has been claimed that the winding problem of galactic warp may be solved by incorporating the effect of gravitational field of the dark matter halo in which the galactic disk is embedded. Recently some works on the dynamics of galactic disk claim that the shape of the dark matter halo is pro late spheroid. In this thesis, the effect of the gravitational field of a prolate spheroidal dark matter halo with varying eccentricity to the galactic warp is calculated and discussed.
Chapter1 gives the general introduction of the topics discussed in the following chapters. The structure of the spiral galaxy, their classifications, and the disk dynamics are discussed in the first few sections. One of the revolutionary concepts that emerged in the previous century was the existence of the dark matter. Presently tracing the mass distribution and the constituent particles of dark matter is one of the major research areas in theoretical and experimental physics. In this thesis, the effect of a particular type of mass distribution in dark matter halo on the warp is discussed in detail.
In the next few sections, the following topics are discussed namely; how the concept of dark matter came into astrophysics, how to measure the total mass inside a given radius and what are the different distributions used for various purposes. A new theory called Modified Newtonian Mechanism was also proposed in the previous century as an alternative to the dark matter concept which is also discussed briefly. Kinematic bending wave theory and the winding problem of the galactic warp is also discussed in detail. In the last section a relation between the pattern speed of the warp and the shape of the dark matter halo is obtained.
The calculation of the potential of a prolate spheroidal mass distribution with varying eccentricity is not done in any literature as we know. The calculation of the potential and the patten speed of prolate spheroidal mass distributions and of the galactic disk are described in chapter 2. The calculations of oblate spheroidal mass distribution are also discussed in this chapter but that is out of main theme.
In chapter 3 we apply the equations obtained in the Chapter 2 to one simple toy model and to the Galaxy. The rotation curve and the pattern speed of a warp in the gravitational field of prolate spheroidal mass distribution of varying eccentricity are described. Usually the Milky Way disk is treated as an in infinitesimally thin disk but for our calculations the three dimensional but thin disk is used. The usually people use some approximation to calculate the potential due to galactic infinitesimal thin disk. The difference of the work from earlier works done by different people(with the approximation mentioned in above line) is also discussed in this Chapter. Chapter 4 discusses the summary of the entire work
Studies of X-Ray Transients and a Future X-Ray Sky Monitor
No full textFor this thesis we studied X-ray transients. In addition we also studied some methods to study these transients, both observationally and in terms of the instrument used.
The first transient studied is a black hole binary system IGR J17091-3624 which showed variabilities in its lightcurves similar to GRS 1915+105, another black hole transient. This thesis used the pre-variability phase data from IGR J17091-3624 to model its mass and draw possible comparisons between its mass and GRS 1915+105. A conjecture on the possible reason for the variabilities was put forth. This opens up
future avenues of works for locating other black hole sources with such variability features. As shown in this work, such variabilities need not be restricted to super Eddington accreting black hole sources and hints of such variabilities have already been seen in GX 339-4. Complete modelling of the different spectral states of GRS 1915+105 and GX339-4 for making further comparisons with IGR J17091-3624 is another work
which can carry this research forward.
The second transient studied is a neutron star binary system 4U 0115-634 which showed cyclotron line features called CRSFs in its energy spectrum. With higher signal to noise and wider energy range data than used previously to model the spectrum, the work done in this thesis indicates a possible presence of two line forming regions in this binary neutron star. This immediately provides opportunities for further work
of verifying this possibility using wide energy high SNR data as available from ASTROSAT and NuSTAR. A second method of probing the line forming regions using polarized spectrum needs to be worked out further in detail using theoretical models and simulations of the observed polarized spectrum. Although such observations may not happen in the next few years time, building such models is an immediate
requirement which can then be verified by these observations, when available.
The last bit of work in this thesis consists of studying a currently operational sky monitor and a semiconductor detector back-end to propose a realisable sky monitor. This sky monitor shall not only be able to monitor long term variations in multiple exciting transients as the two sources mentioned previously, but also be able to stare at one such transient for deeper studies of a single transient source. Optimization between these two use cases of a sky monitor is presented using a possible solution of multiple sky monitor units. The work which this design raises is development, testing and eventual realization of such a monitor network. The challenges in building and testing individual pixels for such a monitor are listed in this thesis.
Thus, in this thesis we have gone from studying two individual X-ray transients systems for understanding the accretion physics in each of them to characterising a current Sky monitor to designing and partially prototyping a future Sky monitor for studying such transients. On the way,the need for monitoring the transient X-ray sky and the utility of having multiple semiconductor based monitor-cum-pointed observing instruments for studying these fascinating transients was highlighted. We also studied the possibility of using a Si PIN based detector for making such instruments. It is hoped that the work done in this thesis is of some practical use to people interested in studying the fascinating world of X-ray transients. It is also hoped that this work shall be extended to get realisable Sky monitors as envisaged in this thesis
Vertical Structure Of Disk Galaxies And Their Dark Matter Halos
Get PDFThe topic of this thesis is the study of the vertical structure of the disk galaxies and their dark matter halos through theoretical modeling and numerical calculations. The basic theoretical model of the galactic disk used involves gravitationally-coupled stars and gas under the force-field of a dark matter halo; the disk is rotationally-supported in the plane and pressure-supported perpendicular to the plane of the galaxy. The first part of the thesis involves evaluating the vertical structure of stars and gas in normal as well as dwarf spiral galaxies. The second part of the thesis deals with probing the dark matter halo density profiles of disk galaxies using both the observed rotation curve and the H i scale height data. Following is the layout of the thesis.
Chapter 1 gives a general introduction to the topic of vertical structure of spiral galaxies and their dark matter halos, followed by a broad overview of the theoretical development of the topic and ends with highlighting the motivation and challenges met in this thesis. Chapters 2 & 3 deal with the vertical structure of stars and gas in galaxies, Chapters 4-6 focus on obtaining the dark matter halo density profiles of disk galaxies from the observed rotation curve and the H i scale height data whereas Chapter 7 is devoted to the summary of results and future research plans.
Vertical structure of stars and gas in galaxies
The vertical thickness of the stars and the gas, namely atomic hydrogen (H i) and molecular hydrogen (H2) in a spiral galaxy, is crucial in regulating the disk dynamics close to the mid-plane, especially in the inner galaxy. However, measuring it observationally is not in general practicable due to the limitations of astronomical observations, and often impossible as in the case of face-on galaxies. Therefore, it is imperative to develop a theoretical model of the galaxy which can predict the thickness of the disk components by using as input parameters the physical quantities, which are more observationally-amenable compared to the disk thickness. The vertical thickness of the disk components is determined by a trade-off between the upward kinetic pressure and the net downward gravitational pull of the galaxy. The fraction of the disk mass due to the stars is an order of magnitude higher than that of the gas in ordinary spiral galaxies, and therefore the gas contribution to the disk gravity is ignored in general. We have developed a multi-component model of gravitationally-coupled stars, HI and H2 subjected to the force-field of an external dark matter halo, and conclusively demonstrated the importance of the inclusion of gas gravity in explaining the steep vertical stellar distribution observed in galaxies. These apart, this model does not implicitly assume a flat rotation curve for the galaxy and therefore is applicable in general to obtain the thickness of stars and gas in dwarfs (with linearly rising rotation curves) as well as in ordinary spirals.
In Chapter 2, we investigate the origin of the steep vertical stellar distribution in the Galactic disk. One of the direct fall outs of our above model of the galaxy, which incor¬porates the self-gravity of the gas unlike the earlier theoretical models, lies in explaining the long-standing puzzle of the steep vertical stellar density distribution of the disk galax¬ies near the mid-plane. Over the past two decades, observations revealed that the vertical density distribution of stars in galaxies near the mid-plane is substantially steeper than the sech2 function that is expected for a self-gravitating system of stars under isothermal ap¬proximation. However, the physical origin for this has not been explained so far. We have clearly demonstrated that the inclusion of the self-gravity of the gas in the dynamical model of the Galaxy solves the problem even under the purview of isothermal approximation for the disk components. Being a low dispersion component, the gas resides closer to the mid¬plane compared to the stars, and forms a thin, compact layer near the mid-plane, thereby strongly governing the local disk dynamics. This novel idea, highlighting the significance of gas gravity has produced substantial impact on the field and triggered research activities by other groups in related areas of disk dynamics. The strong effect of the gas gravity on the vertical density profile of the stellar disk indicates that it should also bear its imprint on the Milky way thick disk, as the epoch of its formation 109 years ago is marked by a value of gas fraction, almost an order of magnitude higher than its present day value. Interest-ingly, the findings of the upcoming Gaia mission can be harnessed to verify this theoretical prediction. It may also hold the clue as to the reason behind the absence of thick disk in superthin galaxies.
In Chapter 3, we use the same model to theoretically determine the H i vertical scale heights in the dwarf galaxies: DDO 154, Ho II, IC 2574 & NGC 2366 for which most of the necessary input parameters are available from observations. We stress the fact that the observational determination of the gas thickness in these dwarf irregulars is not viable. Nevertheless, it is important to estimate it theoretically as it plays a crucial role in calculating the star-formation activities and other related phenomena. However, two vital aspects have to be taken care of while modeling these dwarf galaxies. Firstly, the mass fraction in gas in these galaxies is comparable to that of the stars, and hence the gas gravity cannot be ignored on any account unlike in the case of large spirals. Secondly, dwarf galaxies have a rising rotation curve over most of the disk unlike the flat rotation curves of ordinary spirals. Both these factors have been considered in developing our model of the dwarf galaxies. We find that three out of the four galaxies studied show a flaring of their H i disks with increasing radius, by a factor of a few within several disk scale lengths. The fourth galaxy (Ho II) has a thick H1 disk throughout. A comparison of the size distribution of H1 holes in the four sample galaxies reveals that of the 20 type 3 holes, all have radii that are in agreement with them being still fully contained within the gas layer.
Probing the dark matter halo profiles of disk galaxies
The next part of the thesis involves the dynamical study of the shapes and density profiles of galactic dark matter halos using observational constraints on our theoretical model of a spiral galaxy. The density distribution of the dark matter halo is generally modeled using the observed rotation curve of the spiral galaxies. The rotational velocity at any radius is determined by the radial component of the net gravitational force of the galaxy, which, however, is weakly dependent on the shape of the dark matter halo. Therefore, one cannot trace the dark matter halo shape by the observed rotation curve alone. The vertical thickness of the stars and gas, on the other hand, is strongly dependent on the flattening of the dark matter halo, and therefore the observed gas thickness can be used as a diagnostic to probe the halo shape. In this thesis, we have used the double constraints of the rotation curve and the H i thickness data to obtain the best-fit values of the core density, core radius and the vertical-to-planar axis ratio (or flattening) of the dark matter halos of our largest nearby galaxy Andromeda (or M31), a low-surface brightness (LSB) superthin galaxy UGC 7321 and to study the dark matter halo shape of our Galaxy.
In Chapter 4, we study the dark matter halo of M31 or Andromeda, the largest nearby galaxy to the Milky Way. We find that M31 has a highly flattened isothermal dark matter halo with the vertical-to-horizontal axis ratio equal to 0.4, which interestingly lies at the most oblate end of the halo shapes found in cosmological simulations. This indicates that either M31 is a unusual galaxy, or the simulations need to include additional physics, such as the effect of the baryons, that can affect the shape of the halo. This is quite a remarkable result as it challenges the popular practice of assuming a spherical dark matter halo in the dynamical modeling of the galaxy
In Chapter 5, we have applied this technique to the superthin galaxy UGC 7321. Su¬perthins are somewhat the “extreme” objects in the local Universe because of their high gas fraction and absence of a thick disk component. It is interesting to analyze their so-called extreme characteristics in the light of the physical mechanisms which determined them to understand better the properties of ordinary spirals. We find that UGC 7321 has a spher¬ical isothermal halo, with a core radius almost equal to the disk scale length. This reveals that the dark matter dominates the dynamics of this galaxy at all radii, including the inner parts of the galaxy. This is unlike the case for the large spiral galaxies, where the core radius is typically about 3-4 disk scale lengths. Interestingly, the best-fit halo core density and the core radius are consistent, with deviations of a few percent, with the dark matter fundamental plane correlations, which depict the systematic properties of the dark matter halo in late-type and dwarf spheroidal galaxies. This apart, a high value of the gas velocity dispersion is required to get a better fit to the H i scale height data, although the superthin nature of the stellar disk implies a dynamically cold dynamic galactic disk. However, it explains the low star-formation rates in these galaxies since the Toomre Q criterion (Q < 1) for instability is less likely to be satisfied, and hence the disk is liable to be more stable to star formation.
In Chapter 6, we investigate the shape of the dark matter halo in the outer Galaxy. We find that the halo is prolate, with the vertical-to-planar axis ratio monotonically increasing to 2.0 at 24 kpc, or 8 radial disk scale lengths. The resulting prolate-shaped halo can explain several long-standing puzzles in galactic dynamics, for example, it permits long-lived warps thus explaining their ubiquitous nature. It also imposes novel constraints on the galaxy formation models.
Finally, in Chapter 7, the thesis is concluded with a summary of the main results and a brief discussion of the scope for future work
Understanding the vertical structure of galactic stellar disc and the role of interstellar gas and dark matter halo
No full textThe aim of this thesis is to understand the dynamical effect of interstellar gas and dark matter halo on the vertical distribution of stars in our Galaxy as well as modeling the stellar distribution in a generalized and realistic set-up, consistent with recent observed data. To do this we have modeled the Galaxy as a gravitationally coupled multi-component system of stars, interstellar gas in the potential of dark matter halo. The self-consistent solution of the joint hydrostatic balance-Poisson equation for this system gives us the vertical distribution of stars as well as gas.
We have shown that the gravitational force from gas and dark matter halo constrain the vertical distribution of stars in the inner and the outer Galaxy, respectively, compared to the self-gravitating stars-alone case. It raises the mid-plane density and reduces the scale height of the stellar disc. The outer disc is found to show a flared scale height, in consistence with recent observed data. We have predicted a flared stellar disc in a low surface brightness galaxy UGC 7321 using the above theoretical model. We have also shown that, interestingly, despite the constraining effect of gas on stars, the gravitational potential energy per unit area of the stellar disc remains unchanged in the gravitationally coupled stars plus gas system. Nevertheless, stars are more strongly bound to the mid-plane of the Galaxy due to the
above constraining effect. When the vertical distribution of stars is modeled in a generalized fashion by taking account of the effect of various detailed kinematical features, such as tilt of the velocity ellipsoid, planar random motion, varying rotation curve etc., consistent with recent data, the distribution is found to be affected in the outer Galaxy, as high as 40%. Also, on exploring the effect of an increasing, i.e, a non-isothermal vertical velocity dispersion of stars, we found the total dynamical mid-plane density to be reduced by 16%, in the solar neighborhood. This can affect the determination of the local dark matter density
Multiband Modelling and Radio Observations of Gamma Ray Burst Afterglows
No full textThe widely popular and successful standard fireball model for Gamma Ray Burst (GRB) afterglows is based on ultra-relativistic external shocks sweeping up matter around the explosion site to accelerate electrons up to GOV energies and boost the magnetic field to values close a few Gauss in its downstream. According to the model, the afterglow radiation is the synchrotron emission from these electrons gyrating around the enhanced magnetic field. A contribution from inverse Compton scattering may also appear in the total flux at higher frequencies.
The synchrotron spectrum is characterized by 'breaks' which arise due to various physical processes. The spectral slope changes due to the synchrotron self-absorption below a frequency Va. The synchrotron peak frequency (I'm) corresponds to the emission by electrons at the lower limit of the power law distribution of energies and the cooling break 14 corresponds to the electron energy above which synchrotron radiation loss becomes very significant. Apart from these, the light curves exhibit achromatic slope changes due to dynamical processes within the fireball. The ejected matter is collimated and initially undergoes a radial expansion. Later, the lateral expansion of the jet takes over and this is reflected as an achromatic break (jet break) in the light curve. The next achromatic change of slope marks the transition of the fireball into the non-relativistic regime.
The spectrum of afterglow radiation itself evolves with time, reflecting the expansion of the fireball, hence a data set well sampled in both spectral and in temporal domain is essential for useful study.
Multiband modelling of GRB afterglow (AG) light curves is at present the best available tool to understand the true nature of the explosion and its surroundings. Apart from that, detailed modelling also holds the key to the secrets of particle acceleration processes in collision less shocks.
By modelling the well-sampled data set of an afterglow, the energy content (Etot) of the jet, its angle of collimation (00), the density profile of the ambient medium (n(r) where r is the distance from the site of the explosion) and some relevant parameters of shock microphysics (p, the power law index of the distribution of electrons which are radiating via synchrotron mechanism, G, the fraction of energy in those electrons and that in downstream magnetic field) can be obtained.
Afterglow data of the nearby (z 0.16, one of the nearest GRBs) GRB 030329 was unprecedentedly rich in both optical and radio bands (but unfortunately poor in x-rays) which enabled detailed and well constrained modelling attempts. The rigorous monitoring campaign revealed an unexpected behavior of the radio flux, for which one explanation was that that the early optical emission and the late radio emission arose in two different jets. However, our detailed modelling using the rich data set allowed us to propose a new mechanism in which the initial outflux of energy is 'refreshed' by a later episode of injection.
The standard fireball model uses certain simplistic assumptions owing to our lack of knowledge of the shock acceleration process. One common assumption is that of a universal spectrum of the accelerated electrons, a steep non thermal energy distribution with power law of index 2.2. It owes its origin to theoretical simulations of shock acceleration which often produce a steep (p > 2) spectrum. This also fits many observed cases of such energy distributions. Further, this assumption leads to a simplification in theoretical models, since the upper cut off energy of the distribution plays virtually no role.
The presence of harder, p < 2 spectrum, in a minority of cases, has hence not received a fair share of attention. Calculations to derive the physical parameters of the burst in such cases are often not done consistently. Early attempts to model GRB afterglows with hard electron energy spectrum had several loopholes. In this thesis, we have done these calculations consistently and applied them to a few afterglows with good temporal and spectral coverage.
Apart from multiband modelling, this thesis also presents late time observations of the GRB030329 afterglow in low frequency radio bands. Radio observations have always been special since they allow the estimation of the self-absorption frequency, thus giving a direct clue to the size of the fireball. Afterglows are long lived in low radio frequencies (< 1 GHz) while they quickly decay below visibility in all other bands, even at high radio frequencies (say 15 GHz). Hence monitoring at low radio frequencies is the only way to study the late time evolution including the transition from relativistic to non-relativistic dynamics.
GRB030329 had one such rare bright radio afterglow and we followed it up in low frequencies (1280 MHz and 610 MHz) using the Giant Meter wave Radio Telescope (GMRT). The follow up campaign is continuing thanks to the slow evolution in low radio frequencies. This afterglow has hence become the longest (N 1000 days) observed, beating the earlier record of 500-day long observations of Radio afterglow of GRB970508. It also is the only one which is seen in frequencies below 1 GHz.
This thesis is organized in the following manner:
Chapter 1 gives a general introduction to GR13s and their afterglows. After describing the properties of the burst and the afterglow, we proceed to explain the standard fireball model in detail. The dynamics of the external shock and the profile of the bulk Lorentz factor (I") vs. r is described. We explain the jet break (tj) and non-relativistic transition (tnr), two major developments in the life of the fireball. We then give a detailed description of the synchrotron radiation mechanism, which is the source of afterglow radiation. The spectral breaks (va, I'm and 14) and their time evolution is explained. We conclude this chapter by listing a few unanswered questions relevant to this thesis.
In Chapter 2, we present the theoretical modifications required for the standard model to accommodate electron energy spectra with power-law indices less than 2. The energy spectrum requires a new parameter 7i, which is the Lorentz factor corresponding to the upper cut-off of the hard energy distribution. Above 'i, the distribution either terminates or steepens (double slope electron distribution) to a value of p larger than 2. The functional form of this cut-off is decided by the particle acceleration processes, which are at present poorly understood. We therefore parameterized the temporal evolution of in terms of the bulk Lorentz factor of the shock. We discuss two possible origins for the cut off. As a result of this cut-off in the energy spectrum, a new break Vi is introduced in the radiation spectrum, which is the synchrotron frequency corresponding to 7i. Apart from that, the expressions for l.'m and va differ from the standard scenario. We have calculated the shock dynamics using the method adopted by Huang et. al. 2000, which allows a smooth transition from ultra-relativistic to nonrelativistic regime of the fireball. Using this profile of I' vs. observed time, we calculated the synchrotron spectral evolution from a double slope electron energy distribution semi-analytically. The self-Compton emission also is calculated. For ultra-relativistic and non-relativistic regimes, analytical solutions are presented for both ISM n(r) r0] and stellar wind driven [n(r) ambient medium density profiles.
The way one identifies potential candidates which could have an underlying hard electron energy spectrum, is by looking at the light curve decay index past the jet break. The choice is confirmed by the optical and x-ray spectral indices. According to the standard model, the flux in higher frequencies, past jet break, decay as a power-law of index p; the spectrum below 14 should have a slope of (p — 1)/2 and above it should fall as pp. The value of p one thus obtains from all these methods is expected to be consistent. In chapter 3, we chose three such afterglows (GRB010222, GRB020813 and GRB041006), which show shallow decay of fluxes in the optical as well as in x-ray bands and relatively flat spectra. Out of a dozen such afterglows, these three have well sampled multi-band light curves. We fitted the data set with the model and estimated the physical parameters. For we have estimated the contribution of the associated supernova by subtracting the afterglow model from the total emission. We found the contribution from Compton emission to be negligible in all these cases. Interestingly, all these afterglows had relatively low cooling frequency, which could perhaps be due to some unknown relation to the acceleration mechanism itself.
Chapter 4 and 5 are devoted to GRB030329, one of the best monitored afterglows till date. The 4th Chapter focuses on the radio observations of the afterglow done with the GMRT at low frequencies. To begin with, we give a brief introduction to the interferometric techniques and the instrument. GMRT, an interferometric array with 30 elements, each of diameter 45 meters has an excellent sensitivity at low frequencies which allowed it to detect and monitor the afterglow for a long time. We then present observations in 1280 MHz and 610 MHz bands during the second year of the afterglow Thanks to this long coverage, we were able to pin-point the location of va and the transition of the fireball to the Newtonian regime.
Chapter 5 describes the multiband modelling of this afterglow. The evolution of the afterglow was complex. While the afterglow flux in optical as well as in x-ray exhibited a jet break around half a day, the radio flux past 0.5 days did not follow the expectations from a jet which has already entered the lateral expansion regime. Instead, it showed an achromatic steepening around 10 days. Hence, a novel suggestion of two co-aligned jets, one narrow and one wide, together giving rise to the observed flux has emerged (Berger et. al. 2003). We test the predictions of this conjecture and get a refined set of parameters, prompted primarily by the additional data from GMRT. We then proceed to suggest a different scenario in which the initial jet which gave rise to the x ray and optical flux is reenergized by the central engine during its lateral expansion that makes it once again collimated, now to a wider opening angle. This new jet enters a lateral expansion phase around 10 days, resulting in the jet break seen in radio bands. One peculiarity of this GRB was its association with a supernova (SN2003dh) which dominated the optical flux beyond a week. The refined afterglow flux calculation allowed us to subtract the afterglow contribution from the total optical flux and compare the resulting supernova contribution with the stereotype SN1998bw. While being similar in light curve, SN2003dh is fainter compared to a redshifted SN1998bw.
The contribution of this thesis lies in presenting a consistent modelling platform for 'hard' electron energy spectra as well as in the low frequency campaign of GRB030329 afterglow and the interpretation of its evolution. Chapter 6 concludes the thesis along with a few suggestions for future directions
Dynamical Imprint of Dark Matter Halo and Interstellar Gas on Spiral Structure in Disk Galaxies
No full textThe topic of this thesis deals with the spiral structure in disk galaxies with a specific aim of probing the influence of the dark matter halo and the interstellar gas on the origin and longevity of the spiral arms in late-type galaxies through theoretical modeling and numerical calculations. The basic theoretical model of the galactic disk used involves gravitationally-coupled two-component system (stars and gas) embedded in a rigid and non-responsive dark matter halo, i.e., the static potential of the dark matter is used in the calculations. However, at places, depending on the nature of the problem addressed, the disk is treated as consisting of only stellar component or only gas component followed by proper justifications for the assumptions. The disk is rotationally-supported in the plane and pressure-supported perpendicular to the plane of the disk. The first part of the thesis involves searching for the dynamical effect of dark matter halo on small-scale spiral structure in dwarf low surface brightness (LSB) galaxies and also some dwarf ir-regular galaxies which host an extended H I disk. In both cases, the rotation curves are found to be dominated by the contribution of the dark matter halo over a large radial distance, starting from the inner regions of the galaxies. The next part of the thesis deals with the investigation of the possible effect of the interstellar gas on the persistence is-sue and the pattern speeds of the spiral structure in the disk galaxies. The last part of the thesis involves in studying the dynamical effect of dark matter halo on large-scale spiral structure. Following is the layout of the thesis.
Chapter 1 gives a general introduction to the topic of spiral structure of late-type disk galaxies, followed by a broad overview of the theoretical development of the topic and the present status of the topic. Then the thesis starts with studying the small-scale spiral features and evolves to studying the large-scale spiral features seen in disk galaxies in the following way: Chapters 2 & 3 deal with the effect of dark matter halo on small-
scale spiral structure. Chapters 4 & 5 focus on the dynamical effect of the interstellar gas on the spiral structure using the local dispersion relation. Chapters 6 & 7 discuss the possible effect of dark matter halo on large-scale spiral structure in disk galaxies. Chapter 8 contains the summary of results and future plans.
Effect of dark matter halo on small-scale spiral structure
The spiral arms in the disks of galaxies are often broken into several smaller parts or patches that create a messy visual impression when viewed from a ‘face-on’ configura-tion. They are generally termed as ‘small-scale’ or flocculent spiral arms. Several stud-ies showed that the small-scale spiral arms are basically material arm, i.e., they can be thought of as ‘tubes’ filled with stars and gas. Spiral arms are known to participate in the secular evolution of the disk galaxies. Since disk galaxies are believed to reside within a halo of dark matter, therefore a detailed understanding of possible effects of dark matter halo on the spiral arms is necessary.
In Chapter 2, we investigate the effect of dark matter halo on small-scale spiral fea-tures in the disks of LSB galaxies. Modeling the mass distribution within a galaxy from the rotation curve of a typical small LSB galaxy reveals the generic fact that for most of the radii, dark matter halo dominates over the stellar disk. This trend is found to be true from the very inner regions of an LSB disk which in turn makes the LSBs a suitable laboratory for probing the effect of dark matter halo on the dynamics of disk galaxies. Following a semi-analytic approach, and using the observationally measured input pa-rameters for a typical superthin LSB galaxy, UGC 7321, we showed that the dominant dark matter halo suppresses the small-scale spiral structure in the disk of UGC 7321. Since UGC 7321 possesses features typical of a LSB galaxy, we argued that this finding will also hold true for other typical LSBs. The result is at par with the observational evi-dences for the lack of prominent, strong small-scale spiral structure in LSB galaxies.
In Chapter 3, we employed the similar techniques for probing the effect of dark matter halo on small-scale spiral structure, except this time we took five dwarf irregular galaxies with an extended H I disk as the sample for our investigation. The main im-portant difference between these dwarf irregular galaxies with the earlier LSB galaxies is that for these dwarf irregular galaxies with extended H I disk, the largest baryonic con-tribution comes from the interstellar gas (mainly H I ), and not from the stars (as seen in LSBs). The extended H I disks of these galaxies allow one measure the rotation curve, and hence modeling the dark matter halo parameters for a large radial range from the galactic center. Here also the rotation curves are found to be dominated by dark matter
halo over most of the disk, thus providing yet another ‘laboratory’ for testing the dynam-ical effect of dark matter halo on the dynamics of the disks. Using the observed input parameters for five such dwarf irregular galaxies, we showed that the dense and com-pact dark matter halo is responsible for preventing strong small-scale spiral structure in these galaxies, which is in fair agreement with the observations.
Dynamical effect of interstellar gas on longevity of spiral arms
Any late-type disk galaxy contains a finite amount of interstellar gas along with the stel-lar component. The atomic hydrogen (H I ) constitutes the bulk of the interstellar gas along with the molecular hydrogen (H2), ionized hydrogen (H I I ), and a trace amount of heavy elements like helium. The mass fraction present in the interstellar gas in disk galaxies is found to vary with the Hubble sequence, with the amount of interstellar gas increasing from Sa type to Scd type of galaxies. Due to the lower value of velocity disper-sion as compared to that of stars, gas is known to have a larger destabilizing effect in the disk. Therefore, the natural question arises about what possible role the interstellar gas could play in the origin and the persistence issue of spiral arms.
In Chapter 4, we explored how the interstellar gas could influence the longevity of the spiral arms in late-type disk galaxies by treating the spiral structure as density waves in the disk. The disk is modeled as a gravitationally coupled stars plus gas (two-component) system, where the stars are modeled as a collisionless system and the gas treated as a fluid system. Using the appropriate local dispersion relation for the above mentioned model for the disk of galaxy, we calculated the group velocity of a wavepacket of density wave and then studied the variation of the group velocity with increasing amount of interstellar gas in the system. We showed that the group velocity of a wavepacket in a Milky Way-like disk galaxy decreases steadily with the inclusion of gas, implying that the spiral pattern will survive for a longer time-scale in a more gas-rich galaxy by a factor of few.
In Chapter 5, we investigated the role of interstellar gas in obtaining a stable den-sity wave corresponding to the observed pattern speed for the spiral arms. The under-lying local dispersion relation remains same as that is in Chapter 4. Using the observa-tionally measured pattern speed and the rotation curves for three late-type disk galaxies we showed that the presence of interstellar gas in necessary in order to maintain a stable density wave corresponding to the observed values for pattern speeds. Also we proposed a method to determine a range of pattern speed values at any particular radius, corre-
sponding to which the density wave can be stable. We applied this method to the same three late-type galaxies which we used in the earlier part of this chapter. We found that, for these three galaxies, the observed pattern speed values indeed fall in the predicted range.
Imprint of dark matter halo on large-scale spiral structure
Along with the small-scale spiral arms, there also exists another type of spiral arms – the large-scale spiral structure, like what we see M 51 or in NGC 2997, which occupy almost the entire outer optical disk in the galaxy. These spiral arms are termed as ‘grand-design’ spiral structure. One of the competing theories, namely, Density wave theory proposes that the large-scale structure is basically a density wave in the disk and the pattern ex-hibits a rigid-body rotation with a definite constant pattern speed. In the earlier part this thesis (Chapters 2 & 3), it was shown that the small-scale spiral structure gets damped by the dominant dark matter halo. Therefore, a natural question arises whether dominant dark matter plays any role on these large-scale spiral structure; and if yes, to what extent it affects the large-scale spiral structure.
In Chapters 6 & 7, we investigated how the large-scale structure in disk galaxies gets affected when the disk galaxy hosts a dark matter halo that dominates over most of the disk regions. We again chose the LSB galaxies as laboratory for this study. In Chapter 6, we modeled the stellar component as a fluid system and in Chapter 7, we treated the stellar system as more realistic collisionless system. In both cases, global spiral modes are identified from the appropriate dispersion relations via a novel quantization rule, and they are used as a ‘proxy’ for the large-scale spiral structure. Using the input pa-rameters for UGC 7321, in Chapter 6 we showed that the fluid representation of stellar system failed to make an impression in suppression of the global spiral modes. However, when stellar component is treated as a more realistic collisionless system, we found that the dark matter halo suppresses the large-scale spiral features as well in the disks of LSB galaxies, in fair agreement with the observations.
Finally, in Chapter 8, the thesis concludes with a summary of main results and a brief discussion of the scope for future work
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