In this Thesis, I explore the formation and evolution of stellar spiral structures embedded in realistic dark matter haloes with very high resolution simulations. I first study the impact of the shape of the dark matter haloes. I find that non-adiabatic changes to the dark matter halo shape, commonly found in cosmological simulations due to the assembly history of haloes, can trigger strong two-armed grand-design spiral structures extending from the inner disc to the outer region. The nature of the spiral structures is found to be consistent with kinematic density waves based on the study of their power spectra. Such grand-design spiral structures may help the formation of transient multi-armed spiral structures if the self-gravity in disc is strong enough. Evolution of spiral structures is similar when the disc and the halo are misaligned, although warps develop additionally. I further find a strong correlation between the torque strength from the halo and the strength of the corresponding spiral structures. In the second part of my Thesis I then study the influence of subhaloes by including them from realistic cosmological simulations. I identify five different massive subhaloes that hit the central region of the disc, two out of which hit the disc twice. Aside from disc heating, three distinct generations of spiral structures are found in the stellar disc, which can be related to different subhaloes. For each generation, counter-rotating single-armed spiral structures develop first. They wind up very quickly before two-armed spiral structures become prominent. These spiral structures are again identified as kinematic density waves. We find that rather than interacting with the disc through resonances, subhaloes preferentially trigger spiral structures impulsively, due to their relatively short impact time with the disc. The strength of spiral structures can be related to the integrated strength of the torque generated by subhaloes. The correlation between the torque strength exerted by a triaxial dark matter halo and by subhaloes and the spiral strength may provide constraints on the distribution of dark matter.

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This research uses a Bayesian approach to study the biases that may occur when kinematic data is used to estimate the mass of a galaxy. Data is simulated from the Hernquist (1990) distribution functions (DFs) for velocity dispersions of the isotropic, constant anisotropic, and anisotropic Osipkov (1979) and Merritt (1985) type, and then analysed using the isotropic Hernquist model. Biases are explored when i) the model and data come from the same DF, ii) the model and data come from the same DF but tangential velocities are unknown, iii) the model and data come from different DFs, and iv) the model and data come from different DFs and the tangential velocities are unknown. Mock observations are also created from the Gauthier (2006) simulations and analysed with the isotropic Hernquist model. No bias was found in situation (i), a slight positive bias was found in (ii), a negative bias was found in (iii), and a large positive bias was found in (iv). The mass estimate of the Gauthier system when tangential velocities were unknown was nearly correct, but the mass profile was not described well by the isotropic Hernquist model. When the Gauthier data was analysed with the tangential velocities, the mass of the system was overestimated. The code created for the research runs three parallel Markov Chains for each data set, uses the Gelman-Rubin statistic to assess convergence, and combines the converged chains into a single sample of the posterior distribution for each data set. The code also includes two ways to deal with nuisance parameters. One is to marginalize over the nuisance parameter at every step in the chain, and the other is to sample the nuisance parameters using a hybrid-Gibbs sampler. When tangential velocities, v(t), are unobserved in the analyses above, they are sampled as nuisance parameters in the Markov Chain. The v(t) estimates from the Markov chains did a poor job of estimating the true tangential velocities. However, the posterior samples of v(t) proved to be useful, as the estimates of the tangential velocities helped explain the biases discovered in situations (i)-(iv) above. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-03-26 17:23:14.643

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The 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.

The 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.