arXiv subjects

Monica Valluri

Publications and source records attributed to Monica Valluri.

108 records · Page 6Linked to original sources

arXiv2011

Probing the shape and history of the Milky Way halo with orbital spectral analysis

The phase space coordinates of individual halo stars obtained by Galactic surveys enable the computation of their full 3-dimensional orbits. Spectral analysis of halo orbits can be used to construct "frequency maps" which provide a compact representation of the 6-dimensional phase space distribution function. Frequency maps identify important major orbit families, and the orbital abundances reflect the shape and orientation of the dark matter halo relative to the disk. We apply spectral analysis to halo orbits in a series of controlled simulations of disk galaxies. Although the shape of the simulated halo varies with radius, frequency maps of local samples of halo orbits confined to the inner halo contain most of the information about the global shape of the halo and its major orbit families. Quiescent or adiabatic disk formation results in significant trapping of halo orbits in resonant orbit families (i.e. orbits with commensurable frequencies). If a good estimate of the Galactic potential in the inner halo (within ~50kpc) is available, the appearance of strong, stable resonances in frequency maps of halo orbits will allow us to determine the degree of resonant trapping induced by the disk potential. The locations and strengths of these resonant families are determined both by the global shape of the halo and its distribution function. Identification of such resonances in the Milky Way's stellar halo would therefore provide evidence of an extended period of adiabatic disk growth. If the Galactic potential is not known exactly, a measure of the diffusion rate of large sample of 10^4 halo orbits can help distinguish between the true potential and an incorrect potential. The orbital spectral analysis methods described in this paper provide a strong complementarity to existing methods for constraining the potential of the Milky Way halo and its stellar distribution function (ABRIDGED).

astro-ph.GA↗

arXiv2011

The Orbital Structure of Triaxial Galaxies with Figure Rotation

We survey the properties of all orbit families in the rotating frame of a family of realistic triaxial potentials with central supermassive black holes (SMBHs). In such galaxies, most regular box orbits (vital for maintaining triaxiality) are associated with resonances which occupy two-dimensional surfaces in configuration space. For slow figure rotation all orbit families are largely stable. At intermediate pattern speeds a significant fraction of the resonant box orbits as well as inner long-axis tubes are destabilized by the "envelope doubling" that arises from the Coriolis forces and are driven into the destabilizing center. Thus, for pattern rotation periods .2 Gyr < Tp < 5 Gyr, the two orbit families that are most important for maintaining triaxiality are highly chaotic. As pattern speed increases there is also a sharp decrease in the overall fraction of prograde short-axis tubes and a corresponding increase in the retrograde variety. At the highest pattern speeds (close to that of triaxial bars), box-like orbits undergo a sudden transition to a new family of stable retrograde loop-like orbits, which resemble orbits in three-dimensional bars, and circulate about the short axis. Our analysis implies that triaxial systems (with central cusps and SMBHs) can either have high pattern speeds like fast bars or low patten speeds like triaxial elliptical galaxies or dark matter halos found in N-body simulations. Intermediate pattern speeds produce a high level of stochasticity in both the box and inner long-axis tube orbit families implying that stable triaxial systems are unlikely to have such pattern speeds.

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arXiv2010

Supermassive Dark Stars: Detectable in JWST

The first phase of stellar evolution in the history of the Universe may be Dark Stars, powered by dark matter heating rather than by nuclear fusion. Weakly Interacting Massive Particles, which may be their own antipartners, collect inside the first stars and annihilate to produce a heat source that can power the stars for millions to billions of years. In this paper we show that these objects can grow to be supermassive dark stars (SMDS) with masses $\gtrsim (10^5-10^7) \msun$. The growth continues as long as dark matter heating persists, since dark stars are large and cool (surface temperature $\lesssim 5\times 10^4$K) and do not emit enough ionizing photons to prevent further accretion of baryons onto the star. The dark matter may be provided by two mechanisms: (1) gravitational attraction of dark matter particles on a variety of orbits not previously considered, and (2) capture of WIMPs due to elastic scattering. Once the dark matter fuel is exhausted, the SMDS becomes a heavy main sequence star; these stars eventually collapse to form massive black holes that may provide seeds for supermassive black holes in the Universe. SMDS are very bright, with luminosities exceeding $(10^9-10^{11}) L_\odot$. We demonstrate that for several reasonable parameters, these objects will be detectable with JWST. Such an observational discovery would confirm the existence of a new phase of stellar evolution powered by dark matter.

astro-ph.CO↗

arXiv2010

New tools for probing the phase space structure of dark matter halos

We summarize recent developments in the use of spectral methods for analyzing large numbers of orbits in N-body simulations to obtain insights into the global phase space structure of dark matter halos. The fundamental frequencies of oscillation of orbits can be used to understand the physical mechanism by which the shapes of dark matter halos evolve in response to the growth of central baryonic components. Halos change shape primarily because individual orbits change their shapes adiabatically in response to the growth of a baryonic component, with those at small radii become preferentially rounder. Chaotic scattering of orbits occurs only when the central point mass is very compact and is equally effective for centrophobic long-axis tube orbits as it is for centrophilic box orbits.

astro-ph.CO↗

arXiv2009

Evolution of the Dark Matter Phase-Space Density Distributions of LCDM Halos

We study the evolution of phase-space density during the hierarchical structure formation of LCDM halos. We compute both a spherically-averaged surrogate for phase-space density (Q) and the coarse-grained distribution function f(x,v) for dark matter particles that lie within~2 virial radii of four Milky-Way-sized dark matter halos. The estimated f(x,v) spans over four decades at any radius. Dark matter particles that end up within two virial radii of a Milky-Way-sized DM halo at $z=0$ have an approximately Gaussian distribution in log(f) at early redshifts, but the distribution becomes increasingly skewed at lower redshifts. The value corresponding to the peak of the Gaussian decreases as the evolution progresses and is well described by a power-law in (1+z). The highest values of f are found at the centers of dark matter halos and subhalos, where f can be an order of magnitude higher than in the center of the main halo. The power-law Q(r) profile likely reflects the distribution of entropy (K = sigma^2/rho^{2/3} \propto r^{1.2}), which dark matter acquires as it is accreted onto a growing halo. The estimated f(x, v), on the other hand, exhibits a more complicated behavior. Although the median coarse-grained phase-space density profile F(r) can be approximated by a power-law in the inner regions of halos and at larger radii the profile flattens significantly. This is because phase-space density averaged on small scales is sensitive to the high-f material associated with surviving subhalos, as well as relatively unmixed material (probably in streams) resulting from disrupted subhalos, which contribute a sizable fraction of matter at large radii. (ABRIDGED)

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arXiv2009

Evolution of Dark Matter Phase-Space Density Distributions in Equal-Mass Halo Mergers

We use dissipationless N-body simulations to investigate the evolution of the true coarse-grained phase-space density distribution f(x,v) in equal-mass mergers between dark matter (DM) halos. The halo models are constructed with various asymptotic power-law indices ranging from steep cusps to core-like profiles and we employ the phase-space density estimator ``Enbid'' developed by Sharma & Steinmetz to compute f(x,v). The adopted force resolution allows robust phase-space density profile estimates in the inner ~1% of the virial radii of the simulated systems. We confirm that mergers result in a decrease of the coarse-grained phase-space density in accordance with expectations from Mixing Theorems for collisionless systems. We demonstrate that binary mergers between identical DM halos produce remnants that retain excellent memories of the inner slopes and overall shapes of the phase-space density distribution of their progenitors. The robustness of the phase-space density profiles holds for a range of orbital energies, and a variety of encounter configurations including sequences of several consecutive merger events, designed to mimic hierarchical merging, and collisions occurring at different cosmological epochs. If the progenitor halos are constructed with appreciably different asymptotic power-law indices, we find that the inner slope and overall shape of the phase-space density distribution of the remnant are substantially closer to that of the initial system with the steepest central density cusp. These results explicitly demonstrate that mixing is incomplete in equal-mass mergers between DM halos, as it does not erase memory of the progenitor properties. Our results also confirm the recent analytical predictions of Dehnen (2005) regarding the preservation of merging self-gravitating central density cusps.

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arXiv2008

Signatures of LCDM substructure in tidal debris

In the past decade, surveys of the stellar component of the Galaxy have revealed a number of streams from tidally disrupted dwarf galaxies and globular clusters. Simulations of hierarchical structure formation in LCDM cosmologies predict that the dark matter halo of a galaxy like the Milky Way contains hundreds of subhalos with masses of ~10^8 solar masses and greater, and it has been suggested that the existence of coherent tidal streams is incompatible with the expected abundance of substructure. We investigate the effects of dark matter substructure on tidal streams by simulating the disruption of a self-gravitating satellite on a wide range of orbits in different host models both with and without substructure. We find that the halo shape and the specific orbital path more strongly determine the overall degree of disruption of the satellite than does the presence or absence of substructure, i.e., the changes in the large-scale properties of the tidal debris due to substructure are small compared to variations in the debris from different orbits in a smooth potential. Substructure typically leads to an increase in the degree of clumpiness of the tidal debris in sky projection, and in some cases a more compact distribution in line-of-sight velocity. Substructure also leads to differences in the location of sections of debris compared to the results of the smooth halo model, which may have important implications for the interpretation of observed tidal streams. A unique signature of the presence of substructure in the halo which may be detectable by upcoming surveys is identified. We conclude, however, that predicted levels of substructure are consistent with a detection of a coherent tidal stream from a dwarf galaxy.

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arXiv2007

The Black Hole Mass of NGC 4151: Comparison of Reverberation Mapping and Stellar Dynamical Measurements

We present a stellar dynamical estimate of the black hole (BH) mass in the Seyfert 1 galaxy, NGC 4151. We analyze ground-based spectroscopy as well as imaging data from the ground and space, and we construct 3-integral axisymmetric models in order to constrain the BH mass and mass-to-light ratio. The dynamical models depend on the assumed inclination of the kinematic symmetry axis of the stellar bulge. In the case where the bulge is assumed to be viewed edge-on, the kinematical data give only an upper limit to the mass of the BH of ~4e7 M_sun (1 sigma). If the bulge kinematic axis is assumed to have the same inclination as the symmetry axis of the large-scale galaxy disk (i.e., 23 degrees relative to the line of sight), a best-fit dynamical mass between 4-5e7 M_sun is obtained. However, because of the poor quality of the fit when the bulge is assumed to be inclined (as determined by the noisiness of the chi^2 surface and its minimum value), and because we lack spectroscopic data that clearly resolves the BH sphere of influence, we consider our measurements to be tentative estimates of the dynamical BH mass. With this preliminary result, NGC 4151 is now among the small sample of galaxies in which the BH mass has been constrained from two independent techniques, and the mass values we find for both bulge inclinations are in reasonable agreement with the recent estimate from reverberation mapping (4.57[+0.57/-0.47]e7 M_sun) published by Bentz et al.

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arXiv2006

On relaxation processes in collisionless mergers

We analyze N-body simulations of halo mergers to investigate the mechanisms responsible for driving mixing in phase-space and the evolution to dynamical equilibrium. We focus on mixing in energy and angular momentum and show that mixing occurs in step-like fashion following pericenter passages of the halos. This makes mixing during a merger unlike other well known mixing processes such as phase mixing and chaotic mixing whose rates scale with local dynamical time. We conclude that the mixing process that drives the system to equilibrium is primarily a response to energy and angular momentum redistribution that occurs due to impulsive tidal shocking and dynamical friction rather than a result of chaotic mixing in a continuously changing potential. We also analyze the merger remnants to determine the degree of mixing at various radii by monitoring changes in radius, energy and angular momentum of particles. We confirm previous findings that show that the majority of particles retain strong memory of their original kinetic energies and angular momenta but do experience changes in their potential energies owing to the tidal shocks they experience during pericenter passages. Finally, we show that a significant fraction of mass (~ 40%) in the merger remnant lies outside its formal virial radius and that this matter is ejected roughly uniformly from all radii outside the inner regions. This highlights the fact that mass, in its standard virial definition, is not additive in mergers. We discuss the implications of these results for our understanding of relaxation in collisionless dynamical systems.

astro-ph↗

arXiv2005

The Low End of the Supermassive Black Hole Mass Function: Constraining the Mass of a Nuclear Black Hole in NGC 205 via Stellar Kinematics

Hubble Space Telescope (HST) images and spectra of the nucleated dwarf elliptical galaxy NGC 205 are combined with 3-integral axisymmetric dynamical models to constrain the mass (M_BH) of a putative nuclear black hole. This is only the second attempt, after M33, to use resolved stellar kinematics to search for a nuclear black hole with mass below 10^6 solar masses. We are unable to identify a best-fit value of M_BH in NGC 205; however, the data impose a upper limit of 2.2x10^4 M_sun (1sigma confidence) and and upper limit of 3.8x10^4 M_sun (3sigma confidence). This upper limit is consistent with the extrapolation of the M_BH-sigma relation to the M_BH < 10^6 M_sunregime. If we assume that NGC 205 and M33 both contain nuclear black holes, the upper limits on M_BH in the two galaxies imply a slope of ~5.5 or greater for the M_BH-sigma relation. We use our 3-integral models to evaluate the relaxation time (T_r) and stellar collision time (T_coll) in NGC 205; T_r~10^8 yr or less in the nucleus and T_coll~10^11 yr. The low value of T_r is consistent with core collapse having already occurred, but we are unable to draw conclusions from nuclear morphology about the presence or absence of a massive black hole.

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arXiv2003

Difficulties with Recovering The Masses of Supermassive Black Holes from Stellar Kinematical Data

We investigate the ability of three-integral, axisymmetric, orbit-based modeling algorithms to recover the parameters defining the gravitational potential (M/L ratio and black hole mass Mh) in spheroidal stellar systems using stellar kinematical data. We show that the potential estimation problem is generically under-determined when applied to long-slit kinematical data of the kind used in most black hole mass determinations to date. A range of parameters (M/L, Mh) can provide equally good fits to the data, making it impossible to assign best-fit values. We illustrate the indeterminacy using a variety of data sets derived from realistic models as well as published observations of the galaxy M32. In the case of M32, our reanalysis demonstrates that data published prior to 2000 are equally consistent with Mh in the range 1.5x10^6-5x10^6 solar masses, with no preferred value in that range. While the HST/STIS data for this galaxy may overcome the degeneracy in Mh, HST data for most galaxies do not resolve the black hole's sphere of influence and in these galaxies the degree of degeneracy allowed by the data may be substantial. We investigate the effect on the degeneracy of enforcing smoothness (regularization) constraints. However we find no indication that the true potential can be recovered simply by enforcing smoothness. For a given smoothing level, all solutions in the minimum-chisquare valley exhibit similar levels of noise. These experiments affirm that the indeterminacy is real and not an artifact associated with non-smooth solutions. (Abridged)

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arXiv1999

Orbital instability and relaxation in stellar systems

The orbits of stars in galaxies are generically chaotic: the chaotic behavior arises in part from the intrinsically grainy nature of a potential that is composed of point masses. Even if the potential is assumed to be smooth, however, orbits in non-axisymmetric galaxies can be chaotic due to the presence of central density cusps or black holes. The chaotic nature of orbits implies that perturbations will grow exponentially and this in turn is expected to result in a diffusion in phase space. We show that the degree of orbital evolution is not well predicted by the growth rate of infinitesimal perturbations, i.e. by the Liapunov exponent. A more useful criterion is whether perturbations continue to grow exponentially until their scale is of order the size of the system. We illustrate these ideas in a potential consisting of N fixed point masses. Liapunov exponents are large for all values of N, but orbits become increasingly regular in their behavior as N increases; the reason is that the exponential divergence saturates at smaller and smaller distances as N is increased. The objects which impede diffusion are the invariant tori. When there are few stable tori, an ensemble of chaotic orbits evolves rapidly toward a nearly stationary state. This mixing process occurs on timescales of a few crossing times in triaxial potentials containing massive central singularities, consistent with the rapid evolution observed in N-body simulations of galaxies with central black holes.

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arXiv1999

Torus Construction

The maximally compact representation of a regular orbit is in terms of its action-angle variables. Computing the map between a trajectory's Cartesian coordinates and its action-angle variables is called torus construction. This article reviews various approaches to torus construction and their application to galactic dynamics.

astro-ph↗

arXiv1999

Resonant Orbits in Triaxial Galaxies

Box orbits in triaxial potentials are generically thin, that is, they lie close in phase space to a resonant orbit satisfying a relation of the form lω_1 +mω_2+nω_3=0 between the three fundamental frequencies. Resonant orbits are confined to a membrane; they play roughly the same role, in three dimensions, that closed orbits play in two. Stable resonant orbits avoid the center of the potential; orbits that are thick enough to pass near the center are typically stochastic. Very near the center, where the gravitational potential is dominated by the black hole, resonant orbits continue to exist, including at least one family whose elongation is parallel to the long axes of the triaxial figure.

astro-ph↗

arXiv1999

Dynamical Evolution of Bulge Shapes

Figure rotation substantially increases the fraction of stochastic orbits in triaxial systems. This increase is most dramatic in systems with shallow cusps showing that it is not a direct consequence of scattering by a central density cusp or black hole. In a recent study of stationary triaxial potentials (Valluri & Merritt 1998) it was found that the most important elements that define the structure of phase space are the two dimensional resonant tori. The increase in the fraction of stochastic orbits in models with figure rotation is a direct consequence of the destabilization of these resonant tori. The presence of a large fraction of stochastic orbits in a triaxial bulge will result in the evolution of its shape from triaxial to axisymmetric. The timescales for evolution can be as short as a few crossing times in the bulges of galaxies and evolution is accelerated by figure rotation. This suggests that low luminosity ellipticals and the bulges of early type spirals are likely to be predominantly axisymmetric.

astro-ph↗

arXiv1998

Regular and Chaotic Dynamics of Triaxial Stellar Systems

We use Laskar's frequency mapping technique to study the dynamics of triaxial galaxies with central density cusps and nuclear black holes. For ensembles of 10^4 orbits, we numerically compute the three fundamental frequencies of the motion, allowing us to map out the Arnold web. We also compute diffusion rates of stochastic orbits in frequency space. The objects of fundamental importance in structuring phase space are found to be the 3-dimensional resonant tori; even when stable, such tori are not necessarily associated with periodic orbits as in systems with only two degrees of freedom. Boxlike orbits are generically stochastic, but some tube orbits are stochastic as well. The spectrum of diffusion rates for box-like orbits at a given energy is well approximated as a power law over at least six decades. Models with high central concentrations -- steep central cusps or massive black holes -- exhibit the most stochasticity. A black hole with a mass of 0.3% the mass of the galaxy is as effective as the steepest central density cusp at inducing stochastic diffusion. There is a transition to global stochasticity in box-like phase space when the mass of a central black hole exceeds 2% the galaxy mass. We predict a greater average degree of dynamical evolution in faint ellipticals, due to their high central densities and short crossing times. The evolution time is estimated to be shorter than a galaxy lifetime for absolute magnitudes fainter than about -19 or -20, consistent with the observed change in many elliptical galaxy properties at this luminosity.

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arXiv1997

Self-Consistent Gravitational Chaos

The motion of stars in the gravitational potential of a triaxial galaxy is generically chaotic. However, the timescale over which the chaos manifests itself in the orbital motion is a strong function of the degree of central concentration of the galaxy. Here, chaotic diffusion rates are presented for orbits in triaxial models with a range of central density slopes and nuclear black-hole masses. Typical diffusion times are found to be less than a galaxy lifetime in triaxial models where the density increases more rapidly than 1/r at the center, or which contain black holes with masses that exceed roughly 0.1% of the galaxy mass. When the mass of a central black hole exceeds roughly 0.02 times the mass of the galaxy, there is a transition to global stochasticity and the galaxy evolves to an axisymmetric shape in little more than a crossing time. This rapid evolution may provide a negative feedback mechanism that limits the mass of nuclear black holes to a few percent of the stellar mass of a galaxy.

astro-ph↗

arXiv1996

Chaos and Mixing in Triaxial Stellar Systems

We investigate the timescales for stochasticity and chaotic mixing in a family of triaxial potentials that mimic the distribution of light in elliptical galaxies. Some of the models include central point masses designed to represent nuclear black holes. Most of the boxlike orbits are found to be stochastic, with mean Liapunov times that are 3-6 times the period of the long-axis orbit. In models with large cores or small black holes, the stochastic orbits mimic regular box orbits for hundreds of oscillations at least. However a small core radius or significant black hole mass causes most of the stochastic orbits to diffuse through phase space on the same timescale, visiting a significant fraction of the volume beneath the equipotential surface. We estimate timescales for chaotic mixing in the more strongly stochastic models by evolving ensembles of 10^4 points until their distribution reaches a nearly steady state. Mixing initially takes place rapidly, with characteristic times of 10-30 dynamical times, as the phase points fill a region similar in shape to that of a box orbit. Subsequent mixing is slower, with characteristic times of hundreds of orbital times. Mixing rates were found to be enhanced by the addition of modest force perturbations. The consequences for the structure and evolution of elliptical galaxies are discussed.

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