arXiv subjects

N. W. Evans

Publications and source records attributed to N. W. Evans.

At least 217 records · Page 12Linked to original sources

arXiv2000

Dynamical Mass Estimates for the Halo of M31 from Keck Spectroscopy

The last few months have seen the measurements of the radial velocities of all of the dwarf spheroidal companions to the Andromeda galaxy (M31) using the spectrographs (HIRES and LRIS) on the Keck Telescope. This paper summarises the data on the radial velocities and distances for all the companion galaxies and presents new dynamical modelling to estimate the mass of extended halo of M31. The best fit values for the total mass of M31 are between 7 and 10 x 10^{11} solar masses, depending on the details of the modelling. The mass estimate is accompanied by considerable uncertainty caused by the smallness of the dataset; for example, the upper bound on the total mass is roughly 24 x 10^{11} solar masses, while the lower bound is about 3 x 10^{11} solar masses. These values are less than the most recent estimates of the most likely mass of the Milky Way halo. Bearing in mind all the uncertainties, a fair conclusion is that the M31 halo is roughly as massive as that of the Milky Way halo. There is no dynamical evidence for the widely held belief that M31 is more massive -- it may even be less massive.

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arXiv2000

Asteroids in the Inner Solar System I - Existence

Ensembles of in-plane and inclined orbits in the vicinity of the Lagrange points of the terrestrial planets are integrated for up to 100 million years. The integrations incorporate the gravitational effects of Sun and the eight planets (Pluto is neglected). Mercury is the least likely planet, as it is unable to retain tadpole orbits over 100 million year timescales. Both Venus and the Earth are much more promising, as they possess rich families of stable tadpole and horseshoe orbits. Our survey of Trojans in the orbital plane of Venus is undertaken for 25 million years. Some 40% of the survivors are on tadpole orbits. For the Earth, the integrations are pursued for 50 million years. The stable zones in the orbital plane are larger for the Earth than for Venus, but fewer of the survivors are tadpoles. Both Venus and the Earth also have regions in which inclined test particles can endure near the Lagrange points. For Venus, only test particles close to the orbital plane are stable. For the Earth, there are two bands of stability, one at low inclinations (i < 16 degrees) and one at moderate inclinations (between 24 degrees and 34 degrees). The inclined test particles that evade close encounters are primarily moving on tadpole orbits. Our survey of in-plane test particles near the Martian Lagrange points shows no survivors after 60 million years. Low inclination test particles do not persist, as their inclinations are quickly increased until the effects of a secular resonance with Jupiter cause de-stabilisation. Numerical integrations of inclined test particles for timespans of 25 million years show stable zones for inclinations between 14 and 40 degrees.

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arXiv2000

Asteroids in the Inner Solar System II - Observable Properties

This paper presents synthetic observations of long-lived, coorbiting asteroids of Mercury, Venus, the Earth and Mars. Our sample is constructed by taking the limiting semimajor axes, differential longitudes and inclinations for long-lived stability provided by simulations. The intervals are randomly populated with values to create initial conditions. These orbits are re-simulated to check that they are stable and then re-sampled every 2.5 years for 1 million years. The Mercurian sample contains only horseshoe orbits, the Martian sample only tadpoles. For both Venus and the Earth, the greatest concentration of objects on the sky occurs close to the classical Lagrange points at heliocentric ecliptic longitudes of 60 and 300 degrees. The distributions are broad especially if horseshoes are present in the sample. The full-width half maximum (FWHM) in heliocentric longitude for Venus is 325 degrees and for the Earth is 328 degrees. The mean and most common velocity of these coorbiting satellites coincides with the mean motion of the parent planet, but again the spread is wide with a FWHM for Venus of 27.8 arcsec/hr and for the Earth of 21.0 arcsec/hr. For Mars, the greatest concentration on the sky occurs at heliocentric ecliptic latitudes of 12 degrees. The peak of the velocity distribution occurs at 65 arcsec/hr, significantly less than the Martian mean motion, while its FWHM is 32.3 arcsec/hr. The case of Mercury is the hardest of all, as the greatest concentration occurs at heliocentric longitudes close to the Sun.

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arXiv2000

The Mass of the Andromeda Galaxy

This paper argues that the Milky Way galaxy is probably the largest member of the Local Group. The evidence comes from estimates of the total mass of the Andromeda galaxy (M31) derived from the three dimensional positions and radial velocities of its satellite galaxies, as well as the projected positions and radial velocities of its distant globular clusters and planetary nebulae. The available dataset comprises ten satellite galaxies, seventeen distant globular clusters and nine halo planetary nebulae with radial velocities. We find the halo of Andromeda has a mass of about 12 x 10^11 solar masses, together with a scalelength of roughly 90 kpc and a predominantly isotropic velocity distribution. For comparison, our earlier estimate for the Milky Way halo is 19 x 10^11 solar masses. Though the error bars are admittedly large, this suggests that the total mass of M31 is probably less than that of the Milky Way. We verify the robustness of our results to changes in the modelling assumptions and to errors caused by the small size and incompleteness of the dataset. Future prospects using radial velocity surveys of globular clusters and planetary nebulae, as well as microarcsecond astrometry from the upcoming satellite missions, are discussed.

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arXiv2000

Theory of pixel lensing towards M31 I: the density contribution and mass of MACHOs

POINT-AGAPE is an Anglo-French collaboration which is employing the Isaac Newton Telescope (INT) to conduct a pixel-lensing survey towards M31. In this paper we investigate what we can learn from pixel-lensing observables about the MACHO mass and fractional contribution in M31 and the Galaxy for the case of spherically-symmetric near-isothermal haloes. We employ detailed pixel-lensing simulations which include many of the factors which affect the observables. For a maximum MACHO halo we predict an event rate in V of up to 100 per season for M31 and 40 per season for the Galaxy. However, the Einstein radius crossing time is generally not measurable and the observed full-width half-maximum duration provides only a weak tracer of lens mass. Nonetheless, we find that the near-far asymmetry in the spatial distribution of M31 MACHOs provides significant information on their mass and density contribution. We present a likelihood estimator for measuring the fractional contribution and mass of both M31 and Galaxy MACHOs which permits an unbiased determination to be made of MACHO parameters, even from data-sets strongly contaminated by variable stars. If M31 does not have a significant population of MACHOs in the mass range 0.001-1 Solar masses strong limits will result from the first season of INT observations. Simulations based on currently favoured density and mass values indicate that, after three seasons, the M31 MACHO parameters should be constrained to within a factor four uncertainty in halo fraction and an order of magnitude uncertainty in mass (90% confidence). Interesting constraints on Galaxy MACHOs may also be possible. For a campaign lasting ten years, comparable to the lifetime of current LMC surveys, reliable estimates of MACHO parameters in both galaxies should be possible. (Abridged)

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arXiv1999

Is the Large Magellanic Cloud a Large Microlensing Cloud?

An expression is provided for the self-lensing optical depth of the thin LMC disk surrounded by a shroud of stars at larger scale heights. The formula is written in terms of the vertical velocity dispersion of the thin disk population. If tidal forcing causes 1-5 % of the disk mass to have a height larger than 6 kpc and 10-15 % to have a height above 3 kpc, then the self-lensing optical depth of the LMC is $0.7 - 1.9 \times 10^{-7}$, which is within the observational uncertainties. The shroud may be composed of bright stars provided they are not in stellar hydrodynamical equilibrium. Alternatively, the shroud may be built from low mass stars or compact objects, though then the self-lensing optical depths are overestimates of the true optical depth by a factor of roughly 3. The distributions of timescales of the events and their spatial variation across the face of the LMC disk offer possibilities of identifying the dominant lens population. In propitious circumstances, an experiment lifetime of less than 5 years is sufficient to decide between the competing claims of Milky Way halos and LMC lenses. However, LMC disks can sometimes mimic the microlensing properties of Galactic halos for many years and then decades of survey work are needed. In this case observations of parallax or binary caustic events offer the best hope for current experiments to deduce the lens population. The difficult models to distinguish are Milky Way halos in which the lens fraction is low (< 10 %) and fattened LMC disks composed of lenses with a typical mass of low luminosity stars or greater. A next-generation wide-area microlensing survey, such as the proposed ``SuperMACHO'' experiment, will be able to distinguish even these difficult models with just a year or two of data.

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arXiv1999

The Present and Future Mass of the Milky Way Halo

A simple model for the Milky Way halo is presented. It has a flat rotation curve in the inner regions, but the density falls off sharply beyond an outer edge. This truncated, flat rotation curve (TF) model possesses a rich family of simple distribution functions which vary in velocity anisotropy. The model is used to estimate the total mass of the Milky Way halo using the latest data on the motions of satellite galaxies and globular clusters at Galactocentric radii greater than 20 kpc. This comprises a dataset of 27 objects with known distances and radial velocities, of which 6 also possess measured proper motions. Unlike earlier investigations, we find entirely consistent maximum likelihood solutions unaffected by the presence or absence of Leo I, provided both radial and proper motion data are used. The availability of the proper motion data for the satellites is crucial as, without them, the mass estimates with and without Leo I are inconsistent at the 99 % confidence level. All these results are derived from models in which the velocity normalisation of the halo potential is taken as 220 km/s. A detailed analysis of the uncertainties in our estimate is presented, including the effects of the small dataset, possible incompleteness or correlations in the satellite galaxy sample and the measurement errors. The most serious uncertainties come from the size of the dataset, which may cause a systematic underestimate by a factor of two, and the measurement errors, which cause a scatter in the mass of the order of a factor of two. We conclude that the total mass of the halo is 1.9 x 10^12 solar masses, while the mass within 50 kpc is 5.4 x 10^11 solar masses. Future prospects using radial velocity surveys of blue horizontal branch stars and microarcsecond astrometry from the upcoming satellite missions are discussed.

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arXiv1998

A Caustic View of Halo Microlensing

The only microlensing events towards the Magellanic Clouds for which the location of the lens is strongly constrained are the two binary caustic crossing events. In at least one and possibly both cases, the lens lies at, or close to, the clouds themselves. On the face of it, this seems an improbable occurrence if the Galactic dark halo provides the bulk of the lensing population, as suggested by standard analyses of the MACHO dataset towards the Large Magellanic Cloud (LMC). We use a binomial statistic to assess the prior probability of observing $M$ non-halo binary caustic events given a total sample of $N$ caustic binaries. We generalize for the case of multi-component Galactic and Magellanic Cloud models the Bayesian likelihood method for determining the lens mass and halo fraction from the observed timescales. We introduce a new statistic, the ``outcome discriminator'', which measures the consistency between the binary caustic data, prior expectation, and the MACHO LMC dataset as a whole. If the clouds are not embedded in their own dark halos of MACHOs, then the discovery of two non-halo caustic binary events out of two ($M = N = 2$) is inconsistent with expectation given the MACHO dataset. Galactic models in which $M = 1$ is the likeliest outcome are also inconsistent with the data, though models in which $M = 1$ has a reasonable prior probability are not. We consider the possibilities that the Magellanic Clouds are embedded in dark haloes of their own, or that the Galactic halo is intrinsically deficient in the binary systems which produce caustic crossing events. Either of these possibilities provide greater compatibility between observation and prior expectation, though the idea of Magellanic haloes is perhaps the more natural of the two and has support from kinematical studies.

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arXiv1998

Stability of Power-Law Disks II -- The Global Spiral Modes

This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law disks. Although the cut-out disks are remarkably stable to bisymmetric perturbations, they are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilising influence. A physical mechanism for the generation of the one-armed instabilities is put forward. Incoming trailing waves are reflected as leading waves at the inner cut-out, thus completing the feedback for the swing-amplifier. Growing three-armed and four-armed modes occur only at very low temperatures. The rotation curve index has a marked effect on stability. For all azimuthal wavenumbers, any unstable modes persist to higher temperatures and grow more vigorously if the rotation curve is rising than if the rotation curve is falling. If the central regions or outer parts of the disk are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law disks possess a number of unusual stability properties. There is no natural time-scale in the self-consistent disk. If a mode is admitted at some pattern speed and growth rate, then it must be present at all pattern speeds and growth rates. Our analysis suggests that such a two-dimensional continuum of non-axisymmetric modes does not occur and that the self-consistent power-law disks admit no global non-axisymmetric normal modes whatsoever. Without reflecting boundaries or cut-outs, there is no resonant cavity and no possibility of unstable growing modes. The self-consistent power-law disks certainly admit equiangular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes.

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arXiv1998

Stability of Power-Law Disks I -- The Fredholm Integral Equation

The power-law disks are a family of infinitesimally thin, axisymmetric stellar disks of infinite extent. The rotation curve can be rising, falling or flat. The self-consistent power-law disks are scale-free, so that all physical quantities vary as a power of radius. They possess simple equilibrium distribution functions depending on the two classical integrals, energy and angular momentum. While maintaining the scale-free equilibrium force law, the power-law disks can be transformed into cut-out disks by preventing stars close to the origin (and sometimes also at large radii) from participating in any disturbance. This paper derives the homogeneous Fredholm integral equation for the in-plane normal modes in the self-consistent and the cut-out power-law disks. This is done by linearising the collisionless Boltzmann equation to find the response density corresponding to any imposed density and potential. The normal modes -- that is, the self-consistent modes of oscillation -- are found by requiring the imposed density to equal the response density. In practice, this scheme is implemented in Fourier space, by decomposing both imposed and response densities in logarithmic spirals. The Fredholm integral equation then relates the transform of the imposed density to the transform of the response density. Numerical strategies to solve the integral equation and to isolate the growth rates and the pattern speeds of the normal modes are discussed.

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arXiv1998

The LMC Microlensing Events: Evidence for a Warped and Flaring Milky Way Disk?

The simplest interpretation of the microlensing events towards the Large Magellanic Cloud detected by the MACHO and EROS collaborations is that about one third of the halo of our own Milky Way galaxy exists in the form of objects of around 0.5 solar mass. There are grave problems with this interpretation. A normal stellar population of 0.5 solar mass stars should be visible. The other obvious candidate for the lenses is a population of white dwarfs. But, the precursor population must have polluted the interstellar medium with metals, in conflict with current population II abundance. Here, we propose a more conventional, but at the moment more speculative, explanation. Some of the lenses are stars in the disk of the Milky Way. They lie along the line of sight to the LMC because of warping and flaring of the Galactic disk. Depending on its scalelength and ellipticity, the disk's optical depth may lie anywhere between $0.2 \times 10^{-7}$ and $0.9 \times 10^{-7}$. Together with contributions from the LMC disk and bar and perhaps even intervening stellar contaminants, the total optical depth may match the data within the uncertainties. Microlensing towards the LMC may be telling us more about the distorted structure and stellar populations of the outer Milky Way disk than the composition of the dark halo.

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arXiv1998

Brown Dwarfs, White Knights and Demons

This paper investigates the hypothesis that the lensing objects towards the Large Magellanic Cloud (LMC) are brown dwarfs by analysing the effects of velocity anisotropy on the inferred microlensing masses. To reduce the masses, the transverse velocity of the lenses with respect to the microlensing tube must be minimised. In the outer halo, radial anisotropy is best for doing this; closer to the solar circle, azimuthal anisotropy is best. By using a constraint on the total kinetic energy of the tracer population from the Jeans equations, the microlensing mass is minimised over orientations of the velocity dispersion tensor. This minimum mass is about a tenth of a solar mass, which lies above the hydrogen burning limit. This demonstrates explicitly that populations of brown dwarfs with smoothly decreasing densities and dynamically mixed velocity distributions cannot be responsible for the microlensing events. Brown dwarfs are no white knights! There is one caveat. If there are demons sitting on the microlensing tube, they can drop brown dwarfs so as to reproduce the microlensing data-set exactly. Such a distribution is not smooth and does not give well-mixed velocities in phase space. It is a permissible solution only if the outer halo is dynamically young and lumpy. In such a case, theorists cannot rule out brown dwarfs. Only exorcists can!

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arXiv1998

Microlensing Halo Models with Abundant Brown Dwarfs

All previous attempts to understand the microlensing results towards the Large Magellanic Cloud (LMC) have assumed homogeneous present day mass functions (PDMFs) for the lensing populations. Here, we present an investigation into the microlensing characteristics of haloes with spatially varying PDMFs and anisotropic velocity dispersion tensors. One attractive possibility -- suggested by baryonic dark cluster formation in pregalactic and protogalactic cooling flows -- is that the inner halo is dominated by stellar mass objects, whereas low mass brown dwarfs become more prevalent on moving outwards. The contribution to the microlensing rate must be dominated by dark remnants (of about 0.5 solar masses) to recover the observed timescales of the microlensing experiments. But, even though stellar remnants control the rate, they do not dominate the mass of the baryonic halo, and so the well-known enrichment and mass budget problems are much less severe. Using a simple ansatz for the spatial variation of the PDMF, models are constructed in which the contribution of brown dwarfs to the mass of the baryonic halo is 55 % and to the total halo is 30 %. An unusual property of the models is that they predict that the average timescale of events towards M31 is shorter than the average timescale towards the LMC. This is because the longer line of sight towards M31 probes more of the far halo where brown dwarfs are the most common constituent.

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arXiv1997

On the Origin of Cusps in Stellar Systems

An origin is sought for the ubiquity of cusps, both in computer simulations of halo formation in hierarchical clustering cosmogonies and in observations of galactic nuclei by the Hubble Space Telescope (HST). The encounters of merging clumps that built the galaxies can be described by the collisional Boltzmann equation. Using insights gained by studying the simpler Fokker-Planck equation, we show that there is a steady-state, self-consistent, cusped solution of the collisional Boltzmann equation corresponding to $ρ\sim r^{-4/3}$. This equilibrium is both stable and an attractor. It is the natural end-point of the diffusive encounters of an ensemble of equal mass clumps. The introduction of a mass spectrum weakens the mass density cusp. The spike in the luminosity density can be accentuated or softened, depending on the form of the mass-luminosity relation. Possible applications to the cusped nuclei of early-type galaxies are discussed.

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arXiv1996

Simple Three-Integral Scale-Free Galaxy Models

The Jeans equations give the second moments or stresses required to support a stellar population against the gravity field. A general solution of the Jeans equations for arbitrary axisymmetric scale-free densities in flattened scale-free potentials is given. A two-parameter subset of the solution for the second moments for the self-consistent density of the power-law models, which have exactly spheroidal equipotentials, is examined in detail. In the spherical limit, the potential of these models reduces to that of the singular power-law spheres. We build the physical three-integral distribution functions that correspond to the flattened stellar components. Next, we attack the problem of finding distribution functions associated with the Jeans solutions in flattened scale-free potentials. The third or partial integral introduced by de Zeeuw, Evans and Schwarzschild for Binney's model is generalised to thin and near-thin orbits moving in arbitrary axisymmetric scale-free potentials. The partial integral is a modification of the total angular momentum. For the self-consistent power-law models, we show how this enables the construction of simple three-integral distribution functions. The connexion between these approximate distribution functions and the Jeans solutions is discussed in some detail.

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arXiv1996

The Capture and Escape of Stars

The shape of galaxies depends on their orbital populations. These populations change through capture into and escape from resonance. Capture problems fall into distinct cases depending upon the shape of the potential well. To visualise the effective potential well for orbital capture, a diagrammatic approach to the resonant perturbation theory of Born is presented. These diagrams we call equiaction sections. To illustrate their use, we present examples drawn from both galactic and Solar System dynamics. The probability of capture for generic shapes of the potential well is calculated. A number of predictions are made. First, there are barred galaxies that possess two outer rings of gas and stars (type R1R2). We show how to relate changes in the pattern speed and amplitude of the bar to the strength of the two rings. Secondly, under certain conditions, small disturbances can lead to dramatic changes in orbital shape. This can be exploited as a mechanism to pump counter-rotating stars and gas into the nuclei of disk galaxies. Tidal resonant forcing of highly inclined orbits around a central mass causes a substantial increase in the likelihood of collision. Thirdly, the angular momentum of a potential well is changed by the passage of stars across or capture into the well. This can lead to the creation of holes, notches and high velocity tails in the stellar distribution function, whose form we explicitly calculate.

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arXiv1995

Jeans and Boltzmann Solutions for Oblate Galaxies with Flat Rotation Curves

A general solution of the Jeans equations for oblate scale-free logarithmic potentials is given. This provides all possible second velocity moments that can hold up a stellar population of flattened scale-free density against the gravity field. A two-parameter subset of second moments for the self-consistent density of Binney's model is examined in detail. These solutions have the desirable property that the observable dispersions in the radial and proper motions can be given explicitly. In the spherical limit, the potential of these models reduces to that of the singular isothermal sphere. The Jeans solutions for scale-free densities of arbitrary flattening that can correspond to physical three-integral distribution functions are identified. The problem of finding distribution functions associated with the Jeans solutions in flattened scale-free logarithmic potentials is then investigated for Binney's model. An approximate solution of the collisionless Boltzmann equation is found which provides a third (partial) integral of good accuracy for thin and near-thin tube orbits. It is a modification of the total angular momentum. This enables the construction of many simple three-integral distribution functions. The kinematic properties of these approximate DFs are shown to agree with a subset of the Jeans solutions --- which are thereby confirmed as good approximations to physical solutions.

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arXiv1995

The Nature of the Galactic Dark Matter

Disk-halo models of the Galaxy and LMC are constructed and used to analyse the microlensing data-set. Deflectors in the LMC bar, disk and halo provide an optical depth to microlensing of $\sim 2 \times 10^{-7}$. Deflectors in the Galactic disk and halo contribute $\sim 5 \times 10^{-7}$. The extent, flattening and velocity anisotropy of the dark objects in the Galactic halo are unknown. So, it is crucial to analyse the microlensing data-set with families of models that span the viable ranges of these structural parameters. Also uncertain is the contribution of the Galactic disk to the local circular speed, which affects the normalisation and size of the Galactic halo. Despite all the unknowns, a robust conclusion is that the Galactic and LMC haloes cannot be primarily built from objects in the mass range $10^{-7} \, \msun$ - $0.1 \, \msun$. By contrast, calculations of the baryon mass fraction of the Galactic and LMC haloes are very sensitive to details of the adopted models. This parameter is not constrained by the existing data-set. In particular, it is still possible for the halo to be entirely baryonic and composed of high mass compact objects, like $10^6\, \msun$ clusters or black holes.

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