Posts Tagged vertical dispersion

Recent Postings from vertical dispersion

The difficulty of measuring the local dark matter density

The analysis of the vertical velocity dispersion of disc stars is the most direct astronomical means of estimating the local dark matter density, $\rho_{DM}$. Current estimates based on the mid-plane dynamic density use a local baryonic correction that ignores the non-local effects of spiral structure and significantly underestimates the amount of dynamically relevant gas; the additional gas plus the remaining uncertainties make it practically impossible to measure $\rho_{DM}$ from mid-plane kinematics alone. The sampling of inhomogeneous tracer populations with different scale-heights and scale-lengths results in a systematic increase in the observed dispersion gradients and changes in the nominal density distributions that, if not properly considered, can be misinterpreted as a sign of more dark matter. If the disc gravity is modelled using an infinite disc, the local variation in the vertical gravity due to the globally exponential disc components results in an underestimation of the baryonic contribution by as much as ~40% Given only the assumptions of stationarity, an axially and vertically symmetric disc, doubly exponential tracer and mass-component density profiles, a phenomenologically justified model for the cross-dispersion component $\sigma_{Rz}$, and a realistic model for $g_z$, it is possible to solve the full vertical Jeans equation analytically for the vertical dispersion $\sigma_{z}(z)$ and hence test the robustness of previous attempts at measuring $\rho_{DM}$. When the model parameters are estimated from SEGUE G dwarf star data, it is still not possible to explain the difference in behaviour seen in the simple thick- and thin-disc datasets reported by Buedenbender et al.. Rather than being a fundamental problem with the kinematical model, this effect appears to be a further sign of the difficulty of defining and handling kinematically homogeneous tracer populations.

The Gravitational Potential Near the Sun From SEGUE K-dwarf Kinematics [Replacement]

To constrain the Galactic gravitational potential near the Sun ($\sim$1.5 kpc), we derive and model the spatial and velocity distribution for a sample of 9000 K-dwarfs that have spectra from SDSS/SEGUE, which yield radial velocities and abundances ([Fe/H] & [$\alpha$/Fe]). We first derive the spatial density distribution for stars of three abundance-selected sub-populations by accounting for the survey's selection function. The vertical profile of these sub-populations are simple exponentials and their vertical dispersion profile is nearly isothermal. To model these data, we apply the vertical' Jeans Equation, which relates the observable tracer number density and vertical velocity dispersion to the gravitational potential or vertical force. We explore a number of functional forms for the vertical force law, and fit the dispersion and density profiles of all abundance selected sub-populations simultaneously in the same potential, and explore all parameter co-variances using MCMC. Our fits constrain a disk {\it mass} scale height $\lesssim$ 300 pc and the total surface mass density to be $67 \pm 6 M_{\odot} {\rm pc^{-2}}$ at $|z| = 1.0$ kpc of which the contribution from all stars is $42 \pm 5 M_{\odot} {\rm pc^{-2}}$ (presuming a contribution from cold gas of $13 M_{\odot} {\rm pc^{-2}}$). We find significant constraints on the local dark matter density of $0.0065\pm0.0023 M_{\odot} {\rm pc^{-3}}$ ($0.25\pm0.09 {\rm GeV cm^{-3}}$). Together with recent experiments this firms up the best estimate of $0.0075\pm0.0021 M_{\odot} {\rm pc^{-3}}$ ($0.28\pm0.08 {\rm GeV cm^{-3}}$), consistent with global fits of approximately round dark matter halos to kinematic data in the outskirts of the Galaxy.

The Gravitational Potential Near the Sun From SEGUE K-dwarf Kinematics

To constrain the Galactic gravitational potential near the Sun ($\sim$1.5 kpc), we derive and model the spatial and velocity distribution for a sample of 9000 K-dwarfs that have spectra from SDSS/SEGUE, which yield radial velocities and abundances ([Fe/H] & [$\alpha$/Fe]). We first derive the spatial density distribution for stars of three abundance-selected sub-populations by accounting for the survey's selection function. The vertical profile of these sub-populations are simple exponentials and their vertical dispersion profile is nearly isothermal. To model these data, we apply the vertical' Jeans Equation, which relates the observable tracer number density and vertical velocity dispersion to the gravitational potential or vertical force. We explore a number of functional forms for the vertical force law, and fit the dispersion and density profiles of all abundance selected sub-populations simultaneously in the same potential, and explore all parameter co-variances using MCMC. Our fits constrain a disk {\it mass} scale height $\lesssim$ 300 pc and the total surface mass density to be $67 \pm 6 M_{\odot} {\rm pc^{-2}}$ at $|z| = 1.0$ kpc of which the contribution from all stars is $42 \pm 5 M_{\odot} {\rm pc^{-2}}$ (presuming a contribution from cold gas of $13 M_{\odot} {\rm pc^{-2}}$). We find significant constraints on the local dark matter density of $0.0065\pm0.0023 M_{\odot} {\rm pc^{-3}}$ ($0.25\pm0.09 {\rm GeV cm^{-3}}$). Together with recent experiments this firms up the best estimate of $0.0075\pm0.0021 M_{\odot} {\rm pc^{-3}}$ ($0.28\pm0.08 {\rm GeV cm^{-3}}$), consistent with global fits of approximately round dark matter halos to kinematic data in the outskirts of the Galaxy.

The vertical motions of mono-abundance sub-populations in the Milky Way disk

We present the vertical kinematics of stars in the Milky Way's stellar disk inferred from SDSS/SEGUE G-dwarf data, deriving the vertical velocity dispersion, \sigma_z, as a function of vertical height |z| and Galactocentric radius R for a set of 'mono-abundance' sub-populations of stars with very similar elemental abundances [\alpha/Fe] and [Fe/H]. We find that all components exhibit nearly isothermal kinematics in |z|, and a slow outward decrease of the vertical velocity dispersion: $\sigma_z (z,R\,|[\alpha/Fe],[Fe/H]) ~ \sigma_z ([\alpha/Fe],[Fe/H]) x \exp (-(R-R_0)/7 kpc})$. The characteristic velocity dispersions of these components vary from ~ 15 km/s for chemically young, metal-rich stars, to >~ 50 km/s for metal poor stars. The mean \sigma_z gradient away from the mid plane is only 0.3 +/- 0.2 km/s/kpc. We find a continuum of vertical kinetic temperatures (~\sigma^2_z) as function of ([\alpha/Fe],[Fe/H]), which contribute to the stellar surface mass density as \Sigma_{R_0}(\sigma^2_z) ~ \exp(-\sigma^2_z). The existence of isothermal mono-abundance populations with intermediate dispersions reject the notion of a thin-thick disk dichotomy. This continuum of disks argues against models where the thicker disk portions arise from massive satellite infall or heating; scenarios where either the oldest disk portion was born hot, or where internal evolution plays a major role, seem the most viable. The wide range of \sigma_z ([\alpha/Fe],[Fe/H]) combined with a constant \sigma_z(z) for each abundance bin provides an independent check on the precision of the SEGUE abundances: \delta_[\alpha/Fe] ~ 0.07 dex and \delta_[Fe/H] ~ 0.15 dex. The radial decline of the vertical dispersion presumably reflects the decrease in disk surface-mass density. This measurement constitutes a first step toward a purely dynamical estimate of the mass profile the disk in our Galaxy. [abridged]

The vertical motions of mono-abundance sub-populations in the Milky Way disk [Replacement]

We present the vertical kinematics of stars in the Milky Way's stellar disk inferred from SDSS/SEGUE G-dwarf data, deriving the vertical velocity dispersion, \sigma_z, as a function of vertical height |z| and Galactocentric radius R for a set of 'mono-abundance' sub-populations of stars with very similar elemental abundances [\alpha/Fe] and [Fe/H]. We find that all components exhibit nearly isothermal kinematics in |z|, and a slow outward decrease of the vertical velocity dispersion: \sigma_z (z,R|[\alpha/Fe],[Fe/H]) ~ \sigma_z ([\alpha/Fe],[Fe/H]) x \exp (-(R-R_0)/7 kpc}). The characteristic velocity dispersions of these components vary from ~ 15 km/s for chemically young, metal-rich stars, to >~ 50 km/s for metal poor stars. The mean \sigma_z gradient away from the mid plane is only 0.3 +/- 0.2 km/s/kpc. We find a continuum of vertical kinetic temperatures (~\sigma^2_z) as function of ([\alpha/Fe],[Fe/H]), which contribute to the stellar surface mass density as \Sigma_{R_0}(\sigma^2_z) ~ \exp(-\sigma^2_z). The existence of isothermal mono-abundance populations with intermediate dispersions reject the notion of a thin-thick disk dichotomy. This continuum of disks argues against models where the thicker disk portions arise from massive satellite infall or heating; scenarios where either the oldest disk portion was born hot, or where internal evolution plays a major role, seem the most viable. The wide range of \sigma_z ([\alpha/Fe],[Fe/H]) combined with a constant \sigma_z(z) for each abundance bin provides an independent check on the precision of the SEGUE abundances: \delta_[\alpha/Fe] ~ 0.07 dex and \delta_[Fe/H] ~ 0.15 dex. The radial decline of the vertical dispersion presumably reflects the decrease in disk surface-mass density. This measurement constitutes a first step toward a purely dynamical estimate of the mass profile the disk in our Galaxy. [abridged]

Limits on the local dark matter density

We revisit systematics in determining the local dark matter density (rho_dm) from the vertical motion of stars in the Solar Neighbourhood. Using a simulation of a Milky Way-like galaxy, we determine the data-quality required to detect the dark matter density at its expected local value. We introduce a new method for recovering rho_dm that uses moments of the Jeans equations, combined with a Monte Carlo Markov Chain technique to marginalise over the unknown parameters. Given sufficiently good data, we show that our method can recover the correct local dark matter density even in the face of disc inhomogeneities, non-isothermal tracers and a non-separable distribution function. We illustrate the power of our technique by applying it to Hipparcos data [Holmberg & Flynn 2000,2004]. We first make the assumption that the A and F star tracer populations are isothermal. This recovers rho_dm=0.003^{+0.009}_{-0.007}Msun/pc^3 (with 90 per cent confidence), consistent with previous determinations. However, the vertical dispersion profile of these tracers is poorly known. If we assume instead a non-isothermal profile similar to the blue disc stars from SDSS DR-7 [Abazajian et al. 2009] measured by Bond et al. (2009), we obtain a fit with a very similar chi^2 value, but with rho_dm=0.033^{+0.008}_{-0.009}Msun/pc^3 (with 90 per cent confidence). This highlights that it is vital to measure the vertical dispersion profile of the tracers to recover an unbiased estimate of the local dark matter density.

Limits on the local dark matter density [Replacement]

We revisit systematics in determining the local dark matter density (rho_dm) from the vertical motion of stars in the Solar Neighbourhood. Using a simulation of a Milky Way-like galaxy, we determine the data-quality required to detect the dark matter density at its expected local value. We introduce a new method for recovering rho_dm that uses moments of the Jeans equations, combined with a Monte Carlo Markov Chain technique to marginalise over the unknown parameters. Given sufficiently good data, we show that our method can recover the correct local dark matter density even in the face of disc inhomogeneities, non-isothermal tracers and a non-separable distribution function. We illustrate the power of our technique by applying it to Hipparcos data [Holmberg & Flynn 2000,2004]. We first make the assumption that the A and F star tracer populations are isothermal. This recovers rho_dm=0.003^{+0.009}_{-0.007}Msun/pc^3 (with 90 per cent confidence), consistent with previous determinations. However, the vertical dispersion profile of these tracers is poorly known. If we assume instead a non-isothermal profile similar to the blue disc stars from SDSS DR-7 [Abazajian et al. 2009] measured by Bond et al. (2009), we obtain a fit with a very similar chi^2 value, but with rho_dm=0.033^{+0.008}_{-0.009}Msun/pc^3 (with 90 per cent confidence). This highlights that it is vital to measure the vertical dispersion profile of the tracers to recover an unbiased estimate of the local dark matter density.

The structure of gravitationally unstable gas-rich disk galaxies

We use a series of idealized, numerical SPH simulations to study the formation and evolution of galactic, gas-rich disks forming from gas infall within dark matter halos. The temperature and density structure of the gas is varied in order to differentiate between (i) simultaneous gas infall at a large range of radii and (ii) the inside-out build-up of a disk. In all cases, the disks go through phases of ring formation, gravitational instability and break-up into massive clumps. Ring formation can be enhanced by a focal point effect. The position of the ring is determined by the angular momentum distribution of the material it forms from. We study the ring and clump morphologies, the characteristic properties of the resulting velocity dispersion field and the effect of star formation. In the early phases, gas accretion leads to a high vertical velocity dispersion. We find that the disk fragmentation by gravitational instability and the subsequent clump-clump interactions drive high velocity dispersions mainly in the plane of the disk while at the same time the vertical velocity dispersion dissipates. The result is a strong variation of the line-of-sight velocity dispersion with inclination angle. For a face-on view, clumps appear as minima in the (vertical) dispersion, whereas for a more edge-on view, they tend to correspond to maxima. There exists observational evidence of a systematic variation of the velocity dispersion with inclination angle in high-redshift disks, which could be partly explained by our simulation results. Additional energetic sources to drive velocity dispersion that are not included in our models are also expected to contribute to the observational results.

Vertical structure of debris discs

The vertical thickness of debris discs is often used as a measure of these systems' dynamical excitation and as clues to the presence of hidden massive perturbers such as planetary embryos. However, this argument could be flawed because the observed dust should be naturally placed on inclined orbits by the combined effect of radiation pressure and mutual collisions. We critically reinvestigate this issue and numerically estimate what the "natural" vertical thickness of a collisionally evolving disc is, in the absence of any additional perturbing body. We use a deterministic collisional code, following the dynamical evolution of a population of indestructible test grains suffering mutual inelastic impacts. Grain differential sizes as well as the effect of radiation pressure are taken into account. We find that, under the coupled effect of radiation pressure and collisions, grains naturally acquire inclinations of a few degrees. The disc is stratified with respect to grain sizes, with the smallest grains having the largest vertical dispersion and the bigger ones clustered closer to the midplane. Debris discs should have a minimum "natural" observed aspect ratio $h_{min}\sim 0.04\pm0.02$ at visible to mid-IR wavelengths where the flux is dominated by the smallest bound grains. These values are comparable to the estimated thicknesses of many vertically resolved debris discs, as is illustrated with the specific example of AU Mic. For all systems with $h \sim h_{min}$, the presence (or absence) of embedded perturbing bodies cannot be inferred from the vertical dispersion of the disc