Analysing surveys of our Galaxy I: basic astrometric data

We consider what is the best way to extract science from large surveys of the Milky Way galaxy. The diversity of data gathered in these surveys, together with our position within the Galaxy, imply that science must be extracted by fitting dynamical models to the data in the space of the observables. Models based on orbital tori promise to be superior for this task than traditional types of models, such as N-body models and Schwarzschild models. A formalism that allows such models to be fitted to data is developed and tested on pseudodata of varying richness.Comment: 15 pages, 6 figures, MNRAS accepted, changed to reflect final versio

The uncertainty in Galactic parameters

We reanalyse the measurements of parallax, proper motion, and line-of-sight velocity for 18 masers in high mass star-forming regions presented by Reid et al. (2009). We use a likelihood analysis to investigate the distance of the Sun from the Galactic centre, R_0, the rotational speed of the local standard of rest, v_0, and the peculiar velocity of the Sun, vsol, for various models of the rotation curve, and models which allow for a typical peculiar motion of the high mass star-forming regions. We find that these data are best fit by models with non-standard values for vsol or a net peculiar motion of the high mass star-forming regions. We argue that a correction to vsol is much more likely, and that these data support the conclusion of Binney (2009) that V_sol should be revised upwards from 5.2 km/s to 11 km/s. We find that the values of R_0 and v_0 that we determine are heavily dependent on the model we use for the rotation curve, with model-dependent estimates of R_0 ranging from 6.7 \pm 0.5kpc to 8.9 \pm 0.9kpc, and those of v_0 ranging from 200 \pm 20 km/s to 279 \pm 33 km/s. We argue that these data cannot be thought of as implying any particular values of R_0 or v_0. However, we find that v_0/R_0 is better constrained, lying in the range 29.9-31.6 km/s/kpc for all models but one.Comment: 8 pages. MNRAS accepted. Revised to reflect final versio

Is Galactic Structure Compatible with Microlensing Data?

We generalize to elliptical models the argument of Kuijken (1997), which connects the microlensing optical depth towards the Galactic bulge to the Galactic rotation curve. When applied to the latest value from the MACHO collaboration for the optical depth for microlensing of bulge sources, the argument implies that the Galactic bar cannot plausibly reconcile the measured values of the optical depth, the rotation curve and the local mass density. Either there is a problem with the interpretation of the microlensing data, or our line of sight to the Galactic centre is highly atypical in that it passes through a massive structure that wraps only a small distance around the Galactic centre.Comment: Submitted to ApJ Letters. 8 pages LaTeX, 3 figures. Corrected error in description of microlensing observation

Entropy Evolution of the Gas in Cooling Flow Clusters

We emphasise the importance of the gas entropy in studying the evolution of cluster gas evolving under the influence of radiative cooling. On this basis, we develop an analytical model for this evolution. We then show that the assumptions needed for such a model are consistent with a numerical solution of the same equations. We postulate that the passive cooling phase ends when the central gas temperature falls to very low values. It follows a phase during which an unspecified mechanism heats the cluster gas. We show that in such a scenario the small number of clusters containing gas with temperatures below about 1 keV is simply a consequence of the radiative cooling.Comment: Contribution to Proceedings of `The Riddle of Cooling Flows in Galaxies and Clusters of Galaxies', Charlottesville, VA, USA. May 31 -- June 4, 2003. Editors: Reiprich, T. H., Kempner, J. C., and Soker, N. Requires included style fil

Analysing surveys of our Galaxy -- II. Determining the potential

We consider the problem of determining the Galaxy's gravitational potential from a star catalogue. We show that orbit-based approaches to this problem suffer from unacceptable numerical noise deriving from the use of only a finite number of orbits. An alternative approach, which requires an ability to determine the model's phase-space density at predetermined positions and velocities, has a level of numerical noise that lies well below the intrinsic uncertainty associated with the finite size of the catalogue analysed. A catalogue of 10000 stars brighter than V=17 and distributed over the sky at b>30 degrees enables us to determine the scaleheight of the disc that contributes to the potential with an uncertainty below 20pc if the catalogue gives proper motions, line-of-sight velocities and parallaxes with errors typical of the Gaia Catalogue, rising to 36pc if only proper motions are available. The uncertainty in the disc's scalelength is significantly smaller than 0.25kpc.Comment: 16 pages, MNRAS accepted. Revised to reflect final versio

The dangers of deprojection of proper motions

We re-examine the method of deprojection of proper motions, which has been used for finding the velocity ellipsoid of stars in the nearby Galaxy. This method is only legitimate if the lines of sight to the individual stars are uncorrelated with the stars' velocities. Very simple models are used to show that spurious results similar to ones recently reported are obtained when velocity dispersion decreases with galactocentric radius in the expected way. A scheme that compensates for this bias is proposed.Comment: 5 pages, 5 figures (3 colour), MNRAS submitte

AGN effect on cooling flow dynamics

We analyzed the feedback of AGN jets on cooling flow clusters using three-dimensional AMR hydrodynamic simulations. We studied the interaction of the jet with the intracluster medium and creation of low X-ray emission cavities (Bubbles) in cluster plasma. The distribution of energy input by the jet into the system was quantified in its different forms, i.e. internal, kinetic and potential. We find that the energy associated with the bubbles, (pV + gamma pV/(gamma-1)), accounts for less than 10 percent of the jet energy.Comment: "Accepted for publication in Astrophysics & Space Science

Extracting science from surveys of our Galaxy

Our knowledge of the Galaxy is being revolutionised by a series of photometric, spectroscopic and astrometric surveys. Already an enormous body of data is available from completed surveys, and data of ever increasing quality and richness will accrue at least until the end of this decade. To extract science from these surveys we need a class of models that can give probability density functions in the space of the observables of a survey -- we should not attempt to "invert" the data from the space of observables into the physical space of the Galaxy. Currently just one class of model has the required capability, so-called "torus models". A pilot application of torus models to understanding the structure of the Galaxy's thin and thick discs has already produced two significant results: a major revision of our best estimate of the Sun's velocity with respect to the Local Standard of Rest, and a successful prediction of the way in which the vertical velocity dispersion in the disc varies with distance from the Galactic plane.Comment: 13 pages. Invited review to appear in Pramana - journal of physics (Indian Academy of Sciences

Limitations of the Standard Gravitational Perfect Fluid Paradigm

We show that the standard perfect fluid paradigm is not necessarily a valid description of a curved space steady state gravitational source. Simply by virtue of not being flat, curved space geometries have to possess intrinsic length scales, and such length scales can affect the fluid structure. For modes of wavelength of order or greater than such scales eikonalized geometrical optics cannot apply and rays are not geodesic. Covariantizing thus entails not only the replacing of flat space functions by covariant ones, but also the introduction of intrinsic scales that were absent in flat space. In principle it is thus unreliable to construct the curved space energy-momentum tensor as the covariant generalization of a geodesic-based flat spacetime energy-momentum tensor. By constructing the partition function as an incoherent average over a complete set of modes of a scalar field propagating in a curved space background, we show that for the specific case of a static, spherically symmetric geometry, the steady state energy-momentum tensor that ensues will in general be of the form $T_{\mu\nu}=(\rho+p)U_{\mu}U_{\nu}+pg_{\mu\nu}+\pi_{\mu\nu}$ where the anisotropic $\pi_{\mu\nu}$ is a symmetric, traceless rank two tensor which obeys $U^{\mu}\pi_{\mu\nu}=0$. Such a $\pi_{\mu\nu}$ type term is absent for an incoherently averaged steady state fluid in a spacetime where there are no intrinsic length scales, and in principle would thus be missed in a covariantizing of a flat spacetime $T_{\mu\nu}$. While the significance of such $\pi_{\mu\nu}$ type terms would need to be evaluated on a case by case basis, through the use of kinetic theory we reassuringly find that the effect of such $\pi_{\mu\nu}$ type terms is small for weak gravity stars where perfect fluid sources are commonly used.Comment: Final version to appear in General Relativity and Gravitation (the final publication is available at http://www.springerlink.com). 29 pages, 1 figur