Retention Fractions for Globular Cluster Neutron Stars

Fokker-Planck models are used to give estimates for the retention fractions for newly-born neutron stars in globular clusters as a function of kick velocity. These can be used to calculate the present day numbers of neutron stars in globular clusters and in addressing questions such as the origin of millisecond pulsars. As an example, the Population I kick velocity distribution of Lyne & Lorimer (1994) is used to estimate the retained fractions of neutron stars originating as single stars and in binary systems. For plausible initial conditions fewer than 4% of single neutron stars are retained. The retention fractions from binary systems can be 2 to 5 times higher. The dominant source of retained neutron stars is found to be through binary systems which remain bound after the first supernova, ie. high-mass X-ray binaries. The retained fraction decreases with an increasing number of progenitors, but the retention fraction decreases more slowly than the number of progenitors increases. On balance, more progenitors give more neutron stars in the cluster.Comment: To appear in MNRAS, 15 pages, LaTeX, requires MN and epsf styles, includes 3 PS Figures, compressed, uuencoded forma

Non-analytic magnetic field dependence of quasi-particle properties of two-dimensional metals

We show that in a weak external magnetic field H the quasi-particle residue and the renormalized electron Lande factor of two-dimensional Fermi liquids exhibit a non-analytic magnetic field dependence proportional to |H| which is due to electron-electron interactions. We explicitly calculate the corresponding prefactors to second order in the interaction and show that they are determined by low-energy scattering processes involving only momenta close to the Fermi surface. Experimentally, these non-analytic terms can be detected from measurements of the magnetic field dependence of the density of states and the magnetoconductivity.Comment: 11 pages, 5 figure

The outskirts of globular clusters as modified gravity probes

In the context of theories of gravity modified to account for the observed dynamics of galactic systems without the need to invoke the existence of dark matter, a prediction often appears regarding low acceleration systems: wherever $a$ falls below $a_{0}$ one should expect a transition from the classical to the modified gravity regime.This modified gravity regime will be characterised by equilibrium velocities which become independent of distance, and which scale with the fourth root of the total baryonic mass, $V^{4} \propto M$. The two above conditions are the well known flat rotation curves and Tully-Fisher relations of the galactic regime. Recently however, a similar phenomenology has been hinted at, at the outskirts of Galactic globular clusters, precisely in the region where $a<a_{0}$. Radial profiles of the projected velocity dispersion have been observed to stop decreasing along Keplerian expectations, and to level off at constant values beyond the radii where $a<a_{0}$. We have constructed gravitational equilibrium dynamical models for a number of globular clusters for which the above gravitational anomaly has been reported, using a modified Newtonian force law which yields equilibrium velocities equivalent to MOND. We find models can be easily constructed having an inner Newtonian region and an outer modified gravity regime, which reproduce all observational constraints, surface brightness profiles, total masses and line of sight velocity dispersion profiles. Through the use of detailed single stellar population models tuned individually to each of the globular clusters in question, we derive estimates of the total masses for these systems. Interestingly, we find that the asymptotic values of the velocity dispersion profiles are consistent with scaling with the fourth root of the total masses, as expected under modified gravity scenarios.Comment: Accepted in ApJ, 13 pages, 7 figure

Functional renormalization group approach to the Ising-nematic quantum critical point of two-dimensional metals

Using functional renormalization group methods, we study an effective low-energy model describing the Ising-nematic quantum critical point in two-dimensional metals. We treat both gapless fermionic and bosonic degrees of freedom on equal footing and explicitly calculate the momentum and frequency dependent effective interaction between the fermions mediated by the bosonic fluctuations. Following earlier work by S.-S. Lee for a one-patch model, Metlitski and Sachdev [Phys. Rev. B {\bf{82}}, 075127] recently found within a field-theoretical approach that certain three-loop diagrams strongly modify the one-loop results, and that the conventional 1/N expansion breaks down in this problem. We show that the singular three-loop diagrams considered by Metlitski and Sachdev are included in a rather simple truncation of the functional renormalization group flow equations for this model involving only irreducible vertices with two and three external legs. Our approximate solution of these flow equations explicitly yields the vertex corrections of this problem and allows us to calculate the anomalous dimension $\eta_{\psi}$ of the fermion field.Comment: 21 pages, 10 figure

Searching for Dark Matter with Paleo-Detectors

A large experimental program is underway to extend the sensitivity of direct detection experiments, searching for interaction of Dark Matter with nuclei, down to the neutrino floor. However, such experiments are becoming increasingly difficult and costly due to the large target masses and exquisite background rejection needed for the necessary improvements in sensitivity. We investigate an alternative approach to the detection of Dark Matter-nucleon interactions: Searching for the persistent traces left by Dark Matter scattering in ancient minerals obtained from much deeper than current underground laboratories. We estimate the sensitivity of paleo-detectors, which extends far beyond current upper limits for a wide range of Dark Matter masses. The sensitivity of our proposal also far exceeds the upper limits set by Snowden-Ifft et al. more than three decades ago using ancient Mica in an approach similar to paleo-detectors.Comment: 6 pages, 2 figures. v2: significant revisions. v3: matches the published versio

Central Proper-Motion Kinematics of NGC 6752

We present proper motions derived from WFPC2 imaging for stars in the core of the peculiar globular cluster NGC 6752. The central velocity dispersion in both components of the proper motion is 12 km/s. We discuss the implications of this result as well as the intrinsic difficulties in making such measurements. We also give an alternative correction for the 34-row problem in the WFPC2 CCDs.Comment: 25 pages, 7 figures, 1 table included. Accepted for publication in A

The Initial Mass Functions in the Super-Star-Clusters NGC 1569A and NGC 1705-1

I use recent photometric and stellar velocity dispersion measurements of the super-star-clusters (SSCs) NGC 1569A and NGC 1705-1 to determine their present-day luminosity/mass (L_V/M) ratios. I then use the inferred L_V/M ratios, together with population synthesis models of evolving star-clusters, to constrain the initial-mass-functions (IMFs) in these objects. I find that (L_V/M)_solar=28.9 in 1569A, and (L_V/M)_solar=126 in 1705-1. It follows that in 1569A the IMF is steep with alpha~2.5 for m**(-alpha)dm IMFs which extend to 0.1 M_sun. This implies that most of the stellar mass in 1569A is contained in low-mass (< 1 M_sun) stars. However, in 1705-1 the IMF is either flat, with alpha<2$, or it is truncated at a lower mass-limit between 1 and 3 M_sun. I compare the inferred IMFs with the mass functions (MFs) of Galactic globular clusters. It appears that 1569A has a sufficient reservoir of low-mass stars for it to plausibly evolve into an object similar to Galactic globular clusters. However, the apparent deficiency of low-mass stars in 1705-1 may make it difficult for this SSC to become a globular cluster. If low-mass stars do dominate the cluster mass in 1705-1, the large L_V/M ratio in this SSC may be evidence that the most massive stars have formed close to the cluster cores.Comment: ApJ, in press. 19 Pages, Latex; [email protected]

Temporal distortion of annual modulation at low recoil energies

We show that the main features of the annual modulation of the signal expected in a WIMP direct detection experiment, i.e. its sinusoidal dependence with time, the occurrence of its maxima and minima during the year and (under some circumstances) even the one-year period, may be affected by relaxing the isothermal sphere hypothesis in the description of the WIMP velocity phase space. The most relevant effect is a distortion of the time-behaviour at low recoil energies for anisotropic galactic halos. While some of these effects turn out to be relevant at recoil energies below the current detector thresholds, some others could already be measurable, although some degree of tuning between the WIMP mass and the experimental parameters would be required. Either the observation or non-observation of these effects could provide clues on the phase space distribution of our galactic halo.Comment: 4 pages, 4 figures, typeset with ReVTeX4. The paper may also be found at http://www.to.infn.it/~fornengo/papers/distortion.ps.g

Evolution of Multi-mass Globular Clusters in Galactic Tidal Field with the Effects of Velocity Anisotropy

We study the evolution of globular clusters with mass spectra under the influence of the steady Galactic tidal field, including the effects of velocity anisotropy. Similar to single-mass models, velocity anisotropy develops as the cluster evolves, but the degree of anisotropy is much smaller than isolated clusters. Except for very early epochs of the cluster evolution, nearly all mass components become tangentially anisotropic at the outer parts. We have compared our results with multi-mass, King-Michie models. The isotropic King model better fits to the Fokker-Planck results because of tangential anisotropy. However, it is almost impossible to fit the computed density profiles to the multi-mass King models for all mass components. Thus if one attempts to derive global mass function based on the observed mass function in limited radial range using multi-mass King models, one may get somewhat erratic results, especially for low mass stars. We have examined how the mass function changes in time. Specifically, we find that the power-law index of the mass function decreases monotonically with the total mass of the cluster. This appears to be consistent with the behaviour of the observed slopes of mass functions for a limited number of clusters, although it is premature to compare quantitatively because there are other mechanisms in contributing the evaporation of stars from the clusters. The projected velocity profiles for anisotropic models with the apocenter criterion for evaporation show significant flattening toward the tidal radius compared to isotropic model or anisotropic model with the energy criterion. Such a behaviour of velocity profile appears to be consistent with the observed profiles of collapsed cluster M15.Comment: 13 pages including 18 figures in mn styl