Hosein Haghi

Testing Fundamental Physics with Distant Star Clusters: Analysis of Observational Data on Palomar 14

We use the distant outer halo globular cluster Palomar 14 as a test case for classical versus modified Newtonian dynamics (MOND). Previous theoretical calculations have shown that the line-of-sight velocity dispersion predicted by these theories can differ by up to a factor of 3 for such sparse, remote clusters like Pal 14. We determine the line-of-sight velocity dispersion of Palomar 14 by measuring radial velocities of 17 red giant cluster members obtained using the Very Large Telescope and Keck telescope. The systemic velocity of Palomar 14 is (72.28 ± 0.12) km s^(–1). The derived velocity dispersion of (0.38 ± 0.12) km s^(–1) of the 16 definite member stars is in agreement with the theoretical prediction for the classical Newtonian case according to Baumgardt et al. In order to exclude the possibility that a peculiar mass function might have influenced our measurements, we derived the clusters main-sequence mass function down to 0.53 M⊙ using archival images obtained with the Hubble Space Telescope. We found a mass function slope of α = 1.27 ± 0.44, which is, compared to the canonical mass function, a significantly shallower slope. The derived lower limit on the clusters mass is higher than the theoretically predicted mass in the case of MOND. Our data are consistent with a central density of ρ_0 = 0.1 M⊙ pc^(–3). We need no dark matter in Palomar 14. If the cluster is on a circular orbit, our spectroscopic and photometric results argue against MOND, unless the cluster experienced significant mass loss.

Direct N‐body simulations of globular clusters – I. Palomar 14

We present the first ever direct N-body computations of an old Milky Way globular cluster over its entire lifetime on a star-by-star basis. Using recent GPU hardware at Bonn University, we have performed a comprehensive set of N-body calculations to model the distant outer halo globular cluster Palomar 14 (Pal 14). Pal 14 is unusual in that its mean density is about 10 times smaller than that in the solar neighbourhood. Its large radius as well as its low-mass make it possible to simulate Pal 14 on a star-by-star basis. By varying the initial conditions, we aim at finding an initial N-body model which reproduces the observational data best in terms of its basic parameters, i.e. half-light radius, mass and velocity dispersion. We furthermore focus on reproducing the stellar mass function slope of Pal 14 which was found to be significantly shallower than in most globular clusters. While some of our models can reproduce Pal 14’s basic parameters reasonably well, we find that dynamical mass segregation alone cannot explain the mass function slope of Pal 14 when starting from the canonical Kroupa initial mass function (IMF). In order to seek an explanation for this discrepancy, we compute additional initial models with varying degrees of primordial mass segregation as well as with a flattened IMF. The necessary degree of primordial mass segregation turns out to be very high, though, such that we prefer the latter hypothesis which we discuss in detail. This modelling has shown that the initial conditions of Pal 14 after gas expulsion must have been a half-mass radius of about 20 pc, a mass of about 50 000 M⊙, and possibly some mass segregation or an already established non-canonical IMF depleted in low-mass stars. Such conditions might be obtained by a violent early gas-expulsion phase from an embedded cluster born with mass segregation. Only at large Galactocentric radii are clusters likely to survive as bound entities the destructive gas-expulsion process we seem to have uncovered for Pal 14. In addition, we compute a model with a 5 per cent primordial binary fraction to test if such a population has an effect on the cluster’s evolution. We see no significant effect, though, and moreover find that the binary fraction of Pal 14 stays almost the same and gives the final fraction over its entire lifetime due to the cluster’s extremely low density. Low-density, halo globular clusters might therefore be good targets to test primordial binary fractions of globular clusters.

The velocity dispersion and mass function of the outer halo globular cluster Palomar 4

We obtained precise line-of-sight radial velocities of 23 member stars of the remote halo globular cluster Palomar 4 (Pal 4) using the High Resolution Echelle Spectrograph (HIRES) at the Keck I telescope. We also measured the mass function of the cluster down to a limiting magnitude of V 28 mag using archival HST /WFPC2 imaging. We derived the cluster’s surface brightness prole based on the WFPC2 data and on broad-band imaging with the Low-Resolution Imaging Spectrometer (LRIS) at the Keck II telescope. We nd a mean cluster velocity of 72 :55 0:22 km s 1 and a velocity dispersion of 0:87 0:18 km s 1 . The global mass function of the cluster, in the mass range 0:55 6 M 6 0:85 M , is shallower than a Kroupa mass function and the cluster is signicantly depleted in low-mass stars in its center compared to its outskirts. Since the relaxation time of Pal 4 is of the order of a Hubble time, this points to primordial mass segregation in this cluster. Extrapolating the measured mass function towards lower-mass stars and including the contribution of compact remnants, we derive a total cluster mass of 29,800 M . For this mass, the measured velocity dispersion is consistent with the expectations of Newtonian dynamics and below the prediction of MOND. Pal 4 adds to the growing body of evidence that the dynamics of star clusters in the outer Galactic halo can hardly be explained by MOND.

Declining rotation curves of galaxies as a test of gravitational theory

Unlike Newtonian dynamics which is linear and obeys the strong equivalence principle, in any nonlinear gravitation such as Milgromian dynamics (MOND), the strong version of the equivalence principle is violated and the gravitational dynamics of a system is influenced by the external gravitational field in which it is embedded. This so called External Field Effect (EFE) is one of the important implications of MOND and provides a special context to test Milgromian dynamics. Here, we study the rotation curves (RCs) of 18 spiral galaxies and find that their shapes constrain the EFE. We show that the EFE can successfully remedy the overestimation of rotation velocities in 80\% of the sample galaxies in Milgromian dynamics fits by decreasing the velocity in the outer part of the RCs. We compare the implied external field with the gravitational field for non-negligible nearby sources of each individual galaxy and find that in many cases it is compatible with the EFE within the uncertainties. We therefore argue that in the framework of Milgromian dynamics, one can constrain the gravitational field induced from the environment of galaxies using their RCs. We finally show that taking into account the EFE yields more realistic values for the stellar mass-to-light ratio in terms of stellar population synthesis than the ones implied without the EFE.

The effect of primordial mass segregation on the size scale of globular clusters

We use direct

Possible smoking-gun evidence for initial mass segregation in re-virialized post-gas expulsion globular clusters

N

A Possible Solution for the M/L-[Fe/H] Relation of Globular Clusters in M31: A metallicity and density dependent top-heavy IMF

-body calculations to investigate the impact of primordial mass segregation on the size scale and mass-loss rate of star clusters in a galactic tidal field. We run a set of simulations of clusters with varying degrees of primordial mass segregation at various galactocentric radii and show that, in primordially segregated clusters, the early, impulsive mass-loss from stellar evolution of the most massive stars in the innermost regions of the cluster leads to a stronger expansion than for initially non-segregated clusters. Therefore, models in stronger tidal fields dissolve faster due to an enhanced flux of stars over the tidal boundary. Throughout their lifetimes, the segregated clusters are more extended by a factor of about 2, suggesting that (at least) some of the very extended globular clusters in the outer halo of the Milky Way may have been born with primordial mass segregation. We finally derive a relation between star-cluster dissolution time,

Testing modified gravity with dwarf spheroidal galaxies

T_{diss}

Observational Constraints on the Modified Gravity Model (MOG) Proposed by Moffat: Using the Magellanic System

, and galactocentric radius,

Tully-Fisher relation, key to dark companion of baryonic matter

R_G