1- Frank, M. J., Hilker, M., Baumgardt, H., Côté, P., Haghi, H., Küpper, A. H. W., Djorgovski, S. G., "The velocity dispersion and mass function of the outer halo globular cluster Palomar 4", Mon. Not. R. Astron. Soc, 423, 2917-2932 , (2012).
Abstract:
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 profile based on the WFPC2 data and on broad-band imaging with the Low-Resolution Imaging Spectrometer (LRIS) at the Keck II telescope. We find a mean cluster velocity of 72.55+/-0.22 km/s and a velocity dispersion of 0.87+/-0.18 km/s. The global mass function of the cluster, in the mass range 0.55<=M<=0.85 M_solar, is shallower than a Kroupa mass function and the cluster is significantly 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 29800 M_solar. For this mass, the measured velocity dispersion is consistent with the expectations of Newtonian dynamics and below the prediction of Modified Newtonian Dynamics (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. | 2- Malekjani , M., Haghi, H., Mohammad-Zadeh Jassur, D., "The effect of cosmological background dynamics on the spherical collapse in MOND
", New Astron , 17, 149-153, (2012).
Abstract:
The effect of background dynamics of the universe on formation of large scale structures in the framework of Modified Newtonian Dynamics (MOND) is investigated. A spherical collapse model is used for modeling the formation of the structures. This study is done in two extreme cases: (i) assuming a universe with a low-density baryonic matter without any cold dark matter and dark energy; (ii) a dark energy dominated universe with baryonic matter, without cold dark matter. We show that for the case (ii) the structures virialize at lower redshifts with larger radii compared to the low-density background universe. The dark energy slow downs the collapse of the structures. We show that our results are compatible with recent simulations of the structure formation in MOND. | 3- Hasani Zonoozi, A., H. W. K¨upper, A., Baumgardt, H., Haghi, H., Kroupa, P., Hilker, M., "Direct N-body Simulations of Globular Clusters – I. Palomar 14", Mon. Not. R. Astron. Soc., 411, 1989-2001, (2011).
Abstract:
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 000M, 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. | 4- Haghi, H., Baumgardt, H., Kroupa, P., "Distant star clusters of the Milky Way in MOND", Astron. Astrophys. (A&A), 527: (A33), 1-7, (2011).
Abstract:
We determine the mean velocity dispersion of six Galactic outer halo globular clusters, AM 1, Eridanus, Pal 3, Pal 4, Pal 15, and Arp 2 in the weak acceleration regime to test classical vs. modified Newtonian dynamics (MOND). Owing to the nonlinearity of MOND’s Poisson equation, beyond tidal effects, the internal dynamics of clusters is affected by the external field in which they are immersed. For the studied clusters, particle accelerations are much lower than the critical acceleration a0 of MOND, but the motion of stars is neither dominated by internal accelerations (ai ae) nor external accelerations (ae ai). We use the N-body code N-MODY in our analysis, which is a particle-mesh-based code with a numerical MOND potential solver developed by Ciotti et al.
(2006, ApJ, 640, 741) to derive the line-of-sight velocity dispersion by adding the external field effect. We show that Newtonian dynamics predicts a low-velocity dispersion for each cluster, while in modified Newtonian dynamics the velocity dispersion is much higher. We calculate the minimum number of measured stars necessary to distinguish between Newtonian gravity and MOND with the Kolmogorov-Smirnov test. We also show that for most clusters it is necessary to measure the velocities of between 30 to 80 stars to distinguish between both cases. Therefore the observational measurement of the line-of-sight velocity dispersion of these clusters will provide a test for MOND. | 5- Hasani Zonoozi, A., Haghi, H., "The Distinguishing Factor for Gravity Models: Stellar Population Synthesis", Astron. Astrophys. (A&A), 524, A53-1-8, (2010).
Abstract:
Alternative gravitations of Milgrom (MOND), Moffat (MOG), and CDM scenarios all simulate rotation curves of spirals with reasonable details. They display significant disparities however in predicting the stellar mass-to-light (M∗/L) ratios of the galaxies. We maintain this feature could serve as a distinguishing factor between different alternative theories. We analyze the rotation curves of 46 low- and high-surface brightness galaxies and compare the resulting M∗/Ls with the predictions of the Stellar Population Synthesis (SPS) scheme. The color–M∗/L correlation obtained for MOND is consistent with predictions of SPS models. MOG does not show this consistency, and the M∗/Ls of CDM model shows large dispersions. Furthermore, M∗/L ratios of MOND with Bekenstein interpolating function favor Kroupa’s initial mass function (IMF) of the SPS scheme, while those of MOND with standard and simple interpolating functions are consistent with Salpeter’s IMF. Here is another indication to differentiate between different IMFs that are used in SPS context. |
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