Journal  1 Hasani Zonoozi, A., Haghi, H., H. W. Küpper, A., Baumgardt, H., J. Frank, M., Kroupa, P., "Direct Nbody simulations of globular clusters – II. Palomar 4", MNRAS, 440, 31723183 , (2014).
Abstract: We use direct Nbody calculations to study the evolution of the unusually extended outer halo globular cluster Palomar 4 (Pal 4) over its entire lifetime in order to reproduce its observed mass, halflight radius, velocity dispersion and mass function slope at different radii. We find that models evolving on circular orbits, and starting from a nonmass segregated, canonical initial mass function (IMF) can reproduce neither Pal 4s overall mass function slope nor the observed amount of mass segregation. Including either primordial mass segregation or initially flattened IMFs does not reproduce the observed amount of mass segregation and mass function flattening simultaneously. Unresolved binaries cannot reconcile this discrepancy either. We find that only models with both a flattened IMF and primordial segregation are able to fit the observations. The initial (i.e. after gas expulsion) mass and halfmass radius of Pal 4 in this case are about 57 000 M⊙ and 10 pc, respectively. This configuration is more extended than most globular clusters we observe, showing that the conditions under which Pal 4 formed must have been significantly different from that of the majority of globular clusters. We discuss possible scenarios for such an unusual configuration of Pal 4 in its early years.  2 Derakhshani , K., Haghi, H., "ERRATUM: THE MOND EXTERNAL FIELD EFFECT ON THE DYNAMICS OF THE GLOBULAR CLUSTERS:
GENERAL CONSIDERATIONS AND APPLICATION TO NGC 2419", ApJ , 785, 166, (2014).
Abstract: In this paper, we investigate the external field effect in the context of the MOdified Newtonian Dynamics (MOND) on the surface brightness and velocity dispersion profiles of globular clusters (GCs). Using NMODY, which is an Nbody simulation code with a MOND potential solver, we show that the general effect of the external field for diffuse clusters, which obey MOND in most of their parts, is that it pushes the dynamics toward the Newtonian regime. On the other hand, for more compact clusters, which are essentially Newtonian in their inner parts, the external field is effective mainly in the outer parts of compact clusters. As a case study, we then choose the remote Galactic GC NGC 2419. By varying the cluster mass, halflight radius, and masstolight ratio, we aim to find a model that will reproduce the observational data most effectively, using NMODY. We find that even if we take the Galactic external field into account, a Newtonian Plummer sphere represents the observational data better than MOND to an order of magnitude in terms of the total χ2 of surface brightness and velocity dispersion.  3 Haghi, H., Ghasemi, H., Zhao, H. S., "Evaluation of New MOND Interpolating Function
with Rotation Curves of Galaxies", Iranian Journal of Astronomy and Astrophysics, 1: (1), 4356, (2013).
Abstract: The rotation curves of a sample of 46 low and highsurface brightness galaxies are considered in the context of Milgrom's modi_ed dynamics (MOND) to test a new interpolating function proposed by Zhao et al. (2010) [1] and compare with the results of simple interpolating function. The predicted rotation curves are calculated from the total baryonic matter based on the Bband surface photometry, and the observed distribution of neutral hydrogen, in which the one adjustable parameter is the stellar masstolight ratio. The predicted rotation curves generally agree with the observed curves for both interpolating functions. We show that the _tted M=L in the Bband correlates with BV color in the sense expected from what we know about stellar population synthesis models. Moreover, the masstolight ratios of MOND with new interpolating function is in consistent with scaled Salpeter's initial mass function of the SPS scheme, while those of MOND with simple interpolating function favor Kroupa IMF.  4 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, 29172932 , (2012).
Abstract: We obtained precise lineofsight 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 broadband imaging with the LowResolution 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 lowmass 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 lowermass 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.  5 Malekjani , M., Haghi, H., MohammadZadeh Jassur, D., "The effect of cosmological background dynamics on the spherical collapse in MOND
", New Astron , 17, 149153, (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 lowdensity 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 lowdensity 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. 
Conferences  1 Haghi, H., "The remote Galactic globular clusters as a tool to test
gravity models and direct Nbody simulation", Dynamics and kinetic theory of
selfgravitating systems, IHP Gravasco Trimester, Paris, (2013).  2 Haghi, H., "How primordial mass segregation can increase the size scale
of the star clusters", VlasovPoisson : the numerical approach and its limits, IHP Gravasco Trimester, Paris, (2013).  3 Haghi, H., "Direct Nbody simulations of globular clusters", 1st Doha International Astronomy Conference, Doha, Qatar, (2013).  4 Haghi, H., "Distant star clusters of the Milky Way in MOND ", Modified gravity approach to dark sector, Strasbourg, France, (2010).  5 Haghi, H., "Testing Fundamental Physics with Distant star Clusters", Tidal Dwarf Galaxies, Physics Centre BadHonnef, Germany, (2009). 
