Journal  1 Haghi, H., Khalaj, P., Hasani Zonoozi, A., Kroupa, P., "A Possible Solution for the M/L–[Fe/H] Relation of Globular Clusters in M31. II. The Age–Metallicity Relation", ApJ , 839: (1), 16, (2017).
Abstract: This is the second paper in a series in which we present a new solution to reconcile the prediction of single stellar population (SSP) models with the observed stellar masstolight (M/L) ratios of globular clusters (GCs) in M31 and their trend with respect to $[mathrm{Fe}/{
m{H}}]$. In the present work, our focus is on the empirical relation between age and metallicity for GCs and its effect on the M/L ratio. Assuming that there is an anticorrelation between the age of M31 GCs and their metallicity, we evolve dynamical SSP models of GCs to establish a relation between the M/L ratio (in the V and K band) and metallicity. We then demonstrate that the established M/L–[Fe/H] relation is in perfect agreement with that of M31 GCs. In our models, we consider both the canonical initial mass function (IMF) and the topheavy IMF, depending on cluster birth density and metallicity as derived independently from Galactic GCs and ultracompact dwarf galaxies by Marks et al. Our results signify that the combination of the density and metallicitydependent topheavy IMF, the anticorrelation between age and metallicity, stellar evolution, and standard dynamical evolution yields the best possible agreement with the observed trend of M/L–[Fe/H] for M31 GCs.  2 Hasani Zonoozi, A., Haghi, H., Kroupa, P., Küpper, A. H. W., Baumgardt, H., "Direct Nbody simulations of globular clusters – III. Palomar 4 on an eccentric orbit", Mon. Not. R. Astron. Soc., 467: (1), 758767, (2017).
Abstract: Palomar 4 (Pal 4) is a lowdensity globular cluster (GC) with a current mass ≈30 000 M⊙ in the outer halo of the Milky Way with a twobody relaxation time of the order of a Hubble time. Yet, it is strongly mass segregated and contains a stellar mass function depleted of lowmass stars. Pal 4 was either born this way or it is a result of extraordinary dynamical evolution. Since twobody relaxation cannot explain these signatures alone, enhanced massloss through tidal shocking may have had a strong influence on Pal 4. Here, we compute a grid of direct Nbody simulations to model Pal 4 on various eccentric orbits within the Milky Way potential to find likely initial conditions that reproduce its observed mass, halflight radius, stellar slope of the mass function and lineofsight velocity dispersion. We find that Pal 4 is most likely orbiting on an eccentric orbit with an eccentricity of e ≈ 0.9 and pericentric distance of Rp ≈ 5 kpc. In this scenario, the required 3D halfmass radius at birth is similar to the average sizes of typical GCs (Rh ≈ 4–5 pc), while its birth mass is about M0 ≈ 105 M⊙. We also find a high degree of primordial mass segregation among the cluster stars, which seems to be necessary in every scenario we considered. Thus, using the tidal effect to constrain the perigalactic distance of the orbit of Pal 4, we predict that the proper motion of Pal 4 should be in the range −0.52 ≤ μδ ≤ −0.38 mas yr−1 and −0.30 ≤ μαcos δ ≤ − 0.15 mas yr−1.
 3 Haghi, H., Amiri, ., "Testing Modified Gravity with Dwarf Spheroidal Galaxies", MNRAS, 463, 19441951, (2016).
Abstract: The observed velocity dispersion of the classical dwarf spheroidal (dSph) galaxies of the Milky Way (MW) requires the Newtonian stellar masstolight (M★/L) ratios in the range of about 10 to more than 100 solar units, that are well outside the acceptable limit predicted by stellar population synthesis (SPS) models. Using Jeans analysis, we calculate the lineofsight velocity dispersion (σemphlos) of stars in eight MW dSphs in the context of the Modified Gravity (MOG) theory of Moffat, assuming a constant M★/L ratio without invoking the exotic cold dark matter. First, we use the weak field approximation of MOG and assume the two parameters α and μ of the theory to be constant as has already been inferred from fitting to the observed rotational data of the THINGS catalog of galaxies. We find that the derived M★/L ratios for almost all dSphs are too large to be explained by the stellar population values. In order to fit the lineofsight velocity dispersions of the dSph with reasonable M★/L values we must vary α and μ on a case by case basis. A common pair of values cannot be found for all dSphs. Comparing with the values found from rotation curve fitting, it appears that μ correlates strongly with galaxy luminosity, shedding doubt on it as a universal constant  4 Hasani Zonoozi, A., Haghi, H., Kroupa, P., "A POSSIBLE SOLUTION FOR THE M/L–[Fe/H] RELATION OF GLOBULAR CLUSTERS IN M31. I. A METALLICITY AND DENSITYDEPENDENT TOPHEAVY IMF", APJ, 826: (1), 18, (2016).
Abstract: The observed masstolight (M/L) ratios of a large sample of globular clusters (GCs) in M31 show an inverse trend with metallicity compared to what is expected from simple stellar population (SSP) models with an invariant canonical stellar initial mass function (IMF), in the sense that the observed M/L ratios decrease with increasing metallicity. We show that when incorporating the effect of dynamical evolution the SSP models with a canonical IMF cannot explain the decreasing M/L ratios with increasing metallicity for the M31 GCs. The recently derived topheavy IMF as a function of metallicity and embedded cluster density is proposed to explain the lowerthanexpected M/L ratios of metalrich GCs. We find that the SSP models with a topheavy IMF, retaining a metallicity and clustermassdependent fraction of the remnants within the clusters, and taking standard dynamical evolution into account, can successfully explain the observed M/L–[Fe/H] relation of M31 GCs. Thus we propose that the kinematic data of GCs can be used to constrain the topheaviness of the IMF in GCs.  5 Haghi, H., Ebadati Bazkiaei, A., Hasani Zonoozi, A., Kroupa, p., "Declining rotation curves of galaxies as a test of gravitational theory", MNRAS, 458: (4), 41724187, (2016).
Abstract: 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 per cent 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 nonnegligible 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 masstolight ratio in terms of stellar population synthesis than the ones implied without the EFE. 
Conferences  1 Haghi, H., Kroupa, P., Hasani Zonoozi, A., Banerjee, S., "Possible smokinggun evidence for initial mass segregation in revirialized postgas expulsion starburst clusters ", Modelling and Observing Dense Stellar Clusters in Chile,Universidad de Concepción, Chile
, 2929, (2015).
Abstract: In the present study, we have carried out a series of direct Nbody calculations to investigate the effect of residualgas expulsion from the globular clusters' embedded progenitors on the stellar mass function of different models on circular orbits, starting either tidally filling or underfilling, and either with or without primordial mass segregation. We covered the first 100 Myr of the evolution of modeled clusters and showed for the first time that the expulsion of residual gas from initially masssegregated models leads to the signi_cantly shallower slope of the stellar mass function in the low (≃M _ 0.5M⨀) and intermediatemass ( 0.5 <= 0.8 M⨀) regime. Therefore the imprint of residual gas expulsion, as a direct evidence of primordial segregation, might be visible in the present day MF. We also found that the strength of the external tidal _led, as an essential parameter, inuences the degree of attening in the intermediatemass range, such that the MFs of primordially masssegregated tidallyfilliing clusters with r h =rt values larger than 0.1 show a strongly depleted mass function in the intermediate stellar mass range, while the slower massloss rate of clusters initially lying inside their tidal radii, takes a longer time to lose a given amount of mass. Therefore, the shape of present day MF in intermediate stellar mass range probes the birth place of clusters in Galactic environment.  2 Haghi, H., "How does the gas expulsion phase affect the initial conditions of star clusters?
", Workshop,The Early Life of Stellar Clusters: Formation and Dynamics, 2525, (2014).
Abstract: The study of stellar clusters has played an important rule in developing of our knowledge about the universe. Since most stars in the galactic disc may originate in star clusters, these systems can therefore be investigated as the fundamental building blocks of galaxies to understand the origins of the properties of the galactic stellar population, such as the galactic stellar mass function. Detailed knowledge of the initial condition of globular clusters, is necessary to understand the evolution of stellar system including all physical processes that may happen during their evolution. Zonoozi et al. (2011, 2014), have been found that dynamical mass segregation alone cannot explain the mass function flattening in the cluster centre when starting from a canonical Kroupa IMF, and that a very high degree of primordial mass segregation would be necessary to explain this discrepancy. We concluded that such initial conditions for Pal 14 and Pal 4 might be obtained by a violent early gasexpulsion phase from an embedded cluster born with mass segregation and a canonical IMF for lowmass stars. After modelling some realistic Galactic clusters and finding the initial conditions, as a next stage we need to understand how this connects to what we know of star formation. So the t=0 condition which we constrained is the state of the cluster after revirialisation and after gas expulsion. But how does the prior phase work, and what are the possible birth configurations, given the t=0 boundary condition? Which birth conditions do gasexpulsion computations covering the first 100 Myr of a Pal 14/4 type cluster require for the postgas expulsion revirialised cluster to match up with the initial conditions found for Pal 14/4? Did gas expulsion even play a dynamical role for Pal 14/4? This work would require many more stars in the Nbody models, but covers a much shorter time, and would be done without binaries (as a first step). In my talk I therefore try to answer these questions.  3 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).  4 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).  5 Haghi, H., "Direct Nbody simulations of globular clusters", 1st Doha International Astronomy Conference, Doha, Qatar, (2013). 
