Journal  1 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.  2 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.  3 Sheikhi, N., Hasheminia, M., Khalaj, P., Haghi, H., Hasani Zonoozi, A., Baumgardt, H., "The binary fraction and mass segregation in Alpha Persei open cluster", MNRAS, 457: (1), 10281036, (2016).
Abstract: We have obtained membership probabilities of stars within a field of ∼3deg from the centre of the open cluster Alpha Persei using proper motions and photometry from the PPMXL and Widefield Infrared Survey Explorer catalogues. We have identified 810 possible stellar members of Alpha Persei. We derived the global and radial presentday mass function (MF) of the cluster and found that they are well matched by twostage powerlaw relations with different slopes at different radii. The global MF of Alpha Persei shows a turnover at m = 0.62 M⊙ with low and highmass slopes of αlow = 0.50 ± 0.09 (0.1 < m/ M⊙ < 0.62) and αhigh = 2.32 ± 0.14 (0.62 ≤ m/ M⊙ < 4.68), respectively. The highmass slope of the cluster increases from 2.01 inside 1 ∘.10 to 2.63 outside 2 ∘.2, whereas the mean stellar mass decreases from 0.95 to 0.57 M⊙ in the same regions, signifying clear evidence of mass segregation in the cluster. From an examination of the highquality colour–magnitude data of the cluster and performing a series of Monte Carlo simulations, we obtained a binary fraction of fbin = 34 ± 12 per cent for stars with 0.70 < m/ M⊙ < 4.68. This is significantly larger than the observed binary fraction, indicating that this open cluster contains a large population of unresolved binaries. Finally, we corrected the MF slopes for the effect of unresolved binaries and found low and highmass slopes of αlow = 0.89 ± 0.11 and αhigh = 2.37 ± 0.09 and a total cluster mass of 352 M⊙ for Alpha Persei.  4 Hasani Zonoozi, A., Rabiee, M., Haghi, H., Küpper, A. H. W., "THE SIZES OF GLOBULAR CLUSTERS AS TRACERS OF GALACTIC HALO POTENTIALS", The Astrophysical Journal, 818: (1), 114, (2016).
Abstract: We present Nbody simulations of globular clusters, exploring the effect of different galactic potentials on cluster sizes, rh. For various galactocentric distances, RG, we assess how cluster sizes change when we vary the virial mass and concentration of the host galaxy's darkmatter halo. We show that sizes of GCs are determined by the local galactic mass density rather than the virial mass of the host galaxy. We find that clusters evolving in the inner halos of less concentrated galaxies are significantly more extended than those evolving in more concentrated ones, while the sizes of those orbiting in the outer halo are almost independent of concentration. Adding a baryonic component to our galaxy models does not change these results much, since its effect is only significant in the very inner halo. Our simulations suggest that there is a relation between rh and RG, which systematically depends on the physical parameters of the halo. Hence, observing such relations in individual galaxies can put a new observational constraint on darkmatter halo characteristics. However, by varying the halo mass in a wide range of ${10}^{9}leqslant {M}_{mathrm{vir}}/{M}_{odot }leqslant {10}^{13}$, we find that the rh − RG relationship will be nearly independent of halo mass, if one assumes Mvir and cvir as two correlated parameters, as is suggested by cosmological simulations.  5 Haghi, H., Hasani Zonoozi, A., Kroupa, P., Banerjee, S., Baumgardt, H., "Possible smokinggun evidence for initial mass segregation in revirialized postgas expulsion globular clusters", MNRAS, 454: (4), 38723885, (2015).
Abstract: We perform a series of direct Nbody calculations to investigate the effect of residual gas expulsion from the gasembedded progenitors of presentday globular clusters (GCs) on the stellar mass function (MF). Our models start either tidally filling or underfilling, and either with or without primordial mass segregation. We cover 100 Myr of the evolution of modelled clusters and show that the expulsion of residual gas from initially masssegregated clusters leads to a significantly shallower slope of the stellar MF in the low (m ≤ 0.50 M⊙) and intermediatemass (≃ 0.50–0.85 M⊙) regime. Therefore, the imprint of residual gas expulsion and primordial mass segregation might be visible in the presentday MF. We find that the strength of the external tidal field, as an essential parameter, influences the degree of flattening, such that a primordially masssegregated tidally filling cluster with rh/rt ≥ 0.1 shows a strongly depleted MF in the intermediate stellar mass range. Therefore, the shape of the presentday stellar MF in this mass range probes the birth place of clusters in the Galactic environment. We furthermore find that this flattening agrees with the observed correlation between the concentration of a cluster and its MF slope, as found by de Marchi et al.. We show that if the expansion through the residual gas expulsion in primordial mass segregated clusters is the reason for this correlation then GCs most probably formed in strongly fluctuating local tidal fields in the early protoMilky Way potential, supporting the recent conclusion by Marks & Kroupa. 
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). 
