arXiv subjects

Akram Hasani Zonoozi

Publications and source records attributed to Akram Hasani Zonoozi.

At least 37 records · Page 2Linked to original sources

arXiv2024

Has the Palomar 14 globular cluster been captured by the Milky Way?

We examine a new scenario to model the outer halo globular cluster (GC) Pal 14 over its lifetime by performing a comprehensive set of direct N-body calculations. We assume Pal 14 was born in a now detached/disrupted dwarf galaxy with a strong tidal field. Pal 14 evolved there until the slope of the stellar mass function (MF) became close to the measured value which is observed to be significantly shallower than in most GCs. After about 2-3 Gyr, Pal 14 was then captured by the Milky Way (MW). Although the physical size of such a cluster is indistinguishable from a cluster that has lived its entire life in the MW, other parameters like its mass and the MF-slope, strongly depend on the time the cluster is taken from the dwarf galaxy. After being captured by the MW on a new orbit, the cluster expands and eventually reaches the appropriate mass and size of Pal 14 after 11.5 Gyr while reproducing the observed MF. These simulations thus suggest that Pal 14 may have formed in a dwarf galaxy with a post-gas-expulsion initial half-mass radius and mass of $r_h=7$ pc and $8<M/10^4<10 $ M$_{\odot}$, respectively, with a high degree of primordial mass segregation.

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arXiv2024

The formation and evolution of dark star clusters II: The impact of primordial mass segregation

We investigate the impact of primordial mass segregation on the formation and evolution of dark star clusters (DSCs). Considering a wide range of initial conditions, we conducted $N$-body simulations of globular clusters (GCs) around the Milky Way. In particular, we assume a canonical IMF for all GCs without natal kicks for supernovae remnants, namely neutron stars or black holes. Our results demonstrate that clusters with larger degrees of primordial mass segregation reach their DSC phase earlier and spend a larger fraction of their dissolution time in such a phase, compared to clusters without mass segregation. In primordially segregated clusters, the maximum Galactocentric distance that the clusters can have to enter the DSC phase is almost twice that of the clusters without primordial mass segregation. Primordially segregated clusters evolve with a higher number of stellar mass black holes, accelerating energy creation in their central regions and consequently increasing evaporation rates and cluster sizes during dark phases. The simulations reveal that aggregating heavy components at the centre doubles the time spent in the dark phase. Additionally, the study identifies potential links between simulated dark clusters and initial conditions of Milky Way globular clusters, suggesting some may transition to dark phases before dissolution. Higher primordial mass segregation coefficients amplify the average binary black hole formation rate by 2.5 times, raising higher expectations for gravitational wave emissions.

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arXiv2024

The effect of the environment-dependent stellar initial mass function on the photometric properties of star-forming galaxies

(Abridged) Observational estimates of galaxy properties rely on the inherent galaxy-wide initial mass function (gwIMF), which systematically varies with the global SFR and metallicity, as proposed by the integrated-galactic IMF (IGIMF) theory and supported by empirical evidence. We incorporate PARSEC and COLIBRI stellar isochrones into the GalIMF code, a galaxy chemical evolution (GCE) model featuring real-time updates of environment-dependent gwIMFs. This newly developed photometric GalIMF (photGalIMF) code allows the calculation of photometric properties for galaxies with diverse stellar populations. Subsequently, we analyze observed luminosities and metallicities of local star-forming galaxies to deduce their stellar masses assuming that they have constant SFRs over 13.6 Gyr. We also compute SFR$-$H$α$ luminosity relations for varying stellar metallicities using a separate stellar population synthesis code based on PEGASE. Comparing the IGIMF theory to the canonical universal IMF, our analysis reveals that estimates of the stellar masses and SFRs for local star-forming galaxies differ by factors of $\approx 2$ and 10, respectively. The computed gas-depletion timescale increases with gas mass, implying lower star formation efficiencies in more massive galaxies, possibly due to stronger feedback regulation, aligning with theoretical expectations. Additionally, the characteristic stellar mass buildup timescale increases with stellar mass, indicating that massive disk galaxies initiate star formation earlier than their low-mass counterparts. The photGalIMF code enables self-consistent computations of galactic photometry, self-consistently with GCE modelling within the context of an environment-dependent gwIMF. Utilizing Ks-band and H$α$ luminosities of galaxies, the outcomes include galaxy mass, SFR, and fitting functions for the SFR correction factor.

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arXiv2024

The impact of a top-heavy IMF on the formation and evolution of dark star clusters

The Spitzer instability leads to the formation of a black hole sub-system (BHSub) at the center of a star cluster providing energy to luminous stars (LSs) and increasing their rate of evaporation. When the self-depletion time of the BHSub exceeds the evaporation time of the LSs, a dark star cluster (DSC) will appear. Using the NBODY7 code, we performed a comprehensive set of direct \Nbody simulations over a wide range of initial conditions to study the pure effect of the top-heaviness of the IMF on the formation of the DSC phase. In the Galactic tidal field, top-heavy IMFs lead to the fast evaporation of LSs and the formation of DSCs. Therefore, DSCs can be present even in the outer region of the Milky Way (MW). To successfully transition to the DSC phase, the MW Globular Clusters (GCs) must possess an initial BH mass fraction of $\widetilde{\mathit{M}}_\mathrm{BH}(0)>0.05$. For star clusters with $\widetilde{\mathit{M}}_\mathrm{BH}(0)>0.08$, the DSC phase will be created for any given initial density of the cluster and Galactocentric distance. The duration of the cluster's lifetime spent in the DSC phase shows a negative (positive) correlation with the initial density, and Galactocentric distance of the star cluster if $\widetilde{\mathit{M}}_\mathrm{BH}(0)\leq 0.12$ ($\widetilde{\mathit{M}}_\mathrm{BH}(0)\geq 0.15$). Considering the canonical IMF, it is unlikely for any MW GCs to enter the DSC phase. We discuss the BH retention fraction in view of the observed properties of the GCs of the MW.

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arXiv2023

Stellar collisions in globular clusters: Constraints on the initial mass function of the first generation of stars

Globular clusters display an anticorrelation between the fraction of the first generation of stars ($N({\rm G1})/N({\rm tot})$) and the slope of the present-day mass function of the clusters ($α_{pd}$), which is particularly significant for massive clusters. In the framework of the binary-mediated collision scenario for the formation of the second-generation stars in globular clusters, we test the effect of a varying stellar initial mass function (IMF) of the G1 stars on the $(N({\rm G1})/N({\rm tot}))-α_{pd}$ anticorrelation. We use a simple collision model that has only two input parameters, the shape of the IMF of G1 stars and the fraction of G1 stars that coalesce to form second-generation stars. We show that a variable efficiency of the collision process is necessary in order to explain the $(N({\rm G1})/N({\rm tot}))-α_{pd}$ anticorrelation; however, the scatter in the anticorrelation can only be explained by variations in the IMF, and in particular by variations in the slope in the mass interval $\approx$ (0.1-0.5) M$_{\odot}$. Our results indicate that in order to explain the scatter in the $(N({\rm G1})/N({\rm tot}))-α_{pd}$ relation, it is necessary to invoke variations in the slope in this mass range between $\approx -0.9$ and $\approx -1.9$. Interpreted in terms of a Kroupa-like broken power law, this translates into variations in the mean mass of between $\approx 0.2$ and $0.55$ M$_{\odot}$. This level of variation is consistent with what is observed for young stellar clusters in the Milky Way and may reflect variations in the physical conditions of the globular cluster progenitor clouds at the time the G1 population formed or may indicate the occurrence of collisions between protostellar embryos before stars settle on the main sequence.

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arXiv2022

Has JWST already falsified dark-matter-driven galaxy formation?

The James Webb Space Telescope (JWST) discovered several luminous high-redshift galaxy candidates with stellar masses of $M_{*} \gtrsim 10^{9} \, \rm{M_{\odot}}$ at photometric redshifts $z_{\mathrm{phot}} \gtrsim 10$ which allows to constrain galaxy and structure formation models. For example, Adams et al. identified the candidate ID 1514 with $\log_{10}(M_{*}/M_{\odot}) = {9.8}_{-0.2}^{+0.2}$ located at $z_{\mathrm{phot}} = 9.85_{-0.12}^{+0.18}$ and Naidu et al. found even more distant candidates labeled as GL-z11 and GL-z13 with $\log_{10}(M_{*}/M_{\odot}) = 9.4_{-0.3}^{+0.3}$ at $z_{\mathrm{phot}}=10.9_{-0.4}^{+0.5}$ and $\log_{10}(M_{*}/M_{\odot}) = 9.0_{-0.4}^{+0.3}$ at $z_{\mathrm{phot}} = 13.1_{-0.7}^{+0.8}$, respectively. Assessing the computations of the IllustrisTNG (TNG50-1 and TNG100-1) and EAGLE projects, we investigate if the stellar mass buildup as predicted by the $Λ$CDM paradigm is consistent with these observations assuming that the early JWST calibration is correct and that the candidates are indeed located at $z \gtrsim 10$. Galaxies formed in the $Λ$CDM paradigm are by more than an order of magnitude less massive in stars than the observed galaxy candidates implying that the stellar mass buildup is more efficient in the early Universe than predicted by the $Λ$CDM models. This in turn would suggest that structure formation is more enhanced at $z \gtrsim 10$ than predicted by the $Λ$CDM framework. We show that different star formation histories could reduce the stellar masses of the galaxy candidates alleviating the tension. Finally, we calculate the galaxy-wide initial mass function (gwIMF) of the galaxy candidates assuming the integrated galaxy IMF theory. The gwIMF becomes top-heavy for metal-poor starforming galaxies decreasing therewith the stellar masses compared to an invariant canonical IMF.

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arXiv2022

Asymmetrical tidal tails of open star clusters: stars crossing their cluster's prah challenge Newtonian gravitation

After their birth a significant fraction of all stars pass through the tidal threshold (prah) of their cluster of origin into the classical tidal tails. The asymmetry between the number of stars in the leading and trailing tails tests gravitational theory. All five open clusters with tail data (Hyades, Praesepe, Coma Berenices, COIN-Gaia 13, NGC 752) have visibly more stars within dcl = 50 pc of their centre in their leading than their trailing tail. Using the Jerabkova-compact-convergent-point (CCP) method, the extended tails have been mapped out for four nearby 600-2000 Myr old open clusters to dcl>50 pc. These are on near-circular Galactocentric orbits, a formula for estimating the orbital eccentricity of an open cluster being derived. Applying the Phantom of Ramses code to this problem, in Newtonian gravitation the tails are near-symmetrical. In Milgromian dynamics (MOND) the asymmetry reaches the observed values for 50 < dcl/pc < 200, being maximal near peri-galacticon, and can slightly invert near apo-galacticon, and the Küpper epicyclic overdensities are asymmetrically spaced. Clusters on circular orbits develop orbital eccentricity due to the asymmetrical spill-out, therewith spinning up opposite to their orbital angular momentum. This positive dynamical feedback suggests Milgromian open clusters to demise rapidly as their orbital eccentricity keeps increasing. Future work is necessary to better delineate the tidal tails around open clusters of different ages and to develop a Milgromian direct n-body code.

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arXiv2022

The Escape of Globular Clusters from the Satellite Dwarf Galaxies of the Milky Way

Using numerical simulations, we have studied the escape of globular clusters (GCs) from the satellite dwarf spheroidal galaxies (dSphs) of the Milky Way (MW). We start by following the orbits of a large sample of GCs around dSphs in the presence of the MW potential field. We then obtain the fraction of GCs leaving their host dSphs within a Hubble Time. We model dSphs by a Hernquist density profile with masses between $10^7\,\mathrm{M}_{\odot}$ and $7\times 10^9\,\mathrm{M}_{\odot}$. All dSphs lie on the Galactic disc plane, but they have different orbital eccentricities and apogalactic distances. We compute the escape fraction of GCs from 13 of the most massive dSphs of the MW, using their realistic orbits around the MW (as determined by Gaia). The escape fraction of GCs from 13 dSphs is in the range $12\%$ to $93\%$. The average escape time of GCs from these dSphs was less than 8 $\,\mathrm{Gyrs}$, indicating that the escape process of GCs from dSphs was over. We then adopt a set of observationally-constrained density profiles for specific case of the Fornax dSph. According to our results, the escape fraction of GCs shows a negative correlation with both the mass and the apogalactic distance of the dSphs, as well as a positive correlation with the orbital eccentricity of dSphs. In particular, we find that the escape fraction of GCs from the Fornax dSph is between $13\%$ and $38\%$. Finally, we observe that when GCs leave their host dSphs, their final orbit around the MW does not differ much from their host dSphs.

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arXiv2021

The Kennicutt-Schmidt law and the main sequence of galaxies in Newtonian and Milgromian dynamics

The Kennicutt-Schmidt law is an empirical relation between the star formation rate surface density ($Σ_{SFR}$) and the gas surface density ($Σ_{gas}$) in disc galaxies. The relation has a power-law form $Σ_{SFR} \propto Σ_{gas}^n$. Assuming that star formation results from gravitational collapse of the interstellar medium, $Σ_{SFR}$ can be determined by dividing $Σ_{gas}$ by the local free-fall time $t_{ff}$. The formulation of $t_{ff}$ yields the relation between $Σ_{SFR}$ and $Σ_{gas}$, assuming that a constant fraction ($\varepsilon_{SFE}$) of gas is converted into stars every $t_{ff}$. This is done here for the first time using Milgromian dynamics (MOND). Using linear stability analysis of a uniformly rotating thin disc, it is possible to determine the size of a collapsing perturbation within it. This lets us evaluate the sizes and masses of clouds (and their $t_{ff}$) as a function of $Σ_{gas}$ and the rotation curve. We analytically derive the relation $Σ_{SFR} \propto Σ_{gas}^{n}$ both in Newtonian and Milgromian dynamics, finding that $n=1.4$. The difference between the two cases is a change only to the constant pre-factor, resulting in increased $Σ_{SFR}$ of up to 25\% using MOND in the central regions of dwarf galaxies. Due to the enhanced role of disk self-gravity, star formation extends out to larger galactocentric radii than in Newtonian gravity, with the clouds being larger. In MOND, a nearly exact representation of the present-day main sequence of galaxies is obtained if $ε_{SFE} = \text{constant} \approx 1.1\%$. We also show that empirically found correction terms to the Kennicutt-Schmidt law are included in the here presented relations. Furthermore, we determine that if star formation is possible, then the temperature only affects $Σ_{SFR}$ by at most a factor of $\sqrt{2}$.

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arXiv2021

IMF-induced intrinsic uncertainties on measuring galaxy distances based on the number of giant stars: the case of the ultra-diffuse galaxy NGC 1052-DF2

The surface brightness fluctuation (SBF) technique is one of the distance measurement methods that has been applied on the low surface brightness galaxy NGC 1052-DF2 yielding a distance of about 20 Mpc implying it to be a dark matter deficient galaxy. We assume the number of giant stars above a given luminosity threshold to represent the SBF magnitude. The SBF magnitude depends on the distance, but this is degenerate with the star formation history (SFH). Using a stellar population synthesis model we calculate the number of giant stars for stellar populations with different galaxy-wide stellar initial mass functions (gwIMFs), ages, metallicities and SFHs. If the gwIMF is the invariant canonical IMF, the 1$σ$ (3$σ$) uncertainty in colour allows a distance as low as 12 Mpc (8 Mpc). If instead the true underlying gwIMF is the integrated galaxy-wide IMF (IGIMF) then overestimating distances for low-mass galaxies would be a natural result, allowing NGC 1052-DF2 to have a distance of 11 Mpc within the 1$σ$ colour uncertainty. Finally, we show that our main conclusion on the existence of a bias in the SBF distance estimation is not much affected by changing the luminosity lower limit for counting giant stars.

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arXiv2021

Do ultra compact dwarf galaxies form monolithically or as merged star cluster complexes?

Some ultra-compact dwarf galaxies (UCDs) have elevated observed dynamical V-band mass-to-light ($M/L_{\rm V}$) ratios with respect to what is expected from their stellar populations assuming a canonical initial mass function (IMF). Observations have also revealed the presence of a compact dark object in the centers of several UCDs, having a mass of a few to 15\% of the present-day stellar mass of the UCD. This central mass concentration has typically been interpreted as a super-massive black hole, but can in principle also be a sub-cluster of stellar remnants. We explore the following two formation scenarios of UCDs, i) monolithic collapse and ii) mergers of star clusters in cluster complexes as are observed in massively star-bursting regions. We explore the physical properties of the UCDs at different evolutionary stages assuming different initial stellar masses of the UCDs and the IMF being either universal or changing systematically with metallicity and density according to the Integrated Galactic IMF (IGIMF) theory. While the observed elevated $M/L_{\rm V}$ ratios of the UCDs cannot be reproduced if the IMF is invariant and universal, the empirically derived IMF which varies systematically with density and metallicity shows agreement with the observations. Incorporating the UCD-mass-dependent retention fraction of dark remnants improves this agreement. In addition we apply the results of N-body simulations to young UCDs and show that the same initial conditions describing the observed $M/L_{\rm V}$ ratios reproduce the observed relation between the half-mass radii and the present-day masses of the UCDs. The findings thus suggest that the majority of UCDs that have elevated $M/L_{\rm V}$ ratios could have formed monolithically with significant remnant-mass components that are centrally concentrated, while those with small $M/L_V$ values may be merged star-cluster complexes.

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arXiv2020

Dynamical evolution of star clusters with top-heavy IMF

Several observational and theoretical studies suggest that the initial mass function (IMF) slope for massive stars in globular clusters (GCs) depends on the initial cloud density and metallicity, such that the IMF becomes increasingly top-heavy with decreasing metallicity and increasing the gas density of the forming object. Using N-body simulations of GCs starting with a top-heavy IMF and undergo early gas expulsion within a Milky Way-like potential, we show how such a cluster would evolve. By varying the degree of top-heaviness, we calculate the dissolution time and the minimum cluster mass needed for the cluster to survive after 12 Gyr of evolution.

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arXiv2020

The Lifetimes of Star Clusters Born with a Top-heavy IMF

Several observational and theoretical indications suggest that the initial mass function (IMF) becomes increasingly top-heavy (i.e., overabundant in high-mass stars with mass $m > 1M_{\odot}$) with decreasing metallicity and increasing gas density of the forming object. This affects the evolution of globular clusters (GCs) owing to the different mass-loss rates and the number of black holes formed. Previous numerical modeling of GCs usually assumed an invariant canonical IMF. Using the state-of-the-art $NBODY6$ code, we perform a comprehensive series of direct $N$-body simulations to study the evolution of star clusters, starting with a top-heavy IMF and undergoing early gas expulsion. Utilizing the embedded cluster mass-radius relation of Marks & Kroupa (2012) for initializing the models, and by varying the degree of top-heaviness, we calculate the minimum cluster mass needed for the cluster to survive longer than 12 Gyr. We document how the evolution of different characteristics of star clusters such as the total mass, the final size, the density, the mass-to-light ratio, the population of stellar remnants, and the survival of GCs is influenced by the degree of top-heaviness. We find that the lifetimes of clusters with different IMFs moving on the same orbit are proportional to the relaxation time to a power of $x$ that is in the range of 0.8 to 1. The observed correlation between concentration and the mass function slope in Galactic GCs can be accounted for excellently in models starting with a top-heavy IMF and undergoing an early phase of rapid gas expulsion.

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arXiv2019

The Star Formation History and Dynamics of the Ultra-diffuse Galaxy Dragonfly 44 in MOND and MOG

The observed line-of-sight velocity dispersion $σ_{los}$ of the ultra diffuse galaxy Dragonfly 44 (DF44) requires a Newtonian dynamical mass-to-light ratio of $M_{dyn}/L_I=26^{+7}_{-6}$ Solar units. This is well outside the acceptable limits of our stellar population synthesis (SPS) models, which we construct using the integrated galactic initial mass function (IGIMF) theory. Assuming DF44 is in isolation and using Jeans analysis, we calculate $σ_{los}$ profiles of DF44 in Milgromian dynamics (MOND) and modified gravity (MOG) theories without invoking dark matter. Comparing with the observed kinematics, the best-fitting MOND model has $M_{dyn}/L_I = 3.6_{-1.2}^{+1.6}$ and a constant orbital anisotropy of $β=-0.5_{-1.6}^{+0.4}$. In MOG, we first fix its two theoretical parameters $α$ and $μ$ based on previous fits to the observed rotation curve data of The HI Nearby Galaxy Survey (THINGS). The DF44 $σ_{los}$ profile is best fit with $M_{dyn}/L_I=7.4_{-1.4}^{+1.5}$, larger than plausible SPS values. MOG produces a $σ_{los}$ profile for DF44 with acceptable $M_{dyn}/L_I$ and isotropic orbits if $α$ and $μ$ are allowed to vary. MOND with the canonical $a_0$ can explain DF44 at the $2.40 σ$ confidence level (1.66\%) if considering both its observed kinematics and typical star formation histories in an IGIMF context. However, MOG is ruled out at $5.49 σ$ ($P$-value of $4.07 \times 10^{-8}$) if its free parameters are fixed at the highest values consistent with THINGS data.

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arXiv2019

The radial acceleration relation and dark baryons in MOND

Recent observations of rotationally supported galaxies show a tight correlation between the observed radial acceleration at every radius and the Newtonian acceleration generated by the baryonic mass distribution, the so-called radial acceleration relation (RAR). The rotation curves (RCs) of the SPARC sample of disk galaxies with different morphologies, masses, sizes and gas fractions are investigated in the context of modified Newtonian dynamics (MOND). We include the effect of cold dark baryons by scaling the measured mass in the atomic form by a factor of $c$ in the mass budget of galaxies. In addition to the standard interpolating function, we also fit the RCs and the RAR with the empirical RAR-inspired interpolating function. Slightly better fits for about $47\%$ of galaxies in our sample are achieved in the presence of dark baryons ($c>1$) with the mean value of $c = 2.4\pm 1.3$. Although the MOND fits are not significantly improved by including dark baryons, it results in a decrease in the characteristic acceleration $g_†$ by $40\%$. We find no correlation between the MOND critical acceleration $a_0$ and the central surface brightness of the stellar disk, $μ_{3.6}$. This supports $a_0$ being a universal constant for all galaxies.

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arXiv2019

A new formulation of the external field effect in MOND and numerical simulations of ultra-diffuse dwarf galaxies $-$ application to NGC 1052-DF2 and NGC 1052-DF4

The ultra-diffuse dwarf galaxy NGC 1052-DF2 (DF2) has ten (eleven) measured globular clusters (GCs) with a line-of-sight velocity dispersion of $σ=7.8^{+5.2}_{-2.2}\,$km/s ($σ=10.6^{+3.9}_{-2.3}\,$km/s). Our conventional statistical analysis of the original ten GCs gives $σ=8.0^{+4.3}_{-3.0}\,$km/s. The overall distribution of velocities agrees well with a Gaussian of this width. Due to the non-linear Poisson equation in MOND, a dwarf galaxy has weaker self-gravity when in close proximity to a massive host. This external field effect is investigated using a new analytic formulation and fully self-consistent live $N$-body models in MOND. Our formulation agrees well with that of Famaey and McGaugh (2012). These new simulations confirm our analytic results and suggest that DF2 may be in a deep-freeze state unique to MOND. The correctly calculated MOND velocity dispersion agrees with our inferred dispersion and that of van Dokkum et al. (2018b) if DF2 is within 150 kpc of NGC 1052 and both are 20 Mpc away. The GCs of DF2 are however significantly brighter and larger than normal GCs, a problem which disappears if DF2 is significantly closer to us. A distance of 10-13 Mpc makes DF2 a normal dwarf galaxy even more consistent with MOND and the 13 Mpc distance reported by Trujillo et. al. (2019). We discuss the similar dwarf DF4, finding good agreement with MOND. We also discuss possible massive galaxies near DF2 and DF4 along with their distances and peculiar velocities, noting that NGC 1052 may lie at a distance near 10 Mpc.

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arXiv2019

Evolution of star clusters on eccentric orbits: semi-analytical approach

We study the dynamical evolution of star clusters on eccentric orbits using a semi-analytical approach. In particular we adapt and extend the equations of EMACSS code, introduced by Gieles et al. (2014), to work with eccentric orbits. We follow the evolution of star clusters in terms of mass, half-mass radius, core radius, Jacobi radius and the total energy over their dissolution time. Moreover, we compare the results of our semi-analytical models against $N$-body computations of clusters with various initial half-mass radius, number of stars and orbital eccentricity to cover both tidally filling and under-filling systems. The evolution profiles of clusters obtained by our semi-analytical approach closely follow those of $N$-body simulations in different evolutionary phases of star clusters, from pre-collapse to post-collapse. Given that the average runtime of our semi-analytical models is significantly less than that of $N$-body models, our approach makes it feasible to study the evolution of large samples of globular clusters on eccentric orbits.

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arXiv2019

Does the galaxy NGC1052-DF2 falsify Milgromian dynamics?

A great challenge in present-day physics is to understand whether the observed internal dynamics of galaxies is due to dark matter matter or due to a modification of the law of gravity. Recently, van Dokkum et al. reported that the ultra-diffuse dwarf galaxy NGC1052-DF2 lacks dark matter, and they claimed that this would -- paradoxically -- be problematic for modified gravity theories like Milgromian dynamics (MOND). However, NGC1052-DF2 is not isolated, so that a valid prediction of its internal dynamics in MOND cannot be made without properly accounting for the external gravitational fields from neighbouring galaxies. Including this external field effect following Haghi et al. shows that NGC1052-DF2 is consistent with MOND.

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