arXiv subjects

Andreas Just

Publications and source records attributed to Andreas Just.

At least 37 records · Page 2Linked to original sources

arXiv2018

The long-term evolution of star clusters formed with a centrally-peaked star-formation-efficiency profile

We have studied the long-term evolution of star clusters of the solar neighborhood, starting from their birth in gaseous clumps until their complete dissolution in the Galactic tidal field. We have combined the "local-density-driven cluster formation model" of Parmentier & Pfalzner (2013) with direct N-body simulations of clusters following instantaneous gas expulsion. We have studied the relation between cluster dissolution time, $t_{dis}$, and cluster "initial" mass, $M_{init}$, defined as the cluster {mass at the end of the dynamical response to gas expulsion (i.e. violent relaxation), when the cluster age is 20-30 Myr}. We consider the "initial" mass to be consistent with other works which neglect violent relaxation. The model clusters formed with a high star formation efficiency (SFE -- i.e. gas mass fraction converted into stars) follow a tight mass-dependent relation, in agreement with previous theoretical studies. However, the low-SFE models present a large scatter in both the "initial" mass and the dissolution time, and a shallower mass-dependent relation than high-SFE clusters. Both groups differ in their structural properties on the average. Combining two populations of clusters, high- and low-SFE ones, with domination of the latter, yields a cluster dissolution time for the solar neighborhood in agreement with that inferred from observations, without any additional destructive processes such as giant molecular cloud encounters. An apparent mass-independent relation may emerge for our low-SFE clusters when we neglect low-mass clusters (as expected for extra-galactic observations), although more simulations are needed to investigate this aspect.

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arXiv2018

Gravitational Wave Driven Mergers and Coalescence Time of Supermassive Black Holes

The evolution of Supermassive Black Holes (SMBHs) initially embedded in the centres of merging galaxies realised with a stellar mass function (SMF) is studied from the onset of galaxy mergers till coalescence. We performed a large set of direct N-body simulations with three different slopes of the central stellar cusp and different random seeds. Post Newtonian terms up to order 3.5 are used to drive the SMBH binary evolution in the relativistic regime. The impact of a SMF on the hardening rate and the coalescence time is investigated. We find that SMBH binaries coalesce well within one billion years when our models are scaled to galaxies with a steep cusp at low redshift. Here higher central densities provide larger supply of stars to efficiently extract energy from the SMBH binary orbit and shrink it to the phase where gravitational wave (GW) emission becomes dominant leading to the coalescence of the SMBHs. Mergers of models with shallow cusps that are representative for giant elliptical galaxies having central cores result in less efficient extraction of binary orbital energy due to the lower stellar densities in the centre. However, high values of eccentricity witnessed for SMBH binaries in such galaxy mergers ensure that the GW emission dominated phase sets in earlier at larger values of the semi-major axis. This helps to compensate for the less efficient energy extraction during the phase dominated by stellar encounters resulting in mergers of SMBHs in about one Gyr after the formation of the binary. Additionally, we witness mass segregation in the merger remnant resulting in enhanced SMBH binary hardening rates. We show that at least the final phase of the merger in cuspy low mass galaxies would be observable with the GW detector eLISA.

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arXiv2018

Star-disc interaction in galactic nuclei: formation of a central stellar disc

We perform high resolution direct $N$-body simulations to study the effect of an accretion disc on stellar dynamics in an active galactic nucleus (AGN). We show that the interaction of the nuclear stellar cluster (NSC) with the gaseous disc (AD) leads to formation of a stellar disc in the central part of the NSC. The accretion of stars from the stellar disc onto the super-massive black hole is balanced by the capture of stars from the NSC into the stellar disc, yielding a stationary density profile. We derive the migration time through the AD to be 3\% of the half-mass relaxation time of the NSC. The mass and size of the stellar disc are 0.7\% of the mass and 5\% of the influence radius of the super-massive black hole. An AD lifetime shorter than the migration time would result in a less massive nuclear stellar disc. The detection of such a stellar disc could point to past activity of the hosting galactic nucleus.

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arXiv2017

Impact of a star formation efficiency profile on the evolution of open clusters

We study the effect of the instantaneous gas expulsion on star clusters wherein the residual gas has a density profile shallower than that of the embedded cluster. This is expected if star formation proceeds with a given SFE per free-fall time in a centrally-concentrated molecular clump. We perform direct N-body simulations whose initial conditions are generated by the program "mkhalo" "falcON" adapted for our models. Our model clusters initially have a Plummer profile and are in virial equilibrium with the gravitational potential of the cluster-forming clump. The residual gas contribution is computed based on the model of Parmentier&Pfalzner(2013). Our simulations include mass loss by stellar evolution and the tidal field of the Galaxy. We find that a star cluster with a minimum global SFE of 15% is able to survive instantaneous gas expulsion and to produce a bound cluster. Its violent relaxation lasts no longer than 20 Myr, independently of its global SFE and initial stellar mass. At the end of violent relaxation the bound fractions of surviving clusters with the same global SFEs are similar regardless of their initial stellar mass. Their subsequent lifetime in the gravitational field of the Galaxy depends on their bound stellar masses. We therefore conclude that the critical SFE needed to produce a bound cluster is 15%, which is twice smaller than earlier estimates of 33%. Thus we have improved the survival likelihood of young clusters after instantaneous gas expulsion. Those can now survive instantaneous gas expulsion with global SFEs as low as those observed for embedded clusters of Solar Neighbourhood (15-30%). This is the consequence of the star cluster having a density profile steeper than that of the residual gas. However, in terms of the effective SFE, measured by the virial ratio of the cluster at gas expulsion, our results are in agreement with previous studies.

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arXiv2017

$\mathit{Chempy}$: A flexible chemical evolution model for abundance fitting - Do the Sun's abundances alone constrain chemical evolution models?

Elemental abundances of stars are the result of the complex enrichment history of their galaxy. Interpretation of observed abundances requires flexible modeling tools to explore and quantify the information about Galactic chemical evolution (GCE) stored in such data. Here we present Chempy, a newly developed code for GCE modeling, representing a parametrized open one-zone model within a Bayesian framework. A Chempy model is specified by a set of 5-10 parameters that describe the effective galaxy evolution along with the stellar and star-formation physics: e.g. the star-formation history, the feedback efficiency, the stellar initial mass function (IMF) and the incidence of supernova type Ia (SN Ia). Unlike established approaches, Chempy can sample the posterior probability distribution in the full model parameter space and test data-model matches for different nucleosynthetic yield sets. We extend Chempy to a multi-zone scheme. As an illustrative application, we show that interesting parameter constraints result from only the ages and elemental abundances of Sun, Arcturus and the present-day interstellar medium (ISM). For the first time, we use such information to infer IMF parameter via GCE modeling, where we properly marginalize over nuisance parameters and account for different yield sets. We find that of the IMF $11.6_{-1.6}^{+2.1}$ % explodes as core-collapse SN, compatible with Salpeter 1955. We also constrain the incidence of SN Ia per 10^3 Msun to 0.5-1.4. At the same time, this Chempy application shows persistent discrepancies between predicted and observed abundances for some elements, irrespective of the chosen yield set. These cannot be remedied by any variations of Chempy's parameters and could be an indication for missing nucleosynthetic channels. Chempy should be a powerful tool to confront predictions from stellar nucleosynthesis with far more complex abundance data sets.

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arXiv2016

Swift coalescence of supermassive black holes in cosmological mergers of massive galaxies

Supermassive black holes (SMBHs) are ubiquitous in galaxies with a sizable mass. It is expected that a pair of SMBHs originally in the nuclei of two merging galaxies would form a binary and eventually coalesce via a burst of gravitational waves. So far theoretical models and simulations have been unable to predict directly the SMBH merger timescale from ab-initio galaxy formation theory, focusing only on limited phases of the orbital decay of SMBHs under idealized conditions of the galaxy hosts. The predicted SMBH merger timescales are long, of order Gyrs, which could be problematic for future gravitational wave searches. Here we present the first multi-scale $Λ$CDM cosmological simulation that follows the orbital decay of a pair of SMBHs in a merger of two typical massive galaxies at $z\sim3$, all the way to the final coalescence driven by gravitational wave emission. The two SMBHs, with masses $\sim10^{8}$ M$_{\odot}$, settle quickly in the nucleus of the merger remnant. The remnant is triaxial and extremely dense due to the dissipative nature of the merger and the intrinsic compactness of galaxies at high redshift. Such properties naturally allow a very efficient hardening of the SMBH binary. The SMBH merger occurs in only $\sim10$ Myr after the galactic cores have merged, which is two orders of magnitude smaller than the Hubble time.

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arXiv2016

On the bar formation mechanism in galaxies with cuspy bulges

We show by numerical simulations that a purely stellar dynamical model composed of an exponential disc, a cuspy bulge, and an NFW halo with parameters relevant to the Milky Way Galaxy is subject to bar formation. Taking into account the finite disc thickness, the bar formation can be explained by the usual bar instability, in spite of the presence of an inner Lindblad resonance, that is believed to damp any global modes. The effect of replacing the live halo and bulge by a fixed external axisymmetric potential (rigid models) is studied. It is shown that while the e-folding time of bar instability increases significantly (from 250 to 500 Myr), the bar pattern speed remains almost the same. For the latter, our average value of 55 km/s/kpc agrees with the assumption that the Hercules stream in the solar neighbourhood is an imprint of the bar--disc interaction at the outer Lindblad resonance of the bar. Vertical averaging of the radial force in the central disc region comparable to the characteristic scale length allows us to reproduce the bar pattern speed and the growth rate of the rigid models, using normal mode analysis of linear perturbation theory in a razor thin disc. The strong increase of the e-folding time with decreasing disc mass predicted by the mode analysis suggests that bars in galaxies similar to the Milky Way have formed only recently.

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arXiv2016

Chemical separation of disc components using RAVE

We present evidence from the RAdial Velocity Experiment (RAVE) survey of chemically separated, kinematically distinct disc components in the solar neighbourhood. We apply probabilistic chemical selection criteria to separate our sample into $α$-low (`thin disc') and $α$-high (`thick disc') sequences. Using newly derived distances, which will be utilized in the upcoming RAVE DR5, we explore the kinematic trends as a function of metallicity for each of the disc components. For our $α$-low disc, we find a negative trend in the mean rotational velocity ($V_{\mathrmϕ}$) as a function of iron abundance ([Fe/H]). We measure a positive gradient $\partial V_{\mathrmϕ}$/$\partial$[Fe/H] for the $α$-high disc, consistent with results from high-resolution surveys. We also find differences between the $α$-low and $α$-high discs in all three components of velocity dispersion. We discuss the implications of an $α$-low, metal-rich population originating from the inner Galaxy, where the orbits of these stars have been significantly altered by radial mixing mechanisms in order to bring them into the solar neighbourhood. The probabilistic separation we propose can be extended to other data sets for which the accuracy in [$α$/Fe] is not sufficient to disentangle the chemical disc components a priori. For such datasets which will also have significant overlap with Gaia DR1, we can therefore make full use of the improved parallax and proper motion data as it becomes available to investigate kinematic trends in these chemical disc components.

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arXiv2016

Star-disc interaction in galactic nuclei: orbits and rates of accreted stars

We examine the effect of an accretion disc on the orbits of stars in the central star cluster surrounding a central massive black hole by performing a suite of 39 high-accuracy direct N-body simulations using state-of-the art software and accelerator hardware, with particle numbers up to 128k. The primary focus is on the accretion rate of stars by the black hole (equivalent to their tidal disruption rate for black holes in the small to medium mass range) and the eccentricity distribution of these stars. Our simulations vary not only the particle number, but disc model (two models examined), spatial resolution at the centre (characterised by the numerical accretion radius) and softening length. The large parameter range and physically realistic modelling allow us for the first time to confidently extrapolate these results to real galactic centres. While in a real galactic centre both particle number and accretion radius differ by a few orders of magnitude from our models, which are constrained by numerical capability, we find that the stellar accretion rate converges for models with N > 32k. The eccentricity distribution of accreted stars, however, does not converge. We find that there are two competing effects at work when improving the resolution: larger particle number leads to a smaller fraction of stars accreted on nearly-circular orbits, while higher spatial resolution increases this fraction. We scale our simulations to some nearby galaxies and find that the expected boost in stellar accretion (or tidal disruption, which could be observed as X-ray flares) in the presence of a gas disc is about a factor of 10. Even with this boost, the accretion of mass from stars is still a factor of ~ 100 slower than the accretion of gas from the disc. Thus, it seems accretion of stars is not a major contributor to black hole mass growth.

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arXiv2015

Dynamical and chemical evolution of the thin disc

Our detailed analytic local disc model (JJ-model) quantifies the interrelation between kinematic properties (e.g. velocity dispersions and asymmetric drift), spatial parameters (scale-lengths and vertical density profiles), and properties of stellar sub-populations (age and abundance distributions). Any consistent radial extension of the disc evolution model should predict specific features in the different distribution functions and in their correlations. Large spectroscopic surveys (SEGUE, RAVE, APOGEE, Gaia-ESO) allow significant constraints on the long-term evolution of the thin disc. We discuss the qualitative difference of correlations (like the alpha-enhancement as function of metallicity) and distribution functions (e.g. in [Mg/H] or [Fe/H]) for the construction of a disc model. In the framework of the JJ-model we build a local chemical enrichment model and show that significant vertical gradients for main sequence and red clump stars are expected in the thin disc. A Jeans analysis of the asymmetric drift provides a link to the radial structure of the disc. The derived metallicity-dependent radial scale-lengths can be combined in the future with the abundance distributions at different Galactocentric distances to construct full disc models. We expect to be able to constrain possible scenarios of inside-out growth of the thin disc and to characterise those populations, which require significant radial migration.

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arXiv2015

On the Influence of Minor Mergers on the Radial Abundance Gradient in Disks of Milky Way-like Galaxies

We investigate the influence of stellar migration caused by minor mergers (mass ratio from 1:70 to 1:8) on the radial distribution of chemical abundances in the disks of Milky Way-like galaxies during the last four Gyr. A GPU-based pure N-body tree-code model without hydrodynamics and star formation was used. We computed a large set of mergers with different initial satellite masses, positions, and orbital velocities. We find that there is no significant metallicity change at any radius of the primary galaxy in the case of accretion of a low-mass satellite of 10$^9$ M$_{\odot}$ (mass ratio 1:70) except for the special case of prograde satellite motion in the disk plane of the host galaxy. The accretion of a satellite of a mass $\gtrsim3\times10^9$ M$_{\odot}$ (mass ratio 1:23) results in an appreciable increase of the chemical abundances at galactocentric distances larger than $\sim10$ kpc. The radial abundance gradient flattens in the range of galactocentric distances from 5 to 15 kpc in the case of a merger with a satellite with a mass $\gtrsim3\times10^9$ M$_{\odot}$. There is no significant change in the abundance gradient slope in the outer disk (from $\sim15$ kpc up to 25 kpc) in any merger while the scatter in metallicities at a given radius significantly increases for most of the satellite's initial masses/positions compared to the case of an isolated galaxy. This argues against attributing the break (flattening) of the abundance gradient near the optical radius observed in the extended disks of Milky Way-like galaxies only to merger-induced stellar migration.

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arXiv2015

Towards a fully consistent Milky Way disc model - III. Constraining the initial mass function

We use our vertical Milky Way disc model together with Galaxia to create mock observations of stellar samples in the solar neighbourhood. We compare these to the corresponding volume complete observational samples of dereddened and binary accounted data from Hipparcos and the Catalogue of Nearby Stars. Sampling the likelihood in the parameter space we determine a new fiducial IMF considering constraints from dwarf and giant stars. The resulting IMF observationally backed in the range from 0.5 to 10 Msun is a two slope broken power law with -1.49 +- 0.08 for the low mass slope, a break at 1.39 +- 0.05 Msun and a high mass slope of -3.02 +- 0.06. The Besancon group also converging to a similar IMF even though their observational sample being quite different to ours shows that the forward modelling technique is a powerful diagnostic to test theoretical concepts like the local field star IMF.

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arXiv2014

Bisymmetric normal modes in soft-centred and realistic galactic discs

We test methods for the determination of unstable modes in stellar discs: a point collocation scheme in the action sub-space, a scheme based on expansion of the density and potential on the biorthonormal basis, and a finite element method. Using models of galaxies with low and high mass concentration to the center, the existence of two different kinds of spectra of unstable modes is demonstrated. Characteristic features of methods and obtained spectra are discussed. Despite ignoring any constraint on the continuity or differentiability of the perturbed DF, the collocation scheme is reliable for obtaining spectra and patterns in both kinds of models. The method based on the expansion of the perturbed potential and surface density over a biorthogonal basis was not applicable to a model with high mass concentration. The finite element method successfully used in various fields of science and engineering is currently sensitive to the presence of resonant orbits due to the choice of interpolation functions for the distribution function.

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arXiv2012

Simulating Sinking Satellites with SUPERBOX-10

SUPERBOX-10 is the successor of SUPERBOX, a particle-mesh code where additional grids and sub-grids are applied to regions of high particle density. Previous limitations have been solved. For instance, the vertical resolution is improved considerably when flattened grids are used. Since the computationally most intensive part is the Fast Fourier Transform, we introduce a parallelised version using the library FFTW, resulting in a speed-up of a few. The new features are tested using a galaxy model consisting of an exponential disc, a bulge and a dark matter halo. We demonstrate that the use of flattened grids efficiently reduces numerical heating. We simulate the merging of disc-bulge-halo galaxies with small spherical satellites. As a result, satellites on orbits with both low eccentricity and inclination heat the disc most efficiently. Moreover, we find that most of the satellite's energy and angular momentum is transfered to the halo.

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arXiv2012

Enhanced accretion rates of stars on Super-massive Black Holes by star-disk interactions in galactic nuclei

We investigate the dynamical interaction of a central star cluster surrounding a super-massive black hole and a central accretion disk. The dissipative force acting on stars in the disk leads to an enhanced mass flow towards the super-massive black hole and to an asymmetry in the phase space distribution due to the rotating accretion disk. The accretion disk is considered as a stationary Keplerian rotating disk, which is vertically extended in order to employ a fully self-consistent treatment of stellar dynamics including the dissipative force originating from star-gas ram pressure effects. The stellar system is treated with a direct high-accuracy N-body integration code. A star-by-star representation, desirable in N-body simulations, cannot be extended to real particle numbers yet. Hence, we carefully discuss the scaling behavior of our model with regard to particle number and tidal accretion radius. The main idea is to find a family of models for which the ratio of two-body relaxation time and dissipation time (for kinetic energy of stellar orbits) is constant, which then allows us to extrapolate our results to real parameters of galactic nuclei. Our model is derived from basic physical principles and as such it provides insight into the role of physical processes in galactic nuclei, but it should be regarded as a first step towards more realistic and more comprehensive simulations. Nevertheless, the following conclusions appear to be robust: the star accretion rate onto the accretion disk and subsequently onto the super-massive black hole is enhanced by a significant factor compared to purely stellar dynamical systems neglecting the disk. This process leads to enhanced fueling of central disks in active galactic nuclei and to an enhanced rate of tidal stellar disruptions. [Abridged]

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arXiv2012

Detailed comparison of Milky Way models based on stellar population synthesis and SDSS star counts at the north Galactic pole

We test the ability of the TRILEGAL and Besancon models to reproduce the CMD of SDSS data at the north Galactic pole (NGP). We show that a Hess diagram analysis of colour-magnitude diagrams is much more powerful than luminosity functions (LFs) in determining the Milky Way structure. We derive a best-fitting TRILEGAL model to simulate the NGP field in the (g-r, g) CMD of SDSS filters via Hess diagrams. For the Besancon model, we simulate the LFs and Hess diagrams in all SDSS filters. We use a chi2 analysis and determine the median of the relative deviations in the Hess diagrams to quantify the quality of the fits by the TRILEGAL models and the Besancon model in comparison and compare this with the Just-Jahreiss model. The input isochrones in the colour-absolute magnitude diagrams of the thick disc and halo are tested via the observed fiducial isochrones of globular clusters (GCs). We find that the default parameter set lacking a thick disc component gives the best representation of the LF in TRILEGAL. The Hess diagram reveals that a metal-poor thick disc is needed. In the Hess diagram, the median relative deviation of the TRILEGAL model and the SDSS data amounts to 25 percent, whereas for the Just-Jahreiss model the deviation is only 5.6 percent. The isochrone analysis shows that the representation of the MS of (at least metal-poor) stellar populations in the SDSS system is reliable. In contrast, the RGBs fail to match the observed fiducial sequences of GCs. The Besancon model shows a similar median relative deviation of 26 percent in (g-r, g). In the u band, the deviations are larger. There are significant offsets between the isochrone set used in the Besancon model and the observed fiducial isochrones. In contrast to Hess diagrams, LFs are insensitive to the detailed structure of the Milky Way components due to the extended spatial distribution along the line of sight.

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arXiv2012

Formation and Hardening of Supermassive Black Hole Binaries in Minor Mergers of Disk Galaxies

We model for the first time the complete orbital evolution of a pair of Supermassive Black Holes (SMBHs) in a 1:10 galaxy merger of two disk dominated gas-rich galaxies, from the stage prior to the formation of the binary up to the onset of gravitational wave emission when the binary separation has shrunk to 1 milli parsec. The high-resolution smoothed particle hydrodynamics (SPH) simulations used for the first phase of the evolution include star formation, accretion onto the SMBHs as well as feedback from supernovae explosions and radiative heating from the SMBHs themselves. Using the direct N-body code ϕ-GPU we evolve the system further without including the effect of gas, which has been mostly consumed by star formation in the meantime. We start at the time when the separation between two SMBHs is ~ 700 pc and the two black holes are still embedded in their galaxy cusps. We use 3 million particles to study the formation and evolution of the SMBH binary till it becomes hard. After a hard binary is formed, we reduce (reselect) the particles to 1.15 million and follow the subsequent shrinking of the SMBH binary due to 3-body encounters with the stars. We find approximately constant hardening rates and that the SMBH binary rapidly develops a high eccentricity. Similar hardening rates and eccentricity values are reported in earlier studies of SMBH binary evolution in the merging of dissipation-less spherical galaxy models. The estimated coalescence time is ~ 2.9 Gyr, significantly smaller than a Hubble time. We discuss why this timescale should be regarded as an upper limit. Since 1:10 mergers are among the most common interaction events for galaxies at all cosmic epochs, we argue that several SMBH binaries should be detected with currently planned space-borne gravitational wave interferometers, whose sensitivity will be especially high for SMBHs in the mass range considered here.

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arXiv2012

Mergers of Unequal Mass Galaxies: Supermassive Black Hole Binary Evolution and Structure of Merger Remnants

Galaxy centers are residing places for Super Massive Black Holes (SMBHs). Galaxy mergers bring SMBHs close together to form gravitationally bound binary systems which, if able to coalesce in less than a Hubble time, would be one of the most promising sources of gravitational waves for the Laser Interferometer Space Antenna (LISA). In spherical galaxy models, SMBH binaries stall at a separation of approximately one parsec, leading to the "final parsec problem" (FPP). On the other hand, it has been shown that merger-induced triaxiality of the remnant in equal-mass mergers is capable of supporting a constant supply of stars on so-called centrophilic orbits that interact with the binary and thus avoid the FPP. In this paper, using a set of direct N-body simulations of mergers of initially spherically symmetric galaxies with different mass ratios, we show that the merger-induced triaxiality is able to drive unequal-mass SMBH binaries to coalescence. The binary hardening rates are high and depend only weakly on the mass ratios of SMBHs for a wide range of mass ratios q. The hardening rates are significantly higher for galaxies having steep cusps in comparison with those having shallow cups at centers. The evolution of the binary SMBH leads to relatively shallower inner slopes at the centers of the merger remnants. The stellar mass displaced by the SMBH binary on its way to coalescence is ~ 1-5 times the combined mass of binary SMBHs. The coalescence times for SMBH binary with mass ~ million solar masses are less than 1 Gyr and for those at the upper end of SMBH masses (~ billion solar masses) are 1-2 Gyr for less eccentric binaries whereas less than 1 Gyr for highly eccentric binaries. SMBH binaries are thus expected to be promising sources of gravitational waves at low and high redshifts.

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