We have determined possible cluster members of the nearby open cluster Praesepe (M44) based on J and K photometry and proper motions from the PPMXL catalogue and z photometry from the Sloan Digital ...Sky Survey. In total, we identified 893 possible cluster members down to a magnitude of J = 15.5 mag, corresponding to a mass of about 0.15 M for an assumed cluster distance modulus of (m − M)0 = 6.30 mag (d 182 pc), within a radius of 3
5 around the cluster centre. We derive a new cluster centre for Praesepe (αcentre = 8h39m37s, δcentre = 19°35′02′
′). We also derive a total cluster mass of about 630 M, and a 2D half-number and half-mass radius of 4.25 and 3.90 pc, respectively. The global mass function of the cluster members shows evidence for a turnover around m = 0.65 M. While more massive stars can be fitted by a power law ξ(m) ∼ m
−α with slope α = 2.88 ± 0.22, stars less massive than m = 0.65 M are best fitted with α = 0.85 ± 0.10. In agreement with its large dynamical age, we find that Praesepe is strongly mass segregated and that the mass function slope for high-mass stars steepens from a value of α = 2.32 ± 0.24 inside the half-mass radius to α = 4.90 ± 0.51 outside the half-mass radius. We finally identify a significant population of binaries and triples in the colour-magnitude diagram of Praesepe. Assuming non-random pairing of the binary components, a binary fraction of about 35 per cent for primaries in the mass range 0.6 < m/M < 2.20 is required to explain the observed number of binaries in the colour-magnitude diagram.
Ibata et al. recently reported the existence of a vast thin plane of dwarf galaxies (VTPD) orbiting around Andromeda. We investigate whether such a configuration can be reproduced within the standard ...cosmological framework and search for similar planes of corotating satellite galaxies around Andromeda-like host haloes in the data from the Millennium II simulation combined with a semi-analytic galaxy formation model. We apply a baryonic mass cut of 2.8 × 104 M for the satellite haloes and restrict the data to a Pan-Andromeda Archaeological Survey-like field. If we include the so-called orphan galaxies in our analysis, we find that planes with an rms lower than the VTPD are common in Millennium II. This is partially due to the strong radially concentrated distribution of orphan galaxies. Excluding part of the orphan galaxies brings the radial distributions of Millennium II satellites into better agreement with the satellite distribution of Andromeda while still producing a significant fraction of planes with a lower rms than the VTPD. We also find haloes in Millennium II with an equal or higher number of corotating satellites than the VTPD. This demonstrates that the VTPD is not in conflict with the standard cosmological framework, although a definite answer of this question might require higher resolution cosmological simulations that do not have to consider orphan galaxies. Our results finally show that satellite planes in Millennium II are not stable structures; hence, the VTPD might only be a statistical fluctuation of an underlying more spherical galaxy distribution.
We study the escape rate of stars, , from clusters with different radii on circular orbits in a tidal field using analytical predictions and direct N-body simulations. We find that depends on the ...ratio , where rh is the half-mass radius and rJ the radius of the zero-velocity surface around the cluster. For , the ‘tidal regime’, there is almost no dependence of on . To first order this is because the fraction of escapers per half-mass relaxation time, trh, scales approximately as , which cancels out the r3/2h term in trh. For , the ‘isolated regime’, scales as . The dissolution time-scale, tdis, falls in three regimes. Clusters that start with their initial , in the tidal regime dissolve completely in this regime and their tdis is, therefore, insensitive to the initial rh. Our model predicts that has to be 10−20–10−10 for clusters to dissolve completely in the isolated regime. This means that realistic clusters that start with always expand to the tidal regime before final dissolution. Their tdis has a shallower dependence on than what would be expected when tdis is a constant times trh. For realistic values of , the lifetime varies by less than a factor of 1.5 due to changes in . This implies that the ‘survival’ or ‘vital’ diagram for globular clusters should allow for more small clusters to survive. We note that with our result it is impossible to explain the universal peaked mass function of globular cluster systems by dynamical evolution from a power-law initial mass function, since the peak will be at lower masses in the outer parts of galaxies. Our results finally show that in the tidal regime tdis scales as N0.65/ω, with ω the angular frequency of the cluster in the host galaxy.
We have carried out a large grid of N-body simulations in order to investigate if mass loss as a result of primordial gas expulsion can be responsible for the large fraction of second-generation (SG) ...stars in globular clusters (GCs) with multiple stellar populations (MSPs). Our clusters start with two stellar populations in which 10 per cent of all stars are SG stars. We simulate clusters with different initial masses, different ratios of the half-mass radius of first to SG stars, different primordial gas fractions and Galactic tidal fields with varying strength. We then let our clusters undergo primordial gas loss and obtain their final properties such as mass, half-mass radius and the fraction of SG stars. Using our N-body grid we then perform a Monte Carlo analysis to constrain the initial masses, radii and required gas expulsion time-scales of GCs with MSPs. Our results can explain the present-day properties of GCs only if (1) a substantial amount of gas was present in the clusters after the formation of SG stars and (2) gas expulsion time-scales were extremely short (≲ 105 yr). Such short gas expulsion time-scales are in agreement with recent predictions that dark remnants have ejected the primordial gas from GCs, and pose a potential problem for the asymptotic giant branch scenario. In addition, our results predict a strong anti-correlation between the number ratio of SG stars in GCs and the present-day mass of GCs. So far, the observational data show only a significantly weaker anti-correlation, if any at all.
It has been recently shown that the dynamical V-band mass-to-light ratios of compact stellar systems with masses from 106 to 108 M⊙ are not consistent with the predictions from simple stellar ...population models. Top-heavy stellar initial mass functions (IMFs) in these so-called ultra-compact dwarf galaxies (UCDs) offer an attractive explanation for this finding, the stellar remnants and retained stellar envelopes providing the unseen mass. We therefore construct a model which quantifies by how much the IMFs of UCDs would have to deviate in the intermediate- and high-mass range from the canonical IMF in order to account for the enhanced M/LV ratio of the UCDs. The deduced high-mass IMF in the UCDs depends on the age of the UCDs and the number of faint products of stellar evolution retained by them. Assuming that the IMF in the UCDs is a three-part power law equal to the canonical IMF in the low-mass range and taking 20 per cent as a plausible choice for the fraction of the remnants of high-mass stars retained by UCDs, the model suggests the exponent of the high-mass IMF to be ≈1.6 if the UCDs are 13 Gyr old (i.e. almost as old as the Universe) or ≈1.0 if the UCDs are 7 Gyr old, in contrast to 2.3 for the Salpeter–Massey IMF. If the IMF was as top heavy as suggested here, the stability of the UCDs might have been threatened by heavy mass loss induced by the radiation and evolution of massive stars. The central densities of UCDs must have been in the range 106 to 107 M⊙ pc−3 when they formed with star formation rates of 10 to 100 M⊙ yr−1.
Scaling of N-body calculations Baumgardt, H.
Monthly notices of the Royal Astronomical Society,
08/2001, Letnik:
325, Številka:
4
Journal Article
Recenzirano
Odprti dostop
We report results of collisional N-body simulations aimed at studying the N dependence of the dynamical evolution of star clusters. Our clusters consist of equal-mass stars and are in virial ...equilibrium. Clusters moving in external tidal fields and clusters limited by a cut-off radius are simulated. Our main focus is to study the dependence of the lifetimes of the clusters on the number of cluster stars and the chosen escape condition. We find that star clusters in external tidal fields exhibit a scaling problem in the sense that their lifetimes do not scale with the relaxation time. Isolated clusters show a similar problem if stars are removed only after their distance to the cluster centre exceeds a certain cut-off radius. If stars are removed immediately after their energy exceeds the energy necessary for escape, the scaling problem disappears. We show that some stars that gain the energy necessary for escape are scattered to lower energies before they can leave the cluster. As the efficiency of this process decreases with increasing particle number, it causes the lifetimes not to scale with the relaxation time. Analytic formulae are derived for the scaling of the lifetimes in the different cases.
ABSTRACT
We present the results of the analysis of deep photometric data of 32 Galactic globular clusters. We analysed 69 parallel field images observed with the Wide Field Channel of the Advanced ...Camera for Surveys of the Hubble Space Telescope which complemented the already available photometry from the globular cluster treasury project covering the central regions of these clusters. This unprecedented data set has been used to calculate the relative fraction of stars at different masses (i.e. the present-day mass function) in these clusters by comparing the observed distribution of stars along the cluster main sequence and across the analysed field of view with the prediction of multimass dynamical models. For a subsample of 31 clusters, we were able to obtain also the half-mass radii, mass-to-light ratios, and the mass fraction of dark remnants using available radial velocity information. We found that the majority of globular clusters have single power-law mass functions F(m) ∝ mα with slopes α > −1 in the mass range 0.2 < m/M⊙ < 0.8. By exploring the correlations between the structural/dynamical and orbital parameters, we confirm the tight anticorrelation between the mass function slopes and the half-mass relaxation times already reported in previous works, and possible second-order dependence on the cluster metallicity. This might indicate the relative importance of both initial conditions and evolutionary effects on the present-day shape of the mass function.
ABSTRACT
The ‘chromosome map’ diagram (ChM) proved a successful tool to identify and characterize multiple populations (MPs) in 59 Galactic globular clusters (GCs). Here, we construct ChMs for 11 GCs ...of both Magellanic Clouds (MCs) and with different ages to compare MPs in Galactic and extragalactic environments, and explore whether this phenomenon is universal through ‘place’ and ‘time’. MPs are detected in five clusters. The fractions of 1G stars, ranging from ∼50 per cent to >80 per cent, are significantly higher than those observed in Galactic GCs with similar present-day masses. By considering both Galactic and MC clusters, the fraction of 1G stars exhibits: (i) a strong anticorrelation with the present-day mass, and (ii) with the present-day mass of 2G stars; (iii) a mild anticorrelation with 1G present-day mass. All Galactic clusters without MPs have initial masses smaller than ∼1.5 · 105 M⊙ but a mass threshold governing the occurrence of MPs seems challenged by massive simple-population MC GCs; (iv) Milky Way clusters with large perigalactic distances typically host larger fractions of 1G stars, but the difference disappears when we use initial cluster masses. These facts are consistent with a scenario where the stars lost by GCs mostly belong to the 1G. By exploiting recent work based on Gaia, half of the known Type II GCs appear clustered in a distinct region of the integral of motions space, thus suggesting a common progenitor galaxy. Except for these Type II GCs, we do not find any significant difference in the MPs between clusters associated with different progenitors.
We present new results on the evolution of the mass function of the globular cluster system of the Milky Way, taking the effect of residual gas expulsion into account. We assume that gas embedded ...star clusters start with a power-law mass function with slope β= 2, similar to what is observed for the Galactic open clusters and young, massive star clusters in interacting galaxies. The dissolution of the clusters is then studied under the combined influence of residual gas expulsion driven by energy feedback from massive stars, stellar mass loss, two-body relaxation and an external tidal field. The influence of residual gas expulsion is studied by applying results from a large grid of N-body simulations computed by Baumgardt & Kroupa. In our model, star clusters with masses less than 105M⊙ lose their residual gas on time-scales much shorter than their crossing time and residual gas expulsion is the main dissolution mechanism for star clusters, destroying about 95 per cent of all clusters within a few tens of Myr. We find that in this case the final mass function of globular clusters is established mainly by the gas expulsion and therefore nearly independent of the strength of the external tidal field, and that a power-law mass function for the gas embedded star clusters is turned into a present-day lognormal one, verifying the theory proposed by Kroupa & Boily. Our model provides a natural explanation for the observed (near-)universality of the peak of the globular cluster mass function within a galaxy and among different galaxies. Our simulations also show that globular clusters must have started a factor of a few more concentrated than as we see them today. Another consequence of residual gas expulsion and the associated strong infant mortality of star clusters is that the Galactic halo stars come from dissolved star clusters. Since field halo stars would come mainly from low-mass, short-lived clusters, our model would provide an explanation for the observed abundance variations of light elements among globular cluster stars and the absence of such variations among the halo field stars. Furthermore, our modelling suggests a natural tendency of >107M⊙ gas clouds to retain their residual gas despite multiple supernova events, possibly explaining the complex stellar populations observed in the most massive globular clusters.
The internal dynamics of multiple stellar populations in globular clusters (GCs) provides unique constraints on the physical processes responsible for their formation. Specifically, the present-day ...kinematics of cluster stars, such as rotation and velocity dispersion, could be related to the initial configuration of the system. In recent work, we provided the first study of the kinematics of different stellar populations in NGC 0104 over a large field of view in the plane of the sky, exploiting Gaia Data Release 2 (DR2) proper motions combined with multi-band ground-based photometry. In this paper, we combine Gaia DR2 proper motions with Very Large Telescope radial velocities to investigate the kinematics along the line of sight and in the plane of the sky of multiple populations in seven GCs, namely NGC 0104, NGC 0288, NGC 5904, NGC 6121, NGC 6254, NGC 6752, and NGC 6838. Among the analyzed clusters, only NGC 0104 and NGC 5904 show significant rotation. Separating our sample into two groups of first- and second-population stars (1P and 2P) we find that overall these two populations exhibit a similar rotation pattern in NGC 0104. However, some hints of different rotation are observed in the external regions of this cluster. Interestingly, 1P and 2P stars in NGC 5904 show different rotation curves, with distinct phases and such differences are significant at the ∼2.5 level. The analysis of the velocity-dispersion profiles of multiple populations confirms that 2P stars of NGC 0104 show stronger anisotropy than the 1P.
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