Gravothermal Catastrophe in Anisotropic Spherical Systems

In this paper we investigate the gravothermal instability of spherical stellar systems endowed with a radially anisotropic velocity distribution. We focus our attention on the effects of anisotropy on the conditions for the onset of the instability and in particular we study the dependence of the spatial structure of critical models on the amount of anisotropy present in a system. The investigation has been carried out by the method of linear series which has already been used in the past to study the gravothermal instability of isotropic systems. We consider models described by King, Wilson and Woolley-Dickens distribution functions. In the case of King and Woolley-Dickens models, our results show that, for quite a wide range of amount of anisotropy in the system, the critical value of the concentration of the system (defined as the ratio of the tidal to the King core radius of the system) is approximately constant and equal to the corresponding value for isotropic systems. Only for very anisotropic systems the critical value of the concentration starts to change and it decreases significantly as the anisotropy increases and penetrates the inner parts of the system. For Wilson models the decrease of the concentration of critical models is preceded by an intermediate regime in which critical concentration increases, it reaches a maximum and then it starts to decrease. The critical value of the central potential always decreases as the anisotropy increases.Comment: 7pages, 5figures, to appear in MNRAS (figures have been replaced with their corrected versions

Dynamical evolution of the mass function and radial profile of the Galactic globular cluster system

Evolution of the mass function (MF) and radial distribution (RD) of the Galactic globular cluster (GC) system is calculated using an advanced and a realistic Fokker-Planck (FP) model that considers dynamical friction, disc/bulge shocks and eccentric cluster orbits. We perform hundreds of FP calculations with different initial cluster conditions, and then search a wide-parameter space for the best-fitting initial GC MF and RD that evolves into the observed present-day Galactic GC MF and RD. By allowing both MF and RD of the initial GC system to vary, which is attempted for the first time in the present Letter, we find that our best-fitting models have a higher peak mass for a lognormal initial MF and a higher cut-off mass for a power-law initial MF than previous estimates, but our initial total masses in GCs, M_{T,i} = 1.5-1.8x10^8 Msun, are comparable to previous results. Significant findings include that our best-fitting lognormal MF shifts downward by 0.35 dex during the period of 13 Gyr, and that our power-law initial MF models well-fit the observed MF and RD only when the initial MF is truncated at >~10^5 Msun. We also find that our results are insensitive to the initial distribution of orbit eccentricity and inclination, but are rather sensitive to the initial concentration of the clusters and to how the initial tidal radius is defined. If the clusters are assumed to be formed at the apocentre while filling the tidal radius there, M_{T,i} can be as high as 6.9x10^8 Msun, which amounts to ~75 per cent of the current mass in the stellar halo.Comment: To appear in May 2008 issue of MNRAS, 386, L6

On the Globular Cluster IMF below 1 Solar Mass

(Abridged) Accurate luminosity functions (LF) for a dozen globular clusters have now been measured at or just beyond their half-light radius using HST. They span almost the entire cluster main sequence below ~ 0.75 Msolar. All these clusters exhibit LF that rise continuously from an absolute I magnitude M_I ~ 6 to a peak at M_I ~ 8.5-9 and then drop with increasing M_I. Transformation of the LF into mass functions (MF) by means of the most recent mass luminosity relations that are consistent with all presently available data on the physical properties of low mass, low metallicity stars shows that all the LF observed so far can be obtained from MF having the shape of a log-normal distribution with characteristic mass m_c=0.33 +/- 0.03 Msolar and standard deviation sigma = 1.81 +/- 0.19. After correction for the effects of mass segregation, the variation of the ratio of the number of higher to lower mass stars with cluster mass or any simple orbital parameter or the expected time to disruption recently computed for these clusters shows no statistically significant trend over a range of this last parameter of more than a factor of 100. We conclude that the global MF of these clusters have not been measurably modified by evaporation and tidal interactions with the Galaxy and, thus, should reflect the initial distribution of stellar masses. Since the log-normal function that we find is also very similar to the one obtained independently for much younger clusters and to the form expected theoretically, the implication seems to be unavoidable that it represents the true stellar IMF for this type of stars in this mass range.Comment: Accepted for publication in The Astrophysical Journal. Contains 28 pages with 6 figure

Star count density profiles and structural parameters of 26 Galactic globular clusters

We used a proper combination of high-resolution HST observations and wide-field ground based data to derive the radial star density profile of 26 Galactic globular clusters from resolved star counts (which can be all freely downloaded on-line). With respect to surface brightness (SB) profiles (which can be biased by the presence of sparse, bright stars), star counts are considered to be the most robust and reliable tool to derive cluster structural parameters. For each system a detailed comparison with both King and Wilson models has been performed and the most relevant best-fit parameters have been obtained. This is the largest homogeneous catalog collected so far of star count profiles and structural parameters derived therefrom. The analysis of the data of our catalog has shown that: (1) the presence of the central cusps previously detected in the SB profiles of NGC 1851, M13 and M62 is not confirmed; (2) the majority of clusters in our sample are fitted equally well by the King and the Wilson models; (3) we confirm the known relationship between cluster size (as measured by the effective radius) and galactocentric distances; (4) the ratio between the core and the effective radii shows a bimodal distribution, with a peak at ~ 0.3 for about 80% of the clusters, and a secondary peak at ~ 0.6 for the remaining 20%. Interestingly, the main peak turns out to be in agreement with what expected from simulations of cluster dynamical evolution and the ratio between these two radii well correlates with an empirical dynamical age indicator recently defined from the observed shape of blue straggler star radial distribution, thus suggesting that no exotic mechanisms of energy generation are needed in the cores of the analyzed clusters.Comment: Accepted for publication in The Astrophysical Journal; 19 pages (emulateapj style), 15 figures, 2 table

Stability of dense stellar clusters against relativistic collapse. II Maxwellian distribution functions with different cutoff parameters

We investigate the stability of dense stellar clusters against relativistic collapse by approximate methods described in the previous paper in this series. These methods, together with the analysis of the fractional binding energy of the system, have been applied to sequences of equilibrium models, with cutoff in the distribution function, which generalize those studied by Zeldovich & Podurets. We show the existence of extreme configurations, which are stable all the way up to infinite values of the central redshift

Why haven't loose globular clusters collapsed yet?

We report on the discovery of a surprising observed correlation between the slope of the low-mass stellar global mass function (GMF) of globular clusters (GCs) and their central concentration parameter c=log(r_t/r_c), i.e. the logarithmic ratio of tidal and core radii. This result is based on the analysis of a sample of twenty Galactic GCs with solid GMF measurements from deep HST or VLT data. All the high-concentration clusters in the sample have a steep GMF, most likely reflecting their initial mass function. Conversely, low-concentration clusters tend to have a flatter GMF implying that they have lost many stars via evaporation or tidal stripping. No GCs are found with a flat GMF and high central concentration. This finding appears counter-intuitive, since the same two-body relaxation mechanism that causes stars to evaporate and the cluster to eventually dissolve should also lead to higher central density and possibly core-collapse. Therefore, more concentrated clusters should have lost proportionately more stars and have a shallower GMF than low concentration clusters, contrary to what is observed. It is possible that severely depleted GCs have also undergone core collapse and have already recovered a normal radial density profile. It is, however, more likely that GCs with a flat GMF have a much denser and smaller core than suggested by their surface brightness profile and may well be undergoing collapse at present. In either case, we may have so far seriously underestimated the number of post core-collapse clusters and many may be lurking in the Milky Way.Comment: Four pages, one figure, accepted for publication in ApJ Letter

The influence of residual gas expulsion on the evolution of the Galactic globular cluster system and the origin of the Population II halo

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 \beta=2. 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 (2007). In our model, star clusters with masses less than 10^5 M_sun lose their residual gas on timescales much shorter than their crossing time and residual gas expulsion is the main dissolution mechanism for star clusters, destroying about 95% of all clusters within a few 10s 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 log-normal one. 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 provides 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.Comment: 12 pages, 9 figures, MNRAS accepte

Deep HST-WFPC2 photometry of NGC 288. II. The Main Sequence Luminosity Function

The Main Sequence Luminosity Function (LF) of the Galactic globular cluster NGC 288 has been obtained using deep WFPC2 photometry. We have employed a new method to correct for completeness and fully account for bin-to-bin migration due to blending and/or observational scatter. The effect of the presence of binary systems in the final LF is quantified and is found to be negligible. There is a strong indication of the mass segregation of unevolved single stars and clear signs of a depletion of low mass stars in NGC 288 with respect to other clusters. The results are in good agreement with the prediction of theoretical models of the dynamical evolution of NGC 288 that take into account the extreme orbital properties of this cluster.Comment: 16 pages, 6 .ps figures. Low resolution version of fig. 1; full resolution figure soon available at http://www.bo.astro.it/bap/BAPhome.html l. Latex. emulateapj5.sty macro included. Accepted for publication by The Astronomical Journa

Gemini Spectroscopic Survey of Young Star Clusters in Merging/Interacting Galaxies. II. NGC 3256 Clusters

We present Gemini optical spectroscopy of 23 young star clusters in NGC3256. We find that the cluster ages range are from few Myr to ~150 Myr. All these clusters are relatively massive (2--40)x 10^{5} \msun$ and appear to be of roughly 1.5 \zo metallicity. The majority of the clusters in our sample follow the same rotation curve as the gas and hence were presumably formed in the molecular-gas disk. However, a western subsample of five clusters has velocities that deviate significantly from the gas rotation curve. These clusters may either belong to the second spiral galaxy of the merger or may have formed in tidal-tail gas falling back into the system. We discuss our observations in light of other known cluster populations in merging galaxies, and suggest that NGC 3256 is similar to Arp 220, and hence may become an Ultra-luminous Infrared Galaxy as the merger progresses and the star-formation rate increases. Some of the clusters which appeared as isolated in our ground-based images are clearly resolved into multiple sub-components in the HST-ACS images. The same effect has been observed in the Antennae galaxies, showing that clusters are often not formed in isolation, but instead tend to form in larger groups or cluster complexes.Comment: 20 pages, 10 figures, 3 tables; Accepted Ap

Interpreting the M22 Spike Events

Recently Sahu et al., using the Hubble Space Telescope to monitor stars in the direction of the old globular cluster M22, detected six events in which otherwise constant stars brightened by ~50% during a time of <1 day. They tentatively interpret these unresolved events as due to microlensing of background bulge stars by free-floating planets in M22. I show that if these spike events are due to microlensing, the lensing objects are unlikely to be associated with M22, and unlikely to be part of a smoothly distributed Galactic population. Thus either there happens to be a massive, dark cluster of planets along our line-of-sight to M22, or the spike events are not due to microlensing. The lensing planets cannot be bound to stars in the core of M22: if they were closer than 8 AU, the lensing influence of the parent star would have been detectable. Moreover, in the core of M22, all planets with separations > 1 AU would have been ionized by random stellar encounters. Most unbound planets would have escaped the core via evaporation which preferentially affects such low-mass objects. Bound or free-floating planets can exist in the outer halo of M22; however, for reasonable assumptions, the maximum optical depth to such a population falls short of the observed optical depth, tau ~ 3x10^{-6}, by a factor of 5-10. Therefore, if real, these events represent the detection of a significant free-floating Galactic planet population. The optical depth to these planets is comparable to and mutually exclusive from the optical depth to resolved events measured by microlensing survey collaborations toward the bulge, and thus implies a similar additional mass of lensing objects. Such a population is difficult to reconcile with both theory and observations.Comment: Minor changes. 12 pages, 4 figures, 2 tables. Accepted to ApJ. To appear in Feb 10, 2002 issue (v566