Showing papers on "Mass segregation published in 1997"

Internal dynamics of globular clusters

Abstract: Galactic globular clusters, which are ancient building blocks of our Galaxy, represent a very interesting family of stellar systems in which some fundamental dynamical processes have taken place on time scales shorter than the age of the universe. In contrast with galaxies, these clusters represent unique laboratories for learning about two-body relaxation, mass segregation from equipartition of energy, stellar collisions, stellar mergers, and core collapse. In the present review, we summarize the tremendous developments, as much theoretical as observational, that have taken place during the last two decades, and which have led to a quantum jump in our understanding of these beautiful dynamical systems.

Pal 1: Another Young Galactic Halo Globular Cluster?

Abstract: Deep V and I CCD images of the loosely populated Galactic globular cluster Pal 1 and the surrounding field have been obtained with the INT. A color magnitude diagram down to V(lim) ~ 24, and a luminosity function complete down to V(lim) ~ 23.25 have been constructed. Adopting a reddening E(V-I)=0.20+/-0.04 and comparing the CMD of Pal 1 with 47 Tucanae, we obtain a distance modulus (m-M)o=15.25+/-0.25, indicating that Pal 1 is located 3.7+/-0.4 kpc above the Galactic disc and 17.3+/-1.6 kpc from the Galactic center. Comparison with 47 Tuc and M71 shows that Pal 1 must be significantly younger. The best fitting isochrones (Bertelli et al, 1994) give an age between 6.3 and 8 Gyrs, which would make Pal 1 the youngest Galactic globular cluster so far identified, casting some doubt on the real nature of this object. The luminosity function shows some evidence for mass segregation, consistent with the very short relaxation time. The global mass function can be fitted with a power law of slope x=-1.4+/-0.7. This mass function is anomalously flat, suggesting either a strong dynamical evolution or an initial mass function significantly different from most of the other halo globular clusters. A discussion on the possible nature of Pal 1 is presented.

Deep HST/FOC Imaging of the Central Density Cusp of the Globular Cluster M15

Abstract: Using the Faint Object Camera on the repaired Hubble Space Telescope, we have observed two fields in the globular cluster M15: the central density cusp, and a field at r = 20''. These are the highest-resolution images ever taken of this cluster's dense core, and are the first to probe the distribution of stars well below the main-sequence turnoff. After correction for incompleteness, we measure a logarithmic cusp slope (d log \sigma / d log r) of -0.70 +- 0.05 (1-sigma) for turnoff (~ 0.8 \Msun) stars over the radial range from 0.3'' to 10''; this slope is consistent with previous measurements. We also set an approximate upper limit of ~1.5'' (90% confidence limit) on the size of any possible constant-surface-density core, but discuss uncertainties in this limit that arise from crowding corrections. We find that fainter stars in the cusp also have power-law density profiles: a mass group near 0.7 \Msun has a logarithmic slope of -0.56 +- 0.05 (1-sigma) over the radial range from 2'' to 10''. Taken together, the two slopes are not well matched by the simplest core-collapse or black-hole models. We also measure a mass function at r = 20'', outside of the central cusp. Both of the FOC fields show substantial mass segregation, when compared with a mass function measured with the WFPC2 at r = 5'. In comparing the overall mass functions of the two FOC fields and the r = 5' field, we find that the radial variation of the mass function is somewhat less than that predicted by a King-Michie model of the cluster, but greater than that predicted by a Fokker-Planck model taken from the literature.

Deep HST/FOC Imaging of the Central Density Cusp of the Globular Cluster M15

Abstract: Using the Faint Object Camera on the repaired Hubble Space Telescope, we have observed two fields in the globular cluster M15: the central density cusp, and a field at r = 20''. These are the highest-resolution images ever taken of this cluster's dense core, and are the first to probe the distribution of stars well below the main-sequence turnoff. After correction for incompleteness, we measure a logarithmic cusp slope (d log \sigma / d log r) of -0.70 +- 0.05 (1-sigma) for turnoff (~ 0.8 \Msun) stars over the radial range from 0.3'' to 10''; this slope is consistent with previous measurements. We also set an approximate upper limit of ~1.5'' (90% confidence limit) on the size of any possible constant-surface-density core, but discuss uncertainties in this limit that arise from crowding corrections. We find that fainter stars in the cusp also have power-law density profiles: a mass group near 0.7 \Msun has a logarithmic slope of -0.56 +- 0.05 (1-sigma) over the radial range from 2'' to 10''. Taken together, the two slopes are not well matched by the simplest core-collapse or black-hole models. We also measure a mass function at r = 20'', outside of the central cusp. Both of the FOC fields show substantial mass segregation, when compared with a mass function measured with the WFPC2 at r = 5'. In comparing the overall mass functions of the two FOC fields and the r = 5' field, we find that the radial variation of the mass function is somewhat less than that predicted by a King-Michie model of the cluster, but greater than that predicted by a Fokker-Planck model taken from the literature.

Mass Segregation and Equipartition of Energy in Two Globular Clusters with Central Density Cusps.

Abstract: We begin by presenting the analysis of a set of deep B- and V-band images of the central density cusp of the globular cluster M30 (NGC 7099), taken with the Faint Object Camera aboard the Hubble Space Telescope. These images are the first to resolve lower-mass main-sequence stars in the cluster's central 10''. From the positions of individual stars, we measure an improved position for the cluster center; this new position is 2.6'' from the previously known position. We find no evidence of a ``flat'', constant-surface-density core; however, the data do not rule out the presence of a core of radius up to 1.9'' (95% confidence level). We measure a logarithmic cusp slope (d \log \sigma / d \log r$) of -0.76 +- 0.07 (1-sigma) for stars with masses between 0.69 and 0.76 \Msun, and -0.82 +- 0.11 for stars with masses between 0.57 and 0.69 \Msun. We also compare the overall mass function (MF) of the cluster cusp with the MF of a field at r = 4.6' (near the cluster half-mass radius). The observed degree of mass segregation is well matched by the predictions of an isotropic, multimass King model. We then use the Jeans equation to compare the structure of M30 with that of M15, another cusped cluster, using data from this and a previous paper. We find that M30 is very close to achieving equipartition of energy between stellar species, at least over the observed range in mass and radius, while M15 is not. This difference may be a result of the longer relaxation time in the observed field in M15. The data also suggest that the degree of mass segregation within the two cluster cusps is smaller than one would expect from the measurements at larger radius. If so, this phenomenon might be the result of gravothermal oscillations, of centrally-concentrated populations of binaries, or of a ~10^3 \Msun black hole in one or more clusters.

The IMF Revisited: A Case for Variations

Abstract: A survey of results concerning the IMF derived from star counts is presented, including work up to, but not including, that pre- sented in these proceedings. The situation regarding low-mass stars in the field and in clusters, high-mass stars and intermediate-mass stars in clusters and associations of the Milky Way and LMC, pre-main sequence objects in visible and embedded clusters, and the IMF in galaxies more distant than the Magellanic Clouds is discussed, with an emphasis on the sources of uncertainty. Most of these uncertainties, especially radial mass segregation and unresolved binaries, would steepen the true IMF relative to the apparent IMF. Several cases of apparently large variations in cluster IMFs are pointed out, and a graphical comparison of results for about 60 clusters shows a spread of at least unity in the logarithmic IMF index for all mass ranges above about 1 M ⊙ . I conclude that either: 1. The uncertainties are so large that very little can be said about an average IMF or IMF variations; or 2. If the observations are taken at face value, there are strong indications of IMF variations, which do not seem to correlate with obvious environmental conditions like metallicity or stellar density. If there is an average IMF, I suggest that it is steepest at intermediate masses. If the variations are real, they offer a useful test of theoretical models.

The Faint End of the Luminosity Function of Galaxies in Compact Groups

Abstract: We study the luminosity function of galaxies in Hickson groups using our recent redshift survey of galaxies in and around 17 of these groups We find that the galaxies in these regions have a luminosity function with M* = -195 + 5 log h, and alpha = -10, where M* and alpha are the usual parameters in the standard Schechter form of the luminosity function, and the magnitudes are measured in the B band The formal 95% confidence intervals for M* and alpha range from (-193,-08), to (-197,-12) and are highly correlated as is usual for these fits This luminosity function for galaxies in our Hickson group sample is very similar from that found in large surveys covering a range of environments These values are also consistent with our earlier estimates based on a photometric analysis with statistical background correction, and do not support previous suggestions of an underabundance of intrinsically faint galaxies in compact groups We confirm our earlier finding that the fainter galaxies are more diffusely distributed within individual groups than the brighter ones This can be interpreted either as evidence for mass segregation within the groups or as the result of the selection procedure for Hickson groups

Mass Segregation and Equipartition of Energy in Two Globular Clusters with Central Density Cusps

Abstract: We begin by presenting the analysis of a set of deep B- and V-band images of the central density cusp of the globular cluster M30 (NGC 7099), taken with the Faint Object Camera aboard the Hubble Space Telescope. These images are the first to resolve lower-mass main-sequence stars in the cluster's central 10''. From the positions of individual stars, we measure an improved position for the cluster center; this new position is 2.6'' from the previously known position. We find no evidence of a ``flat'', constant-surface-density core; however, the data do not rule out the presence of a core of radius up to 1.9'' (95% confidence level). We measure a logarithmic cusp slope (d \log \sigma / d \log r$) of -0.76 +- 0.07 (1-sigma) for stars with masses between 0.69 and 0.76 \Msun, and -0.82 +- 0.11 for stars with masses between 0.57 and 0.69 \Msun. We also compare the overall mass function (MF) of the cluster cusp with the MF of a field at r = 4.6' (near the cluster half-mass radius). The observed degree of mass segregation is well matched by the predictions of an isotropic, multimass King model. We then use the Jeans equation to compare the structure of M30 with that of M15, another cusped cluster, using data from this and a previous paper. We find that M30 is very close to achieving equipartition of energy between stellar species, at least over the observed range in mass and radius, while M15 is not. This difference may be a result of the longer relaxation time in the observed field in M15. The data also suggest that the degree of mass segregation within the two cluster cusps is smaller than one would expect from the measurements at larger radius. If so, this phenomenon might be the result of gravothermal oscillations, of centrally-concentrated populations of binaries, or of a ~10^3 \Msun black hole in one or more clusters.

The Hyades: distance, structure, dynamics, and age

Abstract: We use absolute trigonometric parallaxes from the Hipparcos Catalogue to determine individual distances to members of the Hyades cluster, from which the 3-dimensional structure of the cluster can be derived. Inertially-referenced proper motions are used to rediscuss distance determinations based on convergent-point analyses. A combination of parallaxes and proper motions from Hipparcos, and radial velocities from ground-based observations, are used to determine the position and velocity components of candidate members with respect to the cluster centre, providing new information on cluster membership: 13 new candidate members within 20 pc of the cluster centre have been identified. Farther from the cluster centre there is a gradual merging between certain cluster members and field stars, both spatially and kinematically. Within the cluster, the kinematical structure is fully consistent with parallel space motion of the component stars with an internal velocity dispersion of about 0.3 km/s. The spatial structure and mass segregation are consistent with N-body simulation results, without the need to invoke expansion, contraction, rotation, or other significant perturbations of the cluster. The quality of the individual distance determinations permits the cluster zero-age main sequence to be accurately modelled. The helium abundance for the cluster is determined to be Y=0.26+/-0.02 which, combined with isochrone modelling including convective overshooting, yields a cluster age of 625+/-50 Myr. The distance to the observed centre of mass is 46.34+/-0.27 pc, corresponding to a distance modulus m-M=3.33+/-0.01 mag for the objects within 10 pc of the cluster centre (roughly corresponding to the tidal radius). Discrepancies with previous distance estimates are investigated and explained.

The IMF Revisited: A Case for Variations

Abstract: A survey of results concerning the IMF derived from star counts is presented, including work up to, but not including, that presented in these proceedings. The situation regarding low-mass stars in the field and in clusters, high-mass stars and intermediate-mass stars in clusters and associations of the Milky Way and LMC, pre-main sequence objects in visible and embedded clusters, and the IMF in galaxies more distant than the Magellanic Clouds is discussed, with an emphasis on the sources of uncertainty. Most of these uncertainties, especially radial mass segregation and unresolved binaries, would steepen the true IMF relative to the apparent IMF. Several cases of apparently large variations in cluster IMFs are pointed out, and a graphical comparison of results for about 60 clusters shows a spread of at least unity in the logarithmic IMF index for all mass ranges above about 1 $M_{\sun}$. I conclude that either: 1. The uncertainties are so large that very little can be said about an average IMF or IMF variations; or 2. If the observations are taken at face value, there are strong indications of IMF variations, which do not seem to correlate with obvious environmental conditions like metallicity or stellar density. If there is an average IMF, I suggest that it is steepest at intermediate masses. If the variations are real, they offer a useful test of theoretical models.

The Search for Main Sequence Binary Stars in Galactic Globular Clusters

Abstract: Binary stars should be present in relatively large numbers in globular clusters (GCs). While individual binary systems have been previously observed, until now, no large population had been detected in a dense GC. As part of this thesis, we developed a new technique to determine the fraction of main-sequence stars which are binaries. We analyzed the redward spread of the main-sequence ridge-line of the post-core-collapse GC NGC~6752. These data, obtained with post-refurbishment HST data, indicate that in the inner core-radius, the 3-σ lower and upper limits on the binary fraction are 15% and 38%, respectively. The region outside the core has a 3-σ upper limit on the binary fraction of 16%, and is consistent with no binaries. This rapid change in binary fraction is clear evidence of mass segregation operating within the inner 3 core-radii. We also find that the binary fraction increases at fainter magnitudes; mass segregation would also account for such behavior. We discuss the likely effects on the cluster's luminosity function (LF). In particular, we find that if the contribution of binaries to the LF was not removed, the apparent number of low mass stars would be over-estimated. I also examined the time-series data and discovered that one of the blue stragglers in NGC~6752 is an SX Phe pulsator. Its pulsation mass is 1-1.2 M⊙, consistent with the mass of the best fit stellar models from the Yale Isochrones, and also consistent with any of the blue straggler formation scenarios. No contact or eclipsing binaries were unambiguously detected. However, many low-amplitude variable candidates were observed at the limit of our ability to detect variability. The putative period of these candidate objects is consistent with these objects being produced via tidal capture events. In a time-series study of NGC~6397, we found a contact binary. This W~UMa system probably has a mass greater than that of main sequence turn-off stars implying that when this system coalesces due to angular momentum loss, it will become a blue straggler star. The frequency of W~UMas in this cluster is not statistically different from that of other GCs where ~0.1% of the main-sequence stars are contact binarie.

Determination of the globular cluster and halo stellar mass functions and stellar and brown dwarf densities

Abstract: We use recent low-mass star models, which reproduce accurately the observed sequences of various globular clusters, to convert the observed luminosity functions into bolometric luminosity functions. These latter are shown to exhibit a similar behaviour with a rising slope up to Mbol ∼ 9, i.e. m ∼ 0.2 − 0.3M , and a decreasing behaviour beyond this limit. We then derive mass functions for globular star clusters down to the bottom of the main sequence. These mass functions are well described by a slowly rising power-law dN/dm ∝ m−α, with 0.5 ∼< α ∼< 1.5, down to ∼ 0.1M , independently of the metallicity, suggesting a rather universal behaviour of the cluster initial mass functions. The effects of tidal stripping and mass segregation are illustrated by the overabundance of very low-mass stars in the outer parts of NGC6397 and their depletion in the central parts. This analysis confirms that the mass function determined near the half-mass radius has been weakly affected by external and internal dynamical effects and reflects relatively closely the initialmass function. We predict luminosity functions in the NICMOS filters in the stellar and in the brown dwarf domains for different mass functions and metallicities. We apply these calculations to the determination of the mass function in theGalactic halo, including theDeVaucouleurs spheroid and the 1/r2 dark halo.We derive the slope and the normalization of the spheroidmass functionwhich iswell described by the afore-mentioned power-law function with α ∼ 1.7±0.2 down to 0.1 M , although a slowly decreasing mass function below ∼ 0.15M can not be excluded with the data presently available. Comparisonwith theHubbleDeep Field star counts is consistent with such a mass function and excludes a significant stellar population in the dark halo. This shows that essentially all the high-velocity subdwarfs observed in the solar neighborhood belong to the Galactic spheroid. Consistent analysis with recent microlensing experiments towards the LMC shows that the spheroid and the dark-halo stellar+brown dwarf populations represent at most ∼ 1% of ? The bolometric LF’s displayed in Fig. 1 are available at CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html the Galactic dark matter density. This clearly excludes brown dwarfs and low-mass stars as significant darkmatter candidates.

Investigation of the Pleiades cluster. IV. The radial structure

Abstract: On the basis of the best available member list and duplicity information, we have studied the radial distribution of 270 stars and multiple systems earlier than K0 in the Pleiades. Five new long period spectroscopic binaries have been identified from the CORAVEL observations. We have found a clear mass segregation between binaries and single stars, which is explained by the greater average mass of the multiple systems. The mass function of the single stars and primaries appears to be significantly different. While the central part of the cluster is spherical, the outer part is clearly elliptical, with an ellipticity of 0.17. The various parameters describing the Pleiades are (for a distance of 125 pc): core radius r_{c}=0.6 deg (1.4 pc), tidal radius r_{t}=7.4 deg (16 pc), half mass radius r_{m/2}=0.88 deg (1.9 pc), harmonic radius r=1.82 deg (4 pc). Low-mass stars (later than K0) probably extend further out and new proper motion and radial velocity surveys over a larger area and to fainter magnitudes would be very important to improve the description of the cluster structure and complete mass function.

The Search for Main Sequence Binary Stars in Galactic Globular Clusters

Abstract: Binary stars should be present in relatively large numbers in globular clusters (GCs). While individual binary systems have been previously observed, until now, no large population had been detected in a dense GC. As part of this thesis, we developed a new technique to determine the fraction of main-sequence stars which are binaries. We analyzed the redward spread of the main-sequence ridge-line of the post-core-collapse GC NGC~6752. These data, obtained with post-refurbishment HST data, indicate that in the inner core-radius, the 3-σ lower and upper limits on the binary fraction are 15% and 38%, respectively. The region outside the core has a 3-σ upper limit on the binary fraction of 16%, and is consistent with no binaries. This rapid change in binary fraction is clear evidence of mass segregation operating within the inner 3 core-radii. We also find that the binary fraction increases at fainter magnitudes; mass segregation would also account for such behavior. We discuss the likely effects on the cluster's luminosity function (LF). In particular, we find that if the contribution of binaries to the LF was not removed, the apparent number of low mass stars would be over-estimated. I also examined the time-series data and discovered that one of the blue stragglers in NGC~6752 is an SX Phe pulsator. Its pulsation mass is 1-1.2 M⊙, consistent with the mass of the best fit stellar models from the Yale Isochrones, and also consistent with any of the blue straggler formation scenarios. No contact or eclipsing binaries were unambiguously detected. However, many low-amplitude variable candidates were observed at the limit of our ability to detect variability. The putative period of these candidate objects is consistent with these objects being produced via tidal capture events. In a time-series study of NGC~6397, we found a contact binary. This W~UMa system probably has a mass greater than that of main sequence turn-off stars implying that when this system coalesces due to angular momentum loss, it will become a blue straggler star. The frequency of W~UMas in this cluster is not statistically different from that of other GCs where ~0.1% of the main-sequence stars are contact binarie.

The stellar distribution of the globular cluster M 55

Abstract: We have used extensive V , I photometry (down to V =2 0 :9) of 33615 stars in the direction of the globular cluster M 55 to study the dynamical interaction of this cluster with the tidal elds of the Galaxy. An entire quadrant of the cluster has been covered, out to ' 1:5 times the tidal radius. A CMD down to about 4 magnitudes below the turn-off is presented and analysed. A large population of BS has been identied. The BS are signicantly more concentrated than the other cluster stars in the inner 300 arcsec, while they become less concentrated in the cluster envelope. We have obtained luminosity functions at various radial in- tervals from the center and their corresponding mass functions. Both clearly show the presence of mass segregation inside the cluster. A dynamical analysis shows that the observed mass segregation is compatible with what is predicted by multi-mass King-Michie models. The global mass function is very flat with a power-law slope of x = 1:0 0:4. This suggest that M 55 might have suffered selective losses of stars, caused by tidal interactions with the Galactic disk and bulge. The radial density prole of M 55 out to 2 rt suggests thepresenceofextra-tidalstarswhosenaturecouldbeconnected with the cluster.

The Influence of a Mass Spectrum on the Long Term Evolution of a Self-Gravitating System of Softened Particles

Abstract: Using N-body simulations, we study the effects of the mass spectrum in the evolution of self-gravitating systems of softened point-mass particles The mass function is described by a power law and the ratio between the maximum and minimum mass is \({\text{10}}^{\text{4}} \) We showed that the dynamical evolution of the system depends on the mass spectrum: the secular evolution time is longer for flatter mass spectrum For the steepest mass spectrum, the secular evolution time is of the order of the relaxation time The mass segregation effects are achieved rapidly and the core-halo structures are formed The projected number distributions for the systems with mass spectrum change drastically with the evolution while the projected mass distributions are not affected Velocity dispersion profiles are modified in the sense of heating of the central regions of the systems, while the velocity anisotropy profiles are slightly affected The consequence of our results on the dynamical evolution of clusters of galaxies is presented

The spatial distribution and luminosity function of the open cluster NGC 4815

Abstract: NGC 4815 is a distant and populous open cluster, which lies in the galactic plane in a region of strong absorption. As a consequence, its membership, spatial distribution and luminosity function are not well determined. In this paper, we present an algorithm which uses both positional and photometric data simultaneously to search for open cluster members. The contribution of the field stars is estimated by our Galaxy model software. The method has been developed for deep CCD photometric observations, but it can also be used to investigate the membership in an n-dimensional space, including proper motions, radial velocity and metallicity. A clean and well defined colour-magnitude diagram (CMD) for NGC 4815 has been obtained after decontaminating from field stars. We have investigated the spatial distribution of cluster members and the luminosity function. We have shown that the projected surface distribution of stars is well-represented by an exponentially decreasing function with a scale length of 1.67 $\pm$ 0.06 arcmin. We have found evidence for mass segregation. The luminosity function for NGC 4815 is similar to that of the Hyades cluster, and shows a gap at $V$ = 15 mag.

The Luminosity and Mass Function of the Globular Cluster NGC1261

Abstract: I-band CCD images of two large regions of the Galactic globular cluster NGC 1261 have been used to construct stellar luminosity functions (LF) for 14000 stars in three annuli from 1.4' from the cluster center to the tidal radius. The LFs extend to M_I~8 and tend to steepen from the inner to the outer annulus, in agreement with the predictions of the multimass King-Michie model that we have calculated for this cluster. The LFs have been transformed into mass functions. Once corrected for mass segregation the global mass function of NGC 1261 has a slope x_0=0.8+/-0.5

I. A cluster core with encounters between single stars

Abstract: Star clusters with a high central density contain an ecologicalnetworkofevolvingbinaries,affectedbyinteractions with passing stars, while in turn affecting the energy budget of the cluster as a whole by giving off binding energy. This is the rst paper in a series aimed at providing the tools for increasingly realistic simulations of these ecological networks. Here we model the core of a globular star cluster. The two main approximations are: a density of stars constant in space and time, and a purely single star population in which colli- sions between the evolving stars are modeled. In future papers in this series, we will relax these crude approximations. Here, however, they serve to set the stage before proceeding to the additional complexity of binary star interactions, in paper II, and background dynamical evolution, in later papers. Great progress has been made with the rst step, modeling the dynamical evolution of point-mass systems. In the seven- ties, the processes of core collapse and mass segregation were studied with the use of various types of Fokker-Planck approx- imations. In the eighties, these simulations were extended suc- cessfully beyond core collapse, and various studies were made of the phenomenon of gravothermal oscillations, ubiquitous in the post-collapse phase. Of these models a few even include mass loss due to the evolution of the stars (Chernoff & Wein- berg 1990). In the nineties, we are nally beginning to switch overfromFokker-Planckapproximationstomuchmoredetailed and realistic N-body simulations. In 1995, the construction of the GRAPE-4, a special-purpose machine with Teraflops speed, hasmadea32;000{bodysimulationfeasible,providingtherst direct evidence of gravothermal oscillations (Makino, 1996ab). Extending these simulations to the full realm of globular clus- ters (N =1 0 5 10 6 ) will require Petaflops speed, something that could be realized by future special-purpose machines in the GRAPE series by as early as the year 2000.

Mass Segregation in Young LMC Clusters I. NGC 2157

Abstract: We have carried out WFPC2 V- and I-band imaging of the young LMC cluster NGC 2157. Construction of a color-magnitude diagram and isochrone fitting yields an age of tau = 100 000 000 yrs, a reddening E(B-V) = 0.1 and a distance modulus of 18.4 mag. Our data covers the mass range 0.75 < m < 5.1 solar masses. We find that the cluster mass function changes significantly from the inner regions to the outer regions, becoming steeper (larger number of low mass stars relative to high mass stars) at larger radii. The age of NGC 2157 is comparable to its two-body relaxation timescale only in the cluster core. The observed steepening of the mass function at larger radii is therefore most likely an initial condition of the cluster stars. Such initial conditions are predicted in models of cluster star formation in which dissipative processes act more strongly upon more massive stars.