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Register a new userThe luminosity function of young star clusters: implications for the maximum mass and luminosity of clusters
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Authors
Mark Gieles
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We introduce a method to relate a possible truncation of the star cluster mass function at the high mass end to the shape of the cluster luminosity function (LF). We compare the observed LFs of five galaxies containing young star clusters with synthetic cluster population models with varying initial conditions. The LF of the SMC, the LMC and NGC 5236 are characterized by a power-law behavior NdL~L^-a dL, with a mean exponent of <a> = 2.0 +/- 0.2. This can be explained by a cluster population formed with a constant cluster formation rate, in which the maximum cluster mass per logarithmic age bin is determined by the size-of-sample effect and therefore increases with log(age/yr). The LFs of NGC 6946 and M51 are better described by a double power-law distribution or a Schechter function. When a cluster population has a mass function that is truncated below the limit given by the size-of-sample effect, the total LF shows a bend at the magnitude of the maximum mass, with the age of the oldest cluster in the population, typically a few Gyr due to disruption. For NGC 6946 and M51 this implies a maximum mass of M_max = 5*10^5 M_sun. Faint-ward of the bend the LF has the same slope as the underlying initial cluster mass function and bright-ward of the bend it is steeper. This behavior can be well explained by our population model. We compare our results with the only other galaxy for which a bend in the LF has been observed, the ``Antennae galaxies (NGC 4038/4039). There the bend occurs brighter than in NGC 6946 and M51, corresponding to a maximum cluster mass of M_max = 2*10^6 M_sun (abridged).
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We predict near-infrared luminosity functions of young (5 Myr to 1 Gyr) star clusters by combining evolutionary models of very low-mass ($1 M_J$ to $0.15 M_{odot}$) dwarfs with empirical bolometric corrections. We identify several characteristic features in our results. These can be attributed to three causes: (1) deuterium burning in the most massive substellar objects; (2) methane absorption in bodies with $T_{eff}$ less than 1300 K, the temperature of the L/T transition; and (3) the formation of dust clouds and the rainout of dust at roughly the same effective temperature as methane formation. Accurate reconstruction of the substellar mass function from luminosity function observations requires that these phenomena are taken into account. At present, few observational studies extend to sufficient sensitivities to allow detection of these effects. However, the luminosity function of the young open cluster IC 2391 shows a clear peak at $M_I sim 14$ which we attribute to the result of deuterium burning in substellar objects. The location of this feature is a strong function of age, and we estimate an age of 35 Myr for IC 2391. This is significantly younger than the 53 Myr derived from the location of the lithium depletion boundary but agrees with the main sequence turnoff age. We consider the implications of this result and our multi-band luminosity functions for future observational studies. All predicted luminosity function features are, or will be, accessible to observations using new wide-field IR imagers and the Space Infrared Telescope Facility.
When an universal untruncated star cluster initial mass function (CIMF) described by a power-law distribution is assumed, the mass of the most massive star cluster in a galaxy (M_max) is the result of the size-of-sample (SoS) effect. This implies a dependence of M_max on the total number of star clusters (N). The SoS effect also implies that M_max within a cluster population increases with equal logarithmic intervals of age. This is because the number of clusters formed in logarithmic age intervals increases (assuming a constant cluster formation rate). This effect has been observed in the SMC and LMC. Based on the maximum pressure (P_int) inside molecular clouds, it has been suggested that a physical maximum mass (M_max[phys]) should exist. The theory predicts that M_max[phys] should be observable, i.e. lower than M_max that follows from statistical arguments, in big galaxies with a high star formation rate. We compare the SoS relations in the SMC and LMC with the ones in M51 and model the integrated cluster luminosity function (CLF) for two cases: 1) M_max is determined by the SoS effect and 2) M_max=M_max[phys]=constant. The observed CLF of M51 and the comparison of the SoS relations with the SMC and LMC both suggest that there exists a M_max[phys] of 5*10^5 M_sun in M51. The CLF of M51 looks very similar to the one observed in the ``Antennae galaxies. A direct comparison with our model suggests that there M_max[phys]=2*10^6 M_sun.
Young massive clusters (YMCs) differ markedly from old globular clusters in featuring extended, rather than tidally truncated, envelopes. Their projected- luminosity profiles are well fit by Elson-Fall-Freeman (EFF) models with core radii of 0.3 pc < r_c < 8 pc and power-law envelopes of negative exponent 2 < gamma < 3.8. These envelopes form within the first few 10^6 yr and last ~10^8 to 10^9.5 yr, depending on the environment. Many young massive clusters show clumpy substructure that may accelerate their initial relaxation. The cores of Magellanic-Cloud clusters show universal expansion from r_c < 1 pc at birth to r_c = 2 - 3 pc after 10^8 yr, but then seem to evolve along two bifurcating branches in a r_c-log(age) diagram. The lower branch can be explained by mass-loss driven core expansion during the first 10^9 yr, followed by slow core contraction and the onset of core collapse due to evaporation. The upper branch, which shows continued core expansion proportional to logarithmic age, remains unexplained. There is strong evidence for rapid mass segregation in young clusters, yet little evidence for top-heavy IMFs or primordial mass segregation. Finally, YMCs show similar structure throughout the Local Group and as far away as we can resolve them (<~20 Mpc).
I review recent measurements of the faint end of the galaxy luminosity function in galaxy clusters. Evidence is presented that the luminosity function of galaxies in the central parts of clusters is remarkably constant between clusters and that this luminosity function is steep at bright and faint magnitudes and shallow in-between. The curvature is highly significant -- neither a power-law nor a Schechter function is consistent with the data. At no magnitude does alpha=-1 fit the data well. The faintest galaxies in all clusters that have been studied are dwarf spheroidal galaxies.
We present the UV composite luminosity function for galaxies in the Virgo, Coma and Abell 1367 clusters. The luminosity function (LF) is well fitted by a Schechter function with M*(UV} - 5*log h(75) = -20.75 +/- 0.40 and alpha = -1.50 +/- 0.10 and does not differ significantly from the local UV luminosity function of the field. This result is in agreement with recent studies carried out in the Halpha and B-bands which find no difference between the LFs of star forming galaxies in clusters and in the field. This indicates that, whatever mechanisms are responsible for quenching the star formation in clusters, they influence similarly the giant and the dwarf populations, leaving the shape of the LF unchanged and only modifying its normalization.
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