Lognormal Mass Function Research Articles

Evidence for a bottom-light initial mass function in massive star clusters

ABSTRACT We have determined stellar mass functions of 120 Milky Way globular clusters and massive Large Magellanic Cloud/Small Magellanic Cloud star clusters based on a comparison of archival Hubble Space Telescope photometry with a large grid of direct N-body simulations. We find a strong correlation of the global mass function slopes of star clusters with both their internal relaxation times and their lifetimes. Once dynamical effects are being accounted for, the mass functions of most star clusters are compatible with an initial mass function described by a broken power-law distribution N(m) ∼ mα with break masses at 0.4 and 1.0 M⊙ and mass function slopes of αLow = −0.3 for stars with masses m < 0.4 M⊙, αHigh = −2.30 for stars with m > 1.0 M⊙, and αMed = −1.65 for intermediate-mass stars. Alternatively, a lognormal mass function with a characteristic mass log MC = −0.36 and width σC = 0.28 for low-mass stars and a power-law mass function for stars with m > 1 M⊙ also fit our data. We do not find a significant environmental dependence of the initial mass function on cluster mass, density, global velocity dispersion, or metallicity. Our results lead to a larger fraction of high-mass stars in globular clusters compared to canonical Kroupa/Chabrier mass functions, increasing the efficiency of self-enrichment in clusters and helping to alleviate the mass budget problem of multiple stellar populations in globular clusters. By comparing our results with direct N-body simulations, we finally find that only simulations in which most black holes are ejected by natal birth kicks correctly reproduce the observed correlations.

A boosted gravitational wave background for primordial black holes with broad mass distributions and thermal features

Primordial black holes (PBHs) with a wide mass distribution imprinted by the thermal history of the Universe, which naturally produces a high peak at the solar mass scale, could explain the gravitational-wave events seen by LIGO/Virgo and up to the totality of the dark matter. We show that compared to monochromatic or log-normal mass functions, the gravitational wave backgrounds (GWBs) from early PBH binaries and from late binaries in clusters are strongly enhanced at low frequency and could even explain the NANOGrav observations. This enhancement comes from binaries with very low mass ratios, involving solar-mass and intermediate-mass PBHs at low frequency, solar-mass and subsolar-mass at high frequency. LISA could distinguish the various models, while in the frequency band of ground-based detectors, we find that the GWB from early binaries is just below the current LIGO/Virgo limits and above the astrophysical background, if they also explain black hole mergers. The GWB from binaries in clusters is less boosted but has a different spectral index than for neutron stars, astrophysical black holes or early PBH binaries. It is detectable with Einstein Telescope or even with the LIGO/Virgo design sensitivity.

Search for Lensing Signatures from the Latest Fast Radio Burst Observations and Constraints on the Abundance of Primordial Black Holes

Abstract The possibility that primordial black holes (PBHs) form some part of dark matter has been considered for a long time but poorly constrained over a wide mass range. Fast radio bursts (FRBs) are bright radio transients with millisecond duration. Their lensing effect has been proposed to be one of the cleanest probes for constraining the presence of PBHs in the stellar-mass window. In this paper, we first apply the normalized cross-correlation algorithm to search and identify candidates for lensed FRBs in the latest public FRB observations, i.e., 593 FRBs, which mainly consist of the first Canadian Hydrogen Intensity Mapping Experiment FRB catalog, and then derive constraints on the abundance of PBHs from the null search result of the lensing signature. For a monochromatic mass distribution, the fraction of dark matter made up of PBHs could be constrained to ≤87% for ≥500 M ⊙ at the 95% confidence level by assuming signal-to-noise ratios dependent on the flux ratio threshold for each FRB and that apparently one-off events are intrinsic single bursts. This result would be improved by a factor of 3 when a conventional constant flux ratio threshold is considered. Moreover, we derive constraints on PBHs with a log-normal mass function naturally predicted by some popular inflation models and often investigated with gravitational-wave detections. We find that, in this mass distribution scenario, the constraint from the current public FRB observations is relatively weaker than the one from gravitational-wave detections. It is foreseen that upcoming complementary multimessenger observations will yield considerable constraints on the possibilities of PBHs in this intriguing mass window.

Isotropic x-ray bound on primordial black hole dark matter

We revisit the constraints on evaporating primordial black holes (PBHs) from the isotropic X-ray and soft gamma-ray background in the mass range $10^{16}-10^{18}$ g. We find that they are stronger than usually inferred due to two neglected effects: i) The contribution of the annihilation radiation due to positrons emitted in the evaporation process. ii) The high-latitude, Galactic contribution to the measured isotropic flux. We study the dependence of the bounds from the datasets used, the positron annihilation conditions, and the inclusion of the astrophysical background. We push the exclusion limit for non-spinning PBH with monochromatic mass function as the totality of dark matter to 1.5$\times 10^{17}\,$g, which represents a $\sim$15$\%$ improvement with respect to earlier bounds and translates into almost an order of magnitude improvement in the PBH fraction in the already probed region. We also show that the inclusion of spin and/or an extended, log-normal mass function lead to tighter bounds. Our study suggests that the isotropic flux is an extremely promising target for future missions in improving the sensitivity to PBHs as candidates for dark matter.

Possibility of primordial black holes as the source of gravitational wave events in the advanced LIGO detector

The analysis of gravitational Wave (GW) data from advanced LIGO provides the mass of each companion of binary black holes as the source of GWs. The mass of events corresponding to the binary black holes from GW is above $20$ M$_\odot$ which is much larger than the mass of astrophysical black holes detected by x-ray observations. In this work, we examine primordial black holes (PBHs) as the source of LIGO events. Assuming that $100\%$ of the dark matter is made of PBHs, we estimate the rate at which these objects make binaries, merge, and produce GWs as a function of redshift. The gravitational lensing of GWs by PBHs can also enhance the amplitude of the strain. We simulate GWs sourced by binary PBHs, with the detection threshold of $S/N>10$ for both Livingston and Hanford detectors. For the log-normal mass function of PBHs, we generate the expected distribution of events, compare our results with the observed events, and find the best value of the mass function parameters (i.e., $M_c =25 M_\odot$ and $\sigma=0.6$) in the log-normal mass function. Comparing the expected number of events with the number of observed ones rules out the present-Universe binary formation PBH scenario as the candidate for the source of GW events detected by LIGO.

A possible mass distribution of primordial black holes implied by LIGO-Virgo

The LIGO-Virgo Collaboration has so far detected around 90 black holes, some of which have masses larger than what were expected from the collapse of stars. The mass distribution of LIGO-Virgo black holes appears to have a peak at ∼ 30M ☉ and two tails on the ends. By assuming that they all have a primordial origin, we analyze the GWTC-1 (O1&O2) and GWTC-2 (O3a) datasets by performing maximum likelihood estimation on a broken power law mass function f(m), with the result f ∝ m 1.2 for m < 35 M ☉ and f ∝ m -4 for m > 35 M ☉. This appears to behave better than the popular log-normal mass function. Surprisingly, such a simple and unique distribution can be realized in our previously proposed mechanism of PBH formation, where the black holes are formed by vacuum bubbles that nucleate during inflation via quantum tunneling. Moreover, this mass distribution can also provide an explanation to supermassive black holes formed at high redshifts.

Bayesian analysis of LIGO-Virgo mergers: Primordial versus astrophysical black hole populations

We conduct a thorough Bayesian analysis of the possibility that the black hole merger events seen in gravitational waves are primordial black hole (PBH) mergers. Using the latest merger rate models for PBH binaries drawn from a lognormal mass function we compute posterior parameter constraints and Bayesian evidences using data from the first two observing runs of LIGO-Virgo. We account for theoretical uncertainty due to possible disruption of the binary by surrounding PBHs, which can suppress the merger rate significantly. We also consider simple astrophysically motivated models and find that these are favoured decisively over the PBH scenario, quantified by the Bayesian evidence ratio. Paying careful attention to the influence of the parameter priors and the quality of the model fits, we show that the evidence ratios can be understood by comparing the predicted chirp mass distribution to that of the data. We identify the posterior predictive distribution of chirp mass as a vital tool for discriminating between models. A model in which all mergers are PBH binaries is strongly disfavoured compared with astrophysical models, in part due to the over-prediction of heavy systems having $\mathcal{M}_{{\rm chirp}} \gtrsim 40 \, M_\odot$ and positive skewness over the range of observed masses which does not match the observations. We find that the fit is not significantly improved by adding a maximum mass cut-off, a bimodal mass function, or imposing that PBH binaries form at late times. We argue that a successful PBH model must either modify the lognormal shape of the initial mass function significantly or abandon the hypothesis that all observed merging binaries are primordial. We develop and apply techniques for analysing PBH models with gravitational wave data which will be necessary for robust statistical inference as the gravitational wave source sample size increases.

Mean proper motions, space orbits, and velocity dispersion profiles of Galactic globular clusters derived fromGaiaDR2 data

We have derived the mean proper motions and space velocities of 154 Galactic globular clusters and the velocity dispersion profiles of 141 globular clusters based on a combination of Gaia DR2 proper motions with ground-based line-of-sight velocities. Combining the velocity dispersion profiles derived here with new measurements of the internal mass functions allows us to model the internal kinematics of 144 clusters, more than 90% of the currently known Galactic globular cluster population. We also derive the initial cluster masses by calculating the cluster orbits backwards in time applying suitable recipes to account for mass loss and dynamical friction. We find a correlation between the stellar mass function of a globular cluster and the amount of mass lost from the cluster, pointing to dynamical evolution as one of the mechanisms shaping the mass function of stars in clusters. The mass functions also show strong evidence that globular clusters started with a bottom-light initial mass function. Our simulations show that the currently surviving globular cluster population has lost about 80% of its mass since the time of formation. If globular clusters started from a log-normal mass function, we estimate that the Milky Way contained about 500 globular clusters initially, with a combined mass of about $2.5 \cdot 10^8$ $M_\odot$. For a power-law initial mass function, the initial mass in globular clusters could have been a factor of three higher.

CMB bounds on disk-accreting massive primordial black holes

Stellar-mass Primordial Black Holes (PBH) have been recently reconsidered as a Dark Matter (DM) candidate, after the aLIGO discovery of several binary BH mergers with masses of tens of $M_\odot$. Matter accretion on such massive objects leads to the emission of high-energy photons, capable of altering the ionization and thermal history of the universe. This in turn affects the statistical properties of the cosmic microwave background (CMB) anisotropies. Previous analyses have assumed spherical accretion. We argue that this approximation likely breaks down and that an accretion disk should form in the dark ages. Using the most up-to-date tools to compute the energy deposition in the medium, we derive constraints on the fraction of DM in PBH. Provided that disks form early on, even under conservative assumptions for accretion, these constraints exclude a monochromatic distribution of PBH with masses above $\sim 2\, M_\odot$ as the dominant form of DM. The bound on the median PBH mass gets more stringent if a broad, log-normal mass function is considered. A deepened understanding of non-linear clustering properties and BH accretion disk physics would permit an improved treatment and possibly lead to more stringent constraints.

The Formation and Evolution of Star Clusters in Interacting Galaxies

Abstract Observations of globular clusters show that they have universal lognormal mass functions with a characteristic peak at , but the origin of this peaked distribution is highly debated. Here we investigate the formation and evolution of star clusters (SCs) in interacting galaxies using high-resolution hydrodynamical simulations performed with two different codes in order to mitigate numerical artifacts. We find that massive SCs in the range of form preferentially in the highly shocked regions produced by galaxy interactions. The nascent cluster-forming clouds have high gas pressures in the range of , which is times higher than the typical pressure of the interstellar medium but consistent with recent observations of a pre-super-SC cloud in the Antennae Galaxies. Furthermore, these massive SCs have quasi-lognormal initial mass functions with a peak around . The number of clusters declines with time due to destructive processes, but the shape and the peak of the mass functions do not change significantly during the course of galaxy collisions. Our results suggest that gas-rich galaxy mergers may provide a favorable environment for the formation of massive SCs such as globular clusters, and that the lognormal mass functions and the unique peak may originate from the extreme high-pressure conditions of the birth clouds and may survive the dynamical evolution.

NGC 3105: A Young Cluster in the Outer Galaxy∗ †

Abstract Images and spectra of the open cluster NGC 3105 have been obtained with the Gemini Multi-Object Spectrograph on Gemini South. The color–magnitude diagram (CMD) constructed from these data extends from the brightest cluster members to . This is mag fainter than previous CMDs at visible wavelengths and allowing cluster members with sub-solar masses to be sampled. Assuming a half-solar metallicity, comparisons with isochrones yield a distance of 6.6 ± 0.3 kpc. An age of at least 32 Myr is found based on the photometric properties of the brightest stars, coupled with the apparent absence of pre-main-sequence stars in the lower regions of the CMD. The luminosity function of stars between 50 and 70 arcsec from the cluster center is consistent with a Chabrier lognormal mass function. However, at radii smaller than 50 arcsec there is a higher specific frequency of the most massive main-sequence (MS) stars than at larger radii. Photometry obtained from archival SPITZER images reveals that some of the brightest stars near NGC 3105 have excess infrared emission, presumably from warm dust envelopes. Hα emission is detected in a few early-type stars in and around the cluster, building upon previous spectroscopic observations that found Be stars near NGC 3105. The equivalent width of the NaD lines in the spectra of early-type stars is consistent with the reddening found from comparisons with isochrones. Stars with that fall near the cluster MS have a spectral-type A5V, and a distance modulus that is consistent with that obtained by comparing isochrones with the CMD is found assuming solar neighborhood intrinsic brightnesses for these stars.

Binary mass ratios: system mass not primary mass

Abstract Binary properties are usually expressed (for good observational reasons) as a function of primary mass. It has been found that the distribution of companion masses – the mass ratio distribution – is different for different primary masses. We argue that system mass is the more fundamental physical parameter to use. We show that if system masses are drawn from a log-normal mass function, then the different observed mass ratio distributions as a function of primary mass, from M-dwarfs to A-stars, are all consistent with a universal, flat, system mass ratio distribution. We also show that the brown dwarf mass ratio distribution is not drawn from the same flat distribution, suggesting that the process which decides upon mass ratios is very different in brown dwarfs and stars.

THE GLOBULAR CLUSTER MASS FUNCTION AS A REMNANT OF VIOLENT BIRTH

The log-normal shape of the mass function for metal-poor halo globular clusters is proposed to result from an initial M−2 power law modified rapidly by evaporation, collisions with clouds, and mutual cluster interactions in the dense environment of a redshift z ∼ 5–15 disk galaxy. Galaxy interactions subsequently spray these clusters into the galaxy group environment, where they fall into other growing galaxies and populate their halos. Clusters forming later in z ∼ 2–5 galaxies, and those formed during major mergers, produce metal-rich globulars. Monte Carlo models of evolving cluster populations demonstrate the early formation of a log-normal mass function for typical conditions in high-redshift galaxies.

New light on the initial mass function of the Galactic halo globular clusters

We present new constraints on the initial mass spectrum of the Galactic Old Halo globular clusters. This has remained poorly known so far, as both an initial power-law mass spectrum and an initial lognormal mass function could have evolved into the presently observed globular cluster mass distribution, making the initial contribution of now lost low-mass objects ill-determined. Our approach consists of comparing the evolution with time of both the radial mass density profile and the number density profile of the globular cluster system. Using the analytical expression established by Vesperini & Heggie for the temporal evolution of the mass of a globular cluster on a circular orbit in a stable Galactic potential, we evolve the mass and number density profiles of many putative globular cluster systems, each starting with a different initial cluster mass spectrum and initial cluster space density. We then compare the modelled profiles with those of the Old Halo cluster system in order to investigate which system(s) provide(s) the best consistency with the data. Specifically, we build on the following points: (i) the presently observed mass density profile and number density profile of the Old Halo cluster system show the same shape; (ii) assuming that globular clusters were initially distributed the same way in mass at all galactocentric distances, the mass and number density profiles had also the same shape initially; and (iii) according to our simulations, the mass density profile remains well preserved, irrespective of the initial cluster mass spectrum, while the temporal evolution of its number counterpart depends sensitively on initial conditions. We show that to obtain a mass density profile and a number density profile that are identical in shape, both initially and after a Hubble time of evolution, the globular cluster system must have been depleted in low-mass objects from the beginning. We deduce that the initial distribution in mass of the globular clusters was either a lognormal mass function, similar to that today, or a power-law mass spectrum with a slope ≃−2 and truncated at large mass, say, around 105 M⊙. In contrast, a power-law mass spectrum with a similar slope but extending down to low cluster mass (i.e. a few thousand solar masses) seems to be ruled out.

The Substellar Mass Function: A Bayesian Approach

We report our efforts to constrain the form of the low-mass star and brown dwarf mass function via Bayesian inference. Recent surveys of M, L, and T dwarfs in the local solar neighborhood are an essential component of our study. Uncertainties in the age distribution of local field stars make reliable inference complicated. We adopt a wide range of plausible assumptions about the rate of Galactic star formation and show that their deviations from a uniform rate produce little effect on the resulting luminosity function for a given mass function. As an ancillary result, we calculate the age distribution for M, L, and T spectral types. We demonstrate that late L dwarfs, in particular, are systematically younger than objects with earlier or later spectral types, with a mean age of 3 Gyr. Finally, we use a Bayesian statistical formalism to evaluate the probability of commonly used mass functions in the light of recent discoveries. We consider three functional forms of the mass function, including a two-segment power law, a single power law with a low-mass cutoff, and a lognormal distribution. Our results show that at a 60% confidence level the power-law index α for the low-mass arm of a two-segment power law has a value between -0.6 and 0.6 for objects with masses between 0.04 and 0.10 M-circle dot;. The best-fit index is alpha = 0.3 plus or minus; 0.6 at the 60% confidence level for a single-segment mass function. Current data require this function to extend to at least 0.05 M-circle dot with no restrictions placed on a lower mass cutoff. Inferences of the parameter values for a lognormal mass function are virtually unaffected by recent estimates of the local space density of L and T dwarfs. We find that we have no preference among these three forms using this method. We discuss current and future capabilities that may eventually discriminate between mass function models and refine estimates of their associated parameter values.