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NASA NTRS2004

Physics of Galaxy Clusters and How it Affects Cosmological Tests

The main activities in 2004 were focused on completion of the new 400 square degrees ROSAT PSPC survey for distant galaxy clusters. We observed and reduced optical spectra for all X-ray candidates and now we have complete identification for a statistically complete sample of distant 283 clusters. The papers describing the cluster catalog and first science results are in preparation and will be submitted in early 2005. We also completed a project to measure temperature and density profiles at large radii using Chandra observations of a 11 well exposed low-redshift clusters. We were able to demonstrate that the density, temperature, and total mass profiles are self-similar at large radii. This analysis has led to significant improvements in determination of the cluster baryon fraction as well as cosmologically important scaling relations, such as Mtot-T. The paper describing these results is submitted to ApJ in November, 2004. We continued to study evolution of the cluster scaling relations at high redshifts using Chandra and XMM data. We developed code for image and spectral deconvolution of the XMM observations. This code was used to reconstruct the distribution of baryons and total mass from observations of distant clusters which suffer from the finite size of the XMM PSF. This study allowed us to derive a high-redshift relation between cluster temperature and mass and compare it with the local relation obtained. The paper describing the first results is submitted to the ApJ. However, the project is still on-going as more distant cluster observations enter XMh4 and Chandra public data archives. We continued our work on improving techniques for accurate measurements of the cluster mass function and obtaining cosmological constraints from such observations. We published (ApJ, 601, 610) a study in which we derived the baryon mass function for a complete sample of low-redshift clusters. These papers argued that it was an excellent proxy for the total mass function. The baryon mass function can be used to constrain the amplitude and slope of the density fluctuation power spectrum on cluster scales. This method does not use observational determinations of the total mass and thus bypasses major uncertainties in the traditional analyses based on the X-ray temperature function. We derived the measurements for the amplitude of density perturbations, sigma8 = 0.72 +/- 0.04 and the shape parameter Omega*h = 0.l3 +/- 0.07, in good agreement with a number of independent methods.

Oliversen, Ronald J.↗

NASA NTRS1983

Photometry of resolved galaxies. II - Sextans A

Luminosity functions and color-magnitude diagrams are given for 652 stars in the Sextans A dwarf irregular galaxy, and they are compared with other Local Group galaxies. The brightest red and blue stars presently determined are in agreement with those of Sandage and Carlson (1982), and a group of red stars is identified which may be analogous to the bright carbon star population recently found in the Magellanic Clouds. While the similarity of Sextans A's luminosity function with those of the LMC and the Milky Way is in keeping with a universal luminosity function, stellar mass function and birthrate resemble those of the SMC. Per unit gas mass, Sextans A has a birthrate almost identical to the SMC, suggesting that the mean age of stars in Sextans A is significantly less than of those in the Magellanic Clouds.

Hoessel, J. G.↗

NASA NTRS1994

The luminosity function at the end of the main sequence: Results of a deep, large-area, CCD survey for cool dwarfs

The luminosity function at the end of the main sequence is determined from V, R, and I data taken by the charge coupled devices (CCD)/Transit Instrument, a dedicated telescope surveying an 8.25 min wide strip of sky centered at delta = +28 deg, thus sampling Galactic latitudes of +90 deg down to -35 deg. A selection of 133 objects chosen via R - I and V - I colors has been observed spectroscopically at the 4.5 m Multiple Mirror Telescope to assess contributions by giants and subdwarfs and to verify that the reddest targets are objects of extremely late spectral class. Eighteen dwarfs of type M6 or later have been discovered, with the latest being of type M8.5. Data used for the determination of the luminosity function cover 27.3 sq. deg down to a completeness limit of R = 19.0. This luminosity function, computed at V, I, and bolometric magnitudes, shows an increase at the lowest luminosities, corresponding to spectral types later than M6- an effect suggested in earlier work by Reid & Gilmore and Legget & Hawkins. When the luminosity function is segregated into north Galactic and south Galactic portions, it is found that the upturn at faint magnitudes exists only in the southern sample. In fact, no dwarfs with M(sub I) is greater than or equal to 12.0 are found within the limiting volume of the 19.4 sq deg northern sample, in stark contrast to the smaller 7.9 sq deg area at southerly latitudes where seven such dwarfs are found. This fact, combined with the fact that the Sun is located approximately 10-40 pc north of the midplane, suggests that the latest dwarfs are part of a young population with a scale height much smaller than the 350 pc value generally adopted for other M dwarfs. These objects comprise a young population either because the lower metallicities prevelant at earlier epochs inhibited the formation of late M dwarfs or because the older counterparts of this population have cooled beyond current detection limits. The latter scenario would hold if these late-type M dwarfs are substellar. The luminosity function data together with an empirical derivation of the mass-luminosity relation (from Henry & McCarthy) are used to compute a mass function independent of theory. This mass function increases toward the end of the main sequence, but the observed density of M dwarfs is still insufficient to account for the missing mass. If the increases seen in the luminosity and mass functions are indicative of a large, unseen, substellar population, brown dwarfs may yet add significantly to the mass of the Galaxy.

Kirkpatrick, J. Davy↗

DOE OSTI2024

Cosmic quenching and scaling laws for the evolution of supermassive black holes and host galaxies

ABSTRACT Observations suggest a co-evolution of supermassive black holes (SMBHs) and host galaxies. In this paper, we consider the mass and energy flow in a near-equilibrium bulge suffused by gases of varying temperatures. By assuming the rate of energy flow independent of the distance r from the bulge center and the local virial equilibrium for permeated gases on scale r, a key parameter $\varepsilon _b$ was identified that quantifies the mass and energy flow in gases and the efficiency of gas cooling (or the "specific" cooling rate per unit mass), and thus regulates the co-evolution of both SMBHs and hosts. With the help of Illustris simulations and observations, we determined the redshift variation $\varepsilon _b\propto (1+z)^{5/2}$. A higher $\varepsilon _b$ in the early Universe means a higher specific cooling rate that allows rapid evolution of SMBHs and hosts. This simple theory, characterized by a single parameter $\varepsilon _b$, provides the dominant mean cosmic evolution of SMBHs and hosts. All other transient phenomena may only contribute to the dispersion around this mean evolution. Based on this theory and relevant assumptions, scaling laws involving $\varepsilon _b$ were identified for the evolution of SMBHs and hosts. For host galaxies, the mass–size relation $M_b\propto \varepsilon _b^{2/3}r_b^{5/3}G^{-1}$, the dispersion–size relation $\sigma _b^2\propto (\varepsilon _b r_b)^{2/3}\propto (1+z)$, or the mass–dispersion relation $M_b\propto \varepsilon _b^{-1}G^{-1}\sigma _b^5$ were identified, where $r_b\propto (1+z)^{-1}$ is the bulge size. For SMBHs, three evolution phases were found involving an initial rapid growth stage with a rising luminosity $L_B\propto (\varepsilon _b M_{\rm BH})^{4/5}$, a transition stage with a declining $L_B\propto \varepsilon _b^2 M_{\rm BH} \propto (1+z)^5$, and a dormant stage with $L_B\propto (\varepsilon _b M_{\rm BH})^{4/3}$. Our results suggest a rapid initial super-Eddington growth in a short period with a new redshift-dependent luminosity limit $L_X\propto\varepsilon _b^{4/5}M_{\rm BH}^{4/5}G^{-1/5}c$, in contrast to the Eddington limit. Analytical solutions were formulated for the BH mass function $\Phi _{\rm BH}$, active galactic nucleus (AGN) mass function $\Phi _{\rm AGN}$, and duty cycle U that predict $\Phi _L\propto L^{-1/5}$ for the faint-end luminosity function, $\Phi _{\rm AGN}\propto M^{-1/5}$ for small-mass-end AGN mass function $\Phi _L$, and $U\propto M^{-1/5}$ at high redshift.

(galaxies:) quasars: supermassive black holes↗

DOE OSTI2023

VST ATLAS galaxy cluster catalogue I: cluster detection and mass calibration

Taking advantage of ∼4700 deg 2 optical coverage of the Southern sky offered by the VST ATLAS survey, we construct a new catalogue of photometrically selected galaxy groups and clusters using the orca cluster detection algorithm. The catalogue contains ∼22 000 detections with N 200 > 10 and ∼9000 with N 200 > 20. We estimate the photometric redshifts of the clusters using machine learning and find the redshift distribution of the sample to extend to z ∼ 0.7, peaking at z ∼ 0.25. We calibrate the ATLAS cluster mass-richness scaling relation using masses from the MCXC, Planck, ACT DR5, and SDSS redMaPPer cluster samples. We estimate the ATLAS sample to be > 95 per cent complete and > 85 per cent pure at z < 0.35 and in the M 200m >1 x 10 14 h -1 M ⊙ mass range. At z < 0.35, we also find the ATLAS sample to be more complete than redMaPPer, recovering a ~ 40 per cent higher fraction of Abell clusters. This higher sample completeness places the amplitude of the z < 0.35 ATLAS cluster mass function closer to the predictions of a ΛCDM model with parameters based on the Planck CMB analyses, compared to the mass functions of the other cluster samples. However, strong tensions between the observed ATLAS mass functions and models remain. We shall present a detailed cosmological analysis of the ATLAS cluster mass functions in paper II. In the future, optical counterparts to X-ray-detected eROSITA clusters can be identified using the ATLAS sample. The catalogue is also well suited for auxiliary spectroscopic target selection in 4MOST. The ATLAS cluster catalogue is publicly available at http://astro.dur.ac.uk/cosmology/vstatlas/cluster_catalogue/.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1990

Gas flows in elliptical galaxies

In preparation for the next generation of x ray telescopes, researchers have begun a program investigating the evolving x ray properties of elliptical galaxies. Their galaxy models consist of a modified King profile for the luminous portion of the galaxy and can include an isothermal dark halo comprising 90 percent of the total mass. The stellar population is assumed to form at a rate which decreases exponentially on a dynamical time scale with a Salpeter initial mass function. Stellar mass loss occurs instantaneously as stars evolve off the main sequence. All stars more massive than 8 solar mass produce type II supernovae, while less massive stars loss mass through a planetary nebulae. The evolving rate of type I supernovae is normalized to a fraction, gamma sub sn I, of Tammann's (1974) value. All of this information is then incorporated into a one-dimensional hydrodynamics code to determine the evolving dynamical state of the interstellar medium.

David, L. P.↗

NASA NTRS1993

The initial stellar population

Current theories for the origin of stellar masses and the initial mass function are surveyed, with emphasis on the formation of stars in clusters, and the possibility that several different formation mechanisms are at work in the Galaxy. Models are presented for the evolution of the 2.2-micron premain-sequence luminosity function of a young coeval star cluster, and the implications the results have for the conversion of an observed luminosity function into the underlying mass function are discussed. A description of theories which allow spectral energy distributions of young stellar objects to be used as diagnostics of their evolutionary states is given. The question of the existence of substellar objects (brown dwarfs) in nearby young clusters and regions of star formation is addressed.

Zinnecker, Hans↗

NASA NTRS1995

The evolutionary status of the stellar population in the rho Ophiuchi cloud core

This contribution reports the results of an infrared imaging survey aimed at characterizing the stellar populations associated with the three densest star-forming cores in the Ophiuchus molecular cloud complex. The survey has sufficient sensitivity at J, H, and K (at 5 sigma limits of 16.5, 15.4, and 14.2) to provide a complete census of embedded young stellar objects (YSOs) with masses greater than the hydrogen-burning limit, provided that their ages are less than 3 Myr and that they are obscured by no more than approximately 18 mag of visual extinction. Our data suggest (1) a large fraction (greater than 70%) of the sources located within the cores are still surrounded by circumstellar disks and/or envelopes; and (2) the shape of the initial mass function for masses, M less than 1 solar mass, appears to be consistent with that derived from the solar neighborhood. We also report the results of a deeper imaging survey of centimeter continuum sources (14 sources) in these star-forming cores and in the larger Ophiuchus complex (eight sources). A large fraction (11/14) of the radio sources associated with the cores appear to have infrared excesses diagnostic of circumstellar accretion disks and/or infalling circumstellar envelopes. In these cases, the centimeter continuum radiation most likely diagnoses the ionized component of energetic winds or jets which characterizes YSOs during the disk accretion phase. By contrast, of the eight radio sources located outside dense cores, only two show infrared excesses.

Strom, Karen M.↗

DOE OSTI2025

Statistical estimates of the binary properties of rotational variables

ABSTRACT We present a model to estimate the average primary masses, companion mass ranges, the inclination limit for recognizing a rotational variable, and the primary mass spreads for populations of binary stars. The model fits a population’s binary mass function distribution and allows for a probability that some mass functions are incorrectly estimated. Using tests with synthetic data, we assess the model’s sensitivity to each parameter, finding that we are most sensitive to the average primary mass and the minimum companion mass, with less sensitivity to the inclination limit and little to no sensitivity to the primary mass spread. We apply the model to five populations of binary spotted rotational variables identified in ASAS-SN, computing their binary mass functions using RV data from APOGEE. Their average primary mass estimates are consistent with our expectations based on their CMD locations ($\sim 0.75 \, {\rm M}_{\odot }$ for lower main sequence primaries and $\sim 0.9$–$1.2 \, {\rm M}_{\odot }$ for RS CVn and sub-subgiants). Their companion mass range estimates allow companion masses down to $M_2/M_1\simeq 0.1$, although the main sequence population may have a higher minimum mass fraction ($\sim 0.4$). We see weak evidence of an inclination limit $\gtrsim 50^{\circ }$ for the main sequence and sub-subgiant groups and no evidence of an inclination limit in the other groups. No groups show strong evidence for a preferred primary mass spread. We conclude by demonstrating that the approach will provide significantly better estimates of the primary mass and the minimum mass ratio and reasonable sensitivity to the inclination limit with 10 times as many systems.

Phillips, Anya (ORCID:000900051914974X)↗

DOE OSTI2021

Simulations of axion minihalos

The axion, motivated as a solution to the strong CP problem, is also a viable dark matter candidate. The axion field takes random values in causally disconnected regions if the symmetry breaking that establishes the particle occurs after inflation, leading to white-noise density fluctuations at low wave numbers and forming dense minihalos with sub-planetary masses subsequently. There have been two recent proposals that appear capable of testing this scenario, namely using pulsar timing arrays and studying cosmological microlensing caustics. Motivated by these proposals, we use N-body simulations to study the formation of substructures from white-noise density fluctuations. The density profiles of our relaxed axion minihalos can be described by the Navarro–Frenk–White profile, and the minihalos’ concentration number agrees well with a simple, physically-motivated model. We develop a semi-analytic formula to fit the mass function from our simulation, which agrees broadly at different redshifts and only differs at factor of two level from classic halo mass functions. This analytic mass function allows us to consider uncertainties in the post-inflation axion scenario, as well as extrapolate our high-redshift simulations results to the present. Our work estimates the present-day abundance of axion substructures, as is necessary for predicting their effect on cosmological microlensing caustics and pulsar timing. Our calculations suggest that if pulsar timing and microlensing probes can reach recent sensitivity forecasts, they may be sensitive to the post-inflation axion dark matter scenario, even when accounting for uncertainties pertaining to axion strings. For pulsar timing, the most significant caveat is whether axion minihalos are disrupted by stars, which our estimates show is mildly important at the most relevant masses. In conclusion, as our gravitational simulations are scale invariant, the results can be extended to models where the dark matter is comprised of other axion-like particles and even clusters of primordial black holes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Testing dark matter halo properties using self-similarity

ABSTRACT We use self-similarity in N-body simulations of scale-free models to test for resolution dependence in the mass function and two-point correlation functions of dark matter haloes. We use 10243 particle simulations performed with abacus , and compare results obtained with two halo finders: friends-of-friends (fof ), and rockstar . The fof mass functions show a systematic deviation from self-similarity which is explained by resolution dependence of the fof mass assignment previously reported in the literature. Weak evidence for convergence is observed only starting from haloes of several thousand particles, and mass functions are overestimated by at least as much as $20-25{{\ \rm per\ cent}}$ for haloes of 50 particles. The mass function of the default rockstar halo catalogue (with bound virial spherical overdensity mass), on the other hand, shows good convergence of the order of 50 to 100 particles per halo, with no detectable evidence at the few percent level of any systematic dependence for larger particle number. Tests show that the mass unbinding procedure in rockstar is the key factor in obtaining this much improved resolution. Applying the same analysis to the halo–halo two point correlation function, we find again strong evidence for convergence only for rockstar haloes, at separations sufficiently large so that haloes do not overlap. At these separations, we can exclude dependence on resolution at the $5-10{{\ \rm per\ cent}}$ level once haloes have of the order of 50 to 100 particles. At smaller separations results are not converged even at significantly larger particle number, and bigger simulations would be required to establish the resolution required for convergence.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2003

Formation of Brown Dwarfs LTSA 2001

The goals of the work funded by this grant are: 1) The measurement of the mass function and minimum mass of free-floating brown dwarfs down to the mass of Jupiter; 2) The measurement of the frequency of wide brown dwarf and planetary companions down to the mass of Jupiter as function of primary mass (0.02-2 Msun), age (1-10 Myr), and environment (clusters vs. dispersed regions). For the first objective, we have completed the design of guaranteed SIRTF observations of nearby star-forming regions. With the successful launch of the SIRTF mission in August of 2003, we now await the execution of these observations, which should begin in early 2004. In support of these upcoming observations, in the fall of 2002 and spring of 2003 we obtained optical spectroscopy at the MMT, the 1.5 meter telescope at Fred Lawrence Whipple Observatory, and Magellan Observatory for several hundred candidate young low-mass stars and brown dwarfs in the IC348, Taurus, and Chamaeleon star-forming regions. All of these data have been published in three papers in The Astrophysical Journal. We also recently used the MMT to obtain deep near-IR images of IC348 to accompany the SIRTF images and have time in the next month at the IRTF and Keck for spectroscopy of candidate brown dwarfs in IC348 and Taurus. We have submitted proposals for deep optical and near-IR imaging of the SIRTF fields in Chamaeleon and Ophiuchus for spring 2004 with Magellan and the AAT. Results from this research have been presented in invited talks at UU Symposium 221 (July 2003) and at the SIRTF Galactic Science Workshop (August 2003). For the second objective, we have used deep HST WFPC2 images to search for young giant planets and brown dwarfs around approx. 100 low-mass stars and brown dwarfs in the nearby cluster IC348. We have completed all data reduction and have checked these data for candidate companions. We expect to submit the paper describing these observations to The Astrophysical Journal by the end of the year. In addition, in SIRTF guaranteed time observations we plan to search for wide substellar companions (>10 sec) around the youngest nearby field stars (ages of 30-100 Myr, d<30 pc). We have submitted a proposal to use Keck adaptive optics imaging to search these same stars for close-in planets and brown dwarfs at 0.1-10 sec, which will perfectly complement our SIRTF observations.

Luhman, Kevin L.↗

NASA NTRS2004

Formation of Brown Dwarfs LTSA 2001

The goals of the work funded by this grant are: 1) The measurement of the mass function and minimum mass of free-floating brown dwarfs down to the mass of Jupiter. 2) The measurement of the frequency of wide brown dwarf and planetary companions down to the mass of Jupiter as function of primary mass (0.02-2 Msun), age (1-10 Myr), and environment (clusters vs. dispersed regions).

Oliversen, Ronald J.↗

NASA NTRS1992

IRAS observations and the stellar content of H II regions in the Large Magellanic Cloud

IRAS far-infrared fluxes are presented for six H II regions in the LMC. These regions are the sites of recent, massive star formation where the radiative heating source is young stars rather than the general interstellar radiation field. As such, the observations become building blocks for the interpretation of far-infrared emission from spatially unresolved galaxies. In addition, the multiwavelength luminosities of the region then probe the young stellar upper initial mass function. With the long-range goal of determining the stellar content of unresolved star-forming regions, we present the results of a simple model which combines the infrared data with existing H-alpha/H-beta and thermal radio data. For the two OB associations where the mass function has been determined directly, the model correctly 'predicts' a solar neighborhood upper mass function within the uncertainties. No evidence is found for upper mass functions significantly different from that in the solar neighborhood.

Degioia-Eastwood, Kathleen↗

DOE OSTI2021

Diagnosing Open Cluster Stock 2: Member Candidates and Mass Distribution with Gaia DR2 and LAMOST

We identify 1325 member candidates of the open cluster (OC) Stock 2 using data from Gaia DR2. We use the algorithms Clusterix 2.0 and HDBSCAN to select cluster candidates and further refine the final cluster membership by defining neighbors in 5D phase space (X {sub cp}, Y {sub cp}, Z{sub cp},κ⋅μ{sub α}{sup ∗}/ϖ, κ · μ {sub δ}/ϖ). Among these candidates, less than half have G, G {sub BP}, and G {sub RP} extinctions from Gaia. When Gaia extinctions are unavailable, we compute extiction using empirical formulas and E(B − V) = 0.350. We analyze the spatial distribution and mass profile of Stock 2. Our results reveal Stock 2 is still a bound OC and we find evidence of mass segregation. By comparing initial mass functions, the present-day mass function indicates that Stock 2 is a massive stellar cluster with a mass of 4000 M {sub ⊙}. The core radius and tidal radius, calculated via the radial density profile and total mass, are 3.97 pc and 22.65 pc, respectively. Common stars between our selected member candidates and the Large Sky Area Multi-Object Fiber Spectroscopic Telescope DR7 medium-resolution catalog give a metalliclity of [Fe/H] = −0.040 ± 0.147.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

The Sejong Open Cluster Survey (SOS). VII. A Photometric Study of the Young Open Cluster IC 1590

Young open clusters are ideal laboratories to understand the star formation process. We present deep UBVI and Hα photometry for the young open cluster IC 1590 in the center of the H ii region NGC 281. Early-type members are selected from UBV photometric diagrams, and low-mass pre-main-sequence (PMS) members are identified by using Hα photometry. In addition, the published X-ray source list and Gaia astrometric data are also used to isolate probable members. A total of 408 stars are selected as members. The mean reddening obtained from early-type members is &lang;E(B – V)&rang; = 0.40 ± 0.06 (s.d.). We confirm the abnormal extinction law for the intracluster medium. The distance modulus to the cluster determined from the zero-age main-sequence fitting method is 12.3 ± 0.2 mag (d = 2.88 ± 0.28 kpc), which is consistent with the distance d=2.70{sub -0.20}{sup +0.24} kpc from the recent Gaia parallaxes. We also estimate the ages and masses of individual members by means of stellar evolutionary models. The mode of the age of PMS stars is about 0.8 Myr. The initial mass function of IC 1590 is derived. It appears to be a steeper shape (Γ = -1.49 ± 0.14) than that of the Salpeter/Kroupa initial mass function for the high-mass regime (m > 1 M {sub ⊙}). The signature of mass segregation is detected from the difference in the slopes of the initial mass functions for the inner ([[Formula]]) and outer regions of this cluster. We finally discuss the star formation history in NGC 281.

47 OTHER INSTRUMENTATION↗

NASA NTRS2002

Filtered Mass Density Function for Design Simulation of High Speed Airbreathing Propulsion Systems

The objective of this research is to improve and implement the filtered mass density function (FDF) methodology for large eddy simulation (LES) of high speed reacting turbulent flows. NASA is interested in the design of various components involved in air breathing propulsion systems such as the scramjet. There is a demand for development of robust tools that can aid in the design procedure. The physics of high speed reactive flows is rich with many complexities. LES is regarded as one of the most promising means of simulating turbulent reacting flows.

Givi, P.↗

DOE OSTI2021

New Determination of Fundamental Properties of Palomar 5 Using Deep DESI Imaging Data

The legacy imaging surveys for the Dark Energy Spectroscopic Instrument project provides multiple-color photometric data, which are about 2 mag deeper than those from the SDSS. In this study, we redetermine the fundamental properties for an old halo globular cluster of Palomar 5 based on these new imaging data, including structure parameters, stellar population parameters, and luminosity and mass functions. These characteristics, together with its tidal tails, are key for dynamical studies of the cluster and constraining the mass model of the Milky Way. By fitting the King model to the radial surface density profile of Palomar 5, we derive the core radius of [[Formula]], tidal radius of [[Formula]], and concentration parameter of c = 0.78 ± 0.04. We apply a Bayesian analysis method to derive the stellar population properties and get an age of 11.508 ± 0.027 Gyr, metallicity of [Fe/H] = −1.798 ± 0.014, reddening of E(B − V) = 0.0552 ± 0.0005, and distance modulus of (m−M){sub 0} = 16.835±0.006. The main-sequence luminosity and mass functions for both the cluster center and tidal tails are investigated. The luminosity and mass functions at different distances from the cluster center suggest that there is obvious spatial mass segregation. Many faint low-mass stars have been evaporated at the cluster center, and the tidal tails are enhanced by low-mass stars. Both the concentration and relaxation times suggest that Palomar 5 is a totally relaxed system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗