The Distribution of Stars in Globular Clusters

Plummer, H. C.

doi:10.1093/mnras/76.2.107

Cited by 47 publications

(40 citation statements)

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“…(1.4) for α = 2.5 is not appropriate to describe DM halos but corresponds to the Plummer profile describing the density of stars in globular clusters [4,16]. We find that the distribution function for the Plummer profile is approximately thermal only for a small range around the center.…”

Section: Introductionmentioning

confidence: 82%

The dark matter distribution function and halo thermalization from the Eddington equation in galaxies

Vega

Sánchez

2016

Int. J. Mod. Phys. A

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We find the distribution function f (E) for dark matter (DM) halos in galaxies and the corresponding equation of state from the (empirical) DM density profiles derived from observations. We solve for DM in galaxies the analogous of the Eddington equation originally used for the gas of stars in globular clusters. The observed density profiles are a good realistic starting point and the distribution functions derived from them are realistic. We do not make any assumption about the DM nature, the methods developed here apply to any DM kind, though all results are consistent with Warm DM (WDM). With these methods we find: (i) Cored density profiles behaving quadratically for small distances ρ(r) r→0 = ρ(0) − K r 2 produce distribution functions which are finite and positive at the halo center while cusped density profiles always produce divergent distribution functions at the center. (ii) Cored density profiles produce approximate thermal Boltzmann distribution functions for r 3 r h where r h is the halo radius. (iii) Analytic expressions for the dispersion velocity and the pressure are derived yielding at each halo point an ideal DM gas equation of state with local temperature T (r) ≡ m v 2 (r)/3. T (r) turns to be constant in the same region where the distribution function is thermal and exhibits the same temperature within the percent. The self-gravitating DM gas can thermalize despite being collisionless because it is an ergodic system. (iv) The DM halo can be consistently considered at local thermal equilibrium with: (a) a constant temperature T (r) = T0 for r 3 r h , (b) a space dependent temperature T (r) for 3 r h < r R virial , which slowly decreases with r. That is, the DM halo is realistically a collisionless self-gravitating thermal gas for r R virial . (v) T (r) outside the halo radius nicely follows the decrease of the circular velocity squared. Contents

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Section: Introductionmentioning

confidence: 82%

The dark matter distribution function and halo thermalization from the Eddington equation in galaxies

Vega

Sánchez

2016

Int. J. Mod. Phys. A

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“…As a first step in quantifying long-term effects of the cluster, we must define the functional form of the cluster's gravitational potential. An archetypal model of a stellar cluster was first formulated over a century ago by Plummer (1915). Within the context of this model, the system is taken to be spherically symmetric, and the usual Ψ ∝ 1/r potential is softened by a characteristic length-scale, c, such that Ψ approaches a constant value for r c and a point-mass potential for r c. In the same vein, here we consider a class of softened potentials of the form…”

Section: Potential-density Pairsmentioning

confidence: 99%

Dynamics of Planetary Systems within Star Clusters: Aspects of the Solar System’s Early Evolution

Batygin

Adams

Batygin

et al. 2020

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Most planetary systems -including our own -are born within stellar clusters, where interactions with neighboring stars can help shape the system architecture. This paper develops an orbit-averaged formalism to characterize the cluster's mean-field effects as well as the physics of long-period stellar encounters. Our secular approach allows for an analytic description of the dynamical consequences of the cluster environment on its constituent planetary systems. We analyze special cases of the resulting Hamiltonian, corresponding to eccentricity evolution driven by planar encounters, as well as hyperbolic perturbations upon dissipative disks. We subsequently apply our results to the early evolution of our solar system, where the cluster's collective potential perturbs the solar system's plane, and stellar encounters act to increase the velocity dispersion of the Kuiper belt. Our results are two-fold: first, we find that cluster effects can alter the mean plane of the solar system by 1 deg, and are thus insufficient to explain the ψ ≈ 6 deg obliquity of the sun. Second, we delineate the extent to which stellar flybys excite the orbital dispersion of the cold classical Kuiper belt, and show that while stellar flybys may grow the cold belt's inclination by the observed amount, the resulting distribution is incompatible with the data. Correspondingly, our calculations place an upper limit on the product of the stellar number density and residence time of the sun in its birth cluster, η τ 2 × 10 4 Myr/pc 3 . Keywords: planets and satellites: dynamical evolution and stability, 4 ⇡ G c 2 ⇢/ c < l a t e x i t s h a 1 _ b a s e 6 4 = " F R + 8 I K r V C X 4 1 t B U A s y i g 5 M I Z k / w = " > A A A C F X i c b V D L S s N A F J 3 U V 6 2 v q E s 3 g 0 V w U W p S C r o s u t B l B f u A J o b J d N I O n W T C z E Q o I T / h x l 9 x 4 0 I R t 4 I 7 / 8 Z J m 4 W 2 H p j h c M 6 9 3 H u P H z M q l W V 9 G 6 W V 1 b X 1 j f J m Z W t 7 Z 3 f P 3 D / o S p 4 I T D q Y M y 7 6 P pr O 1 N 8 d K Q q l n I a + r s x 3 l 4 t e L v 7 n D R I V X L g p j e J E k Q j P B w U J g 4 r D P C I 4 p I J g x a a a I C y o 3 h X i M R I I K x 1 k R Y d g L 5 6 8 T L q N u m 3 V 7 d t m t X V Z x F E G R + A Y n A I b n I M W u A F t 0 A E Y P I J n 8 A r e j C f j x X g 3 P u a l J a P o O Q R / Y H z + A M r + n p 0 = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " F R + 8 I K r V C X 4 1 t B U A s y i g 5 M I Z k / w = " > A A A C F X i c b V D L S s N A F J 3 U V 6 2 v q E s 3 g 0 V w U W p S C r o s u t B l B f u A J o b J d N I O n W T C z E Q o I T / h x l 9 x 4 0 I R t 4 I 7 / 8 Z J m 4 W 2 H p j h c M 6 9 3 H u P H z M q l W V 9 G 6 W V 1 b X 1 j f J m Z W t 7 Z 3 f P 3 D / o S p 4 I T D q Y M y 7 6 P p K E 0 Y h 0 F F W M 9 G N B U O g z 0 v M n V 7 n f e y B C U h 7 d q W l M 3 B C N I h p Q j J S W P L P W d G p O T P U X I j X G i K X X m V P D 9 w 2 t i D E / c 9 q S e q k j w h R n m W d W r b o 1 A 1 w m d k G q o E D b M 7 + c I c d J S C K F G Z J y Y F u x c l M k F M W M Z B U n k S R G e I J G Z K B p h ...

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“…ρ Oph and NGC 2068/2071). These features can be represented by a Plummer-like density profile (Plummer 1915),…”

Section: The Sph Simulationmentioning

confidence: 99%

How to identify the youngest protostars

Stamatellos¹,

Whitworth²,

Boyd³

et al. 2005

A&A

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Abstract. We study the transition from a prestellar core to a Class 0 protostar, using SPH to simulate the dynamical evolution, and a Monte Carlo radiative transfer code to generate the SED and isophotal maps. For a prestellar core illuminated by the standard interstellar radiation field, the luminosity is low and the SED peaks at ∼190 µm. Once a protostar has formed, the luminosity rises (due to a growing contribution from accretion onto the protostar) and the peak of the SED shifts to shorter wavelengths (80 to 100 µm). However, by the end of the Class 0 phase, the accretion rate is falling, the luminosity has decreased, and the peak of the SED shifts back towards longer wavelengths (90 to 150 µm). In our simulations, the density of material around the protostar remains sufficiently high well into the Class 0 phase that the protostar only becomes visible in the NIR if it is displaced from the centre dynamically. Raw submm/mm maps of Class 0 protostars tend to be much more centrally condensed than those of prestellar cores. However, when convolved with a typical telescope beam, the difference in central concentration is less marked, although the Class 0 protostars appear more circular. Our results suggest that, if a core is deemed to be prestellar on the basis of having no associated IRAS source, no cm radio emission, and no outflow, but it has a circular appearance and an SED which peaks at wavelengths below ∼170 µm, it may well contain a very young Class 0 protostar.

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The Distribution of Stars in Globular Clusters

Cited by 47 publications

References 0 publications

The dark matter distribution function and halo thermalization from the Eddington equation in galaxies

The dark matter distribution function and halo thermalization from the Eddington equation in galaxies

Dynamics of Planetary Systems within Star Clusters: Aspects of the Solar System’s Early Evolution

How to identify the youngest protostars

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