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Register a new userA new method to create initially mass segregated star clusters in virial equilibrium
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Mass segregation stands as one of the most robust features of the dynamical evolution of self-gravitating star clusters. In this paper we formulate parametrised models of mass segregated star clusters in virial equilibrium. To this purpose we introduce mean inter-particle potentials for statistically described unsegregated systems and suggest a single-parameter generalisation of its form which gives a mass-segregated state. We describe an algorithm for construction of appropriate star cluster models. Their stability over several crossing-times is verified by following the evolution by means of direct N-body integration.
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ALMA observations of the Serpens South star-forming region suggest that stellar protoclusters may be completely mass segregated at birth. Independent observations also suggest that embedded clusters form segregated by mass. As the primordial mass segregation seems to be lost over time, we aim to study on which timescale an initially perfectly mass-segregated star cluster becomes indistinguishable from an initially not mass-segregated cluster. As an example, the Orion Nebula Cluster (ONC) is also discussed. We used $N$-body simulations of star clusters with various masses and two different degrees of primordial mass segregation. We analysed their energy redistribution through two-body relaxation to quantify the time when the models agree in terms of mass segregation, which sets in only dynamically in the models that are primordially not mass segregated. A comprehensive cross-matched catalogue combining optical, infrared, and X-ray surveys of ONC members was also compiled and made available. The models evolve to a similar radial distribution of high-mass stars after the core collapse (about half a median two-body relaxation time, $t_mathrm{rh}$) and become observationally indistinguishable from the point of view of mass segregation at time $tau_mathrm{v} approx 3.3,t_mathrm{rh}$. In the case of the ONC, using the distribution of high-mass stars, we may not rule out either evolutionary scenario (regardless of whether they are initially mass segregated). When we account for extinction and elongation of the ONC, as reported elsewhere, an initially perfectly mass-segregated state seems to be more consistent with the observed cluster.
Based on the gravitational redshift, one prediction of Einsteins general relativity theory, of broad optical emission lines in active galactic nuclei (AGNs), a new method is proposed to estimate the virial factors $f$ in measuring black hole masses $M_{rm{RM}}$ by the reverberation mapping of AGNs. The factors $f$ can be measured on the basis of two physical quantities, i.e. the gravitational redshifts $z_{rm{g}}$ and full widths at half maxima $v_{rm{FWHM}}$ of broad lines. In the past it has been difficult to determine the factors $f$ for individual AGNs. We apply this new method to several reverberation mapped Seyfert 1 galaxies. There is a correlation between $f$ and broad-line region (BLR) radius $r_{rm{BLR}}$, $f=5.4 r_{rm{BLR}}^{0.3}$, for the gravitationally redshifted broad lines He II, He I, H$beta$ and H$alpha$ in narrow-line Seyfert 1 galaxy (NLS1) Mrk 110. This correlation results from the radiation pressure influence of the accretion disc on the BLR clouds. The radiation pressure influence seems to be more important than usually thought in AGNs. Mrk 110 has $f approx$ 8--16, distinctly larger than the mean $langle frangle approx 1$, usually used to estimate $M_{rm{RM}}$ in the case of $v_{rm{FWHM}}$. NGC 4593 and NLS1 Mrk 486 has $fapprox 3$ and $fapprox 9$, respectively. Higher $f$ values of several tens are derived for three other NLS1s. There is a correlation between $f$ and accretion rate $mathscr{dot M}_{f=1}$, $f=6.8mathscr{dot M}^{0.4}_{f=1}$ for five objects, where $mathscr{dot M}_{f=1}=dot M_{bullet}/L_{rm{Edd}}c^{-2}$ as $f=1$ is assumed to estimate $M_{rm{RM}}$ used in the Eddington luminosity $L_{rm{Edd}}$, $dot M_{bullet}$ is the mass accretion rate, and $c$ is the speed of light. These larger $f$ values will produce higher $M_{rm{RM}}$ values and lower Eddington ratios.
We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions $W$ that are explicit functions of the elastic deformation gradient $mathbf{F}$ and initial stress $boldsymbol tau$, i.e. $W:= W(mathbf F, boldsymbol tau)$. The restriction is a consequence of energy conservation and ensures that the predicted stress and strain energy do not depend upon an arbitrary choice of reference configuration. We call this restriction: initial stress reference independence (ISRI). It transpires that almost all strain energy functions found in the literature do not satisfy ISRI, and may therefore lead to unphysical behaviour, which we illustrate via a simple example. To remedy this shortcoming we derive three strain energy functions that do satisfy the restriction. We also show that using initial strain (often from a virtual configuration) to model initial stress leads to strain energy functions that automatically satisfy ISRI. Finally, we reach the following important result: ISRI reduces the number of unknowns of the linear stress tensor of initially stressed solids. This new way of reducing the linear stress may open new pathways for the non-destructive determination of initial stresses via ultrasonic experiments, among others.
We use UBVI,Ha images of the Whirlpool galaxy, M51, taken with the ACS and WFPC2 cameras on the Hubble Space Telescope (HST) to select star clusters, and to estimate their masses and ages by comparing their observed colors with predictions from population synthesis models. We construct the mass function of intermediate age (1-4x10^8 yr) clusters, and find that it is well described by a power law, psi(M) propto M^beta, with beta=-2.1 +/- 0.2, for clusters more massive than approximately 6x10^3 Msun. This extends the mass function of intermediate age clusters in M51 to masses lower by nearly a factor of five over previous determinations. The mass function does not show evidence for curvature at either the high or low mass end. This shape indicates that there is no evidence for the earlier disruption of lower mass clusters compared with their higher mass counterparts (i.e., no mass-dependent disruption) over the observed range of masses and ages, or for a physical upper mass limit Mc with which clusters in M51 can form. These conclusions differ from previous suggestions based on poorer-quality HST observations. We discuss their implications for the formation and disruption of the clusters. Ages of clusters in two feathers, stellar features extending from the outer portion of a spiral arm, show that the feather with a larger pitch angle formed earlier, and over a longer period, than the other.
Continuum emissions from dust grains are used as a general probe to constrain the initial physical conditions of molecular dense cores where new stars may born. To get as much information as possible from dust emissions, we have developed a tool, named as $COREGA$, which is capable of identifying positions of dense cores, optimizing a three-dimensional model for the dense cores with well characterized uncertainties. $COREGA$ can also estimate the physical properties of dense cores, such as density, temperature, and dust emissivity, through analyzing multi-wavelength dust continuum data sets. In the numerical tests on $COREGA$, the results of fitting simulated data are consistent with initial built-in parameters. We also demonstrate $COREGA$ by adding random gaussian noises with Monte Carlo methods and show that the results are stable against varying observational noise intensities within certain levels. A beam size $<$ 3 arcsec and rms $<$ 0.2mJy/pixel (1 pixel = 0.1) is needed for ALMA to distinguish different collapse models, such as power law and Bonner-Ebert sphere, during continuum observations of massive dense cores in Orion molecular cloud. Based on its advanced algorithm, $COREGA$ is capable of giving a quick and deep analysis on dust cores.
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