text stringlengths 128 2.05k |
|---|
the quantity [MATH] can be interpreted as the total density of stars of mass [MATH] far from the MBH, where [MATH] and almost all stars are unbound to the MBH. In that case [MATH] |
is the asymptotic number density ratio of star [MATH] relative to the reference star ( [MATH] by definition). The asymptotic population ratios between stars of mass [MATH] and [MATH] are designated below by [MATH] . It is assumed that the asymptotic PMF, and its corresponding population ratios [MATH] depend only on the... |
Stellar dynamics near the MBH are described here in units where [MATH] mass is measured in units of the mass of the reference star, [MATH] specific energy in units of its velocity dispersion [MATH] and time in units of its two-body relaxation time at the radius of influence, |
[EQUATION] where the Coulomb term is estimated as [MATH] . Phase space density is expressed in units of [MATH] and distance in expressed units of the MBH radius of influence [MATH] In these units, the dimensionless specific orbital energy is defined as [MATH] [MATH] is the semi-major axis), the dimensionless time is de... |
The evolution of the dimensionless DF of each stellar mass group, [MATH] , is described by the energy flow integral [MATH] , which expresses the change in energy due to 2-body scattering, and the angular momentum-averaged effective loss-cone term [MATH] |
(Bahcall & Wolf, 1976 1977 [EQUATION] The flow integral is given by [EQUATION] The averaged effective loss-cone term in the diffusive regime (defined here as [MATH] ) is approximated by (Hopman & Alexander, 2006b |
[EQUATION] where [MATH] is the maximal (circular) angular momentum for energy [MATH] [MATH] is the angular momentum of the loss-cone (taken here to be [MATH] , the angular momentum of the last stable orbit for [MATH] ), and [MATH] |
is the approximate 2-body relaxation time. The contribution of the loss-cone in the full loss-cone regime, which typically corresponds to [MATH] , is small (e.g. Syer & Ulmer, 1999 , and is therefore neglected here. Bahcall & Wolf ( 1976 1977 argued that the loss-cone term has only a small effect on the energy dependen... |
Equation ( ) is integrated in time from an arbitrary initial DF until steady-state is achieved, subject to the boundary conditions that the DF falls to zero at some very high energy [MATH] where the stars are destroyed, and that the unbound stars are replenished from a Maxwellian reservoir, |
[EQUATION] where the constant [MATH] is related to the population ratio [MATH] by (see Eq. [EQUATION] Specifically, if the different unbound mass groups are in equipartition (as assumed by BW77), then [MATH] . Conversely, if the unbound stellar population has achieved equilibrium by violent relaxation (Lynden-Bell, 196... |
(Kroupa et al., 1993 , by the absence of an observed vertical color gradient in edge-on disk galaxies (de Grijs & Peletier, 2000 , and by the weak observed spatial color gradients in elliptical galaxies (e.g. Boroson et al., 1983 ; Cohen, 1986 . We confirm the conclusion of BW77 that the steady state DFs do not depend ... |
The spatial density profile that corresponds to the DF is [EQUATION] 3. The relaxational coupling parameter As shown below in § , the nature of the mass segregation solution, weak or strong, is determined by one parameter, which expresses the relative strength of [MATH] [MATH] and [MATH] [MATH] |
interactions. These can be quantified by the corresponding diffusion coefficients, [MATH] [MATH] and [MATH] , which enter the Fokker-Planck equation |
(e.g. Binney & Tremaine, 1987 , Eq. 8-68) . The two quadratic scattering coefficients are similar up to an order unity factor, and are approximated here as equal, [MATH] In a 2-mass system we represent these coefficients for brevity by the notation [MATH] where [MATH] is the scattering star (light or heavy), [MATH] is ... |
The relaxational coupling parameter [MATH] describes the competition between the self-coupling of the heavy stars and the light-heavy coupling in terms of global properties of the system, the mass and number ratios, |
[EQUATION] The definition of [MATH] can in principle be generalized to a multi-mass stellar population by specifying the light/heavy mass boundary, [MATH] |
and performing a weighted integration over the mass function . However, as shown in § below, an evolved stellar population (coeval or continuously star-forming) such as is expected near a MBH, is well approximated by a 2-mass system for this purpose. |
3.1. Asymptotic mass segregation limits The weak segregation limit (the Bahcall-Wolf solution). In the limit [MATH] , which is the zero-flow ( [MATH] limit (§ ), the heavy stars dominate the population and relax to the single mass cusp [MATH] [MATH] ). The light stars heat by scattering against the effectively infinite... |
The strong segregation limit. In the limit [MATH] and when [MATH] , the light stars behave as a single mass population with [MATH] [MATH] ). The rare heavy stars sink to the center by dynamical friction against the effectively infinite reservoir of light stars. Their steady state distribution can be simply derived by n... |
[MATH] ) is then [MATH] so that [MATH] . In steady state, the heavy star current, [MATH] , is independent of radius, [MATH] so that the number density of the heavy stars must scale as [MATH] It then follows that |
[EQUATION] Equivalently, this result can be obtained by expressing the Fokker-Planck equations explicitly in terms of the diffusion coefficients as function of energy (Lightman & Shapiro, 1977 , Eqs. 51a,b) , and solving them under the assumption that only the drift term (dynamical friction) contributes. In practice, i... |
(§ ); [MATH] should be considered an upper limit on the logarithmic slope of the number density distribution of the heavy stars. |
4. The present day mass function The value of [MATH] (Eq. 10 ) depends on the population’s PMF. So-called universal IMFs, which extend all the way from the brown dwarf boundary [MATH] to [MATH] |
(e.g. the Salpeter 1955 IMF and its subsequent refinements, the Miller & Scalo 1979 and Kroupa 2001 IMFs), result in evolved populations (old coeval star-bursts or continuously star forming populations) that naturally separate into two mass scales, the [MATH] |
scale of low-mass main-sequence dwarfs, white dwarfs and neutron stars, and the [MATH] scale of stellar black holes, and typically have [MATH] (Fig. ). Such evolved populations are well-approximated by the simple 2-mass population model. |
Generally, 10 Gyr old, continuously star-forming populations with a power-law IMF, [MATH] have [MATH] for [MATH] , and [MATH] for [MATH] (assuming [MATH] [MATH] |
[MATH] ). This implies that even flatter IMFs than the Salpeter IMF ( [MATH] ) lead to strong mass segregation. It is not clear what is the typical PMF, and the corresponding value of [MATH] , in galactic nuclei. There are indications that star formation deep in the potential well of a MBH can be very different from th... |
pc of the GC suggests that the IMF there could be a flat [MATH] power-law (Maness et al., 2007 . This corresponds to [MATH] in the inner [MATH] pc, if that region evolved as an isolated system. However, that is unlikely, since the PMF reflects not only the local star formation, but also the volume-averaged population i... |
5. Results Figure ( ) shows an example of a steady state solution of the DFs calculated for a 2-mass system in the weak segregation regime with [MATH] and [MATH] [MATH] ), neglecting the loss-cone term. While the logarithmic slopes of the DFs are not constant, they vary only slightly away from the boundaries at [MATH] ... |
When comparing the DF with observations of stars in the GC, a relevant energy scale is [MATH] , which corresponds to orbits with a semi-major axis of [MATH] pc for [MATH] pc in the GC. On that scale the cusp is Keplerian, but there are still enough observed stars for meaningful statistics (e.g. Schödel et al., 2007 Fig... |
[MATH] and [MATH] . The transition between the weak and strong mass segregation solutions at [MATH] is clearly seen. It is interesting to note that the set of models calculated by BW77 all happen to lie at [MATH] , which explains why they found that “…there are no dramatic changes in the shapes of the curves, despite t... |
A useful average of the logarithmic slope is obtained from the corresponding stellar density curve (Eq. , cf Fig. ), which can be directly related to the observable stellar density distribution. A comparison of Figs. ( L) and ( R) shows that the shape of the curves is hardly affected by the method chosen for deriving t... |
The asymptotic limits (§ 3.1 ) are also clearly seen in Fig. ( ). When [MATH] , the weak segregation BW77 solution holds, with [MATH] and [MATH] When [MATH] , the light stars, which dominate the population, assume the single mass population DF, [MATH] while the heavy stars concentrate to the center. For low mass ratios... |
[MATH] , where dynamical friction is less efficient, the heavy stars approximately obey the BW77 relation, [MATH] For higher mass ratios, [MATH] , the heavy stars approach the dynamical friction limit, [MATH] |
The transition between the weak and strong mass segregation solutions is a reflection of the breakdown of the zero-flow assumption as [MATH] The dimensional scale [MATH] of the dimensionless stellar current into the MBH, [MATH] , is |
[MATH] (note that when the loss-cone is neglected, the steady-state current is independent of energy). This is also the order of magnitude of the stellar current into the MBH in a single mass population out of equilibrium. However, |
Bahcall & Wolf ( 1976 , Eq. 63) show that, neglecting the loss-cone, the steady-state current in a single mass population is [MATH] and that steady state zero-flows further imply that [MATH] |
in multi-mass populations (Bahcall & Wolf, 1977 , Eqs. 41-46) . The relevant physical timescale for the heavy star current [MATH] is not the |
[MATH] [MATH] interaction timescale [MATH] (here we choose [MATH] ), but rather the rate of [MATH] [MATH] and [MATH] [MATH] interactions, [MATH] To compare meaningfully the heavy star current [MATH] across the range of our models, we rescale it to [MATH] instead of [MATH] and normalize by the number of heavy stars to o... |
[EQUATION] Figure ( ) shows [MATH] as function of [MATH] for different mass ratios. For [MATH] , which is the range explored by BW77, we confirm their zero-flow result. In contrast, for [MATH] , we find that the zero-flow assumption no longer holds, [MATH] , and the heavy stars sink to the MBH at the maximal possible r... |
is approximately satisfied in this limit even with a loss-cone, as found by BW77 and confirmed here. In the limit strong segregation limit [MATH] , the dynamical friction-driven current of the heavy stars is insensitive to the presence or absence of a loss-cone, since [MATH] |
Figure ( R) shows the expected segregation of the massive stellar objects in the GC (based on the old, continuous star-formation PMF model, Fig. ), and in globular cluster M15, assuming it harbors an IMBH (based on the tentative PMF model of Murphy et al. 1997 which assumes that the most massive remnants in the cluster... |
neutron stars). The GC is expected to lie in the strong relaxation regime ( [MATH] ), while M15 in the weak relaxation regime [MATH] ). |
We refrain here from a more detailed quantitative analysis of the numerical results because the exact values of [MATH] depend somewhat on the way these are evaluated (locally, or from the density curve), and because the convergence of our numerical Fokker-Planck solver becomes progressively worse in the limits [MATH] |
and [MATH] . However, any numerical inaccuracies in those limits are unlikely to have practical implications, since realistic stellar systems are not expected to have [MATH] |
(a possible exception could be the hypothesized steady flow of IMBHs from dense stellar clusters to the MBH, Portegies Zwart et al. 2006 ). |
6. Discussion and summary 6.1. Strong segregation and other relaxation processes Strong mass segregation, or mass segregation instability, shares some common features with the Spitzer, or equipartition, instability in a cluster (Spitzer, 1969 , where the heavy stars decouple from the light ones and evolve away from equ... |
[MATH] (for [MATH] and [MATH] ). In contrast, in the Keplerian potential near a MBH, the Jeans equation dictates that [MATH] (Alexander & Kumar, 2001 , and so equipartition is never achieved, irrespective of the heavy-to-light mass or number ratios. Strong mass segregation is an instability in the spatial distribution ... |
(for [MATH] , Eq. 10 ). Perets et al. ( 2007 focused on the relaxation of light objects, stars, by heavy objects, massive perturbers (e.g. giant molecular clouds or clusters, with [MATH] ), and expressed the efficiency of massive perturber-induced relaxation relative to star-star relaxation by the parameter [MATH] [MAT... |
[MATH] addresses the question “Which mass component dominates the relaxation of the light stars?”, while [MATH] addresses the question “Which mass component dominates the dynamics of the heavy stars?”. The two are related by [MATH] |
Our approximate treatment of the mass segregation process neglects the relaxation of angular momentum to near radial (“loss-cone”) orbits. This, rather than diffusion in energy, is the primary channel for stellar destruction by the MBH. A full treatment of the mass segregation problem in ( [MATH] ) phase space (e.g. Co... |
6.2. Possible implications of strong mass segregation Strong mass segregation occurs in stellar systems with a relatively lower fraction of SBHs, that reach a higher central concentration of SBHs very close to the MBH, compared to systems with a higher fraction of SBHs that undergo weak segregation. To compare two such... |
Accelerated relaxation. The degree of mass segregation affects both the non-coherent 2-body relaxation timescale, which scales as [MATH] |
(see § ), and the resonant relaxation timescale, which scales as as [MATH] (Rauch & Tremaine, 1996 . In particular, the stronger the mass segregation, the shorter is the resonant relaxation timescale, which does not depend on the number of stars, but only on their typical mass. Efficient resonant relaxation near the MB... |
GW event rates. The GW EMRI rate is determined by the number of potential GW sources within the critical radius [MATH] which demarcates the boundary between compact object that inspiral into the MBH those that plunge (infall) into it. The critical radius is a function of the relaxation time, and to good approximation t... |
(Hopman & Alexander, 2005 Strong segregation will affect the EMRI rate both by modifying the 2-body relaxation time and by affecting the number of stars enclosed inside [MATH] , as well as by decreasing the resonant relaxation timescale. Similarly, the rates of detectable GW bursts from fly-bys near the Galactic MBH st... |
SBH–star interactions. A higher central concentration of SBHs affects the probability of SBH–star interactions, which can lead to the randomization of stellar orbits, the heating of a stellar disk |
(Perets et al., 2008 , the 3-body exchange capture of massive young stars near the MBH (Alexander & Livio, 2004 , or the ejection of hyper-velocity stars |
(O’Leary & Loeb, 2008 SBH–accretion disk interactions. A higher central concentration of SBHs within [MATH] gravitational radii of the MBH could exert coherent torques on the accretion disk, warp it and possibly affect its hydrodynamics (Bregman & Alexander, 2008, in prep.). The SBHs may shock the disk as they cross it... |
Enhanced gravitational lensing. SBHs projected near the Einstein angle of the MBH can strongly modify the gravitational lensing properties of the MBH, |
in a way similar to the effect of a planet orbiting a Galactic star that is lensing a background source (Alexander & Loeb, 2001 ; Chanamé et al., 2001 |
6.3. Summary We show that the steady state solution of a relaxed multi-mass stellar system around a MBH has two branches: the known weak (Bahcall-Wolf) mass segregation solution, where the difference in the degree of central concentration of the light and heavy stars is relatively small, and a newly discovered strong s... |
We are grateful to S. Tremaine and M. Freitag for useful discussions. TA is supported by ISF grant 928/06, ERC Starting Grant 202996 and a New Faculty grant by Sir H. Djangoly, CBE, of London, UK. CH is supported by a Veni scholarship from the Netherlands Organization for Scientific Research (NWO). |
# Source: arxiv 0808.3161 # Title: The W40 Cloud Complex # Sections: all # Downloaded: 2026-03-02T07:58:35.782855+00:00 The W40 Cloud Complex |
Abstract The W40 complex is a nearby site of recent massive star formation composed of a dense molecular cloud adjacent to an HII region that contains an embedded OB star cluster. The HII region is beginning to blister out and break free from its envelope of molecular gas, but our line of sight to the central stars is ... |
Institute for Astronomy, University of Hawaii 2680 Woodlawn Dr., Honolulu, HI 96822, USA Institute for Astronomy, University of Hawaii |
640 N. Aohoku Place, Hilo, HI 96720, USA 1. Overview The star forming region known as W40 consists of three interrelated components. First, there is the cold molecular cloud, which is designated using Galactic coordinates as G28.8+3.5, following |
Goss & Shaver ( 1970 . This dark cloud has an angular extent on the order of one degree, and is centered around a dense molecular core with a diameter of approximately [MATH] , identified as TGU 279-P7 in the recent extinction atlas of Dobashi et al. ( 2005 |
Adjacent to this molecular cloud is the large blister HII region denoted as W40 (Westerhout 1958 , and also labeled as S64 by Sharpless ( 1959 , as RCW 174 by Rodgers, Campbell, & Whiteoak (1960), or LBN 90 in the Lynds ( 1965 ) catalog of bright nebulae. The W40 HII region is centered on J2000 coordinates [MATH] |
[MATH] , and has a diameter of [MATH] . The space between the hot, ionized HII region and the cold molecular cloud is marked by a thin CII region and an accompanying neutral interface |
(Vallée 1987 Lastly, the W40 region hosts an embedded stellar cluster that is dominated by three bright IR sources (Zeilik & Lada 1978 . These bright OB stars are the primary excitation sources for the W40 HII region |
(Smith et al. 1985 and show evidence for substantial circumstellar envelopes (Vallée & MacLeod 1994 . The W40 cluster is heavily obscured along our line of sight by the surrounding molecular cloud, which provides |
[MATH] magnitudes of visual extinction throughout, and as much as [MATH] mag at the dense center (Reylé & Robin 2002 . Figure shows the W40 region in the optical from the Digitized Sky Survey and in the infrared from the 2MASS survey. |
2. Distance The distance to W40 has not yet been determined to any satisfactory precision. Measurements of the H109 [MATH] atomic recombination line at 0.7 km s -1 |
(Reifenstein et al. 1970 , the [MATH] 18 cm OH absorption line at 6.3 km s -1 (Downes 1970 and the 21 cm HI absorption line along the line of sight at 7.2 km s -1 |
(Radhakrishnan et al. 1972 collectively suggest a rough kinematic distance estimate of 300-900 pc based on the assumption that the cloud is in circular motion about the Galactic center. Estimates based on the radio/IR continuum of W40’s stellar component allow for a similar range from 400 pc |
(Crutcher & Chu 1982 to 700 pc (Smith et al. 1985 . Using OH line measurements with a unique distance determination technique, Kolesnik & Iurevich ( 1983 |
calculated a distance of 600 pc. Adopting a conservative mean of 600 pc places W40 at a distance of 37 pc above the Galactic plane. The dense central region of the molecular cloud is then [MATH] pc in diameter, and the width of the HII region measures [MATH] pc. |
3. The HII Region and Molecular Cloud After the initial discoveries of the W40 radio emission nebula and its associated HII region around 1960, subsequent radio detections were recorded over a wide range of frequencies. By the early 1970s the radio spectrum was well-constrained from 408 MHz to 5 GHz. Table |
summarizes the radio observations of the HII region’s free-free continuum and carbon recombination lines in the CII shell. The median flux density of the radio continuum in the HII region is 34 Jy. The most detailed radio continuum analysis to date is from the VLA observations of Vallée & MacLeod ( 1991 , which show a ... |
The TGU 279 molecular cloud has also been extensively mapped at millimeter wavelengths. These observations are summarized in Table |
. The properties of the molecular cloud derived from these observations are strongly model-dependent. Vallée et al. ( 1992 find that the total mass of the central cloud core out to a radius of 0.4 pc is [MATH] , and the density profile goes as [MATH] Zhu, Wu, & Wei (2006) measured the mass of the cloud core at the cent... |
The first detailed infrared examination of the W40 region was carried out by Zeilik & Lada ( 1978 . These authors find that the carbon recombination lines and CO molecular lines have velocities that are offset from the published hydrogen recombination lines by [MATH] 4 km s -1 . In addition, the bright IR sources are s... |
In 1982, Crutcher & Chu built on this conclusion by reviewing the available radio recombination line measurements, supplemented with their own molecular and H [MATH] maps. These authors note the presence of two molecular components with velocities that differ by about 3 km s -1 , and suggest that they correspond to the... |
Vallée ( 1987 took measurements of Cn [MATH] recombination lines in the warm neutral interface between the hot HII region and the cold molecular cloud. Fitting a model to their observations, they were able to constrain the properties of the thin CII shell and surmise that the stimulated Cn [MATH] line emission must be ... |
With these observations we may begin to draw a coherent picture of the history and current state of the W40 molecular cloud complex. Star formation in this region was initiated perhaps several million years ago by an external shock which caused a compression of the molecular gas and a distinct shift in the velocity of ... |
4. The Stellar Sources In contrast to the relatively detailed investigations of the cloud complex, very little work has been done on the underlying stellar population. Three dominant IR sources in W40 were noted by |
Zeilik & Lada ( 1978 , and subsequent observations revealed that six of the seven brightest IR sources can be matched with optical counterparts |
(Smith et al. 1985 . Recent high-resolution radio continuum observations using the VLA telescope have produced detailed maps of the W40 cluster at 3.6 cm (Rodríguez, Rodney, & Reipurth 2008, in preparation). These measurements reveal that the W40 cluster harbors 20 compact radio sources, 15 of which have IR counterpart... |
The high energy emission of the stars in the W40 cluster is now being examined with an X-ray study using the Chandra space telescope (Getman, K. et al. 2008, in preparation). Figure shows a preliminary Chandra X-ray map of the cluster, which reveals scores of X-ray point sources coincident with the optical and IR stell... |
The infrared spectral energy distributions of the brightest cluster members were examined by Smith et al. ( 1985 , and later millimeter observations of these sources with the James Clerk Maxwell Telescope in Hawaii have revealed further evidence for substantial circumstellar material surrounding IRS1a and IRS2a (Vallée... |
have been used to deduce column densities, temperatures, and abundance ratios in the foreground region of the W40 molecular cloud |
(Shuping et al. 1999 The Midcourse Space Experiment (MSX) satellite has observed the W40 region, and a map obtained at 8 [MATH] m is shown in Figure |
. Here the full structure of the W40 region is seen with minimal interference from obscuring dust clouds. We see that W40 consists of two interconnected cavities, forming an hour-glass shape. The main cluster is located just northwest of the narrow waist where the two cavities are joined. The total extent of the two ca... |
Zhu, Wu, & Wei (2006) obtained 12 CO J=3-2 and 13 CO J=2-1 and J=3-2 observations of the W40 region and found a molecular outflow associated with the molecular cloud on the southwestern rim of the HII region. The spatial position of the outflow relative to the cluster is seen in Figure Neither the MSX nor the IRAS cata... |
Acknowledgements . We are thankful to Konstantin Getman for providing Figures 1 and and for a thorough and very helpful referee’s report. This work has made use of The Digitized Sky Surveys, produced at the Space Telescope Science Institute. The images of these surveys are based on photographic data obtained using the ... |
# Source: arxiv 0808.3185 # Title: Gamma-Ray Studies of Blazars: Synchro-Compton Analysis of Flat Spectrum Radio Quasars # Sections: all # Downloaded: 2026-03-02T07:58:08.828315+00:00 |
Gamma-Ray Studies of Blazars: Synchro-Compton Analysis of Flat Spectrum Radio Quasars Abstract We extend a method for modeling synchrotron and synchrotron self-Compton radiations in blazar jets to include external Compton processes. The basic model assumption is that the blazar radio through soft X-ray flux is nontherm... |
Subject headings: radiation processes: nonthermal — galaxies: active — supermassive black holes 1. Introduction A class of radio-loud blazar active galactic nuclei (AGNs) that emit luminous fluxes of [MATH] MeV – GeV [MATH] rays was discovered with the Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Obs... |
(Hartman et al., 1992 ; Fichtel et al., 1994 ; Hartman et al., 1999 . This result clarified the nature of 3C 273, which was first identified as a [MATH] -ray emitting AGN in COS-B satellite data (Hermsen et al., 1977 . The [MATH] rays from blazars are certainly nonthermal in origin and associated with the radio jets fo... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.