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We divide these systems into pieces along the axis A in a way that each piece contains approximately the same number of particles. | We divide these systems into pieces along the axis $A$ in a way that each piece contains approximately the same number of particles. |
For this. we divide the first system into pieces. each containing the same number of particles and calculate the corresponding boundaries of these pieces in the first system. | For this, we divide the first system into pieces, each containing the same number of particles and calculate the corresponding boundaries of these pieces in the first system. |
We then divide the second system by means of these boundaries. | We then divide the second system by means of these boundaries. |
In each piece we calculate a given quantity whose value we denonte by Q. | In each piece we calculate a given quantity whose value we denonte by $Q$. |
Let σι]. qo»; be the calculated values in the i-th piece in the first and the second model. respectively. | Let $q_{1,i}$, $q_{2,i}$ be the calculated values in the $i$ -th piece in the first and the second model, respectively. |
If we consider the N-body system | If we consider the $N$ -body system |
with our measurement of the dispersion. | with our measurement of the dispersion. |
Our uncertainty in the unlensed density is therefore dominated by clustering. | Our uncertainty in the unlensed density is therefore dominated by clustering. |
We again turn to simulations to derive the error bars on our measurement. | We again turn to simulations to derive the error bars on our measurement. |
As in §?? we simulate a population that is lensed. by a SIS with 67=13.7 aresec. but in this case we drew the true value of iy from a Gaussian distribution with mean 20.3 aremin? and dispersion 7,=yg. where as derived above. | As in $\S\ref{sec-sim}$ we simulate a population that is lensed by a SIS with $\theta_E=13.7$ arcsec, but in this case we draw the true value of $n_0$ from a Gaussian distribution with mean 20.3 $^2$ and dispersion $\sigma_n=\eta n_0$, where as derived above. |
Using the log-likelihood function in Equation LO and a fixed estimate20.8.. we show the resulting distribution of recovered. Ge for 200 realizations in Fig. 12.. | Using the log-likelihood function in Equation \ref{eqn-lerr} and a fixed estimate, we show the resulting distribution of recovered $\theta_E$ for 200 realizations in Fig. \ref{fig-errsim}. |
We see. by comparison with Fig. | We see, by comparison with Fig. |
LO (the case where no was known precisely). that incorporating an error of produces a much broader distribution. with the result of greatly. increasing the error. bars on our. measurement. | \ref{fig-mldist} (the case where $n_0$ was known precisely), that incorporating an error of produces a much broader distribution, with the result of greatly increasing the error bars on our measurement. |
Applying Equation LO to the real data. we find θε=14n aresec ⋅ ⋰∎≼↛∪⊔↕⊓⇂⋖⊾⊔≼∙⋖⊾⊐∪↓⋅↙⇥∫∶↴∶↓⋅≟⊥⊽⊥↿∖≤⋗⋅↱≻⊲∕⋰∣≼∙∩⊔↕∐⇂⋖⋅⊔≼∙⋖⊾⊐⋡15. | Applying Equation \ref{eqn-lerr} to the real data, we find $\hat{\theta}_E=1.4^{+5.2}_{-1.4}$ arcsec confidence) or $\hat{\theta}_E=1.4^{+15.9}_{-1.4}$ confidence). |
9 ⋅ While the estimate of Gp itself is greatly reduced. the error bars make it compatible with the result of $77 within a 2e range. | While the estimate of $\theta_E$ itself is greatly reduced, the error bars make it compatible with the result of $\S\ref{sec-sim}$ within a $\sigma$ range. |
This section. illustrates the principal weakness of the depletion method as pointed out in SIE. namely the vital importance of accurately measuring ny. | This section illustrates the principal weakness of the depletion method as pointed out in SKE, namely the vital importance of accurately measuring $n_0$. |
With adN/yN0.1 which is not unreasonable eiven clustering on these scales. the depletion effect is made more dillicult to distinguish from variations in the background counts that are not due to lensing. | With a $\delta N/N \sim 0.1$ which is not unreasonable given clustering on these scales, the depletion effect is made more difficult to distinguish from variations in the background counts that are not due to lensing. |
However. this ellect could be countered by selecting similar clusters (e.g. by their A-rav temperatures). and stacking the depletion signal accordingly. thus calibrating the cluster. Zx-mass relation and obtaining an average cluster mass profile. | However, this effect could be countered by selecting similar clusters (e.g. by their X-ray temperatures) and stacking the depletion signal accordingly, thus calibrating the cluster $T_X$ -mass relation and obtaining an average cluster mass profile. |
Choosing a sample of 10 clusters would simultaneously increase the effective. background surface number density by a [factor of LO while reducing the yactional error in ny by a factor of /10.. | Choosing a sample of 10 clusters would simultaneously increase the effective background surface number density by a factor of 10 while reducing the fractional error in $n_0$ by a factor of $\sqrt{10}$. |
Simulations show that for 10 clusters similar to Abell 2219. the confidence region on 8p=13.7 aresce would then shrink rom (as quoted. above) to onlyaresecz a casible project for upcoming LE survey telescopes. | Simulations show that for 10 clusters similar to Abell 2219, the confidence region on $\theta_E=13.7$ arcsec would then shrink from (as quoted above) to only; a feasible project for upcoming IR survey telescopes. |
Note that in practice scatter in the cluster properties would. increase his range somewhat. | Note that in practice scatter in the cluster properties would increase this range somewhat. |
We present a study of the depletion. clleet around Abell 219. the first done in the infrared. using the newlv-available panoramic Ilt camera (CURSL). | We present a study of the depletion effect around Abell 2219, the first done in the infrared, using the newly-available panoramic IR camera (CIRSI). |
We show (see Appendix A) that the sample can be ellectively exploited: bevond the completeness limit. as long as the lensect field anc the background. field. obey the same incompleteness functions and have minimal contamination bv [false objects. | We show (see Appendix A) that the sample can be effectively exploited beyond the completeness limit, as long as the lensed field and the background field obey the same incompleteness functions and have minimal contamination by false objects. |
"This allows us to detect a clear dip in the radial number density profile of background: galaxies at small distances from the cluster centre. | This allows us to detect a clear dip in the radial number density profile of background galaxies at small distances from the cluster centre. |
The optical-infrarecl colours enable. us. to select a population of τοῦ background: galaxies with a Lat number-count slope in order to optimise the lensing signal and reduce foreground-background confusion. | The optical-infrared colours enable us to select a population of red background galaxies with a flat number-count slope in order to optimise the lensing signal and reduce foreground-background confusion. |
For a population of red background. galaxies with an extremely Le slope (a= 0.185). we employ. maximum likelihood methods and a SIS model to derive an estimate ⋅ V. . ∪⊓↓↕∢⊾∟↓⊔⊳∖∢⋅↓⊔↓⋅⋯∐⊔⊳∖↙⇥⇇⊸∶↓⇀⊰⋅⋀⊥⊽⊐⋜↧↓⋅≼∼⊳∖⋖⊾≼⇍↿∖↻↻⊲∕⋰ye40 confidence limit when uncertainties is my are ignored). resulting velocity dispersion m,—S14.H2 Kms. +. | For a population of red background galaxies with an extremely flat slope $\alpha=0.185$ ), we employ maximum likelihood methods and a SIS model to derive an estimate of the Einstein radius $\theta_E=13.7^{+3.9}_{-4.2}$ arcsec confidence limit when uncertainties is $n_0$ are ignored), resulting velocity dispersion $\sigma_v=814^{+112}_{-139}$ km $^{-1}$. |
"Phese values are consistent with the location of the redder of the two giant ares and the estimate a~930 km + of Smail (1995a). | These values are consistent with the location of the redder of the two giant arcs and the estimate $\sigma_v \sim 930$ km $^{-1}$ of Smail (1995a). |
We examine the uncertainty in the number counts. and derive a fractional error of on the normalisation. of he backeround number density (consistent with clustering on these scales). | We examine the uncertainty in the number counts, and derive a fractional error of on the normalisation of the background number density (consistent with clustering on these scales). |
When this error is incorporated into the maximunr-likelihood analysis the error. bars become too arge to make a precise statement about the magnitude of the lensing (although our previous measurement is not ruled out). | When this error is incorporated into the maximum-likelihood analysis the error bars become too large to make a precise statement about the magnitude of the lensing (although our previous measurement is not ruled out). |
This demonstrates the crucial importance of the xickeround density 29 for an accurate depletion analysis as discussed in Schneider. Wine Erben (2000). | This demonstrates the crucial importance of the background density $n_0$ for an accurate depletion analysis as discussed in Schneider, King Erben (2000). |
Finally. while we cannot at present use our current data o distinguish. between alternative models for the cluster | Finally, while we cannot at present use our current data to distinguish between alternative models for the cluster |
Hereafter we show the fit results for the literature sample and the relative x? maps for eerror computation to Fig. 3.4)). | Hereafter we show the fit results for the literature sample and the relative $\chi^2$ maps for error computation (analogous to Fig. \ref{fig_fit_errors}) ). |
The sources are sorted in redshift. | The sources are sorted in redshift. |
In the (analogousright panels we show the spectral decomposition. | In the right panels we show the spectral decomposition. |
The observed spectra are shown as a black continous line. | The observed spectra are shown as a black continous line. |
The modeled components are: power-law continuum (blue dotted line), Balmer pseudo continuum (purple dashed line), nnormalized template (light blue dotted line), eemission line (red dotted line). | The modeled components are: power-law continuum (blue dotted line), Balmer pseudo continuum (purple dashed line), normalized template (light blue dotted line), emission line (red dotted line). |
The sum of the first set of components (power-law continuum + Balmer pseudo continuum + nnormalized is overplotted to the spectrum as green solid line, while the sum of all the components is overplotted as a redtemplate) solid line. | The sum of the first set of components (power-law continuum $+$ Balmer pseudo continuum $+$ normalized template) is overplotted to the spectrum as green solid line, while the sum of all the components is overplotted as a red solid line. |
Telluric absorption bands are indicated over the spectra with the symbol @: they are extracted from the ESO sky absorption spectrum measured on the Paranal site at a nominal airmass of 1. | Telluric absorption bands are indicated over the spectra with the symbol $\Earth$: they are extracted from the ESO sky absorption spectrum measured on the Paranal site at a nominal airmass of 1. |
'The nnormalization, obtained from the fit of the first set of components, depends on the power-law slope and its normalization (intercept). | The normalization, obtained from the fit of the first set of components, depends on the power-law slope and its normalization (intercept). |
In the left panel we show the x? domain analysis for error computation: a) two dimensional projections of the 3D x?-surfaces nnormalization vs Intercept, upper-left plot; nnormalization vs Slope, bottom-left plot; Intercept vs slope, bottom-right plot): contours represent iso-y? levels spaced by factor of 2 while the best fit case is marked with a dot; b) probability distribution for the template normalizationa (upper-right plot): the distribution has been obtained by marginalizing the 3-D probability distribution considering only the triplets for which x?—Xmin<1, the dashed vertical lines mark our estimate of the 1—c confidence level. | In the left panel we show the $\chi^2$ domain analysis for error computation: a) two dimensional projections of the 3D $\chi^2$ -surfaces normalization vs Intercept, upper-left plot; normalization vs Slope, bottom-left plot; Intercept vs slope, bottom-right plot): contours represent $\chi^2$ levels spaced by a factor of 2 while the best fit case is marked with a dot; b) probability distribution for the template normalization (upper-right plot): the distribution has been obtained by marginalizing the 3-D probability distribution considering only the triplets for which $\chi^2 -\chi_{min}^2< 1$, the dashed vertical lines mark our estimate of the $1-\sigma$ confidence level. |
been summarized in Luetal.(2010). | been summarized in \citet*{Luetal10}. |
.. We shall further demonstrate in this paper that au isotropic distribution of ITVS progenitors is incousistent with the spatial distribution of the detected IIVSs if they are originated from the GC. | We shall further demonstrate in this paper that an isotropic distribution of HVS progenitors is inconsistent with the spatial distribution of the detected HVSs if they are originated from the GC. |
IIowever. the disk(s) origination of the detected IIVSs is cousistent with the distribution of the inclination aueles (relative to the disk(s)) of the detected IIVSs which further strenethen the conclusions mace iu Luetal.(2010). | However, the disk(s) origination of the detected HVSs is consistent with the distribution of the inclination angles (relative to the disk(s)) of the detected HVSs which further strengthen the conclusions made in \citet*{Luetal10}. |
. The velocity distribution of IIVSs is related to. not oulv the production mechauisui but also the origi of heir progenitors. | The velocity distribution of HVSs is related to not only the production mechanism but also the origin of their progenitors. |
Sesanaetal.(2007)— have studied he velocity distribution of IIVSs. | \citet{Sesana07} have studied the velocity distribution of HVSs. |
They fouud that he velocity distribution of IIVSs produced bw the Τον wnechanisin for uubound injecting stellar binaries seclus to be consistent with the then detected IIVSs hough with limited statistics. while the IWS velocity distribution produced by the BBIT mechanisu appears o be too flat iu comparison with the observatious. | They found that the velocity distribution of HVSs produced by the TBK mechanism for unbound injecting stellar binaries seems to be consistent with the then detected HVSs though with limited statistics, while the HVS velocity distribution produced by the BBH mechanism appears to be too flat in comparison with the observations. |
Their results suggest that the IIVS velocity distribution nay be useful in distinguishiug the ejection mechanisuis. | Their results suggest that the HVS velocity distribution may be useful in distinguishing the ejection mechanisms. |
Iu this paper. we shall further investigate the effects on the velocity distribution of IIVSs due to ciffereut origins of the ITVS progenitors. e.g.. those (binary) stars initially unbound to the MDBII but later injected iuto the uuediate vicinity of the MDII due to some uukuowu perturbations. and those (binary) stars imitiallvy bound to the MBIT but later evolved outo highly ecceutric orbits and migrated into the immediate vicinity of the MBIT. | In this paper, we shall further investigate the effects on the velocity distribution of HVSs due to different origins of the HVS progenitors, e.g., those (binary) stars initially unbound to the MBH but later injected into the immediate vicinity of the MBH due to some unknown perturbations, and those (binary) stars initially bound to the MBH but later evolved onto highly eccentric orbits and migrated into the immediate vicinity of the MBH. |
The paper is organized as follows. | The paper is organized as follows. |
Iu Section ??.. we first stuarize the observational results on the spatial aud velocity distribution of the detected ITVSs. | In Section \ref{sec:obs}, we first summarize the observational results on the spatial and velocity distribution of the detected HVSs. |
Iu Section ??.. we explore the detailed dynamics of interactions between binary stars on bound orbits aud a central ΑΠΟΠ. | In Section \ref{sec:TBK}, we explore the detailed dynamics of interactions between binary stars on bound orbits and a central MBH. |
The consequences of these interactions are different from that between the unbotud binary stars on parabolic (or lyperbolic) orbits and the. MDII intensively investigated in the literature (οιο,,Hills1985:Bromleyetal.2006:Sesana 2007). | The consequences of these interactions are different from that between the unbound binary stars on parabolic (or hyperbolic) orbits and the MBH intensively investigated in the literature \citep[e.g.,][]{Hills88,Bromley06,Sesana07}. |
. The reason is that the stellar binary may experience multiple close encounters with the MBIT in the former case. while it oulv experiences a single close eucouuter m the latter case. | The reason is that the stellar binary may experience multiple close encounters with the MBH in the former case, while it only experiences a single close encounter in the latter case. |
Assundue realistic distributions of the properties of the initial stellar binaries. we then simulate both the spatial distribution aud the velocity distribution of IIVSs produced by the TBK mechanisin and compare the Ποσα) results with the observations iu Section [. | Assuming realistic distributions of the properties of the initial stellar binaries, we then simulate both the spatial distribution and the velocity distribution of HVSs produced by the TBK mechanism and compare the numerical results with the observations in Section \ref{sec:Result}. |
? Iu Section ??.. we also explore the iuteractious between suele stars on bound orbits with a hvpothesized. DDII iu the GC. | In Section \ref{sec:BBH}, we also explore the interactions between single stars on bound orbits with a hypothesized BBH in the GC. |
These single stars are assumed to be injected iuto the iuiniediate viciuitv of the BBIT from cisk-like stellar structures (0... the CWS disk) surrounding the 3DIT. which is differcut from that adopted in Sesauaetal. (2007). | These single stars are assumed to be injected into the immediate vicinity of the BBH from disk-like stellar structures (e.g., the CWS disk) surrounding the BBH, which is different from that adopted in \citet{Sesana07}. |
. With reasonable but simple assumptions on the parameters of the hypothetical DDBIT. the spatial aud velocity distributions of the ejected IIVSs are obtained. | With reasonable but simple assumptions on the parameters of the hypothetical BBH, the spatial and velocity distributions of the ejected HVSs are obtained. |
Comparison between the sinmlation results aud the observations are also discussed in Section ??.. | Comparison between the simulation results and the observations are also discussed in Section \ref{sec:BBH}. |
The conchisions are elven in Section ??.. | The conclusions are given in Section \ref{sec:Conclusion}. |
Survevs of IIVSs have detected 16 IIVSs uubound to the Galactic halo. 8 bound IIVSs. aud E IIVS ciucdidates (Brownetal.2005:IlirschEdelmannct2005:Brownetal.2007.2009a). | Surveys of HVSs have detected 16 HVSs unbound to the Galactic halo, 8 bound HVSs, and 4 HVS candidates \citep{Brown05,Hirsch05,Edelmann05,Brown07,Brown09a}. |
. We stunuuazrize their spatial and velocity distributions iu this section. | We summarize their spatial and velocity distributions in this section. |
The spatial distribution of the IIVSs detected so far is probably anisotropic (Abadietal.2009:Brownct2 | The spatial distribution of the HVSs detected so far is probably anisotropic \citep{Abadi09,Brown09b}. |
009b).. Luetal.(2010) use exeat circles to fit the spatial distribution of the detected IIVSs projected on the skv of an observer located at the GC. and they find that the distribution can be best fitted by two great. circles. | \citet{Luetal10} use great circles to fit the spatial distribution of the detected HVSs projected on the sky of an observer located at the GC, and they find that the distribution can be best fitted by two great circles. |
Their results sugeest that the spatial distribution of the detected IIVSs is cousistent with beiug located on the planes of two thin disks (Luctal.2010): (1) eleven of the unbound IIVSs (plus four bound oues aud two candidates: totally 17 objects) are spatially associated to a thin disk plaue with an orientation almost the same as that of CWS disk located witlin half a parsec frou the ceutral MDII (see Levin&Beloborodoy2003:Luetal.2009:Patunardetal.2006:Bartko2009.2010) }: (2) four of the uubouud IIVSs (plus three bound ones aud two candidates: totally 9 objects) are spatially associated to a thin disk plane with au orieutation simular to that of the northern aru of the miuispiral (or also the outer warped part of the CWS disk) im the CC. | Their results suggest that the spatial distribution of the detected HVSs is consistent with being located on the planes of two thin disks \citep*{Luetal10}: (1) eleven of the unbound HVSs (plus four bound ones and two candidates; totally 17 objects) are spatially associated to a thin disk plane with an orientation almost the same as that of CWS disk located within half a parsec from the central MBH (see \citealt{LB03,LuJ09,Paumard06,Bartko09a,Bartko09b}) ); (2) four of the unbound HVSs (plus three bound ones and two candidates; totally 9 objects) are spatially associated to a thin disk plane with an orientation similar to that of the northern arm of the minispiral (or also the outer warped part of the CWS disk) in the GC. |
The normals of the best-fit disk planes for these two ITVS populations aro 1 υ) (ο.ον Lk) aud (1767. 53°) πι Calactic coordinates. respectively (Luetal.2010). | The normals of the best-fit disk planes for these two HVS populations are $l$ $b$ $=$ $311\arcdeg$, $-14\arcdeg$ ) and $176\arcdeg$, $-53\arcdeg$ ) in Galactic coordinates, respectively \citep{Luetal10}. |
. IIereafter. we refer to those detected IIVSsassociated with the above two best-fit planes as the first population aud the second population of IIVSs. respectively, | Hereafter, we refer to those detected HVSsassociated with the above two best-fit planes as the first population and the second population of HVSs, respectively. |
We denote the inclination angle of each. IVS to its correspoudiug best-fit plane by O and describe the spatial distribution of the IIVSs by a normalized cumulative distribution fiction of their inclination angles P(O) (hereafter. OCDE). which represeuts the nuuber fraction of theIIVSs with inclination angles higher than Ο. | We denote the inclination angle of each HVS to its corresponding best-fit plane by $\Theta$ and describe the spatial distribution of the HVSs by a normalized cumulative distribution function of their inclination angles $P(\geq\Theta)$ (hereafter, $\Theta$ CDF), which represents the number fraction of theHVSs with inclination angles higher than $\Theta$. |
The observationua OCDFs for both populations of the IIVSs are shown iu Figure d and will be compared with the distributions obtained from numerical models in Sections Lane TY. | The observational $\Theta$ CDFs for both populations of the HVSs are shown in Figure \ref{fig:f1} and will be compared with the distributions obtained from numerical models in Sections \ref{sec:Result} and \ref{sec:BBH}. |
For cach population. we shall compare the 3QO) of all the IIVSs Gucliding uubouud IIVSs. boum IIVSs. aud IIVS candidates) iustead of only uubouik ones. because (1) for the fist IIVS population. our lohuogorov Siürnov (I-8) test finds a likelihood. of 0.91 that the uubouud IIVSs aud all the IIVSs are drawu from the same OCDE: (2) for the second population. the ποτ of the uubouud IIVSs is only and the error cue to Poisson noise in the OCDE is substantial. therefore we do not show their OCDE in Figure 1. (aud eCDF in Figure 2. below. either). | For each population, we shall compare the $P(\geq\Theta)$ of all the HVSs (including unbound HVSs, bound HVSs, and HVS candidates) instead of only unbound ones, because (1) for the first HVS population, our $-$ Smirnov (K-S) test finds a likelihood of $0.94$ that the unbound HVSs and all the HVSs are drawn from the same $\Theta$ CDF; (2) for the second population, the number of the unbound HVSs is only 4 and the error due to Poisson noise in the $\Theta$ CDF is substantial, therefore we do not show their $\Theta$ CDF in Figure \ref{fig:f1} (and $v$ CDF in Figure \ref{fig:f2} below, either). |
The gravitational potential of the Galaxy is not exactly spherical. aud its non-spherical component may deflect the radial trajectories of IIVSs after they were ejected from the GC fee.Yu&Aladau 2007).. | The gravitational potential of the Galaxy is not exactly spherical, and its non-spherical component may deflect the radial trajectories of HVSs after they were ejected from the GC \citep[e.g.,][]{YM07}. . |
Caven the distance and the velocity span (30kpe<Ro«130kpc and 690lans|<v980kins ον sce Section ??4) of the detected IIVSs. however. the deviation due to | Given the distance and the velocity span $30\kpc<R<130\kpc$ and $690 \kms<v<980 \kms$ , see Section \ref{subsec:vd}) ) of the detected HVSs, however, the deviation due to |
System. | System. |
Followiug these discoveries. progress las beeu made in uncderstaucding planet formation. but the theory is still incomplete 2006). | Following these discoveries, progress has been made in understanding planet formation, but the theory is still incomplete . |
. The leading scenario for the formation of eiaut planets is the core accretion mechanuisiu. | The leading scenario for the formation of giant planets is the core accretion mechanism. |
Icy planetesimals located beyond the suow line inb their host disk colide repeatedly to grow a core with a modest. gaseous atmosphere. | Icy planetesimals located beyond the snow line in their host disk collide repeatedly to grow a core with a modest gaseous atmosphere. |
If this co'e succeeds in reachitσα crical 1dass of a few ens ol Earth masses. runaway accretion of a massive gaseous envelope Jloceecs alid leacls. ultimately. o the formation of a gaseous giaut platel 1996). | If this core succeeds in reaching a critical mass of a few tens of Earth masses, runaway accretion of a massive gaseous envelope proceeds and leads, ultimately, to the formation of a gaseous giant planet . |
. Some evidence supporting this scenario |an ©uerged in recent yeas. iut ie [oru ofa uetalliciCl reud for stars hosting planets )5).. he discovery of a high density hot Jupiter all tha of a ΠΡsinely rule‘o-leusing planet2006). | Some evidence supporting this scenario has emerged in recent years, in the form of a metallicity trend for stars hosting planets , the discovery of a high density hot Jupiter and that of a surprisingly low-mass micro-lensing planet. |
. However. a loug-stauclit& clitficulty or the core accret1o scenario. which has not vet |)ee1 fully elucidated. is the fac tha the lnesc:ile recuired o build pe‘itical core nasses aud tlus large gaseous envelopes (109-10* vr ls COLiparable ) he lifetiJes €of proto-petary disks1999). | However, a long-standing difficulty for the core accretion scenario, which has not yet been fully elucidated, is the fact that the timescale required to build-up critical core masses and thus large gaseous envelopes $\sim 10^6$ $10^7$ yr) is comparable to the lifetimes of proto-planetary disks. |
. Orbial inigration acds a layer of complication to theories of plajet. foriuatiOl. | Orbital migration adds a layer of complication to theories of planet formation. |
Ax a result of gravitaticoal interactions with their gaseous disk1986). e orbits of ptlets in the terrestrial mass rauge are predicted to decay ou timescales (~10? vr) short. compa'ed to disk lifetimes19972. | As a result of gravitational interactions with their gaseous disk, the orbits of planets in the terrestrial mass range are predicted to decay on timescales $\sim
10^5$ yr) short compared to disk lifetimes. |
b).. ligratio is slower for jxanets of much sinaller or iuuchi larger masses: in the first case because the Orque causiug[n]0 migration is quaclratic iu pallel Lass. aid in the second. case because the planet opens a gap aud then mierates ou the disks accretion timescale. which can be comparable to its ifetime. | Migration is slower for planets of much smaller or much larger masses: in the first case because the torque causing migration is quadratic in planet mass, and in the second case because the planet opens a gap and then migrates on the disk's accretion timescale, which can be comparable to its lifetime. |
While it is possible or »robable tal Inaly ter'estrial. planets form by agelomeratiouMD of stnaller bodies after tlie gas is goje. this is 1οἱ al option for the solicl cores of Jovian pallets since. iu the core accretion scenario. {1e cores Inst form belo' the gaseous envelopes eau ye accretec. | While it is possible or probable that many terrestrial planets form by agglomeration of smaller bodies after the gas is gone, this is not an option for the solid cores of Jovian planets since, in the core accretion scenario, the cores must form before the gaseous envelopes can be accreted. |
The prevalence of Jovian plauets with orbial periods o only. a few days deepeus the luystery a it suggests that these planets clic ulierate but stopped sli[9]t of mereing with their sta ‘Sal Orjtal adii where even the accretion tiijescale wold seem tolave been very short1996). | The prevalence of Jovian planets with orbital periods of only a few days deepens the mystery as it suggests that these planets did migrate but stopped short of merging with their stars at orbital radii where even the accretion timescale would seem to have been very short. |
. Analytie caleulatious and most hycdro-dynamical sit—tlations of uigration usualM7 assulue a disk that is laminar apart [rom tle waves axl shocks excited by the panet itself | Analytic calculations and most hydro-dynamical simulations of migration usually assume a disk that is laminar apart from the waves and shocks excited by the planet itself. |
.But t leelective viscositv ol disks p'obably involves turbulence.( | But the effective viscosity of disks probably involves turbulence., |
2001)..1).. al( lave found in 3D simulatious of magnueto-roalleoal turbuence that the i1stantaneous torque exe‘tect on a planet iu the terrestrial mwiass ral ge|s subject (to lοιασας many times its mean value. apparently caused by turbulent. density. fluctuations iu le planets vicinity. | and have found in 3D simulations of magneto-rotational turbulence that the instantaneous torque exerted on a planet in the terrestrial mass range is subject to fluctuations many times its mean value, apparently caused by turbulent density fluctuations in the planet's vicinity. |
In [act. uo obviOUS secular decay manifests itself in the orbits of planets with 1vass MyS1OAL. although because the simulationsH are limitedH to 4107> planetary orbits—coHupae >10? for Jupiter during the lifetime ol the proto-solar uebula—aud the predicted decay ii seninmnajor axls is SSCENLO% over this period. | In fact, no obvious secular decay manifests itself in the orbits of planets with mass $M_p\lesssim 10 M_\oplus$, although because the simulations are limited to $\sim 10^2$ planetary orbits—compare $\gtrsim 10^5$ for Jupiter during the lifetime of the proto-solar nebula—and the predicted decay in semimajor axis is $\lesssim 10\%$ over this period, |
value for low mass dwarf irregular galaxies. e.g. Lake et al. | value for low mass dwarf irregular galaxies, e.g. Lake et al. |
1990. Begum et al. | 1990, Begum et al. |
2003). implies that the systematic rotation. if any. in the galaxy is smaller than the velocity dispersion. | 2003), implies that the systematic rotation, if any, in the galaxy is smaller than the velocity dispersion. |
Given the lack of any systematic rotation. it is difficult to accurately determine the total dynamical mass for the galaxy. | Given the lack of any systematic rotation, it is difficult to accurately determine the total dynamical mass for the galaxy. |
From the virial theorem. assuming HI distribution to be spherical with an isotropic velocity dispersion and negligible rotation. the indicative mass is (Hoffman et al. | From the virial theorem, assuming HI distribution to be spherical with an isotropic velocity dispersion and negligible rotation, the indicative mass is (Hoffman et al. |
1996) Assuming c of 8 "and taking the diameter of the galaxy ~ |. Skpe. gives a total mass of HIZSSOO3B to be —5.3.10M... | 1996) Assuming $\sigma$ of 8 and taking the diameter of the galaxy $\sim $ 1.5 kpc, gives a total mass of HIZSS003B to be $\sim 5.3\times10^7 \rm{M_\odot}$. |
For the entire HIZSSOO03 system. if we assume the two galaxies to be in a bound circular orbit. then the indicative orbital mass is where r, is the projected separation and AV the radial velocity difference (Karachentsev. et al. | For the entire HIZSS003 system, if we assume the two galaxies to be in a bound circular orbit, then the indicative orbital mass is where $r_p$ is the projected separation and $\Delta V$ the radial velocity difference (Karachentsev et al. |
2002). | 2002). |
For a projected separation of ~0.7 kpe and a velocity difference of ~34.6 +. the indicative orbital mass is ~6.7.LO" M... in good agreement with the total mass derived from the internal Kinematics. | For a projected separation of $\sim 0.7$ kpc and a velocity difference of $\sim 34.6$ , the indicative orbital mass is $\sim 6.7\times 10^8$ $_\odot$, in good agreement with the total mass derived from the internal kinematics. |
Silva et al. ( | Silva et al. ( |
2005) highlight a puzzle regarding the metallicity of HIZSS003. | 2005) highlight a puzzle regarding the metallicity of HIZSS003. |
The metallicity of HIZSSO03 system calculated from the younger HII region is smaller than that estimated from the color of the older red giant branch stars. | The metallicity of HIZSS003 system calculated from the younger HII region is smaller than that estimated from the color of the older red giant branch stars. |
Given that the bulk of the stars are associated with the bigger galaxy but that the HIT region is in the smaller galaxy. the inconsistency in the derived metallicities is not surprising. | Given that the bulk of the stars are associated with the bigger galaxy but that the HII region is in the smaller galaxy, the inconsistency in the derived metallicities is not surprising. |
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