------------------------------------------------------------------------ From: Ortwin Gerhard Ortwin.Gerhard@unibas.ch Subject: He stars texfile To: gcnews@aoc.nrao.edu MIME-version: 1.0 Content-transfer-encoding: 7bit \documentclass[preprint]{aastex} %\documentstyle[emulateapj,psfig]{article} \usepackage{emulateapj5} \submitted{Submitted to the Astrophysical Journal Letters, May 1, 2000} %\input psfig \def\kpc{{\rm\,kpc}}\def\msun{{\rm\, M}_\odot} %\lta and \gta produce > and < signs with twiddle underneath \def\spose#1{\hbox to 0pt{#1\hss}}\def\lta{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}} \raise 2.0pt\hbox{$\mathchar"13C$}}} \def\gta{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}} \raise 2.0pt\hbox{$\mathchar"13E$}}} \def\kms{\,{\rm km\,s}^{-1}} \def\etal{et al.\ } %\textheight=25cm\textwidth=16cm\voffset=-2.5cm\hoffset=-1.5cm\pagestyle{empty}\ parindent 0pt\parskip 12pt %\hoffset=-.5cm %\voffset=.5cm % Bold math italic \font\fivebmi=cmmib6 \font\sixbmi=cmmib6 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\mathchardef\varsigma="7126 \mathchardef\varphi="7127 \def\chaphead{} \newcount\eqnumber \eqnumber=1 \def\today{\ifcase\month\or January\or February\or March\or April\or May\or June\or July\or August\or September\or October\or November\or December\fi \space\number\day, \number\year} %to name an equation, place command "\eqnam{\Poisson}" before equation, and %thereafter "equation \Poisson)" will generate the proper equation number. \def\eqnam#1{\xdef#1{(\chaphead\the\eqnumber}} \def\newe{(\hbox{\chaphead\the\eqnumber})\global\advance\eqnumber by 1} \def\firste{(\hbox{\chaphead\the\eqnumber a})\global\advance\eqnumber by 1} \def\laste#1{\advance\eqnumber by -1% (\hbox{\chaphead\the\eqnumber #1})\advance\eqnumber by 1} %to refer to an equation which is 5 equations back, write "equation \refe5)" \def\refe#1{\advance\eqnumber by -#1 (\chaphead\the\eqnumber \advance\eqnumber by #1 } \def\ssk{\smallskip}\def\msk{\medskip}\def\bsk{\bigskip} \def\disp{\displaystyle} \def\th{^{\rm th}} %fourth=4\th\ etc \def\dint{\int\!\!\!\int} \def\i{\relax\ifmmode{\rm i}\else\char16\fi} \def\e{{\rm e}} \def\deg{^\circ} %for angular measure in degrees \def\frac#1#2{{\textstyle{#1\over#2}}} \def\p{\partial} \def\d{{\rm d}} \def\dddot#1{\ddot#1\kern-1.4pt\dot{\phantom{#1}}\kern-3pt} \def\xx{} \def\erf{\mathop{\rm erf}\nolimits} %error function \def\sech{ \mathop{\rm sech}\nolimits} %hyperbolic sec \def\csch{ \mathop{\rm csch}\nolimits} %hyperbolic csc \def\arcsinh{\mathop{\rm arcsinh}\nolimits} %arc hyperbolic sin \def\arccosh{\mathop{\rm arccosh}\nolimits} %arc hyperbolic cos \def\arctanh{\mathop{\rm arctanh}\nolimits} %arc hyperbolic tan \def\arccoth{\mathop{\rm arccoth}\nolimits} %arc hyperbolic cot \def\arcsech{\mathop{\rm arcsech}\nolimits} %arc hyperbolic sec \def\arccsch{\mathop{\rm arccsch}\nolimits} %arc hyperbolic csc \def\arccot{\mathop{\rm arccot}\nolimits} %arc cot \def\arcsec{\mathop{\rm arcsec}\nolimits} %arc sec \def\arccsc{\mathop{\rm arccsc}\nolimits} %arc csc \def\ylm{\mathop{\rm Y}_l^m\nolimits} %spherical harmonic \def\ylmp{\mathop{\rm Y}_{l'}^{m'}\nolimits} %spherical harmonic primed \def\scre{{\cal E}} %script E \def\real{\Re\hbox{{\eightrm e}}} %real part \def\imag{\Im\hbox{{\eightrm m}}} %imaginary part \def\spose#1{\hbox to 0pt{#1\hss}} \def\s#1{\widetilde{#1}} \def\=#1{\overline{#1}} %\lta and \gta produce > and < signs with twiddle underneath \def\lta{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}} \raise 2.0pt\hbox{$\mathchar"13C$}}} \def\gta{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}} \raise 2.0pt\hbox{$\mathchar"13E$}}} \def\km{{\rm\,km}} \def\kms{{\rm\,km\,s^{-1}}} \def\kpc{{\rm\,kpc}} \def\Mpc{{\rm\,Mpc}} \def\arcmin{\,{\rm arcmin}} \def\msun{{\rm\,M_\odot}} \def\lsun{{\rm\,L_\odot}} \def\rsun{{\rm\,R_\odot}} \def\pc{{\rm\,pc}} \def\cm{{\rm\,cm}} \def\yr{{\rm\,yr}} \def\Gyr{{\rm\,Gyr}} \def\Myr{{\rm\,Myr}} \def\myr{{\rm\,Myr}} \def\au{{\rm\,AU}} \def\gm{{\rm\,g}} \def\kg{{\rm\,kg}} \def\ergps{{\rm\,erg\,s}^{-1}} \def\K{{\rm\,K}} \def\GHz{\,{\rm GHz}} \def\rms{{\caps rms}} \def\annrev #1 #2 {ARA\&A, #1, #2} \def\aa #1 #2 {A\&A, #1, #2} \def\aasupp #1 #2 {A\&AS, #1, #2} \def\aj #1 #2 {AJ, #1, #2} \def\apj #1 #2 {ApJ, #1, #2} \def\apjlett #1 #2 {ApJ, #1, #2} \def\apjsupp #1 #2 {ApJS, #1, #2} \def\ban #1 #2 {Bull.\ Astron.\ Inst.\ Netherlands, #1, #2} \def\mn #1 #2 {MNRAS, #1, #2} \def\nature #1 #2 {Nat, #1, #2} \def\pasj #1 #2 {PASJ, #1, #2} \def\pasp #1 #2 {PASP, #1, #2} \shorttitle{Origin of Galactic Center HeI Star Cluster} \shortauthors{Ortwin Gerhard} \begin{document} \title{The Galactic Center He I Stars: Remains of a Dissolved Young Cluster?} \author{Ortwin Gerhard} \affil{Astronomical Institute of the University of Basel, Venusstrasse 7, CH-4102 Binningen, Switzerland} %\pubyear{2000}\maketitle \begin{abstract} A massive young star cluster embedded in its parent molecular cloud will spiral into the Galactic Center from $\sim 30\pc$ during the life-time of its most massive stars, if the combined total mass is $\sim 10^6\msun$. On its way inwards the system loses most of its mass to the strong tidal field, until the dense cluster core of high-mass stars is finally disrupted by the central black hole. A simple model is presented to argue that this scenario may under plausible conditions explain the observed location and rotation of the Galactic Center HeI stars. Accretion of star clusters into the Galactic Center could be recurrent, and play an important role in regulating the activity of Sgr A$^\ast$. \end{abstract} \section{Introduction} The central parsec of the Galaxy contains a cluster of young stars, including some 15 very luminous HeI emission line stars (Krabbe \etal 1995), as well as many less massive O and probably B stars (Eckart \etal 1999). From their spectroscopic properties and wind outflow velocities the HeI stars are believed to be evolved supergiant stars of $\sim 20-100\msun$, now in a short-lived post-main sequence phase close to the Wolf-Rayet stage (Najarro \etal 1997). The most massive of these stars have a total age of $\lta 3 \myr$, while the less luminous stars could have ages up to $\sim 8\myr$. Krabbe \etal (1995) have argued that the most likely origin of these stars is in a small starburst $\sim 3-7\myr$ ago. In situ formation of these stars is problematic, however, because of the strong tidal field of the nuclear bulge and central black hole. In this respect the Galaxy may differ from some other late type galaxies with observed young nuclear clusters (Carollo \etal 1998, Matthews \etal 1999, B\"oker \etal 1999). The tidal forces from the Galactic nucleus alone are sufficient to unbind gas clouds with densities $n_{\rm crit}<10^7\cm^{-3} (1.6\pc/R_G)^{1.8}$ at galactocentric radii $R_G$ (e.g., Morris 1993), while clouds in the nuclear gas disk have densities of $10^4 - 3\times 10^5 \cm^{-3}$ (Genzel 1989, G\"usten 1989). Hence Morris (1993) has argued that the formation of the central star cluster must have been externally triggered to achieve the required high densities, e.g., by cloud collisions. An alternative model in which the massive stars form through collisions and mergers of lower mass stars in the high-density nuclear cluster now appears unlikely, both because too few massive stars would form (Lee 1994), and because similar stars have been found in the Arches and Quintuplet clusters some $30\pc$ away from the center (Serabyn \etal 1998, Figer \etal 1999a). This letter explores the idea that the young stars now seen in the Galactic Center (GC) did not in fact form there, but further out in a massive star cluster that subsequently spiralled into the nucleus and tidally dissolved. One of the exciting results from HST has been the discovery of young star clusters in a variety of starburst environments (e.g., Whitmore \& Schweizer 1995, O'Connell \etal 1995, Oestlin \etal 1998). The Arches and Quintuplet clusters at $\sim 30\pc$ distance from the GC testify that a similar star formation mode has been occurring in the nuclear disk of the Galaxy. Both clusters have ages of a few megayears and estimated total masses (extrapolating the IMF to $1\msun$) of $\sim 10^4 \msun$ (Figer \etal 1999b). The orbits of such clusters will evolve by dynamical friction against field stars in sufficiently dense stellar systems (Tremaine, Ostriker \& Spitzer 1975). Here I show that a massive cluster formed near the present location of the Arches cluster and embedded in the remains of its parent molecular cloud will indeed spiral into the central parsec within the lifetime of its most massive stars, losing much of its mass on its way inwards until its dense core is finally disrupted by the central black hole. \section{Massive Cluster Infall} Suppose a massive star cluster is formed at initial galactocentric radius $R_i=30 R_{30}\pc$. The mass distribution of the nuclear bulge in $2\pc 1$ in the region of interest (Binney \& Tremaine 1987). This simple equation suggests that a massive cluster, $m_c \sim 10^6\msun$, when formed in the same region as the present Arches cluster, will indeed spiral into the center within the lifetime of its most massive stars. The friction time-scale is dominated by the time spent at large radii. In these initial phases the cluster will be embedded within its parent molecular cloud while both are dragged inwards together. The time-scale for the cloud envelope of the cluster to be dispersed by the energy input from the massive cluster stars is comparable to the life-times of these stars, so will be a substantial fraction of the time to spiral into the GC. Because the part of the molecular cloud not converted into cluster stars is conceivably the major part of the total initial mass, we need to take into account the dynamical friction on the molecular cloud (Stark \etal 1991) when considering the orbital evolution of the cluster. As it spirals to the Galactic center, the parent cloud and embedded cluster will constantly lose mass because of the strong tidal field. We can estimate the effect of this mass loss on the friction time with a simple model in which the initial mass $m_{ci}$ of the combined cloud and cluster is distributed according to an isothermal profile, tidally limited at radius $r=r_{ti}$: \begin{equation} m_c(r)=m_{ci}(r/r_{ti}), \end{equation} \begin{equation}\label{eqrinitial} r_{ti}=\left( {m_{ci}\over M_G[R_i]} \right)^{1/3} \,\, R_i = 6.2\, m_6^{1/3} v_{130}^{-2/3} R_{30}^{2/3} \pc. \end{equation} For comparison, the half-mass radius of the present Arches cluster ($\sim 10^4\msun$) is approximately $0.2\pc$ (Figer \etal 1999a). As the cluster spirals in, successive outer shells of the mass distribution are peeled off by the tidal field. The division between cluster and cloud need not be specified now, but it is clear that at some stage the cloud envelope will have been removed and the cluster proper will begin to be stripped. The tidal radius decreases according to \begin{equation}\label{eqrtidal} r_t/R_G = r_{ti}/R_i, \end{equation} where $R_G$ is the current galactocentric radius, and if internal evolution is neglected, the cluster mass decreases as \begin{equation}\label{eqclmass} m_c(R_G) = m_{ci} (R_G/R_i). \end{equation} When the entire cluster is finally disrupted at radius $R_{\rm dis}$, only a fraction $\sim R_{\rm dis}/R_i$ of the initial mass $m_{ci}$ will have arrived at $R_{\rm dis}$. Note that assuming an isothermal profile for the cluster will lead us to overestimate its mass loss because real clusters have less extended envelopes than $\propto r^{-2}$, while neglecting internal evolution will lead us to underestimate the mass loss because the cluster will become less dense and more vulnerable to tidal disruption during the evolution. We can now write a modified dynamical friction equation using the same arguments as in Binney \& Tremaine (1987), and assuming that the instantaneous specific angular momentum loss due to the frictional force is the same for stripped material and material that remains bound to the cluster. This gives $R_G \d{R_G}/\d{t} =-0.428 G\ln(0.4N) v_c^{-1} m_{ci} (R_G/R_i)$, the solution of which is \begin{eqnarray}\label{eqtfricprimed} \tau'_{\rm df}(R_i,R_G)= R_i R_G v_c/ 0.428\,\ln(0.4N)\,G m_{ci} & \\ = 6.2 \times 10^6 (R_G/R_i) R_{30}^2 v_{130} m_6^{-1} \lambda_{10}^{-1} \yr.& \nonumber \end{eqnarray} Thus in this simple model the total time to spiral in from radius $R_i$ is just twice that when the mass $m_{ci}$ remains constant [eq.~(\ref{eqtfric})], and the time taken from radius $R_G