Steven W. Stahler

Star Formation in the Orion Nebula Cluster

We study the record of star formation activity within the dense cluster associated with the Orion Nebula. The bolometric luminosity function of 900 visible members is well matched by a simplified theoretical model for cluster formation. This model assumes that stars are produced at a constant rate and distributed according to the field-star initial mass function. Our best-fit age for the system, within this framework, is 2 ? 106?yr. To undertake a more detailed analysis, we present a new set of theoretical pre-main-sequence tracks. These cover all masses from 0.1 to 6.0?M?, and start from a realistic stellar birthline. The tracks end along a zero-age main-sequence that is in excellent agreement with the empirical one. As a further aid to cluster studies, we offer an heuristic procedure for the correction of pre-main-sequence luminosities and ages to account for the effects of unresolved binary companions. The Orion Nebula stars fall neatly between our birthline and zero-age main-sequence in the H-R diagram. All those more massive than about 8?M? lie close to the main sequence, as also predicted by theory. After accounting for the finite sensitivity of the underlying observations, we confirm that the population between 0.4 and 6.0?M? roughly follows a standard initial mass function. We see no evidence for a turnover at lower masses. We next use our tracks to compile stellar ages, also between 0.4 and 6.0?M?. Our age histogram reveals that star formation began at a low level some 107?yr ago and has gradually accelerated to the present epoch. The period of most active formation is indeed confined to a few ? 106?yr, and has recently ended with gas dispersal from the Trapezium. We argue that the acceleration in stellar births, which extends over a wide range in mass, reflects the gravitational contraction of the parent cloud spawning this cluster.

The pre-main-sequence evolution of intermediate-mass stars

We calculate numerically the structure and evolution of pre-main-sequence stars with masses from 1 to 6 M ○. . These stars are assumed to originate from protostars accreting within molecular clouds. For masses from 2 to 4 M ○. , the stellar luminosity first increases markedly during a protracted epoch of nonhomologous contraction and thermal relaxation. Deuterium burns in a subsurface shell throughout this period. More massive objects are thermally relaxed from the start; they contract homologously, with fully radiative interiors. Stars with masses greater then 8 M ○. have no pre-main-sequence phase, since they are already burning hydrogen by the time protostellar accretion has ended

Accelerating Star Formation in Clusters and Associations

We use our own, recently developed pre-main-sequence evolutionary tracks to investigate the star formation histories of relatively nearby associations and clusters. We first employ published luminosities and effective temperatures to place the known members of each region in the H-R diagram. We then construct age histograms detailing that regions history. The groups studied include Taurus-Auriga, Lupus, Chamaeleon, ρ Ophiuchi, Upper Scorpius, IC 348, and NGC 2264. This study is the first to analyze a large number of star-forming regions with the same set of theoretical tracks. Our investigation corroborates and extends our previous results on the Orion Nebula Cluster. In all cases, we find that star formation began at a relatively low level some 107 yr in the past and has more recently undergone a steep acceleration. This acceleration, which lasts several million years, is usually continuing through the present epoch. The one clear exception is the OB association Upper Scorpius, where the formation rate climbed upward, peaked, and has now died off. Significantly, this is also the only region of our list that has been largely stripped of molecular gas. The acceleration represents a true physical phenomenon that cannot be explained away by incompleteness of the samples; nor is the pattern of stellar births significantly affected by observational errors or the presence of unresolved binaries. We speculate that increasing star formation activity arises from contraction of the parent cloud. Despite the short timescale for acceleration, the cloud is likely to evolve quasi-statically. Star formation itself appears to be a critical phenomenon, occurring only in locations exceeding some threshold density. The clouds contraction must reverse itself, and the remnant gas dissipate, in less than 107 yr, even for aggregates containing no massive stars. In this case, molecular outflows from the stars themselves presumably accomplish the task, but the actual dispersal mechanism is still unclear.

Deuterium and the stellar birthline

A series of simplified evolutionary calculations are used to show that deuterium burning acts as an effective thermostat in low-mass protostars over a plausible range of initial conditions and mass accretion rates. The thermostat keeps the central temperature of the accreting hydrostatic core close to 10 to the 6th K, and thereby tightly constrains the cores mass-radius relation. This relation, when combined with premain-sequence evolutionary tracks, yields a theoretical birthline or upper envelope for young stars in the H-R diagram which maintains excellent agreement with observations of T Tauri stars in nearby molecular cloud complexes. This derivation of the birthline helps to explain its insensitivity to protostellar collapse conditions. The calculations indicate that the birthline will be little affected by the inclusion of rotation as long as the newly visible stars have lost most of their accreted angular momentum. 42 references.

The evolution of intermediate-mass protostars. II - Influence of the accretion flow

The growth of spherical protostars that condense from diffuse interstellar clouds is considered. As in previous study, we focus on the internal structure of protostars in the intermediate-mass range: 2 M ⊙ ≤ M * ≤ 10 M ⊙ . Three evolutionary sequences were computed, one with the previous mass accretion rate of dM/dt = 10 -5 M ⊙ /yr, and others with dM/dt = 3 × 10 -5 and 10 -4 M ⊙ /yr. In order to gauge the maximum effect of accretion onto the star through a cirumstellar disk, photospheric boundary conditions were employed

Star Formation in Space and Time: Taurus-Auriga

To understand the formation of stellar groups, one must first document carefully the birth pattern within real clusters and associations. In this study of Taurus-Auriga, we combine pre-main-sequence ages from our own evolutionary tracks with stellar positions from observational surveys. Aided by the extensive millimeter data on the molecular clouds, we develop a picture of the regions history. Star formation began, at a relatively low level and in a spatially diffuse manner, at least 107 yr in the past. Within the last few million years, new stars have been produced at an accelerating rate, almost exclusively within a confined group of striated cloud filaments. The gas both inside and around the filaments appears to be in force balance. Thus, the appearance of the filaments is due to global, quasi-static contraction of the parent cloud material. Gravity drives this contraction and shock dissipation mediates it, but the internal motion of the gas does not appear to be turbulent. The accelerating nature of recent star formation means that the condensation of cloud cores is a threshold phenomenon, requiring a minimum background density. Other, nearby cloud regions, including Lupus and Chamaeleon, contain some locales that have attained this density, and others that have not. In the latter, we find extensive and sometimes massive molecular gas that is still devoid of young stars.

Star Formation in Space and Time: The Orion Nebula Cluster

We examine the pattern of star birth in the Orion Nebula cluster (ONC), with the goal of discerning the clusters formation mechanism. Outside the Trapezium, the distribution of stellar masses is remarkably uniform and is not accurately described by the field-star initial mass function. The deconvolved, three-dimensional density of cluster members peaks at the Trapezium stars, which are truly anomalous in mass. Using theoretical pre-main-sequence tracks, we confirm the earlier finding that star formation has accelerated over the past 107 yr. We further show that the rate of acceleration has been the same for all masses. Thus, there is no correlation between stellar age and mass, contrary to previous claims. Finally, the acceleration has been spatially uniform throughout the cluster. Our reconstruction of the parent molecular cloud spawning the cluster shows that it had a mass of 6700 M☉ prior to its destruction by the Trapezium. If the cloud was supported against self-gravity by mildly dissipative turbulence, then it contracted in a quasi-static but accelerating manner. We demonstrate this contraction theoretically through a simple energy argument. The mean turbulent speed increased to its recent value, which is reflected in the present-day stellar velocity dispersion. The current ONC will be gravitationally unbound once cloud destruction is complete, and is destined to become a dispersing OB association. We hypothesize that similarly crowded groups seen at the centers of distant OB associations are also unbound and do not give rise to the Galactic population of open clusters. Finally, accelerating star formation implies that most clumps within giant molecular complexes should have relatively low formation activity. Sensitive infrared surveys could confirm this hypothesis.

Binary Masses as a Test for Pre-Main-Sequence Tracks

Observations of binaries have traditionally provided the means for ascertaining stellar masses. Here we use the published data on eight pre-main-sequence pairs to gauge the accuracy of our own, recently calculated, evolutionary tracks. We consider both eclipsing, double-lined spectroscopic binaries, which provide the mass of each star separately, and noneclipsing, double-lined systems, which yield only the ratio. We also analyze the visual, quadruple system GG Tau, for which the sum of the two component masses follows from observations of the circumbinary disk. In almost all cases, our theoretically derived masses or mass ratios are in good agreement with the empirical values. For two binaries (NTTS 162814-2427 and P1540), the observational results are still too uncertain for a proper comparison. We also find that the derived contraction ages within each pre-main-sequence pair are nearly equal. This result extends earlier findings regarding visual pairs and indicates that the components of all binaries form in proximity, perhaps within the same dense cloud core. Finally, our study reveals that the Trapezium star BM Ori is very young since both the star itself and its companion have contraction ages less than 105 yr.

Star Formation in Cold, Spherical, Magnetized Molecular Clouds

We present an idealized, spherical model of the evolution of a magnetized molecular cloud that is due to ambipolar diffusion. This model allows us to follow the quasi-static evolution of the clouds core prior to collapse and the subsequent evolution of the remaining envelope. By neglecting the thermal pressure gradients in comparison with magnetic stresses and by assuming that the ion velocity is small compared with the neutral velocity, we are able to find exact analytic solutions to the MHD equations. We show that, in the case of a centrally condensed cloud, a core of finite mass collapses into the origin leaving behind a quasi-static envelope, whereas initially homogeneous clouds never develop any structure in the absence of thermal stresses and collapse as a whole. Prior to the collapse of the core, the clouds evolution is characterized by two phases: a long, quasi-static phase, in which the relevant timescale is the ambipolar diffusion time (treated in this paper), and a short, dynamical phase, in which the characteristic timescale is the free-fall time. The collapse of the core is an outside-in collapse. The quasi-static evolution terminates when the cloud becomes magnetically supercritical; thereafter, its evolution is dynamical, and a singularity develops at the origin—a protostar. After the initial formation of the protostar, the outer envelope continues to evolve quasi-statically, while the region of dynamical infall grows with time—an inside-out collapse. We use our solution to estimate the magnetic flux trapped in the collapsing core and the mass accretion rate onto the newly formed protostar. Our results agree, within factors of order unity, with the numerical results of Fiedler & Mouschovias for the physical quantities in the midplane of a collapsing, magnetized, axisymmetric cloud up to the onset of dynamical collapse. Our simple approach thus captures the basic physics of a self-gravitating, magnetized cloud in which the evolution is driven by ambipolar diffusion. It also enables us to treat the evolution of the accretion onto the protostar after collapse, for which detailed numerical results are as yet unavailable. Remarkably, we find that, at late times, the accretion rate becomes comparable to that of a nonmagnetized, singular isothermal sphere, provided that the ionization is due to Galactic cosmic rays.

A Near-Infrared Multiplicity Survey of Class I/Flat-Spectrum Systems in Six Nearby Molecular Clouds

We present new near-IR observations of 76 Class I/flat-spectrum objects in the nearby (d 320 pc) Perseus, Taurus, Chamaeleon I and II, ρ Ophiuchi, and Serpens dark clouds. These observations are part of a larger systematic infrared multiplicity survey of self-embedded objects in the nearest dark clouds. When combined with the results of our previously published near-infrared multiplicity survey, we find a restricted companion star fraction of 14/79 (18% ± 4%) of the sources surveyed to be binary or higher order multiple systems over a separation range of ~300–2000 AU with a magnitude difference ΔK ≤ 4 and with no correction for background contamination or completeness. This is consistent with the fraction of binary/multiple systems found among older pre–main-sequence T Tauri stars in each of the Taurus, ρ Oph, and Chamaeleon star-forming regions over a similar separation range, as well as the combined companion star fraction for these regions. However, the companion star fraction for solar-type, and lower mass M dwarf, main-sequence stars in the solar neighborhood in this separation range (11% ± 3%) is approximately one-half that of our sample. Together with multiplicity statistics derived for previously published samples of Class 0 and Class I sources, our study suggests that a significant number of binary/multiple objects may remain to be discovered at smaller separations among our Class I/flat-spectrum sample and/or most of the evolution of binary/multiple systems occurs during the Class 0 phase of early stellar evolution.