Joseph Barranco

COHERENCE IN DENSE CORES. II. THE TRANSITION TO COHERENCE

After studying how line width depends on spatial scale in low-mass star-forming regions, we propose that dense cores (Myers & Benson 1983) represent an inner scale of a self-similar process that characterizes larger scale molecular clouds. In the process of coming to this conclusion, we define four distinct types of line width-size relation (ΔvRai), which have power-law slopes a1, a2, a3, and a4, as follows: Type 1—multitracer, multicloud intercomparison; Type 2—single-tracer, multicloud intercomparison; Type 3—multitracer study of a single cloud; and Type 4—single-tracer study of a single cloud. Type 1 studies (of which Larson 1981 is the seminal example) are compendia of Type 3 studies which illustrate the range of variation in the line width-size relation from one region to another. Using new measurements of the OH and C18O emission emanating from the environs of several of the dense cores studied in NH3 by Barranco & Goodman (1998; Paper I), we show that line width increases with size outside the cores with a4 ~ 0.2. On scales larger than those traced by C18O or OH,12CO and 13CO observations indicate that a4 increases to ~0.5 (Heyer & Schloerb 1997). By contrast, within the half-power contour of the NH3 emission from the cores, line width is virtually constant, with a4 ~ 0. We interpret the correlation between increasing density and decreasing Type 4 power-law slope as a transition to coherence. Our data indicate that the radius Rcoh at which the gas becomes coherent (i.e., a4 → 0) is of order 0.1 pc in regions forming primarily low-mass stars. The value of the nonthermal line width at which coherence is established is always less than but still of order of the thermal line width of H2. Thus coherent cores are similar to, but not exactly the same as, isothermal balls of gas. Two other results bolster our proposal that a transition to coherence takes place at ~0.1 pc. First, the OH, C18O, and NH3 maps show that the dependence of column density on size is much steeper (N R-0.9) inside Rcoh than outside of it (N R-0.2), which implies that the volume filling factor of coherent cores is much larger than in their surroundings. Second, Larson (1995) has recently found a break in the power law characterizing the clustering of stars in Taurus at 0.04 pc, just inside of Rcoh. Larson and we interpret this break in slope as the point at which stellar clustering properties change from being determined by the (fractal) gas distribution (on scales greater than 0.04 pc) to being determined by fragmentation processes within coherent cores (on scales less than 0.04 pc). We speculate that the transition to coherence takes place when a dissipation threshold for the MHD turbulence that characterizes the larger scale medium is crossed at the critical inner scale Rcoh. We suggest that the most likely explanation for this threshold is the marked decline in the coupling of the magnetic field to gas motions due to a decreased ion/neutral ratio in dense, high filling factor gas.

THREE-DIMENSIONAL VORTICES IN STRATIFIED PROTOPLANETARY DISKS

We present the results of high-resolution, three-dimensional hydrodynamic simulations of the dynamics and formation of coherent, long-lived vortices in stably stratified protoplanetary disks. Tall, columnar vortices that extend vertically through many scale heights in the disk are unstable to small perturbations; such vortices cannot maintain vertical alignment over more than a few scale heights and are ripped apart by the Keplerian shear. Short, finite-height vortices that extend only 1 scale height above and below the midplane are also unstable, but for a different reason: we have isolated an antisymmetric (with respect to the midplane) eigenmode that grows with an e-folding time of only a few orbital periods; the nonlinear evolution of this instability leads to the destruction of the vortex. Serendipitously, we observe the formation of three-dimensional vortices that are centered not in the midplane, but at 1‐3 scale heights above and below. Breaking internal gravity waves create vorticity; anticyclonic regions of vorticity roll up and coalesce into new vortices, whereas cyclonic regions shear into thin azimuthal bands. Unlike the midplane-centered vortices that were placed ad hoc in the disk and turned out to be linearly unstable,theoff-midplanevorticesformnaturallyoutofperturbationsinthediskandarestableandrobustformany hundreds of orbits. Subject headings: accretion, accretion disks — hydrodynamics — planetary systems: protoplanetary disks Online material: mpeg animations

Deep MMT* Transit Survey of the Open Cluster M37. II. Variable Stars

We have conducted a deep (15 r 23), 20 night survey for transiting planets in the intermediate-age (~550 Myr) open cluster M37 (NGC 2099) using the Megacam wide-field mosaic CCD camera on the 6.5 m MMT. In this paper we present a catalog and light curves for 1445 variable stars; 1430 (99%) of these are new discoveries. We have discovered 20 new eclipsing binaries and 31 new short-period (P < 1 day ) pulsating stars. The bulk of the variables are most likely rapidly rotating young low-mass stars, including a substantial number (500) that are members of the cluster. We identify and analyze five particularly interesting individual variables, including a previously identified variable that we suggest is probably a hybrid γ Doradus/δ Scuti pulsator, two possible quiescent cataclysmic variables, a detached eclipsing binary (DEB) with at least one γ Doradus pulsating component (only the second such variable found in an eclipsing binary), and a low-mass (MP ~ MS ~ 0.6 M☉) DEB that is a possible cluster member. A preliminary determination of the physical parameters for the DEB+γ Doradus system yields MP = 1.58 ± 0.04 M☉, MS = 1.58 ± 0.04 M☉, RP = 1.39 ± 0.07 R☉, and RS = 1.38 ± 0.07 R☉.

DEEP MMT TRANSIT SURVEY OF THE OPEN CLUSTER M37. III. STELLAR ROTATION AT 550 Myr

In the course of conducting a deep (14.5 r 23), 20 night survey for transiting planets in the rich ~550 Myr old open cluster M37, we have measured the rotation periods of 575 stars, which lie near the cluster main sequence, with masses 0.2 M ? M 1.3 M ?. This is the largest sample of rotation periods for a cluster older than 500 Myr. Using this rich sample we investigate a number of relations between rotation period, color, and the amplitude of photometric variability. Stars with M 0.8 M ? show a tight correlation between period and mass with heavier stars rotating more rapidly. There is a group of four stars with P > 15 days that fall well above this relation, which, if real, would present a significant challenge to theories of stellar angular momentum evolution. Below 0.8 M ?, the stars continue to follow the period-mass correlation but with a broad tail of rapid rotators that expands to shorter periods with decreasing mass. We combine these results with observations of other open clusters to test the standard theory of lower main-sequence stellar angular momentum evolution. We find that the model reproduces the observations for solar-mass stars, but discrepancies are apparent for stars with 0.6 M 1.0 M ?. We also find that for late K through early M dwarf stars in this cluster, rapid rotators tend to be bluer than slow rotators in B ? V but redder than slow rotators in V ? IC . This result supports the hypothesis that the significant discrepancy between the observed and predicted temperatures and radii of low-mass main-sequence stars is due to stellar activity.

Deep MMT Transit Survey of the Open Cluster M37. I. Observations and Cluster Parameters

We have conducted a deep ( -->15 r 23), 20 night survey for transiting planets in the intermediate-age open cluster M37 (NGC 2099) using the Megacam wide-field mosaic CCD camera on the 6.5 m MMT. In this paper we describe the observations and data reduction procedures for the survey and analyze the stellar content and dynamical state of the cluster. By combining high-resolution spectroscopy with existing -->BVICKs and new gri color-magnitude diagrams, we determine the fundamental cluster parameters: -->t = 485 ± 28 Myr without overshooting ( -->t = 550 ± 30 Myr with overshooting), -->E(B − V) = 0.227 ± 0.038, -->(m − M)V = 11.57 ± 0.13, and -->[ M/H ] = + 0.045 ± 0.044, which are in good agreement with, although more precise than, previous measurements. We determine the mass function down to 0.3 M☉ and use this to estimate the total cluster mass of -->3640 ± 170 M☉.

Zombie Vortex Instability. I. A Purely Hydrodynamic Instability to Resurrect the Dead Zones of Protoplanetary Disks

There is considerable interest in hydrodynamic instabilities in dead zones of protoplanetary disks as a mechanism for driving angular momentum transport and as a source of particle-trapping vortices to mix chondrules and incubate planetesimal formation. We present simulations with a pseudo-spectral anelastic code and with the compressible code Athena, showing that stably stratified flows in a shearing, rotating box are violently unstable and produce space-filling, sustained turbulence dominated by large vortices with Rossby numbers of order 0.2-0.3. This Zombie Vortex Instability (ZVI) is observed in both codes and is triggered by Kolmogorov turbulence with Mach numbers less than 0.01. It is a common view that if a given constant density flow is stable, then stable vertical stratification should make the flow even more stable. Yet, we show that sufficient vertical stratification can be unstable to ZVI. ZVI is robust and requires no special tuning of boundary conditions, or initial radial entropy or vortensity gradients (though we have studied ZVI only in the limit of infinite cooling time). The resolution of this paradox is that stable stratification allows for a new avenue to instability: baroclinic critical layers. ZVI has not been seen in previous studies of flows in rotating, shearing boxes because those calculations frequently lacked vertical density stratification and/or sufficient numerical resolution. Although we do not expect appreciable angular momentum transport from ZVI in the small domains in this study, we hypothesize that ZVI in larger domains with compressible equations may lead to angular transport via spiral density waves.

DEEP MMT* TRANSIT SURVEY OF THE OPEN CLUSTER M37 IV: LIMIT ON THE FRACTION OF STARS WITH PLANETS AS SMALL AS 0.3RJ

We present the results of a deep (15 r 23), 20 night survey for transiting planets in the intermediate-age open cluster M37 (NGC 2099) using the Megacam wide-field mosaic CCD camera on the 6.5 m MMT. We do not detect any transiting planets among the ~1450 observed cluster members. We do, however, identify a ~1RJ candidate planet transiting a ~0.8 M ? Galactic field star with a period of 0.77 days. The source is faint (V = 19.85 mag) and has an expected velocity semiamplitude of K ~ 220 m s-1(M/MJ ). We conduct Monte Carlo transit injection and recovery simulations to calculate the 95% confidence upper limit on the fraction of cluster members and field stars with planets as a function of planetary radius and orbital period. Assuming a uniform logarithmic distribution in the orbital period, we find that <1.1%, <2.7%, and <8.3% of cluster members have 1.0RJ planets within extremely hot Jupiter (EHJ; 0.4 < P < 1.0 day), very hot Jupiter (VHJ; 1.0 < P < 3.0 day), and hot Jupiter (HJ; 3.0 < P < 5.0 day) period ranges, respectively. For 0.5RJ planets, the limits are less than 3.2% and less than 21% for EHJ and VHJ period ranges, respectively, while for 0.35RJ planets we can only place an upper limit of less than 25% on the EHJ period range. For a sample of 7814 Galactic field stars, consisting primarily of FGKM dwarfs, we place 95% upper limits of <0.3%, <0.8%, and <2.7% on the fraction of stars with a 1.0RJ EHJ, VHJ, and HJ, respectively, assuming that the candidate planet is not genuine. If the candidate is genuine, the frequency of ~1.0RJ planets in the EHJ period range is 0.002% < f EHJ < 0.5% with 95% confidence. We place limits of <1.4%, <8.8%, and <47% for 0.5RJ planets, and a limit of <16% on 0.3RJ planets in the EHJ period range. This is the first transit survey to place limits on the fraction of stars with planets as small as Neptune.

Forming Planetesimals by Gravitational Instability . I . the Role of the Richardson Number in Triggering the Kelvin – Helmholtz Instability

Gravitational instability (GI) of a dust-rich layer at the midplane of a gaseous circumstellar disk is one proposed mechanism to form planetesimals, the building blocks of rocky planets and gas giant cores. Self-gravity competes against the Kelvin-Helmholtz instability (KHI): gradients in dust content drive a vertical shear which risks overturning the dusty subdisk and forestalling GI. To understand the conditions under which the disk can resist the KHI, we perform 3D simulations of stratified subdisks in the limit that dust particles are small and aerodynamically well coupled to gas. This limit screens out the streaming instability and isolates the KHI. Each subdisk is assumed to have a vertical density profile given by a spatially constant Richardson number Ri. We vary Ri and the midplane dust-to-gas ratio mu and find that the critical Richardson number dividing KH-unstable from KH-stable flows is not unique; rather Ri_crit grows nearly linearly with mu for mu=0.3-10. Only for disks of bulk solar metallicity is Ri_crit ~ 0.2, close to the classical value. Our results suggest that a dusty sublayer can gravitationally fragment and presumably spawn planetesimals if embedded within a solar metallicity gas disk ~4x more massive than the minimum-mass solar nebula; or a minimum-mass disk having ~3x solar metallicity; or some intermediate combination of these two possibilities. Gravitational instability seems possible without resorting to the streaming instability or to turbulent concentration of particles.

THREE-DIMENSIONAL SIMULATIONS OF KELVIN-HELMHOLTZ INSTABILITY IN SETTLED DUST LAYERS IN PROTOPLANETARY DISKS

As dust settles in a protoplanetary disk, a vertical shear develops because the dust-rich gas in the midplane orbits at a rate closer to true Keplerian than the slower-moving dust-depleted gas above and below. A classical analysis (neglecting the Coriolis force and differential rotation) predicts that Kelvin-Helmholtz instability occurs when the Richardson number of the stratified shear flow is below roughly one-quarter. However, earlier numerical studies showed that the Coriolis force makes layers more unstable, whereas horizontal shear may stabilize the layers. Simulations with a three-dimensional spectral code were used to investigate these opposing influences on the instability in order to resolve whether such layers can ever reach the dense enough conditions for the onset of gravitational instability. I confirm that the Coriolis force, in the absence of radial shear, does indeed make dust layers more unstable, however the instability sets in at high spatial wavenumber for thicker layers. When radial shear is introduced, the onset of instability depends on the amplitude of perturbations: small amplitude perturbations are sheared to high wavenumber where further growth is damped; whereas larger amplitude perturbations grow to magnitudes that disrupt the dust layer. However, this critical amplitude decreases sharply for thinner, more unstable layers. In three-dimensional simulations of unstable layers, turbulence mixes the dust and gas, creating thicker, more stable layers. I find that layers with minimum Richardson numbers in the approximate range 0.2-0.4 are stable in simulations with horizontal shear.

FORMING PLANETESIMALS BY GRAVITATIONAL INSTABILITY. II. HOW DUST SETTLES TO ITS MARGINALLY STABLE STATE

Dust at the midplane of a circumstellar disk can become gravitationally unstable and fragment into planetesimals if the local dust-to-gas ratio μ0 ≡ ρd/ρg is sufficiently high. We simulate how dust settles in passive disks and ask how high μ0 can become. We implement a hybrid scheme that alternates between a one-dimensional code to settle dust and a three-dimensional shearing box code to test for dynamical stability. This scheme allows us to explore the behavior of small particles having short but non-zero stopping times in gas: 0 < t stop the orbital period. The streaming instability is thereby filtered out. Dust settles until Kelvin-Helmholtz-type instabilities at the top and bottom faces of the dust layer threaten to overturn the entire layer. In this state of marginal stability, μ0 = 2.9 for a disk whose bulk (height-integrated) metallicity Σd/Σg is solar—thus μ0 increases by more than two orders of magnitude from its well-mixed initial value of μ0,init = Σd/Σg = 0.015. For a disk whose bulk metallicity is 4× solar (μ0,init = Σd/Σg = 0.06), the marginally stable state has μ0 = 26.4. These maximum values of μ0, which depend on the background radial pressure gradient, are so large that gravitational instability of small particles is viable in disks whose bulk metallicities are just a few (4) times solar. Our result supports earlier studies that assumed that dust settles until the Richardson number Ri is spatially constant. Our simulations are free of this assumption but provide evidence for it within the boundaries of the dust layer, with the proviso that Ri increases with Σd/Σg in the same way that we found in Paper I. Because increasing the dust content decreases the vertical shear and increases stability, the midplane μ0 increases with Σd/Σg in a faster than linear way, so fast that modest enhancements in Σd/Σg can spawn planetesimals directly from small particles.