Primordial Disk Research Articles

Extreme recoils: impact on the detection of gravitational waves from massive black hole binaries

Abstract Recent numerical simulations of the coalescence of highly spinning massive black hole binaries (MBHBs) suggest that the remnant can suffer a recoil velocity of the order of few thousand km s−1. We study here, by means of dedicated simulations of black hole build-up, how such extreme recoils could affect the cosmological coalescence rate of MBHBs, placing a robust lower limit for the predicted number of gravitational wave (GW) sources detectable by future space-borne missions (such as the Laser Interferometer Space Antenna, LISA). We consider two main routes for black hole formation: one where seeds are light remnants of Population III stars (≃102 M⊙), and one where seeds are much heavier (≳104 M⊙), formed via the direct gas collapse in primordial nuclear discs. We find that extreme recoil velocities do not compromise the efficient MBHB detection by LISA. If seeds are already massive and/or relatively rare, the detection rate is reduced by only ∼15 per cent. The number of detections drops substantially (by ∼60 per cent) if seeds are instead light and abundant, but in this case the number of predicted coalescences is so high that at least ∼10 sources in a three-year observation are guaranteed.

Origin of the metallicity dependence of exoplanet host stars in the protoplanetary disc mass distribution

The probability of a star hosting a planet that is detectable in radial velocity surveys increases as Ppl(Z) ! (10 Z 2 , where Z is stellar metallicity. Models of planet formation by core accretion reproduce this trend, since the protoplanetary disc of a high-metallicity star has a high density of solids, and so forms planetary cores which accrete gas before the primordial gas disc dissipates. This paper considers the origin of the form of the metallicity dependence of Ppl(Z). We introduce a simple model in which detectable planets form when the mass of solid material in the protoplanetary disc, Ms, exceeds a critical value. In this model, the form of Ppl(Z) is a direct reflection of the distribution of protoplanetary disc masses, Mg, and the observed metallicity relation is reproduced if P(Mg > M ) ! (M ) # 2 . We argue that a protoplanetary disc’s dust mass measured in submillimetre observations is a relatively pristine indicator of the mass available for planet-building, and find that the disc mass distribution derived from suchobservationsisconsistentwiththeobservedPpl(Z)ifasolidmassMs >0.5MJ isrequired to form detectable planets. Any planet formation model which imposes a critical solid mass for detectable planets to form would reproduce the observed metallicity relation, and core accretionmodelsareempiricallyconsistentwithsuchathresholdcriterion.Whiletheoutcome of planet formation in individual systems is debatable, we identify seven protoplanetary discs which, by rigid application of this criterion, would be expected to form detectable planets and may provide insight into the physical conditions required to form such planets. A testable prediction of the model is that the metallicity dependence should flatten both for Z > 0.5 dex and as more distant and lower mass planets are discovered. Further, combining this model with one in which the evolution of a star’s debris disc is also influenced by the solid mass in its protoplanetary disc results in the prediction that debris discs detected around stars with planets should be more infrared luminous than those around stars without planets in tentative agreement with recent observations.

Spitzer: Accretion in Low‐Mass Stars and Brown Dwarfs in the λ Orionis Cluster

We present multiwavelength optical and IR photometry of 170 previously known low-mass stars and brown dwarfs of the 5 Myr Collinder 69 cluster (λ Orionis). The new photometry supports cluster membership for most of them, with less than 15% of the previous candidates identified as probable nonmembers. The near-IR photometry allows us to identify stars with IR excesses, and we find that the Class II population is very large, around 25% for stars (in the spectral range M0-M6.5) and 40% for brown dwarfs, down to 0.04 M_⊙, despite the fact that the Hα equivalent width is low for a significant fraction of them. In addition, there are a number of substellar objects, classified as Class III, that have optically thin disks. The Class II members are distributed in an inhomogeneous way, lying preferentially in a filament running toward the southeast. The IR excesses for the Collinder 69 members range from pure Class II (flat or nearly flat spectra longward of 1 μm), to transition disks with no near-IR excess but excesses beginning within the IRAC wavelength range, to two stars with excess only detected at 24 μm. Collinder 69 thus appears to be at an age where it provides a natural laboratory for the study of primordial disks and their dissipation.

Predicting the frequencies of diverse exo-planetary systems

Abstract Extrasolar planetary systems range from hot Jupiters out to icy comet belts more distant than Pluto. We explain this diversity in a model where the mass of solids in the primordial circumstellar disc dictates the outcome. The star retains measures of the initial heavy-element (metal) abundance that can be used to map solid masses on to outcomes, and the frequencies of all classes are correctly predicted. The differing dependences on metallicity for forming massive planets and low-mass cometary bodies are also explained. By extrapolation, around two-thirds of stars have enough solids to form Earth-like planets, and a high rate is supported by the first detections of low-mass exo-planets.

SpitzerObservations of NGC 2362: Primordial Disks at 5 Myr

We present results from a mid-infrared imaging survey of the ~5 Myr old cluster NGC 2362 carried out with the Infrared Array Camera (IRAC) on board the Spitzer Space Telescope. The archival mid-infrared data were merged with extant Hα emission data, optical and near-infrared photometry, and moderate-resolution optical spectroscopy to identify the remnant disk-bearing population of the cluster and to estimate the fraction of stars that still retain primordial circumstellar disks. The principal sample of 232 suspected cluster members with masses ranging from ~10 to 0.3 M_⊙ (B2-M5 spectral types) was drawn from known Hα emission stars, X-ray-detected stars from a single 100 ks archival Chandra observation, and established lithium-rich stars. A second sample of 153 stars over a similar mass range whose membership status was based on optical photometry alone was also examined. Measured fluxes in the optical and infrared passbands were fitted with synthetic, low-resolution spectra created using the NextGen atmospheric models, permitting the detection of infrared excesses relative to predicted stellar photospheric fluxes. Using the measured slope of the stellar spectral energy distribution through the four IRAC channels to characterize disk emission for the 195 out of 232 activity/lithium-selected stars and the 105 out of 153 photometric membership candidates having complete IRAC photometry, we derive an upper limit for the primordial, optically thick disk fraction of NGC 2362 of ~7% ± 2%, with another ~12% ± 3% of suspected members exhibiting infrared excesses indicative of weak or optically thin disk emission. The presence of circumstellar disks among candidate members of NGC 2362 is strongly mass-dependent, such that no stars more massive than ~1.2 M_⊙ exhibit significant infrared excess shortward of 8 μm. An upper limit for the fraction of stars hosting primordial, optically thick disks peaks near 10.7% ± 4% for stars with masses between 1.05 and 0.6 M_⊙, but the Spitzer IRAC survey is sensitivity-limited below ~0.3 M_⊙. From Hα emission-line strengths, an upper limit for the accretion fraction of the cluster is estimated at ~5%, with most suspected accretors associated with primordial, optically thick disks identified with Spitzer. The presence of primordial disk-bearing stars in NGC 2362, some of which are suspected of still experiencing gaseous accretion, may imply that even within dense cluster environments, sufficient numbers of inner disks survive to ages consistent with core accretion models of giant planet formation to account for the observed frequency of exoplanets within 5 AU of all FGKM-type stars.

Origin of scattered disk resonant TNOs: Evidence for an ancient excited Kuiper belt of 50 AU radius

Resonance occupation of trans-neptunian objects (TNOs) in the scattered disk (>48 AU) was investigated by integrating the orbits of 85 observed members for 4 Gyr. Twenty seven TNOs were locked in the 9:4, 16:7, 7:3, 12:5, 5:2, 8:3, 3:1, 4:1, 11:2, and 27:4 resonances. We then explored mechanisms for the origin of the resonant structure in the scattered disk, in particular the long-term 9:4, 5:2, and 8:3 resonant TNOs (median 4 Gyr), by performing large scale simulations involving Neptune scattering and planetary migration over an initially excited planetesimals disk (wide range of eccentricities and inclinations). To explain the formation of Gyr-resident populations in such distant resonances, our results suggest the existence of a primordial planetesimal disk of at least 45–50 AU radius that suffered a dynamical perturbation leading to 0.1–0.3 or greater eccentricities and a range of inclinations up to ∼20° during early stages of the Solar System history, before planetary migration.

Brownian Motion in Planetary Migration

A residual planetesimal disk of mass 10-100 Earth masses remained in the outer solar system following the birth of the giant planets, as implied by the existence of the Oort cloud, coagulation requirements for Pluto, and inefficiencies in planet formation. Upon gravitationally scattering planetesimal debris, planets migrate. Orbital migration can lead to resonance capture, as evidenced here in the Kuiper and asteroid belts, and abroad in extra-solar systems. Finite sizes of planetesimals render migration stochastic (noisy). At fixed disk mass, larger (fewer) planetesimals generate more noise. Extreme noise defeats resonance capture. We employ order-of-magnitude physics to construct an analytic theory for how a planet's orbital semi-major axis fluctuates in response to random planetesimal scatterings. To retain a body in resonance, the planet's semi-major axis must not random walk a distance greater than the resonant libration width. We translate this criterion into an analytic formula for the retention efficiency of the resonance as a function of system parameters, including planetesimal size. We verify our results with tailored numerical simulations. Application of our theory reveals that capture of Resonant Kuiper belt objects by a migrating Neptune remains effective if the bulk of the primordial disk was locked in bodies having sizes 1000 km was less than a few percent. Coagulation simulations produce a size distribution of primordial planetesimals that easily satisfies these constraints. We conclude that stochasticity did not interfere with, nor modify in any substantive way, Neptune's ability to capture and retain Resonant Kuiper belt objects during its migration.

Supermassive black hole formation during the assembly of pre-galactic discs

In this paper, we discuss the evolution of gravitationally unstable pre-galactic discs that result from the collapse of haloes at high redshift z≈ 10 or so, which have not yet been enriched by metals. In cases where molecular hydrogen formation is suppressed, the discs are maintained at a temperature of a few thousand Kelvin. However, when molecular hydrogen is present, cooling can proceed down to a few hundred Kelvin. Analogous to the case of the larger-scale protogalactic discs, we assume that the evolution of these discs is mainly driven by angular momentum redistribution induced by the development of gravitational instabilities in the disc. We also properly take into account the possibility of disc fragmentation. We thus show that this simple model naturally predicts the formation of supermassive black holes in the nuclei of such discs and provides a robust determination of their mass distribution as a function of halo properties. We estimate that roughly 5 per cent of discs resulting from the collapse of haloes with M≈ 107 M⊙ should host a massive black hole with a mass MBH≈ 105 M⊙. We confirm our arguments with time-dependent calculations of the evolution of the surface density and of the accretion rate in these primordial discs. The luminosity of the outer, colder disc is expected to be very low (in the range of a few thousand L⊙), while the formation of the black hole is expected to produce a burst with a luminosity of a few times 109 L⊙. This mechanism offers an efficient way to form seed black holes at high redshift. The predicted masses for our black hole seeds enable the comfortable assembly of 109-M⊙ black holes powering the luminous quasars detected by the Sloan Digital Sky Survey at z= 6 for a concordance cosmology.

Formation and Evolution of Planetary Systems (FEPS): Primordial Warm Dust Evolution from 3 to 30 Myr around Sun‐like Stars

We present data obtained with the Infrared Array Camera (IRAC) aboard the Spitzer Space Telescope (Spitzer) for a sample of 74 young (t < 30 Myr old) Sun-like (0.7 < M*/M☉ < 1.5) stars. These are a subset of the observations that comprise the Spitzer Legacy science program entitled the Formation and Evolution of Planetary Systems (FEPS). Using IRAC, we study the fraction of young stars that exhibit 3.6-8.0 μm infrared emission in excess of that expected from the stellar photosphere, as a function of age from 3 to 30 Myr. The most straightforward interpretation of such excess emission is the presence of hot (300-1000 K) dust in the inner regions (<3 AU) of a circumstellar disk. Five out of the 74 young stars show a strong infrared excess, four of which have estimated ages of 3-10 Myr. While we detect excesses from five optically thick disks and photospheric emission from the remainder of our sample, we do not detect any excess emission from optically thin disks at these wavelengths. We compare our results with accretion disk fractions detected in previous studies and use the ensemble results to place additional constraints on the dissipation timescales for optically thick, primordial disks.

SpitzerObservations of IC 348: The Disk Population at 2-3 Million Years

We present near and mid-infrared photometry obtained with the Spitzer Space Telescope of 300 known members of the IC348 cluster. We merge this photometry with existing ground-based optical and near-infrared photometry in order to construct optical-infrared spectral energy distributions (SEDs) for all the cluster members and present a complete atlas of these SEDs. We employ these observations to both investigate the frequency and nature of the circumstellar disk population in the cluster. The observations are sufficiently sensitive to enable the first detailed measurement of the disk frequency for very low mass stars at the peak of the stellar IMF. Using measurements of infrared excess between 3.6 and 8 microns we find the total frequency of disk-bearing stars in the cluster to be 50 +/- 6%. However, only 30 +/- 4% of the member stars are surrounded by optically thick, primordial disks, while the remaining disk-bearing stars are surrounded by what appear to be optically thin,anemic disks. The disk fraction appears to be a function of spectral type and stellar mass. The disk longevity and thus conditions for planet formation appear to be most favorable for stars which are of comparable mass to the sun. The optically thick disks around later type (> M4) stars appear to be less flared than the disks around earlier type stars. This may indicate a greater degree of dust settling and a more advanced evolutionary state for the late M disk population. Finally we find that the presence of an optically thick dust disk is correlated with gaseous accretion as measured by the strength of Halpha emission. These results suggest that it is more likely for dust disks to persist in the absence of active gaseous accretion than for active accretion to persist in the absence of dusty disks.

Metallicity, debris discs and planets

We investigate the populations of main-sequence stars within 25 pc that have debris discs and/or giant planets detected by Doppler shift. The metallicity distribution of the debris sample is a very close match to that of stars in general, but differs with >99 per cent confidence from the giant planet sample, which favours stars of above average metallicity. This result is not due to differences in age of the two samples. The formation of debris-generating planetesimals at tens of au thus appears independent of the metal fraction of the primordial disc, in contrast to the growth and migration history of giant planets within a few au. The data generally fit a core accumulation model, with outer planetesimals forming eventually even from a disc low in solids, while inner planets require fast core growth for gas to still be present to make an atmosphere.

Dynamical structure and origin of the Trans-Neptunian population

Before the discovery of the first member of the Kuiper belt in 1992, the trans-Neptunian population was supposed to lie on a flat disk and each member would follow a barely eccentric orbit. While less conventional orbits for the trans-Neptunian objects were being discovered, our understanding of its orbital structure and origin was continually changed. A basic classification of the trans-Neptunian population as to their orbits identifies a classical low inclination Kuiper belt population, a resonant population, a high inclination Kuiper belt population, a scattered population and an extended population. Several mechanisms have been proposed to explain the orbital architecture of the Kuiper belt population. Presently, the most plausible scenarios are unequivocally related with the primordial planetary migration induced by a planetesimal disk. Low inclination orbits in the Kuiper belt may have been moderately pushed out from a dynamically cold primordial disk by the resonance sweeping mechanism. The origin of high inclination objects in the classical Kuiper belt is however to be found in a primordial Neptune scattered population, through a perihelion increasing mechanism based on secular resonances. Another push-out mechanism based on the sweeping of the 1:2 resonance with Neptune has also been invoked to explain the low inclination orbits in the classical Kuiper belt. Assuming these last two mechanisms, Kuiper belt objects do not need to have been formed in situ. This kind of formation process would demand a quite large original mass in the Kuiper belt region, which would have brought Neptune beyond its present position at 30 AU. Thus with the exception of the low inclination classical Kuiper belt objects and a few resonant ones, all other trans-Neptunian objects are present or past scattered objects. This notion also includes the case for Sedna, so far the only certain member of the extended population. In its most plausible formation scenario, it was a primordial scattered object by Neptune whose perihelion was increased by the close passage of a star.

ESO large program on Centaurs and TNOs: visible colors—final results

We report 43 new visible colors of Centaurs and TNOs, obtained at NTT and VLT telescopes under the “ESO large program on physical properties of Centaurs and TNOs.” Merging these new measurements with those obtained during the first part of the program (Boehnhardt et al., 2002, Astron. Astrophys. 395, 297–303) and the “Meudon Multicolor Survey” (Doressoundiram et al., 2002, Astron. J. 124, 2279–2296) we have a unique dataset of 109 objects. We checked for correlations and trends between colors, physical and orbital parameters, carrying out an analysis based on Monte Carlo simulation to account for observational error bars. Centaurs show no evidence for correlation between V− R vs. R− I colors which raises the hypothesis that more than one single coloring process might be acting on their surfaces. Classical objects seem to be composed of two different color populations: objects with i<4.5° display only red colors while those with i>4.5° display the whole range of colors from blue to very red. The possibility that the low inclined population is misguiding global conclusions is analyzed. Classical objects also show a stronger color–perihelion correlation for intrinsically brighter objects, corresponding to critical estimated sizes of different formation/evolutionary histories. Scattered disk objects show color resemblances with the classical objects at i>12°, hence surface reflectivities resemblances, pointing to a common origin. No color–aphelion trend is found for SDOs, as expected from the intense irradiation by galactic cosmic-rays beyond the solar wind termination shock. Plutinos show a color–absolute magnitude trend, in which all the intrinsically faintest objects are blue. We see many red Plutinos in highly inclined and highly eccentric orbits, that should have originated in a primordial inner disk under Gomes (2003, Icarus 161, 404–418) migration scenario. This seems to invalidate the assumption that objects originated in this inner disk are mainly blue. Finally, we also find six candidates for light–curve studies: four objects (1998 WU 31, 1999 OE 4, 1999 OX 3, and 2001 KP 77) present significant short term R-magnitude variability, and two objects (1999 XX 143 and 2000 GP 183) evidence possible color variations with rotation.

A search for debris discs around stars with giant planets

Eight nearby stars with known giant planets have been searched for thermal emission in the submillimetre arising from dust debris. The null results imply quantities of dust typically less than 0.02 Earth masses per star. Conversely, literature data for 20 Sun-like stars with debris discs show that 5 per cent have gas giants inside a few astronomical units ‐ but the dust distribution suggests that nearly all have more distant planets. The lack of overlap in these systems ‐ i.e. few stars possess both inner planets and a disc ‐ indicates that these phenomena either are not connected or are mutually exclusive. Comparison with an evolutionary model shows that debris masses are predicted to be low by the stellar ages of 2‐8 Gyr (unless the colliding parent bodies are quite distant, located beyond 100‐200 au), but it remains to be explained why stars that do have debris should preferentially only have distant planets. A simple idea is proposed that could produce these largely different systems, invoking a difference in the primordial disc mass. Large masses promote fast gas giant growth and inwards migration, whereas small masses imply slow evolution, low-mass gas giants and outwards migration that increases the collision rate of Kuiper Belt-like objects. This explanation neglects other sources of diversity between discs (such as density and planetesimal composition and orbits), but it does have the merit of matching the observational results.

Coronae &amp; Outflows from Helical Dynamos, Compatibility with the MRI, and Application to Protostellar Disks

Magnetically mediated disk outflows are a leading paradigm to explain winds and jets in a variety of astrophysical sources, but where do the fields come from? Since accretion of mean magnetic flux may be disfavored in a thin turbulent disk, and only fields generated with sufficiently large scale can escape before being shredded by turbulence, in situ field production is desirable. Nonlinear helical inverse dynamo theory can provide the desired fields for coronae and outflows. We discuss the implications for contemporary protostellar disks, where the MRI (magneto-rotational instability) can drive turbulence in the inner regions, and primordial protostellar disks, where gravitational instability drives the turbulence. We emphasize that helical dynamos are compatible with the magneto-rotational instability, and clarify the relationship between the two.

Gas-drag-assisted capture of Himalia's family

To elucidate the capture of Jupiter's outer moons, we reverse-evolve satellites from their present orbits to their original heliocentric paths in the presence of Jupiter's primordial circumplanetary disk (Lubow et al., 1999, Astrophys. J. 526, 1001–1012; Canup and Ward, 2003, Astron. J. 124, 3404–3423). Our orbital histories use a symplectic integrator that allows dissipation. We assume that the present satellites Himalia, Elara, Lysithea, Leda, and S/2000 J11 are collisional fragments of a single parent. Our simulations show that this “prograde-cluster progenitor” (PCP) could be derived from objects with heliocentric orbits like those of the Hilda asteroid group. We show analytically that this capture is energetically possible. We also compare the spectroscopic characteristics of the prograde cluster members (Grav et al., 2003, Icarus, submitted for publication) with those of the Hildas, and conclude that the surface color of the prograde-cluster progenitor is consistent with an origin within the Hilda group. Accordingly, gas drag in the primordial jovian nebula is found to offer a plausible explanation for the origin of the prograde cluster. A similar capture mechanism is proposed for Saturn's Phoebe.

The Common Origin of the High Inclination TNO's

Numerical integrations of the four major planets orbits inside a primordial planetesimals disk show that a fraction of Neptune primordial scattered objects are deposited into the classical Kuiper Belt at Solar System age. These objects exhibit inclinations as high as 40° and can account for present high inclinations population in the classical Kuiper Belt. The same mechanism can also originate high perihelion scattered objects like 2000 CR105. The process that in the end produced such objects can be divided into two phases, a migration phase where nonconservative dynamics acted to produce some stable objects already at 108 years and a nonmigrating phase that helped to establish some other objects as stable TNO’s. Low inclination CKBO’s have in principle an origin through the resonance sweeping process, although some results from numerical integrations at least suggest a possible origin also from the primordial Neptune scattered population.

The plane of the Edgeworth–Kuiper belt

We examine possible locations for the primordial disk of the Edgeworth–Kuiper Belt (EKB), using several subsets of the known objects as markers of the total mass distribution. Using a secular perturbation theory, we find that the primordial plane of the EKB could have remained thin enough to escape detection only if it is clustered very closely about the invariable plane of the Solar System.

The origin of the Kuiper Belt high–inclination population

I simulate the orbital evolution of the four major planets and a massive primordial planetesimal disk composed of 10 4 objects, which perturb the planets but not themselves. As Neptune migrates by energy and angular momentum exchange with the planetesimals, a large number of primordial Neptune-scattered objects are formed. These objects may experience secular, Kozai, and mean motion resonances that induce temporary decrease of their eccentricities. Because planets are migrating, some planetesimals can escape those resonances while in a low-eccentricity incursion, thus avoiding the return path to Neptune close encounter dynamics. In the end, this mechanism produces stable orbits with high inclination and moderate eccentricities. The population so formed together with the objects coming from the classical resonance sweeping process, originates a bimodal distribution for the Kuiper Belt orbits. The inclinations obtained by the simulations can attain values above 30° and their distribution resembles a debiased distribution for the high-inclination population coming from the real classical Kuiper Belt.

Dynamics of the Edgeworth-Kuiper Belt beyond 50 AU

In this paper we report numerical simulations of the dynamical evolution of the region a > 50 AU. We found that some dynamical effects such as high-order secular resonances with the rate of precession of Neptune's node of the form k u Ω − u ΩNep with k = 4,5, ... or combined mean motion resonances with Uranus and Neptune of the form knN + jnU +mn ∼ 0m ay increase the area of a very thin primordial disk in this region by a factor of up to 2 after 4.5 Gy of evolution.