2,673 research outputs found
Self-consistent size and velocity distributions of collisional cascades
The standard theoretical treatment of collisional cascades derives a
steady-state size distribution assuming a single constant velocity dispersion
for all bodies regardless of size. Here we relax this assumption and solve
self-consistently for the bodies' steady-state size and size-dependent velocity
distributions. Specifically, we account for viscous stirring, dynamical
friction, and collisional damping of the bodies' random velocities in addition
to the mass conservation requirement typically applied to find the size
distribution in a steady-state cascade. The resulting size distributions are
significantly steeper than those derived without velocity evolution. For
example, accounting self-consistently for the velocities can change the
standard q=3.5 power-law index of the Dohnanyi (1969) differential size
spectrum to an index as large as q=4. Similarly, for bodies held together by
their own gravity, the corresponding power-law index range 2.88<q<3.14 of Pan &
Sari (2005) can steepen to values as large as q=3.26. Our velocity results
allow quantitative predictions of the bodies' scale heights as a function of
size. Together with our predictions, observations of the scale heights for
different sized bodies for the Kuiper belt, the asteroid belt, and extrasolar
debris disks may constrain the mass and number of large bodies stirring the
cascade as well as the colliding bodies' internal strengths.Comment: 23 pages, 3 figures, 1 table; submitted to Ap
Atmospheric mass loss due to giant impacts: the importance of the thermal component for hydrogen-helium envelopes
Systems of close-in super-Earths display striking diversity in planetary bulk
density and composition. Giant impacts are expected to play a role in the
formation of many of these worlds. Previous works, focused on the mechanical
shock caused by a giant impact, have shown that these impacts can eject large
fractions of the planetary envelope, offering a partial explanation for the
observed spread in exoplanet compositions. Here, we examine the thermal
consequences of giant impacts, and show that the atmospheric loss caused by
these effects can significantly exceed that caused by mechanical shocks for
hydrogen-helium (H/He) envelopes. When a giant impact occurs, part of the
impact energy is converted into thermal energy, heating the rocky core and the
envelope. We find that the ensuing thermal expansion of the envelope can lead
to a period of sustained, rapid mass loss through a Parker wind, resulting in
the partial or complete erosion of the H/He envelope. The fraction of the
envelope lost depends on the planet's orbital distance from its host star and
its initial thermal state, and hence age. Planets closer to their host stars
are more susceptible to thermal atmospheric loss triggered by impacts than ones
on wider orbits. Similarly, younger planets, with rocky cores which are still
hot and molten from formation, suffer greater atmospheric loss. This is
especially interesting because giant impacts are expected to occur
after formation. For planets where the thermal energy
of the core is much greater than the envelope energy, the impactor mass
required for significant atmospheric removal is , approximately the ratio of the heat capacities of the
envelope and core. When the envelope energy dominates the total energy budget,
complete loss can occur when the impactor mass is comparable to the envelope
mass.Comment: 10 pages, 9 figure
Super-Earth Atmospheres: Self-Consistent Gas Accretion and Retention
Some recently discovered short-period Earth to Neptune sized exoplanets
(super Earths) have low observed mean densities which can only be explained by
voluminous gaseous atmospheres. Here, we study the conditions allowing the
accretion and retention of such atmospheres. We self-consistently couple the
nebular gas accretion onto rocky cores and the subsequent evolution of gas
envelopes following the dispersal of the protoplanetary disk. Specifically, we
address mass-loss due to both photo-evaporation and cooling of the planet. We
find that planets shed their outer layers (dozens of percents in mass)
following the disk's dispersal (even without photo-evaporation), and their
atmospheres shrink in a few Myr to a thickness comparable to the radius of the
underlying rocky core. At this stage, atmospheres containing less particles
than the core (equivalently, lighter than a few % of the planet's mass) can be
blown away by heat coming from the cooling core, while heavier atmospheres cool
and contract on a timescale of Gyr at most. By relating the mass-loss timescale
to the accretion time, we analytically identify a Goldilocks region in the
mass-temperature plane in which low-density super Earths can be found: planets
have to be massive and cold enough to accrete and retain their atmospheres,
while not too massive or cold, such that they do not enter runaway accretion
and become gas giants (Jupiters). We compare our results to the observed
super-Earth population and find that low-density planets are indeed
concentrated in the theoretically allowed region. Our analytical and intuitive
model can be used to investigate possible super-Earth formation scenarios.Comment: Updated (refereed) versio
The Self-Similarity of Shear-Dominated Viscous Stirring
We examine the growth of eccentricities of a population of particles with
initially circular orbits around a central massive body. Successive encounters
between pairs of particles increase the eccentricities in the disk on average.
As long as the epicyclic motions of the particles are small compared to the
shearing motion between Keplerian orbits, there is no preferred scale for the
eccentricities. The simplification due to this self-similarity allows us to
find an analytic form for the distribution function; full numerical
integrations of a disk with 200 planetesimals verify our analytical
self-similar distribution. The shape of this non-equilibrium profile is
identical to the equilibrium profile of a shear-dominated population whose
mutual excitations are balanced by dynamical friction or Epstein gas drag.Comment: 8 pages, 2 figure
Formation of Kuiper Belt Binaries
The discovery that a substantial fraction of Kuiper Belt objects (KBOs)
exists in binaries with wide separations and roughly equal masses, has
motivated a variety of new theories explaining their formation. Goldreich et
al. (2002) proposed two formation scenarios: In the first, a transient binary
is formed, which becomes bound with the aid of dynamical friction from the sea
of small bodies (L^2s mechanism); in the second, a binary is formed by three
body gravitational deflection (L^3 mechanism). Here, we accurately calculate
the L^2s and L^3 formation rates for sub-Hill velocities. While the L^2s
formation rate is close to previous order of magnitude estimates, the L^3
formation rate is about a factor of 4 smaller. For sub-Hill KBO velocities (v
<< v_H) the ratio of the L^3 to the L^2s formation rate is 0.05 (v/v_H)
independent of the small bodies' velocity dispersion, their surface density or
their mutual collisions. For Super-Hill velocities (v >> v_H) the L^3 mechanism
dominates over the L^2s mechanism. Binary formation via the L^3 mechanism
competes with binary destruction by passing bodies. Given sufficient time, a
statistical equilibrium abundance of binaries forms. We show that the frequency
of long-lived transient binaries drops exponentially with the system's lifetime
and that such transient binaries are not important for binary formation via the
L^3 mechanism, contrary to Lee et al. (2007). For the L^2s mechanism we find
that the typical time, transient binaries must last, to form Kuiper Belt
binaries (KBBs) for a given strength of dynamical friction, D, increases only
logarithmically with D. Longevity of transient binaries only becomes important
for very weak dynamical friction (i.e. D \lesssim 0.002) and is most likely not
crucial for KBB formation.Comment: 20 pages, 3 figures, Accepted for publication in ApJ, correction of
minor typo
The Last Stages of Terrestrial Planet Formation: Dynamical Friction and the Late Veneer
The final stage of terrestrial planet formation consists of the cleanup of
residual planetesimals after the giant impact phase. Dynamically, a residual
planetesimal population is needed to damp the high eccentricities of the
terrestrial planets after the giant impact stage. Geochemically, highly
siderophile element (HSE) abundance patterns inferred for the terrestrial
planets and the Moon suggest that a total of about 0.01 M_Earth of chondritic
material was delivered as `late veneer' by planetesimals to the terrestrial
planets after the end of giant impacts. Here we combine these two independent
lines of evidence for a leftover population of planetesimals and show that: 1)
A residual planetesimal population containing 0.01 M_Earth is able to damp the
eccentricities of the terrestrial planets after giant impacts to their observed
values. 2) At the same time, this planetesimal population can account for the
observed relative amounts of late veneer added to the Earth, Moon and Mars
provided that the majority of the late veneer was delivered by small
planetesimals with radii <10m. These small planetesimal sizes are required to
ensure efficient damping of the planetesimal's velocity dispersion by mutual
collisions, which in turn ensures that the planets' accretion cross sections
are significantly enhanced by gravitational focusing above their geometric
values. Specifically we find, in the limit that the relative velocity between
the terrestrial planets and the planetesimals is significantly less than the
terrestrial planets' escape velocities, that gravitational focusing yields an
accretion ratio Earth/Mars~17, which agrees well with the accretion ratio
inferred from HSEs of 12-23. For the Earth-Moon system, we find an accretion
ratio of ~200, which is consistent with estimates of 150-700 derived from HSE
abundances that include the lunar crust as well as mantle component. (Abridged)Comment: accepted for publication in ApJ, 9 pages, 4 figures; minor
corrections, additional references adde
Is turbulent mixing a self convolution process ?
Experimental results for the evolution of the probability distribution
function (PDF) of a scalar mixed by a turbulence flow in a channel are
presented. The sequence of PDF from an initial skewed distribution to a sharp
Gaussian is found to be non universal. The route toward homogeneization depends
on the ratio between the cross sections of the dye injector and the channel. In
link with this observation, advantages, shortcomings and applicability of
models for the PDF evolution based on a self-convolution mechanisms are
discussed.Comment: 4 page
- …