895 research outputs found
The great dichotomy of the Solar System: small terrestrial embryos and massive giant planet cores
The basic structure of the solar system is set by the presence of low-mass
terrestrial planets in its inner part and giant planets in its outer part. This
is the result of the formation of a system of multiple embryos with
approximately the mass of Mars in the inner disk and of a few multi-Earth-mass
cores in the outer disk, within the lifetime of the gaseous component of the
protoplanetary disk. What was the origin of this dichotomy in the mass
distribution of embryos/cores? We show in this paper that the classic processes
of runaway and oligarchic growth from a disk of planetesimals cannot explain
this dichotomy, even if the original surface density of solids increased at the
snowline. Instead, the accretion of drifting pebbles by embryos and cores can
explain the dichotomy, provided that some assumptions hold true. We propose
that the mass-flow of pebbles is two-times lower and the characteristic size of
the pebbles is approximately ten times smaller within the snowline than beyond
the snowline (respectively at heliocentric distance and
, where is the snowline heliocentric distance), due to ice
sublimation and the splitting of icy pebbles into a collection of
chondrule-size silicate grains. In this case, objects of original sub-lunar
mass would grow at drastically different rates in the two regions of the disk.
Within the snowline these bodies would reach approximately the mass of Mars
while beyond the snowline they would grow to Earth masses. The
results may change quantitatively with changes to the assumed parameters, but
the establishment of a clear dichotomy in the mass distribution of protoplanets
appears robust, provided that there is enough turbulence in the disk to prevent
the sedimentation of the silicate grains into a very thin layer.Comment: In press in Icaru
Universal and non-universal behavior in Dirac spectra
We have computed ensembles of complete spectra of the staggered Dirac
operator using four-dimensional SU(2) gauge fields, both in the quenched
approximation and with dynamical fermions. To identify universal features in
the Dirac spectrum, we compare the lattice data with predictions from chiral
random matrix theory for the distribution of the low-lying eigenvalues. Good
agreement is found up to some limiting energy, the so-called Thouless energy,
above which random matrix theory no longer applies. We determine the dependence
of the Thouless energy on the simulation parameters using the scalar
susceptibility and the number variance.Comment: LATTICE98(confine), 9 pages, 11 figure
Spectrum of the SU(3) Dirac operator on the lattice: Transition from random matrix theory to chiral perturbation theory
We calculate complete spectra of the Kogut-Susskind Dirac operator on the
lattice in quenched SU(3) gauge theory for various values of coupling constant
and lattice size. From these spectra we compute the connected and disconnected
scalar susceptibilities and find agreement with chiral random matrix theory up
to a certain energy scale, the Thouless energy. The dependence of this scale on
the lattice volume is analyzed. In the case of the connected susceptibility
this dependence is anomalous, and we explain the reason for this. We present a
model of chiral perturbation theory that is capable of describing the data
beyond the Thouless energy and that has a common range of applicability with
chiral random matrix theory.Comment: 8 pages, RevTeX, 15 .eps figure
Can we do better than Hybrid Monte Carlo in Lattice QCD?
The Hybrid Monte Carlo algorithm for the simulation of QCD with dynamical
staggered fermions is compared with Kramers equation algorithm. We find
substantially different autocorrelation times for local and nonlocal
observables. The calculations have been performed on the parallel computer CRAY
T3D.Comment: Talk presented at LATTICE96(algorithms), LaTeX 3 pages, uses espcrc2,
epsf, 2 postscript figure
Random Matrix Theory, Chiral Perturbation Theory, and Lattice Data
Recently, the chiral logarithms predicted by quenched chiral perturbation
theory have been extracted from lattice calculations of hadron masses. We argue
that the deviations of lattice results from random matrix theory starting
around the so-called Thouless energy can be understood in terms of chiral
perturbation theory as well. Comparison of lattice data with chiral
perturbation theory formulae allows us to compute the pion decay constant. We
present results from a calculation for quenched SU(2) with Kogut-Susskind
fermions at \beta=2.0 and 2.2.Comment: LaTeX, 12 pages, 7 .eps figure
Random Matrix Theory and Chiral Logarithms
Recently, the contributions of chiral logarithms predicted by quenched chiral
perturbation theory have been extracted from lattice calculations of hadron
masses. We argue that a detailed comparison of random matrix theory and lattice
calculations allows for a precise determination of such corrections. We
estimate the relative size of the m*log(m), m, and m^2 corrections to the
chiral condensate for quenched SU(2).Comment: LaTeX (elsart.cls), 9 pages, 6 .eps figures, added reference, altered
discussion of Eq.(9
Beyond the Thouless energy
The distribution and the correlations of the small eigenvalues of the Dirac
operator are described by random matrix theory (RMT) up to the Thouless energy
, where is the physical volume. For somewhat larger
energies, the same quantities can be described by chiral perturbation theory
(chPT). For most quantities there is an intermediate energy regime, roughly
, where the results of RMT and chPT agree with each other. We
test these predictions by constructing the connected and disconnected scalar
susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3)
simulations with staggered fermions for a variety of lattice sizes and coupling
constants. In deriving the predictions of chPT, it is important to take into
account only those symmetries which are exactly realized on the lattice.Comment: LATTICE99(Theoretical Developments), 3 pages, 3 figures, typo in Ref.
[10] correcte
Small eigenvalues of the SU(3) Dirac operator on the lattice and in Random Matrix Theory
We have calculated complete spectra of the staggered Dirac operator on the
lattice in quenched SU(3) gauge theory for \beta = 5.4 and various lattice
sizes. The microscopic spectral density, the distribution of the smallest
eigenvalue, and the two-point spectral correlation function are analyzed. We
find the expected agreement of the lattice data with universal predictions of
the chiral unitary ensemble of random matrix theory up to a certain energy
scale, the Thouless energy. The deviations from the universal predictions are
determined using the disconnected scalar susceptibility. We find that the
Thouless energy scales with the lattice size as expected from theoretical
arguments making use of the Gell-Mann--Oakes--Renner relation.Comment: REVTeX, 5 pages, 4 figure
The solar abundance problem and eMSTOs in clusters
We study the impact of accretion from protoplanetary discs on stellar
evolution of AFG-type stars. We use a simplified disc model computed using the
Two-Pop-Py code that contains the growth and drift of dust particles in the
protoplanetary disc. It is used to model the accretion scenarios for a range of
physical conditions of protoplanetary discs. Two limiting cases are combined
with the evolution of stellar convective envelopes computed using the Garstec
stellar evolution code. We find that the accretion of metal-poor (gas) or
metal-rich (dust) material has a significant impact on the chemical composition
of the stellar convective envelope. As a consequence, the evolutionary track of
the star diverts from the standard scenario predicted by canonical stellar
evolution models, which assume a constant and homogeneous chemical composition
after the assembly of the star has finished. In the case of the Sun, we find a
modest impact on the solar chemical composition. Accretion of metal-poor
material indeed reduces the overall metallicity of the solar atmosphere, and it
is consistent, within the uncertainty, with the solar Z reported by Caffau et
al. (2011), but our model is not consistent with the measurement by Asplund et
al. (2009). Another effect is the change of the position of the star in the
colour-magnitude diagram. We compare our predictions to a set of open clusters
from the Gaia DR2 and show that it is possible to produce a scatter close to
the turn-off of young clusters that could contribute to explain the observed
scatter in CMDs. Detailed measurements of metallicities and abundances in the
nearby open clusters will provide a stringent observational test of our
proposed scenario.Comment: 10 pages, 7 figures, 1 table. Accepted for publication in A&
- âŠ