104 research outputs found
On the Snow Line in Dusty Protoplanetary Disks
The snow line, in Hayashi's (1981) model, is where the temperature of a black
body that absorbed direct sunlight and re-radiated as much as it absorbed,
would be 170~K. It is usually assumed that the cores of the giant planets,
e.g., Jupiter, form beyond the snow line. Since Hayashi, there have been a
series of more detailed models of the absorption by dust of the stellar
radiation, and of accretional heating, which alter the location of the snow
line. We have attempted a "self-consistent" model of a T Tauri disk in the
sense that we used dust properties and calculated surface temperatures that
matched observed disks. We then calculated the midplane temperature for those
disks, with no accretional heating or with small (<10^-8) accretion rates. Our
models bring the snow line in to the neighbourhood of 1 AU; not far enough to
explain the close planetary companions to other stars, but much closer than in
recent starting lines for orbit migration scenarios.Comment: 9 pages, 1 figure, to appear in ApJ,528,200
Instability of the Gravitational N-Body Problem in the Large-N Limit
We use a systolic N-body algorithm to evaluate the linear stability of the
gravitational N-body problem for N up to 1.3 x 10^5, two orders of magnitude
greater than in previous experiments. For the first time, a clear ~ln
N-dependence of the perturbation growth rate is seen. The e-folding time for N
= 10^5 is roughly 1/20 of a crossing time.Comment: Accepted for publication in The Astrophysical Journa
Dispersing the Gaseous Protoplanetary Disc and Halting Type II Migration
More than 30 extra-solar Jupiter-like planets have shorter periods than the
planet Mercury. It is generally accepted that they formed further out, and
migrated inwards. In order to be driven by tidal torques from the gaseous disc,
the disc exterior to the planet had to contain about a planetary mass. The fact
that the planets stopped migrating means that their outer disc was removed. We
suggest that the outer disc was accreted by the planet. In this scenario, the
endgame is a race. The planet survives if it accretes its outer disc before
being accreted by the star. The winner is determined solely by the ratio of the
mass of the outer disc to the local surface density of the disc.Comment: 5 pages, submitted to ApJ
On the effectiveness of mixing in violent relaxation
Relaxation processes in collisionless dynamics lead to peculiar behavior in
systems with long-range interactions such as self-gravitating systems,
non-neutral plasmas and wave-particle systems. These systems, adequately
described by the Vlasov equation, present quasi-stationary states (QSS), i.e.
long lasting intermediate stages of the dynamics that occur after a short
significant evolution called "violent relaxation". The nature of the
relaxation, in the absence of collisions, is not yet fully understood. We
demonstrate in this article the occurrence of stretching and folding behavior
in numerical simulations of the Vlasov equation, providing a plausible
relaxation mechanism that brings the system from its initial condition into the
QSS regime. Area-preserving discrete-time maps with a mean-field coupling term
are found to display a similar behaviour in phase space as the Vlasov system.Comment: 10 pages, 11 figure
An Investigation into the Radial Velocity Variations of CoRoT-7
CoRoT-7b, the first transiting ``superearth'' exoplanet, has a radius of 1.7
R_Earth and a mass of 4.8 M_Earth. Ground-based radial velocity measurements
also detected an additional companion with a period of 3.7 days (CoRoT-7c) and
a mass of 8.4 M_Earth. The mass of CoRoT-7b is a crucial parameter for planet
structure models, but is difficult to determine because CoRoT-7 is a modestly
active star and there is at least one additional companion. A Fourier analysis
was performed on spectral data for CoRoT-7 taken with the HARPS spectrograph.
These data include RV measurements, spectral line bisectors, the full width at
half maximum of the cross-correlation function, and Ca II emission. The latter
3 quantities vary due to stellar activity and were used to assess the nature of
the observed RV variations. An analysis of a sub-set of the RV measurements
where multiple observations were made per night was also used to estimate the
RV amplitude from CoRoT-7b that was less sensitive to activity variations. Our
analysis indicates that the 0.85-d and 3.7-d RV signals of CoRoT-7b and
CoRoT-7c are present in the spectral data with a high degree of statistical
significance. We also find evidence for another significant RV signal at 9
days. An analysis of the activity indicator data reveals that this 9-d signal
most likely does not arise from activity, but possibly from an additional
companion. If due to a planetary companion the mass is m = 19.5 M_Earth,
assuming co-planarity with CoRoT-7b. A dynamical study of the three planet
system shows that it is stable over several hundred millions of years. Our
analysis yields a RV amplitude of 5.04 +/- 1.09 m/s for CoRoT-7b which
corresponds to a planet mass of m = 6.9 +/- 1.4 M_Earth. This increased mass
would make the planet CoRoT-7b more Earth-like in its internal structure.Comment: 20 pages, 20 figure
On the Location of the Snow Line in a Protoplanetary Disk
In a protoplanetary disk, the inner edge of the region where the temperature
falls below the condensation temperature of water is referred to as the 'snow
line'. Outside the snow line, water ice increases the surface density of solids
by a factor of 4. The mass of the fastest growing planetesimal (the 'isolation
mass') scales as the surface density to the 3/2 power. It is thought that
ice-enhanced surface densities are required to make the cores of the gas giants
(Jupiter and Saturn) before the disk gas dissipates. Observations of the Solar
System's asteroid belt suggest that the snow line occurred near 2.7 AU. In this
paper we revisit the theoretical determination of the snow line. In a
minimum-mass disk characterized by conventional opacities and a mass accretion
rate of 10^-8 solar masses per year, the snow line lies at 1.6-1.8 AU, just
past the orbit of Mars. The minimum-mass disk, with a mass of 0.02 solar, has a
life time of 2 million years with the assumed accretion rate. Moving the snow
line past 2.7 AU requires that we increase the disk opacity, accretion rate,
and/or disk mass by factors ranging up to an order of magnitude above our
assumed baseline values.Comment: Accepted for publication in ApJ, 9 pages, 4 figure
The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion
We establish a criterion for the stability of planetary orbits in stellar
binary systems by using Lyapunov exponents and power spectra for the special
case of the circular restricted 3-body problem (CR3BP). The centerpiece of our
method is the concept of Lyapunov exponents, which are incorporated into the
analysis of orbital stability by integrating the Jacobian of the CR3BP and
orthogonalizing the tangent vectors via a well-established algorithm originally
developed by Wolf et al. The criterion for orbital stability based on the
Lyapunov exponents is independently verified by using power spectra. The
obtained results are compared to results presented in the two previous papers
of this series. It is shown that the maximum Lyapunov exponent can be used as
an indicator for chaotic behaviour of planetary orbits, which is consistent
with previous applications of this method, particularly studies for the Solar
System. The chaotic behaviour corresponds to either orbital stability or
instability, and it depends solely on the mass ratio of the binary components
and the initial distance ratio of the planet relative to the stellar separation
distance. Our theoretical results allow us to link the study of planetary
orbital stability to chaos theory noting that there is a large array of
literature on the properties and significance of Lyapunov exponents. Although
our results are given for the special case of the CR3BP, we expect that it may
be possible to augment the proposed Lyapunov exponent criterion to studies of
planets in generalized stellar binary systems, which is strongly motivated by
existing observational results as well as results expected from ongoing and
future planet search missions.Comment: 10 pages, 8 figures, 3 tables; accepted by Astronomy and Astrophysic
Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model
The influence of intrinsic channel noise on the spontaneous spiking activity
of poisoned excitable membrane patches is studied by use of a stochastic
generalization of the Hodgkin-Huxley model. Internal noise stemming from the
stochastic dynamics of individual ion channels is known to affect the
collective properties of the whole ion channel cluster. For example, there
exists an optimal size of the membrane patch for which the internal noise alone
causes a regular spontaneous generation of action potentials. In addition to
varying the size of ion channel clusters, living organisms may adapt the
densities of ion channels in order to optimally regulate the spontaneous
spiking activity. The influence of channel block on the excitability of a
membrane patch of certain size is twofold: First, a variation of ion channel
densities primarily yields a change of the conductance level. Second, a
down-regulation of working ion channels always increases the channel noise.
While the former effect dominates in the case of sodium channel block resulting
in a reduced spiking activity, the latter enhances the generation of
spontaneous action potentials in the case of a tailored potassium channel
blocking. Moreover, by blocking some portion of either potassium or sodium ion
channels, it is possible to either increase or to decrease the regularity of
the spike train.Comment: 10 pages, 3 figures, published 200
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