148 research outputs found

### Jeans Instability of Palomar 5's Tidal Tail

Tidal tails composed of stars should be unstable to the Jeans instability and
this can cause them to look like beads on a string. The Jeans wavelength and
tail diameter determine the wavelength and growth rate of the fastest growing
unstable mode. Consequently the distance along the tail to the first clump and
spacing between clumps can be used to estimate the mass density in the tail and
its longitudinal velocity dispersion. Clumps in the tidal tails of the globular
cluster Palomar 5 could be due to Jeans instability. We find that their spacing
is consistent with the fastest growing mode if the velocity dispersion in the
tail is similar to that in the cluster itself. While all tidal tails should
exhibit gravitational instability, we find that clusters or galaxies with low
concentration parameters are most likely to exhibit short wavelength rapidly
growing Jeans modes in their tidal tails.Comment: sumbmitted to MNRA

### Stability Boundaries for Resonant Migrating Planet Pairs

Convergent migration allows pairs of planet to become trapped into mean
motion resonances. Once in resonance, the planets' eccentricities grow to an
equilibrium value that depends on the ratio of migration time scale to the
eccentricity damping timescale, $K=\tau_a/\tau_e$, with higher values of
equilibrium eccentricity for lower values of $K$. For low equilibrium
eccentricities, $e_{eq}\propto K^{-1/2}$. The stability of a planet pair
depends on eccentricity so the system can become unstable before it reaches its
equilibrium eccentricity. Using a resonant overlap criterion that takes into
account the role of first and second order resonances and depends on
eccentricity, we find a function $K_{min}(\mu_p, j)$ that defines the lowest
value for $K$, as a function of the ratio of total planet mass to stellar mass
($\mu_p$) and the period ratio of the resonance defined as $P_1/P_2=j/(j+k)$,
that allows two convergently migrating planets to remain stable in resonance at
their equilibrium eccentricities. We scaled the functions $K_{min}$ for each
resonance of the same order into a single function $K_c$. The function $K_{c}$
for planet pairs in first order resonances is linear with increasing planet
mass and quadratic for pairs in second order resonances with a coefficient
depending on the relative migration rate and strongly on the planet to planet
mass ratio. The linear relation continues until the mass approaches a critical
mass defined by the 2/7 resonance overlap instability law and $K_c \to \infty$.
We compared our analytic boundary with an observed sample of resonant two
planet systems. All but one of the first order resonant planet pair systems
found by radial velocity measurements are well inside the stability region
estimated by this model. We calculated $K_c$ for Kepler systems without
well-constrained eccentricities and found only weak constraints on $K$.Comment: 11 pages, 7 figure

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