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

The First Post-Kepler Brightness Dips of KIC 8462852

We present a photometric detection of the first brightness dips of the unique variable star KIC 8462852 since the end of the Kepler space mission in 2013 May. Our regular photometric surveillance started in 2015 October, and a sequence of dipping began in 2017 May continuing on through the end of 2017, when the star was no longer visible from Earth. We distinguish four main 1%-2.5% dips, named Elsie, Celeste, Skara Brae, and Angkor, which persist on timescales from several days to weeks. Our main results so far are as follows: (i) there are no apparent changes of the stellar spectrum or polarization during the dips and (ii) the multiband photometry of the dips shows differential reddening favoring non-gray extinction. Therefore, our data are inconsistent with dip models that invoke optically thick material, but rather they are in-line with predictions for an occulter consisting primarily of ordinary dust, where much of the material must be optically thin with a size scale ≪1 μm, and may also be consistent with models invoking variations intrinsic to the stellar photosphere. Notably, our data do not place constraints on the color of the longer-term secular dimming, which may be caused by independent processes, or probe different regimes of a single process

The First Post-Kepler Brightness Dips of KIC 8462852

We present a photometric detection of the first brightness dips of the unique variable star KIC 8462852 since the end of the Kepler space mission in 2013 May. Our regular photometric surveillance started in October 2015, and a sequence of dipping began in 2017 May continuing on through the end of 2017, when the star was no longer visible from Earth. We distinguish four main 1-2.5% dips, named "Elsie," "Celeste," "Skara Brae," and "Angkor", which persist on timescales from several days to weeks. Our main results so far are: (i) there are no apparent changes of the stellar spectrum or polarization during the dips; (ii) the multiband photometry of the dips shows differential reddening favoring non-grey extinction. Therefore, our data are inconsistent with dip models that invoke optically thick material, but rather they are in-line with predictions for an occulter consisting primarily of ordinary dust, where much of the material must be optically thin with a size scale <<1um, and may also be consistent with models invoking variations intrinsic to the stellar photosphere. Notably, our data do not place constraints on the color of the longer-term "secular" dimming, which may be caused by independent processes, or probe different regimes of a single process