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

Dippers and dusty disc edges: New diagnostics and comparison to model predictions

We revisit the nature of large dips in flux from extinction by dusty circumstellar material that is observed by Kepler for many young stars in the Upper Sco and ρ Oph star formation regions. These young, low-mass \u27dipper\u27 stars are known to have low accretion rates and primarily hostmoderately evolved dusty circumstellar discs. Young low-mass stars often exhibit rotating starspots that cause quasi-periodic photometric variations. We found no evidence for periods associated with the dips that are different from the starspot rotation period in spectrograms constructed from the light curves. The material causing the dips in most of these light curves must be approximately corotating with the star.We find that disc temperatures computed at the disc corotation radius are cool enough that dust should not sublime. Crude estimates for stellar magnetic field strengths and accretion rates are consistent with magnetospheric truncation near the corotation radius. Magnetospheric truncation models can explain why the dips are associated with material near corotation and how dusty material is lifted out of the mid-plane to obscure the star that would account for the large fraction of young low-mass stars that are dippers. We propose that variations in disc orientation angle, stellar magnetic field dipole tilt axis and disc accretion rate are underlying parameters accounting for differences in the dipper light curves

Exocomets from a Solar System Perspective

Exocomets are small bodies releasing gas and dust which orbit stars other than the Sun. Their existence was first inferred from the detection of variable absorption features in stellar spectra in the late 1980s using spectroscopy. More recently, they have been detected through photometric transits from space, and through far-IR/mm gas emission within debris disks. As (exo)comets are considered to contain the most pristine material accessible in stellar systems, they hold the potential to give us information about early stage formation and evolution conditions of extra Solar Systems. In the Solar System, comets carry the physical and chemical memory of the protoplanetary disk environment where they formed, providing relevant information on processes in the primordial solar nebula. The aim of this paper is to compare essential compositional properties between Solar System comets and exocomets. The paper aims to highlight commonalities and to discuss differences which may aid the communication between the involved research communities and perhaps also avoid misconceptions. Exocomets likely vary in their composition depending on their formation environment like Solar System comets do, and since exocomets are not resolved spatially, they pose a challenge when comparing them to high fidelity observations of Solar System comets. Observations of gas around main sequence stars, spectroscopic observations of "polluted" white dwarf atmospheres and spectroscopic observations of transiting exocomets suggest that exocomets may show compositional similarities with Solar System comets. The recent interstellar visitor 2I/Borisov showed gas, dust and nuclear properties similar to that of Solar System comets. This raises the tantalising prospect that observations of interstellar comets may help bridge the fields of exocomet and Solar System comets.Comment: 25 pages, 3 figures. To be published in PASP. This paper is the product of a workshop at the Lorentz Centre in Leiden, the Netherland

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

Modeling variability and irregular transits from circumstellar disks and debris

Thesis (Ph. D.)--University of Rochester. Department of Physics and Astronomy, 2017.Circumstellar material can lead to fluctuations in observed stellar flux by either occulting the star or contributing with reradiated light. These changes in flux providers a new window into the inner regions of the circumstellar environment. In Chapter 2, we explore circumbinary disc temperature variations as a source of broad-band infrared light curve variability. Approximating the wall of a circumbinary disc edge as a wide optically thick cylinder with surface temperature dependent on its illumination, we find that a pre-main sequence binary with a ~15.5 day period, would exhibit the largest amplitude variations of ~9% in near infrared. The light curve variations are smooth and very red with a non-sinusoidal shape for most of the parameter space explored. In Chapter 3, we revisit the nature of large dips in flux from extinction by dusty circumstellar material that is observed by Kepler for many young stars in the Upper Sco and p Oph star formation regions. We find the material causing the dips in most of these light curves to be approximately corotating with the star and temperatures computed at the disk corotation radius are cool enough that dust should not sublimate. If material needs to cooler than the dust sublimation temperature, then dippers are preferentially associated with young, low mass stars which is consistent with the sample. Magnetospheric truncation models can explain why the dips are associated with material near corotation and how dusty material is lifted out of the midplane to obscure the star which would account for the large fraction of young low mass stars that are dippers. In Chapter 4, we investigate the plausibility of a cometary source of the unusual transits observed in the KIC 8462852 light curve. We find that a series of large comet swarms provides a good fit for the KIC 8462852 data during Quarters 16 and 17, but does not explain the large dip observed during Quarter 8. A single comet family from a tidally disrupted Ceres-sized progenitor or the start of a Late Heavy Bombardment period explains the last ~ 60 days of the unusual KIC 8462852 light curve