Dynamical mass and multiplicity constraints on co-orbital bodies around stars

Objects transiting near or within the disruption radius of both main sequence (e.g. KOI 1843) and white dwarf (WD 1145+017) stars are now known. Upon fragmentation or disintegration, these planets or asteroids may produce co-orbital configurations of nearly equal-mass objects. However, as evidenced by the co-orbital objects detected by transit photometry in the WD 1145+017 system, these bodies are largely unconstrained in size, mass, and total number (multiplicity). Motivated by potential future similar discoveries, we perform N-body simulations to demonstrate if and how debris masses and multiplicity may be bounded due to second-to-minute deviations and the resulting accumulated phase shifts in the osculating orbital period amongst multiple co-orbital equal point masses. We establish robust lower and upper mass bounds as a function of orbital period deviation, but find the constraints on multiplicity to be weak. We also quantify the fuzzy instability boundary, and show that mutual collisions occur in less than 5%, 10% and 20% of our simulations for masses of 10^{21}, 10^{22} and 10^{23} kg. Our results may provide useful initial rough constraints on other stellar systems with multiple co-orbital bodies

Mass and eccentricity constraints on the planetary debris orbiting the white dwarf WD 1145+017

Being the first of its kind, the white dwarf WD 1145+017 exhibits a complex system of disintegrating debris which offers a unique opportunity to study its disruption process in real time. Even with plenty of transit observations there are no clear constraints on the masses or eccentricities of such debris. Using N-body simulations, we show that masses greater than ≃1020 kg (a tenth of the mass of Ceres) or orbits that are not nearly circular (eccentricity > 10−3) dramatically increase the chances of the system becoming unstable within 2 yr, which would contrast with the observational data over this timespan. We also provide a direct comparison between transit phase shifts detected in the observations and by our numerical simulations

Deposition of steeply infalling debris around white dwarf stars

High-metallicity pollution is common in white dwarf (WD) stars hosting remnant planetary systems. However, they rarely have detectable debris accretion discs, possibly because much of the influx is fast steeply-infalling debris in star-grazing orbits, producing a more tenuous signature than a slowly accreting disk. Processes governing such deposition between the Roche radius and photosphere have so far received little attention and we model them here analytically by extending recent work on sun-grazing comets to WD systems. We find that the evolution of cm-to-km size (a_0) infallers most strongly depends on two combinations of parameters, which effectively measure sublimation rate and binding strength. We then provide an algorithm to determine the fate of infallers for any WD, and apply the algorithm to four limiting combinations of hot versus cool (young/old) WDs with snowy (weak, volatile) versus rocky (strong, refractory) infallers. We find: (i) Total sublimation above the photosphere befalls all small infallers across the entire WD temperature (T_WD) range, the threshold size rising with T_WD and 100X larger for rock than snow. (ii) All very large objects fragment tidally regardless of T_WD: for rock, a_0 >= 10^5 cm; for snow, a_0 >= 10^3 -- 3x10^4 cm across all WD cooling ages. (iii) A considerable range of a_0 avoids fragmentation and total sublimation, yielding impacts or grazes with cold WDs. This range narrows rapidly with increasing T_WD, especially for snowy bodies. Finally, we discuss briefly how the various forms of deposited debris may finally reach the photosphere surface itself

Analysis of hydrogen-rich magnetic white dwarfs detected in the Sloan Digital Sky Survey

Context A large number of magnetic white dwarfs discovered in the SDSS have so far only been analyzed by visual comparison of the observations with relatively simple models of the radiation transport in a magnetised stellar atmosphere. Aims We model the structure of the surface magnetic fields of the hydrogen-rich white dwarfs in the SDSS. Methods We calculated a grid of state-of-the-art theoretical optical spectra of hydrogen-rich magnetic white dwarfs (WDs) with magnetic field strengths of between 1 MG and 1200 MG for different angles between the magnetic field vector and the line of sight,and for effective temperatures between 7000 K and 50 000 K. We used a least squares minimization scheme with an evolutionary algorithm to find the best-fit magnetic field geometry of the observed data. We used centered dipoles or dipoles that had been shifted along the dipole axis to model the coadded SDSS fiber spectrum of each object. Result We analyzed the spectra of all known magnetic hydrogen-rich (DA) WDs from the SDSS (97 previously published, plus 44 newly discovered) and also investigated the statistical properties of the magnetic field geometries of this sample. Conclusions The total number of known magnetic white dwarfs has already been more than tripled by the SDSS and more objects are expected after more systematic searches. The magnetic fields have strengths of between ≈1 and 900 MG. Our results further support the claims that Ap/Bp population is insufficient in generating the numbers and field strength distributions of the observed MWDs, and that of either another source of progenitor types or binary evolution is needed. Clear indications of non-centered dipoles exist in about ∼50%, of the objects which is consistent with the magnetic field distribution observed in Ap/Bp stars

The unstable fate of the planet orbiting the A-star in the HD 131399 triple stellar system

Validated planet candidates need not lie on long-term stable orbits, and instability triggered by post-main-sequence stellar evolution can generate architectures which transport rocky material to white dwarfs, polluting them. The giant planet HD 131399Ab orbits its parent A star at a projected separation of about 50-100 au. The host star, HD131399A, is part of a hierarchical triple with HD131399BC being a close binary separated by a few hundred au from the A star. Here, we determine the fate of this system, and find that (i) stability along the main sequence is achieved only for a favourable choice of parameters within the errors, and (ii) even for this choice, in almost every instance the planet is ejected during the transition between the giant branch and white dwarf phases of HD 131399A. This result provides an example of both how the free-floating planet population may be enhanced by similar systems, and how instability can manifest in the polluted white dwarf progenitor population

Zeeman tomography of magnetic white dwarfs. IV, The complex field structure of the polars EF Eridani, BL Hydri and CP Tucanae

Context. The magnetic fields of the accreting white dwarfs in magnetic cataclysmic variables (mCVs) determine the accretion geometries, the emission properties, and the secular evolution of these objects. Aims. We determine the structure of the surface magnetic fields of the white dwarf primaries in magnetic CVs using Zeeman tomography. Methods. Our study is based on orbital-phase resolved optical flux and circular polarization spectra of the polars EF Eri, BL Hyi, and CP Tuc obtained with FORS1 at the ESO VLT. An evolutionary algorithm is used to synthesize best fits to these spectra from an extensive database of pre-computed Zeeman spectra. The general approach has been described in previous papers of this series. Results. The results achieved with simple geometries as centered or offset dipoles are not satisfactory. Significantly improved fits are obtained for multipole expansions that are truncated at degree lmax = 3 or 5 and include all tesseral and sectoral components with 0 ≤ m ≤ l. The most frequent field strengths of 13, 18, and 10MG for EF Eri, BL Hyi, and CP Tuc, and the ranges of field strength covered are similar for the dipole and multipole models, but only the latter provide access to accreting matter at the right locations on the white dwarf. The results suggest that the field geometries of the white dwarfs in short-period mCVs are quite complex, with strong contributions from multipoles higher than the dipole in spite of a typical age of the white dwarfs in CVs in excess of 1 Gyr. Conclusions. It is feasible to derive the surface field structure of an accreting white dwarf from phase-resolved low-state circular spectropolarimetry of sufficiently high signal-to-noise ratio. The fact that independent information is available on the strength and direction of the field in the accretion spot from high-state observations helps in unraveling the global field structure

Effects of non-Kozai mutual inclinations on two-planet system stability through all phases of stellar evolution

Previous full-lifetime simulations of single-star multi-planet systems across all phases of stellar evolution have predominately assumed coplanar or nearly coplanar orbits. Here we assess the consequences of this assumption by removing it and exploring the effect of giant branch mass loss on the stability of two-planet systems with small to moderate non-Kozai (<40º) relative inclinations. We run nearly 104 simulations over 14 Gyr for F-star, A-star and B-star planet hosts, incorporating main-sequence stellar masses of 1.5, 2.0, 2.5, 3.0 and 5.0 solar masses, and initial planetary semimajor axis ratios that straddle their three-dimensional Hill stability limits. We find that the near-coplanar assumption can approximate well the stability frequencies and critical separations found for higher inclinations, except around strong mean-motion commensurabilities. Late instabilities – after the star has become a white dwarf – occur throughout the explored mutual inclination range. Consequently, non-Kozai mutual inclination should not be used as a predictive orbital proxy for determining which white dwarf multi-planet systems discovered by Gaia should represent high-priority follow-up targets for the detection of metal pollution and planetary debris discs

Binary star influence on post-main-sequence multi-planet stability

Nearly every star known to host planets will become a white dwarf, and nearly 100 planet-hosts are now known to be accompanied by binary stellar companions. Here, we determine how a binary companion triggers instability in otherwise unconditionally stable single-star two-planet systems during the giant branch and white dwarf phases of the planet host. We perform about 700 full-lifetime (14 Gyr) simulations with A0 and F0 primary stars and secondary K2 companions, and identify the critical binary distance within which instability is triggered at any point during stellar evolution. We estimate this distance to be about seven times the outer planet separation, for circular binaries. Our results help characterize the fates of planetary systems, and in particular which ones might yield architectures that are conducive to generating observable heavy metal pollution in white dwarf atmospheres

Explaining the variability of WD 1145+017 with simulations of asteroid tidal disruption

Post-main-sequence planetary science has been galvanised by the striking variability, depth and shape of the photometric transit curves due to objects orbiting white dwarf WD 1145+017, a star which also hosts a dusty debris disc and circumstellar gas, and displays strong metal atmospheric pollution. However, the physical properties of the likely asteroid which is discharging disintegrating fragments remain largely unconstrained from the observations. This process has not yet been modelled numerically. Here, we use the N-body code PKDGRAV to compute dissipation properties for asteroids of different spins, densities, masses, and eccentricities. We simulate both homogeneous and differentiated asteroids, for up to two years, and find that the disruption timescale is strongly dependent on density and eccentricity, but weakly dependent on mass and spin. We find that primarily rocky differentiated bodies with moderate (∼ 3−4 g/cm3 ) bulk densities on near-circular (e . 0.1) orbits can remain intact while occasionally shedding mass from their mantles. These results suggest that the asteroid orbiting WD 1145+017 is differentiated, resides just outside of the Roche radius for bulk density but just inside the Roche radius for mantle density, and is more akin physically to an asteroid like Vesta instead of one like Itokawa

Hubble space telescope STIS spectroscopy of the peculiar nova-like variables BK Lyn, V751 Cygni, and V380 Oph

We obtained Hubble STIS spectra of three nova-like variables: V751 Cygni, V380 Oph, and—the only confirmed nova-like variable known to be below the period gap—BK Lyn. In all three systems, the spectra were taken during high optical brightness state, and a luminous accretion disk dominates their far-ultraviolet (FUV) light. We assessed a lower limit of the distances by applying the infrared photometric method of Knigge. Within the limitations imposed by the poorly known system parameters (such as the inclination, white dwarf mass, and the applicability of steady state accretion disks) we obtained satisfactory fits to BK Lyn using optically thick accretion disk models with an accretion rate of for a white dwarf mass of Mwd = 1.2M and for Mwd = 0.4M. However, for the VY Scl-type nova-like variable V751 Cygni and for the SW Sex star V380 Oph, we are unable to obtain satisfactory synthetic spectral fits to the high state FUV spectra using optically thick steady state accretion disk models. The lack of FUV spectra information down to the Lyman limit hinders the extraction of information about the accreting white dwarf during the high states of these nova-like systems