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Co-orbital systems contain two or more bodies sharing the same orbit around a planet or star. The best-known flavors of co-orbital systems are tadpoles (in which two bodies' angular separations oscillate about the L4/L5 Lagrange points $60^\circ$ apart) and horseshoes (with two bodies periodically exchanging orbital energy to trace out a horseshoe shape in a co-rotating frame). Here, we use N-body simulations to explore the parameter space of many-planet horseshoe systems. We show that up to 24 equal-mass, Earth-mass planets can share the same orbit at 1 au, following a complex pattern in which neighboring planets undergo horseshoe oscillations. We explore the dynamics of horseshoe constellations, and show that they can remain stable for billions of years and even persist through their stars' post-main sequence evolution. With sufficient observations, they can be identified through their large-amplitude, correlated transit timing variations. Given their longevity and exotic orbital architectures, horseshoe constellations may represent potential SETI beacons., 10 pages, 10 figures. Published in MNRAS. YouTube playlist with animations of horseshoe constellation systems here: https://www.youtube.com/playlist?list=PLelMZVM3ka3F335LGLxkxrD1ieiLJYQ5N . Blog post here: https://planetplanet.net/2023/04/20/constellations-of-co-orbital-planets/

Increasing observations of white dwarf atmospheric pollution and disrupting planetesimals is driving increased studies into the fate of exo-asteroids around post-main-sequence stars. Planetesimal populations in the Solar System which are most likely to survive the violent post-main-sequence evolution, such as the Kuiper Belt, display a large binary fraction with a propensity for near equal-mass components and provide a previously unexplored population of planetesimals which are likely to exist around white dwarfs. Here we simulate the dynamical evolution of equal-mass binary asteroid systems around white dwarfs using the N-body integrator REBOUND for 1 Gyr. We confirm that giant planets are efficient at dissociating and ejecting binary asteroid systems on eccentric orbits, while Earth-mass planets are better at keeping planetesimals in their planetary systems. We find binary systems can be dissociated and ejected from their systems across Myr timescales, producing interstellar objects. We do not expect a population of free-floating binary asteroid systems as all ejected planetesimals are gravitationally unbound from each other. Further, we discuss the influence of asteroid binarity on the white dwarf pollution process and find there is little to no impact on how close a body can get to a star. However, the orbital evolution of binary asteroids changes the distribution of planetesimals available in a white dwarf planetary system to be further scattered onto white dwarf polluting orbits., Accepted for publication in MNRAS

Many potential mechanisms for delivering planetary debris to within a few Roche radii of white dwarfs rely on gravitational scattering events that feature perturbers which are giant planets or terrestrial planets. However, the population of these planets orbiting white dwarfs is still unknown, and for a substantial fraction of white dwarfs the largest planetary survivors of stellar evolution may be sub-terrestrial mass minor planets. Here, we attempt to identify the smallest mass perturbers that could pollute white dwarfs. Through computationally expensive numerical simulations of both unstable and stable configurations of minor planets, we find that this critical lower bound equals approximately one Luna mass. Further, we find that as this mass limit is approached from above, the typical cooling age at which white dwarf pollution occurs increases. Consequently, there is a two order-of-magnitude range of perturber masses between Earth and its moon that has remained largely unexplored in white dwarf pollution studies, despite the potential formation of thousands of such Luna-sized objects in these systems., Accepted for publication in MNRAS

White dwarfs which exhibit transit signatures of planetary debris and accreted planetary material provide exceptional opportunities to probe the material composition and dynamical structure of planetary systems. Although previous theoretical work investigating the role of minor body disruption around white dwarfs has focussed on spherical bodies, Solar System asteroids can be more accurately modelled as triaxial ellipsoids. Here we present an analytical framework to identify the type of disruption (tidal fragmentation, total sublimation or direct impact) experienced by triaxial asteroids approaching white dwarfs on extremely eccentric (e \sim 1) orbits. This framework is then used to identify the outcomes for simplified Main belt analogues of 100 bodies across five different white dwarf temperatures. We also present an empirical relationship between cooling age and effective temperature for both DA and DB white dwarfs to identify the age of the white dwarfs considered here. We find that using a purely spherical shape model can underestimate the physical size and radial distance at which an asteroid is subjected to complete sublimation, and these differences increase with greater elongation of the body. Contrastingly, fragmentation always occurs in the largest semi-axis of a body and so can be modelled by a sphere of that radius. Both fragmentation and sublimation are greatly affected by the body's material composition, and hence by the composition of their progenitor asteroid belts. The white dwarf temperature, and hence cooling age, can affect the expected debris distribution: higher temperatures sublimate large elongated asteroids, and cooler temperatures accommodate more direct impacts., Comment: Accepted for publication in MNRAS

The noteworthy four-planet HR 8799 system teeters on the brink of gravitational instability and contains an A-type host star which is characteristic of the progenitors of the majority of known white dwarf planetary system hosts. Gozdziewski and Migaszewski (2020) have demonstrated that the system can retain all four planets for at least 1 Gyr along the main sequence if the planets evolve within an externally unperturbed 8:4:2:1 mean motion resonance configuration. Here we propagate forward their most stable fit beyond the main sequence, and incorporate external effects from Galactic tides and stellar flybys. We find that (i) giant branch mass loss always breaks the resonance, and usually triggers the ejection of two of the planets, (ii) stellar flybys and Galactic tides rarely break the resonance during the main-sequence and giant branch phases, but play a crucial role in determining the final planetary configurations around the eventual white dwarf host star, and (iii) the meanderings of the surviving planets vary significantly, occupying regions from under 1 au to thousands of au. The ubiquitous survival of at least one planet and the presence of the debris discs in the system should allow for dynamical pathways for the white dwarf to be metal-polluted., Accepted for publication in MNRAS

Pollution of white dwarf atmospheres may be caused by asteroids that originate from the locations of secular and mean-motion resonances in planetary systems. Asteroids in these locations experience increased eccentricity, leading to tidal disruption by the white dwarf. We examine how the $\nu_6$ secular resonance shifts outwards into a previously stable region of the asteroid belt, as the star evolves to a white dwarf. Analytic secular models require a planet to be engulfed in order to shift the resonance. We show with numerical simulations that as a planet gets engulfed by the evolving star, the secular resonance shifts and the rate of tidal disruption events increases with the engulfed planet's mass and its orbital separation. We also investigate the behaviour of mean-motion resonances. The width of a mean-motion resonance increases as the star loses mass and becomes a white dwarf. The $\nu_6$ secular resonance is more efficient at driving tidal disruptions than mean-motion resonances with Jupiter. By examining 230 observed exoplanetary systems whose central star will evolve into a white dwarf, we find that along with an Earth mass planet at $1\,\rm au$, hot Jupiters at a semi--major axis $a\gtrsim 0.05\,\rm au$ and super--Earths of mass $10\,\rm M_\oplus$ at $a\gtrsim 0.3\,\rm au$ represent planet types whose engulfment shifts resonances enough to cause pollution of the white dwarfs to a degree in agreement with observations., Comment: 13 pages, 10 figues, Accepted for publication in MNRAS

White dwarfs with emission lines from gaseous debris discs are among the rarest examples of planetary remnant hosts, but at the same time they are key objects for studying the final evolutionary stage of planetary systems. Making use of the large number of white dwarfs identified in Gaia DR2, we are conducting a survey of planetary remnants and here we present the first results of our search: six white dwarfs with gaseous debris discs. This first publication focuses on the main observational properties of these objects and highlights their most unique features. Three systems in particular stand out: WDJ084602.47+570328.64 displays an exceptionally strong infrared excess which defies the standard model of a geometrically-thin, optically-thick dusty debris disc; WDJ213350.72+242805.93 is the hottest gaseous debris disc host known with Teff=29282 K; and WDJ052914.32-340108.11, in which we identify a record number of 51 emission lines from five elements. These discoveries shed light on the underlying diversity in gaseous debris disc systems and bring the total number of these objects to 21. With these numbers we can now start looking at the properties of these systems as a class of objects rather than on a case-by-case basis., 20 pages, 11 figures, accepted for publication in MNRAS. V2 replaced Fig.10 and minor changes to sections 4 and 7

Metal pollution in white dwarf photospheres originates from the accretion of some combination of planets, moons, asteroids, comets, boulders, pebbles and dust. When large bodies reside in dynamically stagnant locations -- unable themselves to pollute nor even closely approach the white dwarf -- then smaller reservoirs of impact debris may become a complementary or the primary source of metal pollutants. Here, we take a first step towards exploring this possibility by computing limits on the recoil mass that escapes the gravitational pull of the target object following a single impact onto an atmosphere-less surface. By considering vertical impacts only with the full-chain analytical prescription from Kurosawa & Takada (2019), we provide lower bounds for the ejected mass for basalt, granite, iron and water-rich target objects across the radii range 10^{0-3} km. Our use of the full-chain prescription as opposed to physical experiments or hydrocode simulations allows us to quickly sample a wide range of parameter space appropriate to white dwarf planetary systems. Our numerical results could be used in future studies to constrain freshly-generated small debris reservoirs around white dwarfs given a particular planetary system architecture, bombardment history, and impact geometries., Accepted for publication in MNRAS

White dwarfs containing orbiting planetesimals or their debris represent crucial benchmarks by which theoretical investigations of post-main-sequence planetary systems may be calibrated. The photometric transit signatures of likely planetary debris in the ZTF J0139+5245 white dwarf system has an orbital period of about 110 days. An asteroid which breaks up to produce this debris may spin itself to destruction through repeated close encounters with the star without entering its Roche radius and without influence from the white dwarf's luminosity. Here, we place coupled constraints on the orbital pericentre ($q$) and the ratio ($\beta$) of the middle to longest semiaxes of a triaxial asteroid which disrupts outside of this white dwarf's Roche radius ($r_{\rm Roche}$) soon after attaining its 110-day orbit. We find that disruption within tens of years is likely when $\beta \lesssim 0.6$ and $q\approx 1.0-2.0r_{\rm Roche}$, and when $\beta \lesssim 0.2$ out to $q\approx 2.5r_{\rm Roche}$. Analysing the longer-timescale disruption of triaxial asteroids around ZTF J0139+5245 is desirable but may require either an analytical approach relying on ergodic theory or novel numerical techniques., Comment: Accepted for publication in MNRAS

Previous investigations have revealed that eccentric super-Earths represent a class of planets which are particularly effective at transporting minor bodies towards white dwarfs and subsequently polluting their atmospheres with observable chemical signatures. However, the lack of discoveries of these planets beyond a few astronomical units from their host stars prompts a better understanding of their orbital architectures from their nascent birth cluster. Here, we perform stellar cluster simulations of 3-planet and 7-planet systems containing super-Earths on initially circular, coplanar orbits. We adopt the typical stellar masses of main-sequence progenitors of white dwarfs ($1.5\,\mathrm{M}_{\odot}$-$2.5\,\mathrm{M}_{\odot}$) as host stars and include 8,000 main-sequence stars following a Kroupa initial mass function in our clusters. Our results reveal that about 30 per cent of the simulated planets generate eccentricities of at least 0.1 by the time of cluster dissolution, which would aid white dwarf pollution. We provide our output parameters to the community for potential use as initial conditions for subsequent evolution simulations., 16 pages, 18 figures, accepted for publication in MNRAS

The atmospheres of a large proportion of white dwarf stars are polluted by heavy elements that are expected to sink out of visible layers on short timescales. This has been interpreted as a signature of ongoing accretion of debris from asteroids, comets, and giant planets. This scenario is supported by the detection of debris discs and transits of planetary fragments around some white dwarfs. However, photospheric metals are only indirect evidence for ongoing accretion, and the inferred accretion rates and parent body compositions heavily depend on models of diffusion and mixing processes within the white dwarf atmosphere. Here we report a 4.4$\sigma$ detection of X-rays from a polluted white dwarf, G29$-$38, using a 106 ks exposure with the Chandra X-ray Observatory, demonstrating directly that the star is currently accreting. From the measured X-ray luminosity, we find an instantaneous accretion rate of $\dot{M_{\rm X}}=1.63^{+1.29}_{-0.40}\times 10^{9}\mathrm{\,g\,s^{-1}}$. This is the first direct measurement of the accretion rate onto the white dwarf, which is independent of stellar atmosphere models. This rate exceeds estimates based on past studies of the photospheric abundances by more than a factor two, and implies that convective overshoot has to be accounted for in modelling the spectra of debris-accreting white dwarfs. We measure a low plasma temperature of $kT=0.5\pm0.2\,\mathrm{keV}$, corroborating the predicted bombardment solution for white dwarfs accreting at low accretion rates. Offering a new method for studying evolved planetary systems, these observations provide the opportunity to independently measure the instantaneous accretion rate of planetary material, and therefore investigate the timescale of accretion onto white dwarfs, and the evolution and replenishment of debris disks., Comment: Author submitted version. Published in Nature, Feb 10 2022 issue

How might an advanced alien civilization manipulate the orbits within a planetary system to create a durable signpost that communicates its existence? While it is still debated whether such a purposeful advertisement would be prudent and wise, we propose that mean-motion resonances between neighboring planets -- with orbital periods that form integer ratios -- could in principle be used to encode simple sequences that one would not expect to form in nature. In this Letter we build four multi-resonant planetary systems and test their long-term orbital stability. The four systems each contain 6 or 7 planets and consist of: (i) consecutive integers from 1 to 6; (ii) prime numbers from 2 to 11; (iii) the Fibonacci sequence from 1 to 13; and (iv) the Lazy Caterer sequence from 1 to 16. We built each system using N-body simulations with artificial migration forces. We evaluated the stability of each system over the full 10 Gyr integration of the Sun's main sequence phase. We then tested the stability of these systems for an additional 10 Gyr, during and after post-main sequence evolution of the central stars (assumed to be Sun-like) to their final, white dwarf phase. The only system that was destabilized was the consecutive integer sequence (system i). The other three sequences therefore represent potential SETI beacons., Comment: Updated acknowledgements. 6 pages, 2 figures, 1 table, accepted for publication in MRNAS

The dynamical excitation of asteroids due to mean motion resonant interactions with planets is enhanced when their parent star leaves the main sequence. However, numerical investigation of resonant outcomes within post-main-sequence simulations is computationally expensive, limiting the extent to which detailed resonant analyses have been performed. Here, we combine the use of a high-performance computer cluster and the general semianalytical libration width formulation of Gallardo et al. (2021) in order to quantify resonant stability, strength and variation instigated by stellar evolution for a single-planet system containing asteroids on both crossing and non-crossing orbits. We find that resonant instability can be accurately bound with only main-sequence values by computing a maximum libration width as a function of asteroid longitude of pericentre. We also quantify the relative efficiency of mean motion resonances of different orders to stabilize versus destabilize asteroid orbits during both the giant branch and white dwarf phases. The 4:1, 3:1 and 2:1 resonances represent efficient polluters of white dwarfs, and even when in the orbit-crossing regime, both the 4:3 and 3:2 resonances can retain small reservoirs of asteroids in stable orbits throughout giant branch and white dwarf evolution. This investigation represents a preliminary step in characterising how simplified extrasolar Kirkwood gap structures evolve beyond the main-sequence., Comment: Accepted for publication in MNRAS

The presence of planetary material in white dwarf atmospheres, thought to be accreted from a dusty debris disc produced via the tidal disruption of a planetesimal, is common. Approximately five per cent of these discs host a co-orbital gaseous component detectable via emission from atomic transitions - usually the 8600 Angstrom CaII triplet. These emission profiles can be highly variable in both morphology and strength. Furthermore, the morphological variations in a few systems have been shown to be periodic, likely produced by an apsidally precessing asymmetric disc. Of the known gaseous debris discs, that around HE1349-2305 has the most rapidly evolving emission line morphology, and we present updated spectroscopy of the CaII triplet of this system. The additional observations show that the emission line morphologies vary periodically and consistently, and we constrain the period to two aliases of 459$\pm$3d and 502$\pm$3d. We produce images of the CaII triplet emission from the disc in velocity space using Doppler tomography - only the second such imaging of a white dwarf debris disc. We suggest that the asymmetric nature of these velocity images is generated by gas moving on eccentric orbits with radially-dependent excitation conditions via photo-ionisation from the white dwarf. We also obtained short-cadence (~ 4 min) spectroscopy to search for variability on the time-scale of the disc's orbital period (~ hours) due to the presence of a planetesimal, and rule out variability at a level of ~ 1.4 per cent., Comment: 14 Pages, 10 Figures, accepted for publication in MNRAS

White dwarf planetary science is a rapidly growing field of research featuring a diverse set of observations and theoretical explorations. Giant planets, minor planets, and debris discs have all been detected orbiting white dwarfs. The innards of broken-up minor planets are measured on an element-by-element basis, providing a unique probe of exoplanetary chemistry. Numerical simulations and analytical investigations trace the violent physical and dynamical history of these systems from astronomical unit (au)-scale distances to the immediate vicinity of the white dwarf, where minor planets are broken down into dust and gas and accrete onto the white dwarf photosphere. Current and upcoming ground-based and space-based instruments are likely to further accelerate the pace of discoveries.

Studies1,2 have shown that the remnants of destroyed planets and debris-disk planetesimals can survive the volatile evolution of their host stars into white dwarfs3,4, but few intact planetary bodies around white dwarfs have been detected5–8. Simulations predict9–11 that planets in Jupiter-like orbits around stars of ≲8 M☉ (solar mass) avoid being destroyed by the strong tidal forces of their stellar host, but as yet, there has been no observational confirmation of such a survivor. Here we report the non-detection of a main-sequence lens star in the microlensing event MOA-2010-BLG-477Lb12 using near-infrared observations from the Keck Observatory. We determine that this system contains a 0.53 ± 0.11 M☉ white-dwarf host orbited by a 1.4 ± 0.3 Jupiter-mass planet with a separation on the plane of the sky of 2.8 ± 0.5 astronomical units, which implies a semi-major axis larger than this. This system is evidence that planets around white dwarfs can survive the giant and asymptotic giant phases of their host’s evolution, and supports the prediction that more than half of white dwarfs have Jovian planetary companions13. Located at approximately 2.0 kiloparsecs towards the centre of our Galaxy, it is likely to represent an analogue to the end stages of the Sun and Jupiter in our own Solar System. © 2021, The Author(s), under exclusive licence to Springer Nature Limited., Data presented in this work were obtained at the W. M. Keck Observatory from telescope time allocated to the National Aeronautics and Space Administration through the agency’s scientific partnership with the California Institute of Technology and the University of California. This work was supported by the University of Tasmania through the UTAS Foundation, ARC grant DP200101909, and the endowed Warren Chair in Astronomy. We acknowledge the support of ANR COLD WORLDS (ANR-18-CE31-0002) at the Institut d’Astrophysique de Paris and the Laboratoire d’Astrophysique de Bordeaux. D.P.B., A.B., N.K., C.R. and S.K.T. were supported by NASA through grant NASA-80NSSC18K0274 and by NASA award no. 80GSFC17M0002. E.B. acknowledges support from NASA grant 80NSSC19K0291. Work by N.K. is supported by JSPS KAKENHI grant no. JP18J00897. C.D. acknowledges financial support from the State Agency for Research of the Spanish MCIU through the ‘Center of Excellence Severo Ochoa’ award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709), and the Group project ref. PID2019-110689RB-I00/AEI/10.13039/501100011033. D.V. gratefully acknowledges the support of the STFC via an Ernest Rutherford Fellowship (grant ST/P003850/1).

The discovery of the intact metallic planetary core fragment orbiting the white dwarf SDSS J1228+1040 within one Solar radius highlights the possibility of detecting larger, unfragmented conducting cores around magnetic white dwarfs through radio emission. Previous models of this decades-old idea focussed on determining survivability of the cores based on their inward Lorentz drift towards the star. However, gravitational tides may represent an equal or dominant force. Here, we couple both effects by assuming a Maxwell rheological model and performing simulations over the entire range of observable white dwarf magnetic field strengths (10^3 -- 10^9 G) and their potential atmospheric electrical conductivities (10^{-1} -- 10^4 S/m) in order to more accurately constrain survivability lifetimes. This force coupling allows us to better pinpoint the physical and orbital parameters which allow planetary cores to survive for over a Gyr, maximizing the possibility that they can be detected. The most robust survivors showcase high dynamic viscosities (>~ 10^{24} Pa*s) and orbit within kG-level magnetic fields., Accepted for publication in MNRAS

Many white dwarf stars show signs of having accreted smaller bodies, implying that they may host planetary systems. A small number of these systems contain gaseous debris discs, visible through emission lines. We report a stable 123.4min periodic variation in the strength and shape of the CaII emission line profiles originating from the debris disc around the white dwarf SDSSJ122859.93+104032.9. We interpret this short-period signal as the signature of a solid body held together by its internal strength., Comment: 11 Figures, 3 Tables

The atmospheres of a large proportion of white dwarf stars are polluted by heavy elements

Accompanying the mounting detections of planets orbiting white dwarfs and giant stars are questions about their physical history and evolution, particularly regarding detectability of their atmospheres and potential for habitability. Here we determine how the size of planetary magnetospheres evolve over time from the end of the main sequence through to the white dwarf phase due to the violent winds of red giant and asymptotic giant branch stars. By using a semianalytic prescription, we investigate the entire relevant phase space of planet type, planet orbit and stellar host mass (1-7Msun). We find that a planetary magnetosphere will always be quashed at some point during the giant branch phases unless the planet's magnetic field strength is at least two orders of magnitude higher than Jupiter's current value. We also show that the time variation of the stellar wind and density generates a net increase in wind ram pressure and does not allow a magnetosphere to be maintained at any time for field strengths less than 10^{-5} T (0.1 G). This lack of protection hints that currently potentially habitable planets orbiting white dwarfs would have been previously inhospitable., Accepted for publication in MNRAS

We promote the teaching of mass functions as an integral part of an interdisciplinary science education. Mass functions characterize the frequency distributions of objects with different masses on all cosmic scales. We intend to enhance experiential learning of this concept with a creative LEGO brick experiment for a diverse student audience. To our surprise, the LEGO mass function is not only qualitatively but also quantitatively comparable to mass functions found across the Universe. We also discuss the relation between gravitation and mass distributions as a possible explanation for the continuity of the universal mass function., This is the version of the article before peer review and submission. The published version is Kautsch, Veras, & Hansotia 2021, European Journal of Physics, 42, 035605, https://doi.org/10.1088/1361-6404/abe75c

Few solar system asteroids and comets are found in high-eccentricity orbits (e > 0.9), but in the primordial planetesimal disks and in exoplanet systems around dying stars such objects are believed to be common. For 2006 HY51, the main belt asteroid with the highest known eccentricity 0.9684, we investigate the probable rotational states today using our computer-efficient chaotic process simulation method. Starting with random initial conditions, we find that this asteroid is inevitably captured into stable spin–orbit resonances typically within tens to a hundred megayears. The resonances are confirmed by direct integration of the equation of motion in the vicinity of endpoints. Most resonances are located at high spin values above 960 times the mean motion (such as 964:1 or 4169:4), corresponding to rotation periods of a few days. We discover three types of resonance in the high-eccentricity regime: (1) regular circulation with weakly librating aphelion velocities and integer-number spin–orbit commensurabilities, (2) switching resonances of higher order with orientation alternating between aligned (0 or π) and sidewise (π/2) angles at aphelia and perihelia, (3) jumping resonances with aphelion spin alternating between two quantum states in the absence of spin–orbit commensurability. The islands of equilibrium are numerous at high spin rates but small in parameter space area, so that it takes millions of orbits of chaotic wandering to accidentally entrap in one of them. We discuss the implications of this discovery for the origins and destiny of high-eccentricity objects and the prospects of extending this analysis to the full 3D treatment.

Our knowledge of white dwarf planetary systems predominately arises from the region within a few Solar radii of the white dwarfs, where minor planets break up, form rings and discs, and accrete onto the star. The entry location, angle and speed into this Roche sphere has rarely been explored but crucially determines the initial geometry of the debris, accretion rates onto the photosphere, and ultimately the composition of the minor planet. Here we evolve a total of over 10^5 asteroids with single-planet N-body simulations across the giant branch and white dwarf stellar evolution phases to quantify the geometry of asteroid injection into the white dwarf Roche sphere as a function of planetary mass and eccentricity. We find that lower planetary masses increase the extent of anisotropic injection and decrease the probability of head-on (normal to the Roche sphere) encounters. Our results suggest that one can use dynamical activity within the Roche sphere to make inferences about the hidden architectures of these planetary systems., Accepted for publication in MNRAS

Of the 21 known gaseous debris discs around white dwarfs, a large fraction of them display observational features that are well described by an eccentric distribution of gas. In the absence of embedded objects or additional forces, these discs should not remain eccentric for long timescales, and should instead circularise due to viscous spreading. The metal pollution and infrared excess we observe from these stars is consistent with the presence of tidally disrupted sub-stellar bodies. We demonstrate, using smoothed particle hydrodynamics, that a sublimating or partially disrupting planet on an eccentric orbit around a white dwarf will form and maintain a gas disc with an eccentricity within 0.1 of, and lower than, that of the orbiting body. We also demonstrate that the eccentric gas disc observed around the white dwarf SDSS J1228+1040 can be explained by the same hypothesis., 5 pages, 5 figures, accepted to MNRAS Letters

White dwarfs with metal-polluted atmospheres have been studied widely in the context of the accretion of rocky debris from evolved planetary systems. One open question is the geometry of accretion and how material arrives and mixes in the white dwarf surface layers. Using the 3D radiation-hydrodynamics code CO$^5$BOLD, we present the first transport coefficients in degenerate star atmospheres which describe the advection-diffusion of a passive scalar across the surface-plane. We couple newly derived horizontal diffusion coefficients with previously published vertical diffusion coefficients to provide theoretical constraints on surface spreading of metals in white dwarfs. Our grid of 3D simulations probes the vast majority of the parameter space of convective white dwarfs, with pure-hydrogen atmospheres in the effective temperature range 6000-18000 K and pure-helium atmospheres in the range 12000-34000 K. Our results suggest that warm hydrogen-rich atmospheres (DA; $\gtrsim$13000 K) and helium-rich atmospheres (DB, DBA; $\gtrsim$30000 K) are unable to efficiently spread the accreted metals across their surface, regardless of the time dependence of accretion. This result may be at odds with the current non-detection of surface abundance variations at white dwarfs with debris discs. For cooler hydrogen- and helium-rich atmospheres, we predict a largely homogeneous distribution of metals across the surface within a vertical diffusion timescale. This is typically less than 0.1 per cent of disc lifetime estimates, a quantity which is revisited in this paper using the overshoot results. These results have relevance for studies of the bulk composition of evolved planetary systems and models of accretion disc physics., Comment: Accepted for publication in MNRAS. 22 pages, 17 figures

A widely-held assumption is that each single white dwarf containing observable rocky debris requires the presence of at least one terrestrial or giant planet to have gravitationally perturbed the progenitor of the debris into the star. However, these planets could have been previously been engulfed by the star or escaped the system, leaving behind asteroids, boulders, cobbles, pebbles, sand and dust. These remaining small bodies could then persist throughout the host star's evolution into a white dwarf at ~2-100 au scales, and then be radiatively dragged into the white dwarf without the help of a planet. Here we identify the parameter space and cooling ages for which this one metal-pollution mechanism is feasible by, for the first time, coupling Poynting-Robertson drag, the Yarkovsky effect and the YORP effect solely from rapidly dimming white dwarf radiation. We find that this no-planet pollution scenario is efficient for remnant 10^{-5}-10^{-4} m dust up to about 80 au, 10^{-4}-10^{-3} m sand up to about 25 au and 10^{-3}-10^{-2} m small pebbles up to about 8 au, and perhaps 10^{-1}-10^{0} m small boulders up to tens of au. Further, young white dwarf radiation can spin up large strength-less boulders with radii 10^{2}-10^{3} m to destruction, breaking them down into smaller fragments which then can be dragged towards the white dwarf. Our work hence introduces a planet-less metal-pollution mechanism that may be active in some fraction of white dwarf planetary systems., Comment: Accepted for publication in MNRAS

Identifying planets around O-type and B-type stars is inherently difficult; the most massive known planet host has a mass of only about 3 M⊙ . However, planetary systems which survive the transformation of their host stars into white dwarfs can be detected via photospheric trace metals, circumstellar dusty and gaseous discs, and transits of planetary debris crossing our line of sight. These signatures offer the potential to explore planet formation efficiency and chemical composition for host stars with masses up to the core-collapse boundary at ≈ 8 M⊙ , a mass regime rarely investigated in planet formation theory. Here, we establish limits on where both major and minor planets must reside around ≈ 6–8 M⊙ stars in order to survive into the white dwarf phase. For this mass range, we find that intact terrestrial or giant planets need to leave the main sequence beyond approximate minimum star–planet separations of, respectively, about 3 and 6 au, as shown here: Further, in these systems, rubble pile minor planets of radii 10, 1.0, and 0.1 km would have been shorn apart by giant branch radiative YORP spin-up if they formed and remained within, respectively, tens, hundreds, and thousands of au, as shown here: Overall, we find that planet formation around 6 M⊙-8 M⊙ stars may be feasible, and hence we encourage dedicated planet formation investigations for these systems.

Robust evidence of an ice giant planet shedding its atmosphere around the white dwarf WD J0914+1914 represents a milestone in exoplanetary science, allowing us to finally supplement our knowledge of white dwarf debris discs, minor planets and metal pollution with the presence of a major planet. Here, I discuss the possible dynamical origins of this planet, WD J0914+1914 b. The very young cooling age of the host white dwarf (13 Myr) combined with the currently estimated planet-star separation of about 0.07 au imposes particularly intriguing and restrictive coupled constraints on its current orbit and its tidal dissipation characteristics. The planet must have been scattered from a distance of at least a few au to its current location, requiring the current or former presence of at least one more major planet in the system in the absence of a hidden binary companion. I show that WD J0914+1914 b could not have subsequently shrunk its orbit through chaotic f-mode tidal excitation (characteristic of such highly eccentric orbits) unless the planet was or is highly inflated and possibly had partially thermally self-disrupted from mode-based energy release. I also demonstrate that if the planet is currently assumed to reside on a near-circular orbit at 0.07 au, then non-chaotic equilibrium tides impose unrealistic values for the planet's tidal quality factor. I conclude that WD J0914+1914 b either (i) actually resides interior to 0.07 au, (ii) resembles a disrupted `Super-Puff' whose remains reside on a circular orbit, or (iii) resembles a larger or denser ice giant on a currently eccentric orbit. Distinguishing these three possibilities strongly motivates follow-up observations. I will also analyse the prospects for exterior extant rocky asteroids, boulders, cobbles, and pebbles to radiatively drift inward past the planet due to the relatively high luminosity of this particularly young white dwarf, and I will place stability bounds on the gas disc formed from the planet's evaporated atmosphere. Caption: Demonstration that WD J0914+1914 b was very unlikely to have experienced high-eccentricity chaotic tidal evolution unless the planet is or was a highly inflated Super-Puff. The solid curves represent the minimum initial semimajor axes (y-axis) for which different types of planets would have experienced chaotic tidal evolution around the white dwarf for given orbital pericentres (x-axes). The vertical dashed lines are representative white dwarf tidal disruption radii for each type of planet, ordered from left to right in the same way as the solid curves. Because Super-Puffs are particularly vunerable to self-disruption through chaotic tides, current observations may be of a partially or fully disrupted ice giant.

We report the discovery of the transiting exoplanet NGTS-12b by the Next Generation Transit Survey (NGTS). The host star, NGTS-12, is a V=12.38 mag star with an effective temperature of T$_{\rm eff}$=$5690\pm130$ K. NGTS-12b orbits with a period of $P=7.53$d, making it the longest period planet discovered to date by the main NGTS survey. We verify the NGTS transit signal with data extracted from the TESS full-frame images, and combining the photometry with radial velocity measurements from HARPS and FEROS we determine NGTS-12b to have a mass of $0.208\pm0.022$ M$_{J}$ and a radius of $1.048\pm0.032$ R$_{J}$. NGTS-12b sits on the edge of the Neptunian desert when we take the stellar properties into account, highlighting the importance of considering both the planet and star when studying the desert. The long period of NGTS-12b combined with its low density of just $0.223\pm0.029$ g cm$^{-3}$ make it an attractive target for atmospheric characterization through transmission spectroscopy with a Transmission Spectroscopy Metric of 89.4., Comment: Accepted for publication in MNRAS, 11 pages

Asteroids and other small celestial bodies have markedly prolate shapes, and the perturbative triaxial torques which are applied during pericenter passages in highly eccentric orbits trigger and sustain a state of chaotic rotation. Because the prograde spin rate around the principal axis of inertia is not bounded from above, it can accidentally reach the threshold value corresponding to rotational break-up. Previous investigations of this process were limited to integrations of $\sim 10^3$ orbits because of the stiff equation of motion. We present here a fast 1D simulation method to compute the evolution of this spin rate over $\sim 10^9$ orbits. We apply the method to the most eccentric solar system asteroid known, 2006 HY51 (with $e = 0.9684$), and find that for any reasonably expected shape parameters, it can never be accelerated to break-up speed. However, primordial solar system asteroids on more eccentric orbits may have already broken up from this type of rotational fission. The method also represents a promising opportunity to investigate the long-term evolution of extremely eccentric triaxial exo-asteroids ($e > 0.99$), which are thought to be common in white dwarf planetary systems, Accepted in ApJ. The computer-heavier version of chaotic rotation simulation with reparameterization is available as a Julia code at https://github.com/agoldin/2006HY51

The lifetime of a planetary disc which orbits a white dwarf represents a crucial input parameter into evolutionary models of that system. Here we apply a purely analytical formalism to estimate lifetimes of the debris phase of these discs, before they are ground down into dust or are subject to sublimation from the white dwarf. We compute maximum lifetimes for three different types of white dwarf discs, formed from (i) radiative YORP breakup of exo-asteroids along the giant branch phases at 2-100 au, (ii) radiation-less spin-up disruption of these minor planets at $\sim 1.5-4.5R_{\odot}$, and (iii) tidal disruption of minor or major planets within about $1.3R_{\odot}$. We display these maximum lifetimes as a function of disc mass and extent, constituent planetesimal properties, and representative orbital excitations of eccentricity and inclination. We find that YORP discs with masses up to $10^{24}$ kg live long enough to provide a reservoir of surviving cm-sized pebbles and m- to km-sized boulders that can be perturbed intact to white dwarfs with cooling ages of up to 10 Gyr. Debris discs formed from the spin or tidal disruption of these minor planets or major planets can survive in a steady state for up to respectively 1 Myr or 0.01 Myr, although most tidal discs would leave a steady state within about 1 yr. Our results illustrate that dust-less planetesimal transit detections are plausible, and would provide particularly robust evolutionary constraints. Our formalism can easily be adapted to individual systems and future discoveries., Accepted for publication in MNRAS

Escalating observations of exo-minor planets and their destroyed remnants both passing through the solar system and within white dwarf planetary systems motivate an understanding of the orbital history and fate of exo-Kuiper belts and planetesimal discs. Here we explore how the structure of a 40-1000 au annulus of planetesimals orbiting inside of a solar system analogue that is itself initially embedded within a stellar cluster environment varies as the star evolves through all of its stellar phases. We attempt this computationally challenging link in four parts: (1) by performing stellar cluster simulations lasting 100 Myr, (2) by making assumptions about the subsequent quiescent 11 Gyr main-sequence evolution, (3) by performing simulations throughout the giant branch phases of evolution, and (4) by making assumptions about the belt's evolution during the white dwarf phase. Throughout these stages, we estimate the planetesimals' gravitational responses to analogues of the four solar system giant planets, as well as to collisional grinding, Galactic tides, stellar flybys, and stellar radiation. We find that the imprint of stellar cluster dynamics on the architecture of $\gtrsim 100$ km-sized exo-Kuiper belt planetesimals is retained throughout all phases of stellar evolution unless violent gravitational instabilities are triggered either (1) amongst the giant planets, or (2) due to a close ($\ll 10^3$ au) stellar flyby. In the absence of these instabilities, these minor planets simply double their semimajor axis while retaining their primordial post-cluster eccentricity and inclination distributions, with implications for the free-floating planetesimal population and metal-polluted white dwarfs., Comment: Accepted for publication in MNRAS

Robust evidence of an ice giant planet shedding its atmosphere around the white dwarf WD J0914+1914 represents a milestone in exoplanetary science, allowing us to finally supplement our knowledge of white dwarf metal pollution, debris discs and minor planets with the presence of a major planet. Here, we discuss the possible dynamical origins of this planet, WD J0914+1914 b. The very young cooling age of the host white dwarf (13 Myr) combined with the currently estimated planet-star separation of about 0.07 au imposes particularly intriguing and restrictive coupled constraints on its current orbit and its tidal dissipation characteristics. The planet must have been scattered from a distance of at least a few au to its current location, requiring the current or former presence of at least one more major planet in the system in the absence of a hidden binary companion. We show that WD J0914+1914 b could not have subsequently shrunk its orbit through chaotic f-mode tidal excitation (characteristic of such highly eccentric orbits) unless the planet was or is highly inflated and possibly had partially thermally self-disrupted from mode-based energy release. We also demonstrate that if the planet is currently assumed to reside on a near-circular orbit at 0.07 au, then non-chaotic equilibrium tides impose unrealistic values for the planet's tidal quality factor. We conclude that WD~J0914+1914~b either (i) actually resides interior to 0.07 au, (ii) resembles a disrupted "Super-Puff" whose remains reside on a circular orbit, or (iii) resembles a larger or denser ice giant on a currently eccentric orbit. Distinguishing these three possibilities strongly motivates follow-up observations., Comment: Accepted for publication in MNRAS

Identifying planets around O-type and B-type stars is inherently difficult; the most massive known planet host has a mass of only about $3\, \mathrm{M}_{\odot }$. However, planetary systems which survive the transformation of their host stars into white dwarfs can be detected via photospheric trace metals, circumstellar dusty and gaseous discs, and transits of planetary debris crossing our line of sight. These signatures offer the potential to explore the efficiency of planet formation for host stars with masses up to the core-collapse boundary at $\approx 8\, \mathrm{M}_{\odot }$, a mass regime rarely investigated in planet formation theory. Here, we establish limits on where both major and minor planets must reside around $\approx 6\rm {-}8\, \mathrm{M}_{\odot }$ stars in order to survive into the white dwarf phase. For this mass range, we find that intact terrestrial or giant planets need to leave the main sequence beyond approximate minimum star–planet separations of, respectively, about 3 and 6 au. In these systems, rubble pile minor planets of radii 10, 1.0, and 0.1 km would have been shorn apart by giant branch radiative YORP spin-up if they formed and remained within, respectively, tens, hundreds, and thousands of au. These boundary values would help distinguish the nature of the progenitor of metal pollution in white dwarf atmospheres. We find that planet formation around the highest mass white dwarf progenitors may be feasible, and hence encourage both dedicated planet formation investigations for these systems and spectroscopic analyses of the highest mass white dwarfs.

Doppler-based planet surveys point to an increasing occurrence rate of giant planets with stellar mass. Such surveys rely on evolved stars for a sample of intermediate-mass stars (so-called retired A stars), which are more amenable to Doppler observations than their main-sequence progenitors. However, it has been hypothesised that the masses of subgiant and low-luminosity red-giant stars targeted by these surveys --- typically derived from a combination of spectroscopy and isochrone fitting --- may be systematically overestimated. Here, we test this hypothesis for the particular case of the exoplanet-host star HD 212771 using K2 asteroseismology. The benchmark asteroseismic mass ($1.45^{+0.10}_{-0.09}\:\text{M}_{\odot}$) is significantly higher than the value reported in the discovery paper ($1.15\pm0.08\:\text{M}_{\odot}$), which has been used to inform the stellar mass-planet occurrence relation. This result, therefore, does not lend support to the above hypothesis. Implications for the fates of planetary systems are sensitively dependent on stellar mass. Based on the derived asteroseismic mass, we predict the post-main-sequence evolution of the Jovian planet orbiting HD 212771 under the effects of tidal forces and stellar mass loss., Accepted for publication in MNRAS; 10 pages, 3 figures, 2 tables

The interstellar object ‘Oumuamua passed through the Solar System in 2017 and exhibited a puzzling combination of physical features. New work tells the story of this visitor.

Over one quarter of white dwarfs contain observable metallic debris from the breakup of exo-asteroids. Understanding the physical and orbital history of this debris would enable us to self-consistently link planetary system formation and fate. One major debris reservoir is generated by YORP-induced rotational fission during the giant branch phases of stellar evolution, where the stellar luminosity can exceed the Sun's by four orders of magnitude. Here, we determine the efficacy of the giant branch YORP effect for asteroids with nonzero internal strength, and model post-fission evolution by imposing simple analytic fragmentation prescriptions. We find that even the highest realistic internal strengths cannot prevent the widespread fragmentation of asteroids and the production of a debris field over 100 au in size. We compute the number of successive fission events as they occur in progressively smaller time intervals as the star ascends the giant branches, providing a way to generate size distributions of asteroid fragments. The results are highly insensitive to progenitor stellar mass. We also conclude that the ease with which giant branch YORP breakup can generate binary asteroid subsystems is strongly dependent on internal strength. Formed binary subsystems in turn could be short-lived due to the resulting luminosity-enhanced BYORP effect., Accepted for publication in MNRAS

The size distribution and orbital architecture of dust, grains, boulders, asteroids, and major planets during the giant branch phases of evolution dictate the preponderance and observability of the eventual debris, which have been found to surround white dwarfs and pollute their atmospheres with metals. Here, we utilize the photogravitational planar restricted three-body problem in one-planet giant branch systems in order to characterize the orbits of grains as the parent star luminosity and mass undergo drastic changes. We perform a detailed dynamical analysis of the character of grain orbits (collisional, escape, or bounded) as a function of location and energy throughout giant branch evolution. We find that for stars with main-sequence masses of $2.0M_{\odot}$, giant branch evolution, combined with the presence of a planet, ubiquitously triggers escape in grains smaller than about 1 mm, while leaving grains larger than about 5 cm bound to the star. This result is applicable for systems with either a terrestrial or giant planet, is largely independent of the location of the planet, and helps establish a radiative size threshold for escape of small particles in giant branch planetary systems., Comment: Published in Astronomy & Astrophysics journal (A&A)

Nearly all known white dwarf planetary systems contain detectable rocky debris in the stellar photosphere. A glaring exception is the young and still evolving white dwarf WD J0914+1914, which instead harbours a giant planet and a disc of pure gas. The stability boundaries of this disc and the future prospects for this white dwarf to be polluted with rocks depend upon the mass and orbit of the planet, which are only weakly constrained. Here we combine an ensemble of plausible planet orbits and masses to determine where observers should currently expect to find the outer boundary of the gas disc. We do so by performing a sweep of the entire plausible phase space with short-term numerical integrations. We also demonstrate that particle-star collisional trajectories, which would lead to the (unseen) signature of rocky metal pollution, occupy only a small fraction of the phase space, mostly limited to particle eccentricities above 0.75. Our analysis reveals that a highly inflated planet on a near-circular orbit is the type of planet which is most consistent with the current observations., Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journal

In about 6 Giga years our Sun will evolve into a red giant and finally end its life as a white dwarf. This stellar metamorphosis will occur to virtually all known host stars of exo-planetary systems and is therefore crucial for their final fate. It is clear that the innermost planets will be engulfed and evaporated during the giant phase and that planets located farther out will survive. However, the destiny of planets in-between, at ~ 1 - 10 au, has not yet been investigated with a multi-planet tidal treatment. We here combine for the first time multi-planet interactions, stellar evolution, and tidal effects in an N-body code to study the evolution of a Neptune-Jupiter planetary system. We report that the fate of the Neptune-mass planet, located closer to the star than the Jupiter-mass planet, can be very different from the fate of a single Neptune. The simultaneous effects of gravitational interactions, mass loss and tides can drive the planetary system towards mean motion resonances. Crossing these resonances affects particularly the eccentricity of the Neptune and thereby also its fate, which can be engulfment, collision with the Jupiter-mass planet, ejection from the system, or survival at a larger separation., Comment: Accepted for publication in ApJL. 10 pages, 5 figures

The WD 1145+017 system shows irregular transit features that are consistent with the tidal disruption of differentiated asteroids with bulk densities $< 4$ g cm$^{-3}$ and bulk masses $\lesssim 10^{21}$ kg (Veras et al., 2017; arXiv:1610.06926). We use the open-source N-body code REBOUND (Rein and Liu, 2011; arXiv:1110.4876) to simulate this disruption with different internal structures: varying the core volume fraction, mantle/core density ratio, and the presence/absence of a thin low-density crust. We allow the rubble pile to partially disrupt and capture lightcurves at a specific point during the disruption at cadences comparable to those from ground-based photometry. As a proof-of-concept we show that varying these structural parameters have observationally distinguishable effects on the transit light curve as the asteroid is disrupted and compare the simulation-generated lightcurves to data from Gary et al., 2017 (arXiv:1608.00026). With the caveat that our simulations do not model the sublimation in detail or account for its effects on orbital evolution, we find that a low core fraction and low mantle/core density ratio asteroid is most consistent with the stable transit feature present for multiple weeks circa April 2016 (referred to as G6121 in Gary et al., 2017 (arXiv:1608.00026) and A1 in Hallakoun et al., 2017 (arXiv:1702.05483). Connecting tidal disruption simulations to photometry suggests characteristics for the interior structure and composition of an exoplanetary body, information that is only possible because we are observing the death of the planetary system in action. All-sky survey missions such as TESS and LSST will be able to detect other systems like WD 1145+017, creating a sample of subjects for a new subfield of planetary science: necroplanetology., Accepted for publication in the Astrophysical Journal on the 11th of March, 2020. 14 pages, 3 figures, 2 tables. Pre-proofs

An ice giant planet was recently reported orbiting white dwarf WD J0914+1914 at an approximate distance of 0.07 au. The striking non-detection of rocky pollutants in this white dwarf's photosphere contrasts with the observations of nearly every other known white dwarf planetary system. Here, I analyze the prospects for exterior extant rocky asteroids, boulders, cobbles and pebbles to radiatively drift inward past the planet due to the relatively high luminosity (0.1 L_Sun) of this particularly young (13 Myr) white dwarf. Pebbles and cobbles drift too slowly from Poynting-Robertson drag to bypass the planet, but boulders and asteroids are subject to the much stronger Yarkovsky effect. In this paper, I (i) place lower limits on the timescales for these objects to reach the planet's orbit, (ii) establish 3 m as the approximate limiting radius above which a boulder drifts too slowly to avoid colliding with the planet, and (iii) compute bounds on the fraction of boulders which succeed in traversing mean motion resonances and the planet's Hill sphere to eventually pollute the star. Overall, I find that the planet acts as a barrier against rather than a facilitator for radiatively-driven rocky pollution, suggesting that future rocky pollutants would most likely originate from distant scattering events., Comment: Accepted for publication in MNRAS

The discovery of numerous debris disks around white dwarfs (WDs), gave rise to extensive study of such disks and their role in polluting WDs, but the formation and evolution of these disks is not yet well understood. Here we study the role of aeolian (wind) erosion in the evolution of solids in WD debris disks. Aeolian erosion is a destructive process that plays a key role in shaping the properties and size-distribution of planetesimals, boulders and pebbles in gaseous protoplanetary disks. Our analysis of aeolian erosion in WD debris disks shows it can also play an important role in these environments. We study the effects of aeolian erosion under different conditions of the disk, and its erosive effect on planetesimals and boulders of different sizes. We find that solid bodies smaller than $\sim 5 \rm{km}$ will be eroded within the short disk lifetime. We compare the role of aeolian erosion in respect to other destructive processes such as collisional fragmentation and thermal ablation. We find that aeolian erosion is the dominant destructive process for objects with radius $\lesssim 10^3 \rm{cm}$ and at distances $\lesssim 0.6 R_\odot$ from the WD. Thereby, aeolian erosion constitutes the main destructive pathway linking fragmentational collisions operating on large objects with sublimation of the smallest objects and Poynting-Robertson drag, which leads to the accretion of the smallest particles onto the photosphere of WDs, and the production of polluted WDs., Comment: Accepted to MNRAS