Hill Sphere Research Articles

Contracting and Expanding Binary Black Holes in 3D Low-mass AGN Disks: The Importance of Separation

LIGO/Virgo has detected several binary black hole (BBH) merger events that may have originated in the accretion disks of active galactic nuclei (AGNs). These events require individual black hole masses that fall within the pair instability supernova mass gap, and therefore these black holes may have been grown from hierarchical mergers. AGN disks are a prime environment for hierarchical mergers and thus a potential location for the progenitors of BBH gravitational wave events. Understanding how a BBH embedded in an AGN disk interacts with the surrounding environment is thus crucial for determining whether this interaction can lead to its merger. However, there are few high-fidelity simulations of this process, and almost all are two-dimensional. We present the results from 3D, high-resolution, local shearing-box simulations of an embedded BBH interacting with an AGN disk. In these first simulations of their kind, we focus on determining the mass accretion rate and the orbital evolution rate at different BBH separations. We find that circular, equal-mass BBHs with separations greater than 10% of their Hill radius contract while accreting at a super-Eddington rate. At smaller separations, however, our 3D simulations find that BBHs expand their orbits. This result suggests that it may be difficult for an AGN disk to push a BBH to merger, but we discuss several mechanisms, including MHD turbulence and radiative and mechanical feedback, which could alleviate this difficulty.

Directly detecting the envelopes of low-mass planets embedded in protoplanetary discs and the case for TW Hydrae

ABSTRACT Despite many methods developed to find young massive planets in protoplanetary discs, it is challenging to directly detect low-mass planets that are embedded in discs. On the other hand, the core-accretion theory suggests that there could be a large population of embedded low-mass young planets at the Kelvin-Helmholtz (KH) contraction phase. We adopt both 1D models and 3D simulations to calculate the envelopes around low-mass cores (several to tens of M⊕) with different luminosities, and derive their thermal fluxes at radio wavelengths. We find that, when the background disc is optically thin at radio wavelengths, radio observations can see through the disc and probe the denser envelope within the planet’s Hill sphere. When the optically thin disc is observed with the resolution reaching one disc scale height, the radio thermal flux from the planetary envelope around a 10 M⊕ core is more than 10 per cent higher than the flux from the background disc. The emitting region can be extended and elongated. Finally, our model suggests that the au-scale clump at 52 au in the TW Hydrae disc revealed by ALMA is consistent with the envelope of an embedded 10–20 M⊕ planet, which can explain the detected flux, the spectral index dip, and the tentative spirals. The observation is also consistent with the planet undergoing pebble accretion. Future ALMA and ngVLA observations may directly reveal more such low-mass planets, enabling us to study core growth and even reconstruct the planet formation history using the embedded ‘protoplanet’ population.

Delivery of Gas onto the Circumplanetary Disk of Giant Planets: Planetary-mass Dependence of the Source Region of Accreting Gas and Mass Accretion Rate

Gas accretion onto the circumplanetary disks and the source region of accreting gas are important to reveal dust accretion that leads to satellite formation around giant planets. We performed local three-dimensional high-resolution hydrodynamic simulations of an isothermal and inviscid gas flow around a planet to investigate the planetary-mass dependence of the gas accretion bandwidth and gas accretion rate onto circumplanetary disks. We examined cases with various planetary masses corresponding to M p = 0.05–1M Jup at 5.2 au, where M Jup is the current Jovian mass. We found that the radial width of the gas accretion band is proportional to for the low-mass regime with M p ≲ 0.2M Jup while it is proportional to M p for the high-mass regime with M p ≳ 0.2M Jup. We found that the ratio of the mass accretion rate onto the circumplanetary disk to that into the Hill sphere is about 0.4 regardless of the planetary mass for the cases we examined. Combining our results with the gap model obtained from global hydrodynamic simulations, we derive a semi-analytical formula of mass accretion rate onto circumplanetary disks. We found that the mass dependence of our three-dimensional accretion rates is the same as the previously obtained two-dimensional case, although the qualitative behavior of accretion flow onto the circumplanetary disk is quite different between the two cases.

Long-term Evolution of Tightly Packed Stellar Black Holes in AGN Disks: Formation of Merging Black Hole Binaries via Close Encounters

We study the long-term evolution of two or more stellar black holes (BHs) on initially separated but unstable circular orbits around a supermassive BH (SMBH). Such a close-packed orbital configuration can naturally arise from BH migrations in the AGN disk. Dynamical instability of the orbits leads to recurring close encounters between two BHs, during which the BH separation r p becomes less than the Hill radius R H. In rare very close encounters, a tight merging BH binary can form with the help of gravitational wave emission. We use N-body simulations to study the time evolution of close encounters of various degrees of closeness. For a typical “SMBH+2BH” system, the averaged cumulative number of close encounters (with r p ≲ R H) scales approximately as ∝ t 0.5. The minimum encounter separation r p follows a cumulative distribution P(<r p) ∝ r p for r p ≪ R H. We obtain a semi-analytical expression for the averaged rate of binary captures that lead to BH mergers. Our results suggest that close-packed BHs in AGN disks may take a long time (≳107 orbits around the SMBH) to experience a sufficiently close encounter and form a bound binary. This time can be shorter if the initial BH orbits are highly aligned. The BH binary mergers produced in this scenario have high eccentricities when entering the LIGO band and broad distribution of orbital inclinations relative to the original AGN disk. We explore the effects of the gas disk and find that simple gas drags on the BHs do not necessarily lead to an enhanced BH binary capture rate.

Screen-printed capacitive pressure sensors with high sensitivity and accuracy on flexible substrates

Printable elastic conductors promise large-area stretchable sensor/actuator networks for healthcare, wearables and robotics, among other areas. Force pressure sensors are one of their most attractive applications, although their large-area integration has been limited by difficulties in their processability or bendability and their use by their insufficient sensitivity or stability. In this work, we present a flexible screen-printed capacitive pressure sensor, able to be modularly integrated in large-area systems thanks to the substrate flexibility, bending within itself capability and not only at its intersections, and cuttability, allowing a range of modifications in size and shape for complex structures. We built the sensors with a microstructured dielectric, whose hill radii were tuned (between 125 and 375 µm) until obtaining a measurement range of five orders of magnitude, with a logarithm sensitivity above 20% dB−1 at the maximum pressure peak of 750 kPa and of 80% kPa−1 at the lowest test value of 0.5 kPa. These results went along completely with the theoretical model that we also developed. Besides, while smaller pillars showed a significant hysteresis for decreasing pressures, we observed how large hills performed with a small hysteresis of down to 3%, way ahead of the published sensors to the best of our knowledge.

Searching for Binary Asteroids in Pan-STARRS1 Archival Images

We developed two different point-spread function (PSF) analysis techniques for discovering wide separation binary asteroids in wide-field surveys. We then applied these techniques to images of main belt asteroids in the 4–60 km size range captured by Pan-STARRS1. Johnston lists fewer than 10 known binaries in this size range with separations greater than 10% of the primary’s Hill radius, so discovering more wide binary asteroids is crucial for understanding the limits of binary stability and improving our knowledge of asteroid masses. We analyzed each image by (i) comparing the major axis orientation of the asteroid’s elliptical PSF to its nonsidereal rate on the sky and (ii) comparing the one-dimensional median profile created by collapsing the image along the asteroid’s direction of motion to that of nearby field stars. For both methods, we flagged any results that deviated significantly from the expected measurements of single asteroids, and those targets with the most flags were identified as binary candidates for confirmation with high-acuity imaging.

The Dynamical Viability of an Extended Jupiter Ring System

Planetary rings are often speculated as being a relatively common attribute of giant planets, partly based on their prevalence within the solar system. However, their formation and sustainability remain a topic of open discussion, and the most massive planet within our planetary system harbors a very modest ring system. Here, we present the results of an N-body simulation that explores dynamical constraints on the presence of substantial ring material for Jupiter. Our simulations extend from within the rigid satellite Roche limit to 10% of the Jupiter Hill radius, and include outcomes from 106 and 107 yr integrations. The results show possible regions of a sustained dense ring material presence around Jupiter that may comprise the foundation for moon formation. The results largely demonstrate the truncation of stable orbits imposed by the Galilean satellites, and dynamical desiccation of dense ring material within the range ∼3–29 Jupiter radii. We discuss the implications of these results for exoplanets, and the complex relationship between the simultaneous presence of rings and massive moon systems.

Orbital stability analysis of hypothetical Earth-mass and Luna-mass moons in the Sagarmatha (HD 100777) star system

Abstract Six of the solar system planets have 150 confirmed moons (Earth—1, Mars—2, Jupiter—53, Saturn—53, Uranus—27, Neptune—14) and seven of them (Ganymede, Titan, Callisto, Io, the Moon, Europa, Triton) have masses &amp;gt;0.001 $M_\oplus$. However, no exomoons have yet been discovered despite the successful detection of ∼5000 exoplanets. We can infer, based on the solar system planets, that these exoplanets are capable of hosting one or more exomoons. In this paper, we study the possible existence of hypothetical Earth-mass and Luna-mass moons orbiting the Jupiter-mass planet, Laligurans (HD 100777b) in the Sagarmatha (HD 100777) star system by means of orbital stability. We apply long-term orbital integrations and the MEGNO (mean exponential growth of nearby orbits) chaos indicator to study the orbital stability of the moons and predict a phase-space region comprising periodic, chaotic, and unstable orbits. The phase spaces primarily constitute the moon's semimajor axis, which extends from the host planet's Roche radius to the Hill radius, and full range of eccentricity. Specific points are picked from three different regions of the MEGNO map and run as single-orbit integration for up to 10 billion periods of the innermost orbit. Furthermore, the lifetime and maximum eccentricity maps are generated from the direct integration to inspect the stable and unstable orbital configurations. The analyses of these maps, with the aid of time-series plots, show that both moons maintain stable orbits in the low-eccentricity regime and semimajor axis between the Roche limit and 28.4% of the Hill radius of the planet.

A low accretion efficiency of planetesimals formed at planetary gap edges

Observations and models of giant planets indicate that such objects are enriched in heavy elements compared to solar abundances. The prevailing view is that giant planets accreted multiple Earth masses of heavy elements after the end of core formation. Such late solid enrichment is commonly explained by the accretion of planetesimals. Planetesimals are expected to form at the edges of planetary gaps, and here we address the question of whether these planetesimals can be accreted in large enough amounts to explain the inferred high heavy element contents of giant planets. We performed a series of N-body simulations of the dynamics of planetesimals and planets during the planetary growth phase, taking gas drag into account as well as the enhanced collision cross section caused by the extended envelopes. We considered the growth of Jupiter and Saturn via gas accretion after reaching the pebble isolation mass and we included their migration in an evolving disk. We find that the accretion efficiency of planetesimals formed at planetary gap edges is very low: less than 10% of the formed planetesimals are accreted even in the most favorable cases, which in our model corresponds to a few Earth masses. When planetesimals are assumed to form beyond the feeding zone of the planets, extending to a few Hill radii from a planet, accretion becomes negligible. Furthermore, we find that the accretion efficiency increases when the planetary migration distance is increased and that the efficiency does not increase when the planetesimal radii are decreased. Based on these results, we conclude that it is difficult to explain the large heavy element content of giant planets with planetesimal accretion during the gas accretion phase. Alternative processes most likely are required, such as accretion of vapor deposited by drifting pebbles.

Search for Stellar Flybys in the Sco-Cen OB Association with the Gaia DR2

High-contrast imaging studies of debris disks have revealed a significant diversity in their morphologies, including large-scale asymmetries. Theories involving stellar flybys, an external source of gravitational disturbance, have offered a plausible explanation for the origin of these morphological variations. Our study is an experiment to gain empirical evidence that has been lacking from such theories. We explore this paradigm by using astrometric and radial velocity measurements from the Gaia DR2 and ground-based observations to trace the trajectories of 625 stars in the Sco-Cen OB association from 5 Myr in the past to 2 Myr in the future. We identified 119 stars that had at least one past flyby event occurring within one Hill radius, and 23 of these experienced flybys within 0.5 Hill radii. We found no evidence of a significant correlation between the presence of flyby events and infrared excess detections, although the sample is not uniformly sensitive to infrared excess emission. Ten stars that had past flyby events host resolved circumstellar disks that appear relatively symmetric in the existing data except for the circumbinary disk surrounding HD 106906. We determined the trajectory and relative velocity of each of these flyby events and compared these to the geometry of the spatially resolved disks. Future work is needed to measure the kinematics of lower-mass stars and to improve sensitivity to circumstellar disks for the entire sample.

The 3D Dust and Opacity Distribution of Protoplanets in Multifluid Global Simulations

Abstract The abundance and distribution of solids inside the Hill sphere are central to our understanding of the giant planet dichotomy. Here, we present a 3D characterization of the dust density, mass flux, and mean opacities in the envelope of subthermal and superthermal-mass planets. We simulate the dynamics of multiple dust species in a global protoplanetary disk model accounting for dust feedback. We find that the meridional flows do not effectively stir dust grains at scales of the Bondi sphere. Thus the dust settling driven by the stellar gravitational potential sets the latitudinal dust density gradient within the planet envelope. Not only does the planet’s potential enhance this gradient, but also the spiral wakes serve as another source of asymmetry. These asymmetries substantially alter the inferred mean Rosseland and Planck opacities. In cases with moderate-to-strong dust settling, the opacity gradient can range from a few percent to more than two orders of magnitude between the midplane and the polar regions of the Bondi sphere. Finally, we show that this strong latitudinal opacity gradient can introduce a transition between optically thick and thin regimes at the scales of the planet envelope. We suggest that this transition is likely to occur when the equilibrium scale height of hundred-micron-sized particles is smaller than the Hill radius of the forming planet. This work calls into question the adoption of a constant opacity derived from well-mixed distributions and demonstrates the need for global radiation hydrodynamics models of giant planet formation that account for dust dynamics.

Gap carving by a migrating planet embedded in a massive debris disc

ABSTRACT When considering gaps in debris discs, a typical approach is to invoke clearing by an unseen planet within the gap, and derive the planet mass using Wisdom overlap or Hill radius arguments. However, this approach can be invalid if the disc is massive, because clearing would also cause planet migration. This could result in a calculated planet mass that is incompatible with the inferred disc mass, because the predicted planet would in reality be too small to carve the gap without significant migration. We investigate the gap that a single embedded planet would carve in a massive debris disc. We show that a degeneracy is introduced, whereby an observed gap could be carved by two different planets: either a high-mass, barely migrating planet, or a smaller planet that clears debris as it migrates. We find that, depending on disc mass, there is a minimum possible gap width that an embedded planet could carve (because smaller planets, rather than carving a smaller gap, would actually migrate through the disc and clear a wider region). We provide simple formulae for the planet-to-debris disc mass ratio at which planet migration becomes important, the gap width that an embedded planet would carve in a massive debris disc, and the interaction time-scale. We also apply our results to various systems, and in particular show that the disc of HD 107146 can be reasonably well-reproduced with a migrating, embedded planet. Finally, we discuss the importance of planet–debris disc interactions as a tool for constraining debris disc masses.

Hyperbolic comets as an indicator of a hypothetical planet 9 in the solar system

In this study, we assess whether a dynamic relationship exists between hyperbolic comets (HCs) with osculating orbit elements and a hypothetical planet 9 (HP9). We have found strong statistical evidence that HCs and parabolic comets are two independent sets of long-periodic comets; thus, HCs can be used as an independent set in this analysis. We have applied numerical integration, minimal orbit intersectional distance (MOID) calculations, close encounter phenomena, and the descending and ascending node distributions of comets to investigate the possible dynamic relationship between planet candidates and HCs. Transitions between the two groups (from a hyperbolic orbit to a parabolic orbit or vice versa) of these comets require a strong perturbation from a massive body. Notable clusters have been obtained for the descending and ascending node distributions of HCs for distances of 250–300 AU and 200–250 AU with respect to the ecliptic, accordingly, and for distances of 260–400 AU relative to the predicted HP9 plane at Ωp = 2710.6 and ip = 840.3. These clusters may arise from perturbations caused by HP9 near these distances.Our findings show that the MOID values of 30 comets are lower than the Hill sphere radius of HP9 sub-models. The changing eccentricity of comet C/2007J A21 (LINEAR) and its close encounter with the orbit of the HP9 sub-model were demonstrated by numerical integration and MOID calculation methods. We also assessed the possible dynamic perturbation of HCs caused by massive trans-Neptunian objects using MOID value analysis.

Synchronous satellites of Venus

Synchronous satellites of Venus have long been thought unstable, but we use Poincare's surface of section technique to show that synchronous quasi-satellites orbiting just outside Venus' Hill sphere are quite stable, at least for centuries. Such synchrosats always remain within a few degrees of Venus' equator, and drift very slowly in longitude. These synchrosats could be useful for continuous monitoring of points on Venus' surface, such as active landforms or long-lived landers.

Modeling Meteoroid Impacts on the Juno Spacecraft

Abstract Events which meet certain criteria from star-tracker images on board the Juno spacecraft have been proposed to be due to interplanetary dust particle impacts on its solar arrays. These events have been suggested to be caused by particles with diameters larger than 10 μm. Here, we compare the reported event rates to expected dust-impact rates using dynamical meteoroid models for the four most abundant meteoroid/dust populations in the inner solar system. We find that the dust-impact rates predicted by dynamical meteoroid models are not compatible with either the Juno observations in terms of the number of star-tracker events per day, or with the variations of dust flux on Juno’s solar panels with time and position in the solar system. For example, the rate of star-tracker events on Juno’s antisunward surfaces is the largest during a period in which Juno is expected to experience the peak impact fluxes on the opposite, sunward hemisphere. We also investigate the hypothesis of dust leaving the Martian Hill sphere originating either from the surface of Mars itself or from one of its moons. We do not find such a hypothetical source to be able to reproduce the star-tracker event-rate variations observed by Juno. We conclude that the star-tracker events observed by Juno are unlikely to be the result of instantaneous impacts from the zodiacal cloud.

Testing planet formation from the ultraviolet to the millimetre

ABSTRACT Gaps imaged in protoplanetary discs are suspected to be opened by planets. We compute the present-day mass accretion rates $\dot{M}_{\rm p}$ of seven hypothesized gap-embedded planets, plus the two confirmed planets in the PDS 70 disc. The accretion rates are based on disc gas surface densities Σgas from C18O observations, and planet masses Mp from simulations fitted to observed gaps. Assuming accretion is Bondi-like, we find in eight out of nine cases that $\dot{M}_{\rm p}$ is consistent with the time-averaged value given by the current planet mass and system age, Mp/tage. As system ages are comparable to circumstellar disc lifetimes, these gap-opening planets may be undergoing their last mass doublings, reaching final masses of $M_{\rm p} \sim 10\rm{\!-\!}10^2 \, M_\oplus$ for the non-PDS 70 planets, and $M_{\rm p} \sim 1\!-\!10 \, M_{\rm J}$ for the PDS 70 planets. For another 15 gaps without C18O data, we predict Σgas by assuming their planets are accreting at their time-averaged $\dot{M}_{\rm p}$. Bondi accretion rates for PDS 70b and c are orders of magnitude higher than accretion rates implied by measured U-band and H α fluxes, suggesting most of the accretion shock luminosity emerges in as yet unobserved wavebands, or that the planets are surrounded by dusty, highly extincting, quasi-spherical circumplanetary envelopes. Thermal emission from such envelopes or from circumplanetary discs, on Hill sphere scales, peaks at wavelengths in the mid-to-far-infrared and can reproduce observed mm-wave excesses.

Binaries are softer than they seem: effects of an external potential on the scattering dynamics of binaries

ABSTRACT Binary evolution is influenced by dynamical scattering with other stars in dense environments. Heggie’s law states that, due to their environments, hard binaries (whose orbital energy surpasses the typical energy of single stars) tend to harden (increase their orbital energy), while soft binaries typically soften. Here, we show that Heggie’s law sometimes needs to be revised, by accounting for an external potential, for example, for binaries in nuclear stellar discs or active galactic nucleus discs, that are affected by the central massive black hole, or binary planetesimals in protoplanetary discs, affected by the host star. We find that in such environments, where the Hill radius is finite, binary-single scattering can have different outcomes. In particular, a three-body encounter could be cut short due to stars being ejected beyond the Hill radius, thereby ceasing to participate in further close interactions. This leads to a systematic difference in the energy changes brought about by the encounter, and in particular slows binary hardening, and even causes some hard binaries to soften, on average, rather than harden. We use our previously derived analytical, statistical solution to the bound chaotic three-body problem to quantitatively characterise the revision of the hardening-softening phase transition and evolution of binaries. We also provide an analytical calculation of the mean hardening rate of binaries in any environment (also reproducing the results of detailed N-body simulations). We show that the latter exhibits a non-trivial dependence on the Hill radius induced by the environment.

Constraining the nature of the possible extrasolar PDS110b ring system

The young star PDS110 in the Ori OB1a association underwent two similar eclipses in 2008 and 2011, each of which lasted for a period of at least 25 days. One plausible explanation for these events is that the star was eclipsed by an unseen giant planet (named PDS110b) circled by a ring system that fills a large fraction of its Hill sphere. Through thousands of numerical simulations of the three-body problem, we constrain the mass and eccentricity of this planet as well the size and inclination of its ring, parameters that are not well determined by the observational data alone. We carried out a broad range of different configurations for the PDS110b ring system and ruled out all that did not match with the observations. The result shows that the ring system could be prograde or retrograde; the preferred solution is that the ring has an inclination lower than 60° and a radius between 0.1 and 0.2 au and that the planet is more massive than 35 MJup and has a low eccentricity (&lt;0.05).

A search for transiting companions in the J1407 (V1400 Cen) system

Context. In 2007, the young star 1SWASP J140747.93-394 542.6 (V1400 Cen) underwent a complex series of deep eclipses over 56 days. This was attributed to the transit of a ring system filling a large fraction of the Hill sphere of an unseen substellar companion. Subsequent photometric monitoring has not found any other deep transits from this candidate ring system, but if there are more substellar companions and if they are coplanar with the potential ring system, there is a chance that they will transit the star as well. This young star is active, and the light curves show a 5% modulation in amplitude with a dominant rotation period of 3.2 days due to starspots rotating into and out of view. Aims. We model and remove the rotational modulation of the J1407 light curve and search for additional transit signatures of substellar companions orbiting around J1407. Methods. We combine the photometry of J1407 from several observatories, spanning a 19 yr baseline. We remove the rotational modulation by modeling the variability as a periodic signal, whose periodicity changes slowly with time over several years due to the activity cycle of the star. A transit least squares (TLS) analysis is used to search for any periodic transiting signals within the cleaned light curve. Results. We identify an activity cycle of J1407 with a period of 5.4 yr. A TLS search does not find any plausible periodic eclipses in the light curve, from 1.2% amplitude at 5 days up to 1.9% at 20 days. This sensitivity is confirmed by injecting artificial transits into the light curve and determining the recovery fraction as a function of transit depth and orbital period. Conclusions. J1407 is confirmed as a young active star with an activity cycle consistent with a rapidly rotating solar mass star. With the rotational modulation removed, the TLS analysis reaches down to planetary mass radii for young exoplanets, ruling out transiting companions with radii larger than about 1 RJup.

Perturbers: SPHERE detection limits to planetary-mass companions in protoplanetary disks

The detection of a wide range of substructures such as rings, cavities, and spirals has become a common outcome of high spatial resolution imaging of protoplanetary disks, both in the near-infrared scattered light and in the thermal millimetre continuum emission. The most frequent interpretation of their origin is the presence of planetary-mass companions perturbing the gas and dust distribution in the disk (perturbers), but so far the only bona fide detection has been the two giant planets carving the disk around PDS 70. Here, we present a sample of 15 protoplanetary disks showing substructures in SPHERE scattered-light images and a homogeneous derivation of planet detection limits in these systems. To obtain mass limits we rely on different post-formation luminosity models based on distinct formation conditions, which are critical in the first million years of evolution. We also estimate the mass of these perturbers through a Hill radius prescription and a comparison to ALMA data. Assuming that one single planet carves each substructure in scattered light, we find that more massive perturbers are needed to create gaps within cavities than rings, and that we might be close to a detection in the cavities of RX J1604.3-2130A, RX J1615.3-3255, Sz Cha, HD 135344B, and HD 34282. We reach typical mass limits in these cavities of 3–10 MJup. For planets in the gaps between rings, we find that the detection limits of SPHERE high-contrast imaging are about an order of magnitude away in mass, and that the gaps of PDS 66 and HD 97048 seem to be the most promising structures for planet searches. The proposed presence of massive planets causing spiral features in HD 135344B and HD 36112 are also within SPHERE’s reach assuming hot-start models. These results suggest that the current detection limits are able to detect hot-start planets in cavities, under the assumption that they are formed by a single perturber located at the centre of the cavity. More realistic planet mass constraints would help to clarify whether this is actually the case, which might indicate that perturbers are not the only way of creating substructures.