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At least 145 records · Page 8

A step towards unveiling the nature of three cataclysmic variables: LS Cam, V902 Mon, and SWIFT J0746.3-1608

ABSTRACT We have carried out detailed time-resolved timing analyses of three cataclysmic variables (CVs) namely LS Cam, V902 Mon, and SWIFT J0746.3-1608, using the long-baseline, high-cadence optical photometric data from the Transiting Exoplanet Survey Satellite. Our analysis of LS Cam observations hints the presence of a superorbital period of ∼4.025 ± 0.007 d along with negative and positive superhump periods of ∼3.30 and 3.70 h, respectively. These results can be explained as an interaction of nodal and apsidal precession of the accretion disc with orbital motion. For the other two sources, V902 Mon and SWIFT J0746.3-1608, we have found evidence of a beat period of 2387.0 ± 0.6 and 2409.5 ± 0.7 s, respectively, which were not found in earlier studies. Our results presented in this study indicate the change in the accretion mode during the entire observing period for both sources. For V902 Mon, an apparent orbital period derivative of (6.09 ± 0.60) × 10−10 was also found. Moreover, the second harmonic of orbital frequency dominates the power spectrum of SWIFT J0746.3-1608, suggestive of ellipsoidal modulation of the secondary star. Present analyses suggest that LS Cam could be a superhumping CV, whereas V902 Mon and SWIFT J0746.3-1608 are likely to be variable disc-overflow accreting intermediate polars.

Rawat, Nikita (ORCID:0000000246336832)↗

TOI-1634 b: An Ultra-short-period Keystone Planet Sitting inside the M-dwarf Radius Valley

Studies of close-in planets orbiting M dwarfs have suggested that the M-dwarf radius valley may be well explained by distinct formation timescales between enveloped terrestrials and rocky planets that form at late times in a gas-depleted environment. This scenario is at odds with the picture that close-in rocky planets form with a primordial gaseous envelope that is subsequently stripped away by some thermally driven mass-loss process. These two physical scenarios make unique predictions of the rocky/enveloped transition’s dependence on orbital separation such that studying the compositions of planets within the M-dwarf radius valley may be able to establish the dominant physics. Here, we present the discovery of one such keystone planet: the ultra-short-period planet TOI-1634 b (P = 0.989 days, F=121F{sub ⊕}, r{sub p}=1.790{sub -0.081}{sup +0.080} R {sub ⊕}) orbiting a nearby M2 dwarf (K {sub s} = 8.7, R {sub s} = 0.450 R {sub ⊙}, M {sub s} = 0.502 M {sub ⊙}) and whose size and orbital period sit within the M-dwarf radius valley. We confirm the TESS-discovered planet candidate using extensive ground-based follow-up campaigns, including a set of 32 precise radial velocity measurements from HARPS-N. We measure a planetary mass of 4.91{sub -0.70}{sup +0.68} M {sub ⊕}, which makes TOI-1634 b inconsistent with an Earth-like composition at 5.9σ and thus requires either an extended gaseous envelope, a large volatile-rich layer, or a rocky composition that is not dominated by iron and silicates to explain its mass and radius. The discovery that the bulk composition of TOI-1634 b is inconsistent with that of Earth supports the gas-depleted formation mechanism to explain the emergence of the radius valley around M dwarfs with M{sub s}≲0.5 M {sub ⊙}.

36 MATERIALS SCIENCE↗

Insights into ENSO Diversity from an Intermediate Coupled Model. Part II: Role of Nonlinear Dynamics and Stochastic Forcing

Abstract In this study, we investigate how a single leading linear El Niño–Southern Oscillation (ENSO) mode, as studied in Part I, leads to the irregular coexistence of central Pacific (CP) and eastern Pacific (EP) ENSO, a phenomenon known as ENSO spatiotemporal diversity. This diversity is fundamentally generated by deterministic nonlinear pathways to chaos via the period-doubling route and, more prevailingly, the subharmonic resonance route with the presence of a seasonally varying basic state. When residing in the weakly nonlinear regime, the coupled system sustains a weak periodic oscillation with a mixed CP/EP pattern as captured by the linear ENSO mode. With a stronger nonlinearity effect, the ENSO behavior experiences a period-doubling bifurcation. The single ENSO orbit splits into coexisting CP-like and EP-like ENSO orbits. A sequence of period-doubling bifurcation results in an aperiodic oscillation featuring irregular CP and EP ENSO occurrences. The overlapping of subharmonic resonances between ENSO and the seasonal cycle allows this ENSO irregularity and diversity to be more readily excited. In the strongly nonlinear regime, the coupled system is dominated by regular EP ENSO. The deterministic ENSO spatiotemporal diversity is thus confined to a relatively narrow range corresponding to a moderately unstable ENSO mode. Stochastic forcing broadens this range and allows ENSO diversity to occur when the ENSO mode is weakly subcritical. A close relationship among a weakened mean zonal temperature gradient, stronger ENSO activity, and more (fewer) occurrences of EP (CP) ENSO is noted, indicating that ENSO–mean state interaction may yield ENSO regime modulations on the multidecadal time scale.

Geng, Licheng↗

Decaying Orbit of the Hot Jupiter WASP-12b: Confirmation with TESS Observations

Theory suggests that the orbits of some close-in giant planets should decay due to tidal interactions with their host stars. To date, WASP-12b is the only hot Jupiter reported to have a decaying orbit, at a rate of 29 ± 2 ms yr{sup −1}. We analyzed data from NASA’s Transiting Exoplanet Survey Satellite (TESS) to verify that WASP-12b’s orbit is indeed changing. We find that the TESS transit and occultation data are consistent with a decaying orbit with an updated period of 1.091420090 ± 0.000000041 days and a decay rate of 32.53 ± 1.62 ms yr{sup −1}. We find an orbital decay timescale of τ=P/| P-dot |=2.90±0.14 Myr. If the observed decay results from tidal dissipation, the modified tidal quality factor is Q{sub ⋆}{sup ′}=1.39±0.15×10{sup 5}, which falls at the lower end of values derived for binary star systems and hot Jupiters. Our result highlights the power of space-based photometry for investigating the orbital evolution of short-period exoplanets.

47 OTHER INSTRUMENTATION↗

Lagrangian formulation of nuclear–electronic orbital Ehrenfest dynamics with real-time TDDFT for extended periodic systems

Here, we present a Lagrangian-based implementation of Ehrenfest dynamics with nuclear–electronic orbital (NEO) theory and real-time time-dependent density functional theory for extended periodic systems. In addition to a quantum dynamical treatment of electrons and selected protons, this approach allows for the classical movement of all other nuclei to be taken into account in simulations of condensed matter systems. Furthermore, we introduce a Lagrangian formulation for the traveling proton basis approach and propose new schemes to enhance its application for extended periodic systems. Validation and proof-of-principle applications are performed on electronically excited proton transfer in the o-hydroxybenzaldehyde molecule with explicit solvating water molecules. These simulations demonstrate the importance of solvation dynamics and a quantum treatment of transferring protons. This work broadens the applicability of the NEO Ehrenfest dynamics approach for studying complex heterogeneous systems in the condensed phase.

Calculus of variations↗

A Tidal Origin for a Three-body Resonance in Kepler-221

Over the course of the last two decades, traditional models of planet formation have been repeatedly challenged by the emerging census of extrasolar planets. Key among them is the orbital architecture problem: while standard models of orbital migration predict resonant orbits for short-period objects, most planets do not appear to lie in orbital resonances. Here, we show that the four-planet system Kepler-221, not previously recognized to have active orbital resonances, has a three-body commensurability relation unique within the Kepler sample. Using a suite of numerical experiments as well as a perturbative analysis, we demonstrate that this system likely began as a resonant chain and proceeded to undergo large-scale divergence away from resonance, under the action of tidal dissipation. Our results further indicate that obliquity tides, driven by a secular spin–orbit resonance and mutual inclination, are an excellent candidate for driving this orbital divergence, and that the high tidal luminosity may also explain the anomalous size of planet b, which lies within the Fulton radius gap.

79 ASTRONOMY AND ASTROPHYSICS↗

A giant planet candidate transiting a white dwarf

Astronomers have discovered thousands of planets outside the Solar System1, most of which orbit stars that will eventually evolve into red giants and then into white dwarfs. During the red giant phase, any close-orbiting planets will be engulfed by the star2, but more distant planets can survive this phase and remain in orbit around the white dwarf3,4. Some white dwarfs show evidence for rocky material floating in their atmospheres5, in warm debris disks6,7,8,9 or orbiting very closely10,11,12, which has been interpreted as the debris of rocky planets that were scattered inwards and tidally disrupted13. Recently, the discovery of a gaseous debris disk with a composition similar to that of ice giant planets14 demonstrated that massive planets might also find their way into tight orbits around white dwarfs, but it is unclear whether these planets can survive the journey. So far, no intact planets have been detected in close orbits around white dwarfs. Here we report the observation of a giant planet candidate transiting the white dwarf WD 1856+534 (TIC 267574918) every 1.4 days. We observed and modelled the periodic dimming of the white dwarf caused by the planet candidate passing in front of the star in its orbit. The planet candidate is roughly the same size as Jupiter and is no more than 14 times as massive (with 95 per cent confidence). Other cases of white dwarfs with close brown dwarf or stellar companions are explained as the consequence of common-envelope evolution, wherein the original orbit is enveloped during the red giant phase and shrinks owing to friction. In this case, however, the long orbital period (compared with other white dwarfs with close brown dwarf or stellar companions) and low mass of the planet candidate make common-envelope evolution less likely. Instead, our findings for the WD 1856+534 system indicate that giant planets can be scattered into tight orbits without being tidally disrupted, motivating the search for smaller transiting planets around white dwarfs.

79 ASTRONOMY AND ASTROPHYSICS↗

Stellar kinematics of dwarf galaxies from multi-epoch spectroscopy: application to Triangulum II

ABSTRACT We present new MMT/Hectochelle spectroscopic measurements for 257 stars observed along the line of sight to the ultrafaint dwarf galaxy Triangulum II (Tri II). Combining results from previous Keck/DEIMOS spectroscopy, we obtain a sample that includes 16 likely members of Tri II, with up to 10 independent redshift measurements per star. To this multi-epoch kinematic data set, we apply methodology that we develop in order to infer binary orbital parameters from sparsely sampled radial velocity curves with as few as two epochs. For a previously identified (spatially unresolved) binary system in Tri II, we infer an orbital solution with period $296.0_{-3.3}^{+3.8} \rm ~ d$, semimajor axis $1.12^{+0.41}_{-0.24}\rm ~au$, and systemic velocity $-380.0 \pm 1.7 \rm ~km ~s^{-1}$ that we then use in the analysis of Tri II’s internal kinematics. Despite this improvement in the modelling of binary star systems, the current data remain insufficient to resolve the velocity dispersion of Tri II. We instead find a 95 per cent confidence upper limit of $\sigma _{v} \lesssim 3.4 \rm ~km~s^{-1}$.

Buttry, Rachel (ORCID:0000000155017609)↗

A Collage of Small Planets from the Lick–Carnegie Exoplanet Survey: Exploring the Super-Earth and Sub-Neptune Mass Regime

Analysis of new precision radial velocity (RV) measurements from the Lick Automated Planet Finder and Keck HIRES has yielded the discovery of three new exoplanet candidates orbiting the nearby stars HD 190007 and HD 216520. We also report new velocities from the APF and the Planet Finder Spectrograph and updated orbital fits for the known exoplanet host stars GJ 686 and HD 180617. Of the newly discovered planets, HD 190007 b has a period of P = 11.72 days, an RV semiamplitude of K = 5.64 ± 0.55 m s{sup −1}, a minimum mass of M {sub pl} = 16.46 ± 1.66 M {sub ⊕}, and orbits the slightly metal-rich, active K4V star HD 190007. For HD 216520 b, we find P = 35.45 days, K = 2.28 ± 0.20 m s{sup −1}, and M {sub pl} = 10.26 ± 0.99 M {sub ⊕}, while for HD 216520 c, P = 154.43 days, K = 1.29 ± 0.22 m s{sup −1}, and M {sub pl} = 9.44 ± 1.63 M {sub ⊕}. Both planets orbit the slightly metal-poor, inactive K0V star HD 216520. Our updated best-fit models for HD 180617 b and GJ 686 b are in good agreement with the published results. For HD 180617 b, we obtain P = 105.91 days and M {sub pl} = 12.214 ± 1.05 M {sub ⊕}. For GJ 686 b, we find P = 15.53 days and M {sub pl} = 6.624 ± 0.432 M {sub ⊕}. Using an injection-recovery exercise, we find that HD 190007 b and HD 216520 b are unlikely to have additional planets with masses and orbital periods within a factor of 2, in marked contrast to ∼85% of planets in this mass and period range discovered by Kepler.

79 ASTRONOMY AND ASTROPHYSICS↗

The BAT AGN Spectroscopic Survey. XVIII. Searching for Supermassive Black Hole Binaries in X-Rays

Theory predicts that a supermassive black hole binary (SMBHB) could be observed as a luminous active galactic nucleus (AGN) that periodically varies on the order of its orbital timescale. In X-rays, periodic variations could be caused by mechanisms including relativistic Doppler boosting and shocks. In this paper we present the first systematic search for periodic AGNs using 941 hard X-ray light curves (14–195 keV) from the first 105 months of the Swift Burst Alert Telescope (BAT) survey (2004–2013). We do not find evidence for periodic AGNs in Swift-BAT, including the previously reported SMBHB candidate MCG+11–11–032. We find that the null detection is consistent with the combination of the upper-limit binary population in AGNs in our adopted model, their expected periodic variability amplitudes, and the BAT survey characteristics. We have also investigated the detectability of SMBHBs against normal AGN X-ray variability in the context of the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) survey. Under our assumptions of a binary population and the periodic signals they produce, which have long periods of hundreds of days, up to 13% true periodic binaries can be robustly distinguished from normal variable AGNs with the ideal uniform sampling. However, we demonstrate that realistic eROSITA sampling is likely to be insensitive to long-period binaries because longer observing gaps reduce their detectability. In contrast, large observing gaps do not diminish the prospect of detecting binaries of short, few-day periods, as 19% can be successfully recovered, the vast majority of which can be identified by the first half of the survey.

79 ASTRONOMY AND ASTROPHYSICS↗

Shearless effective barriers to chaotic transport induced by even twin islands in nontwist systems

For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions where they occur are natural places to look for barriers to transport. Here we describe a kind of effective barrier that persists after the shearless torus is broken. Because phenomena are generic, for convenience we study the standard nontwist map (SNM), an area-preserving map that violates the twist condition locally in the phase space. The barrier occurs in nontwist systems when twin even period islands are present, which happens for a broad range of parameter values in the SNM. With a phase space composed of regular and irregular orbits, the movement of chaotic trajectories is hampered by the existence of shearless curves, total barriers, and a network of partial barriers formed by the stable and unstable manifolds of the hyperbolic points. Being a degenerate system, the SNM has twin islands and, consequently, twin hyperbolic points. We show that the structures formed by the manifolds intrinsically depend on period parity of the twin islands. For this even scenario the structure that we call a torus free barrier occurs because the manifolds of different hyperbolic points form an intricate chain atop a dipole configuration and the transport of chaotic trajectories through the chain becomes a rare event. This structure impacts the emergence of transport, the escape basin for chaotic trajectories, the transport mechanism, and the chaotic saddle. The case of odd periodic orbits is different: we find for this case the emergence of transport immediately after the breakup of the last invariant curve, and this leads to a scenario of higher transport, with intricate escape basin boundary and a chaotic saddle with nonuniformly distributed points.

classical mechanics↗

Retention of Long-period Gas Giant Planets: Type II Migration Revisited

During their formation, emerging protoplanets tidally interact with their natal disks. Proto–gas giant planets, with Hill radii larger than the disk thickness, open gaps and quench gas flow in the vicinity of their orbits. It is usually assumed that their type II migration is coupled to the viscous evolution of the disk. Although this hypothesis provides an explanation for the origin of close-in planets, it also encounters a predicament on the retention of long-period orbits for most gas giant planets. Moreover, numerical simulations indicate that the planets' migrations are not solely determined by the viscous diffusion of their natal disk. In this work, we carry out a series of hydrodynamic simulations combined with analytic studies to examine the transition between different paradigms of type II migration. We find a range of planetary mass for which gas continues to flow through a severely depleted gap so that the surface density distribution in the disk region beyond the gap is maintained in a quasi-steady state. The associated gap profile modifies the location of corotation and Lindblad resonances. In the proximity of the planet's orbit, high-order Lindblad and corotation torque are weakened by the gas depletion in the gap, while low-order Lindblad torques near the gap walls preserve their magnitude. Consequently, the intrinsic surface density distribution of the disk delicately determines both the pace and direction of the planets' type II migration. We show that this effect might stall the inward migration of giant planets and preserve them in disk regions where the surface density is steep.

79 ASTRONOMY AND ASTROPHYSICS↗

A Gaussian Process Regression Reveals No Evidence for Planets Orbiting Kapteyn’s Star

Radial–velocity (RV) planet searches are often polluted by signals caused by gas motion at the star’s surface. Stellar activity can mimic or mask changes in the RVs caused by orbiting planets, resulting in false positives or missed detections. Here we use Gaussian process regression to disentangle the contradictory reports of planets versus rotation artifacts from Kapteyn’s star. To model rotation, we use joint quasiperiodic kernels for the RV and Hα signals, requiring that their periods and correlation timescales be the same. We find that the rotation period of Kapteyn’s star is 125 days, while the characteristic active-region lifetime is 694 days. Adding a planet to the RV model produces a best-fit orbital period of 100 yr, or 10 times the observing time baseline, indicating that the observed RVs are best explained by star rotation only. We also find no significant periodic signals in residual RV data sets constructed by subtracting off realizations of the best-fit rotation model and conclude that both previously reported “planets” are artifacts of the star’s rotation and activity. Our results highlight the pitfalls of using sinusoids to model quasiperiodic rotation signals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

BVR{sub c}I{sub c} Observations, Third-body Orbital Study, and Analysis of the UV Leo-type, Pre-W UMA Binary V642 Virginis

V642 Vir is a polar spotted, well-detached, UV Leo-type, low-mass, pre-WUMa (T1 ~ 4250K, ~K6V) eclipsing binary. It was observed in 2020 April, May, and June at the Dark Sky Observatory in North Carolina, USA with the 0.81 m reflector of Appalachian State University. A total of 88 timings were used in our 22-year period study which included 12 Transiting Exoplanet Survey Satellite (TESS) timings. The O - C plots show a low-amplitude oscillation of residuals that points to the existence of an orbiting third body, a dwarf of minimum mass, 0.15 M {sub ⊙} in an eccentric orbit (e = 0.41), with an orbital period of 20.07 yr. The odd light curves of V642 Virginis indicate that it has polar spots similar to UV Leo and the recently published V1023 Per. Its present large polar spot region indicates that it must have a strong magnetic field and that it is synchronously rotating. The BVR{sub c}I{sub c} simultaneous Wilson–Devinney Program solution gives a detached binary (primary and secondary components are underfilling their respective Roche Lobes, with 76% and 78% fill outs respectively). The cool spot region models near the pole of the primary component (centered at 10° colatitude) and is angled toward the secondary component. Its large radius (68°) and T-fact (T{sub spot}/T{sub surface} = 0.69) also attest to the conclusion of the strength of the magnetic field. The small ΔT in the components (~318 K) and mass ratio near unity (0.9542 ± 0.0005) show that the stars are similar in spectral type (secondary ~K9V). The inclination is high, ~86.87 ± 0.04°, yet there is no time of constant light due to the two stars’ essentially equal radii.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

White Dwarf Binaries across the H-R Diagram

We created the APOGEE-GALEX-Gaia catalog to study white dwarf (WD) binaries. This database aims to create a minimally biased sample of WD binary systems identified from a combination of GALEX, Gaia, and APOGEE data to increase the number of WD binaries with orbital parameters and chemical compositions. We identify 3414 sources as WD binary candidates, with nondegenerate companions of spectral types between F and M, including main-sequence stars, main-sequence binaries, subgiants, sub-subgiants, red giants, and red clump stars. Among our findings are (a) a total of 1806 systems having inferred WD radii R < 25 R ⊕ , which constitute a more reliable group of WD binary candidates within the main sample; (b) a difference in the metallicity distribution function between WD binary candidates and the control sample of most luminous giants (M H < -3.0); (c) the existence of a population of sub-subgiants with WD companions; (d) evidence for shorter periods in binaries that contain WDs compared to those that do not, as shown by the cumulative distributions of APOGEE radial velocity shifts; (e) evidence for systemic orbital evolution in a sample of 252 WD binaries with orbital periods, based on differences in the period distribution between systems with red clump, main-sequence binary, and sub-subgiant companions and systems with main-sequence or red giant companions; and (f) evidence for chemical enrichment during common envelope (CE) evolution, shown by lower metallicities in wide WD binary candidates (P > 100 days) compared to post-CE (P < 100 days) WD binary candidates.

79 ASTRONOMY AND ASTROPHYSICS↗

Sub-m s−1 upper limits from a deep HARPS-N radial-velocity search for planets orbiting HD 166620 and HD 144579

ABSTRACT Minimizing the impact of stellar variability in radial velocity (RV) measurements is a critical challenge in achieving the 10 cm s−1 precision needed to hunt for Earth twins. Since 2012, a dedicated programme has been underway with HARPS-N, to conduct a blind RV rocky planets search (RPS) around bright stars in the Northern hemisphere. Here we describe the results of a comprehensive search for planetary systems in two RPS targets, HD 166620 and HD 144579. Using wavelength-domain line-profile decorrelation vectors to mitigate the stellar activity and performing a deep search for planetary reflex motions using a trans-dimensional nested sampler, we found no significant planetary signals in the data sets of either of the stars. We validated the results via data-splitting and injection recovery tests. Additionally, we obtained the 95th percentile detection limits on the HARPS-N RVs. We found that the likelihood of finding a low-mass planet increases noticeably across a wide period range when the inherent stellar variability is corrected for using scalpelsU-vectors. We are able to detect planet signals with Msin i ≤ 1 M⊕ for orbital periods shorter than 10 d. We demonstrate that with our decorrelation technique, we are able to detect signals as low as 54 cm s−1, which brings us closer to the calibration limit of 50 cm s−1 demonstrated by HARPS-N. Therefore, we show that we can push down towards the RV precision required to find Earth analogues using high-precision radial velocity data with novel data-analysis techniques.

Anna John, A. (ORCID:0000000217156939)↗

Spikey: self-lensing flares from eccentric SMBH binaries

Here, we examine the light curves of two quasars, motivated by recent suggestions that a supermassive black hole binary (SMBHB) can exhibit sharp lensing spikes. We model the variability of each light curve as due to a combination of two relativistic effects: the orbital relativistic Doppler boost and gravitational binary self-lensing. In order to model each system, we extend previous Doppler plus self-lensing models to include eccentricity. The first quasar is identified in optical data as a binary candidate with a 20-yr period (Ark 120), and shows a prominent spike. For this source, we rule out the lensing hypothesis and disfavour the Doppler-boost hypothesis due to discrepancies in the measured versus recovered values of the binary mass and optical spectral slope. The second source, which we nickname Spikey, is the rare case of an active galactic nucleus identified in Kepler’s high-quality, high-cadence photometric data. For this source, we find a model, consisting of a combination of Doppler modulation and a narrow symmetric lensing spike, consistent with an eccentric SMBHB with a mass of $M_{\text{tot}} = 3\times 10^{7} {\, \mathrm{M}_{\odot }}$, rest-frame orbital period T = 418 d, eccentricity e = 0.5, and seen at an inclination of 8° from edge-on. This interpretation can be tested by monitoring Spikey for periodic behaviour and recurring flares in the next few years. In preparation for such monitoring, we present the first X-ray observations of this object taken by the Neil Gehrels Swift Observatory.

79 ASTRONOMY AND ASTROPHYSICS↗

Cometary Activity Begins at Kuiper Belt Distances: Evidence from C/2017 K2

We study the development of activity in the incoming long-period comet C/2017 K2 over the heliocentric distance range 9 ≲ r {sub H} ≲ 16 au. The comet continues to be characterized by a coma of submillimeter-sized and larger particles ejected at low velocity. In a fixed co-moving volume around the nucleus we find that the scattering cross section of the coma, C, is related to the heliocentric distance by a power law, C∝r{sub H}{sup -s}, with heliocentric index s = 1.14 ± 0.05. This dependence is significantly weaker than the r {sub H} {sup -2} variation of the insolation as a result of two effects. These are, first, the heliocentric dependence of the dust velocity and, second, a lag effect due to very slow-moving particles ejected long before the observations were taken. A Monte Carlo model of the photometry shows that dust production beginning at r {sub H} ~ 35 au is needed to match the measured heliocentric index, with only a slight dependence on the particle size distribution. Mass-loss rates in dust at 10 au are of order 10{sup 3} kg s{sup -1}, while loss rates in gas may be much smaller, depending on the unknown dust to gas ratio. Consequently, the ratio of the nongravitational acceleration to the local solar gravity, α', may, depending on the nucleus size, attain values of ~10{sup -7} ≲ α' ≲ 10{sup -5}, comparable to values found in short-period comets at much smaller distances. Nongravitational acceleration in C/2017 K2 and similarly distant comets, while presently unmeasured, may limit the accuracy with which we can infer the properties of the Oort cloud from the orbits of long-period comets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗