Distribution Of Orbital Elements Research Articles

What long-period comets tell us about the Oort Cloud

Context. The Oort Cloud is located in the farthest outskirts of the Solar System, extending to a heliocentric distance of several tens of thousands of au, and remains the last region of the Solar System where no object has been detected. Thus, all our knowledge of the Oort Cloud has been deduced from the observed long-period comets that are thought to originate from it. Aims. We aimed to retrieve valuable information that might be hidden in the orbital distributions of the observed long-period comets. Such information will allow us to impose constraints not only on the present shape of the Oort Cloud but also on its initial shape 4.5 Gyr ago. This has direct implications for the scenario proposed for its formation. Methods. We used two different databases of long-period comets. First, we calculated the distribution of orbital elements that might carry valuable information about the shape of the Oort Cloud. Then, we compared the distribution with that obtained from two synthetic samples of observable comets. These samples correspond to two considerably different initial configurations: one is a disk model, where we consider a swarm of comets with orbits aligned to the ecliptic plane and with a cometary perihelion close to the giant planets. The other is an isotropic model, where we consider a fully isotropic and thermalized initial distribution of comets. Results. The comparison revealed that the databases contained several features that were in better agreement with the disk model than with the isotropic model. The Oort Cloud contained an initial disk of objects with perihelia close to the planetary region of the Solar System and aphelia extending out to roughly 20 000 au. Some parts of this disk likely remain in the present Solar System. However, the fit to the disk model is poor. The discrepancy between the observational and synthetic results indicates that some dynamical processes in the current Oort Cloud were not included in either model. Conclusions. This initial shape of the Oort Cloud implies that planetary scattering was crucial during its formation. In addition, the fact that some dynamical features are still detec table 4.5 Gyr after the cloud formation imposes constraints on the role of exosolar effects, such as giant molecular clouds, Galactic tides, and the stellar cluster surrounding the Solar System at the time of its formation.

A Sublime Opportunity: The Dynamics of Transitioning Cometary Bodies and the Feasibility of In Situ Observations of the Evolution of Their Activity

Abstract The compositional and morphological evolution of minor bodies in the solar system is primarily driven by the evolution of their heliocentric distances, as the level of incident solar radiation regulates cometary activity. We investigate the dynamical transfer of Centaurs into the inner solar system, facilitated by mean motion resonances with Jupiter and Saturn. The recently discovered object P/2019 LD2 will transition from the Centaur region to the inner solar system in 2063. In order to contextualize LD2, we perform N-body simulations of a population of Centaurs and Jupiter-family comets. Objects between Jupiter and Saturn with Tisserand parameter T J ∼ 3 are transferred onto orbits with perihelia q < 4 au within the next 1000 yr with notably high efficiency. Our simulations show that there may be additional LD2-like objects transitioning into the inner solar system in the near future, all of which have low ΔV with respect to Jupiter. We calculate the distribution of orbital elements resulting from a single Jovian encounter and show that objects with initial perihelia close to Jupiter are efficiently scattered to q < 4 au. Moreover, approximately 55% of the transitioning objects in our simulated population experience at least one Jovian encounter prior to reaching q < 4 au. We demonstrate that a spacecraft stationed near Jupiter would be well positioned to rendezvous, orbit-match, and accompany LD2 into the inner solar system, providing an opportunity to observe the onset of intense activity in a pristine comet in situ. Finally, we discuss the prospect of identifying additional targets for similar measurements with forthcoming observational facilities.

Nauyaca: a New Tool to Determine Planetary Masses and Orbital Elements through Transit Timing Analysis

Abstract The transit timing variations method is currently the most successful method to determine dynamical masses and orbital elements for Earth-sized transiting planets. Precise mass determination is fundamental to restrict planetary densities and thus infer planetary compositions. In this work, we present Nauyaca, a Python package dedicated to finding planetary masses and orbital elements through the fitting of observed midtransit times from an N-body approach. The fitting strategy consists of performing a sequence of minimization algorithms (optimizers) that are used to identify high probability regions in the parameter space. These results from optimizers are used for initialization of a Markov chain Monte Carlo method, using an adaptive Parallel-Tempering algorithm. A set of runs are performed in order to obtain posterior distributions of planetary masses and orbital elements. In order to test the tool, we created a mock catalog of synthetic planetary systems with different numbers of planets where all of them transit. We calculate their midtransit times to give them as an input to Nauyaca, testing statistically its efficiency in recovering the planetary parameters from the catalog. For the recovered planets, we find typical dispersions around the real values of ∼1–14 M ⊕ for masses, between 10–110 s for periods, and between ∼0.01–0.03 for eccentricities. We also investigate the effects of the signal-to-noise ratio and number of transits on the correct determination of the planetary parameters. Finally, we suggest choices of the parameters that govern the tool for the usage with real planets, according to the complexity of the problem and computational facilities.

Simulating the Eclipsing Binary Yields of the Rubin Observatory in the Galactic Field and Star Clusters

Abstract We present a study of the detection and recovery efficiency of the Rubin Observatory for detached eclipsing binaries (EBs) in the galactic field, globular clusters (GCs), and open clusters (OCs), with a focus on comparing two proposed observing strategies: a standard cadence (baseline) and a cadence that samples the galactic plane more evenly (colossus). We generate realistic input binary populations in all observing fields of the Rubin Observatory, simulate the expected observations in each filter, and attempt to characterize the EBs using these simulated observations. In our models, we predict that the baseline cadence will enable the Rubin Observatory to observe about three million EBs; our technique could recover and characterize nearly one million of these in the field and thousands within star clusters. If the colossus cadence is used, the number of recovered EBs would increase by an overall factor of about 1.7 in the field and in globular clusters, and a factor of about 3 in open clusters. Including semidetached and contact systems could increase the number of recovered EBs by an additional factor of about 2.5 to 3. Regardless of the cadence, observations from the Rubin Observatory could reveal statistically significant physical distinctions between the distributions of EB orbital elements between the field, GCs, and OCs. Simulations such as these can be used to bias correct the sample of Rubin Observatory EBs to study the intrinsic properties of the full binary populations in the field and star clusters.

Stellar Radial Velocities in the Old Open Cluster M67 (NGC 2682). II. The Spectroscopic Binary Population

Abstract We present and analyze 120 spectroscopic binary and triple cluster members of the old (4 Gyr) open cluster M67 (NGC 2682). As a cornerstone of stellar astrophysics, M67 is a key cluster in the WIYN Open Cluster Study (WOCS); radial-velocity (RV) observations of M67 are ongoing and extend back over 45 yr, incorporating data from seven different telescopes, and allowing us to detect binaries with orbital periods ≲104 days. Our sample contains 1296 stars (604 cluster members) with magnitudes of 10 ≤ V ≤ 16.5 (about 1.3–0.7 M ⊙), from the giants down to ∼4 mag below the main-sequence turnoff, and extends in radius to 30′ (7.4 pc at a distance of 850 pc, or ∼7 core radii). This paper focuses primarily on the main-sequence binaries, but orbital solutions are also presented for red giants, yellow giants, and sub-subgiants. Out to our period detection limit and within our magnitude and spatial domain, we find a global main-sequence incompleteness-corrected binary fraction of 34% ± 3%, which rises to 70% ± 17% in the cluster center. We derive a tidal circularization period of . We also analyze the incompleteness-corrected distributions of binary orbital elements and masses. The period distribution rises toward longer periods. The eccentricity distribution, beyond P circ, is consistent with a uniform distribution. The mass-ratio distribution is also consistent with a uniform distribution. Overall, these M67 binaries are closely consistent with similar binaries in the galactic field, as well as with the old (7 Gyr) open cluster NGC 188. WOCS. 83.

Centaur and giant planet crossing populations: origin and distribution

The current giant planet region is a transitional zone where transneptunian objects (TNOs) cross in their way to becoming Jupiter Family Comets (JFCs). Their dynamical behavior is conditioned by the intrinsic dynamical features of TNOs and also by the encounters with the giant planets. We address the Giant Planet Crossing (GPC) population (those objects with $5.2$ au $ < q < 30$ au) studying their number and their evolution from their sources, considering the current configuration of the Solar System. This subject is reviewed from previous investigations and also addressed by new numerical simulations of the dynamical evolution of Scattered Disk Objects (SDOs). We obtain a model of the intrinsic orbital element distribution of GPCs. The Scattered Disk represents the main source of prograde GPCs and Centaurs, while the contribution from Plutinos lies between one and two orders of magnitude below that from the SD. We obtain the number and size distribution of GPCs from our model, computing 9600 GPCs from the SD with $D > 100$ km and $\sim 10^8$ with $D > 1$ km in the current population. The contribution from other sources is considered negligible. The mean lifetime in the Centaur zone is 7.2 Myr, while the mean lifetime of SDOs in the GPC zone is of 68 Myr. The latter is dependent on the initial inclination, being the ones with high inclinations the ones that survive the longest in the GPC zone. There is also a correlation of lifetime with perihelion distance, where greater perihelion leads to longer lifetime. The dynamical evolution of observed GPCs is different for prograde and retrograde objects. Retrograde GPCs have lower median lifetime than prograde ones, thus experiencing a comparatively faster evolution. However, it is probable that this faster evolution is due to the fact that the majority of retrograde GPCs have low perihelion values and then, lower lifetimes.

Twisted debris: how differential secular perturbations shape debris disks

Context. Resolved images suggest that asymmetric structures are a common feature of cold debris disks. While planets close to these disks are rarely detected, their hidden presence and gravitational perturbations provide plausible explanations for some of these features. Aims. To put constraints on the properties of yet undetected planetary companions, we aim to predict what features such a planet imprints in debris disks undergoing continuous collisional evolution. Methods. We discuss the basic equations, analytic approximations and timescales governing collisions, radiation pressure and secular perturbations. In addition, we combine our numerical model of the collisional evolution of the size and spatial distributions in debris disks with the gravitational perturbation by a single planet. Results. We find that the distributions of orbital elements in the disks are strongly dependent on grain sizes. Secular precession is differential with respect to involved semi-major axes and grain sizes. This leads to observable differences between the big grains tracing the parent belt and the small grains in the trailing halo. Observations at different wavelengths can be used to constrain the properties of a possible planet.

Orbital element distribution of invariant manifolds associated with Lyapunov family of periodic orbits around L1 and L2

Abstract This study explores the initial configurations that lead to an eventual approach to a given planet, particularly Jupiter, using the invariant manifold of Lyapunov orbits around Lagrangian points L1 or L2. Reachability to the vicinity of planets would provide information on developing a process for capturing irregular satellites, which are small bodies orbiting around a giant planet with a high eccentricity that are considered to have been captured by the mother planet, rather than formed in situ. A region several times the Hill radius is often used for determining reachability, combined with checking the velocity of the planetesimal with respect to the mother planet. This kind of direct computation is inapplicable when the Hill sphere is widely open and its boundary cannot be clearly recognized. Here, we thus employ Lyapunov periodic orbits (LOs) as a formal definition of the vicinity of Jupiter and numerically track the orbital distribution of the invariant manifold of an LO while varying the Jacobi constant, CJ. Numerical tracking of the manifold is carried out directly via repeated Poincaré mapping of points initially allocated densely on a fragment of the manifold near the fixed points, with the assistance of multi-precision arithmetic using the Multiple Precision Floating-Point Reliable Library. The numerical computations show that the distribution of the semi-major axis of points on the manifolds is quite heavily tailed and that its median spans roughly 1–2 times the Jovian orbital radius. The invariant manifold provides a distribution profile of a that is similar to that obtained using a direct method.

OSSOS. XIX. Testing Early Solar System Dynamical Models Using OSSOS Centaur Detections

Abstract We use published models of the early solar system evolution with a slow, long-range and grainy migration of Neptune to predict the orbital element distributions and the number of modern-day Centaurs. The model distributions are biased by the Outer Solar System Origins Survey (OSSOS) simulator and compared with the OSSOS Centaur detections. We find an excellent match to the observed orbital distribution, including the wide range of orbital inclinations which was the most troublesome characteristic to fit in previous models. A dynamical model, in which the original population of outer disk planetesimals was calibrated from Jupiter trojans, is used to predict that OSSOS should detect 11 ± 4 Centaurs with semimajor axes of a &lt; 30 au, perihelion distances of q &gt; 7.5 au, and diameter of D &gt; 10 km (absolute magnitude H r &lt; 13.7 for a 6% albedo). This is consistent with 15 actual OSSOS Centaur detections with H r &lt; 13.7. The population of Centaurs is estimated to be 21,000 ± 8000 for D &gt; 10 km. The inner scattered disk at 50 &lt; a &lt; 200 au should contain (2.0 ± 0.8) × 107 D &gt; 10 km bodies and the Oort cloud should contain (5.0 ± 1.9) × 108 D &gt; 10 km comets. Population estimates for different diameter cutoffs can be obtained from the size distribution of Jupiter trojans (N(&gt;D) ∝ D −2.1 for 5 &lt; D &lt; 100 km). We discuss model predictions for the Large Synoptic Survey Telescope observations of Centaurs.

Massive binary star mergers in galactic nuclei: implications for blue stragglers, binary S-stars, and gravitational waves

ABSTRACT Galactic nuclei are often found to contain young stellar populations and, in most cases, a central supermassive black hole (SMBH). Most known massive stars are found in binaries or higher multiplicity systems, and in a galactic nucleus the gravitational interaction with the SMBH can affect their long-term evolution. In this paper, we study the orbital evolution of stellar binaries near SMBHs using high precision N-body simulations, and including tidal forces and post-Newtonian corrections to the motion. We focus on the Lidov–Kozai (LK) effect induced by the SMBH on massive star binaries. We investigate how the properties of the merging binaries change with varying the SMBH mass, the slope of the initial mass function, the distributions of the binary orbital parameters, and the efficiency in energy dissipation in dissipative tides. We find that the fraction of merging massive binary stars is in the range ∼4–$15{{\ \rm per\ cent}}$ regardless of the details of the initial distributions of masses and orbital elements. For a Milky Way-like nucleus, we find a typical rate of binary mergers $\Gamma \approx 1.4\times 10^{-7} {\, \rm yr}^{-1}$. The merger products of massive binaries can be rejuvenated blue-straggler stars, more massive than each of their original progenitors, and G2-like objects. Binary systems that survive the LK cycles can be source of X-rays and gravitational waves, observable with present and upcoming instruments.

Identifying Interstellar Objects Trapped in the Solar System through Their Orbital Parameters

Abstract The first interstellar object, ‘Oumuamua, was discovered in the solar system by Pan-STARRS in 2017, allowing for a calibration of the abundance of interstellar objects of its size and an estimation of the subset of objects trapped by the Jupiter–Sun system. Photographing or visiting these trapped objects would allow us to learn about the conditions in other planetary systems, relieving the need to send interstellar probes. Here, we explore the orbital properties of captured interstellar objects in the solar system using dynamical simulations of the Jupiter–Sun system and initial conditions drawn from the distribution of relative velocities of stars in the Solar neighborhood. We compare the resulting distributions of orbital elements to those of the most similar population of known asteroids, namely Centaurs, to search for a parameter space in which interstellar objects should dominate and therefore be identifiable solely by their orbits. We find that there should be thousands of ‘Oumuamua-size interstellar objects identifiable by Centaur-like orbits at high inclinations, assuming a number density of ‘Oumuamua-size interstellar objects of ∼1015 pc−3. We note eight known objects that may be of interstellar origin. Finally, we estimate that the Large Synoptic Survey Telescope will be able to detect several hundreds of these objects.

Survivability of moon systems around ejected gas giants

ABSTRACT We examine the effects that planetary encounters have on the moon systems of ejected gas giant planets. We conduct a suite of numerical simulations of planetary systems containing three Jupiter-mass planets (with the innermost planet at 3 au) up to the point where a planet is ejected from the system. The ejected planet has an initial system of 100 test-particle moons. We determine the survival probability of moons at different distances from their host planet, measure the final distribution of orbital elements, examine the stability of resonant configurations, and characterize the properties of moons that are stripped from the planets. We find that moons are likely to survive in orbits with semi-major axes out beyond 200 planetary radii (0.1 au in our case). The orbital inclinations and eccentricities of the surviving moons are broadly distributed and include nearly hyperbolic orbits and retrograde orbits. We find that a large fraction of moons in two-body and three-body mean-motion resonances also survive planetary ejection with the resonance intact. The moon–planet interactions, especially in the presence of mean-motion resonance, can keep the interior of the moons molten for billions of years via tidal flexing, as is seen in the moons of the gas giant planets in the solar system. Given the possibility that life may exist in the subsurface ocean of the Galilean satellite Europa, these results have implications for life on the moons of rogue planets – planets that drift through our Galaxy with no host star.

A Comprehensive Model of the Meteoroid Environment around Mercury

Abstract To characterize the meteoroid environment around Mercury and its contribution to the planet’s exosphere, we combined four distinctive sources of meteoroids in the solar system: main-belt asteroids, Jupiter-family comets, Halley-type comets, and Oort Cloud comets. All meteoroid populations are described by currently available dynamical models. We used a recent calibration of the meteoroid influx onto Earth as a constraint for the combined population model on Mercury. We predict vastly different distributions of orbital elements, impact velocities, and directions of arrival for all four meteoroid populations at Mercury. We demonstrate that the most likely model of Mercury’s meteoroid environment—in the sense of agreement with Earth—provides good agreement with previously reported observations of Mercury’s exosphere by the MESSENGER spacecraft and is not highly sensitive to variations of uncertain parameters such as the ratio of these populations at Earth, the size–frequency distribution, and the collisional lifetime of meteoroids. Finally, we provide a fully calibrated model consisting of high-resolution maps of mass influx and surface vaporization rates for different values of Mercury’s true anomaly angle.

Orbital Alignment of Main-belt Comets

Abstract We examine the orbital element distribution of main-belt comets (MBCs), which are objects that exhibit cometary activity yet orbit in the main asteroid belt and may be potentially useful as tracers of ice in the inner solar system. We find that the currently known and currently active MBCs have remarkably similar longitudes of perihelion, which are also aligned with that of Jupiter. The clustered objects have significantly higher current osculating eccentricities relative to their proper eccentricities, consistent with their orbits being currently, though only temporarily, secularly excited in osculating eccentricity due to Jupiter’s influence. At the moment, most MBCs seem to have current osculating elements that may be particularly favorable for the object becoming active (e.g., maybe because of higher perihelion temperatures or higher impact velocities causing an effective increase in the size of the potential triggering impactor population). At other times, other icy asteroids will have those favorable conditions and might become MBCs at those times as well.

Orbits for the Impatient: A Bayesian Rejection-sampling Method for Quickly Fitting the Orbits of Long-period Exoplanets

Abstract We describe a Bayesian rejection-sampling algorithm designed to efficiently compute posterior distributions of orbital elements for data covering short fractions of long-period exoplanet orbits. Our implementation of this method, Orbits for the Impatient (OFTI), converges up to several orders of magnitude faster than two implementations of Markov Chain Monte Carlo (MCMC) in this regime. We illustrate the efficiency of our approach by showing that OFTI calculates accurate posteriors for all existing astrometry of the exoplanet 51 Eri b up to 100 times faster than a Metropolis–Hastings MCMC. We demonstrate the accuracy of OFTI by comparing our results for several orbiting systems with those of various MCMC implementations, finding the output posteriors to be identical within shot noise. We also describe how our algorithm was used to successfully predict the location of 51 Eri b six months in the future based on less than three months of astrometry. Finally, we apply OFTI to 10 long-period exoplanets and brown dwarfs, all but one of which have been monitored over less than 3% of their orbits, producing fits to their orbits from astrometric records in the literature.

OBSERVATIONAL SIGNATURES OF A MASSIVE DISTANT PLANET ON THE SCATTERING DISK

ABSTRACT The orbital element distribution of trans-Neptunian objects (TNOs) with large pericenters has been suggested to be influenced by the presence of an undetected, large planet at &gt;200 au from the Sun. To find additional observables caused by this scenario, we present here the first detailed emplacement simulation in the presence of a massive ninth planet on the distant Kuiper Belt. We perform 4 Gyr N-body simulations with the currently known solar system planetary architecture, plus a 10 M ⊕ planet with similar orbital parameters to those suggested by Trujillo &amp; Sheppard or Batygin &amp; Brown, and 105 test particles in an initial planetesimal disk. We find that including a distant super-Earth-mass planet produces a substantially different orbital distribution for the scattering and detached TNOs, raising the pericenters and inclinations of moderate semimajor axis (50 &lt; a &lt; 500 au) objects. We test whether this signature is detectable via a simulator with the observational characteristics of four precisely characterized TNO surveys. We find that the qualitatively very distinct solar system models that include a ninth planet are essentially observationally indistinguishable from an outer solar system produced solely by the four giant planets. We also find that the mass of the Kuiper Belt’s current scattering and detached populations is required to be 3–10 times larger in the presence of an additional planet. We do not find any evidence for clustering of orbital angles in our simulated TNO population. Wide-field, deep surveys targeting inclined high-pericenter objects will be required to distinguish between these different scenarios.

MODELING THE NEARLY ISOTROPIC COMET POPULATION IN ANTICIPATION OF LSST OBSERVATIONS

ABSTRACT We run simulations to determine the expected distribution of orbital elements of nearly isotropic comets (NICs) in the outer solar system, assuming that these comets originate in the Oort Cloud at thousands of au and are perturbed into the planetary region by the Galactic tide. We show that the Large Synoptic Survey Telescope should detect and characterize the orbits of hundreds to thousands of NICs with perihelion distance outside 5 au. Observing NICs in the outer solar system is our only way of directly detecting comets from the inner Oort Cloud, as these comets are dynamically excluded from the inner solar system by the giant planets. Thus, the distribution of orbital elements constrains the spatial distribution of comets in the Oort Cloud and the environment in which the solar system formed. Additionally, comet orbits can be characterized more precisely when they are seen far from the Sun as they have not been affected by nongravitational forces.

Dynamics and distribution of Jovian dust ejected from the Galilean satellites

AbstractIn this paper, the dynamical analysis of the Jovian dust originating from the four Galilean moons is presented. High‐accuracy orbital integrations of dust particles are used to determine their dynamical evolution. A variety of forces are taken into account, including the Lorentz force, solar radiation pressure, Poynting‐Robertson drag, solar gravity, the satellites' gravity, plasma drag, and gravitational effects due to nonsphericity of Jupiter. More than 20,000 dust particles from each source moon in the size range from 0.05 μm to 1 cm are simulated over 8000 (Earth) years until each dust grain hits a sink (moons, Jupiter, or escape from the system). Configurations of dust number density in the Jovicentric equatorial inertial frame are calculated and shown. In a Jovicentric frame rotating with the Sun the dust distributions are found to be asymmetric. For certain small particle sizes, the dust population is displaced towards the Sun, while for certain larger sizes, the dust population is displaced away from the Sun. The average lifetime as a function of particle size for ejecta from each source moon is derived, and two sharp jumps in the average lifetime are analyzed. Transport of dust between the Galilean moons and to Jupiter is investigated. Most of the orbits for dust particles from Galilean moons are prograde, while, surprisingly, a small fraction of orbits are found to become retrograde mainly due to solar radiation pressure and Lorentz force. The distribution of orbital elements is also analyzed.

GRAVITATIONAL ENCOUNTERS AND THE EVOLUTION OF GALACTIC NUCLEI. IV. CAPTURES MEDIATED BY GRAVITATIONAL-WAVE ENERGY LOSS

Direct numerical integrations of the two-dimensional Fokker-Planck equation are carried out for compact objects orbiting a supermassive black hole (SBH) at the center of a galaxy. As in Papers I-III, the diffusion coefficients incorporate the effects of the lowest-order post-Newtonian corrections to the equations of motion. In addition, terms describing the loss of orbital energy and angular momentum due to the 5/2-order post-Newtonian terms are included. In the steady state, captures are found to occur in two regimes that are clearly differentiated in terms of energy, or semimajor axis; these two regimes are naturally characterized as "plunges" (low binding energy) and "EMRIs," or extreme-mass-ratio inspirals (high binding energy). The capture rate, and the distribution of orbital elements of the captured objects, are presented for two steady-state models based on the Milky Way: one with a relatively high density of remnants and one with a lower density. In both models, but particularly in the second, the steady-state energy distribution and the distribution of orbital elements of the captured objects are substantially different than if the Bahcall-Wolf energy distribution were assumed. The ability of classical relaxation to soften the blocking effects of the Schwarzschild barrier is quantified.These results, together with those of Papers I-III, suggest that a Fokker-Planck description can adequately represent the dynamics of collisional loss cones in the relativistic regime.

The main-belt comets: The Pan-STARRS1 perspective

We analyze a set of 760475 observations of 333026 unique main-belt objects obtained by the Pan-STARRS1 (PS1) survey telescope between 2012 May 20 and 2013 November 9, a period during which PS1 discovered two main-belt comets, P/2012 T1 (PANSTARRS) and P/2013 R3 (Catalina-PANSTARRS). PS1 comet detection procedures currently consist of the comparison of the point spread functions (PSFs) of moving objects to those of reference stars, and the flagging of objects that show anomalously large radial PSF widths for human evaluation and possible observational follow-up. Based on the number of missed discovery opportunities among comets discovered by other observers, we estimate an upper limit comet discovery efficiency rate of ∼70% for PS1. Additional analyses that could improve comet discovery yields in future surveys include linear PSF analysis, modeling of trailed stellar PSFs for comparison to trailed moving object PSFs, searches for azimuthally localized activity, comparison of point-source-optimized photometry to extended-source-optimized photometry, searches for photometric excesses in objects with known absolute magnitudes, and crowd-sourcing. Analysis of the discovery statistics of the PS1 survey indicates an expected fraction of 59 MBCs per 106 outer main-belt asteroids (corresponding to a total expected population of ∼140 MBCs among the outer main-belt asteroid population with absolute magnitudes of 12<HV<19.5), and a 95% confidence upper limit of 96 MBCs per 106 outer main-belt asteroids (corresponding to a total of ∼230 MBCs), assuming a detection efficiency of 50%. We note however that significantly more sensitive future surveys (particularly those utilizing larger aperture telescopes) could detect many more MBCs than estimated here. Examination of the orbital element distribution of all known MBCs reveals an excess of high eccentricities (0.1<e<0.3) relative to the background asteroid population. Theoretical calculations show that, given these eccentricities, the sublimation rate for a typical MBC is orders of magnitude larger at perihelion than at aphelion, providing a plausible physical explanation for the observed behavior of MBCs peaking in observed activity strength near perihelion. These results indicate that the overall rate of mantle growth should be slow, consistent with observational evidence that MBC activity can be sustained over multiple orbit passages.