arXiv subjects

Renu Malhotra

Publications and source records attributed to Renu Malhotra.

At least 73 records · Page 4Linked to original sources

arXiv2018

A comprehensive understanding of planet formation is required for assessing planetary habitability and for the search for life

Dozens of habitable zone, approximately earth-sized exoplanets are known today. An emerging frontier of exoplanet studies is identifying which of these habitable zone, small planets are actually habitable (have all necessary conditions for life) and, of those, which are earth-like. Many parameters and processes influence habitability, ranging from the orbit through detailed composition including volatiles and organics, to the presence of geological activity and plate tectonics. While some properties will soon be directly observable, others cannot be probed by remote sensing for the foreseeable future. Thus, statistical understanding of planetary systems' formation and evolution is a key supplement to the direct measurements of planet properties. Probabilistically assessing parameters we cannot directly measure is essential to reliably assess habitability, to prioritizing habitable-zone planets for follow-up, and for interpreting possible biosignatures.

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arXiv2018

The mid-plane of the Main Asteroid Belt

We measure the mid-plane of the main asteroid belt by using the observational data of a nearly complete and unbiased sample of asteroids, and find that it has inclination $\bar{I}=0.93\pm0.04$ degrees and longitude of ascending node $\barΩ=87.6\pm2.6$ degrees (in J2000 ecliptic-equinox coordinate system). This plane differs significantly from previously published measurements, and it is also distinctly different than the solar system's invariable plane as well as Jupiter's orbit plane. The mid-plane of the asteroid belt is theoretically expected to be a slightly warped sheet whose local normal is controlled by the gravity of the major planets. Specifically, its inclination and longitude of ascending node varies with semi-major axis and time (on secular timescales), and is defined by the forced solution of secular perturbation theory; the $ν_{16}$ nodal secular resonance is predicted to cause a significant warp of the mid-plane in the inner asteroid belt. We test the secular theory by measuring the current location of the asteroids' mid-plane in finer semi-major axis bins. We find that the measured mid-plane in the middle and outer asteroid belt is consistent, within 3--$σ$ confidence level, with the prediction of secular perturbation theory, but a notable discrepancy is present in the inner asteroid belt near $\sim2$ AU.

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arXiv2017

Prospects for unseen planets beyond Neptune

Several anomalous features in the orbital distribution of distant Kuiper Belt objects have recently sparked suggestions of an unseen large planet (or two) orbiting beyond Neptune. I review the theoretical arguments and the prospects for the existence of unseen massive bodies in the distant solar system.

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arXiv2017

The curiously warped mean plane of the Kuiper belt

We measured the mean plane of the Kuiper belt as a function of semi-major axis. For the classical Kuiper belt as a whole (the non-resonant objects in the semi-major axis range 42--48~au), we find a mean plane of inclination $i_m=1.8^{\circ}$$^{+0.7^{\circ}}_{-0.4^{\circ}}$ and longitude of ascending node $Ω_m=77^{\circ}$$^{+18^{\circ}}_{-14^{\circ}}$ (in the J2000 ecliptic-equinox coordinate system), in accord with theoretical expectations of the secular effects of the known planets. With finer semi-major axis bins, we detect a statistically significant warp in the mean plane near semi-major axes 40--42~au. Linear secular theory predicts a warp near this location due to the $ν_{18}$ nodal secular resonance, however the measured mean plane for the 40.3-42~au semi-major axis bin (just outside the $ν_{18}$) is inclined $\sim13^{\circ}$ to the predicted plane, a nearly 3-$σ$ discrepancy. For the more distant Kuiper belt objects of semi-major axes in the range 50--80~au, the expected mean plane is close to the invariable plane of the solar system, but the measured mean plane deviates greatly from this: it has inclination $i_m=9.1^{\circ}$$^{+6.6^{\circ}}_{-3.8^{\circ}}$ and longitude of ascending node $Ω_m=227^{\circ}$$^{+18^{\circ}}_{-44^{\circ}}$. We estimate this deviation from the expected mean plane to be statistically significant at the $\sim97-99\%$ confidence level. We discuss several possible explanations for this deviation, including the possibility that a relatively close-in ($a\lesssim100$~au), unseen small planetary-mass object in the outer solar system is responsible for the warping.

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arXiv2017

ALMA 1.3 Millimeter Map of the HD 95086 System

Planets and minor bodies such as asteroids, Kuiper-belt objects and comets are integral components of a planetary system. Interactions among them leave clues about the formation process of a planetary system. The signature of such interactions is most prominent through observations of its debris disk at millimeter wavelengths where emission is dominated by the population of large grains that stay close to their parent bodies. Here we present ALMA 1.3 mm observations of HD 95086, a young early-type star that hosts a directly imaged giant planet b and a massive debris disk with both asteroid- and Kuiper-belt analogs. The location of the Kuiper-belt analog is resolved for the first time. The system can be depicted as a broad ($ΔR/R \sim$0.84), inclined (30\arcdeg$\pm$3\arcdeg) ring with millimeter emission peaked at 200$\pm$6 au from the star. The 1.3 mm disk emission is consistent with a broad disk with sharp boundaries from 106$\pm$6 to 320$\pm$20 au with a surface density distribution described by a power law with an index of --0.5$\pm$0.2. Our deep ALMA map also reveals a bright source located near the edge of the ring, whose brightness at 1.3 mm and potential spectral energy distribution are consistent with it being a luminous star-forming galaxy at high redshift. We set constraints on the orbital properties of planet b assuming co-planarity with the observed disk.

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arXiv2017

Simplified derivation of the collision probability of two objects in independent Keplerian orbits

Many topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of Öpik (1951) and Wetherill (1967), the collision probability was derived by linearizing the motion near the collision points, and there is now a vast literature using their method. We present here a simpler and more physically motivated derivation for non-tangential collisions in Keplerian orbits, as well as for tangential collisions that were not previously considered. Our formulas have the added advantage of being manifestly symmetric in the parameters of the two colliding bodies. In common with the Öpik-Wetherill treatments, we linearize the motion of the bodies in the vicinity of the point of orbit intersection (or near the points of minimum distance between the two orbits) and assume a uniform distribution of impact parameter within the collision radius. We point out that the linear approximation leads to singular results for the case of tangential encounters. We regularize this singularity by use of a parabolic approximation of the motion in the vicinity of a tangential encounter.

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arXiv2017

Mean motion resonances at high eccentricities: the 2:1 and the 3:2 interior resonances

Mean motion resonances [MMRs] play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system as well as exo-planetary systems. Most previous theoretical analyses have focused on the low-to-moderate eccentricity regime, but with new discoveries of high eccentricity resonant minor planets and even exoplanets, there is increasing motivation to examine MMRs in the high eccentricity regime. Here we report on a study of the high eccentricity regime of MMRs in the circular planar restricted three-body problem. Non-perturbative numerical analyses of the 2:1 and the 3:2 interior resonances are carried out for a wide range of secondary-to-primary mass ratio, and for a wide range of eccentricity of the test particle. The surface-of-section technique is used to study the phase space structure near resonances. We identify transitions in phase space at certain critical eccentricities related to the geometry of resonant orbits; new stable libration zones appear at high eccentricity at libration centers shifted from those at low eccentricities. We present novel results on the mass and eccentricity dependence of the resonance libration centers and their widths in semi-major axis. Our results show that MMRs have sizable libration zones at high eccentricities, comparable to those at lower eccentricities.

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arXiv2016

Eccentricity distribution in the main asteroid belt

The observationally complete sample of the main belt asteroids now spans more than two orders of magnitude in size and numbers more than 64,000 (excluding collisional family members). We undertook an analysis of asteroids' eccentricities and their interpretation with simple physical models. We find that Plummer's (1916) conclusion that the asteroids' eccentricities follow a Rayleigh distribution holds for the osculating eccentricities of large asteroids, but the proper eccentricities deviate from a Rayleigh distribution: there is a deficit of eccentricities smaller than $\sim0.1$ and an excess of larger eccentricities. We further find that the proper eccentricities do not depend significantly on asteroid size but have strong dependence on heliocentric distance: the outer asteroid belt follows a Rayleigh distribution, but the inner belt is strikingly different. Eccentricities in the inner belt can be modeled as a vector sum of a primordial eccentricity vector of random orientation and magnitude drawn from a Rayleigh distribution of parameter $\sim0.06$, and an excitation of random phase and magnitude $\sim0.13$. These results imply that a late dynamical excitation of the asteroids occurred, it was independent of asteroid size, it was stronger in the inner belt than in the outer belt. We discuss implications for the primordial asteroid belt and suggest that the observationally complete sample size of main belt asteroids is large enough that more sophisticated model-fitting of the eccentricities is warranted and could serve to test alternative theoretical models of the dynamical excitation history of asteroids and its links to the migration history of the giant planets.

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arXiv2016

Corralling a distant planet with extreme resonant Kuiper belt objects

The four longest period Kuiper belt objects have orbital periods close to integer ratios with each other. A hypothetical planet with orbital period $\sim$17,117 years, semimajor axis $\sim$665 AU, would have N/1 and N/2 period ratios with these four objects. The orbital geometries and dynamics of resonant orbits constrain the orbital plane, the orbital eccentricity and the mass of such a planet, as well as its current location in its orbital path.

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arXiv2016

Lightcurves of the Karin family asteroids

The Karin family is a very young asteroid family created by an asteroid breakup 5.8 Myr ago. Since the members of this family probably have not experienced significant orbital or collisional evolution yet, it is possible that they still preserve properties of the original family-forming event in terms of their spin state. As we carried out a series of photometric observations of the Karin family asteroids, here we report an analysis result of lightcurves including the rotation period of eleven members. The mean rotation rate of the Karin family members turned out to be much lower than those of NEAs or smaller MBAs (diameter D<12 km), and even lower than that of larger MBAs (D>130 km). We investigated a correlation between the peak-to-peak variation magnitude reduced to zero solar phase angle and the rotation period of the eleven Karin family asteroids, and found a possible trend that elongated members have lower spin rate, and less elongated members have higher spin rate. However, this has to be confirmed by another series of future observations.

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arXiv2015

The Mass Distribution Function of Planets

The distribution of orbital period ratios of adjacent planets in extra-solar planetary systems discovered by the {\it Kepler} space telescope exhibits a peak near $\sim1.5$--$2$, a long tail of larger period ratios, and a steep drop-off in the number of systems with period ratios below $\sim1.5$. We find from this data that the dimensionless orbital separations have an approximately log-normal distribution. Using Hill's criterion for the dynamical stability of two planets, we find an upper bound on planet masses such that the most common planet mass does not exceed $10^{-3.2}m_*$, or about two-thirds Jupiter mass for solar mass stars. Assuming that the mass ratio and the dynamical separation (orbital spacings in units of mutual Hill radius) of adjacent planets are independent random variates, and adopting empirical distributions for these, we use Hill's criterion in a statistical way to estimate the planet mass distribution function from the observed distribution of orbital separations. We find that the planet mass function is peaked in logarithm of mass, with a peak value and standard deviation of $\log m/M_\oplus$ of $\sim(0.6-1.0)$ and $\sim(1.1-1.2)$, respectively.

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arXiv2015

The current impact flux on Mars and its seasonal variation

We calculate the present-day impact flux on Mars and its variation over the Martian year, using the current data on the orbital distribution of known Mars-crossing minor planets. We adapt the {Ö}pik-Wetherill formulation for calculating collision probabilities, paying careful attention to the non-uniform distribution of the perihelion longitude and the argument of perihelion owed to secular planetary perturbations. We find that these previously neglected non-uniformities have a significant effect on the mean annual impact flux as well as its seasonal variation. The impact flux peaks when Mars is at aphelion, but the near-alignment of Mars' eccentricity vector with the mean direction of the eccentricity vectors of Mars-crossers causes the mean annual impact flux as well as the amplitude of the seasonal variation to be significantly lower than the estimate based on a uniform random distribution of perihelion longitudes of Mars-crossers. We estimate that the flux of large impactors (of absolute magnitude $H<16$) within $\pm30^\circ$ of Mars' aphelion is about four times larger than when the planet is near perihelion. Extrapolation of our results to a model population of meter-size Mars-crossers shows that if these small impactors have a uniform distribution of their angular elements, then their aphelion-to-perihelion impact flux ratio would be as large as 25. These theoretical predictions can be tested with observational data of contemporary impacts that is becoming available from spacecraft currently in orbit about Mars.

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arXiv2014

Debris Distribution in HD 95086 - A Young Analog of HR 8799

HD 95086 is a young early-type star that hosts (1) a 5 MJ planet at the projected distance of 56 AU revealed by direct imaging, and (2) a prominent debris disk. Here we report the detection of 69 um crystalline olivine feature from the disk using the Spitzer/MIPS-SED data covering 55-95 um. Due to the low resolution of MIPS-SED mode, this feature is not spectrally resolved, but is consistent with the emission from crystalline forsterite contributing 5% of the total dust mass. We also present detailed analysis of the disk SED and re-analysis of resolved images obtained by Herschel. Our results suggest that the debris structure around HD 95086 consists of a warm (175 K) belt, a cold (55 K) disk, and an extended disk halo (up to 800 AU), and is very similar to that of HR 8799. We compare the properties of the three debris components, and suggest that HD 95086 is a young analog of HR 8799. We further investigate and constrain single-planet, two-planet, three-planet and four-planet architectures that can account for the observed debris structure and are compatible with dynamical stability constraints. We find that equal-mass four-planet configurations of geometrically spaced orbits, with each planet of mass 5 MJ, could maintain the gap between the warm and cold debris belts, and also be just marginally stable for timescales comparable to the age of the system.

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arXiv2014

Planetary chaotic zone clearing: destinations and timescales

We investigate the orbital evolution of particles in a planet's chaotic zone to determine their final destinations and their timescales of clearing. There are four possible final states of chaotic particles: collision with the planet, collision with the star, escape, or bounded but non-collision orbits. In our investigations, within the framework of the planar circular restricted three body problem for planet-star mass ratio $μ$ in the range $10^{-9}$ to $10^{-1.5}$, we find no particles hitting the star. The relative frequencies of escape and collision with the planet are not scale-free, as they depend upon the size of the planet. For planet radius $R_p\ge0.001R_H$ where $R_H$ is the planet's Hill radius, we find that most chaotic zone particles collide with the planet for $μ\lesssim10^{-5}$; particle scattering to large distances is significant only for higher mass planets. For fixed ratio $R_p/R_H$, the particle clearing timescale, $T_{cl}$, has a broken power-law dependence on $μ$. A shallower power-law, $T_{cl}\sim μ^{-{1/3}}$, prevails at small $μ$ where particles are cleared primarily by collisions with the planet; a steeper power law, $T_{cl}\simμ^{-{3/2}}$, prevails at larger $μ$ where scattering dominates the particle loss. In the limit of vanishing planet radius, we find $T_{cl}\approx0.024μ^{-{3\over2}}$. The interior and exterior boundaries of the annular zone in which chaotic particles are cleared are increasingly asymmetric about the planet's orbit for larger planet masses; the inner boundary coincides well with the classical first order resonance overlap zone, $Δa_{cl,int}\simeq1.2μ^{0.28}a_p$; the outer boundary is better described by $Δa_{cl,ext}\simeq1.7μ^{0.31}a_p$, where $a_p$ is the planet-star separation.

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arXiv2014

The inner solar system cratering record and the evolution of impactor populations

We review previously published and newly obtained crater size-frequency distributions in the inner solar system. These data indicate that the Moon and the terrestrial planets have been bombarded by two populations of objects. Population 1, dominating at early times, had nearly the same size distribution as the present-day asteroid belt, and produced the heavily cratered surfaces with a complex, multi-sloped crater size-frequency distribution. Population 2, dominating since about 3.8-3.7 Ga, has the same size distribution as near-Earth objects (NEOs), had a much lower impact flux, and produced a crater size distribution characterized by a differential -3 single-slope power law in the crater diameter range 0.02 km to 100 km. Taken together with the results from a large body of work on age-dating of lunar and meteorite samples and theoretical work in solar system dynamics, a plausible interpretation of these data is as follows. The NEO population is the source of Population 2 and it has been in near-steady state over the past ~3.7-3.8 gigayears; these objects are derived from the main asteroid belt by size-dependent non-gravitational effects that favor the ejection of smaller asteroids. However, Population 1 were main belt asteroids ejected from their source region in a size-independent manner, possibly by means of gravitational resonance sweeping during giant planet orbit migration; this caused the so-called Late Heavy Bombardment (LHB). The LHB began some time before ~3.9 Ga, peaked and declined rapidly over the next ~100 to 300 megayears, and possibly more slowly from about 3.8-3.7 Ga to ~2 Ga. A third crater population (Population S) consists of secondary impact craters that can dominate the cratering record at small diameters.

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arXiv2013

Predictions for Shepherding Planets in Scattered Light Images of Debris Disks

Planets can affect debris disk structure by creating gaps, sharp edges, warps, and other potentially observable signatures. However, there is currently no simple way for observers to deduce a disk-shepherding planet's properties from the observed features of the disk. Here we present a single equation that relates a shepherding planet's maximum mass to the debris ring's observed width in scattered light, along with a procedure to estimate the planet's eccentricity and minimum semimajor axis. We accomplish this by performing dynamical N-body simulations of model systems containing a star, a single planet, and a disk of parent bodies and dust grains to determine the resulting debris disk properties over a wide range of input parameters. We find that the relationship between planet mass and debris disk width is linear, with increasing planet mass producing broader debris rings. We apply our methods to five imaged debris rings to constrain the putative planet masses and orbits in each system. Observers can use our empirically-derived equation as a guide for future direct imaging searches for planets in debris disk systems. In the fortuitous case of an imaged planet orbiting interior to an imaged disk, the planet's maximum mass can be estimated independent of atmospheric models.

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arXiv2013

On the Non-uniform Distribution of the Angular Elements of Near-Earth Objects

We examine the angular distributions of near-Earth objects (NEOs) which are often regarded as uniform. The apparent distribution of the longitude of ascending node, $Ω$, is strongly affected by well-known seasonal effects in the discovery rate of NEOs. The deviation from the expected $π$-periodicity in the apparent distribution of $Ω$ indicates that its intrinsic distribution is slightly enhanced along a mean direction, $\barΩ=111^\circ$; approximately 53% of NEOs have $Ω$ values within $\pm90^\circ$ of $\barΩ$. We also find that each sub-group of NEOs (Amors, Apollos and Atens) has different observational selection effects which cause different non-uniformities in the apparent distributions of their arguments of perihelion $ω$, and longitudes of perihelion $\varpi$. For their intrinsic distributions, our analysis reveals that the Apollo asteroids have non-uniform $ω$ due to secular dynamics associated with inclination-eccentricity-$ω$ coupling, and the Amors' $\varpi$ distribution is peaked towards the secularly forced eccentricity vector. The Apollos' $ω$ distribution is axial, favoring values near 0 and $180^\circ$; the two quadrants centered at 0 and $180^\circ$ account for 55% of the Apollos' $ω$ values. The Amors' $\varpi$ distribution peaks near $\bar\varpi=4^\circ$; sixty-one percent of Amors have $\varpi$ within $\pm90^\circ$ of this peak. We show that these modest but statistically significant deviations from uniform random distributions of angular elements are owed to planetary perturbations, primarily Jupiter's. It is remarkable that this strongly chaotic population of minor planets reveals the presence of Jupiter in its angular distributions.

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arXiv2013

Do Centaurs preserve their source inclinations?

The Centaurs are a population of small, planet-crossing objects in the outer solar system. They are dynamically short-lived and represent the transition population between the Kuiper belt and the Jupiter family short-period comets. Dynamical models and observations of the physical properties of the Centaurs indicate that they may have multiple source populations in the trans-Neptunian region. It has been suggested that the inclination distribution of the Centaurs may be useful in distinguishing amongst these source regions. The Centaurs, however, undergo many close encounters with the giant planets during their orbital evolution; here we show that these encounters can substantially determine the inclination distribution of the Centaurs. Almost any plausible initial inclination distribution of a Kuiper belt source results in Centaurs having inclinations peaked near 10-20 degrees. Our studies also find that the Kuiper belt is an extremely unlikely source of the retrograde Centaur that has been observed.

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