arXiv subjects

David S. Spiegel

Publications and source records attributed to David S. Spiegel.

At least 19 recordsLinked to original sources

arXiv2024

A new timestep criterion for N-body simulations

We derive a new criterion for estimating characteristic dynamical timescales in N-body simulations. The criterion uses the second, third, and fourth derivatives of particle positions: acceleration, jerk, and snap. It can be used for choosing timesteps in integrators with adaptive step size control. For any two-body problem the criterion is guaranteed to determine the orbital period and pericenter timescale regardless of eccentricity. We discuss why our criterion is the simplest derivative-based expression for choosing adaptive timesteps with the above properties and show its superior performance over existing criteria in numerical tests. Because our criterion uses lower order derivatives, it is less susceptible to rounding errors caused by finite floating point precision. This significantly decreases the volume of phase space where an adaptive integrator fails or gets stuck due to unphysical timestep estimates. For example, our new criterion can accurately estimate timesteps for orbits around a 50m sized Solar System object located at 40AU from the coordinate origin when using double floating point precision. Previous methods where limited to objects larger than 10km. We implement our new criterion in the high order IAS15 integrator which is part of the freely available N-body package REBOUND.

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arXiv2016

Radio Emission from Red-Giant Hot Jupiters

When planet-hosting stars evolve off the main sequence and go through the red-giant branch, the stars become orders of magnitudes more luminous and, at the same time, lose mass at much higher rates than their main-sequence counterparts. Accordingly, if planetary companions exist around these stars at orbital distances of a few AU, they will be heated up to the level of canonical hot Jupiters and also be subjected to a dense stellar wind. Given that magnetized planets interacting with stellar winds emit radio waves, such "Red-Giant Hot Jupiters" (RGHJs) may also be candidate radio emitters. We estimate the spectral auroral radio intensity of RGHJs based on the empirical relation with the stellar wind as well as a proposed scaling for planetary magnetic fields. RGHJs might be intrinsically as bright as or brighter than canonical hot Jupiters and about 100 times brighter than equivalent objects around main-sequence stars. We examine the capabilities of low-frequency radio observatories to detect this emission and find that the signal from an RGHJ may be detectable at distances up to a few hundred parsecs with the Square Kilometer Array.

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arXiv2014

IAS15: A fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits

We present IAS15, a 15th-order integrator to simulate gravitational dynamics. The integrator is based on a Gauß-Radau quadrature and can handle conservative as well as non-conservative forces. We develop a step-size control that can automatically choose an optimal timestep. The algorithm can handle close encounters and high-eccentricity orbits. The systematic errors are kept well below machine precision and long-term orbit integrations over $10^9$ orbits show that IAS15 is optimal in the sense that it follows Brouwer's law, i.e. the energy error behaves like a random walk. Our tests show that IAS15 is superior to a mixed-variable symplectic integrator (MVS) and other popular integrators, including high-order ones, in both speed and accuracy. In fact, IAS15 preserves the symplecticity of Hamiltonian systems better than the commonly-used nominally symplectic integrators to which we compared it. We provide an open-source implementation of IAS15. The package comes with several easy-to-extend examples involving resonant planetary systems, Kozai-Lidov cycles, close encounters, radiation pressure, quadrupole moment, and generic damping functions that can, among other things, be used to simulate planet-disc interactions. Other non-conservative forces can be added easily.

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arXiv2014

Prospects for Detecting Oxygen, Water, and Chlorophyll on an Exo-Earth

The goal of finding and characterizing nearby Earth-like planets is driving many NASA high-contrast flagship mission concepts, the latest of which is known as the Advanced Technology Large-Aperture Space Telescope (ATLAST). In this article, we calculate the optimal spectral resolution $R=λ/δλ$ and minimum signal-to-noise ratio per spectral bin (SNR), two central design requirements for a high-contrast space mission, in order to detect signatures of water, oxygen, and chlorophyll on an Earth twin. We first develop a minimally parametric model and demonstrate its ability to fit synthetic and observed Earth spectra; this allows us to measure the statistical evidence for each component's presence. We find that water is the easiest to detect, requiring a resolution $R \gtrsim 20$, while the optimal resolution for oxygen is likely to be closer to $R = 150$, somewhat higher than the canonical value in the literature. At these resolutions, detecting oxygen will require $\sim$2 times the SNR as water. Chlorophyll requires $\sim$6 times the SNR as oxygen for an Earth twin, only falling to oxygen-like levels of detectability for a low cloud cover and/or a large vegetation covering fraction. This suggests designing a mission for sensitivity to oxygen and adopting a multi-tiered observing strategy, first targeting water, then oxygen on the more favorable planets, and finally chlorophyll on only the most promising worlds.

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arXiv2014

A Statistical Analysis of SEEDS and Other High-Contrast Exoplanet Surveys: Massive Planets or Low-Mass Brown Dwarfs?

We conduct a statistical analysis of a combined sample of direct imaging data, totalling nearly 250 stars. The stars cover a wide range of ages and spectral types, and include five detections ($κ$ And b, two $\sim$60 M$_{\rm J}$ brown dwarf companions in the Pleiades, PZ Tel B, and CD$-$35 2722B). For some analyses we add a currently unpublished set of SEEDS observations, including the detections GJ 504b and GJ 758B. We conduct a uniform, Bayesian analysis of all stellar ages using both membership in a kinematic moving group and activity/rotation age indicators. We then present a new statistical method for computing the likelihood of a substellar distribution function. By performing most of the integrals analytically, we achieve an enormous speedup over brute-force Monte Carlo. We use this method to place upper limits on the maximum semimajor axis of the distribution function derived from radial-velocity planets, finding model-dependent values of $\sim$30--100 AU. Finally, we model the entire substellar sample, from massive brown dwarfs to a theoretically motivated cutoff at $\sim$5 M$_{\rm Jup}$, with a single power law distribution. We find that $p(M, a) \propto M^{-0.65\pm0.60} a^{-0.85\pm0.39}$ (1$σ$ errors) provides an adequate fit to our data, with 1.0--3.1\% (68\% confidence) of stars hosting 5--70 $M_{\rm Jup}$ companions between 10 and 100 AU. This suggests that many of the directly imaged exoplanets known, including most (if not all) of the low-mass companions in our sample, formed by fragmentation in a cloud or disk, and represent the low-mass tail of the brown dwarfs.

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arXiv2014

CHARIS Science: Performance Simulations for the Subaru Telescope's Third-Generation of Exoplanet Imaging Instrumentation

We describe the expected scientific capabilities of CHARIS, a high-contrast integral-field spectrograph (IFS) currently under construction for the Subaru telescope. CHARIS is part of a new generation of instruments, enabled by extreme adaptive optics (AO) systems (including SCExAO at Subaru), that promise greatly improved contrasts at small angular separation thanks to their ability to use spectral information to distinguish planets from quasistatic speckles in the stellar point-spread function (PSF). CHARIS is similar in concept to GPI and SPHERE, on Gemini South and the Very Large Telescope, respectively, but will be unique in its ability to simultaneously cover the entire near-infrared $J$, $H$, and $K$ bands with a low-resolution mode. This extraordinarily broad wavelength coverage will enable spectral differential imaging down to angular separations of a few $λ/D$, corresponding to $\sim$$0.\!\!''1$. SCExAO will also offer contrast approaching $10^{-5}$ at similar separations, $\sim$$0.\!\!''1$--$0.\!\!''2$. The discovery yield of a CHARIS survey will depend on the exoplanet distribution function at around 10 AU. If the distribution of planets discovered by radial velocity surveys extends unchanged to $\sim$20 AU, observations of $\sim$200 mostly young, nearby stars targeted by existing high-contrast instruments might find $\sim$1--3 planets. Carefully optimizing the target sample could improve this yield by a factor of a few, while an upturn in frequency at a few AU could also increase the number of detections. CHARIS, with a higher spectral resolution mode of $R \sim 75$, will also be among the best instruments to characterize planets and brown dwarfs like HR 8799 cde and $κ$ And b.

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arXiv2014

Some inconvenient truths about biosignatures involving two chemical species on Earth-like exoplanets

The detection of strong thermochemical disequilibrium in the atmosphere of an extrasolar planet is thought to be a potential biosignature. In this article we present a new kind of false positive that can mimic a disequilibrium or any other biosignature that involves two chemical species. We consider a scenario where the exoplanet hosts a moon that has its own atmosphere and neither of the atmospheres is in chemical disequilibrium. Our results show that the integrated spectrum of the planet and the moon closely resembles that of a single object in strong chemical disequilibrium. We derive a firm limit on the maximum spectral resolution that can be obtained for both directly-imaged and transiting planets. The spectral resolution of even idealized space-based spectrographs that might be achievable in the next several decades is in general insufficient to break the degeneracy. Both chemical species can only be definitively confirmed in the same object if absorption features of both chemicals can be unambiguously identified and their combined depth exceeds 100%.

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arXiv2013

The Structure of Exoplanets

The hundreds of exoplanets that have been discovered in the past two decades offer a new perspective on planetary structure. Instead of being the archetypal examples of planets, those of our Solar System are merely possible outcomes of planetary system formation and evolution, and conceivably not even terribly common outcomes (although this remains an open question). Here, we review the diverse range of interior structures that are known to, and speculated to, exist in exoplanetary systems -- from mostly degenerate objects that are more than 10 times as massive as Jupiter, to intermediate-mass Neptune-like objects with large cores and moderate hydrogen/helium envelopes, to rocky objects with roughly the mass of the Earth.

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arXiv2013

Targeting Young Stars with Kepler: Planet Formation, Migration Mechanisms and the Early History of Planetary Systems

This white paper discusses a repurposed mission for the Kepler spacecraft that focusses on solving outstanding problems in planet formation and evolution by targeting the study of the hot Jupiter population of young stars. This mission can solve the question of the mode of migration of hot Jupiters, address the problem of whether Jupiters form by hot-start (gravitational instability) or cold-start (core accretion) mechanisms, and provide a wealth of data on the early stages of planetary system evolution during the active phases of stars which impact planetary habitability. In one year of observations of three weeks dwell time per field, Kepler would increase by more than an order of magnitude the number of known hot Jupiters, which can be followed up with fast cadence observations to to search for transit timing variations and to perform asteroseismological characterization of the host stars. This mission scenario continues to operate Kepler in the photometric monitoring mode for which it was designed, and is generally flexible with regards to field selection enabling prioritization of fuel usage and attitude control constraints.

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arXiv2013

Binary Evolution Leads to Two Populations of White Dwarf Companions

Planets and other low-mass binary companions to stars face a variety of potential fates as their host stars move off the main sequence and grow to subgiants and giants. Stellar mass loss tends to make orbits expand, and tidal torques tend to make orbits shrink, sometimes to the point that a companion is directly engulfed by its primary. Furthermore, once engulfed, the ensuing common envelope (CE) phase can result in the companion becoming fully incorporated in the primary's envelope; or, if the companion is massive enough, it can transfer enough energy to eject the envelope and remain parked in a tight orbit around the white dwarf core. Therefore, ordinary binary evolution ought to lead to two predominant populations of planets around white dwarfs: those that have been through a CE phase and are in short-period orbits, and those that have entirely avoided the CE and are in long-period orbits.

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arXiv2013

Spectral and Photometric Diagnostics of Giant Planet Formation Scenarios

Gas-giant planets that form via core accretion might have very different characteristics from those that form via disk-instability. Disk-instability objects are typically thought to have higher entropies, larger radii, and (generally) higher effective temperatures than core-accretion objects. We provide a large set of models exploring the observational consequences of high-entropy (hot) and low-entropy (cold) initial conditions, in the hope that this will ultimately help to distinguish between different physical mechanisms of planet formation. However, the exact entropies and radii of newly-formed planets due to these two modes of formation cannot, at present, be precisely predicted. We introduce a broad range of "Warm Start" gas-giant planet models. Between the hottest and the coldest models that we consider, differences in radii, temperatures, luminosities, and spectra persist for only a few million to a few tens of millions of years for planets that are a few times Jupiter's mass or less. For planets that are ~five times Jupiter's mass or more, significant differences between hottest-start and coldest-start models persist for on the order of 100 Myrs. We find that out of the standard infrared bands (J, H, K, L', M, N) the K and H bands are the most diagnostic of the initial conditions. A hottest-start model can be from ~4.5 magnitudes brighter (at Jupiter's mass) to ~9 magnitudes brighter (at ten times Jupiter's mass) than a coldest-start model in the first few million years. In more massive objects, these large differences in luminosity and spectrum persist for much longer than in less massive objects. We consider the influence of atmospheric conditions on spectra, and find that the presence or absence of clouds, and the metallicity of an atmosphere, can affect an object's apparent brightness in different bands by up to several magnitudes.

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arXiv2013

A simple, quantitative method to infer the minimum atmospheric height of small exoplanets

Amongst the many hundreds of transiting planet candidates discovered by the Kepler Mission, one finds a large number of candidates with sizes between that of the Earth and Neptune. The composition of these worlds is not immediately obvious with no Solar System analog to draw upon and there exists some ambiguity as to whether a given candidate is a rocky Super-Earth or a gas-enveloped Mini-Neptune. The potential scientific value and observability of the atmospheres of these two classes of worlds varies significantly and given the sheer number of candidates in this size-range, there is evidently a need for a quick, simple metric to rank whether the planets have an extended atmosphere or not. In this work, we propose a way to calculate the 'minimum atmospheric height' (R_MAH) using only a planet's radius and mass as inputs. We assume and exploit the boundary condition that the bulk composition of a solid/liquid Super-Earth cannot be composed of a material lighter than that of water. Mass-radius loci above a pure-water composition planet correspond to R_MAH>0. The statistical confidence of a planet maintaining an extended atmosphere can be therefore easily calculated to provide a simple ranking of target planets for follow-up observations. We also discuss how this metric can be useful in the interpretation of the spectra of observed planetary atmospheres.

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arXiv2013

Thermal Processes Governing Hot-Jupiter Radii

There have been many proposed explanations for the larger-than-expected radii of some transiting hot Jupiters, including either stellar or orbital energy deposition deep in the atmosphere or deep in the interior. In this paper, we explore the important influences on hot-Jupiter radius evolution of (i) additional heat sources in the high atmosphere, the deep atmosphere, and deep in the convective interior; (ii) consistent cooling of the deep interior through the planetary dayside, nightside, and poles; (iii) the degree of heat redistribution to the nightside; and (iv) the presence of an upper atmosphere absorber inferred to produce anomalously hot upper atmospheres and inversions in some close-in giant planets. In particular, we compare the radius expansion effects of atmospheric and deep-interior heating at the same power levels and derive the power required to achieve a given radius increase when night-side cooling is incorporated. We find that models that include consistent day/night cooling are more similar to isotropically irradiated models when there is more heat redistributed from the dayside to the nightside. In addition, we consider the efficacy of ohmic heating in the atmosphere and/or convective interior in inflating hot Jupiters. Among our conclusions are that (i) the most highly irradiated planets cannot stably have uB > (10 km/s Gauss) over a large fraction of their daysides, where u is the zonal wind speed and B is the dipolar magnetic field strength in the atmosphere, and (ii) that ohmic heating cannot in and of itself lead to a runaway in planet radius.

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arXiv2013

Signatures of X-rays in the early Universe

[abridged] With their long mean free paths and efficient heating of the intergalactic medium (IGM), X-rays could have a dramatic impact on the thermal and ionization history of the Universe. We explore this in various signals: (i) Reionization history: including X-rays results in an earlier, more extended reionization. Efficient thermal feedback from X-ray heating could yield an extended, ~10% ionized epoch. (ii) Reionization morphology: a sizable (~10%) contribution of X-rays to reionization results in a more uniform morphology, though the impact is modest when compared at the same global neutral fraction, xH. However, changes in morphology cannot be countered by increasing the bias of the ionizing sources, making them a robust signature. (iii) The kinetic Sunyaev-Zel'dovich (kSZ) effect: at a fixed reionization history, X-rays decrease the kSZ power at l=3000 by ~0.5 microK^2. Our extreme model in which X-rays dominate reionization is the only one that is marginally consistent with upper limits from the South Pole Telescope, assuming no thermal Sunyaev-Zel'dovich (tSZ) - dusty galaxy correlation. Since this extreme model is unlikely, we conclude that there should be a sizable tSZ-dusty galaxy signal. (iv) The cosmic 21cm signal: the impact of X-rays on the 21cm power spectrum during the advanced stages of reionization (xH<0.7) is modest, except in extreme, X-ray dominated models. The largest impact of X-rays is to govern IGM heating. In fact, unless thermal feedback is efficient, the epoch of X-ray heating likely overlaps with the beginning of reionization (xH>0.9). This results in a 21cm power spectrum which is ~ 10-100 times higher than obtained from naive estimates ignoring this overlap. However, if thermal feedback is efficient, the resulting extended epoch between X-ray heating and reionization could provide a clean probe of the matter power spectrum in emission.

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arXiv2012

NIMBUS: The Near-Infrared Multi-Band Ultraprecise Spectroimager for SOFIA

We present a new and innovative near-infrared multi-band ultraprecise spectroimager (NIMBUS) for SOFIA. This design is capable of characterizing a large sample of extrasolar planet atmospheres by measuring elemental and molecular abundances during primary transit and occultation. This wide-field spectroimager would also provide new insights into Trans-Neptunian Objects (TNO), Solar System occultations, brown dwarf atmospheres, carbon chemistry in globular clusters, chemical gradients in nearby galaxies, and galaxy photometric redshifts. NIMBUS would be the premier ultraprecise spectroimager by taking advantage of the SOFIA observatory and state of the art infrared technologies. This optical design splits the beam into eight separate spectral bandpasses, centered around key molecular bands from 1 to 4 microns. Each spectral channel has a wide field of view for simultaneous observations of a reference star that can decorrelate time-variable atmospheric and optical assembly effects, allowing the instrument to achieve ultraprecise calibration for imaging and photometry for a wide variety of astrophysical sources. NIMBUS produces the same data products as a low-resolution integral field spectrograph over a large spectral bandpass, but this design obviates many of the problems that preclude high-precision measurements with traditional slit and integral field spectrographs. This instrument concept is currently not funded for development.

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arXiv2012

Jupiter will become a hot Jupiter: Consequences of Post-Main-Sequence Stellar Evolution on Gas Giant Planets

When the Sun ascends the red giant branch (RGB), its luminosity will increase and all the planets will receive much greater irradiation than they do now. Jupiter, in particular, might end up more highly irradiated than the hot Neptune GJ 436b and, hence, could appropriately be termed a "hot Jupiter." When their stars go through the RGB or asymptotic giant branch (AGB) stages, many of the currently known Jupiter-mass planets in several-AU orbits will receive levels of irradiation comparable to the hot Jupiters, which will transiently increase their atmospheric temperatures to ~1000 K or more. Furthermore, massive planets around post-main-sequence stars could accrete a non-negligible amount of material from the enhanced stellar winds, thereby significantly altering their atmospheric chemistry as well as causing a significant accretion luminosity during the epochs of most intense stellar mass loss. Future generations of infrared observatories might be able to probe the thermal and chemical structure of such hot Jupiters' atmospheres. Finally, we argue that, unlike their main-sequence analogs (whose zonal winds are thought to be organized in only a few broad, planetary-scale jets), red-giant hot Jupiters should have multiple, narrow jets of zonal winds and efficient day-night redistribution.

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arXiv2012

Bayesian analysis of the astrobiological implications of life's early emergence on Earth

Life arose on Earth sometime in the first few hundred million years after the young planet had cooled to the point that it could support water-based organisms on its surface. The early emergence of life on Earth has been taken as evidence that the probability of abiogenesis is high, if starting from young-Earth-like conditions. We revisit this argument quantitatively in a Bayesian statistical framework. By constructing a simple model of the probability of abiogenesis, we calculate a Bayesian estimate of its posterior probability, given the data that life emerged fairly early in Earth's history and that, billions of years later, curious creatures noted this fact and considered its implications. We find that, given only this very limited empirical information, the choice of Bayesian prior for the abiogenesis probability parameter has a dominant influence on the computed posterior probability. Although terrestrial life's early emergence provides evidence that life might be common in the Universe if early-Earth-like conditions are, the evidence is inconclusive and indeed is consistent with an arbitrarily low intrinsic probability of abiogenesis for plausible uninformative priors. Finding a single case of life arising independently of our lineage (on Earth, elsewhere in the Solar System, or on an extrasolar planet) would provide much stronger evidence that abiogenesis is not extremely rare in the Universe.

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arXiv2012

Optical and X-ray Transients from Planet-Star Mergers

We evaluate the prompt observational signatures of the merger between a massive close-in planet (a `hot Jupiter') and its host star, events with an estimated Galactic rate of ~0.1-1/yr. Depending on the ratio of the mean density of the planet rho_p to that of the star rho_star, a merger results in three possible outcomes. If rho_p/rho_star > 5, then the planet directly plunges below the stellar atmosphere before being disrupted by tidal forces. Dissipation of orbital energy creates a hot wake behind the planet, producing a EUV/soft X-ray transient as the planet sinks below the stellar surface. The peak luminosity L_X ~ 1e36 erg/s is achieved weeks-months prior to merger, after which the stellar surface is enshrouded by an outflow. The final inspiral is accompanied by an optical transient powered by the recombination of hydrogen in the outflow, which peaks at L~1e37-38 erg/s on a timescale ~days. If instead rho_planet/rho_star < 5, then Roche Lobe overflow occurs above the stellar surface. For rho_p/rho_star < 1, mass transfer is stable, resulting the planet being accreted on a relatively slow timescale. However, for 1 < rho_p/rho_star < 5, mass transfer may instead be unstable, resulting in the planet being dynamically disrupted into an accretion disk around the star. Super-Eddington outflows from the disk power an optical transient with L~1e37-38 erg/s and characteristic duration ~week-months. The disk itself becomes visible once the accretion rate become sub-Eddington, resulting in a bolometric brightening and spectral shift to the UV. Optical transients from planet merger events may resemble classical novae, but are distinguished by lower ejecta mass and velocity ~100s km/s, and by hard pre- and post-cursor emission, respectively. Promising search strategies include combined optical, UV, and X-ray surveys of nearby massive galaxies with cadences from days to months.

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