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Stein B. Jacobsen

Publications and source records attributed to Stein B. Jacobsen.

18 recordsLinked to original sources
arXiv2026

Exoplanet Orbital Distribution around FGK Sun-like Host Stars I: planet occurrence rate derived from the Kepler Mission and theoretical interpretations from planet formation

Recent astronomical observations, in particular from the Kepler and TESS missions and their related follow-ups, have revealed an abundance of exoplanets in the size range between Neptune (4 Earth radii) and Earth (1 Earth radii ), as well as a low occurrence rate of planets around twice the radius of Earth (2 Earth radii). This paper uses statistical methods, in particular, the survival function analysis, to address the known exoplanet population observed mainly from the Kepler's primary mission, in order to mathematically elucidate the orbital distributions (expressed in either the orbital period P or the orbital semi-major axis a), for each of the host stars, in both a collective way, and also separately for the planets grouped into various radius bins. We uncover a log-uniform distribution for the majority of planets except the giants. Based on the results of the statistics, we then visit several possible formation scenarios and pathways for planets in different size ranges, in order to explain the results from a theoretical point-of-view.

astro-ph.EP↗
arXiv2026

Exoplanet Orbital Distribution around FGK Sun-like Host Stars II: a valley in the orbital semi-major axis distribution of sub-Neptunes

More than one hundred years ago, physics has been revolutionized when people realized that electronic orbitals, or electromagnetic interactions in general, are quantized. Now, in this study, we are presenting evidence of quantization of planet orbits around stars. Confining a wave in spatial dimensions "quantizes" its wave number. Therefore, this study points to the evidence of the existence of long-range standing waves in the proto-planetary disks. Such waves, although being on a much larger scale of few tens of AU, have already been found by ALMA observation-so called ring-like structure. Now we see that it may exist within 1 AU, and may exert its effect on the existence and distribution of planets within this distance range to the host star. Careful analysis has been carried out to compare the results of different surveys.

astro-ph.EP↗
arXiv2025

Comparison of Australasian tektites with Australasian microtektites and BeLaU spherules recovered from the ocean

The Australasian strewn field covers more than 15% of Earth's surface, consisting of tektites and microtektites. Australasian tektites from Southeast Asia and Australia, as well as microtektites recovered from deep sea sediments and Antarctica, are established to be derived from upper continental crust sediments. An expedition to retrieve remnants of bolide CNEOS 2014 January 8 (IM1), held in the Pacific Ocean, was in proximity to the known extent of the Australasian strewn field, and yielded "BeLaU"-spherules, whose compositions did not match most well-studied solar system material. We therefore report precise and comprehensive elemental data for Australasian tektites to compare their elemental abundances to those of microtektites from deep sea sediments, and BeLaU. Our findings corroborate previous studies that Australasian tektites and microtektites closely resemble the elemental abundance patterns of the upper continental crust. Meanwhile, the elemental patterns of the BeLaU-spherules are distinct from the Australasian tektite/microtektite compositions.

physics.geo-ph↗
arXiv2025

Planetesimal Impact Vapor Plumes and Nebular Shocks form Chondritic Mixtures

The origin of chondrules, and the chondritic sedimentary rocks that dominate the meteoritic record, is a long-standing problem in planetary science. Here, we develop a physical model for the formation of chondritic mixtures as an outcome of vaporizing collisions between planetesimals that were dynamically excited by the growth and migration of planets. We present calculations of nebular shock waves generated by impact vapor plumes and focus on aspects of the plume interaction with the nebular gas and dust that have been neglected in previous studies of impact ejecta. We find that, when water dominates the vapor, the plumes are relatively cool. However, the plume expansion is supersonic and can drive strong shock waves in the dusty nebular gas. Portions of these nebular shock fronts initially melt nebular dust, forming chondrules that are coupled to the moving front. As the shock front expands and cools, the chondrules solidify while the shock front entrains additional dust. Eventually, the plume expansion stalls and then hydrodynamically collapses, turbulently mixing variably processed dust and size-sorted chondrules. For probable impact parameters and nebular conditions during giant planet growth and migration, the impact-generated mixtures have characteristics that span the range observed in chondritic meteorites, providing an environment for rapid formation of chondritic assemblages after chondrule formation. Our impact vapor and nebular shocks (IVANS) model links chondrule formation to the overall context of planet formation and provides a framework for interpreting the detailed chronological and geochemical record contained in chondritic meteorites.

astro-ph.EP↗
arXiv2025

An investigation of the relationship between morphology and chemistry of the D-type spherules from the recovery expedition of the CNEOS 2014-01-08 bolide: Implications for origins

Cosmic spherules have largely been classified into S-, I-, and G-types according to their compositions, and are identified to have chondritic or achondritic materials as precursors. A recent recovery expedition attempted to sample fragments of the CNEOS 2014-01-08 bolide retrieved roughly 850 magnetic particles, some of which have unknown origins. Among those identified were a new group of highly differentiated materials consisting of close to 160 specimens categorized as "D-type" particles. We studied the D-type particles with the goal of comparing their various morphological features to their chemical compositional groupings. Four morphological classifications are considered: "scoriaceous," "stubby," "blocky," and "vesicular." The specimens from the "scoriaceous" and "stubby" groups exhibit a spinel/magnetite rim in at least one instance, characteristic of atmospheric entry, and textures indicative of quenching such as dendritic microcrystalline structures, suggesting that a subset of specimens from these groups are candidates for materials of extraterrestrial origin. The particles exhibiting "blocky" and "vesicular" textures are likely to be terrestrial in origin, with no obvious quench features or signs of ablation. The D-type particles identified and characterized in this study have a spectrum of terrestrial and probable extraterrestrial origins.

astro-ph.EP↗
arXiv2024

Cosmic Hydrogen and Ice Loss Lines

We explain the overall equilibrium-temperature-dependent trend in the exoplanet mass-radius diagram, using the escape mechanisms of hydrogen and relevant volatiles, and the chemical equilibrium calculation of molecular hydrogen (H$_2$) break-up into atomic hydrogen (H). We identify two Cosmic Hydrogen and Ice Loss Lines (CHILLs) in the mass-radius diagram. Gas disks are well known to disperse in ten million years. However, gas-rich planets may lose some or almost all gas on a much longer timescale. We thus hypothesize that most planets that are born out of a hydrogen-gas-dominated nebular disk begin by possessing a primordial H$_2$-envelope. This envelope is gradually lost due to escape processes caused by host-stellar radiation.

astro-ph.EP↗
arXiv2022

EOS Manual

The exoplanet field now abounds with new discoveries of planets and planetary systems. It is of great interest for the scientific community to understand the compositions and internal structures of these new planets outside our own solar system, and then infer their formation scenarios. In particular, the proper implementation of the equation-of-states of various matters into the calculation of internal structure is crucial. Thus, we have come up with this write-up that provides the detailed steps to turn an equation-of-state (EOS) into a mass-radius relation of exoplanets, and highlight the physics and chemistry involved in these calculations. It must be visualized!

astro-ph.EP↗
arXiv2022

New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State

Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune. A low occurrence rate of planets has been identified at around twice the size of Earth, known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass-radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature-density graph and the entropy-pressure graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets and larger planets that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane) and gaseous envelopes. In particular, among the larger planets, when viewed from the perspective of planet equilibrium temperature, the hot ones are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones have more diverse compositions, including various amounts of gaseous envelopes.

astro-ph.EP↗
arXiv2020

The Shock Physics of Giant Impacts: Key Requirements for the Equations of State

We discuss major challenges in modeling giant impacts between planetary bodies, focusing on the equations of state (EOS). During the giant impact stage of planet formation, rocky planets are melted and partially vaporized. However, most EOS models fail to reproduce experimental constraints on the thermodynamic properties of the major minerals over the required phase space. Here, we present an updated version of the widely-used ANEOS model that includes a user-defined heat capacity limit in the thermal free energy term. Our revised model for forsterite (Mg$_2$SiO$_4$), a common proxy for the mantles of rocky planets, provides a better fit to material data over most of the phase space of giant impacts. We discuss the limitations of this model and the Tillotson equation of state, a commonly used alternative model.

astro-ph.EP↗
arXiv2019

Growth Model Interpretation of Planet Size Distribution

The radii and orbital periods of 4000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. Yet an important question about the composition of planets ranging from 2 to 4 Earth radii still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multi-component, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 Earth masses, if half-ice and half-rock by mass, have radii of 2.5 Earth radii, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2-4 Earth radii range requires a gas envelope of at most a few mass percentage points, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are water worlds.

astro-ph.EP↗
arXiv2018

Survival Function Analysis of Planet Size Distribution with GAIA Data Release 2 Updates

Applying the survival function analysis to the planet radius distribution of the Kepler confirmed/candidate planets, we have identified two natural divisions of planet radius at 4 Earth radii and 10 Earth radii. These divisions place constraints on planet formation and interior structure model. The division at 4 Earth radii separates small exoplanets from large exoplanets above. When combined with the recently-discovered radius gap at 2 Earth radii, it supports the treatment of planets 2-4 Earth radii as a separate group, likely water worlds. For planets around solar-type FGK main-sequence stars, we argue that 2 Earth radii is the separation between water-poor and water-rich planets, and 4 Earth radii is the separation between gas-poor and gas-rich planets. We confirm that the slope of survival function in between 4 and 10 Earth radii to be shallower compared to either ends, indicating a relative paucity of planets in between 4-10 Earth radii, namely, the sub-Saturnian desert there. We name them transitional planets, as they form a bridge between the gas-poor small planets and gas giants. Accordingly, we propose the following classification scheme: (<2 Earth radii) rocky planets, (2-4 Earth radii) water worlds, (4-10 Earth radii) transitional planets, and (>10 Earth radii) gas giants.

astro-ph.EP↗
arXiv2018

Survival Function Analysis of Planet Size Distribution

Applying the survival function analysis to the planet radius distribution of the Kepler exoplanet candidates, we have identified two natural divisions of planet radius at 4 Earth radii and 10 Earth radii. These divisions place constraints on planet formation and interior structure model. The division at 4 Earth radii separates small exoplanets from large exoplanets above. When combined with the recently-discovered radius gap at 2 Earth radii, it supports the treatment of planets 2-4 Earth radii as a separate group, likely water worlds. Thus, for planets around solar-type FGK main-sequence stars, we argue that 2 Earth radii is the separation between water-poor and water-rich planets, and 4 Earth radii is the separation between gas-poor and gas-rich planets. We confirm that the slope of survival function in between 4 and 10 Earth radii to be shallower compared to either ends, indicating a relative paucity of planets in between 4-10 Earth radii, namely, the sub-Saturnian desert there. We name them transitional planets, as they form a bridge between the gas-poor small planets and gas giants. Accordingly, we propose the following classification scheme: (<2 Earth radii) rocky planets, (2-4 Earth radii) water worlds, (4-10 Earth radii) transitional planets, and (>10 Earth radii) gas giants.

astro-ph.EP↗
arXiv2018

Survival Function Analysis of Planet Orbit Distribution and Occurrence Rate Estimate

Applying survival function analysis to the planet orbital period (P) and semi-major axis (a) distribution from the Kepler sample, we find that all exoplanets are uniformly distributed in (ln a) or (ln P), with an average inner cut-off of 0.05 AU to the host star. More specifically, this inner cut-off is 0.04 AU for rocky worlds (1-2 Earth radii) and 0.08 AU for water worlds (2-4 Earth radii). Moreover, the transitional planets (4-10 Earth radii) and gas giants (>10 Earth radii) have a change of slope of survival function at 0.4 AU from -1 to -1/2, suggesting a different statistical distribution uniform in \Sqrt[a] inside 0.4 AU, compared to small exoplanets (<4 Earth radii). This difference in distribution is likely caused by the difference in planet migration mechanism, and susceptibility to host stellar irradiation, for gas-poor (<4 Earth radii) versus gas-rich (>4 Earth radii) planets. Armed with this knowledge and combined with the survival function analysis of planet size distribution, we can make precise estimates of planet occurrence rate and predict the TESS mission yield.

astro-ph.EP↗
arXiv2018

The origin of the Moon within a terrestrial synestia

The giant impact hypothesis remains the leading theory for lunar origin. However, current models struggle to explain the Moon's composition and isotopic similarity with Earth. Here we present a new lunar origin model. High-energy, high-angular momentum giant impacts can create a post-impact structure that exceeds the corotation limit (CoRoL), which defines the hottest thermal state and angular momentum possible for a corotating body. In a typical super-CoRoL body, traditional definitions of mantle, atmosphere and disk are not appropriate, and the body forms a new type of planetary structure, named a synestia. Using simulations of cooling synestias combined with dynamic, thermodynamic and geochemical calculations, we show that satellite formation from a synestia can produce the main features of our Moon. We find that cooling drives mixing of the structure, and condensation generates moonlets that orbit within the synestia, surrounded by tens of bars of bulk silicate Earth (BSE) vapor. The moonlets and growing moon are heated by the vapor until the first major element (Si) begins to vaporize and buffer the temperature. Moonlets equilibrate with BSE vapor at the temperature of silicate vaporization and the pressure of the structure, establishing the lunar isotopic composition and pattern of moderately volatile elements. Eventually, the cooling synestia recedes within the lunar orbit, terminating the main stage of lunar accretion. Our model shifts the paradigm for lunar origin from specifying a certain impact scenario to achieving a Moon-forming synestia. Giant impacts that produce potential Moon-forming synestias were common at the end of terrestrial planet formation.

astro-ph.EP↗
arXiv2017

Exoplanet Radius Gap Dependence on Host Star Type

Exoplanets smaller than Neptune are numerous, but the nature of the planet populations in the 1-4 Earth radii range remains a mystery. The complete Kepler sample of Q1-Q17 exoplanet candidates shows a radius gap at ~ 2 Earth radii, as reported by us in January 2017 in LPSC conference abstract #1576 (Zeng et al. 2017). A careful analysis of Kepler host stars spectroscopy by the CKS survey allowed Fulton et al. (2017) in March 2017 to unambiguously show this radius gap. The cause of this gap is still under discussion (Ginzburg et al. 2017; Lehmer & Catling 2017; Owen & Wu 2017). Here we add to our original analysis the dependence of the radius gap on host star type.

astro-ph.EP↗
arXiv2016

A Simple Analytical Model for Rocky Planet Interiors

This work aims at exploring the scaling relations among rocky exoplanets. With the assumption of internal gravity increasing linearly in the core, and staying constant in the mantle, and tested against numerical simulations, a simple model is constructed, applicable to rocky exoplanets of core mass fraction (CMF) $\in 0.1\sim0.4$ and mass $\in 0.1 \sim 10 M_{\oplus}$. Various scaling relations are derived: (1) core radius fraction $\rm CRF \approx \sqrt{CMF}$, (2) Typical interior pressure $P_{\text{typical}} \sim g_{\rm{s}}^2$ (surface gravity squared), (3) core formation energy $E_{\rm diff} \sim \frac{1}{10} E_{\rm grav}$ (the total gravitational energy), (4) effective heat capacity of the mantle $C_{\rm p}\approx \left( \frac{M_{\rm{p}}}{M_{\oplus}} \right) \cdot 7 \cdot 10^{27}$ J K$^{-1}$, and (5) the moment of inertia $I\approx \frac{1}{3} \cdot M_{\rm{p}} \cdot R_{\rm{p}}^2$. These scaling relations, though approximate, are handy for quick use owing to their simplicity and lucidity, and provide insights into the interior structures of rocky exoplanets. As examples, this model is applied to several planets including Earth, GJ 1132b, Kepler-93b, and Kepler-20b, and made comparison with the numerical method.

astro-ph.EP↗
arXiv2016

Variational Principle for Planetary Interiors

In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have a simple analytical framework for describing planetary structures. Variational principle is a fundamental principle in physics, entailing that a physical system follows the trajectory which minimizes its action. It is alternative to the differential equation formulation of a physical system. Applying this principle to planetary interior can beautifully summarize the set of differential equations into one, which provides us some insight into the problem. From it, a universal mass-radius relation, an estimate of error propagation from equation of state to mass-radius relation, and a form of virial theorem applicable to planetary interiors are derived.

astro-ph.EP↗