S. M. Wahl

Bio: S. M. Wahl is an academic researcher from University of California, Berkeley. The author has contributed to research in topics: Planet & Jupiter. The author has an hindex of 14, co-authored 20 publications receiving 1087 citations.

Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core

Abstract: The Juno spacecraft has measured Jupiter's low-order, even gravitational moments, J2–J8, to an unprecedented precision, providing important constraints on the density profile and core mass of the planet. Here we report on a selection of interior models based on ab initio computer simulations of hydrogen-helium mixtures. We demonstrate that a dilute core, expanded to a significant fraction of the planet's radius, is helpful in reconciling the calculated Jn with Juno's observations. Although model predictions are strongly affected by the chosen equation of state, the prediction of an enrichment of Z in the deep, metallic envelope over that in the shallow, molecular envelope holds. We estimate Jupiter's core to contain a 7–25 Earth mass of heavy elements. We discuss the current difficulties in reconciling measured Jn with the equations of state and with theory for formation and evolution of the planet.

Jupiter's atmospheric jet streams extend thousands of kilometres deep.

Abstract: The depth to which Jupiter’s observed east–west jet streams extend has been a long-standing question. Resolving this puzzle has been a primary goal for the Juno spacecraft, which has been in orbit around the gas giant since July 2016. Juno’s gravitational measurements have revealed that Jupiter’s gravitational field is north–south asymmetric, which is a signature of the planet’s atmospheric and interior flows. Here we report that the measured odd gravitational harmonics J_3, J_5, J_7 and J_9 indicate that the observed jet streams, as they appear at the cloud level, extend down to depths of thousands of kilometres beneath the cloud level, probably to the region of magnetic dissipation at a depth of about 3,000 kilometres. By inverting the measured gravity values into a wind field, we calculate the most likely vertical profile of the deep atmospheric and interior flow, and the latitudinal dependence of its depth. Furthermore, the even gravity harmonics J_8 and J_(10) resulting from this flow profile also match the measurements, when taking into account the contribution of the interior structure. These results indicate that the mass of the dynamical atmosphere is about one per cent of Jupiter’s total mass.

A suppression of differential rotation in Jupiter’s deep interior

Abstract: Jupiter’s atmosphere is rotating differentially, with zones and belts rotating at speeds that differ by up to 100 metres per second. Whether this is also true of the gas giant’s interior has been unknown, limiting our ability to probe the structure and composition of the planet. The discovery by the Juno spacecraft that Jupiter’s gravity field is north–south asymmetric and the determination of its non-zero odd gravitational harmonics J_3, J_5, J_7 and J_9 demonstrates that the observed zonal cloud flow must persist to a depth of about 3,000 kilometres from the cloud tops. Here we report an analysis of Jupiter’s even gravitational harmonics J_4, J_6, J_8 and J_(10) as observed by Juno and compared to the predictions of interior models. We find that the deep interior of the planet rotates nearly as a rigid body, with differential rotation decreasing by at least an order of magnitude compared to the atmosphere. Moreover, we find that the atmospheric zonal flow extends to more than 2,000 kilometres and to less than 3,500 kilometres, making it fully consistent with the constraints obtained independently from the odd gravitational harmonics. This depth corresponds to the point at which the electric conductivity becomes large and magnetic drag should suppress differential rotation. Given that electric conductivity is dependent on planetary mass, we expect the outer, differentially rotating region to be at least three times deeper in Saturn and to be shallower in massive giant planets and brown dwarfs.

Measurement and implications of Saturn's gravity field and ring mass.

Abstract: The interior structure of Saturn, the depth of its winds, and the mass and age of its rings constrain its formation and evolution. In the final phase of the Cassini mission, the spacecraft dived between the planet and its innermost ring, at altitudes of 2600 to 3900 kilometers above the cloud tops. During six of these crossings, a radio link with Earth was monitored to determine the gravitational field of the planet and the mass of its rings. We find that Saturn's gravity deviates from theoretical expectations and requires differential rotation of the atmosphere extending to a depth of at least 9000 kilometers. The total mass of the rings is (1.54 ± 0.49) × 1019 kilograms (0.41 ± 0.13 times that of the moon Mimas), indicating that the rings may have formed 107 to 108 years ago.

Measurement of Jupiter’s asymmetric gravity field

Abstract: The gravity harmonics of a fluid, rotating planet can be decomposed into static components arising from solid-body rotation and dynamic components arising from flows. In the absence of internal dynamics, the gravity field is axially and hemispherically symmetric and is dominated by even zonal gravity harmonics J_(2n) that are approximately proportional to q^n, where q is the ratio between centrifugal acceleration and gravity at the planet’s equator. Any asymmetry in the gravity field is attributed to differential rotation and deep atmospheric flows. The odd harmonics, J_3, J_5, J_7, J_9 and higher, are a measure of the depth of the winds in the different zones of the atmosphere. Here we report measurements of Jupiter’s gravity harmonics (both even and odd) through precise Doppler tracking of the Juno spacecraft in its polar orbit around Jupiter. We find a north–south asymmetry, which is a signature of atmospheric and interior flows. Analysis of the harmonics, described in two accompanying papers, provides the vertical profile of the winds and precise constraints for the depth of Jupiter’s dynamical atmosphere.

Ultraluminous X-Ray Sources

Abstract: We review observations of ultraluminous X-ray sources (ULXs). X-ray spectroscopic and timing studies of ULXs suggest a new accretion state distinct from those seen in Galactic stellar-mass black hole binaries. The detection of coherent pulsations indicates the presence of neutron-star accretors in three ULXs and therefore apparently super-Eddington luminosities. Optical and X-ray line profiles of ULXs and the properties of associated radio and optical nebulae suggest that ULXs produce powerful outflows, also indicative of super-Eddington accretion. We discuss models of super-Eddington accretion and their relationship to the observed behaviors of ULXs. We review the evidence for intermediate-mass black holes (IMBHs) in ULXs. We consider the implications of ULXs for super-Eddington accretion in active galactic nuclei, heating of the early Universe, and the origin of the black hole binary recently detected via gravitational waves.

Forming a Moon with an Earth-like composition via a Giant Impact

Abstract: In the giant impact theory, the Moon formed from debris ejected into an Earth-orbiting disk by the collision of a large planet with the early Earth. Prior impact simulations predict that much of the disk material originates from the colliding planet. However, Earth and the Moon have essentially identical oxygen isotope compositions. This has been a challenge for the impact theory, because the impactor’s composition would have likely differed from that of Earth. We simulated impacts involving larger impactors than previously considered. We show that these can produce a disk with the same composition as the planet’s mantle, consistent with Earth-Moon compositional similarities. Such impacts require subsequent removal of angular momentum from the Earth-Moon system through a resonance with the Sun as recently proposed.

Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core

Abstract: The Juno spacecraft has measured Jupiter's low-order, even gravitational moments, J2–J8, to an unprecedented precision, providing important constraints on the density profile and core mass of the planet. Here we report on a selection of interior models based on ab initio computer simulations of hydrogen-helium mixtures. We demonstrate that a dilute core, expanded to a significant fraction of the planet's radius, is helpful in reconciling the calculated Jn with Juno's observations. Although model predictions are strongly affected by the chosen equation of state, the prediction of an enrichment of Z in the deep, metallic envelope over that in the shallow, molecular envelope holds. We estimate Jupiter's core to contain a 7–25 Earth mass of heavy elements. We discuss the current difficulties in reconciling measured Jn with the equations of state and with theory for formation and evolution of the planet.

Jupiter's interior and deep atmosphere: The initial pole-to-pole passes with the Juno spacecraft

Abstract: On 27 August 2016, the Juno spacecraft acquired science observations of Jupiter, passing less than 5000 kilometers above the equatorial cloud tops Images of Jupiter’s poles show a chaotic scene, unlike Saturn’s poles Microwave sounding reveals weather features at pressures deeper than 100 bars, dominated by an ammonia-rich, narrow low-latitude plume resembling a deeper, wider version of Earth’s Hadley cell Near-infrared mapping reveals the relative humidity within prominent downwelling regions Juno’s measured gravity field differs substantially from the last available estimate and is one order of magnitude more precise This has implications for the distribution of heavy elements in the interior, including the existence and mass of Jupiter’s core The observed magnetic field exhibits smaller spatial variations than expected, indicative of a rich harmonic content

The rotation of the earth: a geophysical discussion.

Abstract: This book gives an account of certain observed irregularities on the rotation of the Earth, both in its rate of rotation (giving a variable length of day) and in the position of its axis. These irregularities are caused by events on and within the Earth and provide a means of studying a number of geophysical problems. Seasonal shifts in air masses and variable winds are causes of short-period fluctuations in the rotation. Climatic changes and their attendant sea levels are in part responsible for long-term fluctuations. Modern observations of the Moon and descriptions of ancient elipses both establish a secular increase in the length of day. The interpretation involves atmospheric, oceanic and bodily tides. The book provides a unified treatment of the rotation of the Earth, making this method of studying geophysical phenomena more readily accessible to geophysicists and others.