Hao Cao

Bio: Hao Cao is an academic researcher from Harvard University. The author has contributed to research in topics: Jupiter & Magnetic field. The author has an hindex of 16, co-authored 43 publications receiving 1275 citations. Previous affiliations of Hao Cao include Imperial College London & University of Science and Technology of China.

Growth model interpretation of planet size distribution

Abstract: The radii and orbital periods of 4,000+ 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. However, an important question about the composition of planets ranging from 2 to 4 Earth radii (R⊕) still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multicomponent, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 M⊕, if half-ice and half-rock by mass, have radii of 2.5 R⊕, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2- to 4-R⊕ 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."

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 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.

Saturn's magnetic field revealed by the Cassini Grand Finale.

Abstract: During 2017, the Cassini fluxgate magnetometer made in situ measurements of Saturn's magnetic field at distances ~2550 ± 1290 kilometers above the 1-bar surface during 22 highly inclined Grand Finale orbits. These observations refine the extreme axisymmetry of Saturn's internal magnetic field and show displacement of the magnetic equator northward from the planet's physical equator. Persistent small-scale magnetic structures, corresponding to high-degree (>3) axisymmetric magnetic moments, were observed. This suggests secondary shallow dynamo action in the semiconducting region of Saturn's interior. Some high-degree magnetic moments could arise from strong high-latitude concentrations of magnetic flux within the planet's deep dynamo. A strong field-aligned current (FAC) system is located between Saturn and the inner edge of its D-ring, with strength comparable to the high-latitude auroral FACs.

Geophysical fluid dynamics.

Abstract: The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Solar Prominences: Observations

Abstract: Solar prominences are one of the most common features of the solar atmosphere. They are found in the corona but they are one hundred times cooler and denser than the coronal material, indicating that they are thermally and pressure isolated from the surrounding environment. Because of these properties they appear at the limb as bright features when observed in the optical or the EUV cool lines. On the disk they appear darker than their background, indicating the presence of a plasma absorption process (in this case they are called filaments). Prominence plasma is embedded in a magnetic environment that lies above magnetic inversion lines, denoted a filament channel. This paper aims at providing the reader with the main elements that characterize these peculiar structures, the prominences and their environment, as deduced from observations. The aim is also to point out and discuss open questions on prominence existence, stability and disappearance. The review starts with a general introduction of these features and the instruments used for their observation. Section 2 presents the large scale properties, including filament morphology, thermodynamical parameters, magnetic fields, and the properties of the surrounding coronal cavity, all in stable conditions. Section 3 is dedicated to small-scale observational properties, from both the morphological and dynamical points of view. Section 4 introduces observational aspects during prominence formation, while Section 5 reviews the sources of instability leading to prominence disappearance or eruption. Conclusions and perspectives are given in Section 6.

Large Longitude Libration of Mercury Reveals a Molten Core

Abstract: Observations of radar speckle patterns tied to the rotation of Mercury establish that the planet occupies a Cassini state with obliquity of 2.11 ± 0.1 arc minutes. The measurements show that the planet exhibits librations in longitude that are forced at the 88-day orbital period, as predicted by theory. The large amplitude of the oscillations, 35.8 ± 2 arc seconds, together with the Mariner 10 determination of the gravitational harmonic coefficient C22, indicates that the mantle of Mercury is decoupled from a core that is at least partially molten.

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.