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NASA NTRS1988

Active galactic nuclei. II - The acceleration of relativistic particles in a cluster of accreting black holes

An accreting cluster of black holes in an active galactic nucleus is a natural site for a system of shock structures with a hierarchy of sizes, corresponding to the distribution of masses in the cluster. Accreted gas containing some magnetic fields and supersonically falling onto the core forms shocks on the outside of each hole and these shocks are capable of accelerating relativistic particles. The energies reached in a single shock are size rather than acceleration time limited and are proportional to the mass of the hole with a proportionality constant being a function of the position of the hole within a cluster and the model of the cluster and the shock formation. These energies are adequate to explain the observed properties of synchrotron and inverse-Compton radiation from these objects. The resulting energy spectrum of particles in the cluster in 'zeroth' approximation has the form of a doubly broken power law with indices of two and three on both extremes of the energy domain respectively, bridged by an index of about 2.5.

Pacholczyk, A. G.↗
NASA NTRS2014

Modeling the Deterioration of Engine and Low Pressure Compressor Performance During a Roll Back Event Due to Ice Accretion

The main focus of this study is to apply a computational tool for the flow analysis of the engine that has been tested with ice crystal ingestion in the Propulsion Systems Laboratory (PSL) of NASA Glenn Research Center. A data point was selected for analysis during which the engine experienced a full roll back event due to the ice accretion on the blades and flow path of the low pressure compressor. The computational tool consists of the Numerical Propulsion System Simulation (NPSS) engine system thermodynamic cycle code, and an Euler-based compressor flow analysis code, that has an ice particle melt estimation code with the capability of determining the rate of sublimation, melting, and evaporation through the compressor blade rows. Decreasing the performance characteristics of the low pressure compressor (LPC) within the NPSS cycle analysis resulted in matching the overall engine performance parameters measured during testing at data points in short time intervals through the progression of the roll back event. Detailed analysis of the fan-core and LPC with the compressor flow analysis code simulated the effects of ice accretion by increasing the aerodynamic blockage and pressure losses through the low pressure compressor until achieving a match with the NPSS cycle analysis results, at each scan. With the additional blockages and losses in the LPC, the compressor flow analysis code results were able to numerically reproduce the performance that was determined by the NPSS cycle analysis, which was in agreement with the PSL engine test data. The compressor flow analysis indicated that the blockage due to ice accretion in the LPC exit guide vane stators caused the exit guide vane (EGV) to be nearly choked, significantly reducing the air flow rate into the core. This caused the LPC to eventually be in stall due to increasing levels of diffusion in the rotors and high incidence angles in the inlet guide vane (IGV) and EGV stators. The flow analysis indicating compressor stall is substantiated by the video images of the IGV taken during the PSL test, which showed water on the surface of the IGV flowing upstream out of the engine, indicating flow reversal, which is characteristic of a stalled compressor.

Veres, Joseph P.↗
NASA NTRS2014

Modeling the Deterioration of Engine and Low Pressure Compressor Performance During a Roll Back Event Due to Ice Accretion

The main focus of this study is to apply a computational tool for the flow analysis of the engine that has been tested with ice crystal ingestion in the Propulsion Systems Laboratory (PSL) of NASA Glenn Research Center. A data point was selected for analysis during which the engine experienced a full roll back event due to the ice accretion on the blades and flow path of the low pressure compressor. The computational tool consists of the Numerical Propulsion System Simulation (NPSS) engine system thermodynamic cycle code, and an Euler-based compressor flow analysis code, that has an ice particle melt estimation code with the capability of determining the rate of sublimation, melting, and evaporation through the compressor blade rows. Decreasing the performance characteristics of the low pressure compressor (LPC) within the NPSS cycle analysis resulted in matching the overall engine performance parameters measured during testing at data points in short time intervals through the progression of the roll back event. Detailed analysis of the fan-core and LPC with the compressor flow analysis code simulated the effects of ice accretion by increasing the aerodynamic blockage and pressure losses through the low pressure compressor until achieving a match with the NPSS cycle analysis results, at each scan. With the additional blockages and losses in the LPC, the compressor flow analysis code results were able to numerically reproduce the performance that was determined by the NPSS cycle analysis, which was in agreement with the PSL engine test data. The compressor flow analysis indicated that the blockage due to ice accretion in the LPC exit guide vane stators caused the exit guide vane (EGV) to be nearly choked, significantly reducing the air flow rate into the core. This caused the LPC to eventually be in stall due to increasing levels of diffusion in the rotors and high incidence angles in the inlet guide vane (IGV) and EGV stators. The flow analysis indicating compressor stall is substantiated by the video images of the IGV taken during the PSL test, which showed water on the surface of the IGV flowing upstream out of the engine, indicating flow reversal, which is characteristic of a stalled compressor.

Jorgenson, Philip C. E.↗
NASA NTRS2018

Core-Mantle Fractionation of Carbon in Earth and Mars: the Effects of Sulfur

Constraining carbon (C) fractionation between silicate magma ocean (MO) and core-forming alloy liquid during early differentiation is essential to understand the origin and early distribution of C between reservoirs such as the crust-atmosphere, mantle, and core of Earth and other terrestrial planets. Yet experimental data at high pressure (P)-temperature (T) on the effect of other light elements such as sulfur (S) in alloy liquid on alloy-silicate partitioning of C and C solubility in Fe-alloy compositions relevant for core formation is lacking. Here we have performed multi-anvil experiments at 6–13 GPa and 1800–2000 °C to examine the effects of S and Ni on the solubility limit of C in Fe-rich alloy liquid as well as partitioning behavior of C between alloy liquid and silicate melt (𝐷𝐷(sub C)(sup alloy/silicate)). The results show that C solubility in the alloy liquid as well as 𝐷𝐷(sub C)(sup alloy/silicate) decreases with increasing in S content in the alloy liquid. Empirical regression on C solubility in alloy liquid using our new experimental data and previous experiments demonstrates that C solubility significantly increases with increasing temperature, whereas unlike in S-poor or S-free alloy compositions, there is no discernible effect of Ni on C solubility in S-rich alloy liquid. Our modelling results confirm previous findings that in order to satisfy the C budget of BSE, the bulk Earth C undergoing alloy-silicate fractionation needs to be as high as those of CI-type carbonaceous chondrite, i.e., not leaving any room for volatility-induced loss of carbon during accretion. For Mars, on the other hand, an average single-stage core formation at relatively oxidized conditions (1.0 log unit below IW buffer) with 10-16 wt.% S in the core could yield a Martian mantle with a C budget similar to that of Earth’s BSE for a bulk C content of ~0.25-0.9 wt.%. For the scenario where C was delivered to the proto-Earth by a S-rich differentiated impactor at a later stage, our model calculations predict that bulk C content in the impactor can be as low as ~0.5 wt.% for an impactor mass that lies between 9-20% of present day Earth’s mass. This value is much higher than 0.05-0.1 wt.% bulk C in the impactor predicted by Li et al. (2016) because C-solubility limit of 0.3 wt.% in a S-rich alloy predicted by their models is significantly lower than the experimentally derived C-solubility of ~1.6 wt. % for the relevant S-content in the core of the impactor.

Carbon↗
NASA NTRS2013

Characterizing Uranus with an Ice giant Planetary Origins Probe (Ice-POP)

We now know from studies of planetary transits and microlensing that Neptune-mass planets are ubitquitous and may be the most common class of planets in the Galaxy. As such it is crucial that we understand the formation and evolution of the ice giant planets in our own solar system so that we can better understand planet formation throughout the galaxy. An entry probe mission to Uranus would help accomplish this goal. In fact the Planetary Decadal Survey recommended a Uranus orbiter with entry probe but did not explore in detail the specifications for the entry probe. NASA Ames is currently studying thermal protection system requirements for such a mission and this has led to questions regarding the minimum interesting science payload of such an entry probe. The single most important in-situ measurement for an ice giant entry probe is a measurement of atmospheric composition. For Uranus this would specifically include the methane and noble gas abundances. An in situ measurement of the methane abundance, from below the methane cloud, would constrain the atmospheric carbon abundance, which is believed to be roughly 30 to 50 times solar. There are hints from the transiting planets that extrasolar ice giants show comparable or even greater enhancements of heavy elements compared to their primary stars. However the origin of this carbon enhancement is controversial. Is Uranus a "failed core" of a larger gas giant or was the atmosphere enhanced by accretion of icy planetesimals' Constraining atmospheric abundances of C and perhaps S or even N from below 5 bars would provide badly needed data to address such issues. A measurement of the N abundance would provide clues on the origin of the planetesimals that formed Uranus. Low N-abundance indicates planetesimals from 'warmer' regions where N was mainly in form of NH3, whereas a strong enrichment could indicate planetesimals / cometary material from the colder outer regions of the nebula. Furthermore CO and HCN have been detected in Neptune but not in Uranus. A measurement of the abundance of either would constrain the source mechanisms for these molecules (exogenic or internal). A major surprise from the Galileo Entry Probe was that the heavier noble gases Ar, Kr, and Xe are enhanced in Jupiter's atmosphere at a level comparable to what was seen for the chemically active volatiles N, C, and S. It had been generally expected that Ar, Kr, and Xe would be present in solar abundances, as all were expected to accrete with hydrogen during the gravitational capture of nebular gases. Enhanced abundances of Ar, Kr, and Xe is equivalent to saying that these noble gases have been separated from hydrogen. There are several mechanisms that could accomplish this but these hypotheses require further testing. Measurement of noble gas abundances in an ice giant would constrain the planetary formation and nebular mechanisms responsible for this enhancement. Standard three-layer models of Uranus find that the outer, predominantly H/He layer of Uranus does not reach pressures high enough (approximately 1 Mbar) for H2 to transition to liquid metallic hydrogen. However, valid models can also be constructed with a smaller intermediate water-rich layer, with hydrogen then reaching the metallic hydrogen phase. If this occurs, He should phase separate from the hydrogen and ``rain out," taking along a substantial abundance of Ne, as suggested for Jupiter (and likely also for Saturn). Hence He and Ne depletions could be probes of the planet's structure in the much deeper interior. A determination of Uranus' atmospheric abundances, particularly of the noble gasses, is thus critical to understanding the formation of Uranus, and giant planets in general. These measurements can only be performed with an entry probe. The second key measurement would be a temperature-pressure sounding to provide ground truth for remote measurements of atmospheric temperature and composition and to constrain the internal heat flow. This would also establish that the methane abundance measurements have indeed been made below any possible methane cloud. Finally an ultra stable oscillator would measure wind speeds and constrain atmospheric dynamics. In our presentation we will discuss the importance of all of these measurements and argue that an entry probe is a crucial component of any ice giant mission.

Marley, Mark S.↗
NASA NTRS2014

An Accreting White Dwarf near the Chandrasekhar Limit in the Andromeda Galaxy

The iPTF (Intermediate Palomar Transient Factory) detection of the most recent outburst of the recurrent nova system RX J0045.4+4154 in the Andromeda Galaxy has enabled the unprecedented study of a massive (mass is greater than 1.3 solar masses) accreting white dwarf (WD). We detected this nova as part of the near daily iPTF monitoring of M31 to a depth of R (red band-pass filter) approximately equal to magnitude 21 and triggered optical photometry, spectroscopy and soft X-ray monitoring of the outburst. Peaking at an absolute magnitude of MR (red, mid-infrared band-pass filter) equals magnitude −6.6, and with a decay time of 1 magnitude per day, it is a faint and very fast nova. It shows optical emission lines of He/N and expansion velocities of 1900 to 2600 kilometers per second 1-4 days after the optical peak. The Swift monitoring of the X-ray evolution revealed a supersoft source (SSS) with kT (energy: Boltzmann constant times temperature) (sub eff (effective)) approximately equal to 90-110 electronvolts that appeared within 5 days after the optical peak, and lasted only 12 days. Most remarkably, this is not the first event from this system, rather it is a recurrent nova with a time between outbursts of approximately 1 year, the shortest known. Recurrent X-ray emission from this binary was detected by ROSAT in 1992 and 1993, and the source was well characterized as a mass greater than 1.3 solar masses WD SSS. Based on the observed recurrence time between different outbursts, the duration and effective temperature of the SS phase, MESA models of accreting WDs allow us to constrain the accretion rate to mass greater than 1.7x10 (sup −7) solar masses per year and WD mass greater than 1.30 solar masses. If the WD keeps 30 percent of the accreted material, it will take less than a million years to reach core densities high enough for carbon ignition (if made of C/O) or electron capture (if made of O/Ne) to end the binary evolution.

dwarf↗
NASA NTRS2002

Kronos: A Multiwavelength Observatory for Mapping Accretion-Driven Sources

Kronos is a multiwavelength observatory proposed as a NASA Medium Explorer. Kronos is designed to make use of the natural variability of accreting sources to create microarcsecond-resolution maps of the environments of supermassive black holes in active galaxies and stella-size black holes in binary systems and to characterize accretion processes in Galactic compact binaries. Kronos will obtain broad energy range spectroscopic data with co-aligned X-ray, ultraviolet, and optical spectrometers. The high-Earth orbit of Kronos enables well-sampled, high time-resolution observations, critical for the innovative and sophisticated methods that are used to understand the accretion flows, mass outflows, jets, and other phenomena found in accreting sources. By utilizing reverberation mapping analysis techniques, Kronos produces advanced high-resolution maps of unprecedented resolution of the extreme environment in the inner cores of active galaxies. Similarly, Doppler tomography and eclipse mapping techniques characterize and map Galactic binary systems, revealing the details of the physics of accretion processes in black hole, neutron star, and white dwarf binary systems. The Kronos instrument complement, sensitivity, and orbital environment make it suitable to aggressively address time variable phenomena in a wide range of astronomical objects from nearby flare stars to distant galaxies.

Peterson, Bradley M.↗
NASA NTRS1994

Dense molecular shocks and accretion onto protostellar disks

We have examined the physical and chemical processes which accompany the propagation of a J-type shock through molecular astrophysical gas of density 10(exp 7.5) - 10(exp 12) H nuclei per cu cm. Our study is primarily relevant to the high-density accretion shocks which are associated with the supersonic infall of material during the collapse of a molecular cloud core to form a protostar. We have carried out a general parameter study to determine the characteristic infrared emission spectrum of dense molecular shocks and the extent of grain destruction within such shocks as a function of relevant shock parameters. Accretion shocks with mass accretion rates approximately greater than 10(exp -5) solar masses per y are plausible sources of the CO v = 2-0 vibrational band emission observed in many protostars, at least for sources of moderate CO v = 2-0 luminosity (approximately less than few x 10(exp 23) W). Rovibrational emissions from H2O and OH are also predicted to be luminous in dense molecular accretion shocks. Vaporization is the dominant mechanism of grain destruction within dense molecular shocks, leading to the efficient removal of those grains which are heated to their vaporization temperature by the combined effects of radiative heating, drag heating, and thermal heating by the hot postshock gas. The criteria for grain vaporization are obtained for grains composed of several different materials: metallic iron, silicate, troilite, refractory organic materials, volatile organic materials, and water ice.

Neufeld, David A.↗
NASA NTRS2004

Low Abundances of Highly Siderophile Elements in the Lunar Mantle: Evidence for Prolonged Late Accretion

The highly siderophile elements (HSE: including Re, Au, Ir, Os, Ru, Pt, Pd, Rh) are strongly partitioned into metal relative to silicates. In the terrestrial planets these elements are concentrated in metallic cores. Earth s mantle has sufficiently high abundances of the HSE (~0.008 times CI abundances) that it has been hypothesized approximately 0.1-0.5% of the mass of the Earth was added following the last major interaction between the core and mantle [e.g. 1]. The additional material added to the Earth and Moon has been termed a late veneer , and the process has often been termed late accretion [2]. The timing of the dominant late accretionary period of the Earth and Moon is still poorly known. The abundances of HSE in the lunar mantle could provide important constraints on when the late veneer was added. The material that ultimately became the silicate portion of the Moon was likely stripped of most of its HSE prior to and during coalescence of the Moon. Consequently the initial lunar mantle likely had very low concentrations of the HSE. Unlike Earth, the generation of permanent lunar crust by ~4.4 Ga prevented subsequent additions of HSE to the lunar mantle via continued accretion. Thus, if a substantial portion of the late veneer was added after 4.4 Ga, the lunar mantle should have retained very low HSE concentrations. Conversely, if the late veneer was mostly added prior to 4.4 Ga, HSE abundances in the lunar mantle may be roughly similar to abundances in the terrestrial mantle.

Walker, R. J.↗
NASA NTRS2003

Formation of Giant Planets and Brown Dwarves

According to the prevailing core instability model, giant planets begin their growth by the accumulation of small solid bodies, as do terrestrial planets. However, unlike terrestrial planets, the growing giant planet cores become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. Models predict that rocky planets should form in orbit about most stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large enough to gravitationally trap substantial quantities of gas. Ongoing theoretical modeling of accretion of giant planet atmospheres, as well as observations of protoplanetary disks, will help decide this issue. Observations of extrasolar planets around main sequence stars can only provide a lower limit on giant planet formation frequency . This is because after giant planets form, gravitational interactions with material within the protoplanetary disk may cause them to migrat~ inwards and be lost to the central star. The core instability model can only produce planets greater than a few jovian masses within protoplanetary disks that are more viscous than most such disks are believed to be. Thus, few brown dwarves (objects massive enough to undergo substantial deuterium fusion, estimated to occur above approximately 13 jovian masses) are likely to be formed in this manner. Most brown dwarves, as well as an unknown number of free-floating objects of planetary mass, are probably formed as are stars, by the collapse of extended gas/dust clouds into more compact objects.

Lissauer, Jack J.↗
NASA NTRS2012

From the Blazar Sequence to the Blazar Envelope: Revisiting the Relativistic Jet Dichotomy in Radio-Loud AGN

We revisit the concept of a blazar sequence that relates the synchrotron peak frequency (Vpeak) in blazars with synchrotron peak luminosity (Lpeak, in vLv) using a large sample of radio-loud AGN. We present observational evidence that the blazar sequence is formed from two populations in the synchrotron Vpeak - Lpeak plane, each forming an upper edge to an envelope of progressively misaligned blazars, and connecting to an adjacent group of radio galaxies having jets viewed at much larger angles to the line of sight. When binned by jet kinetic power (Lkin; as measured through a scaling relationship with extended radio power), we find that radio core dominance decreases with decreasing synchrotron Lpeak, revealing that sources in the envelope are generally more misaligned. We find population-based evidence of velocity gradients in jets at low kinetic powers (approximately 10(exp 42) - 10(exp 44.5) erg s(exp -1)), corresponding to FR I radio galaxies and most BL Lacs. These low jet power 'weak jet' sources, thought to exhibit radiatively inefficient accretion, are distinguished from the population of non-decelerating, low synchrotron-peaking (LSP) blazars and FR II radio galaxies ('strong' jets) which are thought to exhibit radiatively efficient accretion. The two-population interpretation explains the apparent contradiction of the existence of highly core-dominated, low-power blazars at both low and high synchrotron peak frequencies, and further implies that most intermediate synchrotron peak (ISP) sources are not intermediate in intrinsic jet power between LSP and high synchrotron-peaking (HSP) sources, but are more misaligned versions of HSP sources with similar jet powers.

Meyer, Eileen T.↗
NASA NTRS2018

Ag Isotopic Evolution of the Mantle During Accretion: New Constraints from Pd and Ag Metal-Silicate Partitioning

Decay of (sup 107) Pd to (sup 107) Ag has a half-life of 6.5 times 10 (sup 6) mega-annums. Because these elements are siderophile but also volatile, they offer potential constraints on the timing of core formation as well as volatile addition. Initial modelling has shown that the Ag isotopic composition of the bulk silicate Earth (BSE) can be explained if accretion occurs with late volatile addition. These arguments were tested for sensitivity for pre-cursor Pd/Ag contents, and for a fixed Pd/Ag ratio of the BSE of 0.1. New Ag and Pd partitioning data has allowed a better understanding of the partitioning behavior of Pd and Ag during core formation. The effects of S, C and Si, and the effect of high temperature and pressure has been evaluated. We can now calculate D(Ag) and D(Pd) over the wide range of PT conditions and variable metallic liquid compositions that are known during accretion. We then use this new partitioning information to revisit the Ag isotopic composition of the BSE during accretion.

Righter, K.↗
NASA NTRS1977

Accretion of rotating fluids by barytropes - Numerical results for white-dwarf models

Numerical sequences of rotating axisymmetric nonmagnetic equilibrium models are constructed which represent the evolution of a barytropic star as it accretes material from a rotating medium. Two accretion geometries are considered - one approximating accretion from a rotating cloud and the other, accretion from a Keplerian disk. It is assumed that some process, such as Ekman spin-up or nonequilibrium oscillations, maintains nearly constant angular velocity along cylinders about the rotation axis. Transport of angular momentum in the cylindrically radial direction by viscosity is included. Fluid instabilities and other physical processes leading to enhancement of this transport are discussed. Particular application is made to zero-temperature white-dwarf models, using the degenerate electron equation of state. An initially nonrotating 0.566-solar-mass white dwarf is followed during the accretion of more than one solar mass of material. Applications to degenerate stellar cores, to mass-transfer binary systems containing white dwarfs, such as novae and dwarf novae, to Type I supernovae, and to galactic X-ray sources are considered.

Durisen, R. H.↗
NASA NTRS1977

The origin of iron meteorites

The chemistry of iron meteorites is compared with predictions of the chemical fractionations that develop during the cosmic history of the metal phase, from condensation and accretion through melting, segregation, and freezing. Of the 12 resolved iron meteorite groups, three appear to have evolved in bodies which accreted at temperatures in excess of 1000 K. In several cases, the core-forming process seems to have ceased prematurely, just as the metal began to melt and flow (group IAB with its silicate inclusions) or after the metal aggregated into pods but before it sank to form a core (group IVA, with groups IIAB and IIIAB being in more advanced stages). The Shaw chondrite contains residual metal from a partial melting process, as required to complement the fractional melts which refroze prematurely in the case of group IAB meteorites.

Kelly, W. R.↗
NASA NTRS1986

Isotopic constraints on planetary evolution

Direct observations are considered that have been made on terrestrial and lunar materials in the search for answers to questions such as: when did the major structural elements (core, mantle, and crust) come into being and evolved. Measurements of isotope ratios of Pb, Sr, Nd, Hf, Ar, and other elements provide information about the internal evolution of the earth and moon since their formation 4.5 Gyr ago. The existing evidence indicates the core formed more than 4.4 Gyr ago, possibly while the earth was still accreting. Though the moon crust is similarly very old, the moon ceased to differentiate after about 1 Gyr whereas earth differentiation has continued to the present. Cataclysmic episodes have occurred, the largest 2.8 Gyr ago, when about half of the present continental mass formed.

Depaolo, D. J.↗
NASA NTRS1988

Resurrecting hot dark matter - Large-scale structure from cosmic strings and massive neutrinos

These are the results of a numerical simulation of the formation of large-scale structure from cosmic-string loops in a universe dominated by massive neutrinos (hot dark matter). This model has several desirable features. The final matter distribution contains isolated density peaks embedded in a smooth background, producing a natural bias in the distribution of luminous matter. Because baryons can accrete onto the cosmic strings before the neutrinos, the galaxies will have baryon cores and dark neutrino halos. Galaxy formation in this model begins much earlier than in random-phase models. On large scales the distribution of clustered matter visually resembles the CfA survey, with large voids and filaments.

Scherrer, Robert J.↗
NASA NTRS1989

Was the millisecond pulsar in SN1987A spun up or born spinning fast?

It is argued here that the millisecond pulsar in SN1987A has been spun up by accretion. The accreted angular momentum in this case comes from the mixed mantle and helium core of the ejecta, of which roughly 0.1 solar mass fell back during the first day after the explosion. This sizable mass, and hence angular momentum, of the reimploded material is at least partly a consequence of the blue supergiant nature of the progenitor star.

Woosley, S. E.↗
NASA NTRS1993

Core formation, wet early mantle, and H2O degassing on early Mars

Geophysical and geochemical observations strongly suggest a 'hot origin of Mars,' i.e., the early formation of both the core and the crust-mantle system either during or just after planetary accretion. To consider the behavior of H2O in the planetary interior it is specifically important to determine by what mechanism the planet is heated enough to cause melting. For Mars, the main heat source is probably accretional heating. Because Mars is small, the accretion energy needs to be effectively retained in its interior. Therefore, the three candidates of heat retention mechanism are discussed first: (1) the blanketing effect of the primordial H2-He atmosphere; (2) the blanketing effect of the impact-induced H2O-CO2 atmosphere; and (3) the higher deposition efficiency of impact energy due to larger impacts. It was concluded that (3) the is the most plausible mechanism for Mars. Then, its possible consequence on how wet the early martian mantle was is discussed.

Kuramoto, K.↗