Showing posts with label theia. Show all posts
Showing posts with label theia. Show all posts

Saturday, April 20, 2019

Pondering the Precambrian #27

Proterozoic:

NeoProterozoic:

Did a massive volcanic eruption trigger the Gaskiers Glaciation?

Deposits from British Columbia may be evidence of deep sea conditions just prior to the Gaskiers Glaciation.

Fossil fats from the Cryogenian may actually be from algae instead of sponges.

Amoebozoa diversified earlier than expected during the Tonian 750 million years ago.

How were banded iron formations created in Egypt from the NeoProterozoic?

Was the Cambrian Explosion really that big a deal? Or did it really originate in the Ediacaran?

First record of carbonates with spherulites and cone-in-cone structures from the Ediacaran of Norway has been found.

MesoProterozoic:

The Yili Block was likely located in the NW margin of the supercontinent Rodinia.

PaleoProterozoic:

The apparent cyclical deposition of the Dales Gorge Member banded iron formation appears to be related to sea level rise and fall or tectonic activity.

The Vempalle Formation dolomites of India appear to have more in common with Phanerozoic carbonates than Proterozoic ones.

There's a sedimentation record from 2.27 BYA to 1.96 BYA in West Africa with evidence of volcanic ash and activity in the layers.

The first drillings into the Temagami Anomaly have uncovered potential links to the Sudbury Impact.

The Francevillian Biota of Rhyacian Gabon seems to have had something able to move.  Scientists have found evidence of trackways from shallow, oxygenated waters.

Archean:

Evidence from Mauritania suggests the Archean geophysics were as complicated as today.

Evidence of a breakup of a continent from the Archean.

There appears to be evidence of major crustal growth circa 2.6 BYA and 3.2 BYA.

There is evidence plate tectonics were active, despite prior theory, during the Archean.

MesoArchean:

There is evidence of a continental margin at the tail end of the MesoArchean in North China.

A subduction zone has been found from the MesoArchean/NeoArchean boundary.

Evidence of a continental rift was found in Hainan, China from the MesoArchean.

There is evidence of ephemeral oxygen oases in the Mesoarchean Ocean.

PaleoArchean:

South African barite deposits were not laid down in a marine environment, but from a spring.

Life was thriving during the paleoarchean 3.5 billion years ago.

EoArchean:

How the first continents formed in the EoArchean.

Hadean:

Was the Theia impact the reason for the heterogeneity of Earth's crust?

Origin of Life:

Was the repeated drying and wetting cycle of the margin of water the source of energy for the original polymerization of amino acids et al?

Did hydrogen peroxide play a crucial role in the origin of life?

Pluripotency and the origin of multicellular life.

Could the RNA world hypothesized never have existed?

Shallow pools of water might have been the original location for the origin of life, not the sea.

Thursday, July 07, 2016

Did the Martian Moons Form in a Theia-like Impact?


Scientists believe that Phobos, one of Mars' two moons, is destined to be torn to shreds and form a ring around the Red Planet, and if so, it might be a fitting callback to how it got there in the first place. The mystery of the origins of the moons may have been solved by a new study that gives weight to the theory a huge collision between Mars and an ancient protoplanet resulted in the creation of Phobos and Deimos, as well as several other now-missing moons.

Two main hypotheses are debated regarding the birth of the Martian moons. One suggests that Phobos and Deimos were originally asteroids that became trapped in orbit about Mars. But a study, conducted by researchers in France, Belgium and Japan, suggests that the shape and orientation of their orbits, as well as the fine, grainy composition of the moons, makes that scenario unlikely.

There's a second, more explosive theory that Mars collided with a protoplanet about a third of its size between 4 and 4.5 billion years ago. The debris thrown up by that colossal impact formed a disk around the planet, which, over the course of millions of years, led to the formation of Phobos, Deimos, and other moons which no longer exist.

Sunday, May 08, 2016

Theia and Tellus (Earth) Impacted Between 100 to 250 Million Years After Formation

Dynamical sequestration of the Moon-forming impactor in co-orbital resonance with Earth

Authors:

Kortenkamp et al

Abstract:

Recent concerns about the giant impact hypothesis for the origin of the Moon, and an associated “isotope crisis” may be assuaged if the impactor was a local object that formed near Earth. We investigated a scenario that may meet this criterion, with protoplanets assumed to originate in 1:1 co-orbital resonance with Earth. Using N-body numerical simulations we explored the dynamical consequences of placing Mars-mass companions in various co-orbital configurations with a proto-Earth of 0.9 Earth-masses (M⊕). We modeled 162 different configurations, some with just the four terrestrial planets and others that included the four giant planets. In both the 4- and 8-planet models we found that a single Mars-mass companion typically remained a stable co-orbital of Earth for the entire 250 million year (Myr) duration of our simulations (59 of 68 unique simulations). In an effort to destabilize such a system we carried out an additional 94 simulations that included a second Mars-mass co-orbital companion. Even with two Mars-mass companions sharing Earth's orbit about two-thirds of these models (66) also remained stable for the entire 250 Myr duration of the simulations. Of the 28 2-companion models that eventually became unstable 24 impacts were observed between Earth and an escaping co-orbital companion. The average delay we observed for an impact of a Mars-mass companion with Earth was 102 Myr, and the longest delay was 221 Myr. In 40% of the 8-planet models that became unstable (10 out of 25) Earth collided with the nearly equal mass Venus to form a super-Earth (loosely defined here as mass ≥1.7 M⊕). These impacts were typically the final giant impact in the system and often occurred after Earth and/or Venus has accreted one or more of the other large objects. Several of the stable configurations involved unusual 3-planet hierarchical co-orbital systems.

Monday, April 25, 2016

Evidence From the Small Moons of Pluto That Charon Formed From a Theia-like Impact With Pluto

The Small Satellites of Pluto as Observed by New Horizons

Authors:

Weaver et al

Abstract:

The New Horizons mission has provided resolved measurements of Pluto's moons Styx, Nix, Kerberos, and Hydra. All four are small, with equivalent spherical diameters of ≈40 km for Nix and Hydra and ~10 km for Styx and Kerberos. They are also highly elongated, with maximum to minimum axis ratios of ≈2. All four moons have high albedos ( ≈50-90 %) suggestive of a water-ice surface composition. Crater densities on Nix and Hydra imply surface ages ≳ 4 Ga. The small moons rotate much faster than synchronous, with rotational poles clustered nearly orthogonal to the common pole directions of Pluto and Charon. These results reinforce the hypothesis that the small moons formed in the aftermath of a collision that produced the Pluto-Charon binary.

Wednesday, March 16, 2016

Tellus (Earth) and Theia Were Water Rich When the Moon Forming Impact Took Place

Oxygen isotopic evidence for vigorous mixing during the Moon-forming Giant Impact

Authors:

Young

Abstract:

Earth and Moon are shown here to be composed of oxygen isotope reservoirs that are indistinguishable, with a difference in {\Delta}"17O of -1 +/- 5ppm (2se). Based on these data and our new planet formation simulations that include a realistic model for oxygen isotopic reservoirs, our results favor vigorous mixing during the giant impact and therefore a high-energy high- angular-momentum impact. The results indicate that the late veneer impactors had an average {\Delta}"17O within approximately 1 per mil of the terrestrial value, suggesting that these impactors were water rich.

Thursday, January 28, 2016

New Evidence Bolsters Theia Impact Forming Earth's Moon

The moon was formed by a violent, head-on collision between the early Earth and a "planetary embryo" called Theia approximately 100 million years after the Earth formed, UCLA geochemists and colleagues report.

Scientists had already known about this high-speed crash, which occurred almost 4.5 billion years ago, but many thought the Earth collided with Theia (pronounced THAY-eh) at an angle of 45 degrees or more -- a powerful side-swipe. New evidence reported Jan. 29 in the journal Science substantially strengthens the case for a head-on assault.

The researchers analyzed seven rocks brought to the Earth from the moon by the Apollo 12, 15 and 17 missions, as well as six volcanic rocks from the Earth's mantle -- five from Hawaii and one from Arizona.

The key to reconstructing the giant impact was a chemical signature revealed in the rocks' oxygen atoms. (Oxygen makes up 90 percent of rocks' volume and 50 percent of their weight.) More than 99.9 percent of Earth's oxygen is O-16, so called because each atom contains eight protons and eight neutrons. But there also are small quantities of heavier oxygen isotopes: O-17, which have one extra neutron, and O-18, which have two extra neutrons. Earth, Mars and other planetary bodies in our solar system each has a unique ratio of O-17 to O-16 -- each one a distinctive "fingerprint."

In 2014, a team of German scientists reported in Science that the moon also has its own unique ratio of oxygen isotopes, different from Earth's. The new research finds that is not the case.

"We don't see any difference between the Earth's and the moon's oxygen isotopes; they're indistinguishable," said Edward Young, lead author of the new study and a UCLA professor of geochemistry and cosmochemistry.

Young's research team used state-of-the-art technology and techniques to make extraordinarily precise and careful measurements, and verified them with UCLA's new mass spectrometer.

The fact that oxygen in rocks on the Earth and our moon share chemical signatures was very telling, Young said. Had Earth and Theia collided in a glancing side blow, the vast majority of the moon would have been made mainly of Theia, and the Earth and moon should have different oxygen isotopes. A head-on collision, however, likely would have resulted in similar chemical composition of both Earth and the moon.

"Theia was thoroughly mixed into both the Earth and the moon, and evenly dispersed between them," Young said. "This explains why we don't see a different signature of Theia in the moon versus the Earth."

Thursday, August 27, 2015

Theia Wasn't Alone: Uranus Formed From Two Protoplanets Colliding

Stimulated Radiative Molecular Association in the Early Solar System. II. Orbital Radii of the Planets and Other Satellites of the Sun

Author:

Lombardi

Abstract:

In a previous investigation, the orbital radii of regular satellites of Uranus, Jupiter, Neptune, and Saturn are shown to be directly related to photon energies in the spectra of atomic and molecular hydrogen. To explain these observations a model was developed involving stimulated radiative molecular association (SRMA) reactions among photons and atoms in the protosatellite disks of the planets. In the present investigation, the previously developed model is applied to the planets and important satellites of the Sun. A key component of the model involves resonance associated with SRMA. Through this resonance, thermal energy is extracted from the protosun's protoplanetary disk at specific distances from the protosun wherever there is a match between the local thermal energy of the disk and the energy of photons impinging on the disk. Orbital radii of the planets and satellites are related to photon energies (EP values) in the spectrum of atomic hydrogen. An expression determined previously is used to relate EP values to temperatures in the disk. Results indicate the surface temperature of the protosun at the time when the evolution of the planets begins is higher than the surface temperature of a typical T Tauri star. The present investigation offers an explanation for the existence of the asteroid and classical Kuiper belts and predicts that a primordial belt once existed in the vicinity of Neptune. It also indicates that Uranus is formed from two protoplanets and is thus consistent with the theory that the large tilt of Uranus's axis of rotation was created by the collision of two bodies.

Sunday, June 21, 2015

Three Different Theias

Melting and Mixing States of the Earth's Mantle after the Moon-Forming Impact

Authors:

Nakajima et al

Abstract:

The Earth's Moon is thought to have formed by an impact between the Earth and an impactor around 4.5 billion years ago. This impact could have been so energetic that it could have mixed and homogenized the Earth's mantle. However, this view appears to be inconsistent with geochemical studies that suggest that the Earth's mantle was not mixed by the impact. Another plausible outcome is that this energetic impact melted the whole mantle, but the extent of mantle melting is not well understood even though it must have had a significant effect on the subsequent evolution of the Earth's interior and atmosphere. To understand the initial state of the Earth's mantle, we perform giant impact simulations using smoothed particle hydrodynamics (SPH) for three different models: (a) standard: a Mars-sized impactor hits the proto-Earth, (b) fast-spinning Earth: a small impactor hits a rapidly rotating proto-Earth, and (c) sub-Earths: two half Earth-sized planets collide. We use two types of equations of state (MgSiO3 liquid and forsterite) to describe the Earth's mantle. We find that the mantle remains unmixed in (a), but it may be mixed in (b) and (c). The extent of mixing is most extensive in (c). Therefore, (a) is most consistent and (c) may be least consistent with the preservation of the mantle heterogeneity, while (b) may fall between. We determine that the Earth's mantle becomes mostly molten by the impact in all of the models. The choice of the equations of state does not affect these outcomes. Additionally, our results indicate that entropy gains of the mantle materials by a giant impact cannot be predicted well by the Rankine-Hugoniot equations. Moreover, we show that the mantle can remain unmixed on a Moon-forming timescale if it does not become mixed by the impact.

Monday, April 20, 2015

Could There be Remnants of the Theia-Earth Impact Embedded in Places Throughout the Solar System?

Dating the Moon-forming impact event with asteroidal meteorites

Authors:

Bottke et al

Abstract:

The inner solar system’s biggest and most recent known collision was the Moon-forming giant impact between a large protoplanet and proto-Earth. Not only did it create a disk near Earth that formed the Moon, it also ejected several percent of an Earth mass out of the Earth-Moon system. Here, we argue that numerous kilometer-sized ejecta fragments from that event struck main-belt asteroids at velocities exceeding 10 kilometers per second, enough to heat and degas target rock. Such impacts produce ~1000 times more highly heated material by volume than do typical main belt collisions at ~5 kilometers per second. By modeling their temporal evolution, and fitting the results to ancient impact heating signatures in stony meteorites, we infer that the Moon formed ~4.47 billion years ago, which is in agreement with previous estimates.

Tuesday, March 31, 2015

Another Take on the Earth After Theia

Terrestrial aftermath of the Moon-forming impact.

Authors:

Sleep et al

Abstract:

Much of the Earth's mantle was melted in the Moon-forming impact. Gases that were not partially soluble in the melt, such as water and CO2, formed a thick, deep atmosphere surrounding the post-impact Earth. This atmosphere was opaque to thermal radiation, allowing heat to escape to space only at the runaway greenhouse threshold of approximately 100 W m(-2). The duration of this runaway greenhouse stage was limited to approximately 10 Myr by the internal energy and tidal heating, ending with a partially crystalline uppermost mantle and a solid deep mantle. At this point, the crust was able to cool efficiently and solidified at the surface. After the condensation of the water ocean, approximately 100 bar of CO2 remained in the atmosphere, creating a solar-heated greenhouse, while the surface cooled to approximately 500 K. Almost all this CO2 had to be sequestered by subduction into the mantle by 3.8 Ga, when the geological record indicates the presence of life and hence a habitable environment. The deep CO2 sequestration into the mantle could be explained by a rapid subduction of the old oceanic crust, such that the top of the crust would remain cold and retain its CO2. Kinematically, these episodes would be required to have both fast subduction (and hence seafloor spreading) and old crust. Hadean oceanic crust that formed from hot mantle would have been thicker than modern crust, and therefore only old crust underlain by cool mantle lithosphere could subduct. Once subduction started, the basaltic crust would turn into dense eclogite, increasing the rate of subduction. The rapid subduction would stop when the young partially frozen crust from the rapidly spreading ridge entered the subduction zone.

Earth After Theia


Bounding Theia


I suspect the Grand Tack folks ought to think on this one.  It bounds the wandering jupiter in a big way.

Monday, March 02, 2015

Theia Formed in the Same Region as the Earth

A primordial origin for the composition similarity between the Earth and the Moon

Authors:

Mastrobuono-Battisti et al

Abstract:

Most of the properties of the Earth-Moon system can be explained by a collision between a planetary embryo and the growing Earth late in the accretion process. Simulations show that most of the material that eventually aggregates to form the Moon originates from the impactor. However, analysis of the terrestrial and lunar isotopic composition show them to be highly similar. In contrast, the compositions of other solar system bodies are significantly different than the Earth and Moon. This poses a major challenge to the giant impact scenario since the Moon-forming impactor is then thought to also have differed in composition from the proto-Earth. Here we track the feeding zones of growing planets in a suite of simulations of planetary accretion, in order to measure the composition of Moon-forming impactors. We find that different planets formed in the same simulation have distinct compositions, but the compositions of giant impactors are systematically more similar to the planets they impact. A significant fraction of planet-impactor pairs have virtually identical compositions. Thus, the similarity in composition between the Earth and Moon could be a natural consequence of a late giant impact.

Wednesday, January 28, 2015

Mars had its own mini, Iron Theia


The two hemispheres of Mars are more different from any other planet in our solar system. Non-volcanic, flat lowlands characterise the northern hemisphere, while highlands punctuated by countless volcanoes extend across the southern hemisphere. Although theories and assumptions about the origin of this so-called and often-discussed Mars dichotomy abound, there are very few definitive answers. ETH Zurich geophysicists under Giovanni Leone are now providing a new explanation. Leone is the lead author of a paper recently published in the journal Geophysical Research Letters.

Using a computer model, the scientists have concluded that a large celestial object must have smashed into the Martian south pole in the early history of the Solar System. Their simulation shows that this impact generated so much energy that it created a magma ocean, which would have extended across what is today's southern hemisphere. The celestial body that struck Mars must have been at least one-tenth the mass of Mars to be able to unleash enough energy to create this magma ocean. The molten rock eventually solidified into the mountainous highlands that today comprise the southern hemisphere of Mars.

Tuesday, November 11, 2014

Is Theia Responsible for the Earth Being Habitable?


Atmospheric mass loss during planet formation: The importance of planetesimal impacts

Authors:

Schlichting et al

Abstract:

Quantifying the atmospheric mass loss during planet formation is crucial for understanding the origin and evolution of planetary atmospheres. We examine the contributions to atmospheric loss from both giant impacts and planetesimal accretion. Giant impacts cause global motion of the ground. Using analytic self-similar solutions and full numerical integrations we find (for isothermal atmospheres with adiabatic index γ=5/3γ=5/3) that the local atmospheric mass loss fraction for ground velocities vg≲0.25vescvg≲0.25vesc is given by χloss=(1.71vg/vesc)4.9χloss=(1.71vg/vesc)4.9, where vescvesc is the escape velocity from the target. Yet, the global atmospheric mass loss is a weaker function of the impactor velocity vImpvImp and mass mImpmImp and given by Xloss≃0.4x+1.4x2-0.8x3Xloss≃0.4x+1.4x2-0.8x3 (isothermal atmosphere) and Xloss≃0.4x+1.8x2-1.2x3Xloss≃0.4x+1.8x2-1.2x3 (adiabatic atmosphere), where x=(vImpm/vescM)x=(vImpm/vescM). Atmospheric mass loss due to planetesimal impacts proceeds in two different regimes: (1) large enough impactors View the MathML sourcem≳2ρ0(πhR)3/2 (25 km for the current Earth), are able to eject all the atmosphere above the tangent plane of the impact site, which is h/2Rh/2R of the whole atmosphere, where View the MathML sourceh,R and ρ0ρ0 are the atmospheric scale height, radius of the target, and its atmospheric density at the ground. (2) Smaller impactors, but above m greater than 4πρ0h3m greater than 4πρ0h3 (1 km for the current Earth) are only able to eject a fraction of the atmospheric mass above the tangent plane. We find that the most efficient impactors (per unit impactor mass) for atmospheric loss are planetesimals just above that lower limit (2 km for the current Earth). For impactor flux size distributions parametrized by a single power law, N( greater than r)∝r-q+1N( greater than r)∝r-q+1, with differential power law index q , we find that for 1 less than q less than 31 less than q less than 3 the atmospheric mass loss proceeds in regime (1) whereas for q grater than 3q greater than 3 the mass loss is dominated by regime (2). Impactors with m≲4πρ0h3m≲4πρ0h3 are not able to eject any atmosphere. Despite being bombarded by the same planetesimal population, we find that the current differences in Earth’s and Venus’ atmospheric masses can be explained by modest differences in their initial atmospheric masses and that the current atmosphere of the Earth could have resulted from an equilibrium between atmospheric erosion and volatile delivery to the atmosphere from planetesimal impacts. We conclude that planetesimal impacts are likely to have played a major role in atmospheric mass loss over the formation history of the terrestrial planets.

Friday, October 31, 2014

Simulating the Dynamical Evolution of Earth, Moon & Theia

Dynamical Evolution of the Earth-Moon Progenitors - Whence Theia?

Authors:

Quarles et al

Abstract:

We present integrations of a model Solar System with five terrestrial planets (beginning ~30-50 Myr after the formation of primitive Solar System bodies) in order to determine the preferred regions of parameter space leading to a giant impact that resulted in the formation of the Moon. Our results indicate which choices of semimajor axes and eccentricities for Theia (the proto-Moon) at this epoch can produce a late Giant Impact, assuming that Mercury, Venus, and Mars are near the current orbits. We find that the likely semimajor axis of Theia, at the epoch when our simulations begin, depends on the assumed mass ratio of Earth-Moon progenitors (8/1, 4/1, or 1/1). The low eccentricities of the terrestrial planets are most commonly produced when the progenitors have similar semimajor axes at the epoch when our integrations commence. Additionally, we show that mean motion resonances among the terrestrial planets and perturbations from the giant planets can affect the dynamical evolution of the system leading to a late Giant Impact.

The Origin and Composition of Theia

On the origin and composition of Theia: Constraints from new models of the Giant Impact

Authors:

Meier et al

Abstract:

Knowing the isotopic composition of Theia, the proto-planet which collided with the Earth in the Giant Impact that formed the Moon, could provide interesting insights on the state of homogenization of the inner solar system at the late stages of terrestrial planet formation. We use the known isotopic and modeled chemical compositions of the bulk silicate mantles of Earth and Moon and combine them with different Giant Impact models, to calculate the possible ranges of isotopic composition of Theia in O, Si, Ti, Cr, Zr and W in each model. We compare these ranges to the isotopic composition of carbonaceous chondrites, Mars, and other solar system materials. In the absence of post-impact isotopic re-equilibration, the recently proposed high angular momentum models of the Giant Impact ("impact-fission", Cuk & Stewart, 2012; and "merger", Canup, 2012) allow - by a narrow margin - for a Theia similar to CI-chondrites, and Mars. The "hit-and-run" model (Reufer et al., 2012) allows for a Theia similar to enstatite-chondrites and other Earth-like materials. If the Earth and Moon inherited their different mantle FeO contents from the bulk mantles of the proto-Earth and Theia, the high angular momentum models cannot explain the observed difference. However, both the hit-and-run as well as the classical or "canonical" Giant Impact model naturally explain this difference as the consequence of a simple mixture of two mantles with different FeO. Therefore, the simplest way to reconcile the isotopic similarity, and FeO dissimilarity, of Earth and Moon is a Theia with an Earth-like isotopic composition and a higher (~20%) mantle FeO content.

Thursday, June 12, 2014

Explaining the Farside of the Moon

Earthshine on a Young Moon: Explaining the Lunar Farside Highlands

Authors:

Roy et al

Abstract:

The lunar farside highlands problem refers to the curious and unexplained fact that the farside lunar crust is thicker, on average, than the nearside crust. Here we recognize the crucial influence of Earthshine, and propose that it naturally explains this hemispheric dichotomy. Since the accreting Moon rapidly achieved synchronous rotation, a surface and atmospheric thermal gradient was imposed by the proximity of the hot, post-Giant-Impact Earth. This gradient guided condensation of atmospheric and accreting material, preferentially depositing crust-forming refractories on the cooler farside, resulting in a primordial bulk chemical inhomogeneity that seeded the crustal asymmetry. Our model provides a causal solution to the lunar highlands problem: the thermal gradient created by Earthshine produced the chemical gradient responsible for the crust thickness dichotomy that defines the lunar highlands.

Sunday, January 19, 2014

Modeling the Results of Theia's Impact

Investigation of the Initial State of the Moon-Forming Disk: Bridging SPH Simulations and Hydrostatic Models

Authors:

Nakajima et al

Abstract:

According to the standard giant impact hypothesis, the Moon formed from a partially vaporized disk generated by a collision between the proto Earth and a Mars sized impactor. The initial structure of the disk significantly affects the Moon forming process, including the Moons mass, its accretion time scale, and its isotopic similarity to Earth. The dynamics of the impact event determines the initial structure of a nearly hydrostatic Moon forming disk. However, the hydrostatic and hydrodynamic models have been studied separately and their connection has not previously been well quantified. Here, we show the extent to which the properties of the disk can be inferred from Smoothed Particle Hydrodynamic (SPH) simulations. By using entropy, angular momentum and mass distributions of the SPH outputs as approximately conserved quantities, we compute the two dimensional disk structure. We investigate four different models: (a) standard, the canonical giant impact model, (b) fast spinning Earth, a collision between a fast spinning Earth and a small impactor, (c) sub Earths, a collision between two objects with half Earths mass, and (d) intermediate, a collision of two bodies whose mass ratio is 7:3. Our SPH calculations show that the initial disk has approximately uniform entropy. The disks of the fast spinning Earth and sub Earths cases are hotter and more vaporized (80-90% vapor) than the standard case (20%). The intermediate case falls between these values. In the highly vaporized cases, our procedure fails to establish a unique surface density profile of the disk because the disk is unstable according to the Rayleigh criterion. In these cases, we estimate non-unique disk models by conserving global quantities. We also develop a semi analytic model for the thermal structure of the disk, which requires only two inputs: the average entropy and the surface density of the disk.