How does accretion heat a planet

Note that at large a the protoplanets are still growing. The result of the N -body simulation is consistent with the estimation based on the oligarchic growth model described below. Figure 10 shows the isolation mass of protoplanets against the semimajor axis for the standard disk model for solar system formation [ 24 ].

This suggests that they are leftover protoplanets. In order to complete Venus and Earth, whose masses are one order of magnitude larger than that of protoplanets, further accretion of protoplanets is necessary. However, their growth timescale is longer than the age of the solar system. Isolation mass of protoplanets against the semimajor axis with the mass of planets in the solar system and the ice line dotted. The oligarchic growth model of protoplanets is now generally accepted as the standard process of planet formation, though it still has some discrepancies.

The generalized oligarchic growth model is used to study the diversity of extrasolar planets together with the core accretion model, as will be shown in Sect.

It is generally accepted that the final stage of terrestrial planet formation is the giant impact stage, where protoplanets planetary embryos formed by oligarchic growth collide with one another to complete planets [ 20 , 28 ]. This stage is being actively studied as many small extrasolar planets are discovered. Though protoplanets perturb each other, the protoplanet system is orbitally stable when disk gas exists, since its gravitational drag damps their eccentricities see Sect.

However, it is observationally inferred that disk gas depletes on a timescale of 1—10 million years [ 13 ]. Thus, in the long term, the protoplanet system becomes unstable through mutual gravitational perturbation after the dispersal of the gas disk. Figure 11 shows the orbital instability timescale of a protoplanet system consisting of 10 equal-mass 0. The semi-logarithm dependence on the initial orbital separation of protoplanets is clearly shown.

Timescale of orbital instability against the initial orbital separation of protoplanets. The solid line shows the result of Chambers et al. After a protoplanet system becomes orbitally unstable, the giant impact stage of protoplanets begins. As this process is stochastic in nature, it is necessary to quantify it statistically in order to clarify it. Kokubo et al. Figure 12 shows an example where three terrestrial planets are formed from 16 protoplanets [ 31 ].

In the standard disk model, two Earth-sized planets typically form in the terrestrial planet region. The effects of the surface density distribution of the disk are unified using M tot. This result shows that protoplanet accretion proceeds globally, in other words, over the whole terrestrial planet region.

Thus the large-scale radial mixing of material is expected. Time evolution of the semimajor axes solid lines and pericenter and apocenter distances dotted lines of planets left.

The size of circles is proportional to the physical size of planets. Average spin angular velocity against planet mass left and normalized cumulative distribution of obliquity with the isotropic distribution dotted line right of all planets formed in the 50 runs of the standard model. Prograde spin with small obliquity, which is common to terrestrial planets in the solar system except for Venus, is not a common feature of planets assembled by giant impacts. It should be noted, however, that the initial obliquity of a planet determined by giant impacts can be modified substantially by stellar tide if the planet is close to the star Mercury and by satellite tide if the planet has a large satellite Earth.

So far, we have discussed the dynamics and accretion of solid rocky and icy planets. In the solar system, gas giant planets, Jupiter and Saturn, exist. Since gas giants are at least times more massive than terrestrial planets, the architecture of planetary systems is sculpted by the giants, if they exist in the systems. The mass of protoplanetary disks is about one order of magnitude larger than that of giant planets, which implies that planetary orbits are significantly affected by interactions with disk gas.

Here we briefly summarize the current understanding of planet—gas disk interactions and the formation process of gas giant planets. Since distributions of gas giants in extrasolar planetary systems have been revealed by rapidly developing observations, we can compare the theoretical predictions with the observed distributions.

Although some aspects of the observed distributions are explained by the theory, there still remain important unsolved problems. While orbits of planetesimals and protoplanets can be eccentric, disk gas rotates in a circular orbit. Thereby, planet—disk interaction generally damps the orbital eccentricity of planetesimals and protoplanets. For small planetesimals, aerodynamic gas drag is dominant because the ratio of the surface area to the volume is higher for smaller bodies.

Equations 6. While the eccentricities of small planetesimals are excited by nearby protoplanets, allowing mutual collisions and accretion by the protoplanets, the eccentricities of the protoplanets are not excited, so that protoplanet—protoplanet collisions are generally inhibited in the presence of gas.

Orbital migration of protoplanets due to planetesimal scattering gravitational interactions with a planetesimal disk also exists, as pointed out in Sect. However, the migration speed and direction have not been clarified yet. For the formation of gas giant planets, two models have been proposed. Here, we summarize the core accretion model. Note that a possibility of disk instability is now being revisited, because extrasolar gas giants with large orbital radii, which are not easily formed in situ through core accretion, are being observed by direct imaging.

After M c exceeds M c,cr , heat generation due to gravitational contraction of the gas envelope itself supports the envelope against dynamical collapse and the envelope undergoes quasi-static contraction [ 40 ]. The contraction allows disk gas to flow from the protoplanetary disk into the Bondi radius of the planet, so that the contraction rate determines the rate of gas accretion onto the planet.

Since t g,acc rapidly decreases with increasing M , the gas accretion is a runaway process and initial contraction regulates the total gas accretion timescale. Equation 6. Using the results in Sects. Using the results in the last subsection, we discuss the diversity of planetary systems [ 7 , 12 ] Fig. On the other hand, in high-mass disks, it is expected that multiple gas giants are formed since the range between a in and a out is broad. Multiple giants often undergo close scattering among them, resulting in the formation of gas giants in eccentric orbits that are found in extrasolar planetary systems.

In massive disks, cores and gas giants form early enough when the full amount of disk gas still exists. Then, the gas giant that has opened up a gap in the gas disk would migrate together with disk accretion type-II migration [ 47 , 48 ] to the vicinity of the host star.

Thus, initial disk masses would produce a diversity of planetary systems [ 7 ]. The gas accretion rate onto the core and the mechanism to stop gas accretion are subjects of discussion for many authors, as is a realistic type-I migration rate. Although these processes sill have large uncertainties, the planetesimal dynamics and accretion described here are relatively well understood and they are fundamental processes for a discussion on the formation of planetary systems.

In the standard scenario of planet formation, terrestrial and icy planets and cores of gaseous planets are formed by accretion of planetesimals.

The random velocity eccentricity e and inclination i of planetesimals controls planetesimal accretion, and then the growth of planetesimals changes the random velocity. This interplay between planetesimal dynamics and accretion demonstrates the interesting phenomena of planetesimal accretion. We have demonstrated the basic dynamical and accretionary processes of planetesimals by showing examples of N -body simulations.

In the orbital evolution of planetesimals, two-body gravitational relaxation plays key roles. The important basic processes are viscous stirring and dynamical friction. Orbital repulsion is one of the key processes that realize the oligarchic growth of protoplanets. All these elementary processes control the basic mode, timescale, and spatial structure of planetesimal accretion. This is due to gravitational focusing, which enhances the collisional cross-section of planetesimals by self-gravity.

Once the mass of a protoplanet runaway-growing body exceeds a critical mass, it effectively heats up the random velocity of local planetesimals, which results in orderly growth among protoplanets.

This growth mode is called oligarchic growth of protoplanets, where similar-sized protoplanets predominantly grow with certain orbital separations. These processes of planetesimal dynamics and accretion are relatively well understood and are now incorporated into the standard model of planet formation. The final stage of terrestrial planet formation is known as the giant impact stage.

At this stage, accretion proceeds globally and the total mass of protoplanets M tot is a key parameter that determines the mass of planets. The masses of the largest and the second-largest planets increase with M tot almost linearly.

The spin parameters of planets are determined by giant impacts. The obliquity of the planets follow an isotropic distribution. We also discussed the orbital evolution of planets by planet—gas disk interaction. The core accretion model for gas giant formation is summarized and used to discuss the diversity of planetary systems. As we have shown, planet formation consists of multi-scale, multi-layer processes regulated by a variety of physical mechanisms. Some fundamental processes are still unclear, in particular, the formation of planetesimals from dust and orbital migration of proto planets.

Both processes are regulated by the structure and evolution of a protoplanetary disk. The diversity of observed extrasolar planets suggests that secular gravitational perturbations among planets also play an important role in creating the architecture of planetary systems.

We need to deeply explore secular orbital dynamics as well as planet—disk interactions to understand the diversity of planetary systems. We can calibrate theoretical models by using data from rapidly developing observations of extrasolar planets. In the theoretical model of planet formation, there are many unsolved problems related to many different kinds of physics.

However, we already have tools to attack the problems. Studies on planet formation are now at an exciting, rapidly developing stage. Google Scholar. When a dense insulating atmosphere is present, the majority of magma oceans would still be present when the next impact occurs.

Time until the next impact versus magma ocean crystallisation time for Earth-building giant impacts embryo-embryo collisions. All points above the line represent magma oceans that crystallise before the next impact. The magma ocean crystallisation model described above is used to determine the depth of the crystallising magma ocean at the time of the next planetesimal impact.

Based on the hydrodynamic model of Deguen et al. In the case of an embryo impact onto a pre-existing magma ocean, the volume of the calculated melt pool that extends below the base of the magma ocean into a previously solid mantle is added to the volume of the magma ocean to calculate a new magma ocean depth. Metal-silicate equilibration of the embryo material will likely occur at the bottom of the melt pool prior to isostatic readjustment.

Assuming that metal-silicate equilibration and segregation of metal to the proto-core occur only when a large volume of melt is created by an embryo-embryo collision giant impact , we have the following possibilities for equilibration:.

Embryo-embryo collisions : Equilibration takes place at the bottom of the melt pool or at the core-mantle boundary if the melt pool extends into the core before a global magma ocean is created by isostatic readjustment and lateral spreading. In this case, the equilibration pressure will generally be close to the core-mantle boundary pressure Fig. Equilibration pressures calculated for the Earth-forming impacts.

Large symbols are embryo-embryo collisions—these giant impacts create enough melting for a core-formation event to occur and material equilibrates at the bottom of the melt pool, created by the impact.

Small symbols are planetesimal impacts into a leftover magma ocean MO that equilibrate at the bottom of this magma ocean e. A horizontal line indicates planetesimal collisions that occur on a solid surface and equilibrate at the time of the next giant impact e. Impacts in the red ellipse are planetesimal impacts on a solid surface after the last giant impact has occurred.

Planetesimal impact in a magma ocean that survives from a previous embryo-embryo collision : Equilibration will take place at the base of the magma ocean. The depth of the magma ocean is dependent on the time between the embryo-embryo collision and the planetesimal impact as well as the cooling rate of the magma ocean Fig.

Planetesimal impact on a solid surface before the last giant impact : In this case, there is insufficient melt at the time of impact for significant metal-silicate equilibration. However, the next giant impact will mix this material with the target material.

Therefore, equilibration takes place at the bottom of the deep melt pool created by the next giant impact Fig. Planetesimal impact on a solid surface after the last giant impact or in the case of no giant impacts : In this case, there is no subsequent significant melting event available to equilibrate the material and little mixing of the impactor and target material will occur, the impactor material forms a late veneer Fig.

Embryo-embryo collisions large symbols are visible as maxima, whereas the planetesimal impacts in a residual magma ocean result in a decreasing equilibration pressure with increasing time. Planetesimal impacts onto a solid surface result in a plateau at a pressure corresponding to the depth of the next magma ocean or a zero pressure when the material is late veneer and there is no subsequent giant impact.

Equilibration pressures determined by Rubie et al. As expected, the fast-cooling models without an insulating atmosphere mainly show plateaus because magma oceans crystallise before the next planetesimals impact the surface of the planet. The equilibration pressures for almost all collisions are then dominated by the initial depths of the melt pools that are created by embryo-embryo collisions i.

These pressures are mostly higher than the equilibration pressures in the slow-cooling models, where many planetesimals equilibrate in partially crystallised magma oceans. The differences in equilibration pressures between the slow-cooling and fast-cooling models are greatest when the time between embryo-embryo collisions is just long enough for the magma ocean to crystallise in the slow-cooling models.

This results in many small impacts in a partially crystallised magma ocean as can be seen in Fig. In models with smaller embryo masses model —0. This results in embryo impacts into partially crystallised magma oceans, resulting in magma oceans that reach almost to the core-mantle-boundary. Equilibration pressures become similar to equilibration pressures in the fast cooling model where most of the equilibration takes place at or near the core-mantle boundary.

The dotted lines in Fig. Our calculations show that equilibration at the bottom of melt pools created by giant impacts likely occur at higher pressures.

However, in the case of a planet with a dense insulating atmosphere, many of the planetesimal impacts in a slow-cooling magma ocean equilibrate at lower pressures. This scenario is therefore most consistent with the results of Rubie et al. The planetesimals in the N-body accretion models used here are unrealistically large and are actually tracers that represent swarms of much smaller bodies.

However, since small planetesimal impacts do not create enough melt to cause a significant equilibration event, these bodies equilibrate either in a pre-existing magma ocean or at the bottom of the melt pool created by a subsequent giant impact. The exact size and timing of the planetesimal impactors therefore have little or no influence on the equilibration pressure. Because of a number of simplifying assumptions, the results presented here must be considered to be preliminary.

For example, the simple analytical model of melt production may not be accurate Marchi et al. In addition, the cooling models, based on constant time-averaged heat fluxes, are extremely simple. For instance, a pre-existing steam atmosphere could conceivably be removed by a giant impact and then subsequently replenished by outgassing from the interior. At this stage, our main intention is to emphasise the potential of this novel approach for modelling multistage core formation.

Our results show that metal-silicate equilibration pressures during core formation are likely to depend strongly on the rate of magma ocean crystallisation compared to the time interval between impacts. On a planet with a dense atmosphere, or one which develops a solid crust, magma oceans will cool slowly and numerous small impactors will equilibrate at the bottom of this magma ocean. If the liquid magma radiates heat directly to space, most magma oceans will have crystallised before the next impact and then planetesimal material generally only equilibrates when the next giant impact creates a large and deep melt volume.

This is unlikely because, based on the partitioning of siderophile elements between the core and mantle, average equilibration pressures must have been considerably lower e. Wood et al. Thus, based on the present results, the Earth most likely had magma oceans with lifetimes comparable to or longer than the interval between impacts.

A single, long-lived magma ocean is a possibility, especially if a solid crust developed. This possibility, however, is not favoured based on noble gas isotopic arguments which have been used to argue for several generations of magma oceans Tucker and Mukhopadhyay Conversely, these isotopic results are consistent with an Earth possessing a thick, insulating atmosphere for much of its accretion history.

The accretion history also strongly influences the equilibration pressures for slow-cooling models. The three N-body simulations used for this study started with different sizes and different numbers of embryos. When there are fewer embryo-embryo collisions, there are more planetesimal impacts in global magma oceans.

This difference may help determine which scenarios are most realistic for the Earth by combining N-body simulations with core formation models in which equilibration pressures are calculated as in this study. Icarus — Article Google Scholar. Aitta A Iron melting curve with a tricritical point. J Stat Mech P Barr AC, Citron RI Scaling of melt production in hypervelocity impacts from high-resolution numerical simulations.

Int J Impact Eng — Science — Nature — Chambers JE Making more terrestrial planets. Chambers JE Late-stage planetary accretion including hit-and-run collisions and fragmentation.

Clauser C Thermal storage and transport properties of rocks, I: heat capacity and latent heat. In: Gupta H ed Encyclopedia of solid earth geophysics. Springer, Dordrecht. Google Scholar. Earth Planet Sci Lett — Sci Lett — Phil Trans R Soc A Tucson, Arizona, USA. Geochim Cosmochim Acta — Kokubo E, Ida S Oligarchic growth of protoplanets.

Lambrechts M, Johansen A Rapid growth of gas-giant cores by pebble accretion. Astron Astrophys A J Geophys Res Planets — Earth Planet Sci Lett —— Elsevier-Pergamon, Oxford, pp — Chapter Google Scholar. Navrotsky A Thermodynamic properties of minerals. In: Ahrens TJ ed Mineral physics and crystallography. In: Carlson RW ed Treatise on geochemistry—the mantle and core, vol 2, 2nd edn. Elsevier-Pergamon, Oxford, pp 1— Righter K Prediction of metal—silicate partition coefficients for siderophile elements: An update and assessment of PT conditions for metal—silicate equilibrium during accretion of the Earth.

Elsevier, Amsterdam, pp 43— Nat Geosci — Samuel H A re-evaluation of metal diapir breakup and equilibration in terrestrial magma oceans. Another source for the heating of Earth's core is the fact that it is under immense gravitational pressure due to forces exerted by the sun and moon, as well as the fact that the earth is rotating.

This pressure helps to keep the core hot. It's like there is a giant nuclear reactor inside of the Earth and these processes generate a lot of heat! Why is the inner core of the Earth so hot? Answer 1: Excellent question! Answer 2: We have answers on our database that can help you with this question, while we receive more answers from our scientists: click here to read1 click here to read2 click here to read3. Answer 3: The inner core of the Earth is hot because radioactive decay heats the Earth's interior.

Answer 4: Earth's core is hot for a few reasons.