Tuesday, August 5, 2014

Giant Planet Formation: “Cold-Start” VS “Hot-Start”

Giant planets are thought to form in two possible ways. The first method involves accreting a solid core and once the solid core attains ~10 Earth masses, it becomes massive enough to accrete hydrogen and helium in a runaway process to form a giant planet. This mode of giant planet formation is known as “core accretion”. In the Solar System, the giant planets Jupiter and Saturn are believed to have formed via core accretion. The second mode of giant planet formation involves a protoplanetary disk becoming gravitationally unstable and collapses directly to form a giant planet. This is known as “disk instability”.

Figure 1: Artist’s impression of a giant planet. Giant planets range in mass from a fraction of Jupiter’s mass to tens of Jupiter’s mass.

In the core accretion scenario, the solid core accretes gas through an accretion disk. This process cools the gas, causing it to lose much of its initial entropy and forms a giant planet that has low initial entropy (i.e. a “cold-start”). For disk instability, the gas that collapses directly to form a giant planet retains most of it intitial entropy, resulting in high initial entropy (i.e. a “hot-start”). If the age of a giant planet is known well enough, it might be possible to distinguish a “cold-start” from a “hot-start” based on observables such as the giant planet’s entropy, radius, effective temperature and spectrum.

However, the radiating efficiency of the gas could complicate the “cold-start” / “hot-start” idea. It can cause a “cold-start” that might not be as cold or a “hot-start” that might not be as hot, leading to what could be thought of as a “warm-start”. For instance, the accreting gas in the core accretion scenario may not cool as efficiently and the giant planet formed at the end of the accretion process would have a “cold-start” that is not as cold. On the contrary, the gas in the disk instability scenario may cool more efficiently than thought, resulting in a “hot-start” that is not as hot.

A giant planet formed by disk instability is expected to have higher entropy, larger radius and higher effective temperature than if it had formed by core accretion. Basically, disk instability corresponds to a “hot-start”, while core accretion corresponds to a “cold-start”. Observable differences between “cold-start” and “hot-start” scenarios can be used to distinguish whether a giant planet formed by core accretion or disk instability. These observational differences are substantial when the giant planet is young and diminish after several tens of millions of years.

When a giant planet cools (i.e. loses entropy), its radius shrinks and its effective temperature drops. More massive giant planets retain heat longer than less massive ones, and so evolve slower. As “cold-start” and “hot-start” giant planets of equivalent masses cool over time, their entropies, radii, and effective temperatures gradually converge (Figures 2, 3 & 4). For a giant planet with 10 Jupiter masses, the “memory” of the initial conditions (i.e. whether the giant planet had a “cold-start” or “hot-start”) is lost within a few hundred million years after formation. For lower mass giant planets, the convergence is more rapid because they cool more quickly and the initial differences between “cold-start” and “hot-start” models is smaller for them.

Figure 2: Evolution of entropy for giant planets with 1, 2, 5 and 10 times Jupiter’s mass. Spiegel & Burrows (2012).

Figure 3: Evolution of radius for giant planets with 1, 2, 5 and 10 times Jupiter’s mass. Spiegel & Burrows (2012).

 Figure 4: Evolution of effective temperature for giant planets with 1, 2, 5 and 10 times Jupiter’s mass. Spiegel & Burrows (2012).

At early times, the difference between “cold-start” and “hot-start” models can be quite large. For a giant planet with ~5 times Jupiter’s mass, the differences can persist for ~100 million years. For lower mass giant planets with ~1 to 2 times Jupiter’s mass, the differences fade within ~10 to 30 million years. During the first few million years after formation, giant planets that started hot (i.e. “hot-start”) can be ~10 to 1,000 times more luminous than those that started cold (i.e. “cold-start”), depending on the giant planet’s mass and spectral band.

Spiegel & Burrows, “Spectral and Photometric Diagnostics of Giant Planet Formation Scenarios”, 2012 ApJ 745 174