Question

Warm Jupiters are giant exoplanets with orbits between $0.1\text{ AU}$ and $1.0\text{ AU}$. Astronomers propose three models to explain their origin:

* Model 1 (In-Situ Formation): Warm Jupiters form at their current orbital distances. Because this region contains little mass in typical protoplanetary disks, Model 1 assumes that the local disk surface density must have been at least 100 times greater than the minimum mass solar nebula. Under this hypothesis, dust grains coagulated rapidly to form a $10\ M_\oplus$ core, which then triggered runaway gas accretion from the local gas reservoir. This entire process must be completed within 1–2 million years, before the stellar wind disperses the gas.
* Model 2 (Disk Migration): Warm Jupiters form beyond the 'ice line' ($>3\text{ AU}$), where water ice can condense, providing abundant solid material to build a massive core. The planet then migrates inward because of tidal torque from the gas disk (Type II migration). This migration is driven by the exchange of angular momentum between the planet and the gas disk. Model 2 assumes that migration ceases when the planet reaches the inner edge of the gas disk or when the gas disk is photodissipated by the host star.
* Model 3 (High-Eccentricity Tidal Migration): Like Model 2, Model 3 assumes Jovian planets must form beyond the ice line ($>3\text{ AU}$) to acquire enough solid ice and dust for core growth. However, after formation, the planet is perturbed into a highly eccentric orbit ($e > 0.9$) by the gravitational influence of a distant companion star or planet. During periastron (closest approach to the host star), the intense tidal forces stretch and compress the planet, dissipating orbital energy as heat within the planet. This process, known as tidal circularization, slowly shrinks and circularizes the orbit over hundreds of millions of years. Model 3 assumes that the gas disk is completely gone before the gravitational perturbations trigger this high-eccentricity phase.

Based on the models described, is the following statement true or false?

'Model 2 and Model 3 both hypothesize that the initial formation of a gas giant's core requires a region of the protoplanetary disk where temperatures are low enough for water ice to condense, whereas Model 1 assumes that core formation can occur in much warmer regions closer to the star provided there is an exceptionally high density of dust.'