Why Massive Stars are More Prone to Form Massive Planets? (Planetary Science)

Summary:

○ According to Flor-Torres and colleagues, massive stars rotating faster than low-mass stars, had more massive protoplanetary disks (PPDs) with higher angular momentum, explaining why they formed more massive planets rotating faster around their stars.

○ They also found that most stars and planets lost their angular momentum due to the fact that there are interactions of the planets with their PPDs and that massive PPDs dissipates more angular momentum than lower mass PPD.

○ Thus, high mass exoplanets (HMEs) to have higher orbital angular momentum than the LMEs and to have lost more angular momentum through migration.


The discovery of gas giant planets rotating very close to theirs stars (hot Jupiter, or HJs) has forced Flor-Torres and colleagues to reconsider their model for the formation of planets around low mass stars by including in an ad hoc way large scale migration. Since this did not happen in the solar system, it brings the natural question of understanding under what conditions large scale migration could be triggered in a proto-planetary disk (PPD). By stating such question, they adopted the simplest view that there is only one universal process for the formation of planets, following the collapse of dense regions in a molecuar cloud.


This reduces the problem to a more specific one which is: how do we include migration in a well developed model like the core collapse scenario (the standard model), which explains in details how the solar system formed

— said Flor-Torres, lead author of the study.

In the literature, two migration mechanisms are favored for HJs. The first is disk migration, which proposes that a planet looses its orbit angular momentum by tidal interactions with the PPD, while the second, high-eccentricity migration, suggests a planet interacting with other planets gains a higher eccentricity, which brings it close to its star where it reaches equilibrium by tidal interactions (a process known as circularization). In terms of migration, these two mechanisms might suggest massive disks somehow amplified the level of migration compared to what happened in the solar system, because more massive PPDs either increase the intensity of interactions of the planets with their disks or favor the formation of a higher number of planets. Within the standard model this would suggest that what counts is whether the PPD follows the minimum mass model, with a mass between 0.01 to 0.02 M⊙, or the maximum mass model with a mass above 0.5 M⊙. There are few clues which could help determining which path the PPD of the solar system followed (and strong difficulties compared to direct observations of PPD). One is the total mass of the planets, which represents only 0.1% the mass of the Sun. This implies the solar system PPD have lost an important amount of its mass after the formation of the planets. Another clue is that 99% of the angular momentum of the solar system is located in the planets, suggesting that the initial angular momentum of the PPD might have been conserved in the planets. However, this is obviously not the case when large scale migration occurs, so what was the difference?

Fig. 1. Star rotational velocity vs. temperature, distinguishing between stars hosting HMEs and LMEs. The position of the Sun is included as well as the star with a BD as companion. © Flor-Torres et al.

If the initial angular momentum of the PPD passes to the planets, then one could use the orbital rotation momentum in exoplanetary systems to test different scenarios connecting the formation of the planets to the formation of their stars. For example, how is the angular momentum of the PPD coupled to the angular momentum of the stars? Since large scale migration represents a loss of angular momentum of the planets (at least by a factor 10), what was the initial angular momentum of the PPD when it formed and how does this compared to the initial mass of the PPD? Does this influence the masses of the planets and their migration? The answers are not trivial, considering that the physics involved is still not fully understood.


In particular, we know that the angular momentum is not conserved during the formation of stars. This is obvious when one compares how fast the Sun rotates with how fast its rotation should have been assuming the angular momentum of the collapsing molecular cloud where it formed was conserved.

— said Jack, co-author of the study.

Actually, working the math (a basic problem, but quite instructive; see course notes by Alexander 2017), the Sun effective angular momentum, j⊙ = J⊙/M⊙, is ∼ 10^6 times lower than expected. Intriguingly, j⊙ is also 10³ lower than the angular momentum of its breaking point, jb, the point where the centripetal force becomes stronger than gravity. If that was not true, then no stars whatever massive would be able to form. In fact, observations revealed that, in general, the angular momentum of stars with spectral type O5 to A5 trace a power law, J ∝ Mα, with α ∼ 2, with typical J∗ values that are exactly ten times lower than their breaking point. How universal is this “law”and how stars with different masses get to it, however, is unexplained. To complicate the matter, it is clear now that lower mass stars, later than A5, do not follow this law, their spin going down exponentially (cf. Fig.6 in Paper I). For low-mass stars, McNally, Kraft and Kawaler suggested a steeper power law, J ∝ M5.7, which suggests they loose an extra amount of angular momentum as their mass goes down. What is interesting is that low-mass stars are also those that form PPDs and planets, which had led some researchers to speculate there could be a link between the two.

To explain how low-mass stars loose their angular momentum, different mechanisms are considered. The most probable is stellar wind, which is related to the convective envelopes of these stars. This is how low-mass stars would differ from massive ones. However, whether this mechanism is sufficient to explain the break in the J – M relation is not obvious, because it ignores the possible influence of the PPD (the formation of a PPD seems crucial). This is what the magnetic braking model takes into account. Being bombarded by cosmic rays and UV radiation from ambient stars, the matter in a molecular cloud is not neutral, and thus permeable to magnetic fields. This allows ambipolar diffusion (the separation of negative and positive charges) to reduce the magnetic flux, allowing the cloud to collapse. Consequently, a diluted field follows the matter through the accretion disk to the star forming its magnetic field. This also implies that the accretion disk (or PPD) stays connected to the star through its magnetic field as long as it exists, that is, a period that although brief includes the complete phase of planet formation and migration. According to the model of disk-locking, a gap opens between the star and the disk at a distance Rt from the star, and matter falling between Rt and the radius of corotation, Rco (where the Keplerian angular rotation rate of the PPD equals that of the star), follow the magnetic field to the poles of the star creating a jet that transports the angular momentum out. In particular, this mechanism was shown to explain why the classic T-Tauri rotates more slowly than the weak T-Tauri. How this magnetic coupling could influence the planets and their migrations, on the other hand, is still an open question.

To investigate further these problems, Flor-Torres and colleagues started a new observational project to observe host stars of exoplanets using the 1.2 m robotic telescope TIGRE, which is installed near their department at the LA Luz Observatory (in central Mexico). In paper I, they explained how they succeeded in determining in an effective and homogeneous manner the physical characteristics ( Teff , log g, [M/H], [Fe/H], and V sin i) of a initial sample of 46 bright stars using iSpec. In this study, they explored the possible links between the physical characteristics of these 46 stars and the physical characteristics of their planets, in order to gain new insight about a connection between the formation of stars and their planets.


Our main goal is to check is there could be a coupling between the angular momentum of the planets and their host stars.

— said Flor-Torres, lead author of the study.

Table 1: Physical parameters of the High Mass Exoplanets (HME) & Low Mass Exoplanets (LME) in their samples. © For-Torres et al.

Separating our sample in two, stars hosting high-mass exoplanets (HMEs) and low-mass exoplanets (LMEs), we found the former to be more massive and to rotate faster than the latter.

– said Schmitt, co-author of the study.

They found that there is a connection between the stars and their exoplanets, which passes by their protoplanetary disks (PPDs). Massive stars rotating faster than low-mass stars, had more massive PPDs with higher angular momentum, explaining why they formed more massive planets rotating faster around their stars. However, in terms of stellar spins & planets orbit angular momentum, they found that both the stars and their planets have lost a huge amount of angular momentum (by more than 80% in the case of the planets), a phenomenon which could have possibly erased any correlations expected between the two. The fact that all the planets in their sample stop their migration at the same distance from their stars irrespective of their masses, might favor the views that the process of migration is due to the interactions of the planets with their PPDs and that massive PPDs dissipates more angular momentum than lower mass PPD. Consistent with this last conclusion, authors proposed that HMEs might have different structures than LMEs which made them more resilient to circularization.

We also found the HMEs to have higher orbital angular momentum than the LMEs and to have lost more angular momentum through migration. These results are consistent with the view that the more massive the star and higher its rotation, the more massive was its protoplanetarys disk and rotation, and the more efficient the extraction of angular momentum from the planets.

— concluded authors of the study.

Reference: (1) L. M. Flor-Torres, R. Coziol, K.-P. Schröder, D. Jack, J. H. M. M. Schmitt, S. Blanco-Cuaresma, “Connecting the formation of stars and planets. I — Spectroscopic characterization of host stars with Tigre”, ArXiv, 27 Jan 2021. https://arxiv.org/abs/2101.11666v1 (2) L. M. Flor-Torres, R. Coziol, K.-P. Schröder, D. Jack, J. H. M. M. Schmitt, “Connecting the formation of stars and planets. II: coupling the angular momentum of stars with the angular momentum of planets”, ArXiv, 27 Jan 2021. https://arxiv.org/abs/2101.11676v1


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