process

tidal migration

Planetary orbital migration driven by tidal interactions with the star or other bodies.
69 related articles · 4 formulas

Description

Tidal migration is a process by which a planet's orbit changes over time due to tidal interactions with its host star or other celestial bodies. These interactions cause a transfer of angular momentum and energy, gradually altering the planet's orbital distance and eccentricity. This mechanism is particularly important for understanding the orbits of 'hot Jupiters'—giant planets that orbit very close to their stars—as they are thought to have formed farther out and migrated inward.

History

The concept of tidal migration was developed in the late 20th century, with key contributions from researchers like Peter Goldreich and Scott Tremaine, who studied the tidal evolution of planetary systems.

How it works

Tidal forces arise because the gravitational pull on the near side of a planet is stronger than on the far side, creating a tidal bulge. If the planet's rotation is not synchronized with its orbit, this bulge is not aligned with the line connecting the planet and the star, leading to a torque that changes the planet's orbital angular momentum. Over long timescales, this can cause the planet to spiral inward or outward, and also circularize its orbit.

In practice

Tidal migration is used to explain the orbital evolution of exoplanets, particularly the existence of hot Jupiters and the circularization of their orbits, and is also relevant for understanding the dynamics of moons in our solar system.

Fun fact

Tidal migration is also responsible for the fact that the Moon is slowly drifting away from Earth at a rate of about 3.8 centimeters per year.

Concept graph →

Formulas

$$\tilde{\Lambda}$$
Dimensionless tidal deformability parameter for compact objects.
What is in the formula
Λ̃variableDimensionless tidal deformability parameter — tidal deformability
\tilde{\lambda}<34.8 · 2512.01918
$$r_t = R_* igg( rac{M_ullet}{M_*}igg)^{1/3}$$
Distance where tidal forces overcome stellar self-gravity.
What is in the formula
r_tvariableTidal disruption radius — radius metre
R_*variableRadius of the star — radius metre
M_\bulletvariableMass of the black hole — mass kilogram
M_*variableMass of the star — mass kilogram
r_t=r_*(\frac{m_\bullet}{m_*})^{1/3} · 2606.02692v1
r_{\rmtide}=r_*(\frac{m_{\rmbh}}{m_*})^{1/3} · 2606.04966v1
r_t=r_p(\frac{2m}{m_p})^{1/3} · 2606.06884v1
r_t\approxr_{ns}(\frac{m_{bh}}{m_{ns}})^{1/3} · 2607.20609v1
$$t_{\text{peak}} \propto M^{1/2} M_p^{-1} R_p^{3/2}$$
Time from disruption to peak accretion rate in tidal events.
What is in the formula
t_peakvariableTime from disruption to peak accretion rate — time second
MvariableMass of the black hole — mass kilogram
M_pvariableMass of the disrupted star — mass kilogram
R_pvariableRadius of the disrupted star — radius metre
t_{{peak}}\approx1.6~{дня}(\frac{m}{10^7m_\odot})^{1/2}(\frac{m_p}{100m_\oplus})^{-1}(\frac{r_p}{6r_\oplus})^{3/2} · 2606.06884v1
$$v_c = \sqrt{\frac{G M}{r}}$$
Orbital speed for circular motion around a central mass.
What is in the formula
v_cvariableCircular orbital speed — velocity metre per second
MvariableCentral mass — mass kilogram
rvariableOrbital radius (distance from center of mass) — radius metre
GconstantNewtonian gravitational constant — gravitational constant = 6.67430e-11 metre cubed per kilogram per second squared
v_c(r)=\sqrt{\frac{g_nm_{{tot}}}{r}} · 2607.14450

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