The Roche valve refers to the critical equipotential plane surrounding the celestial body. The matter within this critical plane will be bound by the gravity of the celestial body and encircle in orbit.If the star expands beyond the range of the Roche valve, these substances will get rid of the constraints of the star's gravity.If this star is a conjoint system, these materials will fall into the range of the companion star through the inner Lagrange L1 point.The shape of the critical gravitational boundary of the equipotential surface is similar to the teardrop shape, and the tip of the teardrop shape points to the companion star (the tip is located at the L1 Lagrange point of the system).
It is different from the Roche limit, which refers to the fact that the matter held together only by gravity is affected byTidal forceThe distance from which the action begins to disintegrate;It is also different from the Roche sphere, which is in the space around one celestial body and can maintain the orbit stability of small celestial bodies when being perturbed by the larger celestial body around which it is surrounded, approaching the spherical gravitational sphere.Roche valveRoche limitAnd the Roche sphereEdward RocheIs named after.
In a linked star system with a circular orbit, it can usually be effectively described in a coordinate system that rotates with the celestial body.In theseNon inertial system, besides gravity, we must also considercentrifugal force。Can be usedpotential energyThese two forces have been described so that, for example, the surface of a star can extend along the surface of an equipotential plane.When approaching a star, the sameGravity equipotential surfaceShape is close toSphericalAnd is concentric with the nearby star.At a distance from the stellar system, the shape of the equipotential plane is close toEllipsoidAnd the direction of extension is parallel to the direction of the centroid axis of the two stars.
The critical equipotential plane intersects the L1 Lagrangian point of the system itself, forming an 8-shaped petal pattern between the two stars in their respective petal patterns.This critical equipotential plane defines the Roche lobe.When the material flows relative to the co rotating system, it seems thatCoriolis forceact.This is not derived from the model of the Roche valve. The Coriolis force isNonconservative force(In other words, it cannot be treated as a scalar.).
At a mass ratio of 2Conjoint starThree dimensional space under the same rotation direction systemRoche equipotential surface。The teardrop pattern at the bottom of the equipotential plane is called the Roche valve of the star.L1, L2 and L3 are mutually counteracted by gravityLagrange point。Iffixed starThe material of has been filled with the Roche valve, thenmaterialCan be obtained from the star L1SaddleTo its companion star.
Quality transfer
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When a star "exceeds the Roche valve" - that is, when its surface extends beyond the Roche valve, the material beyond the Roche valve will fall into the companion star's Roche valve through the L1 Lagrange point.In the process of the evolution of conjoined stars, this mass transfer is calledRoche valve overflow。As shown in Figure 1
Red, orange, yellow, green, cyan, blue and purple areas of different colors represent areas between different equipotential lines. L4/L5 has the highest potential, followed by L3, followed by L2, and the lowest L1.
All five Lagrange points are singular.The debris within L2/L3/L4/L5 operates in low orbit, the angular velocity is larger than that of two stars circling each other, and the relative motion is clockwise circling each other;The debris higher than 2/L3/L4/L5 runs in high orbit, and the angular velocity is smaller than that of the two stars, and the relative motion is reverse.(In fact, they are all direct).
The yellow area outside the 8-shaped Roche valve is the so-called Roche valve overflow or Roche valve superfluid. When the debris breaks through L1 point from three areas into the two star Hill ball, the direction of motion will change from anterograde to retrograde.This is a maddening result: this is what we play with the eight shaped orbit of the moon, but if the objects captured from the main star world run in this way, the rotation direction of the planet will be opposite to the revolution direction!
The orange and gold regions are like pig gall. If the mass difference between the two celestial bodies is large, they will show a clear horseshoe shape, which is called "horseshoe orbit".If sundries converge at L4/L5 to form a new celestial body, the rotation direction of the newly formed celestial body will be opposite to the revolution direction!This is also a maddening result.
Whether a celestial body expands beyond the Roche valve and can enter the Roche valve superfluid region depends on the rotation of the expanding celestial body.If the celestial body rotates at a high speed, its rotation speed will catch up with or even exceed the surrounding speed, and the material that crosses the Roche valve will certainly enter the superfluid region;However, if the rotation speed of the celestial body is very slow, the material passing the Roche valve will only be directly donated to the companion star.
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In principle, the mass transfer may lead to the complete disintegration of the celestial body, because the reduction of mass will lead to the atrophy of the falling petals.However, there are several reasons why this usually does not happen.First, the mass reduction of donor stars will lead to the shrinking of donors, which may hinder subsequent donations.Secondly, the mass transfer between the two stars of a conjoined star also includesangular momentumTransmission of.
When matter is transferred from a star with a larger mass to a star with a smaller mass, it usually causes the orbit to shrink, resulting in the expansion of the orbit of a conjoint star (based on the assumption of conservation of mass and angular momentum).The expansion of the multi star orbit will lead to less dramatic contraction, or even the expansion of the donor's Roche valve, which usually avoids the destruction of donors.
Figure 2
revise advise,analysis:
Both primary and secondary objects are represented by particles. Under the condition of the same distance and total mass, the force between different particles is the largest when the mass of two objects is the same;
Figure 3
In this case, the angular momentum and total angular momentum of the celestial bodies are also the largest when the mass of the two celestial bodies is the same;
Because of the conservation of angular momentum, when the mass difference between the two celestial bodies becomes larger, the mutual winding distance increases,
Figure 4
So,Conjoint starWhether the system is stable when quality transmission occurs depends on the direction of quality transmission:
Figure 5
Mass transmission will lead to the shrinking of the donor's Roche valve. If the donor is a low-density large body, the donor and the predator will rise and fall, seemingly leading to the collapse of the donor. But in fact, because the structure of large bodies is dense inside and sparse outside, other bodies can only snatch some sparse gas from the outer layer, rather than shake the dense material inside.
For example,sunlightThe average density of is 1408kg/m. If other small bodies with large density plunder materials from the sun's surface, even if the part beyond the radius of 70% is cut off, it will be only a thin gas with a density of 200kg/m;
Even if it can absorb most of the sun, because the core density of the sun is as high as 160000kg/m, leaving only 25% of the radius of the sun still has half of the original mass, and the predator has long become a small density celestial body because of the addition of thin gas in the outer layer. Donation and plunder cannot be an endless process of terror.
Only high densityMassive celestial bodyThe plundering of other celestial bodies is a more terrible thing. As long as the parts of the prey objects are within the Roche valve of the high-density and massive celestial bodies, they will be mercilessly devoured. Until the average density of the remaining parts of the prey reaches three times the average density of the devourers, the predatory will stop suddenly.
end revise.
To measure the stability of mass transfer and the exact contraction of the donor, it is necessary to actually calculate the radius of the donor star and the subsequent mass transfer of the Roche lobe;If the star expands faster than the Roche lobe or shrinks slower than the Roche lobe, the mass transmission will become unstable, leading to the possible collapse of the donor star.If the donor star expands slowly or contracts faster than the Roche lobe, the mass transmission will generally remain stable and can last for a long time.
1. The teardrop shaped interface on the left, with L1 as the endpoint and the big object as the center, is the Roche valve (hereinafter referred to as A valve) of the big object, and the interface is wrapped with the gravitational sphere of the big object.
2. The teardrop shaped interface with L1 as the end point in the middle and Xiaotian as the center is the Roche valve (hereinafter referred to as the B valve) of the small object, and the interface is wrapped with the gravitational sphere of the small object.
3. The concave spherical interface with L2 point as the node and the sky as the center on the outside is the system's Roche lobe (hereinafter referred to as C-lobe), and the gravitational sphere with the mass center of the two celestial bodies is outside the interface.
Figure 7
4. The shell sandwiched by the A and C lobes and cut off by the B lobe is the joint action area of large and small celestial bodies, where the matter is free to wander between the two celestial bodies under the joint action of the two celestial bodies, (hereinafter referred to as the D area).
5. The space materials that cannot leap over the L1 barrier due to insufficient kinetic energy can only move in the same orbit with small bodies in Area D. The relative motion of these space materials at the approach point with small bodies is in the direction of revolution.
After leaving the approach point, retreat at a high place, which is the horseshoe track.
Figure 8
6. Once the space material has enough kinetic energy to cross the L1 barrier, it will move around the small object under the effect of the residual speed, in the opposite direction to the revolution direction of the small object.
