- Title: The Solar System’s Post-Main Sequence Escape Boundary
- Authors: D. Veras and M. C. Wyatt
- First Author’s Institution: Institute of Astronomy, University of Cambridge
At the present moment 8 light-minutes away, the sun is happily fusing hydrogen into helium in its core. In another 6 Gyrs however, the core will have consumed all of its hydrogen fuel. It will then experience several post-main sequence phases as various nuclear fusion processes occur in the shell and core. It will expand into a red giant before blowing off its outer layers as a planetary nebula. Only the ashes of the solar core will remain as a lonely cool white dwarf.
These post-main sequence phases are indeed violent, as the sun’s radius and luminosity will vary by several orders of magnitude. The sun will eject half its mass through intense winds and will shrink to the size of the earth as a white dwarf. There is no question that these last quick phases of the sun’s evolution will have drastic effects on the solar system. Several studies have explored exactly how the effects of the Sun’s post main- sequence phases might change the dynamics and evolution of the solar system planets.
Past studies have offered differing conclusions. In fact, the Earth’s fate is rather controversial. Such a mass loss will cause any surviving planetary body to increase its semimajor axis and possibly vary its eccentricity. But the question remains as to whether or not the earth will “outrun” the Sun’s expanding envelope at such a time. First we must understand the Sun’s evolution in order to look at the fate of the Solar System.
As the Main-Sequence Phase Continues…
While the Sun continues in its main-sequence phase, the planets will be unaffected by the Solar mass loss. In other words the Sun’s currently small mass loss (in the range of 10-14 Mo/yr – 10-13 Mo/yr) will not change their eccentricities and their semimajor axes will increase by 0.055% at most. Instead small perturbations of the orbiting bodies themselves drive dynamic change. Due to these perturbations the inner planets will observe chaotic motion and it is likely that Mercury will suffer a close encounter with Venus. The outer planets however will remain stable in near-circular orbits.
While many studies have shown similar results, they remain inconclusive. It is impossible to know with certainty the exact orbital structures of the planets at the beginning of the Sun’s post-main sequence lifetime. This makes further studies of their orbital structures at this point rather challenging. Specifically it is difficult to understand the fate of the inner planets. Since the outer planets are assumed to remain stable throughout the entire main sequence phase of the Sun, we may be able to understand these better.
The Aftermath of the Post-Main Sequence Phase
Solar Evolution Models
Veras & Wyatt focused on exploring the prospects for dynamical ejection from the Solar System during the Sun’s post-main sequence phase. They did so by first utilizing the SSE code, which describes the evolution of a star for a given mass, metallicity, and mass loss. For this specific model, the solar mass is set to the current value of the Sun’s mass, the metallicity is 0.02, and it is assumed that the Sun has already been evolving on the main sequence for 4.6 Gyr.
In all cases, the Sun undergoes a 0.5 Gyr transition from the main-sequence to the base of the red giant branch (RGB), throughout which it fuses hydrogen into helium in its shell. When reaching the red giant branch it fuses helium into carbon in its core until it moves on to the asymptotic giant branch (AGB). Here it enters a thermally pulsating phase before becoming a white dwarf. The rate of each phase and mass loss throughout each phase is determined by the solar reimers mass loss coefficient: η. Experimental considerations place η in the range: 0.2 ≤ η ≤ 0.8.
The models suggest that the greatest amount of mass lost occurs while the sun is in the RGB and early AGB phase. In all cases the total percent of mass lost is 46.5%-49.0%. While nearly half of the Sun’s mass is lost, the exact phase during which it is lost depends on the input parameter η. For instance if η is less than 0.5 than most of the mass is lost on the AGB and if it is greater most of the mass is lost beforehand on the RGB.
Solar System Dynamics
Once we understand the solar evolution in the various post-main sequence phases it is possible to see how this will affect the planets. A star that is expelling mass beyond an orbiting object will cause the object’s orbit to expand. If the mass loss is large enough during a single orbit then the object will be expelled from the system. If this is not the case, then all orbiting bodies will expand their semimajor axis at the same rate.
Veras & Wyatt determined a critical semimajor axis, within which an orbiting body will remain bound to the dying Sun, by using N-body simulations of orbiting objects. It was unfeasible to simulate orbital evolution throughout the remaining lifetime of the Solar System. Instead the team focused on the behavior of objects when they are most likely to escape. Having already determined when the greatest mass loss occurs they looked at these stages, simulating the entire RGB and AGB phases.
The critical semimajor axis within which bodies will remain bound to the dying Sun is 103 AU – 104 AU. Thus all 8 of the inner and outer planets will evolve “adiabatically” such that their semi-major axis increases but their eccentricity remains the same. They will remain bound to the dying sun. Objects with semi-major axes greater than this critical value are in the “runaway” regime. Their semi-major axis continues to increase and their eccentricities may change to any value from 0 to 1.
The Solar System beyond the Kuiper Belt is divided into two regions: the scattered disc and the Oort Cloud. The inner and outer population of the Oort Cloud is located at 2 x 104 AU. This is a factor of 2 – 20 times as high as the Solar System’s post main-sequence escape boundary (i.e. the critical semi-major axis). So comets from both locations are likely to escape. Sedna, the most distant Solar System object yet observed (q = 76 AU, a = 480 AU) will remain bound if it maintains its orbit throughout the rest of the Sun’s main-sequence lifetime. Further unobserved objects will most likely escape.
Most objects in the “runaway” regime will escape depending on their orbital architectures and their position along their orbits at the beginning of the Sun’s post-main sequence lifetime. In other words the fraction of bodies which escape does not necessarily scale with the critical semimajor axis. If η is small than objects near pericenter are likely to escape. Here the chance of escaping is less dependent on the critical semi-major axis. Whereas if η is large then it is more dependent on the critical semi-major axis.
After the Sun has become a white dwarf, objects that managed to remain bound in the Solar System will retain the orbital parameters they achieved the moment the Sun stopped losing its mass. These objects will remain on these orbits unless subjected to additional perturbations. The main source of perturbations will come from other surviving planets. This could lead to instabilities on Gyr timescales or longer.
It is clear that the future of the solar system will be highly chaotic. Collisions throughout the rest of the Sun’s main-sequence lifetime will occur due to planet perturbations. Many orbiting bodies will then be lost due to the dying Sun. And bodies that remain bound will still be unstable due to other bound orbiting bodies. While exact values cannot be simulated it is evident that the dynamics of the Solar System will be just as violent as the Sun’s death.
Random thought of the day:
Reducing the solar system to an “Island alone in the Universe” light would travel further in the second year of its journey than in the first. But by how much? (Complex relativity calculations to follow!) 😉 Great post tho!