Planets in the Alpha Centauri System’s Habitable Zones:

What might we expect to find?

 

Tony Dunn

 

Abstract

 

Any planets that orbit either Alpha Centauri A or Alpha Centauri B likely orbit in the same plane as Alpha Centauri A and Alpha Centauri B orbit each other.  If they do not, it is likely that each star has either no planets or 1 planet.  If either star in the Alpha Centauri system has a planet in its habitable zone, this planet’s orbit will undergo periodic eccentricity changes similar to the ones experienced by Earth, except with a much faster period.  This may affect the climate of these planets, just like Earth’s climate is effected by the Milankovitch cycle. It is also necessary that such planets remain within ~4 AU of their host star, or perturbations from the other star will destabilize their orbits.

 

 

 

Introduction

 

Alpha Centauri is the closest star system to our solar system.  Depending on who you believe, it is either a double or triple star system.  According to the abstract of Wertheimer and Laughlin’s 1997 paper, Proxima Centauri is near the edge of the AB pair’s Hill Sphere with respect to the Galactic potential. For the purposes of this paper, Proxima Centauri will be ignored.  Whether it is bound or not, it likely does not have life-bearing planets, and its effect on the AB binary is insignificant.  Alpha Centauri A and Alpha Centauri B are both G dwarf stars like the Sun.  Alpha Centauri A is 1.1 times as massive as the Sun, while Alpha Centauri B is 0.9 times as massive as the Sun.  The similarities between these stars and the Sun create an optimism that life-friendly planets may exist in this star system.

 

Plane of Planetary Orbits in the Alpha Centauri System

 

The paths that Alpha Centauri A and Alpha Centauri B trace around their common barycenter form a plane.  According to n-body simulations performed by Dr. Paul Wiegert[1], planets around either star would have to orbit their host star in approximately the same plane as defined by the orbits of the AB members.  If the inclinations of the planets exceeded plus or minus 40 degrees they would be subject to the Kozai Mechanism, an effect that results in the periodic exchange of eccentricity and inclination in a 3-body system.  The orbits of such planets would be pulled out of round.  Their orbits would be stretched from near-circular to their most eccentric value in a period described by formula 2 in Takda and Rasio, 2005[2]

 

 

 

 

 

Where

  • PKOZ is the period from maximum to minimum eccentricity
  • 0 is the host star
  • 1 is the planet
  • 2 is the secondary star
  • P1 is the orbital period of the planet
  • M0-3 is the mass secondary star, 3: planet
  • a0-3 is the semi-major axis
  • e0-3 is the eccentricity

 

 

 

 

It is likely that the orbits of planets heavily influenced by the Kozai Mechanism would cross each other.  Under such conditions, the planets could happily orbit their host star for short periods of time.  But the eccentricity delivered to each planet would subject it to one of 4 long-term fates: 

 

  1. collision with the host star as its eccentricity shrinks its periastron to less than stellar radii.
  2. ejection from the star as its eccentricity expands its apiastron beyond the region where planets remain stable.
  3. Collision with another planet.

4.   Ejection from the system by a close pass of another planet.

 

In the case of planets in the Alpha Centauri system, the Kozai Period would range from thousands to tens of thousands of years, many magnitudes less than the age of the system.

 

The maximum eccentricity a planet, originally in a circular orbit, would gain from the Kozai mechanism can be asymptotically expressed by formula 1 in Takda and Rasio, 2005[2]

 

 

 

Where

  • emax is the eccentricity’s highest value in each cycle
  • i0 is the inclination between the planes of the AB binary and the planet

 

In the case of the planets in the Alpha Centauri system, the maximum eccentricity of the planets would cause their orbits to intersect as the periastron of an interior planet expanded to meet the contracting aphelion of an exterior planet.  This would ultimately result in a planetary collision, or an ejection from the star of one of the two planets, while the other planet took on an even more eccentric orbit in return.

 

After all but one planet has been removed from each star, it is possible that the sole survivor can remain indefinitely in orbit about its host star, forever experiencing luctuating eccentricity.

 

I created a simulation of a hypothetical set of planets, identical in properties to the inner planets of our solar system, around both the A and B members of Alpha Centauri.  The plane of the AB pair is 60 degrees from the plane of the hypothetical Earth.  Figure 1 shows their orbits, rearranged by the Kozai mechanism, after only 1800 years.

 

a)

 

b)

 

c)

 

Figure 1

a) Planets analgous to Mercury, Venus, Earth/Moon, and Mars are placed in orbits around each of the AB members of Alpha Centauri.  The AB pair orbit each other in a plane that is inclined to Earth’s orbit by 60 degrees.

b) The Alpha Centauri A system after 1800 years

c)The Alpha Centauri B system after 1800 years

 

 

 

 

 

 

Figure 2 is an animation of two planets with semi-major axes of 1 and 2 AUs around Alpha Centauri A.  Every ~80 years as the AB pair experience periastron, the inclination and eccentricity of the planets jump to new values.

 

 

 

Figure 2

The orbits of planets with semi-major axes of 1 and 2 AUs around Alpha Centauri A.  (Obviously if you are reading the hardcopy version of this paper, the image is not animated J.  Please visit www.orbitsimulator.com/astrobiology/finalproject.html for the online version where the animations and interactive elements of this paper come to life).

 

 

 

 

Semi-Major Axes of planets in the Alpha Centauri System

 

N-body simulations performed by Dr. Paul Wiegert[1] have revealed that planets in co-planar prograde orbits around Alpha Centaur A and Alpha Centauri B must remain within 4 AUs of their host star or their orbits will be unstable.  Planets in retrograde orbits can wander a bit further from their host star, but such planets would be unlikely, and if they existed, their origins would remain a mystery. 

 

I created a simulation to show Wiegert’s conclusions.  My simulation begins with 50 massless test particles around Alpha Centauri A, and an additional 50 massless test particles around Alpha Centauri B.  They are distributed randomly in circular orbits with semi-major axes ranging from 0.6 to 5.4 AU.  After only a few thousand years, all particles that orbited beyond the bounds described by Wiegert were ejected from the system.  Figure 3 shows the results of my simulation.

 

 

 

 

a)

b)

 c)     

            

 

            

 

 

 

Figure 3

a) 50 test particles were placed in circular orbits around both Alpha Centauri A and Alpha Centauri B.  Their semi-major axes range from 0.6 to 5.4 AU.

b) After only a few thousand years, all particles whose semi-major axes exceeded 3 AU were ejected from the system, in agreement with Wieger’s conclusions.

 

Expanding upon the work of Wiegert, I simulated two planets, one around Alpha Cen A, and one around Alpha Cen B.  Each planet was placed at a distance where its insolation was identical to the insolation Earth receives from the Sun.  Considering the Luminosities of Alpha Centauri A and Alpha Centauri B to be 1.6 and 0.45 respectively, I used the formula

 

 

to determine the semi-major axes of the planets’.  I found them to be 1.265 AU for Alpha Centauri A, and 0.671 for Alpha Centauri B.  I ran the simulation overnight for a total of 30,000 simulated years, at a time step of 1024 seconds (~17 minutes).  The planets experienced a periodic fluctuation in eccentricity similar to what Earth experiences due primarily to Jupiter’s influence.  This eccentricity cycle was comparable to Earth’s in its magnitude.  The planet around Alpha Centauri A had an eccentricity that ranged from 0 to 0.049.  The planet around Alpha Centauri B had an eccentricity that ranged from 0 to .088.  For comparison, the Earth’s eccentricity ranges from near 0 to around 0.06.

 

Although the magnitude of the eccentricity changes were comparable to Earth’s, the period was not.  Earth’s eccentricity changes in small cycles of about 100,000 years and larger cycles of about 400,000 years.  The eccentricity of the simulated planet around Alpha Centauri A alternates between its minimum and maximum values in cycles of about 7200 years.  For the planet around Alpha Centauri B, the period of the cycle is about 15.2 thousand years.  In addition to the large eccentricity cycles, a smaller cycle is seen every 80 years, the period of the AB system. Figure 4 shows the fluctuating eccentricities of the simulated planets around their host stars, as well as Earth’s fluctuating eccentricity for comparison.

 

(a)

(b)

 

(c)

Figure 4

a)       Eccentricity vs. Time for the hypothetical planets around Alpha Centauri A and B over 30,000 years.

b)       Zoomed in on the first 1000 years of graph A.  The eccentricities jump every 80 years in response to periastron
.

c)       Earth’s eccentricity over a 1 million year period.

 

 

 

 

Wiegert also found that planets may also orbit the AB pair from a distance, provided that their semi-major axes are no greater than three times the semi-major axis of the AB pair.  I performed a simulation which demonstrates that such planets are not subject to the Kozai mechanism, and may exist in various inclined orbits.  However, this is probably not an ideal place to search for Earth-like worlds as they lie outside the classical habitable zone.

 

 

 

Conclusions And Discussion


Living on a planet in the Alpha Centauri star system would indeed be an alien experience.  The system sports two habitable zones, one around each of the AB binary members, where planets can exist in stable orbits for the life of the star system.  Such planets would have to orbit within 40 degrees of the plane of the AB binary members.  Additionally, a single planet may exist around either star in orbits inclined more than 40 degrees.  However, any planets in these stable habitable zones would experience frequent climate change.  The Milankovich cycles cause the Earth to cycle through ice ages and interglacial periods over the course of hundreds of thousands of years.  Earth’s changing eccentricity is a contributor to these cycles.  Planets in the Alpha Centauri system would also experience a Milankovich cycle, but every few thousand years instead of hundreds of thousands of years.  Additionally, the changing eccentricity would not be smooth, but rather it would take large jumps every 80 years in response to periastron of the AB stellar members.  This may present a challenge to evolution.  Climates would not remain steady for millennia at a time.  Life would have to adapt to keep pace with the constant and rapid changes their environments would throw at them.

 

 

References

1.  P.A. Wigert and M.J. Holman (1997). "The stability of planets in the Alpha Centauri system". The Astronomical Journal 113: 1445–1450.

 

2.  http://arxiv.org/PS_cache/astro-ph/pdf/0502/0502404.pdf