Habitable Planets in the Planetary System of HD 69830
Sarah Rugheimer
Advisor: Nader Haghighipour
ABSTRACT
We present the results of a study of the dynamical evolution and habitability
of HD 69830 planetary system. Being the first multiplanet extarsolar planetary
system with three Neptune-sized objects, HD 69830 provides new grounds for
testing the possibility of the existence of smaller objects, such as terrestrial plan-
ets, particularly in its habitable zone. We numerically integrated the orbits of
the planets of this system for different values of their masses, and also studied
the long-term stability of many Earth-like objects in its habitable zone. Results
indicate that the planetary system of HD 69830 is dynamically stable and its
habitable zone can harbor terrestrial planet for long times. The only exception
is at 0.735 AU inside this region where an island of stability appears.
Subject headings: extrasolar planets: HD 69830: habitable planets
1. Introduction
Among approximately 170 planetary systems discovered as of July 2006, 21 contain more
than one planet1. The planetary system of HD 69830 is one of such extrasolar multiplanet
systems (Lovis et al. 2006). This system consists of a nearby K0V star at a distance of
approximately 12.6pc from the Earth, and is host to 3 planets with minimum masses of
10.2, 11.8 , 18.1 Earth-masses (Lovis et al. 2006). This is the first observed planetary
system that, unlike other multiplanet systems in which the planets are gas-giant Jovian-type
objects, contains only Neptune-mass bodies.
There are many observational techniques that are used in searching for extrasolar plan-
ets. The precision radial velocity technique is by far the most celebrated one. This technique
that has been successful in detecting more than 180 planets around other stars, measures the
amplitude of variations in the radial velocity of a star as that star is affected by its orbiting
1The extrasolar planets encyclopedia, http://www.exoplanet.eu/
– 2 –
extrasolar planet. From Newton’s law of gravitation, two orbiting bodies exert a mutually
attractive gravitaional force on one another. As a planet orbits its host star, the planet’s
gravity causes the star to undergo small wobbling. For a star, whose mass is much greater
than that of the planet, this effect, although very small, is detectable. Since stellar wobbling
is the result of the gravitational pull of the planet, the radial velocity technique is far more
sensitive to large close-orbiting objects. At present, with current technology, the sensitivity
of this method is increasing, and still hasn’t reached its limit.
Current radial velocity techniques can measure velocity variations down to 1 m/s, al-
lowing discovery of smaller and farther orbiting planets such as in the case of HD 69830.
However the radial velocity technique is still not sensitive enough to measure the effects
of terrestrial planets. Currently, theoretical investigations are the only ways to examine
the possibility of the existance of a system with an Earth-like body. Another consideration
with this technique is that fitting routines are not able to constrain the mass of planets
precisely. Only the minimum mass can be found, and since the stability of a system changes
for different planetary masses, a theoretical analysis accounting for this, is necessary when
determining the long-term stability of a system.
1.1. HD 69830
HD 69830 is a main-sequence star with temperature and size similar to our Sun. This
star is between 4 and 10 Gyr old, and its effective temperature is approximately 5385 K.
The mass of HD 69830 is 0.86 ± 0.03M�, and its luminosity is 0.60 ± 0.03L� (Lovis et al.
2006).
As mentioned in the introduction, HD 69830 is host to three planets. The innermost
planet of this star is at 0.0785AU, and the other two are located at 0.186AU and 0.630AU
from this star. A summary of the orbital parameters for these 3 planets is given in Table 1.
1.2. Habitability
Beyond having a stable energy source, the requirements for habitability are largely
derived from conditions on Earth. Since life seems to be flourishing here, it is reasonable
to impose certain conditions based on our experience when dealing with extrasolar planets.
The Habitable Zone (HZ) of a star is defined as a spherical shell encompassing the star where
liquid water would be able to be present on the surface of a habitable planet (Haghighipour
2006). This capability is dependent on many factors such as atmospheric circulation models
– 3 –
and also the amount of radiation the planet receives from the star [F (r)]. This radiation
itself is a function of the star’s luminosity (L), which depends on the star’s radius (R), of
the star and it’s surface temperature (T ). Equation (1) presents the brightness at a distance
r,
F (r) =1
4πL(R, T )r−2 = σT 4R2r−2. (1)
In this equation, σ is Boltzmann’s constant and F (r) is the apparent brightness, which is
the amount of radiation that is distributed over the unit area of a sphere with radius r.
When calculating the HZ of a star, we compare that star with our Sun. We then
determine the star’s HZ as a place where an Earth-like planet would receive the same amount
of energy as Earth receives from the Sun. That is,
F (r) = (T
T�
)4(R
R�
)2(r
r⊕)−2F�(r⊕), (2)
where T� and R� are the temperature and radius of the Sun, r⊕ is the distance of the Earth
from the Sun, and F�(r⊕) is the brightness of the Sun at the location of Earth. Setting F (r)
for the star equal to F�(r⊕), we obtain
r2 = (T
T�
)2(R
R�
)r�. (3)
Given that the HZ of our Sun is between 0.95AU and 1.15AU (Kasting 1993), the corre-
sponding HZ for HD 69830 will be from 0.736AU to 0.891AU.
It should be mentioned that the orbital eccentricity of an Earth-like planet is an impor-
Table 1. Orbital Parameters of the three planets in the HD 69830 system
Parameter HD 69830 b HD 69830 c HD 69830 d
Orbital Period (days) 8.667 ± 0.003 31.56 ± 0.04 197 ± 3
Semi-major Axis (AU) 0.0785 0.186 0.630
Eccentricity 0.10 ± 0.04 0.13 ± 0.06 0.07 ± 0.07
Longitude of periastron 340◦ ± 26◦ 221◦ ± 35◦ 224◦ ± 61◦
Minimum Mass (M⊕) 10.2 11.8 18.1
Note. — All orbital parameters and physical characteristics are from
Lovis et al. (2006).
– 4 –
tant factor in its habitability. Since eccentricity defines the closest and farthest2 approaches
a planet makes to a star, it is possible that large eccentricities keep the planet out of the
habitable zone long enough so that it may effect the evolution of life. Unfortunately, most
extrasolar planets appear to have large eccentricities and our solar system seems to be some-
what rare.3 But this maybe due to a sampling bias.
2. Methodology and Results
In this project we studied the general stability and the habitability of the planetary
system HD 69830. We carried out numerical integrations of the equations of motion of the
system, using the hybrid routine of the N-body integration package MERCURY (Chambers
1999). This routine requires a timestep of equal to or shorter than 1/20th of the smallest
period in the system. The innermost planet of HD 69830 has a period of 8.667 days. The
time step for all integrations was chosen to be 0.43335 days.
2.1. General Stability of HD 69830
Using the orbital parameters listed in Table 1, we started by simulating the dynamics of
the planetary system of HD 69830. Any orbital parameter not listed in that table, was taken
to be zero. Results indicate that long-term stability of this system is very likely. Figures 1
and 2 show the plot of the semimajor axes and eccentricities of all three planets.
As mentioned before, the radial velocity technique yields only the minimum mass of
an extrasolar planet. Depending on the orientation of the orbit with respect to the plane
of the sky, the mass of an object may be much larger. To test the stability of the system
for different values of the masses of its planets, we scaled the three planets to have different
effective masses by changing their inclinations. The largest planet in the system is HD 69830
d. This planet was taken to be the standard to which the other planets were scaled. We
increased the mass of HD 69830 d to 0.1 MJ , 1.0 MJ , and 1.5 MJ , (corresponding, repectively,
to an inclination of 55.3◦,86.74◦, and 87.82◦, with respect to the plane of the sky) and scaled
the other two planets by the same amount. The system was then numerically integrated for
10 Myr. Results indicate that the outer planet was most effected by the increase in mass,
particularly with a mass of 1.0 MJ (Fig. 3 and 4).
2The closest and furthest approaches are given by a(1 − e) and a(1 + e), respectively.
3The average is approximately 0.25, and the Earth’s eccentricity is 0.02
– 5 –
0 1 2 3 4 5 6 7 8 9 10Time (Myr)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Sem
i−m
ajor
Axi
s (A
U)
Planet B
Planet C
Planet D
Fig. 1.— Graph of the semimajor axes of the planets of HD 69830 for 10 Myr. The closest
and furthes approaches, a(1 ± e), are also shown.
0.0000 0.9999 1.9998 2.9997 3.9996 4.9995 5.9994 6.9993 7.9992 8.9991 9.99900.00
0.05
0.10
0.15
0.20
0.25
0.30
ecce
ntric
ity
HD 69830 b
0.0000 0.9999 1.9998 2.9997 3.9996 4.9995 5.9994 6.9993 7.9992 8.9991 9.99900.00
0.05
0.10
0.15
0.20
0.25
0.30
ecce
ntric
ity
HD 69830 c
0.0000 0.9999 1.9998 2.9997 3.9996 4.9995 5.9994 6.9993 7.9992 8.9991 9.99900.00
0.05
0.10
0.15
0.20
0.25
0.30
ecce
ntric
ity
HD 69830 d
Fig. 2.— Graph of the eccentricity of the planets of HD 69830 for 10 Myr.
– 6 –
0 1 2 3 4 5 6 7 8 9 10Time (Myr)
0.500.55
0.60
0.65
0.70
0.750.80
Sem
i−m
ajor
Axi
s (A
U)
Scaled to 0.1 Mj
0 1 2 3 4 5 6 7 8 9 10Time (Myr)
0.500.55
0.60
0.65
0.70
0.750.80
Sem
i−m
ajor
Axi
s (A
U)
Scaled to 1.0 Mj
0 1 2 3 4 5 6 7 8 9 10Time (Myr)
0.500.55
0.60
0.65
0.70
0.750.80
Sem
i−m
ajor
Axi
s (A
U)
Scaled to 1.5 Mj
Fig. 3.— Graphs of the semimajor axes and a(1 ± e) for HD 69830 d scaled to 0.1 MJ , 1.0
MJ , and 1.5 MJ .
0 1 2 3 4 5 6 7 8 9 10Time (Myr)
0.00
0.05
0.10
0.15
0.20
ecce
ntric
ty
Scaled to 0.1 Mj
0 1 2 3 4 5 6 7 8 9 10Time (Myr)
0.00
0.05
0.10
0.15
0.20
ecce
ntric
ity
Scaled to 1.0 Mj
0 1 2 3 4 5 6 7 8 9 10Time (Myr)
0.00
0.05
0.10
0.15
0.20
Ecc
entr
icity
Scaled to 1.5 Mj
Fig. 4.— Graphs of the eccentricity for HD 69830 d scaled to 0.1 MJ , 1.0 MJ , and 1.5 MJ .
– 7 –
We also investigated the possibility of an asteroid belt in the system. We numerically
integrated a system of 500 test particles evenly distributed between 0.80 AU and 1.00 AU,
the location of an asteroid belt as mentioned by Lovis et al. (2006). The particles were
given random eccentricities between 0.0 and 0.34, corresponding to the average eccentricities
of particles in the Kuiper Belt. Simulations indicated that the system became unstable in a
very short time.
2.2. Stability of an Earth-like Planet in HD 69830
Along with the general stability of the HD 69830, we also studied the habitability of
this system. Since current detection techniques are incapable of detecting small terrestial
planets, study of habitability is at present limited to theoretical modeling. To study the
habitability, one has to first study the long term stability of a habitable planet in the HZ of
the central star. We placed an Earth-like planet at 12 different locations within the HZ of
HD 69830 and integrated its orbit for 10-100 Myr.
Except for one case in which the Earth-like planet was at a distance of 0.753AU, in
general, the orbit of a habitable planet in the HZ of the system is stable. Figures 5 and 6
show the lifetimes and stability of these objects. At a distance of 0.753 AU the Earth-like
planet showed instability early on by making a large number of close encounters with the
outer most planet (Fig. 7 and 8). All other simulations remained stable for 10 Myr. The
eccentricity of the Earth-like planet in these simulations showed variations between 0.0 and
0.12. Due to these variations, it is possible that some of the Earth-like planets at the inner
edge of the HZ that appeared to be stable for 10 Myr, may eventually get too close to the
orbit of HD 69830 d, and become unstable. At 0.788AU and beyond, these simulations are
safely away from the orbit of HD 69830 d, and all are stable for 10-100Myr. Figures 9 and
10 show the results of one such simulation.
– 8 –
0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88Initial Semi-major Axis (AU)
1e+00
1e+01
1e+02
1e+03
1e+04
1e+05
1e+06
1e+07
1e+08
Surv
ival
Tim
e (y
rs)
Fig. 5.— The graph of the lifetime vs. the initial semimajor axis of an Earth-like planet
in the HZ of HD 69830. Though some numerical integrations were carried out for 100 Myr,
only the data up to 10 Myr are presented here.
0.70 0.75 0.80 0.85 0.90Semimajor (AU)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Ecc
entr
icity
Fig. 6.— The graph of eccentricity vs. semimajor axis of all simulations for an Earth-like
planet in the HZ of HD 69830.
– 9 –
0 1 2 3 4Time (Myr)
0.000
0.324
0.647
0.971
1.294
1.618
1.942
Sem
i−m
ajor
Axi
s (A
U)
Planet B
Planet C
Planet D
Earth−like Planet
Fig. 7.— Graphs of the semimajor axis for all planets with a Earth-like planet placed at
0.753AU
0.00 0.42 0.84 1.25 1.67 2.09 2.51 2.92 3.34 3.76 4.180.00.10.20.30.40.50.6
ecce
ntric
ity
HD 69830 b
0.00 0.42 0.84 1.25 1.67 2.09 2.51 2.92 3.34 3.76 4.180.00.10.20.30.40.50.6
ecce
ntric
ity
HD 69830 c
0.00 0.42 0.84 1.25 1.67 2.09 2.51 2.92 3.34 3.76 4.180.00.10.20.30.40.50.6
ecce
ntric
ity
HD 69830 d
0.00 0.42 0.84 1.25 1.67 2.09 2.51 2.92 3.34 3.76 4.18Time (Myr)
0.00.10.20.30.40.50.6
ecce
ntric
ity
Earthlike planet at 0.753000 AU
Fig. 8.— Graphs of the eccentricity for all planets with a Earth-like planet placed at 0.753AU
– 10 –
0 2 4 6 8 10Time (Myr)
0.0
0.2
0.4
0.6
0.8
1.0
Sem
i−m
ajor
Axi
s (A
U)
Planet B
Planet C
Planet D
Earth−like Planet
Fig. 9.— Graphs of the semimajor axis for all planets with a Earth-like planet placed at
0.805AU
0 1 2 3 4 5 6 7 8 9 100.000.050.100.150.200.250.30
ecce
ntric
ity
HD 69830 b
0 1 2 3 4 5 6 7 8 9 100.000.050.100.150.200.250.30
ecce
ntric
ity
HD 69830 c
0 1 2 3 4 5 6 7 8 9 100.000.050.100.150.200.250.30
ecce
ntric
ity
HD 69830 d
0 1 2 3 4 5 6 7 8 9 10Time (Myr)
0.000.050.100.150.200.250.30
ecce
ntric
ity
Earthlike planet at 0.805000 AU
Fig. 10.— Graphs of the eccentricity for all planets with a Earth-like planet placed at
0.805AU
– 11 –
3. Conclusion
We have presented an analysis of the stability of the multiple planetary system of HD
69830. We also studied the habitability of this system by simulating the dynamics of an
Earth-like planet in its HZ. Results indicate that the system is indeed long-term stable. An
Earth-like planet within the HZ may not have long term stability for distances less that
0.788AU. This is most likely due to the interaction of the orbits of the outer planet with
that of the latter object. All other Earth-like planets from 0.788AU to 0.891AU are stable
for 10-100 Myr. Due to the consistancy of the orbital parameters over these time periods,
we believe that long-term stability is very likely.
The orbital parameters of the Earth-like planet near the edge of the HZ would place
that object briefly outside the HZ. However, since our estimate of the HZ of this system is
very conservative, the actual HZ may extend to farther distances.
In addition to the long-term stability of an Earth-like planet, we also presented evidence
that HD 68930 system can be stable for planets of larger mass, given that the radial velocity
technique provides only the minimum mass of each planet. We also studied the dynamics
of an asteroid belt placed between 0.80 and 1.00 AU. Numerical integrations showed a high
rate of collisions among these objects, implying that it is unlikely for the system to have an
asteroid belt.
We are thankful to Simon Poole and the Undergraduate Computer Laboratories at
the University of Calgary for access to their computational facilities. This work has been
supported by an NSF grant to the REU Program at the Institute for Astronomy at the
University of Hawaii - Manoa.
REFERENCES
Chambers, J.E. 1999, MNRAS, 304, 793
Haghihgipour, N. 2006, ApJ, 644, 543
Kasting, J.F., Whitmire, D.P., & Reynolds, R.T. 1993, Icarus, 101, 108
Lovis et al. 2006, Nature, 441, 305
This preprint was prepared with the AAS LATEX macros v5.0.
Top Related