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.