Download habitable extrasolar planetary systems, the case of 55 cnc

“HABITABLE EXTRASOLAR PLANETARY SYSTEMS, THE CASE
OF 55 CNC”
Desiree Cotto-Figueroa
University of Puerto Rico at Humacao
Institute for Astronomy, University of Hawaii
Mentor : Nader Haghighipour
ABSTRACT
The results of a study of the orbital evolution and habitability of the ρ Cnc system are
presented. Initial integration of the system using the reported orbital parameters
(McArthur et. al 2004) indicates that the system is unstable. In search of the stable
planetary orbits, an extensive search of the parameter-space of the system was carried out
and a stable region was identified. Within this region, dynamical stability of an Earthlike planet in the habitable zone of the system was studied and two regions of harboring
habitable planets were recognized.
INTRODUCTION:
The notion of planetary worlds orbiting stars other than our Sun is not new.
History has revealed that human ponderings over the possibility of other solar systems
beyond our own dates as far back as early Greek times, when the Greek philosopher
Epicurus wrote: “There exist countless worlds like ours also as well as others.” It wasn’t
until 1991 when radio signals from the pulsar PSR B1257+12 in the constellation Virgo
led Alexander Wolszczan, an astronomer from Pennstate University to discover the first
planets ever known outside our solar system. Later, in the following year, using radial
velocity measurements, Michel Mayor and Didier Queloz from the University of Geneva
announced the discovery of the first extrasolar planet around a main sequence star (51
Pegasi) (Mayor & Queloz ,1995). Two years later, at the Lick Observatory, Geoffrey
Marcy and Paul Butler confirmed the existence of that planet using the Hamilton
Spectrograph (Marcy et al. 1997). Since then more than 160 planets have been detected.
Considering the vastness of the universe, containing in all probability millions of
planets, it is difficult to imagine that our solar system is unique and our planet is the only
one that harbors life. In fact, discovery of multiple planets around a star is not
unexpected. Among the currently known extrasolar planetary systems, there are over 14
systems with more than one planet. The planetary system of ρ Cancri (55Cnc) is one of
such systems. This project has to do with exploring the possibility of habitable worlds in
the ρ Cancri system.
The single most crucial factor in the evolution of life is the availability of liquid
water. In our solar system, the habitable zone (HZ) lies approximately between 0.8 to 1.3
AU where water can sustain its liquid form. In a extrasolar multiple planet system, one
Element
Orbital Period
(days)
Eccentricity
ω (°)
a (AU)
M (MJUP)
Velocity
Amplitude (ms-1)
ρ Cnc e
2.808 ± 0.002
Table 1.
ρ Cnc b
14.67±0.01
ρ Cnc c
43.93±0.25
ρ Cnc d
4517.4±77.8
0.174±0.127
261.65±41.14
0.038±0.001
0.056±0.017
6.665±0.81
0.0197±0.012
131.49±33.27
0.115±0.003
0.982±0.19
67.365±0.82
0.44±0.08
244.39±10.65
0.240±0.008
0.272±0.07
12.946±0.86
0.327±0.28
234.73±6.74
5.257±0.208
4.9±1.1
49.786±1.53
major question, would then be; Can the system support a habitable planet? The HZ of a
main-sequence star is defined as where liquid water can exist on the surface of a planet.
This implies a moderate planetary surface temperature suitable for the development and
subsistence of life. The size and location of the HZ depend on the physical properties of
the star in question. ρ Cancri (55 Cnc) is a visual binary system in the constellation of
Cancer. It consists of a middle-aged, Sun-like (G8V) primary of high metallicity (Rho A)
and a red dwarf companion mass (Rho B). A mean distance of approximately 1,150 AU
separates these two stars. Four planets, Ab, Ac, Ad, and Ae, have been discovered in
orbits around the primary star. Table 1 shows the orbital parameters of these objects.
This is the largest number of planets currently known to exist around a star other than our
Sun. Ab was announced as the fourth extrasolar planet discovered (Butler et al. 1997) and
apparently also was listed as the second "Hot Jupiter" found after 51 Pegasi b.
In 2002, the second planet Ad, a high-mass classical jovian, was discovered
(Marcy et al. 2002). When signals of the first two planets were removed from the radial
velocity measurements of ρ Cancri, a sharp peak remained indicating the possibility of a
lower mass planet with a period of 44 days. Despite the similarity between the planet’s
period and the period of the rotation of the star (35-42 days), the third planet Ac, was
tentatively added to the list of extrasolar planets. Since ρ Cancri is a quiet star, showing
no signs of photospheric irregularities, the planet interpretation is more likely viable.
Analysis of the dynamics of this planet indicates that it orbits bring it very close to Ab,
resulting in a near 3:1 resonance. The most recent planet discovered in the ρ Cnc system,
Ae, is a "Neptune-class" extrasolar planet (McArthur et al. 2004). The discovery of this
planet confirmed the existence of Ac as well. Ac shows an amplitude of the signal of 12
m s-1 when the effects produced by stellar activity normally do not exceed 3 ms-1.
Having the largest number of planets and an outer planet that orbits at 5.3 AU
which is comparable to Jupiter’s distance from our Sun, ρ Cancri becomes one of the
most interesting systems for investigating the following question: Could a planet harbors
life in this system?
METHOD
The goal of this project is to identify regions within the habitable zone of ρ Cancri where
a life-harboring planet can have a long-term stable orbit. The habitable zone of the
system is identified as the appropriate position for an Earth-like planet where it would
receive the same amount of radiation as our Earth receives from our Sun. The amount of
radiation emitted by a star depends on its luminosity, and varies with the radius and
surface temperature of the star (Stefan-Boltzman law E=σT4). That is,
L=4πr2b(r)= 4πR2σT4
Where L is the luminosity of the star, R is its radius, T is the star’s surface temperature,
and b(r) represents the star’s brightness at a distance r. From this equation, the amount of
radiation receive by a planet at a distance r relative to the radiation received by Earth
from the sun is given by
This equation indicates a habitable zone with an inner edge at 0.598 AU and an outer
edge at 0.972 AU. Previous studies, however, reported different boundaries for this
region (Table 2). In this paper, in order to be consistent with previous studies, we choose
the habitable zone to have a range of 0.4 to 1.3 AU.
Table 2
Reference
Menou & Tabachnick (2003)
Rivera &Haghighipour (2003)
Bloh,Cuntz,Franck &Bounama (2003)
Whitmire et. al (1998)
Habitable Zone
1.00 ± 0.10 AU
0.7 – 1.3 AU
0.66 ± 0.02 – 1.14 ± 0.04 AU
0.95 – 1.15 AU
The orbit of an Earth-like planet along with the orbits of the four planets of the
system were integrated numerically using Mercury N-body integrator (Chambers 1999).
The time step of integrations were set to 0.14 days, equivalent to 1/20 of the inner
planet’s orbital period (2.808 days). We simulated the dynamics of ρ Cnc system with the
orbital parameters reported by McArthur et al. (2004), and assumed coplanarity of the
system. Using these orbital elements, our simulations indicated that the system was
unstable. There was an ejection of Planet Ae from the system at 23,877 years. Figure 1
shows the semi-major axes of these planets. Searching the orbital parameters space of the
system, we were able to identify a region of the parameter space where the system is
stable. Figure 2 shows the semi-major axis of the planets of the system for one of such
cases. As shown here the system is stable for 10 million years.
Figure 1
Figure 2
Using the orbital parameters of the system of Figure 2 as our initial parameters,
we simulated the dynamics of an Earth-like planet in the Habitable Zone of the system.
The results are shown in Figure 3. An Earth-like planet with an initial semi-major axis of
0.4 AU was ejected at 4,579 years. Simulations testing the following three regions: 0.5 0.85 AU, 1 AU, and 1.13 - 1.3 AU, were unsuccessful: the Earth-like planet escaped the
Habitable Zone in parts of it’s orbit. At 0.98 AU planet E was ejected at 4.4 Myr and at
1.03 AU planet E collided with the star at 6.8 Myr. Our studies have shown that in order
for an Earth-like planet to survive in the ρ Cnc planetary system and remain habitable, it
must reside within the ranges of : 0.9 - 0.95 AU or 1.05 - 1.1 AU. Figure 4 shows the
semi-major axes of the four planets of the system and that of a hypothetical Earth-like
planet for a stable and also an unstable configuration.
1.E+08
1.E+07
1.E+05
1.E+04
1.E+03
1.E+02
1.E+01
Initial Semi-major Axis (AU)
Figure 3
1.30
1.20
1.15
1.13
1.10
1.08
1.05
1.03
1.00
0.98
0.95
0.93
0.90
0.85
0.80
0.70
0.60
0.50
1.E+00
0.40
Time (yrs)
1.E+06
(a)
(b)
Figure 4
Fig. 4 is an example of the evolution of the system. The system became unstable
with an Earth-like planet at 1.03 AU (left column), and became stable with the Earth-like
planet at 1.05 AU (right column)
SUMMARY AND CONCLUSION
We ran simulations of the orbital evolution of ρ Cnc system using the parameters
reported by McArthur et al. (2004). Our results indicated that the system was not stable;
the innermost planet would eject at less than 30,000 years. Increasing the value of the
longitude of the periastron of planet Ab (ωB), within the margin of error, to 164.76° the
system became stable for 107 years. We then added a hypothetical Earth-like planet with a
circular orbit to the system’s habitable zone and we integrated the orbit of this planet for
10 millions years. In general a habitable planet in the habitable zone of ρ Cnc is stable.
Our results indicated that, in addition to the region between 0.9 to 0.95 AU and 1.05 to
1.1 AU, there is a region of 0.85 to 1 AU where an Earth-like will be temporarily out of
the habitable zone. Such a planet may still be habitable as long as it’s greenhouse
process is not affected too much causing no loss or addition of CO2. The greenhouse
effect is what makes the Earth suitable for life as we know it. It consists of the warming
of the Earth's surface and lower atmosphere that tends to intensify with an increase in
atmospheric carbon dioxide. The atmosphere allows a large percentage of the rays of
visible light from the Sun to reach the Earth's surface and heat it. The warmed Earth
emits back into space part of this energy in the form of long-wave infrared radiation,
much of which is absorbed by molecules of carbon dioxide and water vapour in the
atmosphere, and is reflected back to the surface.
The ρ Cnc system is very similar to our own solar system. Currently, it has four
planets orbiting its star and it is possible that this number will increase with time.
However, the question that interests humanity concerns the possibility of being able to
find life outside of our own solar system. ρ Cnc is a good system to conduct this type of
search. Our knowledge in the study of extrasolar planets has gradually grown, by first
discovering planets larger than Jupiter, and very recently a planet with a mass similar to
Neptune’s like ρ Cnc E. It just matter of time till planets with masses like our Earth are
discovered and the question of whether life exists outside our solar system is answered.
The detection of Earth-like planets would be more effective with the missions that the
space agencies ESA and NASA are preparing, such as Darwin and Terrestrial Planet
Finder.
REFERENCES
McArthur, Barbara E.; Endl, Michael; Cochran, William D.; Benedict, G. Fritz;
Fischer, Debra A.; Marcy, Geoffrey W.; Butler, R. Paul; Naef, Dominique;
Mayor, Michel; Queloz, Diedre; 2004 ApJ...614L..81M
Barnes, Roy and Raymond, Sean ; 2004ApJ...617..569B
Rivera, Eugenio J. and Haghighipour, Nader; 2003ASPC..294..205R
Menou, Kristen and Tabachnick, Serge; 2003ApJ...583..473M
Bloh, W.; Cuntz, M.; Franck, S.; and Bounama, C.; 2003AsBio...3..681V
Marcy, Geoffrey; Butler, Paul; Fischer, Debra; Laughlin, Greg; Vogt, Steven; Henry,
Gregory; Pourbaix, Dimitri; 2002ApJ...581.1375M
Whitmire, Daniel P.; Matese , John J.; Criswell, Lee and Mikola,
Seppo;1998Icar..132..196W
Butler, Paul; Marcy, Geoffrey; Williams, Eric; Hauser, Heather; Shirts, Phill;
1997ApJ...474L.115B
Marcy Geoffrey; Butler, Paul; Williams, Eric; Bildsten, Lars; Graham, James; Ghez,
Andrea; Jernigan, Garrett; 1997ApJ...481..926M
Mayor, M.; Queloz, D.; 1997isia.conf...63M