Vanessa Barnett-Loro and Anne-Marie Turner

3/14/02

Origins of Life Mini-term

 

Exploration of an Extrasolar Planet: 55 Rho Cancri A b

 

Objectives:    

·To gain a cosmic view of planetary systems

·To explore and learn about one extrasolar planet in depth

·To compare our extrasolar planet to planets in our own solar system

·To identify our planet’s star in the nighttime sky

·To observe the relationship between the (approximate) temperature at

                        which a planet forms and the composition of that planet

·To apply the physics concepts learned in class to our discovery of the

                        physical characteristics of our planet

·To speculate regarding the potential for life on our extrasolar planet

 

Procedure:  Our first step was to choose a recently discovered extrasolar planet from a provided list of about eighty-five, basing our selection upon the classification of the planet’s star.  The star was to belong to a recognizable constellation visible at this time of year, and to have a magnitude less than or equal to 5, in order that we might be able to see it plainly at night.  Next, we researched our planetary system and identified basic physical properties and characteristics, such as the mass of the planet and the star, luminosity of its star and the planet’s distance from it, information regarding the orbit of the planet, and scientists’ predicted temperatures for the planet’s surface.  Using these figures, and providing estimated values for the planet’s albedo, we calculated a range of temperatures for our planet using the following equation derived during class for the temperature of a planet (Tp):

 

Tp = [{L(1-A)}/(16Πơd2)]^(1/4)

 

where L is the luminosity of the planet’s star in watts, A is the albedo of the planet, ơ is a constant equivalent to 5.6705E-8 watts m^-2 K^-4, and d is the distance of the planet from its star.  Based on these calculated temperatures, we evaluated the possible compositions of the planet.  Finally, we investigated the ways in which the phenomenon of planetary migration applied to our planet’s location in its system. 

Data/Results:  The planet that we selected for our investigation, called 55 Rho Cancri A b, is located in the 55 Rho Cancri binary system, which lies approximately 40.9 light years from our sun in the northeastern portion of the constellation Cancer (Sol Company).  This planetary system consists, first of all, of a three to five billion year old main sequence dwarf star, 55 Rho Cancri A, with spectral type and luminosity G8V, indicating a yellow-orange star like Sol.  The star contains about 1.03 times the mass of our sun, with 1.1 times its diameter and between 57 and 62 percent of its luminosity (California and Carnegie Planet Search), with an apparent brightness of 5.95.  55 Rho Cancri A has a (2000 equinox) right ascension of 08 52m 35.8s and a declination of +28º19’51” (Extrasolar Visions). 

            The discovery of the planet 55 Rho Cancri A b itself was announced on April 12, 1996 by an astronomy team led by Geoffrey W. Marcy and R. Paul Butler using radial velocity methods, which makes use of the Doppler shift, or periodic shortening and lengthening of emitted wavelengths, that occurs when stars move towards and away from the Earth due to the effects of a planet on its orbit.  (Sol Company).  55 Rho Cancri A b has a mass approximately equivalent to 84% of that of Jupiter, and 300 times that of Earth.  The planet orbits its star at a distance of .118 AU in a slightly elliptical orbit with an eccentricity of .03 that lasts for 14.66 days, or .04014 years.  (Extrasolar Visions).  The derived temperature of the planet is 700 K, or 427ºC, or 800ºF (Sol Company). 

Only speculation exists as to whether or not 55 Rho Cancri A b could be a planet that supports life, but based on what scientists know regarding the planet’s distance from its star and its mass, they are skeptical about the possibilities.  To begin with, 55 Rho Cancri A b is only .118 AU from its star, a distance that, when compared to the positions of planets in our own solar system, lies within Mercury’s orbital distance of Sol.  Sol

55 Rho Cancri

This extreme proximity to its star not only ensures an enormous surface temperature, but also increases the possibility of a tectonically active volcanic surface produced by the tidal forces of the star.  In addition, the carbon dioxide, water vapor, and sulfur dioxide gases produced by this volcanic activity would only serve to exacerbate the intense heat by producing a runaway greenhouse effect that trapped the heat between the planet’s surface and its atmosphere.  Some scientists believe that the planet’s atmosphere precipitates sulfuric acid rain, and is filled constantly with super bolts of lighting.  The overall impression in the astronomic community from these conjectures seems to be that 55 Rho Cancri A b is tremendously hostile to life.  

Calculations:

Static values:

            --Luminosity of our star, 55 rho cancri A: L = Lsun(2.512)^(4.72-M)

            where Lsun is 3.9E26 W and M is the star’s absolute magnitude, or 6. 

            L = (3.9E26)(2.512^(4.72-6)

            L = 1.2E26

            --Distance of our planet from its star = .118 au

            D = .118 au x 149.6 m

            D = 1.765E10 m

Trial 1: If our planet’s albedo resembled that of a very rocky planet with little or no atmosphere, such as Mercury:

            A = .106

            Tp = [{1.2E26(1-.106)}/{16Π(5.6705E-8 W m^-2 K^-4)(1.765E10 m)2}]^(1/4)

            Tp = 589.6 K

Trial 2: If our planet’s albedo resembled that of a very cloudy planet, such as Venus:

            A = .65

            Tp = [{1.2E26(1-.65)}/{16Π(5.6705E-8 W m^-2 K^-4)(1.765E10 m)2}]^(1/4)

            Tp = 466.4 K

Trial 3: If our planet’s albedo resembled that of a planet with a moderately cloudy atmosphere, such as Earth:

            A = .37

            Tp = [{1.2E26(1-.37)}/{16Π(5.6705E-8 W m^-2 K^-4)(1.765E10 m)2}]^(1/4)

            Tp = 540.2 K

 

Conclusions:  For this investigation we were successfully able to select a planet orbiting a star located in a recognizable constellation—that of Cancer, the crab—but our choice turned out to be not so ideal in terms of magnitude; we wanted a star with a spectral type that, when converted into absolute magnitude using the Luminosity Classes chart on page 477 of our Universe textbook, had a value less than or equal to 5.  However, 55 Rho Cancri A has an absolute magnitude of approximately +6, so our star was less luminous than we would have preferred it to be.  This variation only presented a problem when we attempted to find our star in the night sky; it certainly would have been easier to identify a brighter, more obvious star, but we successfully located 55 Rho Cancri with the help of our Finder Chart and our instructor. 

            We were also able to satisfactorily compute the likely temperature of our extrasolar planet, and, from this information, extrapolate the possible materials that compose it.  We based our calculations upon a formula for the temperature of a planet that we arrived at during class—a formula that incorporates L, the luminosity of the planet’s star, the percentage of this energy emitted per time that hits our planet [(Πr2)/(4Πd2), or the area of the planet over the area of the star], A, the albedo of the planet, or the fraction of the energy that hits the planet and is reflected, d, the distance of the planet from its sun, and the temperature flux inherent in Stefan’s law of energy (Tp4).  We knew all of the values we needed for the calculations except for the albedo, and so we plugged in three different values, representing different possible atmospheric conditions that might exist on 55 Rho Cancri A b in order to have a range of temperatures.  According to this calculated range of temperatures for our extrasolar planet, and the condensation temperatures for different substances, our planet has a current average temperature around 540.2 K, and is therefore most likely to be composed of silicates (condensation temperatures between 1200 and 1800 K) and metals (condensation temperatures between 500 and 1000 K).  Our value for the temperature of the planet varies from that derived by the group that discovered the planet (700 K), but this discrepancy can be explained because we did not take into account the effects of radioactive decay, the gravitational energy converted into kinetic energy during the planet’s accretion, or any potential atmospheric absorption of infrared radiation by greenhouse gases in our simplified calculations of planet temperature.  Also, we made the assumption in our calculations that the current temperature of the planet is also the temperature at formation, which is unlikely for reasons we discuss shortly.  However, even with this difference between our theoretical temperatures and the official predicted temperature of the planet, our speculation about the components of the planet remains accurate because the condensation ranges for universal materials overlap and are constant. 

            Another unexpected result that we found in our investigation was the distance of the planet from its star (.118 AU).  It is highly unlikely that a Jupiter-sized planet could have formed so close to the star because of restrictions placed on planet size by temperature, which limits what substances can condense and become part of the planet.  Therefore, we can only conclude that the planet was initially located much further away from the star, and has since migrated closer because of the phenomenon of conservation of angular momentum.  Because angular momentum is constant [L = Σmidi2(2Π/P)], if the tidal forces of the star’s nebulous disc act upon the planet to slow down its rotation, increasing the 2ΠP term, to compensate the Σmidi2 term must decrease, and because the mass of the planet is, for the most part, immutable, the distance of the planet from its rotation axis, or center of mass (located very close to its star), must decrease.

 

An important influence on this process could be the presence of a second, much larger planet in this system.  The evidence for this additional planet can be found in the star’s “residual drift in radial velocity” (citation).  Radial velocity is the rate at which the star moves towards or away from our sun.  Based on scientists’ calculations concerning the known planet, there is a small percentage of radial velocity that cannot be accounted for that they believe may result from the existence of an even larger, unconfirmed planet in an outer orbit at approximately 4 AU from 55 Rho Cancri A.  This planet is projected to contain about 126 times the mass of Jupiter and to have a highly circular orbit, but there is also speculation that the “planet” might actually be a dim red dwarf stellar companion to Rho Cancri A.  The presence of this planet would compensate for the residual drift in the radial velocity. 

 

Works Cited List:

“55 Cancri System.” Online posting. Extrasolar Visions. 12 March 2002.

            http://www.jtwinc.com/Extrasolar/55Can.html

 

“55 (Rho1) Cancri 2.” Online posting. 1998-2002. Sol Company. 10 March 2002.

            http://www.solstation.com/stars2/55cnc2.htm

 

“Masses and Orbital Characteristics of All Known Extrasolar Planets.” Online posting.

            11 March 2002. California and Carnegie Planet Search. 12 March 2002.

            http://exoplanets.org/almanacframe.html

 

Both of us contributed equally to the research, calculations, and analysis that went into this paper,  

Vanessa Barnett-Loro               Anne-Marie Turner