Exoplanet Activity - Part 2

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ASTR 3000 — Exoplanet Properties, Part II 1

Introduction

Last time we started to find out about the planet orbiting star HD4308, a K0 star with an apparent magnitude of 6.54. It is located in the constellation Tucana at a distance of 21.9 pc. Observations taken from the European Southern Observatory’s 3.6 meter telescope at La Sillia Observatory with the HARPS eschelle spectrograph over between September 7, 2003 and July 28, 2005 indicate that this star has a slight wobble, most likely due to a planetary companion. The radial velocity of the star for each observation is shown in figure 1. These data indicate that the orbital period of the star-planet system is 15.56 days.

Figure 1: Intermediate season of HARPS radial velocities for HD4308. The best fit of the data gives an orbital period of 15.56 days for the planet (from Udry et al. 2006. “The HARPS search for southern extra-solar planets V.” Astronomy & Astrophysics 447: 361–367)

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Information from Part I

In the first part of the exercise we estimated the distance between the planet and the star to be 0.115 A.U. (1.72 × 107 km) which is too close to be in the habitable zone of a K0 star. We also found from momentum conservation that the planet’s mass is at least 4.66 × 10−5 M , but the actual mass depends on the inclination. We will assume that the inclination is 0 and use 4.66 × 10−5 M as the mass of the planet for the remainder of the exercise.

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Surface Properties

Now that you have the mass of your planet, you can learn a lot about it by comparing it to planets in our Solar System (see the appendix for properties of solar system planets). The first thing we will do is check to see if it is terrestrial or jovian. A terrestrial planet could be much like Earth, while a jovian planet is composed primarily oh hydrogen and helium. We will find this by comparing masses. 1. Convert the mass of the planet to kilograms using a conversion in the appendix.

2. Check the properties of solar system planets. Which planet is most like this planet?

3. Is this planet more likely to be terrestrial or jovian?

4. What is the mass of this planet in Earth masses?

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Size

Finally we can try to figure out how big the planet is. The best way to measure the size of something is to observe it directly, but we cannot do that in this case. We will make assumptions about the density in order to rind the size of the planet. We will assume a terrestrial planet has an average density of 5,000 kg m−3 , while a jovian planet has an average density of 1,000 kg m−3 . 1. Use one of the equations in the appendix to find the volume of the planet around HD4308 using the mass of the planet in kilograms and an assumed density.

2. Assuming the planet is a perfect sphere, what is the radius of this planet in meters?

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Escape Velocity

One way to estimate the surface gravity is to calculate the escape velocity on the surface of a planet. The escape velocity is the speed you would have to achieve in order to escape from the gravitational influence of the planet. The higher the escape velocity, the higher the surface gravity and the more energy it takes to overcome it. Escape velocity depends on both the mass and radius of a planet. The escape velocity (vesc ) in meters per second is given by the expression È 2GM vesc = , (1) r where M is the mass of the planet in kilograms, r is the radius of the planet in meters, and G is the constant 6.7 × 10−11 m3 kg−1 s−2 .

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1. Find the escape velocity in meters per second using equation 1.

2. Convert the escape velocity to kilometers per second.

3. How does it compare to other planets in the solar system?

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Summary

Do you think this planet is likely to support life? In the space below indicate why this planet may or may not support life and if this planet would be a good candidate planet for a robotic exploration mission.

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Main sequence star properties Class O2 O5 B0 B5 A0 A5 F0 F5 G0 G2 G5 K0 K5 M0 M5 M8

Radius R/R 16 14 5.7 3.7 2.3 1.8 1.5 1.2 1.05 1.0 0.98 0.89 0.75 0.64 0.36 0.15

Mass M /M 158 58 16 5.4 2.6 1.9 1.6 1.35 1.08 1.0 0.95 0.83 0.62 0.47 0.25 0.10

Luminosity L/L 2,000,000 800,000 16,000 750 63 24 9.0 4.0 1.45 1.0 0.70 0.36 0.18 0.075 0.013 0.0008

Temperature K 54,000 46,000 29,000 15,200 9,600 8,700 7,200 6,400 6,000 5,700 5,500 5,150 4,450 3,850 3,200 2,500

Example Sanduleak -71 51 Sanduleak -66 41 Phi1 Orionis Pi Andromedae A Vega Beta Pictoris Gamma Virginis Eta Arietis Beta Comae Berenices Sun Alpha Mensae 70 Ophiuchi A 61 Cygni A Gliese 185 EZ Aquarii A Van Biesbroeck’s star

Properties of Main sequence stars (from Wikipedia http://en.wikipedia.org/wiki/Main_sequence.

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Solar System Data Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune

Radius km 2,440 6,052 6,378 3,394 71,492 60,268 25,559 24,766

Mass kg 3.30 × 1023 4.87 × 1024 5.97 × 1024 6.42 × 1023 1.90 × 1027 5.68 × 1026 8.68 × 1025 1.02 × 1026

Mean Density kg m−3 5,430 5,240 5,520 3,930 1,330 690 1,270 1,640

Escape Velocity km s−1 4.2 10.4 11.2 5.0 60 36 21 24

Taken from Eric Chaisson & Steve McMillan. Astronomy Today Upper Saddle River, NJ: Pearson Prentice Hall, 2005.

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Conversion Factors • 1 year = 365.25 days = 3.16 × 107 seconds. • 1 AU = 1.496 × 108 km. • 1 M = 1.99 × 1030 kg = 1,050 M Jupiter = 333,000 MEarth . • 1 M Jupiter = 1.90 × 1027 kg.

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• 1 MEarth = 5.98 × 1024 kg. • 1 km = 1000 m.

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Other Equations • The mass M of an object with volume V and density ρ is given by the expression

• The volume V of a sphere of radius r is

M = ρV .

(2)

4 V = πr 3 . 3

(3)