Exoplanets Composition

Science

California State University Northridge

Question Description

In this lab, we will use Transit Light Curves and Radial Velocity Curves to determine the composition of 5 exoplanets. In the first part of this lab, we will determine the color and lifetime of the 5 stars that host the 5 exoplanets we are considering. In the next part of this lab, we will use Transit Light Curves and Radial Velocity Curves to determine the mass of the 5 exoplanets we are considering. In the following part of this lab, we will use Transit Light Curves to determine the volume of the 5 exoplanets we are considering. In the last part of this lab, we will use the values of the mass and the volume to determine the density of each exoplanet. From the density of each exoplanet, we will be able to determine the composition of each exoplanet.

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Lab Report #12 – Exoplanets Composition Purpose: In this lab, we will use Transit Light Curves and Radial Velocity Curves to determine the composition of 5 exoplanets. In the first part of this lab, we will determine the color and lifetime of the 5 stars that host the 5 exoplanets we are considering. In the next part of this lab, we will use Transit Light Curves and Radial Velocity Curves to determine the mass of the 5 exoplanets we are considering. In the following part of this lab, we will use Transit Light Curves to determine the volume of the 5 exoplanets we are considering. In the last part of this lab, we will use the values of the mass and the volume to determine the density of each exoplanet. From the density of each exoplanet, we will be able to determine the composition of each exoplanet. Part 1: Properties of Stars Hosting Exoplanets In this part of the lab, we will determine some of the properties of the 5 stars that host the 5 exoplanets we will consider for this lab. In the second column of Table 1, we are given the temperature of each star. Use Table 2 to determine the color of each star. Record your answers for the colors in the third column of Table 1. In the fourth column of Table 1, we are given the mass for each star. Use the equation below Table 2 to determine the lifetime for each star. The lifetime for each star is the amount of time the star will remain in the main sequence. Record your answers for the lifetime for each star in the fifth column of Table 1. Table 1: Properties of the 5 stars for the 5 exoplanets we will consider. System Corot 2 Corot 18 HAT-P 32 Kepler 12 WTS 1 Temperature (K) 5575 5440 6000 5947 6250 Color Mass (Mass of the Sun) 0.97 0.95 1.176 1.166 1.2 Lifetime (Billions of Years) Table 2: Temperature Ranges and Colors of Stars Temperature Range 0 K to 3,700 K 3,700 K to 5,200 K 5,200 K to 6,000 K 6,000 K to 11,000 K 11,000 K and above Color Red Orange Yellow White Blue 10 πΏπ‘–π‘“π‘’π‘‘π‘–π‘šπ‘’ = 2.5 π‘π‘–π‘™π‘™π‘–π‘œπ‘› π‘¦π‘’π‘Žπ‘Ÿπ‘  𝑀 Part 2: Determining the Mass of Exoplanets In this part of the lab, we will use Transit Light curves and Radial Velocity curves to determine the mass of each exoplanet. The data for the 5 exoplanets we will consider is shown in the last 5 pages of this file. The goal for this part of the lab is to use the exoplanet data to fill in Table 3, shown below. In the second column of Table 3, the radius of each star, 𝑅𝑆 , is listed. In the third column of Table 3, the mass of each star, 𝑀𝑆 , is listed. In the fourth and fifth columns of Table 3, we show the times 𝑑𝐴 and 𝑑𝐢 . We will use the transit light curves to determine the times 𝑑𝐴 and 𝑑𝐢 . As shown in Figure 1 on the next page, 𝑑𝐴 is the time when the planet begins to transit the star and 𝑑𝐢 is the time when the planet begins to leave the star. With 𝑑𝐴 and 𝑑𝐢 , we will then use the equation shown in the sixth column of Table 3 to calculate 𝑣𝑝 , the speed of each exoplanet. In the sixth column of Table 3, we show the speed of the star 𝑣𝑆 . We will use the radial velocity curves to determine the speeds of the stars 𝑣𝑆 . As shown in Figure 2 on the next page, 𝑣𝑆 is the height of the maximum value in the radial velocity curve. With 𝑣𝑝 and 𝑣𝑆 , we will then use the equation shown in the last column of Table 3 to calculate π‘šπ‘ , the mass of each exoplanet. Table 3: Values and Equations we will use to Calculate π‘šπ‘ , the Mass of each Exoplanet 𝑅𝑆 𝑀𝑆 𝑑𝐴 𝑑𝐢 (Jupiter (Jupiter (Hours) (Hours) Radius) Mass) Corot 2b 8.8 1016.2 Corot 18b 9.7 995.2 HAT-P 32b 11.9 1215.2 Kepler 12b 14.4 1221.5 WTS 1b 11.2 1257.1 Exoplanet 38889 𝑅𝑠 (𝑑𝐢 βˆ’ 𝑑𝐴 ) (m/sec) 𝑣𝑝 = 𝑣𝑆 (m/sec) 𝑀𝑆 𝑣𝑠 𝑣𝑝 (Jupiter Mass) π‘šπ‘ = Figure 1: Schematic of Transit Light Curve to Identify the Times 𝑑𝐴 and 𝑑𝐢 Figure 2: Schematic of Radial Velocity Curve to Identify 𝑣𝑆 , the Speed of each Star Part 3: Determining the Size (Volume) of Exoplanets In this part of the lab, we will use Transit light curves to determine volume of the exoplanet. The data for the 5 exoplanets we will consider is shown in the last 5 pages of this file. The goal for this part of the lab is to use the exoplanet data to fill in Table 4, shown below. In the second column of Table 4, the radius of each star, 𝑅𝑆 , is listed. In the third column of Table 4, the brightness (flux) of the star 𝐹𝑑 , while the planet is between us and the star, is listed. We will use the Transit light curves to determine 𝐹𝑑 . Figure 3 shows a schematic on how we will use the Transit light curve to find 𝐹𝑑 . With 𝐹𝑑 , we will then use the equation shown in the fourth column of Table 4 to calculate 𝑅𝑝 , the radius of each exoplanet. With 𝑅𝑝 , we will then use the equation shown in the fifth column of Table 4 to calculate 𝑉𝑝 , the volume of each exoplanet. Table 4: Values and Equations we will use to Calculate 𝑉𝑝 , the Volume of each Exoplanet Exoplanet Corot 2b Corot 18b HAT-P 32b Kepler 12b WTS 1b 𝑅𝑆 (Jupiter Radius) 8.8 9.7 11.9 14.4 11.2 𝐹𝑑 (No Units) 𝑅𝑝 = 𝑅𝑆 √1 βˆ’ 𝐹𝑑 (Jupiter Radius) 3 𝑉𝑝 = 4.2(𝑅𝑝 ) (Jupiter Volume) Figure 3: Schematic of Transit Light Curve to Identify 𝐹𝑑 , the Flux from the Star while the Exoplanet is Transiting the Star Part 4: Determining the Density and Composition of Exoplanets In this part of the lab, we will use the values for π‘šπ‘ (the masses of the exoplanets) from Part 2 of the lab and the values for 𝑉𝑝 (the volumes of the exoplanets) from Part 3 of the lab to determine 𝐷, the density of each exoplanet. With the density of each exoplanet, we will be able to determine the composition of each exoplanet. The goal for this part of the lab is to fill in Table 5, shown below. In the second column of Table 5, record your values for π‘šπ‘ from the last column of Table 3. In the third column of Table 5, record your values for 𝑉𝑝 from the last column of Table 4. With π‘šπ‘ and 𝑉𝑝 , we will use the equation shown in the fourth column of Table 5 to calculate 𝐷𝐽 , the density of each exoplanet, in terms of the density of Jupiter. With 𝐷𝐽 , we will then use the equation shown in the fifth column of Table 5 to calculate 𝐷, the density of each exoplanet. In the sixth column of the Table 5, we will use the value of the density for each exoplanet to determine the composition for each exoplanet. We will then compare the values of the sixth column of Table 5 to the values of the densities for different materials in Table 6. If the density of an exoplanet is in between the density of two materials, then the exoplanet is made out of those two materials. For example, let’s consider an exoplanet with a density of 5 g/cm3. Since 5 g/cm3 is in between the density of Rock and Iron, the exoplanet is made out of Rock and Iron. In the last column of Table 5, we are given the temperature of each exoplanet. Table 5: Values and Equations we will use to Calculate 𝐷, the Density of each Exoplanet. From the Density, we will then determine the Composition of each Exoplanet. Exoplanet π‘šπ‘ 𝑉𝑝 (Jupiter (Jupiter Mass) Volume) π‘šπ‘ 𝑉𝑝 (Jupiter Density) 𝐷𝐽 = 𝐷 = 1.33 Γ— 𝐷𝐽 (g/cm3) Composition Corot 2b Corot 18b HAT-P 32b Kepler 12b WTS 1b Temperature (K) 1393 1396 1677 1354 1362 Table 6: Density of Common Materials that Planets are made out of. Material Gas Rock Iron Density (g/cm3) 0.00009 2.7 7.9 ...
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