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Sam Houston State University *

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1404

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Astronomy

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Oct 30, 2023

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M“\w W\W\?‘\\\ Lw Transit Light Curves In this lab, we are going to look at (simulated) light curve data and Infer properties of the exoplanets that are transiting, but measuring the amount of light they block from their parent star as they transit. LAB EXERCISE PART I: A SIMPLE PLANETARY TRANSIT In this lab, we are going to answer the research question “What effect does a transiting exoplanet have on the light we receive from its parent star and what can that tell us about the planet?” As a reminder from the Eclipses & Transits Lab, 1. What does it mean for a planet to transit a star? A eYopott vasxs diveeivy BEARLA Eacx OV Planey X . 2. Will thégistanceé::y:n exoplanet from its parent star have any effect on what we observe? U, % wond 1ar 1SS Regerve by WO En Qwony 141\S. Below is a light curve of a star with a transiting exoplanet. We are going to analyze this light curve to determine properties of the exoplanet. T 1 1 o I A T 1 1.0000 —mﬂ x 3 L. 0.9980 o 2 I % D 0.9960 - 1 0.9940 U 1 1 1 1 1 -0.5 0 0.5 1 15 2 Time (Days) Here we have a light curve of a nearby star. Note the properties plotted on each axis: - X-axis: Orbital Phase (days) - Y-axis: Relative Flux (where 1.000 is the full brightness of the star) Astronomers make observations of a star over numerous days. They first establish the baseling level of brightness observed from the star, and then note the decrease in brightness over time: due to the transiting event, recurring periodically over time as the planet orbits its star. Scanned with CamScanner

\ ! vV ¥V W V¥YEsw ¥ » - mame:\NNCHON YNUVEY [0 crion miprte SUTVES 3. Looking at the light curve above, what property of the transiting exoplanet can we easily determine? Describe how. i~ WE (o A revmiese Yhexnow Aeaent\i i wangit 0COvS ond K, ey 6 6 \\ v 4. Using the light curve, determine the value of that property. 5. Based on what you learned in the Moons of Jupiter lab, what other property can you calculate, based on what you measured in the previous questions (assuming the exoplanet TS e Wi 1€ Y ML Vit kRS . 'sing the formula derived in the Moons of Jupiter lab, what value do you calculate for that ‘operty? (Show your work.) W=p? g° Scanned with CamScanner

cerres \v*\c',i—; "'T\"Y h\-' 1 / _ Transit Light Curves In the Moons of Jupiter lab, we found a relationship between the period of orbit of an object and its average orbital radius, which can be written as MP=3a? Where P = the period of orbit (measured in years) a = the average orbital radius (measured in Astronomical Units) M = constant of proportionality For objects that orbit the Sun, the constant of proportionality is equal to 1. For other stars, it is equal to the mass of the star, relative to the mass of the Sun. Once astronomers have determined that a transit has occurred (usually through multiple, repetitive observations to ensure that the event is a transit and not something else), they can focus on the transit event itself, adding multiple observations together to get a combined light curve of the transit, to determine further information about the exoplanet. In the graph above, the amount of light detected from the star is measured relative to the maximum value we detect, when nothing is blocking it. That is why it is labeled as “relative flux”. Notice that the maximum value is “1”. 7. What value is it when the exoplanet is difectly in front of it, at its lowest value? Do993> 8. If that s the relative amount of light we still see when the exoplanet is in front of it, what fraction of light is blocked by the exoplanet? T [0OD The fraction of light that is blocked by the exoplanet is given by fraction = area of planet's disk _ nr? >\2 area of star'sdisk ~ mrZz (:-—s) Therefore, if we know the radius of the star (which can be determined based on other means), we can determine the radius of the exoplanet as \ Tplanet = Tstar X y/fraction of light blocked 79 Scanned with CamScanner

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\ A 2 SRt 1 /11 name: VRN NWNQVVH - o = e 9. Based on this, what is the radius of the exoplanet ... relative to the radius of the star? Y planey . — Y sxav relative to the radius of Earth? (Assume that the star has the same radius as our Sun.) (plowiek = (&L e [ 160 *10\7,/ |60 6 \6%\) A5 Scanned with CamScanner

Name: ‘\“CL\ YV\\NY)\\J\ . Transit Light Curves PART 11: MULTIPLE PLANETS SorneﬂmeswedetectMmfimmm“w.hmbmlhekmmiight curve is more complex. 1.0001 1.0000 ; 09995 09998 : 09297 Relative Flux = T 0 5 10 15 20 %5 39 40 50 60 70 Time Days Here we have a simulated light curve of a nearby star observed over a pe"io_‘j of 100 days. Note that three exoplanets are detected. The planets are known to orbit star with a mass equal to 90% the mass of our Sun (0.90 Mo) and has a radius equal to 92% the radius of our Sun (0.92 Re) 10. How can you determine that there is more than one exoplanet? e FIuX Bhows o 1 diecevs HoNoNe e it deYS 81 Scanned with CamScanner

rome. LTS TIWNAY 20 ot L e Given the light curve above, determine the following. {Note, punaurewpiu”yn-medmmsuquovfit,htheordertheywerediscmfed Starting with the letter “b%, with the star being designated as “a”.) Orbdital Period Orbital Radius Planet Radius T (days) (AV) (Earth radii) . \2 Q¢ 105 .51 | . 20 -\141 11.5%28 “ 1% M5 .55 11. Describe the process you went through to determine these values. ; 0d 15 how mony Wes e oy Q) pnod iy wakches Ly N 4 S\ ?J\)\\]M M Q%UAHW YN\~ \Qh ar OaNA VS VLOW WA €O‘N\é W\'( \(G‘Q)\JSS (0 Plowsk vagis = Yyt {\YL—: 1 82 Scanned with CamScanner

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Nam:“\‘w YY\\H(V\"‘ le Transit Light Curves In reality, when astronomers observe light from stars, there is always a level of noise associated with the data. 10001 oy | Wi} AN i 09999 09908 09997 - 0999 09995 - [ 0.9993 Rlad? 45 0.9992 ‘ » 09991 |- : £ C 0 10 20 30 40 50 60 70 80 90 100 Time Days Relative Flux Here we have the same simulated light curve as before, but now with noise included. 12. Can you still detect three exoplanets? Why or why not? & Infhe lonve s, Ipecanse fILles 3 s QY QPR L pIeTs. Scanned with CamScanner

NameN\C/U ‘Y\\l \(\Q\\\\ '1/\\0— Transit Light Curves PART I1I: SEARCHING FOR EXTRASOLAR PLANETARY SYSTEMS With the advent of the Kepler Space Telescope and others which are solely dedicated to the detection of exoplanet transits, astronomers have detected thousands of extrasolar planets. |n many cases, they have detected solar systems with multiple planets orbiting around a common star. Your lab instructor will provide you with a light curve for a multiple planetary system, ranging from 4 to 6 planets. Use what you have learned to determine the orbital properties of these planets. You may assume that the planets orbit a star with the same mass and radius as the Sun. Create a table in Microsoft Excel, similar to the one in the previous section. Record your measured values in the appropriate column, then use formulae within Excel to calculate the remaining values. (If you need a reminder of how to do this, refer to the Appendix.) Once you have completed your table, submit it to your ab instructor. They will inform you of which planetary system you were assigned. Go to the Exoplanet Data Explorer website (exoplanets.org) and find your solar system! 28 e Click on Table to access the table of information o On the right-hand side, click the “+” button and add the following columns o Mass of Star o Radius of Star o (You can delete the reference columns to make room for the new ones) o Click on the “Name” column to sort the data by name Record the following information: Mass of star: ¢ q @ l Radius of star: ‘ 6 ‘06 Number of detected exoplanets: (0 Scanned with CamScanner

Name: N\.C)L): \(V\VW 1l planet Orbital Period Orbital Radius Planet Radiusﬂ (days) (AU) (Earth radii) o 10.% NI Vo 0.160] ; |3 N/W . 255X d 20.¢3 N/ X FAEX. . 2\.99 N/W B T5Y : Ue. 6% | N/R SEbBT g 50 .€ N/ B B3] | 13. How do your answers compare to the accepted values? Explain any discrepancies. FWOS 0 Cone WS Ay VPN 98¢ Scanned with CamScanner

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Name: N\ C/t\ \Y\W\Q\N'X ,l’(( Transit Light Curves PART IV: FURTHER INVESTIGATIONS In today’s lab you investigated a few simulated light curves in order to deduce the size and orbit of one or more extrasolar planets, as well as looked at a database filled with information about detected extrasolar planets. Following procedures similar to the ones you conducted in the lab you performed today, what other related research questions could you pursue? Come up with at least TWO questions related to today’s lab that could be answered by gathering and analyzing data similar to what you did in lab. HOW Qon W junkiey b onisy O€ Qe low (Pes L poplantt 0t €0 Cecech \S kwa% AWHAT DO I TURN IN? » 'n addition to the Lab Exercise pages which contain your answers, please upload the following: * Your Excel spreadsheet and any calculations which you completed for part il e Your labreport Scanned with CamScanner