31:T90b,md`Since the discovery of the first planet orbiting a star similar to our Sun in 1995, one thing has become clear - the Universe is abrim with planets. Thanks to the dedicated work of astronomers and citizen scientists, aided by telescopes on Earth and in space, we now know of over 4000 planets outside our Solar System, known as exoplanets. Large-scale searches for exoplanets have shown that they are extremely common objects in our Galaxy, and they may even outnumber stars. Planets are thousands to billions of times fainter than the stars they orbit, and tens to hundreds of times smaller, so how can we find them at all? In this blog post, we explore the most common technique used to detect exoplanets: the transit method. A "transit" occurs when a planet crosses between us and the star it is orbiting, blocking out a small fraction of the star's light. However, this chance alignment between the star, planet, and us is relatively rare, so we search many stars to make up for the low probability. These ephemeral shadows of planets contain a wealth information about the planet and star's properties, allowing us to learn a lot about their nature. In the figure below, we visualize what is occuring when a planet transits its star. The top panel is not what we observe - other stars are too distant for our telescopes to be able to resolve the system in this detail. Instead, astronomers use telescopes to measure the amount of light we receive from a star over time - called a lightcurve. We then look for periodic dips in the brightness of the star. The bottom panel shows the changing fraction of the star's light we observe as a transit occurs - this is what we actually observe. Make note of where the planet is in the top panel at different points in the plot on the bottom. This is an idealized lightcurve, assuming the star's surface is uniformly bright. These sliders allow you to control the size of the planet and star, the orbital period of the planet, and the impact parameter of the planet. An impact parameter of 0 means that the planet crosses exactly across the midline of the star. An impact parameter of 1 means that the planet is crossing just the edge of the star, which is called a grazing transit. It is harder to extract information about the system from a grazing transit. `32:Te92,{ replay; const svg = d3.select(DOM.svg(innerWidth, 1.5*h)) .style("color",'#fff'); svg.append("rect") .attr("width", "100%") .attr("height", "100%") .attr("fill", "black"); var rplanetm = rplanet*earth_radiusm; var rstarm = rstar*sun_radiusm; // const path2 = svg.append("path") // .attr("fill", "none") // .attr("stroke", "black") // .attr("stroke-width", 1.5) // .attr("stroke-miterlimit", 1) // .attr("d", timeline(timelinedata)); // const text = svg.append("text") // .attr("fill", "white") // .attr("x", x(w/2+margin.left)) // .attr("y", y(1-1.6*((rplanet*earth_radiusm)/(rstar*sun_radiusm))**2)) // .text(`${d3.format(".1f")(crossingtime_hr)} Hours`) // .attr("anchor", "middle"); var star = svg.append("circle") .attr("r", rstarm*m_to_pix) .attr("fill", d3.color(c(rstar))) .attr("cx", innerWidth/2) .attr("cy", h/2); var planet = svg.append("circle") .attr("r", rplanetm*m_to_pix) .attr("cx", margin.left) .attr("cy", h/2-b*rstarm*m_to_pix) .attr("fill", "black") .attr("stroke", "#d83208") .attr("stroke-width", 0.75); // svg.append("rect") // .attr("width", margin.left+1) // .attr("height", "100%") // .attr("fill", "white"); svg.append("rect") .attr("width", margin.right+2*rplanetm*m_to_pix) .attr("height", "66%") .attr("fill", "black") .attr("x", w+margin.left-2*rplanetm*m_to_pix); svg.append("rect") .attr("width", "110%") .attr("height", "34%") .attr("fill", "black") .attr("y", h-2); const path = svg.append("path") .attr("fill", "none") .attr("stroke", "white") .attr("stroke-width", 1.5) .attr("stroke-miterlimit", 1) .attr("d", line(data)); // path.call(reveal).node(); var reveal = svg.append("rect") .attr("width", "110%") .attr("height", "34%") .attr("fill", "black") .attr("y", h-2); // svg.append("rect") // .attr("width", "100%") // .attr("height", margin.bottom) // .attr("fill", "white") // .attr("y", 1.5*h-margin.bottom); const gx = svg.append("g") .call(xAxis, x); const gy = svg.append("g") .call(yAxis, y); const xlabel = svg.append("text") .attr("fill", "white") .attr("x", innerWidth/2) .attr("y", 1.5*h-7) .text(`Time [Hours]`) .attr("text-anchor", "middle"); const ylabel = svg.append("text") .attr("fill", "white") // .attr("x", margin.left+10) // .attr("y", (0.66+0.33/2)*1.5*h) .text(`% Light Observed`) .attr("text-anchor", "middle") .attr("transform", `translate(${margin.left+10},${(0.66+0.33/2)*1.5*h}) rotate(90)`); const trans_prob = svg.append("text") .attr("fill", "white") .attr("x", margin.left) .attr("y", margin.top) .text(`Probability of Observable Transit: ${d3.format(".2%")(transit_probability)}`) .attr("text-anchor", "left"); const trans_dur = svg.append("text") .attr("fill", "white") .attr("x", margin.left) .attr("y", margin.top+20) .text(`Transit Duration: ${d3.format(".0f")(transdur)} Hours`) .attr("text-anchor", "left"); for (let i = 0, n = steps; i < n; ++i) { const t = (i + 1) / n; planet.attr("cx", `${margin.left+ t * w }`); reveal.attr("x", `${margin.left+ t * w }`); if(i==n-1){ svg.append("text") .attr("fill", "white") .attr("x", innerWidth/2) .attr("y", y(1-transdepth)+20) .text(`Transit Depth: ${Math.round(transplace(transdepth)[0],1)} ${transplace(transdepth)[1]}`) .attr("text-anchor", "middle");} yield svg.node(); } // return svg.node(); }33:Tec5,md` #### Consider these questions as you play around with the sliders. First, we suggest changing the planet radius and stellar radius. When is the transit signal largest - that is, what combination of star radius and planet radius will create the biggest decrease in the amount of light we observe? What kinds of planets are easiest to detect? When is it easier to detect small planets? Next, change the period of the planet and the radius of the star. When is the transit probability highest? In other words, when is it most likely that the planet will pass between the star and us? As you change the period of the planet, how does the length of the transit change? That is, how long does the decrease in the brightness of the star last? Finally, set the impact parameter to 1, use a smaller star and a larger planet. How is the shape of the transit signal in the lightcurve different? Can you change the impact parameter to 0.9 and change the size of the planet to get a similar signal? #### Now let's talk about the answers to these questions! The transit signal is largest when planets are bigger, and their star is smaller. So, it's easiest to detect planets like Jupiter. But if we want so find planets similar in size to Earth, we have an advantage when observing smaller stars. You may be wondering how deep the transit must be for us to be able to observe it. Observing from the ground, we can only detect transits that are roughly 0.5 percent or deeper. From space, without the atmosphere, we can observe transits that are as shallow as 0.01 percent - just 100 parts per million! Transits are quite unlikely events, and a given planet's transit probability depends on its distance from the host star and its radius. As you adjust the sliders below, you will see the transit probability range from over 30% for a short period planet orbiting a large star, to less than 0.3% for a long period planet orbiting a small dwarf star. Therefore, we are biased toward detecting shorter-period planets. As you caused the length of the transit to vary, it ranges from just a couple hours to a significant fraction of a day. For astronomers to turn the observation of a transit into precise information about the system, they need to observe the brightness of the star during the entire transit event, and even some time before and after the dip in brightness. If this time is longer than a few hours, the rotation of the Earth means that someone observing on the ground won't be able to keep their telescope pointed at the star for the whole transit. This means that to observe longer-period planets, we must use telescopes based in space. And this is all just to observe a single transit event. In order to confirm a planet and to measure its orbital period, we must observe multiple transits. This means that longer period planets are especially hard to confirm and discover because of the required observation time. Because of this, longer period planets, like those with Earth's orbital period, are less well-characterized than short period planets. Finally, grazing transits - transits with a high impact parameter - don't have the flat-bottomed shape of perfectly-aligned transits. This is also the shape of the transit that occurs when one star passes in front of another - a common type of "false-positive" event that looks similar to a grazing planet transit but does not indicate the presence of a planet. Now that we understand the transit method for detecting planets, let's take a look at the planets discovered using this method. Below is a plot showing all of the known transiting exoplanets. By default, it is showing all of these planets, but you can use the dropdown menu to limit it to planets detected from ground- or space-based observatories. `34:T673,{ const svg = d3.select(DOM.svg(innerWidth, .75*innerWidth)) .style("color",'#fff') .style("font-size", 20); svg.append("rect") .attr("width", "100%") .attr("height", "100%") .attr("fill", "black"); svg.append("g") .selectAll("circle") .data(planets) .join("circle") .attr("cx", d => x2(d.pl_orbper)) .attr("cy", d => y2(d.pl_rade)) .attr("fill", "white") .attr("r", 1) .attr("opacity", 1); svg.append("g") .selectAll("circle") .data(inner_planets) .join("circle") .attr("cx", d => x2(d.per)) .attr("cy", d => y2(d.rad)) .attr("fill", "orange") .attr("r", 3) .attr("opacity", 0.75); svg.append("g") .selectAll("text") .data(inner_planets) .join("text") .attr("x", d => x2(d.per)) .attr("y", d => y2(d.rad)+20) .attr("fill", "orange") .text(d=>d.planet) .attr("opacity", 0.75) .attr("text-anchor", "middle"); const gx = svg.append("g") .call(xAxis2, x2); const gy = svg.append("g") .call(yAxis2, y2); const xlabel = svg.append("text") .attr("fill", "white") .attr("x", innerWidth/2) .attr("y", 0.75*innerWidth-margin.bottom/5) .text(`Orbital Period [Days]`) .attr("text-anchor", "middle"); const ylabel = svg.append("text") .attr("fill", "white") // .attr("x", margin.left+10) // .attr("y", (0.66+0.33/2)*1.5*h) .text(`Planet Radius [Earth radii]`) .attr("text-anchor", "middle") .attr("transform", `translate(${margin.left/5},${0.75*innerWidth/2}) rotate(90)`); return svg.node(); }35:Te5a,md`Looking at all transiting planets, you'll see that we haven't detected planets with the same radius and period as those in our Solar System. But remember that the transit method is best at detecting large planets. Moreover, if you want to detect a planet with the period of Earth, you have to be staring at a star for at least two years - because it is difficult to be confident that a transit is a sign of a planet based on just a single transit. Also, at longer periods, the transit probability is lower. All of this means that this diagram is more "complete" at the top left, and less complete at the bottom right. Planets like those in our Solar System exist, we just haven't detected them yet with this method. When you select only planets discovered using telescopes that are ground-based, you'll see that the types of planets discovered are limited in their radius and period. From the ground, Earth's turbulent atmosphere adds noise to light curve measurements, making it nearly impossible to detect small planets, and the length of the day limits us to only planets with short transits. Most of the planets we've discovered from the ground are "hot Jupiters" - planets with masses similar to Jupiter but with orbital periods less than 10 days! While they appear common, it is only due to the biased nature of the transit method - they are actually pretty rare, [occurring around roughly 1% of stars like the Sun](https://arxiv.org/abs/1205.2273). For more information about hot Jupiters, see [our earlier post about them](https://observablehq.com/@jhhamer/tides-in-hot-jupiter-systems)! Space-based observatories, on the other hand, are not hindered by the day-night cycle or Earth's atmosphere, making them well-suited to observe more precisely and over longer times. This makes them much more sensitive to smaller planets and planets at longer periods. NASA's [TESS](https://www.nasa.gov/tess-transiting-exoplanet-survey-satellite) and [Kepler](https://www.nasa.gov/mission_pages/kepler/overview/index.html) missions are two successful space-based exoplanet surveys that have collectively found several thousand transiting planets. The surveys are quite different in their design: Kepler stared for a long time at one patch of the sky, and TESS is staring at the whole sky for a short time. Kepler was a survey mission whose main goal was to measure planet occurrence rates, or the frequency of planets of a certain size and period. Its large mirror and 4-year observing time allowed us to measure the fraction of Sun-like stars hosting Earth-like planets, which we now know to be roughly 1-10%. TESS, on the other hand, is an ongoing all-sky survey sampling just the nearest stars at moderate precision, typically spending a month on any given star. Its main goal is to find the nearest planets which are best-suited for follow-up measurements of their masses and atmospheric compositions. You should now be an expert in how the transit method works and what kinds of planets are easy to detect with it. However, we've neglected to mention all the intricate details which make this method more difficult than it sounds, such as natural variations in the brightness of stars as well as the other types of signals which can be mistaken for a planet transit. We have also only scratched the surface of what can be done with transits. They are amazingly "information rich" - containing details about the stellar density, the [composition of the planet's atmosphere](https://www.nasa.gov/feature/goddard/2020/nasa-s-webb-will-seek-atmospheres-around-potentially-habitable-exoplanets), and even revealing interactions between multiple planets in a system.` 36:[{"id":"e79e2cdf3b0b7e48637c2653b6248594aa96853b2076499d5ba354de34aa9509f82b42840ea996050d9393fbf732062b2121346df695215608a06e9d1ab218ad","href":"https://static.observableusercontent.com/files/e79e2cdf3b0b7e48637c2653b6248594aa96853b2076499d5ba354de34aa9509f82b42840ea996050d9393fbf732062b2121346df695215608a06e9d1ab218ad","name":"transiting_planets@2.csv","type":"text/csv","lastModified":1609877530265.145,"size":158176},{"id":"fa4a74f1cdf862bdd4123f0ddea81f15dd3ede5486d1179f3024d195ff9dce1f87601ee3acd025c1d2c4568553a5f7e385ee946d7928bcce3cec6cdd726391ff","href":"https://static.observableusercontent.com/files/fa4a74f1cdf862bdd4123f0ddea81f15dd3ede5486d1179f3024d195ff9dce1f87601ee3acd025c1d2c4568553a5f7e385ee946d7928bcce3cec6cdd726391ff","name":"inner_planets1.csv","type":"text/csv","lastModified":1609881946715.988,"size":80}] 2f:{"title":"Detecting Exoplanets with Transits","cells":[{"id":0,"value":"md`# Detecting Exoplanets with Transits`","pinned":false,"hidden":false,"mode":"ojs"},{"id":468,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":24,"value":"viewof rplanet = slider({\n min: 0.34, \n max: 24.45, \n precision: 1, \n value: 1, \n title: \"Planet Radius [Earth radii]\", \n format: v => `${v} Earth radii or ${d3.format(\".2f\")(v/11.5)} Jupiter radii`,\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":20,"value":"viewof rstar = slider({\n min: 0.1, \n max: 2, \n precision: 2, \n value: 1, \n title: \"Stellar Radius [Solar radii]\",\n format: v => `${v} Solar radii`,\n\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":472,"value":"viewof period = slider({\n min: 1, \n max: 100, \n precision: 0, \n value: 20, \n title: \"Orbital Period\", \n format: v => `${v} Days`,\n\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"viewof b = slider({\n min: 0, \n max: 1, \n step: 0.1, \n value: 0, \n title: \"Impact Parameter\", \n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":242,"value":"viewof replay = html`