NASA's first mission capable of NASA's first mission capable of finding Earth-size and smaller finding Earth-size and smaller

planets around other starsplanets around other stars

Kepler OverviewKepler Overview

• The question of is there other worlds has been answered.

• There is now clear evidence for substantial numbers of three types of exoplanets; – gas giants– hot-super-Earths in short period orbits– ice giants

• The challenge now is to find terrestrial planets – (i.e., those one half to twice the size of the Earth)– especially those in the habitable zone of their stars

where liquid water might exist on the surface of the planet.

Who was Kepler? Who was Kepler?

• Johannes Kepler Dec. 27, 1571 – Nov. 15, 1630 (59 years) was a German mathematician, astronomer and astrologer, and key figure in the 17th century scientific revolution.

• He is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy.

• Kepler’s laws also provided one of the foundations for Isaac Newton's theory of universal gravitation.

Johannes KeplerJohannes Kepler• During his career, Kepler was a

mathematics teacher at a seminary school in Graz, Austria, an assistant to astronomer Tycho Brahe, the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II, a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein.

• He also did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope).

Johannes KeplerJohannes Kepler• The Keplerian Telescope, invented

in 1611, is an improvement on Galileo's design.

• It uses a convex lens as the eyepiece instead of Galileo's concave one.

• The advantage of this arrangement is the rays of light emerging from the eyepiece are converging.

• This allows for a much wider field of view and greater eye relief but the image for the viewer is inverted.

• Considerably higher magnifications can be reached with this design but to overcome aberrations the simple objective lens needs to have a very high f-ratio.

Galileo's design

Kepler's design

Keplerian TelescopeKeplerian Telescope

• (Johannes Hevelius built Keplerian telescope with a 45 m (150 ft) focal length and even longer tubeless "aerial telescopes" were constructed). The design also allows for use of a micrometer at the focal plane (used to determining the angular size and/or distance between objects observed).

The Kepler MissionThe Kepler Mission• The Kepler Mission, NASA Discovery mission #10, is

specifically designed to survey our region of the Milky Way galaxy to discover hundreds of Earth-size and smaller planets in or near the habitable zone and determine the fraction of the hundreds of billions of stars in our galaxy that might have such planets

The Kepler MissionThe Kepler Mission

• In astronomy, the habitable zone (HZ) is the region in a star-centered orbit where an Earth-like planet can maintain liquid water on its surface and Earth-like life.

• The habitable zone is the intersection of two regions that must both be favorable to life; one within a planetary system, and the other within a galaxy.

The Transit Method of Detecting The Transit Method of Detecting Extrasolar PlanetsExtrasolar Planets

• When a planet passes in front of a star as viewed from Earth, the event is called a “transit”. On Earth, we can observe an occasional Venus or Mercury transit.

• These events are seen as a small black dot creeping across the Sun—Venus or Mercury blocks sunlight as the planet moves between the Sun and us.

• Kepler finds planets by looking for tiny dips in the brightness of a star when a planet crosses in front of it—we say the planet transits the star.

The Transit Method of Detecting The Transit Method of Detecting Extrasolar PlanetsExtrasolar Planets

• Once detected, the planet's orbital size can be calculated from the period (how long it takes the planet to orbit once around the star) and the mass of the star using Kepler's Third Law of planetary motion.

• The size of the planet is found from the depth of the transit (how much the brightness of the star drops) and the size of the star. From the orbital size and the temperature of the star, the planet's characteristic temperature can be calculated.

• From this the question of whether or not the planet is habitable (not necessarily inhabited) can be answered.

Kepler's Third Law Kepler's Third Law of planetary motionof planetary motion

• Johannes Kepler went to work for Tycho Brahe near the end of Tycho's life. When Tycho died, Kepler used Tycho's data to deduce three laws of planetary motion.

• Tycho's data were far more accurate than any previously collected data on planetary positions which is why neither Ptolemy's nor Copernicus's models of the cosmos worked.

• Tycho’s accuracy enable Kepler to produce mathamatical models that worked.

Kepler's Third Law Kepler's Third Law of planetary motionof planetary motion

Kepler's third law, which is often called the harmonic law, is a mathematical relationship between the time it takes the planet to orbit the Sun and the distance between the planet and the Sun. The time it takes for a planet to orbit the Sun is its orbital period, which is often simply called its period. For the average distance between the planet and the Sun, Kepler used what we call the semi-major axis of the ellipse. The semi-major axis is half the major axis, which is the longest distance across the ellipse. Think of it as the longest radius of the ellipse.

Illustration of Kepler's three laws with two planetary orbits. (1) The orbits are ellipses, with focal points ƒ1 and ƒ2 for the first planet and ƒ1 and ƒ3 for the second planet. The Sun is placed in focal point ƒ1. (2) The two shaded sectors A1 and A2 have the same surface area and the time for planet 1 to cover segment A1 is equal to the time to cover segment A2. (3) The total orbit times for planet 1 and planet 2 have a ratio a1

3/2 : a23/2.

Kepler's Third Law Kepler's Third Law of planetary motionof planetary motion

• Kepler's third law states that the square of the period, P, is proportional to the cube of the semi-major axis, a. In equation form Kepler expressed the third law as: P^2=ka^3. k is the proportionality constant.

• To Kepler it was just a number that he determined from the data. • Kepler did not know why this law worked. He found it by playing

with the numbers.

Kepler's Third Law of planetary motionKepler's Third Law of planetary motionNewton's Form of Kepler's Third Law• There were two problems with this relation.

– First, Kepler did not know how it worked, he just knew it did.– Second, the relation does not work for objects which are not orbiting the Sun,

for example, the Moon orbiting the Earth.• Isaac Newton solved both these problems with his Theory of Gravity,

and discovered that the masses of the orbiting bodies also play a part. • Newton developed a more general form of what was called Kepler's

Third Law that could apply to any two objects orbiting a common center of mass. This is called Newton's Version of Kepler's Third Law:

M1 + M2 = A3 / P2

• Special units must be used to make this equation work. If the data are not given in the proper units, they must be converted. – The masses must be measured in solar masses, where one solar mass is 1.99 X

1033 grams, or 1.99 X 1030 kilograms. – The semi-major axis must be measured in Astronomical Units, where 1 AU is

149,600,000 kilometers, or 93,000,000 miles. – The orbital period must be measured in years, where 1 year is 365.25 days.

Solar Mass 1 + Solar Mass 2 = Astronomical Units 3 / Orbit Years 2

Significance of Kepler's Third Lawor Why aren’t you talking about the mission?• Kepler's third law is extremely important to astronomers. Because it

involves the mass. It allows astronomers to find the mass of any astronomical object with something orbiting it.

• Astronomers find the masses of all astronomical objects by applying Kepler's third law to orbits. They measure the mass of the Sun by studying the orbits of the planets. They measure the mass of the planets by studying the orbits of their moons.

• Moons have nothing orbiting them, so to find the mass of the moons astronomers need to send a probe to be affected by their gravity. Astronomers find the masses of stars by studying the orbits of stars in binary systems. They can not measure the masses of stars that are not in binary systems. In all these cases astronomers use Kepler's third law.

• Kepler's third law is the only way to measure the masses of astronomical objects

• When you read of the mass of a star not in a orbital relationship it was done by modeling. A rough way to estimate mass based on other similar stars.

Back to the MissionBack to the MissionKepler’s instrumentsKepler’s instruments

• The Kepler instrument is a specially designed 0.95-meter diameter telescope called a photometer or light meter.

• It has a very large field of view for an astronomical telescope — 105 square degrees, which is comparable to the area of your hand held at arm's length.

• It needs that large a field in order to observe the necessary large number of stars.

• It stares at the same star field for the entire mission and continuously and simultaneously monitors the brightnesses of more than 100,000 stars for the life of the mission—3.5 or more years.

The Kepler photometerThe Kepler photometer• The photometer is composed of

just one "instrument," which is, an array of 42 CCDs (charge coupled devices).

• Each 50x25 mm CCD has 2200x1024 pixels. The CCDs are read out every three seconds to prevent saturation.

• Only the information from the CCD pixels where there are stars brighter than about 14 magnitude is recorded. (The CCDs are not used to take pictures. The images are intentionally defocused to 10 arc seconds to improve the photometric precision.)

• The data are integrated for 30 minutes. Another words a 30 minute exposure.

Kepler Focal Plane ArrayThe focal plane consists of an array of 42 charge coupled devices (CCDs). Each CCD is 2.8 by 3.0 cm with 1024 by 1100 pixels. The entire focal plane contains 95 mega pixels. Credit: NASA and Ball Aerospace

The Kepler photometerThe Kepler photometer

• The instrument has the sensitivity to detect an Earth-size transit of an mv=12 G2V (solar-like) star at 4 sigma in 6.5 hours of integration. The instrument has a spectral bandpass from 400 nm to 850 nm.

• Data from the individual pixels that make up each star of the 100,000 main-sequence stars brighter than mv=14 are recorded continuously and simultaneously.

• The data are stored on the spacecraft and transmitted to the ground about once a week.

KeplerKepler

• The continuous viewing needed for a high detection efficiency for planetary transits requires that the field-of-view (FOV) of the photometer be out of the ecliptic plane so as not to be blocked periodically by the Sun or the Moon. A star field near the galactic plane that meets these viewing constraints and has a sufficiently high star density has been selected.

• An Earth-trailing heliocentric orbit with a period of 372.5 days provides the optimum approach to meeting of the combined Sun-Earth-Moon avoidance criteria within the Boeing launch vehicle capability. In this orbit the spacecraft slowly drifts away from the Earth and is at a distance of 0.5 AU (worst case) at the end of four years. Telecommunications and navigation for the mission are provided by NASA's Deep Space Network (DSN).

Mission LifetimeMission Lifetime• The mission must last long enough to detect and confirm

the periodic nature of the transits of planets in or near the HZ. – A four year mission is proposed which enables a four-transit

detection of all orbits up to one year in length and a three-transit detection of periods up to 1.33 years.

– This mission duration also provides three-transit detections for 50% of 1.6 year orbits and 10% of 1.9 year orbits.

• We have also proposed a two year mission extension which greatly enhances the ability to detect planets smaller than Earth and reliably detect Earth-size planets in orbits corresponding to that of Mars (2 year periods).

Magnified measurements of HAT P7b showing transits and occultations

Kepler PhotometryKepler Photometry

• The Kepler Mission uses spacebased photometry to detect planetary transits. It offers far greater sensitivity for finding terrestrial and smaller planets than ground-based techniques.

• By providing a statistically robust census of the sizes and orbital periods of terrestrial and smaller planets orbiting a wide variety of stellar types, results from this mission will allow us to place our Solar System within the continuum of planetary systems in the Galaxy and develop theories based on empirical data.

Where to Look For Habitable Planets

• The numerical modeling of Wetherill (1991) shows that the accumulation of planetesimals during molecular cloud collapse can be expected to produce, on the average, four inner planets.

• Two of these are approximately Earth-size and two are smaller. These results indicate that the position of the terrestrial planets can be anywhere from the position of Mercury's orbit to that of Mars'.

• Therefore, a search for terrestrial planets should include a wide range of orbits.

Where to Look For Habitable Planets

• The Terrestrial Accretion Zone and The Habitable Zone for Various Stellar Types.

• The continuously habitable zone is bounded by the range of distances from a star for which liquid water would exist and by the range of stellar spectral types for which planets had enough time to form and complex life had enough time to evolve (less massive than F) and for which stellar flares and atmospheric condensation due to tidal locking do not occur (more massive than M).

• The figure shows the continuously habitable zone as calculated by Kasting, Whitmire, and Reynolds, (1993) for main-sequence stars as a function of spectral type.

• The Kepler Mission performs an unbiased search for all orbital periods less than two years, that is, out to a Martian orbit, and for all spectral types of stars. It is not affected by solar or extrasolar zodiacal background and can detect planets within binary star systems.

Planet Size• Many factors determine if transits caused by a particular

planet size are detectable. These include the:– Size of the star – Brightness of the star, photometer aperture and optical efficiency

(photon shot noise) – Stellar variability (inherent noise of the source) – Instrument differential precision (instrument noise) – Number of transits (mission life divided by the orbital period) – Detection efficiency (SNR and false alarm rate) and – Duration of the transit (central or grazing)

• The baseline sensitivity of the Kepler Mission photometer is designed to detect Earth-size, 1.0 Re, planets in 1 AU orbits around mv=12 solar-like stars in 6.5 hours (grazing transit) with a signal to noise ratio (SNR) of >8. These values can be scaled to define the range of detection possibilities. The result of modeling all of this for the Kepler Mission is shown below

Planet Size• The figure below presents the minimum detectable planet size for:

– A range of apparent stellar brightnesses (mv=9, 12 and 14); – A range of stellar masses and – A range of planetary orbital sizes (semi-major axis).

• Planets of a given size are detectable to the left of each contour. Detections are based on a total (Signal to Noise Ratio)SNR >8 sigma and >3 transits in 4 years. The detectable planet sizes are shown for a near-central transit. Each plot is for a given stellar brightness. Planet radius and area are relative to the Earth.

• Note that although the mission is optimized to detect Earth-size planets in the habitable zone of solar-like stars, planets even as small as Mercury are detectable in the habitable zone of K and M stars. For shorter period orbits, more transits are observed for a given mission lifetime, thereby enabling the detection of planets smaller than Earth or enabling detection of Earth-size planets around stars larger than the Sun.

Target Field of ViewSince transits only last a fraction of a day, all the stars must be monitored continuously, that is, their brightnesses must be measured at least once every few hours. (We must sum the light accumulated in this time to obtain a statistically significant measurement). The ability to continuously view the stars being monitored dictates that the field of view (FOV) must never be blocked at any time during the year. Therefore, to avoid the Sun the FOV must be out of the ecliptic plane.

The payload envelope of the launch vehicle limits the sunshade size and hence the target field to be >55º from the ecliptic plane. The secondary requirement is that the FOV have the largest possible number of stars. This leads to the selection of a region along the Cygnus arm of our Galaxy as shown.To meet the goals of making statistically meaningful conclusions, the mission design should be such at least 45 terrestrial planets (R<1.3 Re) are expected, requiring many thousands of stars to be observed simultaneously in one FOV. (Continuously re-orienting the photometer to view fewer bright stars in many different fields-of-view (FOV) increases the mission complexity and cost and is less efficient than using a single FOV.)

A region of the extended solar neighborhood in the Cygnus region along the Orion arm centered on galactic coordinates (76.32º,+13.5º) or RA=19h 22m 40s, Dec=+44º 30' 00' has been chosen. The star field is far enough from the ecliptic plane so as not to be obscured by the Sun at any time of the year. This field also virtually eliminates any confusion resulting from occultations by asteroids and Kuiper-belt objects. Comet-size objects in the Oort cloud subtend too small an angular size and move too rapidly to be a problem.

Stellar Classification

• The Stellar Classification Program is led by David Latham at the Smithsonian Astrophysical Observatory.

• It's purpose is to characterize stars in the Kepler field of view and identify the best targets for Kepler photometric monitoring.

Number of Stars• Planets and Binary Stars• About half of the stellar systems monitored are

expected to be multiple systems. • Doppler spectroscopy observations have already

shown the presence of planets orbiting individual stars in multiple star systems (Cochran et al., 1997).

• We expect to be able to determine the range of binary separations for which planetary orbits do exist.

• The average frequency of planets around binary stars could be similar to that around single stars.

Number of Stars

• Of the 223,000 stars in the FOV with mv<14, an estimated 61% or 136,000 are dwarfs.

• In the first year of operation about 25% of these are identified and excluded as being too young, rotating too fast, or too variable to be useful.

• What was left is the resulting in 100,000 usable target stars.

Number of Stars

Based on the model of stellar distribution and dependence of detectable planet size on stellar type and brightness, the number and type of stars monitored as a function of planet size is shown in the figure.

Number of Stars• The solid lines show the number of dwarf stars of each spectral type for which a planet of a given radius can be detected at >8 sigma. The conservative numbers are based on 4 near-grazing transits with a 1 yr period and stars with mv<14.

• The symbols along each solid line indicate the approximate apparent magnitude of the stars contributing to the integral number of stars.

• The dashed lines show a significant increase in the number of stars (a factor of 2 at R=1.0 Re) when assuming 4 near-central transits with a 1-yr period. An even greater increase is realized for 8 near-grazing transits with a 0.5-yr period.

Earth-size• We define Earth-size to be between 0.5 and 2.0 Earth

masses (0.8 Re to 1.3 Re) and large terrestrial planets to be between 2 to 10 Earth masses (1.3 Re to 2.2 Re). Planets less than about 0.5 Me that reside in or near the HZ are likely to lose their life-supporting atmospheres because of their low gravity and lack of plate tectonics.

• Planets of more than about 10 Me (R>2.2 Re) are considered to be giant cores like Uranus and Neptune. They are likely to attract a hydrogen-helium atmosphere and become gas giants like Jupiter and Saturn.

Follow-up Observing

For all candidate transit cases, complementary follow-up observations are made to confirm that the transits are due to planets and to learn more about the characteristics of the parent stars and planetary systems.

All known 400+ exoplanets as of Dec 2009 plus the 5 new planets found with Kepler. The green band represents the parameters for habitable planets. Too close to the Sun and water vaporizes. Too far from the Sun and water freezes. Too low of a mass, and the planet does not have enough surface gravity to hold onto a life sustaining atmosphere. Too large of a mass and the planet has enough gravity to hold onto the most abundant element in the universe, hydrogen, and become

a gas-giant planet.

Two common types of astrophysical phenomena that can masquerade as a planetary transit are grazing eclipsing binaries (left), where a pair of stars orbit each other, and background eclipsing binaries (right), where a distant binary star system is aligned very close to the star of interest. These require significant amount of ground-based observations to eliminate using radial velocity techniques

Kepler releases first 43 days of data, and is performing well 07.13.2010

• The project team recently completed another roll of the Kepler spacecraft and science data download. Accomplished over June 22-23, 2010, the operation was a complete success, as the roll placed Kepler in its summer attitude. With this download and quarterly roll, Kepler completed its fifth quarter of science data collection and has begun its sixth quarter of science data collection.

• The Kepler flight segment continues to operate within nominal parameters. There have been no unplanned events since the recovery of the spacecraft from a Safe mode malfunction in February 2010. A flight software update, completed on the spacecraft in April 2010, continues to operate as designed.

• Kepler mission data collected over the first 43 days of operations were made available at the Multi-Mission Archive at STScI (MAST: http://archive.stsci.edu) on June 15, 2010. Metrics indicate many downloads of the data have been made by multiple users since the data were made public.

• In the first 43 days of data-taking, Kepler found about 175 transit candidates.

• Fifty of these were scrutinized to find the five confirmed planets that were announced.

• Some 125 candidates remain, and that's just from the first six weeks of data.

• Tidal waves of subsequent data are already in hand.

• Lots more planets are coming — probably hundreds by the time the mission is scheduled to end three years from now.

• The host stars in the five fully confirmed Kepler exoplanets are somewhat larger and brighter than our Sun, with 1.4 to 2.0 times the Sun’s diameter.

• This is because these stars were chosen for early followups based on showing many narrow spectral lines, good for radial-velocity measurements.

• Such large stars are not very common; this bodes well for greater numbers of planets to be found around smaller dwarf stars, which are much more abundant.

• Any such planet has only a 1-in-200 chance of being in an orbit that's oriented just right to cross a Sun-sized host star as seen from our viewpoint. That's one reason why Kepler is watching so many stars.

Another is statistics. Kepler is intended not just to identify a few individual exo-Earths. It was designed to watch enough stars to give a firm statistical reading on the abundance — or rarity — of terrestrial-size planets generally, throughout the galaxy and the universe.

• Kepler is routinely achieving 1-part-in-40,000 brightness precision (0.000025 magnitude) for measurements of 12th-magnitude stars. That is good enough to find transits of worlds as small as Earth, as planned.

variable stars

• Thousands of new variable stars are turning up, and Kepler’s extremely high-precision, near-continuous light curves offer rich material for new study. For instance, a third of the stars most similar to our Sun turn out to have tiny, short-term variabilities greater than the Sun’s. But not by much. And in time, we may be able to see the equivalent of our own star's sunspot cycle.

• A star’s placement on the detector’s array of pixels yields its position to better than a thousandth of a pixel-width, or 4 milliarcseconds.

• This is that way that many eclipsing binary stars are being weeded out, by their proper-motion wobbles.S

• Such precision will also provide the best-yet parallaxes (distances) for most of the faint stars in Kepler’s catalog. Good distances are needed to help to characterize any planets the stars are seen to have.

• Slight, periodic variations can also reveal a star’s rotation rate, due to temporary starspots rotating in and out of view. In this way Kepler scientists expect to better calibrate the relation between a star’s rotation rate and its age and mass, the most widely useful way to assign ages to individual stars everywhere.

Good News

• One important piece of Kepler news, is the finding that Sun-like stars are generally quiescent, showing only very small brightness variations.

• That's good news for astrobiology, and it's also good news for us.

• It tells us that solar-type stars spend most of their time in quiescent states, so we ourselves are in a good, safe place, not just enjoying a lucky quiet time next to a star that may act up.