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ESP Background

STILL IN DRAFT

The Photometric ESP Study

Review of the Burgeoning Study of Extrasolar Worlds, & How Transit, Other Surveys Interrelate

 

First, a little background if you are new to Extrasolar Planets (ESPs); and as a sidebar, you might want to understand the basics of Kepler’s Laws, then two to n-body motions… And check out these animations from Murray & Dermott’s book. Then read Joshi’s paper about some exciting prospects about Habitable Zones (HZ’s) about even tidally locked terrestrial exoplanets…. But let’s next go over the basic means thus far available to finding and characterizing exoplanets, and along the way mention a little of the history of exoplanet detections…

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Current methods of exoplanet detection include direct, astrometry, radial velocity (Doppler spectroscopy), pulsar timing, and (differential) photometry, gravitational lensing, and spectro-chemical analyses. No single method can fully evaluate exoplanets so thoroughly as to rigorously describe an exoplanet without use in two or more complementary methods, and this is notably true of photometry.

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Each means has its strengths, and to date, the Doppler method has led in initial detections (particularly for hot Jupiters), yet cannot fully develop orbital mechanics, masses and the like, for which photometry is most useful. Photometry can also be used to observe gravitational lensing, previously reserved for study of vastly larger objects. In general, it is worthwhile then to understand the basics of each current detection method because they each support overall detection and of interest here, transit photometry.

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Direct Image/Coronal Nulling.

Direct imaging would be rigorous proof of exoplanets, but is extremely difficult to perform. It requires an enormous star/planet flux ratio as well as significant resolution (and seeing) due to intense obfuscation; the ratio is improved by blocking the stellar photosphere to “see” exoplanets (coronography); the resolution is further improved by interferometry (nulling) and adaptive optics.

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Astrometry.

This method relies on precise measurement of position; if edge-on with sufficient MP, stellar motion can be detected (primarily for closer stars). As the planet orbits the star orbits the system’s barycenter. Since MStar>>MP, the barycenter will most likely lie within the star itself, and the stellar path will move in a much smaller circle. Magnitudeof effect is shown by amplitude of the stellar wobble, based on mass ratio q = MP/M*. Actual mass can then be derived (unlike many other methods restricted to Msini (or MP/M*). Note of course that larger orbital periods require longer survey timelines.

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As Radial Velocity, Spectro-Chemical Analysis.

As with astrometry, the radial velocity method measures stellar wobble so the calculations bear resemblance. If the system is about edge-on, orbital movement will blue/red shift the spectra, observed using a precise (usually Echelle) spectrometer measuring absorption lines, hence the term Doppler spectroscopy. The motions are tiny, so this method suits itself to large masses in tight orbits (e.g., for a 1-Mž star, a planet at 1-AU edge-on must be 67MEarth to be detected). Hot Jupiters fit here [and so defying extant planet-formation theory] – and are well-suited to Doppler wobble detection, followed with transit verification; measurements are now achieving <3 m/sec precision on spectrally stable stars. Soon, variations in smooth shifts may be reveal orbital parameters in collusion with photometric analysis. Spectro-chemical analysis is a yet newer, related study that discerns absorption signatures to indicate stable planetary atmospheres in a system (perhaps life-supportive), and so pressing toward planet searches in habitability zones (HZ’s) and discerning composition (again in concert with photometry; Henry, et.al., 2000).

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Pulsar Timing

Stars at 15-30 Mž can devolve via SNe to pulsars (Backer); the latter’s extremely regular radio signature which typically varies<1sec/10Myr, allows small timing anomalies to betray the presence of exoplanets; indeed, MP MEarth detections are possible. Theory has it any planets around pulsars may well have formed post-SNe, prior planets being destroyed. Of the ~650 pulsars, at least 4 planets have been found orbiting them. Timing calculations are relatively intuitive, in that the pulse period can be determined very precisely, and particularly so for millisecond pulsars; any nonlinearities to the least squares fit, or annealing (omitting earth/solar motion rotation) still present, may indicate exoplanets. Of note, Pulsar timing associates least with photometric methods. It did, however, preceed all methods of detection but astrometry.

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Gravitational Lensing

The latest method, lensing occurs when a background source is relativistically lensed by the foreground object. Light-curves from stellar [micro]-lensing are usually smooth, so when a companion of ample brightness moves behind the ‘lens’, a sharp perturbation results (and can be seen photometrically). Lensing conserves surface brightness, so for Einstein ring radius Ro = , (moving), so ro is the lens-free apparent “source-lens” distance in the lens-plane, that that gives u = ro/Ro. Amplification becomes A = and crossing time to = Ro/ν  MHat which gives τ = , (the optical depth) that allows for detections — usually a few-fold — of brief (minutes to weeks) brightening, much and is an offspring of transit photometry. MEarth-sized planets may be detectable this way, but bent light makes statistical estimates of the properties of planets (and often of the star) difficult unless the system is distant (~5kly), itself an impediment to resolution; and some-times lensing is non-cyclical.

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Photometry

Our main focus here, transit searches via photometry have come into their own in the past 5 years. With a system oriented edge-on, the the star can be “annularly eclipsed” by a transiting exoplanet, resulting in a small but measurable ~1% drop in brightness (for gas giants). Large array and HAD CCDs can detect such variation. For rP<<R*, probability of transit PT = sinθ  (R*/a), or based Kepler’s third Law, P2M* = a3; so small “a” improves detection. Transit duration is given by ,  while fractional change in brightness or transit depth is equal to the ratio of the area of the planet to the area of the star, and for a given star and for Kepler’s third law, the SNR relative to that at 1AU, SNR1AU, increases with decreasing a as a-1/2 so that  . The fraction of light blocked is called the depth of transit, or ΔF/Fo = (rP/R*)2; for an earth-like planet this ratio is an (eventually) achievable ~1:10-4 (refer to Schneider, 1999, for details). Critical to this method, transits can only be identified if the orbit nears the LOS, such that that the planet’s orbital pole is within an angle of d*/a measured from the center of the star and perpendicular to the LOS, where d* is the stellar diameter and a is the planet’s orbital radius; this is possible for a total of 4pi d*/2a steradians of pole positions on the celestial sphere. So, the geometric probability for seeing a transit for any random planetary orbit is simply d*/2a (Borucki & Summers, 1984; and Koch, 2003). Notably, transit photometry gives an estimate of planet size whereas most others do not.

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Some Detection History

How exoplanet study came about clarifies photometry’s place and developments therein. Although Greek atomists founded much speculation, the first modern quest for extrasolar planets took place in the late seventeenth century by Huygens. After this, documentation for other searches remains sparse until Peter van de Kamp reviewed photographic plates of Bernard’s Star from 1938-1962, charting a contentious 10.3 arcsecond annual proper motion of an eccentric ~1.6 MJ planet, later refined to two planets in circular orbits with 0.7 MJ and 0.5 MJ. The 1980’s had witnessed pulsar timing studies, and by 1991 Wolszczan and Frail (1995) proclaimed finding exoplanets this way; in short, a few varied studies proclaimed first-ever exoplanet detection on different dates over the last 20 years. Early on (1991),  LaLande 21185 showed odd proper motions that were also considered possible exoplanet perturbations. By October 1995 a systematic radial velocity survey of 142 local dwarfs by Mayor and Queloz revealed detection of the first extrasolar planet orbiting a solar-type star, 51Peg (which, along with pulsar timing surveys, had laid foundation for detection of exoplanets by transit detection).

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Note that, until very recently, photometric detections were inadequate for intial detects in and of themselves, but with proper targeting in the survey, candidates found by timing or spectral methods could prove immensely useful in the (1) characterization of masses and orbital mechanics, and (2) development of more accurate transit detection methods to perhaps someday allow initial photometric detections. Photometry indeed is a step toward coronographic and then direct observation of planets (and most intriguingly terrestrial ones in HZs).Meanwhile by 1996, Marcy and Butler (1996) surveyed 120 stars to find 5 more candidates (3 similar to 51Peg) as the Doppler method gained dominance in initial detections [of generally hot Jupiters], including Tau Bootes, which was first suspected to have a planet about a binary system. In 1997 Doppler-detected Upsilon Andromedae gained attention as a sun-like star with a Jupiter-like planet and has been in several transit target lists for consideration; then 70 Virginis sparked an ongoing debate whether its companion was a planet or brown dwarf. By Summer 1998 eight planets were known, and by year’s end that number doubled (owed to growing time and search bases).

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As of April 1999 twenty planets were detected, mostly spectrally, including the first confirmed multiple system (υAnd), creating a basis for a viable multi-planet model (see UC Berkeley). In November 1999 the first photometric transit (across HD 209458) was cleanly observed, allowing for calculation of mp, rp and ρp, adding to the spectroscopic data; this also precipitated a widely publicized small-telescope venture to photometrically capture transits (Laughlin, Castellano, 2002, Hudgins at UWS, 2001). By Spring 2000 several candidates were spectrally discovered <MSaturn and by August nine new candidates were announced at the IAU, including 2 more known multiple systems: HD 83443 (with 2 subsaturns) and HD 168443, a resonant system. These produced a growing candidate list for potential photometric observation and spurned collaboration between transit and Doppler teams. In January 2001 another 2-planet resonant system was discovered, as were 11 new planetary candidates (including 2 new multiple systems) by the
Geneva team.
Then that year, NASA’s Kepler mission to detect ~MEarth planet transits was selected for funding, which is expected to be an enormous leap in capability for large-scale transit detection surveys.

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Meanwhile in January 2002, Fischer et.al. reported that by Doppler, a second, more distant companion to the Butler/Marcy 1996 UMa47 was discovered; this planet is in a 7 year (rare ~circular) orbit; unfortunately for the author, recent scrutiny reveals it turns out to be a less-than suitable photometric candidate (Henry, 2003, 1999). In January 2003 a sub-saturnian planet was discovered around HD 3651 by Fischer et al, (now called OGLE-TR-56b) and became the first transit-discovered Exoplanet; days later the OGLE lensing experiment produced 62 more likely transits, of the microlensing variety. In February, Horne described new wide-angle CCD/light curve methods to improve photometric “hot Jupiter” detection ten-fold. By March a comet-like tail (i.e., atmosphere) around HD 209458b was postulated; then Gliese 876, the least massive star known to have planets, was found close by at 15Ly and has become the nearest exoplanet (and is being scrutinized for photometric work), while another, 55 Cancri, now has the longest period (14-years). The latest discoveries can be found in Espenak’s a recent capitulation (2003), and baselines a de facto “targeted survey” of exoplanets.

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By 2003 there were a reported 92 planetary systems, 106 planets, and 12 multiple systems, from 0.12 MJ for HD 49674, up to 13MJ; subsequent updates are found in the “French Encyclopedia” (Schneider, 2003; also see, Willman, 2003), while there are maps of the finds to date, at “Exoplanets and their stars” (GED, 2003).   Red dwarfs are becoming interesting targets for harboring smaller-massed planets, and remains the target of choice for the GEMSS study. Recently, Rivera et.al discovered a third planet, likely of terrestrial composition and a mere 7.5 earth masses in size, and this, along with postulations by Laughlin et.al, spurred a large photometric campaign to seek an understanding of the GL 876 system. At the Jovian end of the search interests, N2K studies led by Fischer et.al have targeted metal-rich stars. Other systems are being discovered, with the number surpassing 200 in late 2006. Exoplanet history can be further examined using Bell’s chronology (2001) and Marcy & Butler’s Encarta (date unk), and the latest information being gleaned from online sources such as the exoplanet encyclopedia and exoplanet.org.

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Results, Postulations

Numerous facts are reviewed in the Exoplanet Encyclopedia. There have been many extrasolar validations; of the various techniques, radial velocity seems most successful at initial detection, but that may change as new photometric techniques are employed. Also, there have been proclamation disputes, which infer some have been quick to publish, leading to errors and then discoveries defended. Using this review of the state of transit (and other) methods, pondering the ideal photometric target for effective survey.

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David Blank’s Discussion on Surveys

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Types:  

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General-purpose survey

means the survey will not exclude a specific class of objects. For example in the Super Cosmos Sky Survey (Hambly et al. 2001) , the photographic plates will have images of Stars, galaxies, asteroids,  ECT.

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Targeted Survey

 means that one is studying a specific class of object.  The extrasolar planet searches relying  on  radial velocity are targeted searches. That is one specific class of  known objects (here F to M class stars) are  studied spectroscopically  to see if any have orbiting  planets.

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Blind Survey

  One points the telescope not at a specific class of objects, but at a specific part of the sky. For example, the  Hubble Deep Field Surveys were blind. The Hubble Space Telescope (HST) was pointed at two specific locations in the sky, which had no known objects. The integration times were about a week which allowed the discovery of fainter objects. The Deep Field Surveys were also pencil beam since the HST  covered an area of sky only about 15 arcminutes across.All Sky Surveys Opposite of pencil beam  surveys since the area covered is either the whole sky  or the whole sky visible from some locations. Studying the properties of a sample of objects is a  statistical exercise. Typical statistical questions include desiring to know the range and  average  luminosities of some class of astronomical  objects. Therefore one wants a sample that is representative of the population as a whole. Getting answers  from a biased sample will be misleading. However getting a reasonably bias free sample is usually hard.

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Malmquist Bias

Any survey that is magnitude limited will be over-represented  by the the more luminous objects of that class.  Nearby, one will observe both the dim and bright members. At greater distances, only the brighter members  can be observed because the less luminous members are too dim to be seen.  Thus the overall sample will consist of nearby objects that could be intrinsically luminous or intrinsically faint and more distant, intrinsically luminous members. The more  Malmquist biased the sample, the more the sample will be over represented by the brighter members. In extragalactic astronomy there is the further complication that  the range in values of some property  in nearby objects will not be the same for more distant objects. This is because the population as a whole may evolve with time.

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For example, more distant quasars seem to be more luminous on the whole than nearby quasars. The space density of quasars was also much higher in the past than at present. Separating evolution from bias is not easy and for quasars the first study that managed to get the correct answer was by Schmidt (1968) using a statistical test  he devised.Using a distance-limited sample is one way to correct for Malmquist Bias. Here one selects a distance in which all members of  the sample can be seen. Basically this means the furthest distance that the dimmest  member could still be seen.

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One then draws up a new sample which consists only  of those objects which are no further out then the maximum possible distance that the dimmest member can be seen.As an example, you have a sample of  one type of  galaxy and find that the most intrinsically dimmest galaxy would be still recognised as a galaxy if it was no further than say 100 Megaparsecs.  The next step then is to make a second, smaller sample consisting  only of galaxies which are nearer than 100 Megaparsecs. The second, smaller sample will be a more representative sample of  that galaxy population.

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Hopefully the second sample will still be large enough to be statistically significant. That is working out the average luminosity from a set of five objects is not likely to be statistically significant. Keep in mind that there may still be galaxies too faint to be seen unless they  were VERY close. For example consider  that the local group of galaxies consists of three spiral galaxies and fifty  much fainter dwarf galaxies. Yet the sample in  galaxy catalogs such as  the Shapley-Ames is dominated by the much brighter  spiral and elliptical galaxies.

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NON DETECTIONS

Working out the range in some property of a population is hard to do when one can’t detect a significant fraction of that population. This is where “survival analysis” statistics becomes useful. See the on-line  article by Eric Feigelson which is one of  the required readings.

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Measurement Errors

Getting a representative sample is worse when one includes measurement  errors. For example, a bright galaxy may still be recognised as a galaxy even if the CCD image or photographic plate was noisy. A noisy CCD image or photographic plate is much more likely to hide a fainter galaxy. One is more likely to miss fainter members in bad data than brighter members.

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Selection effects by Waveband

This refers to a biased sample that may result from selecting your sample according to some waveband. This is best illustrated by giving some examples. The first quasars were discovered in 1963 when Maartin Schmidt found that some of the objects observed by radio telescopes were the most distant objects then known. For the next two years more quasars  were found by photographing and getting spectra of  radio sources. Thus it was mistakenly concluded by some  that most, if not all quasars were luminous at radio frequencies or “radio loud”. 

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Alan Sandage found in 1965 that there was a much larger  population of quasars that appeared blue in colour  and were “radio quiet”.  The latter meaning that at the time radio telescopes was not sufficiently sensitive to receive their weak radio signals.  From  1965 to 1973  more  distant quasars were discovered, but it would take a another decade  before  more distant quasars were found. The reason was that the searches for distant quasars  were based on colour. They assumed all quasars would be bluish in colour. Nearby quasars are bluish because more of their radiation are emitted in the blue to ultraviolet  than at longer optical wavelengths. 

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At high redshifts this “ blue bump” is redshifted into the infrared region and the quasars lose their blue colour.The story has not yet played itself out; there are those that claim that there is a population of dust enshrouded quasars. The dust would preferentially block or scatter  blue light giving a reddish appearance to even nearby members.

 

 

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