הפקולטה למדעים מדויקים RAYMOND AND BEVERLY SACKLER "ע ש ריימונד ובברלי סאקלר FACULTY OF EXACT SCIENCES בית הספר לפיסיקה ול אסטרונומיה SCHOOL OF PHYSICS & ASTRONOMY

SEARCH FOR PLANETS IN ECLIPSING BINARY SYSTEMS

Submitted towards the degree "Doctor of Philosophy"

by

Aviv Ofir

The research was carried out under the supervision of Prof. Artie Hatzes (TLS, Germany) and Prof. Sara Beck

Submitted to the Senate of Tel Aviv University December 2010

This is my quest, to follow the star

No matter how hopeless, no matter how far

To fight for the right, without question or pause

To be willing to march into hell for a heavenly cause

And I know, if I'll only be true to the glorious quest

That my heart lies peaceful and calm

When I'm laid to my rest

And the world will be better for this

That one man scorned and covered with scars

Still strove with his last dance of courage

To reach the unreachable star

Extract from: "The Impossible Dream" by Mitch Leigh and Joe Darion With special credit to performance by Carter USM

− I − − II − Abstract

Bound binary stars are one of the most common environments in the Galaxy. Studying planet formation and evolution without including the formation and evolution of planets in binary star systems is surely incomplete. Planets are already known to readily form in wide binaries despite serious observational biases against such detections: at least 17% of the known exoplanets are known to revolve around one component of a wide binary. On the other hand, planet formation in tight binaries remain poorly constrained. This research program aimed to fill-in observational data on these types of systems.

Planetary transits surveys, both ground- and space- based, collect huge amounts of photometric data that also include many eclipsing binaries (EBs). Since planets in EB systems are expected to be (at least initially) co-planar with the host binary, I used the alignment of EBs with the line of sight (by their pre-selection as eclipsing) to enhance the geometrical probability of planets in the system to transit any of the binary components.

I used photometric data mainly from the CoRoT space mission. I started from the raw photometry and de-trended it to remove all sources of systematic noise. I elaborate on a special technique developed during this work called "SARS" that allowed me to clean the data enough to detect many transit-like signals in the data that were not previously detected. For variable stars, like EBs, I show how to de-trend the data while not removing the intrinsic variability. I also describe a novel searching algorithm developed during this work called "CB-BLS" to look for planets in the EB systems using the refined data. All this allows me to search for planets in almost every possible configuration: transiting planets around either or both components, non-transiting planets around both components, transiting planets in background objects, and – as a (very successful) by-product – improved searches for "regular" transiting planets around single stars.

In this thesis I present the first significant results of the research program, including the detection of four transiting planets, a transiting brown dwarf, and the detection of background and eclipse timing signals. Those are just preliminary results: this research program will extend beyond the scope of this thesis and into my future postdoc, so that by the end of the program I will be able to empirically compare planet formation rate in close binaries to that of planets around single stars, thus providing a significant constraint to theories of star and planet formation, one that does not exist today.

− III − Acknowledgements

Some parts of these studies were not easy on me, not at all. For this reason completing this PhD thesis gives me great satisfaction. However, I myself could not rise to this challenge on my own, and I thank the following for making this possible:

First and foremost – my dearest, my wife Michaela : in great storms you were my anchor, in great darkness you were my light. When I wanted you gave me space, and when I needed you gave me a hug. This could not have possibly succeeded without you. "Thank you" can't quite say it, so I plan to spend the rest of my life with you to try to find the way that does.

I wish to thank my advisors - prof. Artie Hatzes and prof. Sara Beck : Artie : thank you for your warm and positive attitude, for showing uncommon trust and openness, for your time and efforts. Thank you for allowing me to work with you. Sara : thank you for making possible for me – yet again – to explore the science question I find the most intriguing, even if means confusing bureaucracy and venturing out of the TAU faculty.

I wish to thank my main collaborators during this thesis - the CoRoT Exoplanets Science Team in general, and the CoRoT detection team in particular. Special thanks are due to Eike Gunther , Pierre Barge , Hans Deeg and Claud Lacy who played pivotal roles in my entry into these wonderfully collaborative teams.

Last, but certainly not least – my family: quite literally, I really couldn't reach this point in my life without you. Thank you Mom for your love, time and encouragement. Thank you Dad and Rivka for your support, knowledge and faith in me.

I hope that making you all proud is the best way of saying thank you, from the bottom of my heart.

− IV − Table of Contents

ABSTRACT ...... III ACKNOWLEDGEMENTS ...... IV TABLE OF CONTENTS ...... V

PART 1: INTRODUCTION TO PUBLISHED PAPERS ...... 1

1. EXOPLANETS AROUND SINGLE STARS ...... 2 1.1. PRIMER ON EXOPLANETS THEORY ...... 2 1.2. INPUT DATA ...... 6 1.3. DETECTION TECHNIQUES ...... 7 1.3.1. RADIAL VELOCITY (RV)...... 7 1.3.2. TRANSITS ...... 8 1.3.3. MICROLENSING ...... 11 1.3.4. DIRECT IMAGING ...... 13 1.3.5. TIMING VARIATIONS ...... 17 1.3.6. ASTROMETRY ...... 17 1.4. CHARACTERIZATION OF EXOPLANETS ...... 19 1.4.1. HIGH -PRECISION PHOTOMETRY ...... 20 1.4.2. SPECTRA OF EXOPLANETS ...... 25 1.4.3. THE ROSSITER -MCLAUGHLIN (RM) EFFECT ...... 26 2. EXOPLANETS AND BINARY STARS ...... 27 2.1. PRELUDE ...... 27 2.1.1 . DEFINITIONS AND BIASES ...... 27 2.1.2. MOTIVATION : WHAT CAN BE LEARNED FROM PLANETS IN BINARIES ? ...... 28 2.2 . PREVIOUS STUDIES ...... 30 2.2.1 . THEORETICAL STUDIES ...... 30 2.2.2 . OBSERVATIONAL STUDIES ...... 31 2.3 . LOOKING FOR PLANETS IN BINARIES IN THIS STUDY ...... 34 2.3.1 . DE-TRENDING ...... 34 2.3.2 . S-TYPE ORBIT ...... 36 2.3.3 . P-TYPE ORBIT ...... 36 2.3.3.1 . MODELING ...... 36 2.3.3.2 . TRANSIT DETECTION – CIRCULAR ORBIT ...... 37 2.3.3.3 . TRANSIT DETECTION – ECCENTRIC ORBIT ...... 38 2.3.3.4 . ECLIPSE TIMING ...... 41 2.3.4 . BACKGROUND OBJECTS ...... 42 2.4. SERENDIPITOUS DISCOVERY ...... 43

PART 2: THE PAPERS...... 45

PART 3: CONCLUSIONS ...... 69

1. SUMMARY ...... 70 2. CURRENT STATUS AND FUTURE DEVELOPMENT ...... 71 3. REFERENCES ...... 72 4. TABLE OF ACRONYMS ...... 76

− V −

− VI −

Part 1: Introduction To Published Papers

− 1 − This thesis is based on the papers in Part 2. These papers are enumerated differently than other references: by a hash (#) symbol with a bibliographic list of these references given in Part 2. The entire Part 1 is meant to serve as an overview of the field of exoplanets, emphasizing observations as this thesis is observational. In the later sections of Part 1 I will arrive at the problems I dealt with during the thesis, now in the proper context of the preceding text, helping to understand Part 2 as a part of one coherent research program, before concluding in Part 3.

1. Exoplanets Around Single Stars

1.1. Primer on Exoplanets Theory

Below I briefly describe the major theoretical chapters of the young science of Exoplanets, along the thread of mutual influence of the theoretical and observational efforts. It is thus dotted with references to observational techniques elaborated on latter in the text, as observations in general – and planetary transits in particular – are the focus of this work.

The classical, Solar-system focused, theory for planet formation suggested that giant planets can only form and grow beyond the so-called "ice line" (where conditions in the protoplanetary disk allow for water to condensate). Since the "ice-line" of the early solar system fell between Mars and Jupiter (Pollack et al. 1996) it nicely explained the stark contrast between the inner-and-small versus the outer-and-giant planets in the Solar System. However, the very first widely-accepted 1 extrasolar planet discovered around a sun-like star (51 Peg b [Mayor & Queloz 1995]) was, very surprisingly, a gas giant very close to its star. This called for a major revision of the then-current planetary formation theories and (among other things) a new major process was introduced: planetary migration. Thus, according to current theories (e.g., Alibert et al. 2005) giant planets still form beyond the ice line, but then migrate inwards (through interaction with the protoplanetary disk and/or other planetesimals) to their observed positions.

With the picture of planets moving substantial distances during formation in mind, it was not surprising to find planetary systems with very different dynamical history than the relatively placid Solar System environment. Indeed, just from the very basic quantities available from radial velocity (hereafter RV, and see § 1.3.1) one can see that the known exoplanets have a

1 HD 114762b is a planet candidate with a minimum mass of 11 M J and a period of 83d that was discovered much earlier than 51 Peg (Latham et al. 1989). However, it was so different from everything what was known at the time that only later was it widely accepted as a planet candidate.

− 2 − bi-modal period distribution (with peaks around 3 days, and 1-2 years, see Figure 1). Also, RV revealed that significantly eccentric orbits are the rule and circular orbits are the exception, and mean-motion resonances between planets are common (more below). The cause of these observed phenomena are the interactions of the young planets with their protoplanetary disk and/or other planetesimals, so the details of these interactions dictate the resultant planetary architecture and thus the relevant theories can be put to test.

Figure 1. The distribution of periods of all known exoplanets as of mid-2011 (logarithmic period scale). Note the bimodal distribution with peaks at about ~3d and 1-2yr. Source: The Extrasolar Planets Encyclopedia (http://exoplanet.eu)

A mean motion resonance (MMR) can happen between several objects orbiting the same primary if they periodically interact gravitationally strongly enough to alter each other's orbit. This usually happens when the ratio of their orbital periods can be expressed by small integers. These interactions can lead, in the long run, to both stable and unstable systems. MMRs exist in the Solar System too: the most famous of them is the triple MMR of three of the Jovian moons: the orbital periods of Io, Europa, and Ganymede have a relative ratio of 1:2:4. MMRs are important because if indeed exoplanets move substantial distances during their formation, then they are all but expected to reach one of these MMRs along their track - and they are more likely to stay in such stable and resonant configurations. Indeed, a significant fraction of the multi-planet systems known are found in MMRs (Correia et al . 2009 and references therein). MMRs are significant also because they amplify greatly the gravitational interaction between planets, allowing for deeper insight into these systems (e.g., through transit timing variations - e.g. see Holman & Murray 2005, Holman et al . 2010 and § 1.4.1).

One of the main drivers behind the current work is the appreciation that many (most?) stars are gravitationally bound to other stellar objects (Abt & Levy 1976). The presence of a distant massive companion affects the formation process, and thus from the differences between

− 3 − planets in binaries and planets around single stars one can probe the formation process. For example, one of the effects of the distant companion is the Kozai mechanism: It is widely known that if a third body is misaligned with the central binary, it can cause the orbital plane of the latter to precess. Kozai (1962) showed that there is also a critical angle ic such that if iinitial is between i c and 180º−ic, then the orbit of the inner binary cannot remain circular as it precesses: both the eccentricity of the inner binary ein and the mutual inclination i execute periodic oscillations known as Kozai cycles. Kozai oscillations are thought contribute to the observed population of planets with mis-alignment between the planetary orbit and stellar spin (detected through the Rossiter-McLaughlin effect, see § 1.4.1).

Of the total of >550 known exoplanets, there is a special subgroup of about ~140 exoplanets that allow for a much more detailed examination: transiting exoplanets 2. I elaborate on the transit technique in section § 1.3.2, but here is the place to note that transiting planets allow for a multitude of characterization studies of the planets, well beyond the simple detection of orbital parameters usually allowed for non-transiting planets. These studies allow for much more detailed comparison between observations and theory of exoplanets, in subjects ranging from formation and evolution to structure and composition.

1) First and foremost, by combining the planetary radius and mass one can compute the mean density of the planet, which is a first proxy to its composition. Indeed, planets are found to have remarkably different compositions: from planets that are almost as dense as lead (e.g, WASP-18b at 10 g/cc, Hellier et al . 2009) to planets that have the mean density of Styrofoam (e.g. Kepler-7b at 0.166 g/cc, Latham et al . 2010). These differences have lead to models in which some planets have significant cores made of heavy metals (HD 149026b, Sato et al. 2005), other planets, like WASP-17b (Anderson et al . 2010), can't possibly have significant cores, and still other planets probably contain large amounts of exotic states of matter like supercritical ice (GJ 1214b, Charbonneau et al . 2009).

2) When multi-transiting systems are detected, one may be able to measure the k2b (tidal Love number) of the planets from their mutual interaction (Batygin et al . 2009). Since both the structure of individual planets, as well as the distributions of planet's compositions, can be inferred from theory these observational efforts are very important.

2 The transiting planets subgroup will probably grow dramatically in the near future: Borucki et al . (2011) reported that the Kepler mission found no less than 1235 candidates of transiting planets, most of them relatively small, with radii smaller than half of that of Jupiter. These candidates are currently undergoing follow up observations to determine their nature.

− 4 − 3) By studying the RV "anomaly" known as the Rossiter-McLaughlin effect during a transit (Rossiter 1924 and McLaughlin 1924 – see § 1.4.1) one can learn about the alignment (or mis-alignment) between the planetary orbit- and stellar spin- axes. As mentioned earlier, this may shed light on formation/evolution mechanisms such as Kozai oscillations. 4) By measuring the exact time of consecutive transits one may be able to detect other, non-transiting planets in the system (e.g. Holman & Murray 2005). 5) By looking at the infra-red secondary eclipse one can measure the flux coming from the day-side face of the planet , which, when combined with the known radius of the planet, allows for inference of the temperature on that part of the planet. This, in turn, allows one to find just how efficient is the heat re-distribution from the day side to the night side, which is probably done through major winds systems on the planet (Knutson et al . 2007a). 6) By measuring the flux coming from the planet during its full orbit (and not just during transit) one can reconstruct longitudinal map of the planet (!) (Knutson et al . 2007a). 7) Transmission spectroscopy of the planetary atmosphere can be achieved by realizing that the upper few scale heights of the planetary atmosphere are rarefied enough to not be completely opaque. Light from the host star passes through these atmospheric layers is absorbed, at wavelengths depending on the atmospheric composition. Thus, by looking at the differences between spectra taken in- and out- of transit one can actually measure the composition of the upper planetary atmosphere (e.g. Vidal- Madjar et al . 2003). 8) Similarly, by taking spectra in- and out- of secondary eclipse, especially in the infra- red, one can measure the emission spectrum of the planet (more in § 1.4.2).

All that (and more) is possible without resolving the planet at all because of the serendipitous geometry of transits. All these studies allow a wide array of theoretical predictions: from orbital dynamic studies to planetary structure to atmospheric composition to global wind and aerosols patterns under extreme conditions. And, these models can be tested.

While this work is more focused on the most successful planet detection techniques to date – namely RV (§ 1.3.1) and transits (§ 1.3.2) – detection of exoplanets can also be done with several other techniques, each with its unique parameters set, advantages and challenges, which are summarized below: microlensing (see § 1.3.3), direct imaging (§ 1.3.4) timing variations (§ 1.3.5) and astrometry (§ 1.3.6).

− 5 − 1.2. Input Data

The raw input for this research program can be divided to two main categories: ground-based and space-based:

Space-based photometry: The primary input for the research program was light curves from the CoRoT space-based transit search (Baglin et al . 2006). These very high quality, up to 150d long uninterrupted light curves, are the best photometric dataset publicly available today combining high precision and long duration of observations. In addition, very recently the light curves from the early part of the Kepler space-based transit search (Borucki et al . 2003) became available. The Kepler data is of even higher precision – but currently only 43 days of data are publicly available.

Ground-based photometry: I used relatively little ground-based data; only the TrES Lyr1 field 3 (from the now-closed TrES survey [Alonso et al . 2004]) and some open-literature high- quality eclipsing binaries (EBs) collected for their study as EBs (and not in a transit survey). These have the added benefit of being already fully modeled. There are, however, much larger databases out there. For example, the major ground-based transit surveys in operation: SuperWASP, HATNet, OGLE, XO and MEarth (Pollacco et al . 2006, Bakos et al . 2004, Udalski 2003 McCullough et al. 2006 and Irwin et al . 2009, respectively) and a few more are planned (e.g. ASTEP [Crouzet et al . 2010]). Much of the data of these surveys are proprietary and unavailable, (the open OGLE data being a notable exception to the rule) but this is changing as each survey finishes its work on some of the earlier data. For example, SuperWASP 4 , HATNet 3 and XO 3 have all recently opened their early-years archive. Moreover, the entire TEP photometry of CM Dra (Deeg 2008) as well as the SuperWASP fields of exoplanets WASP-1 and WASP-2 (Collier Cameron 2008), the USNW data of fields R1 and R2 (Christiansen 2008) and the MMT deep survey of M37 (Hartman 2008) were all made available to me upon request. In short, a lot of ground based photometry is available.

3 Available on the NASA NStED website: http://nsted.ipac.caltech.edu 4 SuperWASP public archive: http://www.wasp.le.ac.uk/public/

− 6 − 1.3. Detection techniques

Simply taking pictures of extrasolar planets – and especially Earth-like planets – is very difficult: such planets are very close to their host star (a planet 1 AU from its host star at a nearby distance of 10 pc is only 0.1 arcsec from it on the sky), and they are extremely faint relative to their host star (for Rp<< a the visible flux is roughly:

surface of planetary disk  πR2  ≈  p  which is less than 10 -9 that of the star). This is often  2  surface of orbit -size sphere  4πa  likened to trying to spot a firefly sitting right next to a large searchlight from many kilometers away. Despite these challenges, humans have a strong desire not just to detect such planets, but to also characterize them. Fortunately, direct imaging is not the only detection technique and there are several avenues for both detection and characterization, with a recurring (and expected) phenomenon in all techniques: every higher precision level allows for not only lower error bars on the observables, but also for new observables to become significant. In section § 1.2 I first discuss the first-order approximation of each technique, that allow one to simply detect the presence of a sub-stellar companion to the host, while in § 1.4 I elaborate on the higher-order terms of some of these techniques that allow us to gain further insight to the nature of the planet.

1.3.1. Radial Velocity (RV)

The use of the Doppler Effect to extract the RV from spectra of stellar objects (such as binaries) is known for well over a century. Struve (1952) was the first to propose to look for exoplanets using this technique, Figure 2 As the (unseen) planet but real detection had to wait untill technology caught moves around the center of mass in a large orbit, the host star wobbles up, and allowed the detection of RV variations with with a tiny orbital radius – usually smaller than the stellar radius itself amplitude as small as 10s of m/sec (Campbell & (figure is exaggerated). During the Walker 1979). Today, RV is the most successful parts of that orbit that the star is moving towards/away the observer, planet detection technique. The basic observation is a blue/red shift (respectively) is measured in the stellar spectrum, that planets do not revolve around their host stars, but allowing inferring the exis tence of both the planets and the host star revolve around the the planet. common center of mass (see Figure 2). This is often neglected because the mass of planets is so much smaller than that of stars: even Jupiter, the heaviest and largest planets in the Solar system, has less than 0.001 of the Sun's mass. Thus, while the orbital velocity of Jupiter is

− 7 − about 13,000 m/sec, the reflex motion velocity of the Sun caused by Jupiter is only about 13 m/sec. Earth exerts even a smaller pull on the Sun, which causes a tiny RV amplitude of about 0.1 m/sec, well below even walking speed.

The main technological advancement that allowed the remarkable RV precision is the understanding that the problem of long-term precision (over years) is tightly related to fine and stable calibration of the spectrograph. This is done by recording simultaneously the constant calibration source spectrum to that of the star. There are a number of sources currently used on different instrument and optimized for different targets: an Iodine absorption cell is used on the Keck telescopes' HIRES instrument (Vogt et al. , 1994) and many others, a Thorium-Argon gas cell is used on the both the SOPHIE (Bouchy & The Sophie Team 2006) and HARPS (Pepe et al . 2000) spectrographs, and other gases are used for RV measurement in the infra-red (e.g., Bean et al . 2010).

The direct observables of RV are: period P, center-of-mass velocity γ, the modulation semi- amplitude K, the eccentricity and argument of periastron passage e and ω, and time of periastron passage T. From these parameters one can deduce the mass function:

3 3 3 2 2/3 mp sin (i) PK (1− e ) f ()M *, m p = 2 = ()M * + mp 2πG where G is the universal gravitational constant. From there, if the mass of the star is assumed or known (e.g. by measuring the spectral type of the star), one can finally deduce the value of mpsin( i), or the minimum mass of the planet.

1.3.2. Transits

Figure 3 — Illustration of transits and occultations. Only the combined flux of the star and planet is observed. During a transit, the flux dro ps because the planet blocks a fraction of the starlight. Then the flux rises as the planet’s dayside comes into view. The flux drops again when the planet is occulted b y the star. Figure and caption taken from fig. 1 of Winn (2010).

Planetary transits rely on the serendipitous alignment of the line of sight and the orbital plane

− 8 − of the planet. If such an alignment is indeed present, than once every orbit the (opaque) planetary disk crosses the face of the host star as seen from Earth, causing the stellar flux to appear smaller for this short while (see Figure 3). Since the stellar disk is approximately uniformly illuminating, the relative drop in stellar flux is simply the percentage of the stellar

2 2 disk blocked: Rp R* . Giant planets have radius similar to that of Jupiter which is about

1/10 of the Sun's radius, so such planets produce a dimming of about ( 10/1 )2 = 1% . Thus, by measuring the periodic dimming of the star one can determine the (relative) radius of the occulting body, and by assuming a certain stellar radius (by measuring the star's spectral type), one can finally deduce the linear size of the occulting body. From the above it is easy to see that the transit method is biased towards the largest planets, making small planets very difficult to detect (the transit depth caused by Earth when it transits the Sun is about 0.000084 – 84ppm).

Finding a transiting planet is difficult for a number of reasons: 1)The probability of a planet to R + R transit at all is small. For example, for circular orbits it is: p = * p (where a is orbital a semimajor axis). The bias to small a means that transit surveys are highly biased towards short-period (few-days) planets and even for these planets p is rarely larger than 10%. 2) The R planets spend only a small fraction (order of * = few percent) of the time in-transit so one πa needs thousands of measurements to positively identify the faint signal. 3) Approximately 95% of solar-type stars actually do not have short period giant planets at all (Howard et al .

2010) (giant: with masses larger than 30 MEarth ), and many stars have radii much larger than solar (making planetary transits too shallow). The above, combined with the fact that transit surveys are "blind", i.e. the targets are not picked but simply all stars in a given patch of sky, means that one has to monitor many thousands of stars for thousands of times (taking months and years) in order to stumble upon just one star with a transiting planet. This, in turn, means that all surveys need to build highly automated, yet very efficient, data-processing pipelines.

The challenge of actually finding transiting planets and giving an initial description of them can be divided to four steps: 1. Obtaining good-precision photometry for many thousands of stars simultaneously. 2. Detecting shallow transit signals in the photometric data. 3. Rejecting false positives based on the same data. 4. Follow-up (FU) observations aimed at confirming or ruling out the candidates (see more on § 1.3.2).

− 9 − In the end of this process a new planet can be announced. This thesis is focused at analyzing discovery data (steps 1 to 3), while step 4 (and subsequent characterization FU as in § 1.4) require further observations.

Step 1. Obtaining good-precision photometry There are currently five ground-based transit surveys that have repeatedly succeeded in detecting transiting planets: SuperWASP, HATnet, OGLE, XO, and TrES. A few other surveys also detected (so far) only a single planet: MEarth and Qatar. The numerous problems that need to be overcome in an automatic fashion are both difficult and diverse: bad pixels, extremely wide fields, source confusion, robotic operation, automated precision photometry of 10s of thousands of stars on every frame, etc.

Step 2. Detecting shallow transit signals As mentioned above the fraction of time spent on-transit, or duty cycle, is very low and varies

 2 2  1 R (1+ Rp R* ) − b as sin −1  *  where b in the impact parameter of the transit (Winn π  a sin i    2010), meaning that a 3-day transiting planet spends only about 3% of the time in-transit, and an Earth analogue would have a duty cycle of only 0.15%. Moreover, the sampling of the data is non-uniform: it suffers from gaps. In ground-based surveys these are mostly the large, periodic gaps caused by the day time. All these make the standard tool for periodicity detection, the discrete Fourier transform, ineffective for the detection of shallow transit signals. For this reason a number of transit detection algorithms were proposed and compared (e.g., Tingley 2003) and indeed one algorithm has gained popularity due to its high sensitivity: the BLS (Box Least Squares) algorithm (Kovács et al . 2002).

BLS, as the name implies, fits a box-shaped model to the data in the least squares sense. This algorithm is specifically tailored for the detection of very shallow and sudden drops in the otherwise normally-distributed white noise. BLS's sensitivity is largely due to the simplicity of its model: while it has little sensitivity to the shape of the signal, it is well designed to spot the existence of shallow signals. Thus, only a three-dimensional search is needed to fully scan all possible BLS models: a search in period, reference phase and phase-width of the signal.

Step 3. Rejecting false positives. Due to the high number of stars that need to be observed (which means a large field of view), and due to the fact many hundreds, if not thousands, of images need to be taken of the same patch of sky, most transit surveys need to use dedicated hardware, and so are usually limited

− 10 − to small "telescopes", sometimes simply using commercial 10cm photographic lenses. All this, in turn, makes the spatial resolution of these telescopes very poor, with pixels spanning typically 30 arcsec, and the observed fields are usually chosen to be rich. Therefore, often more than one star occupies the same few pixels of a photometric aperture. As it turns out, the vast majority of the "transit-like" signals detected in step 2 above are not transits at all, but are one of several common false positives: I) extreme EBs of a giant and a dwarf, or of an early- type primary and a (very) late type secondary II) grazing EBs III) diluted EBs, where the third star is either bound or coincidentally on the same line of sight. A significant fraction of the signals can be uniquely identified already from the discovery data as "imposters" of types I or II, but here manual verification is the norm, and so this is more time consuming.

The next steps needed to verify whether a signal is indeed caused by transiting exoplanet are resource-heavy with dedicated efforts and observations for each object. These follow-up (FU) efforts are a major and indispensable component of all transit surveys (e.g.: Deeg et al . 2009 for CoRoT and Gautier et al . 2010 for Kepler ) exactly because of the high rate of false positives. The goal of the FU chain is firstly to limit the number of objects than are observed in the most expensive FU technique – high-precision RV – to the most promising candidates only. Secondly, FU aims to find a plausible explanation for all detected signals, and if that is not possible to at least exclude planetary origin of the signal. Once determined to be a planet, the FU of such an object aims to fully characterize it. These FU efforts are not the focus of the current work, but they will be visited in section § 1.4. Importantly, in the context of this work, which is focused on detection and not on FU, if the initial signal cannot be proved to be something other than an exoplanet, its discovery is considered a success. FU observations may later show that the signal in question is any one of a number of possible phenomena and not an exoplanet, but as long as one cannot reach the same conclusion based on discovery data alone, the detection of the photometric signal is considered successful.

1.3.3. Microlensing

Microlensing is another photometric method for the detection of exoplanets that has already produced detections: despite the fact that microlensing surveys were mainly aimed at the detection of a certain types of proposed dark matter, and not planets, already 10 planets have been detected via microlensing (as of this writing). The most notable surveys are: OGLE, MOA, MicroFUN and the PLANET Collaborations and they often share data for better data sets (e.g. Sumi et al . 2010). This technique is based on the relativistic bending of light rays near massive bodies (see Figure 4): when a foreground object (the "lens") pass in front of a nearly-aligned background star (the "source"), the light from the source object deflects ever so

− 11 − slightly. In this configuration there may be several (curved) light paths from the source to the observer and not one. The former is then seen as "multiplied" to several images that can be individually distorted and/or magnified. The deflection angle is determined by the mass of the lens (which determines a characteristic radius called the Einstein Radius R E) and by the impact parameter of each ray relative to R E. Stellar objects always produce tiny deflection angles relative to their far-more-massive and famous siblings: the lensing galaxy clusters. Also, when the deflection angle is small – smaller than the resolving power of the instrument – one does not see several separate images of the source, but rather an increase in the total flux from the source+lens combination and this is called microlensing. The observed amplification of the light can be sometimes very significant; flux amplification by a factor of >2200 (!) was observed (Gould et al . 2009). On such high-amplification events, even less massive objects near the lens – such as planets orbiting the lensing star – produce detectable anomalies to the single-lens light curve, and this is how microlensing planets are discovered.

Figure 4. From the magnification pattern, and especially – deviations from the simple bell- like shape of a single lens (see solid red line at the top ) one can deduce the information about the mass of the lens star, and whether it may have companions. I n the figure the lens star+planet system moves and crosses the line of sight between the source and the telescope. During this passage (that typically last a up to a few weeks) the source star's light is microlensed and amplified.

Despite the apparent technical similarities (monitoring dense stellar fields for brightness variation) - there are several key differences between microlensing and transits: I) Microlensing events are single events, not periodic events, caused by the temporary chance alignment of the source and lens due to their relative (and random) motions. This alone means that accurate orbital parameters cannot be obtained and that FU characterization observations are nearly impossible. II) Usually there is virtually no knowledge about the host star, III) The alignment requirement is very stiff, making the events far more rare than transits: many millions of stars need to be monitored to in order to find a single microlensing planet. IV) the most important planetary parameter probed by this technique is different: mass ratio, and not size ratio. V) microlensing is sensitive to planets much farther and much smaller than is possible for a ground-based transit survey. VI) the temporal evolution of simple microlensing signals has a time scale of several days and it is approximately predictable (once the onset of a signal is detected) so the typical cadences are much lower (once a day, vs. once every 5

− 12 − minutes or so for transit surveys). The predictability of simple models is used to look for deviations from them in real time: such deviations, which may indicate a more complicated system (with a planet present, for example), can evolve on much shorter time scales and thus often trigger concentrated efforts to observe the target during expected times of peak amplification and evolution. VII) The relevant deflection angles are so small and the corresponding distances so large (range of kilo-parsecs from Earth to lens and from lens to source) that microlensing surveys target far-away stellar populations: the galactic bulge and even nearby galaxies such as the Magellanic Clouds. This makes any FU extremely difficult, but allows probing very different stellar populations.

It is interesting to note that high-magnification events become sensitive to a host of second- order and interesting effects, such as: finite-source (Bennett et al . 2010), orbital motion of binary lenses (Albrow et al . 2000), differential limb darkening (Johnson et al . 2010), differential parallax of different observers (even while all are on Earth) (Gould et al . 2009), and more.

1.3.4. Direct imaging

Eventually, direct imaging and then spectroscopy of exoplanets is one of the prime observational goals of all efforts related to exoplanets. There is little doubt that one can learn the most about the target objects using this technique. However, this is extremely difficult due to the enormous contrast ratio and small separation angle between the target planets and its host star. Still, in a number of favorable cases (currently about 10 systems) direct imaging of exoplanets was indeed achieved, including one system with four directly-imaged planets imaged from the ground (see Figure 6, more details below) (Marois et al 2008).

While very simple conceptually – direct imaging really is simply taking images of planetary systems – actually making such a detection is a significant challenge, and especially so when it is done from the ground. All the techniques described below try to somehow remove the bright light of the host star while keeping the light from its faint companions uninterrupted, and some of them are even used simultaneously:

1) Adaptive Optics (AO) : adaptive optics is probably one of the biggest recent technological breakthroughs in astronomy. AO works by using a test signal (be it a natural nearby star or an artificial "star" generated by laser light from the ground) to learn about the distortions of the wavefront of the star as it passes through the turbulent atmosphere, and then to apply a correction in the opposite direction by

− 13 − means of a deformable mirror before focusing the star on the detector. This process has to be done many times per seconds (frequencies of tens to hundreds to even 1000 Hz) so that the deformable mirror can keep up with the changing atmosphere. AO's first contribution to the field of exoplanets was the direct detection of a giant planet near a young brown dwarf 2MASSWJ 1207334-393254 (Chauvin el at . 2004). AO can make telescopic observations diffraction-limited instead of seeing-limited, allowing achieving from the ground resolutions better than those obtainable from the HST (Figure 5).

Figure 5 A central region of the globular cluster M92 at 1.6m as observed with the Hubble Space Telescope (left) and the LBT in AO mode (right). [MPIA Science Release 2010-06-15]

2) PSF subtraction : The most naïve method to try to detect faint companions is by subtracting the estimated PSF (Point Spread Function) the central star, and looking at the residuals image. This, however, is not possible in reality because of the imperfect optical train that induces quasi-static "speckles", and several techniques were developed to tackle this difficulty. The speckles are aberrations and reflections from the imperfect telescope system (mirror segments, spider, etc.) that evolve slowly over the course of the observation (hours time scale) and so are difficult to separate from true signals. Some speckle-fighting techniques are part of the data-taking procedure, like ADI (Angular Differential Imaging) (Marois et al . 2006), and its sister-technique: SDI (Spectral Differential Imaging) (Smith 1987). ADI uses the fact that some telescopes (and most modern ones) use 2-axes tracking to keep the target in the frame, plus a third axis to keep the image rotated at the desired position angle. By disabling or adjusting this last axis, the field of view (FOV) rotates from image to image during the night in a well-known manner. By de-rotating the images astrophysical objects are positively co-added, while instrumental speckles now seem to rotate in the FOV and are averaged-out. Other techniques help the data processing after acquisition, such as the LOCI algorithm ("Locally Optimized Combination of Images" - Lafrenière et al .

− 14 − 2007). In Figure 6 one can see the only multi-planet system directly imaged so far – using AO and ADI and LOCI – around HR 8799 (Marois et al. 2008, 2010). Similarly to ADI, SDI uses the color-dependence of the location of the speckles (vs. the achromatic location of astrophysical objects) to separate the two. Exploiting different properties, the two techniques are not mutually exclusive, and therefore one

Figure 6 Image of the residuals of the HR 8799 system from the Keck telescope – the four planets are labeled b to e, the later is marked with an arrow. To produce these extremely high resolution and contrast images both the AO system and ADI/LOCI techniques (see text) were used.

can apply ADI and SDI to the same images simultaneously.

3) Coronagraphy : is the attenuation of the central source by a mean of a physical disk (called occulter) blocking (some of) its light, and allowing light from off-axis sources, such as a nearby planet, to pass (relatively) unimpeded. The problem is that at the desired attenuation levels and angles are very difficult to achieve: attenuation factor of 10 -9 at angles of 2-3 λ / D where λ is the central wavelength and D is the telescope's diameter. Diffraction around simple occulters causes significant and wavelength-dependent portions of the stellar light to "leak" behind the occulter, making deep nulls of the star difficult.

I note that in all cases of ground-based coronagraphy I am aware of coronagraphy is heavily dependant on a preceding AO step to stabilize the PSF of the source (e.g. CT Cha b [Schmidt et al . 2008]). HST does not need AO at all, an indeed had already detected the planet Fomalhaut b (see Figure 7, Kalas et al . 2008).

Coronagraphy can be achieved in several very different ways: I) Theoretically, the best occulter has a smooth transition from zero to full transmission over its surface (e.g. Indebetouw 1990, Watson et al . 1991). However, this in incredibly difficult to manufacture to the relevant tolerances, and so a more practical way is to manufacture

− 15 − a binary occulter (one that is either opaque or transparent) that is easier to manufacture but is less effective. II) The occulter can also be position either internally (as part of the telescope's structure) or externally (very far from the telescope - order of 50,000km [e.g. Glassman et al . 2010 and references therein]). Internal occulters impose extremely stringent requirement on the entire optical train, while external occulters (which is a space-based-only concept) are difficult to move between targets. III) Advanced concepts in the field employ techniques such as optical vortex coronagraph (Swartzlander et al . 2007) are now under development.

Figure 7 A sharp image from the HST showing Fomalhaut's surrounding ring of dusty debris in detail, with overwhelming glare from the star masked by an occulting disk in the camera's coronagraph. Fomalhaut b is shown in two different orbital positions in the small insert at the right. The Hubble data represent the first visible-light image of an exoplanet.

4) Nulling interferometry : another option for suppressing the host star's light is using a nulling interferometer. These devices introduce an intentional differential optical path of π radians between the arms of the interferometer, causing a localized destructive interference at the center of the field (the location of the star) allowing faint sources outside that localized zone to be detected. The only experiment using this technique is the "Keck Interferometer" which combines the two twin Keck telescopes (Colavita et al . 2009). It has no planet detections so far.

All the next-generations giant telescopes with diameters of 25m or more (i.e, TMT, GMT and E-ELT) have planned programs for exoplanet detection by direct imaging. It is interesting to note that the very fact that these extremely capable observatories are so large produces new difficulties, as the host star's disks start to be resolved (Aime et al . 2010). Direct detection by coronagraphy is a challenging endeavor and it is sure to evolve significantly over the coming years.

− 16 − 1.3.5. Timing Variations

This technique is suitable for astrophysical sources that naturally include a strictly-periodic observable, such as pulsars, pulsating stars such as sdB stars and some white dwarfs, and importantly - EBs. For these objects, by carefully monitoring the exact time of arrival of the periodic signals one may be able to deduce the presence of a third body, possibly even with a planetary mass. The basic idea is very similar to the one behind RV (§ 1.3.1), meaning that both the planet and the host star are orbiting the common center of mass and host star's motion is detected. In Timing Variations, one exploits the fact that the host star, depending on where it is in its orbit, is sometimes closer or farther away from the observe. This causes the observed signals to arrive earlier or later than expected due to the finite light travel time (sometimes called LITE effect). Here one actually measures the radially-projected stellar orbit around the common center of mass, which causes timing variations with semi-amplitude of: a sin( i) M A = (assuming circular orbit), where = p and c is the speed of light. I c M * + M p note that the masses obtained from this technique are degenerate in sin (i) so the true mass cannot be inferred but only a lower limit to it (similarly to RV). The timing variations method is similar to the RV method in its bias towards massive planets, but unlike RV it is also biased towards long period planets. I note that the majority of planets detected via timing variations (below) indeed have very long periods (3 years or longer), as the method's bias would suggest.

Already 5 planets around 3 single-star systems were detected via timing variations: two planetary systems around pulsars PSR 1257+12 (Wolszczan & Frail 1992, see Currie & Hansen 2007 and references therein for updates) (3 planets) and pulsar PSR B1620-26 (Backer et al . 1993) (one planet), and a planet around extreme horizontal branch star V 391 Pegasi (Silvotti et al . 2007), using its pulsations as natural clock.

Importantly, this technique naturally lends itself to EBs by using the eclipses of short-period EBs as a natural clock to look for P-type (see § 2.1) planets. Previous studies in this area are further discussed in § 2.2.2 for, and similar studies made during this thesis are discussed in § 2.3.3.4.

1.3.6. Astrometry

Astrometry is also an indirect detection technique, like RV (§ 1.3.1) and Timing Variations (§ 1.3.5), meaning that observations of the host star allow us to detect the presence of a

− 17 − planetary companion, but with very limited characterization capability. In this technique the (relative) sky position of the target star is measured to high precision, allowing the detection of the on-sky orbital motion of the star along its orbit around the common center of mass. The benefits of detecting planets using this technique is that it is relatively insensitive to the orientation of the planetary orbit (i.e., its inclination), and that all the orbital elements of the planets are accessible. The biases of astrometry are also somewhat different, as it is biased towards massive and long period planets similarly to Timing Variations above.

However, as expected, the astrometric signal from exoplanets is very small: a Jupiter-like planet 10pc away would have an astrometric signal of only 0.5 mas, while Earth-like planet at the same distance would create a signal with amplitude of only 0.0003mas (or: 0.3 as). Achieving this level of precision is extremely difficult. However, very recently the first astrometric detection of a known planet was made (McArthur et al . 2010), and even the first discovery of substellar objects via astrometery was reported (Muterspaugh et al . 2010).

In the near future, though, this field is expected to change dramatically: ground-based AO systems already achieve relative astrometric precision <0.2 mas (Lu et al . 2010), the important global astrometric space mission GAIA will launce in 2012 and will map everything brighter than magnitude V=20 (>10 9 objects) with astrometric precision down to 20 as, which means that many (thousands) of planets are expected to be found.

− 18 − 1.4. Characterization of Exoplanets

All the detection techniques above described the first-order detection of a planetary companion to some unknown star. Fortunately, the ability of FU observers to fine-tune the observation to a particular object has a dramatic effect on the achieved precision of the signal (see Figure 8). The FU challenge is thus twofold: firstly, to observe the target with the highest possible precision, in multiple wavelengths and techniques, and to thus gain insight to different processes in the system. Secondly, the modeling and understanding of these processes. As a successful illustration to the above process I refer to Paper # 4 which describes the detection of the transiting exoplanet HAT-P-5b, where my contribution was the simultaneous modeling of 6 FU light curves using the Mandel & Agol formalism (Mandel & Agol 2002) – see § 1.4.1 below. Recently it has become almost routine that the FU observations are done very well: the uncertainties of the derived planetary parameters become dominated by errors of the stellar model, and not by the quality of the data (Johnson et al . 2009, Adams et al . 2010, Holman & Winn 2006 are a few examples).

Figure 8 left: discovery light curve of the planet WASP-10b [Christian et al . 2009 ]. Right: ground-based follow-up light curve of a single event of the same object [Johnson et al . 2009 ]. The differences in signal-to-noise ratio (SNR) are dramatic. This figure shows nicely that challenge of discovering new exoplanets (the subject of this thesis) is that of finding shallow signals as in the left panel, and this is the SNR of regime the reader should have in mind.

In this section I will consider the cases where such observations exist that higher-order phenomena become important, or that the combinations of different methods gives physically interesting new results. The first such quantity that comes to mind is the mean planetary density – the first proxy of planetary structure – as was indeed already discusses in § 1.1. Below I list, by technique, other ways to characterize transiting exoplanets and their systems.

− 19 − 1.4.1. High-precision photometry

A very crude box-like model is used to detect the shallow transit signal with BLS. This model is very effective at detecting shallow transits, but its use is limited to that only. Similarly, a trapeze-shaped model is also a toy model, but it includes the important ingress and egress features, and so it is much more reliable at the estimation of the direct transit observables (see Figure 10) as they are usually presented: depth, epoch and durations (assuming symmetric transit). These few observables remain unchanged even in more complicated models that are required once high-precision photometry is available, at which time other effects become important, such as: exact geometrical solution of the ingress/egress and limb darkening (e.g. see Figure 9) and orbital eccentricity (Kipping 2008). All these are included in what became the de-facto standard for light curve analysis: the Mandel and Agol formalism (Mandel & Agol 2002).

*

*

Figure 10 . Definition of transit light curve direct observables. Top: the planet moves from left to st th Figure 9. Normalized HST data for 10 right through 1 to 4 contacts at times T1 to T4. Both an equatorial transit ( b=0) and high-latitude bandpasses (roughly evenly divided between 300nm in violet to 1000nm in red), w ith their (b ≅1) geomet ries are shown, as well as the corresponding theoretical transit curves definitions of R and R ,. Bottom: resultant * P overplotted. Note the significant curvature of trapezoidal model light curves in b old and dotted the bottom of the transit caused by limb lines for low and high b, respectively. Also darkening, and variability of t he limb F indicated the fraction of lost flux , the total darkening effect with wavelength [adopted transit duration, T and the transi t duration between T form Knutson et al . 2007b] ingress and egress TF. [adopted from Seager & Mallén -Ornelas 2003 ].

Fortunately, by combining the direct observables from high-precision photometry and from high-precision RV, it is possible to construct two completely model-free and astrophysically- interesting quantities: the mean density of the host star (Seager & Mallén-Ornelas

− 20 − 2 3 2 2  2 2   4π (1+ F ) − b []1− sin ()tT π P  2003): ρ* =    and the surface gravity of the  P 2G  sin 2 t π P   ()T 

2π 1 - e 2 K transiting planet (Winn 2010): g p = 2 . The former is very useful at P ()R p a sin i determining whether it is likely that the system is made from a planet and a dwarf host star, or from a giant star orbited by a dwarf (as discussed in Step 3 of § 1.3.2). The latter can reveal details about the conditions found on the surface of these far-off worlds.

Once a number of high-precision light curves of different transit events become available, one can look for variations in any of the three observables. Specifically, deviations of Tmid from strict periodicity (usually called "Transit Time Variations" or TTVs) are highly sought after since such deviations can betray the presence of other planets in the system, even if these planets do not transit themselves. Moreover, planets in low-order mean motion resonances (as discussed in § 1.1) cause relatively large deviations (even many minutes) on short time scales (few orbits) making searches for planets in such configurations using TTVs very sensitive (e.g.: Holman & Murray 2005). Recently, the first claim of such variation was detected in the WASP-3 system (Maciejewski et al . 2010), followed by a beautiful textbook-like detection of TTVs in a 2:1 resonant multi-transiting planetary system Kepler-9 (Holman et al . 2010, see Figure 11). Similarly, changes in the total duration of the transit (Transit Duration Variations - TDuVs) can point to a change in the inclination of the planet (e.g. Shporer et al . 2009), and changes in the transit depth F can reveal planetary oblateness (see below).

Figure 11 Detrended, binned and phased light curved of Kepler-9b (left panel) and Kepler-9c (right). In each panel the upper light curve shows the significant TTVs caused by gravitational interactions between the planets, and the lower light curve shows the result of modeling-out these interactions (see Holman et al . (2010) for details). Note that consecutive transit events are marked in different colors.

It is interesting to note that large planets may have moons of their own, and their presence may be inferred from either TTVs or TDuVs of their host planet (Kipping 2009a,b). The tiny

− 21 − moons become detectable since while their mass is small, they are close to their host planet and thus induce noticeable gravitational pull. If the quality of the data becomes high enough, even more subtle effects become observable. The first effect is the color dependence of the transit shape: this is cause by the different limb- darkening at different wavelengths, and was graphically demonstrated by Knutson et al (2007b) (see Figure 9). Next, and most importantly, one needs to account for the fact that the planets themselves are "shining": both in reflected visible light (from the host star) and in emitted thermal radiation (due to their non-zero temperature). Both are very tiny fluxes, especially when compared to the host star. However, when transiting planets pass behind their host star (a "secondary eclipse") one can see the drop of flux during secondary eclipse, due to the fact that during that time one sees only the star, while just before and just after that time the total flux of the star and the planet are observed. Moreover: the changing phases of the

Figure 12 The infrared planetary phase curve of HD 189733 b [Knutson et al . 2007 ]. Top: the entire dataset spans more than half an orbit: from before the transit till after the secondary eclipse. Bottom: same as above, zoomed-in. The exquisitely precise data allows to clearly see the secondary eclipse. Moreover, since both the lowest- and highest- flux points are visible in the same half of the (full) ligh t curve, one learns that the hottest and coldest longitudes are not sub- and anti-stellar, and are on the same hemisphere - with dramatic implication to the understanding of the planetary atmosphere.

planet throughout its orbit around the host create – similar to the Moon's phases – a sine-like signal in the out-of-transit data. All these effects were detected together for the first time in the photometry of HD 189733 (see Figure 12, Knutson et al . 2007a). These observations provide for a leap in the understanding of these planets: • From the exact timing of the secondary eclipse one can put stringent constraints on the eccentricity, since the phase deviation of the secondary eclipse from phase 0.5 is ecos ω . • When observed in the visual band pass, one can measure the planetary albedo, since

2  R   p  the reflected planetary flux is FR = Af ()φ   where f (φ)is the phase function  a  (e.g. for a Lambertian sphere) and all the other quantities are known from transit observations.

− 22 − • When the secondary eclipse is observed in infra-red, one can estimate the disk- averaged temperature of the planet on its day side. Measuring the temperature of exoplanets is, of course, an extremely impressive achievement, but one that was already achieved for a number of transiting planets (see compilation of results in Seager & Deming 2010). These were done mostly by using the Spitzer space telescope, but also from the ground. • By knowing the temperature of the day side (from the emitted flux), and the total flux falling on the planets from the host star, one can start making energy budget calculations for the planet in order to understand how the intense stellar flux is redistributed to the night side. This is usually explained with convection; it needs to be appreciated that "convection" is actually just winds, so now it is possible to measure global wind patterns on exoplanets that are extremely far away, and actually not seen or resolved from their host star. Such is the power of the serendipitous alignment that causes transits. • The above observational advances opened up a whole new theoretical field of the modeling of exoplanetary atmosphere of very hot gas giant planets, that are very different from the cold gas giants of the Solar System. For example, one of the currently popular ideas is that one can divide these planets to two types, the pL and pM types, that are analogous to the stellar L and M stellar types. These types are supposed to be differentiated by the content of TiO and VO (metal oxides that are gaseous at the high temperatures found on these planets), that is, possibly, responsible for the observational fact that some planets have thermal inversion in their atmospheres and other planets do not (Fortney et al . (2008)). • In the future (e.g., with JWST), one may be able to even observe the non-zero night- side emission from the exoplanet (Kipping & Tinetti 2010) to better understand the global energy budget of hot Jupiters and their prevailing energy-redistribution patterns.

As successful as the Mandel & Agol formalism is (it was used in all the above investigations), it is still rather simple in that it simply describes the full or partial overlap of two circular disks (of which one is limb-darkened). The real world is, however, a bit more complicated and further effects are expected, and indeed sometimes observed: • Information about the star spots distribution can be deduced both from the slow pseudo-cyclic variation of the light curve (which is assumed to be related to the rotational period) and from transits events that happen to transit stellar surface

− 23 − features too. This analysis was applied to a few planet-host stars, e.g. CoRoT-2 (Wolter 2009, Huber et al . 2010). • The large planets of the Solar System have rings. If any transiting exoplanets may have a ring system of their own, then they can also create a detectable signature in the light curve (Barnes & Fortney 2004). • By observing the first transiting planet HD 209458b using a narrow-band filter centered on the Lyman α line it was discovered that this planet has a large exosphere of atomic Hydrogen that fills its Roche lobe and even overflows it, and thus should have a comet-like tail of escaping Hydrogen trailing behind it (Vidal-Madjar et al . 2003). I note that this detection is somewhat controversial, see Ben-Jaffel (2007). • Observing transit events on (narrow) band passes where the stellar atmosphere is optically thin causes the transits light curve to show a distinctive "W" shape, as opposed the canonical "U" shape (Schlawin et al . 2010). This may be particularly useful for the detection of planets around giants. • The finite integration time smears and distorts the instantaneous Mandel and Agol model, as was recently modeled by Kipping (2010) and demonstrated by Kipping and Bakos (2010). • The upper layers of the planetary atmosphere refract some of the host star's, changing the overall light curve (e.g. Hui & Seager 2002, Sidis & Sari 2010). • Extremely precise light curves may offer the possibility of extracting information about the planetary oblateness and rotation period (Hui & Seager 2002, Barnes & Fortney 2003). It may be possible that some of the oblate planets also undergo spin precession, and that this signature may also be observable (Carter & Winn 2010). • Wind and energy redistribution patterns also have photometric and spectroscopic signatures on the transit signal (Burrows et al . 2010).

This extra-long subsection on high precision photometry shows the great progress that was already made in the understanding and characterization of exoplanets in the last few years, and the imaginative ways invented to take advantage of the available photometric data. Indeed, the entire section § 2 deals with the application of high-precision photometry to the special case of planets in binary systems, and may be considered as a continuation of this effort.

− 24 − 1.4.2. Spectra of exoplanets

The best description of exoplanets will require the resolved image of their surface, coupled with high-resolution spectra of their light. While this is beyond current (or anticipated) capabilities, low and medium resolutions spectra of the entire planetary disk are resources we can use right now. Since the images of exoplanets are, generally, unresolved from their host star (for exceptions see Direct Imaging § 1.3.4) measurement of exoplanetary spectra is possible only for transiting planets by resolving the planetary signal in time : taking spectra on and off transits or secondary eclipse, and computing the difference to obtain the planetary signal. This, so far, enabled: λ • Low-resolution R = ≈1−10 "spectra" by observing secondary eclipses at λ different photometric bands. Later on, medium resolution spectra were also taken using similar technique. This technique was already used to reveal chemical species

on the planet like: H 2O, CH 4, CO and CO 2, and vertical temperature profiles of the planetary atmosphere (see recent review by Seager & Deming 2010 and references therein). • Transmission spectra measures the spectrum of the upper layers of the planetary atmosphere as the light passes through the optically-thin upper few scale heights of the atmosphere during transit. This has been done in the visible band. This technique allowed the detection of atomic hydrogen (Vidal-Madjar et al . 2003) and Oxygen, Carbon (Vidal-Madjar et al . 2004) and Carbon monoxide (Snellen et al . 2010) on HD 209458b. In particular, the detected CO allowed measuring of the Doppler effect on the planet, measuring the planet's orbital velocity (vs. the reflex velocity of the host star). This allowed for a model-independent solution of the very last stage of RV (§ 1.3.1), the transition from the measured mass function to planetary mass, which is usually model-dependant and may be affected by systematic errors. By detecting the planetary Doppler shift Snellen et al . 2010 could determine the absolute masses of both the planet and the star directly from Newton's laws, just like double-lined spectroscopic binaries.

One of the important discoveries was that some of these species appear in emission (see review by Seager & Deming 2010), i.e. there is a thermal inversion in the exoplanetary atmosphere. This, together with other atmospheric observables, should allow to further characterize these atmospheres but the current models seem to have difficulties explaining all the observables.

− 25 − 1.4.3. The Rossiter-McLaughlin (RM) effect

The RM effect was first noted early in the 20 th century in the context of binary stars. This effect describes the "anomalous" RV signal measured when EBs (and transiting planets) undergo eclipse (transit), where "anomalous" is relative to the regular Keplerian RV curves. The signal stems from the fact that spectrographs "see" rotating stars as disks half blue-shifted and half red-shifted (the approaching and receding sides, respectively). Usually, these two sides balance each other to give a symmetrical rotational broadening of the spectral lines. However, during eclipses only part of the surface of the disk is occulted, making the blue- and red- sides of the star not completely balanced, producing an apparent shift in the line's center, and so producing the distortions to the normal RV curve (see Figure 13).

The useful aspect about the RM effect is that by measuring the shape of the "anomaly" one can deduce the sky-projected angle between the angular momenta of the planetary orbit and the stellar spin - λ. This angle is important because different planet formation/evolution scenarios predict different values (or: distribution of values) for this particular parameter. For example, the Kozai oscillations mechanism is predicted to give a specific distribution of λ values (Fabrycky & Tremaine 2007). The main idea is, very briefly, that while interaction of a planetesimal with its natal disk can usually damp eccentricities and inclinations, interactions with other planets and planetesimals via planet-planet scattering (e.g. Raymond et al . 2009) can excite these very qualities, and even to very high degree.

Figure 13. Top: The spectroscopic view of the face of a rotating star: the advancing side is blue- shifted, and the receding side is red-shifted. As the planet transverses the face of the star it blocks some of the light, creating an apparent RV shift in the opposite direction (relative to the no-transit state). In this illustration a prograde planetary orbit is from right to left, and vice versa in a retrograde planetary orbit. Right: two real examples of a prograde planet (WASP-3b, top) and retrograde planet (WASP-8b, bottom) [Tripathi et al . 2010 and Queloz, et al . (2010), respectively].

− 26 − 2. Exoplanets and Binary Stars

2.1. Prelude

2.1.1. Definitions and Biases

Stable planetary orbits in stellar binary systems have been separated into two main 5 families (Dvorak

1986, see also Figure 14). In wide binaries there are stable orbits around one of the components of the binary (the so-called S- Figure 14 . Illustrations of P-type (left) and S-type (right) planetary type orbit) up to a certain orbits in binary systems . Stars are in orange and the planet is pale blue. critical distance from the parent star: the outer acrit . Below I shall call these also circumprimary (CP) planets although it is usually not possible to tell which component is the planet's host without a detailed study. On the other end of the binary separation scale are tight binaries 6: in these systems stable orbits exist outside and around both components (P-type orbit) starting from some inner acrit and outwards. I shall call these circumbinary (CB) planets. Similarly, I shall call planetary orbits around single star "single-type" orbits.

The different types of orbits call for different types of theoretical considerations and observational techniques, and in the following text a clear distinction will be made between the families. In this work I look for both CP and CB transiting planets, and also for non- transiting CB planets. I will also describe how advances made in the course of this thesis were also used to better detect single-type planets.

Since a large fraction of stars, possibly most of them, form in multiple systems (e.g., Abt & Levy 1976), it is important to investigate the relationship between stellar- and sub-stellar multiplicities. The two most successful planet detection techniques (RV and transits) do not work well with binaries: companions contaminate RV spectra, induce too-large RV variation,

5 A third family - L-type orbits - refers to orbits around the L 4 and L 5 Lagrangian points, is less relevant and will not be discuss here 6 We note that even moderately-close and wide binaries may have CB planets - but they will have very long periods and so will be extremely hard to detect, and so are beside the scope of this work.

− 27 − and dilute transit depths. These properties make binary stars the "enemies" of most exoplanets surveys, which try to avoid them as much as possible. Despite these biases, already at least 17% of the known exoplanets are known to revolve around one component of a wide binary (Mugrauer & Neuhaeuser 2008) - and this is just a lower limit to the true fraction. In sharp contrast to the above tendency, this research program aims squarely at binaries: I optimize all that is in my control for the detection of planets in EBs.

2.1.2. Motivation: what can be learned from planets in binaries?

Firstly, simply by detection, the frequency of planets in binaries can be better constrained. Comparing this with the frequency of planets around single stars can help constrain formation theories, which ought to predict both distributions. Secondly, additional information on the detected systems such as the distributions of periods, masses, mass ratios, semi-major axes, etc. can further allow testing of theoretical models by looking at differences between the S-, P- and Single- type populations (or even lack thereof). These differences are important because some planet formation theories are degenerate in such a way that the degeneracy can be lifted by looking at these differences as tracers of planet formation processes (Muterspaugh et al . 2007 and references therein). These differences may manifest themselves as correlations that were already found, such as between the planet's mass and the binary separation (Desidera & Barbieri 2007), or some new correlations. These observational constraints can then allow us to look for the theoretical reason behind them in the micro-physics of planet formation (e.g. Téhbault, Marzari & Scholl 2006). Thus the differences between planets in binaries and planets around single stars can probe the formation process

Thirdly, the mechanisms that produce close binaries can be connected to those that produce planets (e.g., Fabrycky & Tremaine 2007) so observing planets in binaries immediately leads to better comparisons between the two processes since the formation conditions of both stellar and substellar companions were the same in such systems.

Next, as shown in section § 1.4, planetary transits have proven to be invaluable to the study of extrasolar planets, since transiting exoplanets allow for far more planetary parameters to become subject of observational studies; those suggested range from the obvious (planetary radii) through the impressive (temperature map of the planet , which was indeed done) to the bizarre (identification of artificial planet-sized objects) (see Winn 2009 and references therein for a longer list). So finding transiting CB planets can significantly improve the description of

− 28 − the individual systems as well characterizing the population of CB planets. Possible measurements include:

• Transiting planets around single stars are being followed-up with high-precision photometry and RV to the point that the uncertainties on the planet's properties are dominated by the uncertainties in the properties of the host star, not by instrumental precision (e.g., Johnson et al. 2009, Gillon et al. 2008 and discussion therein). For a transiting CB planet around an EB much better constraints on the planetary parameters can be obtained by using the much better constraints on the properties of the host EB.

• By detecting the inclinations of both the transiting CB planets and the host binary, it may be possible to test the predicted co-planarity of the two orbits. (While our sample is selected for near-coplanarity, it may be possible to detect small deviations, especially for long-period CB planets around short-period EBs).

• Orbits of close-in CB planet are expected to evolve on relatively short time scales (down to a few 100s of days - Schneider 1994) and this evolution may be detectable from the transits.

• Transiting CB planets produce not one but four distinct RM effects: when each star occults the other star and when the planet transits either one of the stars. Combining all these measurements can put stringent constraints on the geometry of the systems.

I therefore built a processing pipeline aimed at detecting transiting planets, both S- and P- type, in EB systems. I then began a study aimed at the detection of such systems to further our understanding of both the individual systems and the planetary population.

− 29 − 2.2. Previous Studies

2.2.1. Theoretical studies

As a population, CP planets are a lot like planets around single stars - and differences between the two populations can therefore be attributed to the presence of the distant binary companion. For (an extreme) example: if the companion is so close that CP orbits past the primary's ice line are not stable, giant planets should not be able to form. Therefore, finding giant CP planets is such systems can pose a great challenge to formation theories. (Such an extreme example was thought to have been discovered [Konacki 2005], but it was later shown to be a false detection [Eggenberger et al. 2007]).

CB planets are much less studied. CB planets are expected to form in CB discs, and indeed several CB discs are already observed (e.g., Duchêne et al. 2004, Monin et al. 2007). As early as 1994 Bonnell & Bate (1994) pointed out that the binary interaction with its (natal) CB disc promotes the disc's fragmentation and the creation of additional companions. They also found that the additional companions will, at least initially, have a nearly coplanar orbit with the original binary. Moreover, several theoretical works have investigated the migration and evolution of planets embedded in CB discs (e.g., Pierens & Nelson 2007, Quintana & Lissauer 2007 and references therein); these authors found that CB planets can grow and settle in stable orbits close to the host binary.

Holman and Wiegert (1999) have investigated the end-state of both CP and CB systems and show that planetary orbits in binary systems can remain stable for a surprisingly wide range of orbits, a range that in turn depends on the binary mass ratio and eccentricity. For example, a

CP planet in a circular and equal-mass system is stable out to a distance of 0.464 ab from the host component (where ab is the binary semi-major axis). A CB planet in a similar system may have a semimajor axis of only 2 ab and still be long-term stable.

To summarize: theory and simulations show that planets in binary systems can form and survive for long periods even in rather tight configurations, and are likely to be coplanar with their host stars. This is reason to be somewhat optimistic about the prospects for observing transiting planets around EBs.

− 30 − 2.2.2. Observational studies

CP planets: Even a single CP planet can be a challenge to theoretical models if found in a place theory predicts there should be none. Such was the case of HD 188753 (Konacki 2005), that was claimed to revolve around one member of a relatively close binary. So close is that binary, that there is no region between the two stars cold enough for the condensation of water, and as a consequence, ripe for the growth of giant planets. This claim posed a great challenge to formation theories, until it was later proven that the claim itself was unfounded and there is no evidence in the data for such a planet (Eggenberger et al . 2007). It is noteworthy that even in systems that have relatively narrow beyond-ice-line regions giant planets did manage to form (Hatzes et al . 2003), so the whole concept of "ice-line" as the most important discriminator between systems that can have giant planets and those that do not seem more likely.

Less extreme cases can constrain planet formation theories by their statistical distributions. For example already at least 17% of the known exoplanets are known to revolve around one component of a wide binary (Mugrauer & Neuhaeuser 2008). Desidera & Barbieri (2007) found that (S-type) planets in wide binaries have a mass distribution similar to that of planets around single stars, but planets in tight binaries (companions closer than 100-300 AU) are more massive. They conclude that only companions at this range of separations are able to modify the formation/migration/dynamical evolution history of the giant planets in the system.

CB planets: To date, there have been several announcements of the possible detection of a CB planet, none of them transiting:

• Correia et al. (2005) detected RV variation of HD 202206 consistent with a three- body system. Since RV is degenerate in the inclination angle i, at m

sin (i) = 17 4. M Jup the inner "planet" has a minimum mass heavy enough to border the planet - brown dwarf (BD) regime. Thus, if sin(i) is significantly less than unity, the outer planet may be considered as a CB planet around a stellar-BD binary, rather than a binary of two main-sequence stars. • Recently, eclipse timing (see § 1.3.5 for general timing variations discussion) was used to detect a few CB planet candidates: Lee et al. (2009), Qian et al. (2010) and Beuermann et al. (2010) discovered planet candidates around HW Vir (two planets - see Figure 15), DP Leo and NN ser (two planets), respectively, by measuring timing variations with amplitudes between 5.7 and 77 seconds. V471 Tau (Guinan & Ribas

− 31 − 2001, Kami ński et al . 2007) is also a strong candidate. All these objects are post- common-envelope binaries, made of a white dwarf and a main-sequence star. The large temperature differences cause deep and sharp eclipses, making the eclipses particularly suitable for precise timing. In § 2.3.3.4 I will discuss work relevant to eclipse timing made during this thesis.

None of these contain two main-sequence stars as binary components, none of them is transiting, and all are still only planet candidates because of the sin (i) degeneracy.

Figure 15. On the top panel: the observed-minus-calculates (O–C) diagram of HW Vir constructed with previously known linear ephemeris. The quadratic plus two-LITE ephemeris is drawn as the solid curve and the dashed parabola is due to only the quadratic terms. The second and third panels display the residuals from the quadratic term ( leaving both LITE signals) and the residuals from the quadratic term plus one LITE signal (leaving the last one) , respectively. The lowest panel shows the residuals from the complete model. In all panels, error bars are shown for only the timings with known errors (figure and caption adapted from Lee et al . 2009).

I note the only attempt to look for transiting CB planets before this study was the TEP project (Deeg et al . 1998, Doyle et al . 2000) which was focused mainly on one target: CM Dra, with a null result. TEP also tried to look for eclipse timing variation using the same data (Deeg et

− 32 − al . 2000, 2008), but the only candidate signal found was unconvincing (Ofir, Deeg and Lacy 2009).

In principle, the RV method can also be applied to the detection of CB planets. This is, however, more difficult than using RV to look for planets around single stars for a number of reasons: 1) The reflex motion induced by the planet on the host binary is smaller, as the central body is heavier than a single star. 2) Achieving high accuracy of the individual data points is more difficult since the disentanglement of the two sets of spectral lines is complicated, and imperfect disentanglement induces errors in the RV. 3) Since one has to solve a 3-body problem (two stars and a planet), and not just a 2-body problem, the number of data points that need to be taken per object is larger, making many-objects surveys more difficult. Still, the difficulties did not deter at least one group, and indeed a single dedicated RV survey for the identification of CB planets, aptly called TATOOINE 7, is in progress (Konacki et al . 2009), with no detections so far.

7 Tatooine is a fictional CB planet. It is the name of the home planet of Luke Skywalker, the hero of the classical movie: Star Wars.

− 33 − 2.3. Looking For Planets In Binaries In This Study

After establishing the importance of planets in binaries in general, and CB planets in particular, and combined with the striking lack of knowledge about them, I now advance to the core topic of this thesis: the attempt to change this state of affairs by identifying planets in binaries. For this reason most of what I had to say on this matter is already published and is part of Part 2 of this work. Below, I shall concentrate on making the logical connection between all my published papers, and add some material not present in these papers.

There were many possible sources for large photometric datasets at my disposal (see § 1.2). The various detection techniques discussed latter in this section assume that these are high- quality light curves with only white noise. However, this is never the direct output of the instruments, and both ground- and space- based data need significant pre-processing to reduce the level of systematic error before being committed to the detection algorithms. This pre- processing is described in § 2.3.1. Once the de-trended light curves are created, specific procedure for the detection of CP, CB and background planets are discussed in § 2.3.2, § 2.3.3 and 2.3.4, respectively.

However, the above logical order does not reflect the true order of how this thesis actually progressed. In reality, I first developed an algorithm for the detection of transiting CP planets (§ 2.3.3.2) and then wanted to apply it to CoRoT light curves. However, I found myself facing a wall of systematics that prevented detection. I therefore had to solve this problem, and developed a de-trending algorithm (§ 2.3.1 below). This turned out to be quite successful, so taking advantage of this unexpected progress actually took the rest of my time to the end of the thesis with significant results on that front.

2.3.1. De-trending

Planetary transits are usually considered as shallow signals, with small SNR (Signal to Noise Ratio ), and this is certainly true from the ground. Giant planets in space surveys could have very large SNRs, but these surveys usually aim at small planets, which cause shallow transit signals with lower SNR. Detecting these transits against randomly varying background is difficult, if not impossible, unless the noise is brought under control. However, Pont et al. (2006) showed that not only the noise level, but also the noise's color is very important. Red noise, or systematic noise, is devastating to transit searches: they create a huge population of

− 34 − false signals that clog the processing pipelines, hiding all but the deepest (and rarest) transits. Systematics in the data can never be completely avoided and one can model many systematic effects that relate to known physical processes (e.g. airmass, moon distance, moon phase, CCD temperature, etc). However, there are always un-modeled or poorly-modeled processes that still need correction. Fortunately, there are two algorithms for the identification and removal of systematic noises of unknown sources: SysRem (Tamuz et al. 2005) and TFA (Kovács et al. 2005). These algorithms allow one to take advantage of the large number of stars in each image to identify (and remove) any variability that is common to many stars simultaneously, and thus presumed to be non-astrophysical in nature.

The SysRem algorithm was further generalized during this thesis (See Ofir et al. 2010, paper # 3) to a technique called the SARS algorithm. SARS allows the inclusion of external parameters in a SysRem-like solution, simultaneously with the unknown effect. This enables one to disentangle the behavior due to known effects (e.g., air mass and temperature) in an explicit way, and to do that simultaneously with the detection of the next, as of yet unidentified source, effect. SARS turned out to be quite successful, and following its development I became a member of the general CoRoT detection group (vs. just for planets in binaries) and thus contributed to the detection of-, and became a co-author of-, currently 3 new CoRoT transiting planets (CoRoT-12b, -13b and -14b) and one transiting brown dwarf (CoRoT-15b). All are part of Part 2 of this thesis (Papers # 8 through # 11). The much wider scope of work that need to be done in order to actually arrive these successful detections is captured in a series of papers that are largely meant to document the work at done by the CoRoT science team (papers # 6, # 7, # 12 and # 13). I note that despite the many co-authors of the SARS paper (Paper # 3) it is entirely my own work. The only reason that all the CoRoT co- investigators (Co-Is) were added as co-authors was that the paper uses data that was proprietary at the time and CoRoT regulation require Co-Is co-authorship in such cases.

When using either SARS, SysRem or TFA one must remember that both algorithms expect that all light curves consist of only Gaussian noise + systematics, so the strong EB signal can cause the light curve to be very poorly corrected. Therefore the de-trending procedure must be applied on the residuals around some model or smoothed light curve iteratively and resulting in a better model after each pass. This procedure converges very rapidly, and can have a very significant impact on the quality of the light curve, as was indeed shown in Ofir, Deeg and Lacy 2009 (Paper # 2).

− 35 − 2.3.2. S-type Orbit

Detecting transiting planets in S-type orbits is fairly straight forward: as Holman and Wiegert (1999) showed, CP planets cannot survive unless their semimajor axis is smaller than 0.464 the binary semimajor axis. So the maximal PPlanet is shorter than Pbin /3. It is therefore expected that wherever there is a transiting CP planet, the stellar companion must be so far from the planet's host star that their mutual eclipses comprise only a small fraction of the data points, and that the binary components themselves are well-detached. Since the maximum span of the CoRoT data is 150 days, I identify long-period EBs in the CoRoT data as LCs with only a single deep eclipse. In order therefore to search for CP planets in these LCs I simply remove all in-eclipse points and apply the usual BLS to the remaining data. An example of such a long-period EB is shown on Figure 16.

Figure 16. A CoRoT target showing a single, deep, <5hr long eclipse in a 112d long near- continuous data. This target is almost certainly a long-period EB, with P>87d .

2.3.3. P-Type orbit

2.3.3.1. Modeling

Modeling EBs is a long standing problem in astronomy despite the fact that EBs are important to all field of astronomy, and that there are many EBs. Translating light curve to a model is a non-trivial reverse problem and usually requires a significant amount of human resources.

Despite these difficulties, there are already tools that allow non-experts to model well- behaved EBs. I already operate three EB modeling tools that allow me to model large fraction of the EBs population relatively quickly, especially if these are used in series as different tiers

− 36 − of complexity and accuracy. The DEBiL package (Devor 2004, 2005) is a completely automatic but limited package for analyzing detached EBs: it can reliably model only limb darkened spherical stars with no reflections or third light. Next in complexity is the JKTEBOP program (Southworth et al. 2004a,b) that can model little-deformed stars by using the EBOP (Etzel 1981, Popper & Etzel 1981) model (in which the stars are modeled as biaxial spheroids) taking also reflections, gravity brightening and third light into account. The most capable and accurate is the Willson-Devinney code (hereafter WD) (Wilson & Devinney 1971, Wilson 1979, 1990). I use its PHOEBE implementation (Prša & Zwitter 2005). PHOEBE allows to model nearly all types of EBs (from detached to overcontact) using the more physically accurate Roche geometry, with a host of other parameters including nonzero first period derivative, star spots, non-synchronous rotation, etc. Once an EB is modeled I can search for transiting CB planets in that EB's residuals, and non-transiting planets using eclipse timing (below).

I note that simply by looking for high quality raw data to produce high-quality EB light curves I am bound to find interesting systems among the many EBs. Indeed, I have already identified what seemed to be a quadruple systems of two pairs of massive EBs in the OGLE database, with orbital periods in 3:2 resonance, suggesting that the entire quadruple system is rather compact (Ofir 2008c, see more on § 2.4).

The method of identification depends on the geometry of the system, and differs for CP planets (S-type orbits) and CB planets (P-type orbits); for each configuration techniques that are in principal the same take on different emphasis. There are many detection techniques for planets in binaries: Some, such as RV, transits, microlensing (e.g.: Lee et al. 2008) and astrometry are common to planets around single stars. Some, like eclipse timing and even gravitational waves (Seto 2008) are unique to binaries. In this work I focus on transits and also, to a lesser extent, on eclipse timing.

2.3.3.2. Transit detection – circular orbit

Typical ground-based planetary transit discovery light curves have very low signal/noise ratios. Positive detections so far were obtained by folding the light curve on the correct period, which co-adds multiple events. Even with space-based data it is possible to discover the smallest planets only in phase-folded LCs. However, for the P-type planes that are the topic here no such phase-folding is possible (or beneficial) since the transit signal is no longer strictly periodic.

− 37 −

I thus developed CB-BLS (Ofir 2008, Paper # 1) to allow the detection of the complicated signal of transiting CB planets. I later further developed the CB-BLS technique to make it more sensitive, gave an analytical estimates for its detection limits, blind-tested it, and finally applied it to real data (Ofir, Deeg and Lacy 2009, Paper # 2).

2.3.3.3. Transit detection – eccentric orbit

This subsection describes further evolution of CB-BLS that has not yet been published. The concept: Since Papers # 1 and # 2 were published some progress has been made in generalizing CB- BLS to account for moderate planetary eccentricity. I refer the reader to these papers for a review of the CB-BLS algorithm, which I hereafter assume to be well known. Back in Paper # 1 the radius of the circular planetary orbit (in the appropriate units) is fully determined from the ratio of the planetary to binary periods (and a reference time). Since real 3-body systems do not move in circular (or even Keplerian) orbits, a correction factor to the effective semi- major axis was then introduced to deal with complicating elements such as the non-central potential which was meant to be a measure (close to unity) of just how Keplerian (or: non- Keplerian) the actual orbit is (note it was originally labeled " a" in Paper # 1, but we hereafter label it " S"). It was further emphasized in Paper # 1 that the then-current CB-BLS does not account for eccentric planetary orbits. I will soon use the S factor to this purpose exactly.

In general, there are two differences between circular and eccentric planetary orbits: 1) the radius of the orbit is not constant throughout the orbit, and 2) the orbital velocity is not constant throughout the orbit. Also, transit searches do not require a good description of the full planetary orbit: a satisfactory description of the orbit is required only for the part of the orbit that passes in front of the star (see Figure 17 between the vertical dotted lines in each panel). The combination of the above is that a transit detection algorithm can limit itself to trying to correct for the local radius and tangential velocity of the planet during transit and avoid describing the full eccentric orbit. Thus, one can re-interpret the multiplicative factor S as the describing the local radius S ≡ r a p (in panel A: the long-dashed line) which is the approximate radius when the planet passes in front of the star only (i.e., the long-dashed line and the ellipse have the similar local radii between the dotted lines) but with the same period. Now S may have values very different than unity as long as the underlying orbit is still stable (see below). Next, one can also use the knowledge of S (at each test orbit) to better constrain the local orbital velocity. At that point the employed model for planetary motion may not be a

− 38 − closed curve any longer: it can be a line with arbitrary start/end points, along which the planet moves once during each period. As long as the model crosses the system baricenter at the correct time and speed, it is photometricaly identical to the true eccentric orbit. This is an economical way of correcting for eccentric planetary orbits, accounting for both e and ω in a single degree of freedom. This is already built into the (circular) CB-BLS.

A B C

ap S⋅ap

α Figure 17. A schematic of CB-BLS with eccentric planetary orbits. The real planetary orbit is the solid ellipse, and its equivalent circular orbit (same semi-major axis, same period) is the solid circle. The host EB orbit is the filled ellipse, and the observer is assumed to be situated at the bottom. Panel A: only the part of the orbit that passes in fron t of the EB contributes to the transit signal (between the dotted lines), and therefore CB-BLS checks for planets having the same period but radii multiplied by S to match the local radius (long-dashed line). Panel

B: Highlighting the angle α - here at the minimal distance rmin geometry. Note

sin(α ) ≈ab / r = 1/ aS p . Panel C: Once the local transverse velocity VT is also known there is no need to model a closed planetary orbit.

In practice: I will now develop the explicit expressions for the local orbital radius and tangential velocity using the S correction factor, and the correct minimum/critical sampling of S: Local orbital radius : If the binary semi-major axis is defined as unity, the planetary semi-

2/3 major axis is ap= ( P p P b ) . The maximal and minimal distances of the planet from the host binary are rmin = (1− e)a and rmax = (1+ e)a (e.g.: see the minimal distance in panel B of Figure 17). From stability consideration the minimal distance should be larger than acrit (which is defined on Holman & Wiegert 1999 eq. 3). This means that the maximal a eccentricity is e =1 − crit and so the maximal distance is: r=2 a − a . Also, in order max a max crit to not miss any transit event, the discrete sampling of S should be such that the planet model displacements due to S would be smaller than the radius of the smaller component of the

− 39 − R two stars, i.e.: Ssin α = R or: S =min = R S (see panel B above). Thus the min sin α min multiplicative S factor above should span the range [ acrit /ap,2-acrit /ap] (or: r=[ acrit ,2a p-acrit ]) in logarithmic sampling.

Local orbital velocity : the local orbital radius relative to a focus of an ellipse is:

2 2 a p (1− e ) r (1− e ) r = , so we now have a geometrical expression: S ≡ = where ν is 1+ ecos ν a p 1+ ecos ν the ellipse's angular coordinate of the planet's orbital position. Also, the sky-projected (or: tangential), orbital velocity of the planet is: V = rθ& = ()1+ ecos ν where p is the semi- T p latus rectum, ≡ G(M * + M p ) , and M* and Mp are the total masses of the binary components and the mass of the planet, respectively. By setting e=0 we can use VT to find the

e=0 2π ap proper conversion from physical units to CB-BLS's system of ab ≡1: VT = = ap P p

2π 3/ 2 so = ap . Going back to eccentric orbits we find that Pp

1− e2 VT = 2 ()1+ ecos ν = . Since we have no knowledge of e we will use a p ()1− e a p S

1 2π ap the approximated value of VT ≈ = as our approximated result. To gauge the ap S PS p error in the last approximation we find the next non-zero order in the approximation is

2 ap e  VT ≈1 −  which is accurate to better than 10% up to e≅0.44, so that all but the S 2  most eccentric orbits are well-described (note that the linear correction with e is included in S). Now that we can describe both the location and the tangential velocity of the eccentric planetary orbit during transit using the S parameter, we no longer need the (anyhow superfluous) circular model: we can use a linear model for the planetary motion. This model will be similar to the true orbit during transits and very different from it otherwise but that discrepancy does not affect the light curve, and thus transit detection (see panel C). Using a linear model is also more computationally efficient.

− 40 − Finally, I note that VT can also be written exactly in terms of a conserved (but unknown)

2π 2 2 quantity: the orbital angular momentum of the planet: L= VT Sa p so L= ap 1 − e . Pp

2 3 2 2 4π a p 4π Also rV T = 2 ()1+ ecos ν = 2 ()1+ ecos ν . If in the future it will become possible Pp Pb to use L to better constrain e2, it will improve the detectability of high-eccentricity planets (most, if not all, approximations will turn into exact expressions).

2.3.3.4. Eclipse timing

As described in section § 2.2.2, P-type planets can be detected by eclipse timing of their host EB. In order to compute the precise mid-eclipse times and their errors I used the classical formulation of Kwee and van Woerden (1956) on a small part of the available data, mainly to test the performance of my code (the data was even not yet de-trended). A possible timing signal was found, but if it is from a 3 rd object the minimum mass is in the stellar range (Figure 18). It was therefore not explored further due to the lower priority of stellar triplets in the context of the current project. I note that the vastly better timing precision presented in § 2.2.2 was made possible by the careful choice of targets there: post-common-envelope objects have much deeper and far sharper eclipses than main-sequence EBs, as well as carrying out targeted observations optimized for these targets, that enabled the more precise timings.

I note that CoRoT 's theoretical timing accuracy is of the order of 4 to 15 seconds (depending on the target's brightness) (Sybilski et al . 2010). Factoring in the length of observing runs (maximum of 150d), one concludes that planet detection is rather borderline for CoRoT and probably limited to brown dwarfs only at the best cases. For this reason I did not invest a lot of time exploring this avenue.

Figure 18. CoRoT ID 0100805120 is a 2.27d EB observed during CoRoT LRc01. This figure shows the timing residuals of a linear model, clearly showing a cyclic period of about ~100 days. Timing of both t he primary eclipses (blue) and the secondary eclipses (green) is shown. The error bars are also derived using the Kwee and van Woerden (1956) technique.

− 41 − 2.3.4. Background objects

Sometimes an EB may have another star close to it (either as a hierarchical triplet or coincidentally near the line of sight) and that other object may have a transiting planet around it. The high precision of space-based photometry allows looking for these objects by examining the residuals of the EBs and applying standard techniques such as BLS. Indeed, I detected such a 13.48d signal in the residuals of a CoRoT ID 0102842120 which is a 1.1d EB observed during IRa01, the very first run of CoRoT (see Figure 19 ). This signal cannot be from an S-type orbit, and is strictly periodic, and therefore is probably not from a P-type orbit. We therefore concluded that this is a background object, and indeed another star can be found in the CoRoT aperture of this object. The shallowness of the signal (about 2mmag) implied that even if heavily diluted this signal could still come from an exoplanet, and this object got selected for FU.

However, since I joined CoRoT a long time after it was launched, FU observations of this object started very late, when transit ephemeris were already essentially lost. Combined with the fact that this star is relatively faint and a difficult target the FU was never completed, and only one RV point was taken. This eliminates some scenarios but does not solve the case.

Figure 19. Top: CoRoT ID 0102842120 data (after removing the long-term trends) phased to it's orbital period (blue) and a smoothed light curve (red). The high quality of the CoRoT data is apparent. Bottom, left: a transit-like signal is found in the residuals of the smoothed LC. Bottom, right: same, but zoomed-in.

− 42 − 2.4. Serendipitous discovery

Looking for planets in EBs required me to examine a large number of EB light curves. In the freely available OGLE catalogue 8 of EBs in the field of the Large Magellanic Cloud I noticed one particular EB that had a too-large dispersion, for its magnitude. Indeed, that EB appears to be a superposition of two EB-like signals in exactly 2:3 resonance (see Figure 20). Since this is highly unlikely to happen by chance, I concluded that the whole quadruple star system (two EBs) is an interacting and fairly compact system (Ofir 2008, Paper # 5).

This caused others (Kołaczkowski et al. 2010, Rivinius et al . 2010) to further investigate the system using the UVES spectrograph at the VLT, and they arrived at the conclusion that only one of the periods is actually an orbital period on an EB, while the cause for the second, synchronized, periodicity remains currently unexplained.

Figure 20. Top: the two disentangled EB-like signals found in the light curve of OGLE 051343.14-691837.1 as disentangled by Kołaczkowski et al . 2010 . Bottom: the observed signal. Note that in both panels the time/phase span is the super period of the two

periodicities: Psuper = 3⋅P1 = 2⋅P2.

8 http://ogle.astrouw.edu.pl/

− 43 − − 44 −

Part 2: The Papers

− 45 − List of Papers – Chronological Order:

Here in full text:

1. A. Ofir (2008): An Algorithm For Photometric Identification Of Transiting Circumbinary Planets; MNRAS 387, 1597. 2. A. Ofir , H. J. Deeg and C. H. S. Lacy (2009); Searching For Transiting Circumbinary Planets in CoRoT and Ground-Based Data Using CB-BLS; A&A, 506, 445. 3. A. Ofir et al . (2010); The SARS algorithm: detrending CoRoT light curves with Sysrem using simultaneous external parameters. MNRAS 404, L99.

Other papers:

4. G. A. Bakos et al . (including A. Ofir ) (2007): HAT-P-5b: A Jupiter-like Hot Jupiter Transiting a Bright Star; ApJ, 671L, 173B. 5. A. Ofir (2008): Two Pairs Of Interacting EBs Towards The LMC In The OGLE Database; IBVS No. 5868. 6. S. Carpano et al . (including A. Ofir ) (2009); Planetary transit candidates in CoRoT- IRa01 field; A&A, 506, 491. 7. J. Cabrera et al . (including A. Ofir ) (2009); Planetary transit candidates in CoRoT- LRc01 field; A&A, 506, 501. 8. M. Gillon et al . (including A. Ofir ) (2010); Transiting exoplanets from the CoRoT space mission XII. CoRoT-12b: a short-period low-density planet transiting a solar analog star; A&A 520, A97. 9. J. Cabrera et al . (including A. Ofir ) (2010); Transiting exoplanets from the CoRoT space mission: XVI. CoRoT-13b: a dense hot Jupiter in transit around a star with solar metallicity and super-solar lithium content; A&A, 522, A110. 10. F. Bouchy et al . (including A. Ofir ) (2011); Transiting exoplanets from the CoRoT space mission XV. CoRoT-15b: a brown dwarf transiting companion. A&A, 525, 68. 11. B. Tingley et al . (including A. Ofir ) (2010); Transiting exoplanets from the CoRoT space mission XIII. CoRoT-14b: an unusually dense very hot Jupiter. A&A accepted. 12. A. Erikson et al . (including A. Ofir ) ; Planetary transit candidates in the CoRoT-SRc01 field. In preparation. 13. L. Carone et al . (including A. Ofir ); Planetary transits candidates in CoRoT-LRa01 field. In preparation.

− 46 − Mon. Not. R. Astron. Soc. 387, 1597–1604 (2008) doi:10.1111/j.1365-2966.2008.13336.x

An algorithm for photometric identification of transiting circumbinary planets

A. Ofir School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

Accepted 2008 April 14. Received 2008 April 10; in original form 2008 March 3

ABSTRACT Transiting planets manifest themselves by a periodic dimming of their host star by a fixed amount. On the other hand, light curves of transiting circumbinary (CB) planets are expected to be neither periodic nor to have a single depth while in transit. These propertied make the popular transit-finding algorithm Box Least Squares (BLS) almost ineffective so a modified version of BLS for the identification of CB planets was developed – CB-BLS. We show that using this algorithm it is possible to find CB planets in the residuals of light curves of eclipsing binaries that have noise levels of 1 per cent and more – quality that is routinely achieved by current ground-based transit surveys. Previous searches for CB planets using variation in eclipse times minima of CM Dra and elsewhere are more closely related to radial velocity than to transit searches and so are quite distinct from CB-BLS. Detecting CB planets is expected to have significant impact on our understanding of exoplanets in general, and exoplanet formation in particular. Using CB-BLS will allow to easily harness the massive ground- and space-based photometric surveys in operation to look for these hard-to-find objects. Key words: methods: data analysis – binaries: close – binaries: eclipsing – planetary systems.

the correct period. In this paper, we will describe a method for the 1 INTRODUCTION detection of transiting CB planets in the light curve residuals of Since a large fraction, and maybe even most, stars form in mul- eclipsing binaries (EBs) – in much the same sense that the BLS al- tiple systems (e.g. Duquennoy & Mayor 1991), one may wish to gorithm (Kovacs,´ Zucker & Mazeh 2002 – hereafter KZM) is used investigate to relations between stellar- and substellar multiplicities. to find planets in the light curves of single stars. Indeed, already 27 of the known exoplanets are known to revolve This paper is organized as follows. In Section 2, we will briefly around one component of a wide binary1 (the so called S-type or- review the current literature about CB planets. In Section 3, we bit), and several works (e.g. Mugrauer, Neuhauser¨ & Mazeh 2007, will list the special difficulties one faces when trying to identify and references therein) have already investigated this relation. transiting CB planets, and give an algorithm that solves most of On the other end of the binary separation scale are binaries with them. In Section 4, we will present tests of an initial implementation periods of a few days, and sometimes shorter than a day. These of the algorithm on simulated data. Finally, in Section 5 we will short-period binaries are compact enough to allow for a theoretical discuss some of the implication of the proposed algorithm. planet to have a stable orbit outside and around both components (P- type orbit) – hereafter circumbinary (CB) planet. These objects are relatively unstudied, and the most serious attempt so far to detect 2 SHORT LITERATURE REVIEW CB planets was the TEP project (Deeg et al. 1998, 2000, 2008; To our knowledge, so far there have been three announcements of Doyle et al. 2000) which was focused mainly on CM Dra – but the possible detection of a CB planet – albeit none of which is none was found. transiting (in chronological order): Typical planetary transit discovery light curves have very low signal-to-noise ratios so positive detections so far were only ob- (i) Bennett et al. (1999) claimed the detection of a CB planet tained by co-adding multiple events by folding the light curve on via microlensing, but Albrow et al. (2000) later found that the light curve can be explained by a binary star where the binary orbital motion had been resolved by the motion of the caustics. E-mail: avivofi[email protected] (ii) Deeg et al. (2000, 2008) claimed that they were able to 1 As of 2008 February, from The Extrasolar Planets Encyclopaedia at detected non-linear changes in the observed − calculated (O−C) http://exoplanet.eu/. eclipse times of M dwarf EB CM Dra. They then fitted two models

C 2008 The Author. Journal compilation C 2008 RAS 1598 A. Ofir to the data – both including a planetary mass third body orbiting (a) CM Dra. We note that both of these fits critically depend on data 1 1 1 1 1 2 3 4 from a single epoch and are invalid without it. 0.995 0.995 0.995 0.995 0.99 0.99 0.99 0.99 1.6 1.7 1.8 1.9 2 2.1 2.2 9.2 9.3 9.4 9.5 9.6 9.7 9.8 16.9 17 17.1 17.2 17.3 17.4 17.5 24.6 24.7 24.8 24.9 25 25.1 25.2 (iii) Correia et al. (2005) had detected radial velocity (RV) 1 1 1 1

5 6 7 8 variation in HD 202206 consistent with a three-body system. At 0.995 0.995 0.995 0.995 = 0.99 0.99 0.99 0.99 m sin i 17.4MJup the inner ‘planet’ is heavy enough to border the 32.3 32.4 32.5 32.6 32.7 32.8 32.9 40 40.2 40.4 40.6 47.8 48 48.2 55.448.4 55.5 55.6 55.7 55.8 55.9 56 1 1 1 1

i 9 10 11 12 planet – brown dwarf (BD) regime. Thus, if sin is significantly 0.995 0.995 0.995 0.995 less than unity, the outer planet may be considered as a CB planet 0.99 0.99 0.99 0.99 63.2 63.4 63.6 63.8 70.9 71 71.1 71.2 71.3 71.4 78.471.5 78.5 78.6 78.7 78.8 78.9 79 86.1 86.2 86.3 86.4 86.5 86.6 86.7 around a stellar–BD binary, but probably not a CB planet orbiting 1 1 1 1 13 14 15 16 two main sequence stars. 0.995 0.995 0.995 0.995 0.99 0.99 0.99 0.99 93.9 94 94.1 94.2 94.3 94.4 94.5 101.6 101.7 101.8 101.9 102 102.1 109.2102.2 109.3 109.4 109.5 109.6 109.7 109.8 116.9 117 117.1 117.2 117.3 117.4 117.5 1 1 1 1

From the theoretical side, as early as 1994 Bonnell & Bate (1994) 17 18 19 20 0.995 0.995 0.995 0.995 pointed out that the binary interaction with its (natal) CB disc pro- 0.99 0.99 0.99 0.99 124.6 124.7 124.8 124.9 125 125.1 125.2 132.3 132.4 132.5 132.6 132.7 132.8 132.9 140 140.1 140.2 140.3 140.4 140.5 140.6 147.7 147.8 147.9 148 148.1 148.2 148.3 motes the disc’s fragmentation and the creation of additional com- (b) panions. They also found that the additional companions will, at 1 1 1 1 17 18 19 20 least initially, have a nearly coplanar orbit with the original binary. 0.995 0.995 0.995 0.995 0.99 0.99 0.99 0.99 Holman & Wiegert (1999) had found that CB planets can have 124.6 124.7 124.8 124.9 125 125.1 125.2 132.3 132.4 132.5 132.6 132.7 132.8 132.9 140 140.1 140.2 140.3 140.4 140.5 140.6 147.7 147.8 147.9 148 148.1 148.2 148.3 stable orbits in all binary configurations (i.e. at different mass ratios Figure 1. Panel (a): a gallery of 20 consecutive transit events of a system q and orbital eccentricities e) starting at some critical distance acrit identical to the Default System (see Section 4.2) but continuously sam- and farther out. Their simulations showed that acrit may be as low as pled. Events are numbered at the left-hand side of each subpanel. Note the 2 (in binary semimajor axis units) for near-circular binaries, and they highly variable durations and depths: all are purely geometrical effects (no also found that some configurations may be stable interior to acrit limb darkening). The (red) dashed vertical lines are uniformly spaced be- due to resonances. Closeness of CB planets to the host binary is an tween the first and 20th transit to show relative shifts of the times of transit. observationally desired attribute since such planets may complete Panel (b): the last four transits from panel (a) after regularization (see Sec- multiple orbits in the typical survey time-span of one observing tion 3.3). season. planet – largely determines the duration of the transits since they CB planets are expected to from in CB discs, and indeed sev- can move either parallel or anti-parallel to the planet’s own motion eral CB discs were already observed (e.g. Ducheneˆ et al. 2004; (enabling very long and very short transits, respectively). Monin et al. 2007). In turn, several theoretical works had investi- gated the migration and evolution of planets embedded in CB discs In short, the solutions for the photometric characteristics are: (1) (e.g. Pierens & Nelson 2007; Quintana & Lissauer 2007, and refer- regularizing the depths of all transits, and (2) allowing for different ences therein). These authors too found that CB planets can grow effective temperatures of the binary components. The solution for and have stable orbits close to the host binary. the temporal characteristics is to abandon the view that transits are To summarize, simulations show that CB planets can form and a function of time: One must recall that transits (and eclipses) are survive for long periods even rather close to their host binary, and not temporal phenomena, but rather geometrical phenomena – the are more likely to be coplanar with their host binary. This, in turn, alignment of celestial bodies. gives us some optimism as for the prospects of having transiting We remind that in the BLS algorithm, for each test frequency planets around EBs. one searches for the phases of the beginning and end of the transit signal in the folded light curve. For CB planets, the search is not in time or phase, but rather in orbital parameters space: for a given 3 IDENTIFYING TRANSITING CB PLANETS planetary (and binary) orbit, the projected distances between the planet and each of the stars are known, and occurrence of a transit 3.1 The problems and the solutions – general view is exactly true or false at each point in time (ignoring planetary Transiting planets manifest themselves by a periodic dimming of ingress/egress). One can then, similarly to BLS, fit a discrete-valued their host star. The efficient and popular BLS algorithm (KZM) function to the data – where all the in-transit and out-of-transit points relies on that periodicity, together with a simple two-level model of are already separated (see Fig. 2). The output is a multidimensional a (low signal-to-noise ratio) light curve. However, light curves of ‘periodogram’ – where the peak value corresponds to the best fit transiting CB planets are neither periodic nor do they have a single not only in orbital period, but also all other tested orbital elements. depth while in transit, from the following reasons [see Fig. 1, panel (a) for illustration]. 3.2 Preparing the light curves (i) Photometric characteristics. There is no single amount of We assume that the all light curves were already searched for pe- dimming of the stellar flux while in transit, since this amount de- riodic variables, but one should take great care in preparing these pends on the surface brightness of the hidden part of the binary light curves when trying to identify such a small signal under an components relative to the instantaneous total binary flux. Further- already varying background. more, the two stars repeatedly eclipse each other (changing the instantaneous total flux) and may be tidally distorted and/or have (i) All transit searches nowadays use some kind of detrending different surface brightness. [such as Syerem (Tamuz, Mazeh & Zucker 2005) or TFA, (Kovacs,´ (ii) Temporal characteristics. The transit signal is not periodic Bakos & Noyes 2005)] in order to reduce the scatter and systematics since each time the planet transits one member of the binary – that of the light curves. However, these algorithms expect that all light star is at a different position along the binary orbit, or it may transit curves are made of only Gaussian noise + systematics, so the strong the other member altogether. Moreover, transit durations are highly EB signal will cause the light curve to be very poorly corrected. non-uniform: the motion of the binary members – and not of the Therefore, the detrending procedure must be applied on the residuals

C 2008 The Author. Journal compilation C 2008 RAS, MNRAS 387, 1597–1604 Identification of circumbinary planets 1599

x 10 Folding a CB planet light curve in phase and in projected distance subtracted from the data light curve giving the residual light curve, 1 A and for brevity we will hereafter call that residual light curve just light curve. We will search for a transiting CB planet in this light 0 curve. x 10 x 10 (ii) Regularize the depths. To create a well-defined depth for the 0 0 transit regardless of the binary eclipses or ellipsoidal variation, we multiply the light curve (and the associated errors) with the model at all times, which means that all depths are now well defined as the amount of blocked flux relative to the maximum binary flux. For example, a Jupiter-like CB planet around a binary made of two normalized LC sun-like stars would create a 0.5 per cent transit at full binary flux, but a 1 per cent transit against full binary eclipse ∼ Pb/4 later. After regularization, all transits would be 0.5 per cent, regardless of B C binary phase (see Fig. 1, panel b). 0 0.1 0.2 0.3 0.2 0.25 0.3 (iii) Not having spectroscopic information, we assume a binary min (d1,d2) Phase mass ratio q = m2/(m1 + m2). For each tested q one can now derive

0 0.5 1 1.5 2 2.5 3 3.5 the sky-projected relative positions of each component, or specifi- min (d1,d2) cally: the X and Z position of each component in binary semimajor axis units at each moment of the time series. The coordinate system Figure 2. Fitting orbital models to the planet allows to ‘fold’ the light curve in projected distance from the members of the binary (labelled as is set up so that the origin is at the centre of mass, the Y-axis is d1 and d2). We plot (panel A, also zoomed-in on panel B) such a folding towards the observer, and the Y–Z plane contains the binary orbital of the default light curve (see the text) with very low white noise of only angular momentum vector. A condition for the correct binary mass 0.01 per cent to aid visibility. The regularized light curve is plotted against ratio sampling can be constructed: q will be such that between min(d1,d2) as derived from one model (only the half of the points where two adjacent q values the binary members will change their pro- the planet is in front of the stars are shown). Evidently, in-transit points are jected position by no more than one mean stellar radius. Since the well separated from out-of-transit points. The different surface brightness length unit is defined as the binary semimajor axis, q = mean(R)/ and sizes of the stars mean different depths and distances where transits (1 + e), where e is the binary eccentricity. We remind that q can begin to occurs, respectively. For comparison, a simple phase-folding of be very well constrained from independent sources (spectroscopy) the same data is given in panel C showing that in- and out-of-transit points and may need not be searched at all. are not well separated, significantly reducing the detectability of the signal. Note that for this plot, we use only the minimum projected distance – but (iv) For each stellar mass ratio we assume a certain planetary in CB-BLS more conditions sort out exactly which component is being orbit. In the simplest case of a circular CB planet with orbit exactly transited. coplanar with the binary orbit, one needs to assume f p, ϕ0 and a for planetary orbital frequency, orbital phase at the first data point and planetary semimajor axis (in binary semimajor axis units), respec- 2 around some model or smoothed light curve iteratively – each tively. Although it appears that a can be computed from Kepler’s time detrending better and generating a better model/smooth. This 2/3 laws by a = (Pp/Pb) (where Pp = 1/f p), effects of binary–planet procedure can have a very significant impact on the quality of the interaction cause the effective gravity at the planet, and so the semi- light curve. major axis, to be slightly different. One therefore needs to search (ii) Once final light curves are obtained, we assume that the for a better fitting a in a small range around Kepler’s laws value. In binary is accurately solved, probably with the WD code (Wilson addition, ϕ0 also has a natural scale which can be set similarly to & Devinney 1971; Wilson 1979, 1990) or one of its derivatives, the q condition: ϕ0 is set so the planet’s position will change by giving: Pb, T0, e, ω, i and R1,2 for binary orbital period, time of less than one mean stellar radius between adjacent ϕ0,or:ϕ0 = priastron passage (or time of primary eclipse for circular orbits), mean(R)/(2πa). In practice, one specifies a as multiples of Kepler’s eccentricity, inclination and stellar radii (as a fraction of the binary laws value (probably within a small range around unity), and the semimajor axis), respectively. desired phase resolution as a multiple of above ϕ0. (iii) Close binaries are not spherical in shape. CB-BLS will per- While eccentric binary orbits are already accounted for in the form better [see Section 3.3 step (v)] if this is accounted for by current implementation of CB-BLS, eccentric planetary orbits are pre-calculating the sky-projected shape of the components at each not accounted for in the current implementation. Eccentricity is binary phase in the data. expected to have limited impact since the part of the orbit were transits are possible is fairly small and so the effects of eccentricity + 3.3 CB-BLS will be usually small. The entire search space is then 1 (orbital model) dimensional, or between four- and seven-dimensional, as The algorithm we propose, which we dub CB-BLS has the following long as the low-mass planet approximation in maintained. We note steps. that the original BLS is a three-dimensional search. (i) The binary model and the data light curve are normalized (v) At each combination of q and planetary orbit, one can com- so that the maximum model flux is exactly 1. The model is then pute the projected position of all components, and so determine for each data point whether the planet was transiting either the primary or the secondary binary components. One can then compute the CB- 2 We have good experience with the Savitzky–Golay smoothing as imple- BLS statistic – which is a generalized version of the BLS statistic to mented in the MATLAB procedure SMOOTH: using it with a large window (5– a two-box BLS (see below). The best-fitting planetary system will 10 per cent of the phase) and polynomial degree of three or four usually be a peak in that ‘periodogram’ hyperspace, and the exact location gives excellent results. of the peak can be found by non-linear minimization.

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Since the binary components may have different surface bright- System 1j (1% white noise). Correct frequency=0.13d ness, the amount of flux blocked by the planet will depend on the binary component being transited. We therefore need to generalize 8 the BLS statistic from a two-level function to a three-level discrete 6 function, namely: H (out of transit) L1 (transit of the primary) and 4 L2 (transit of the secondary). For clarity, we use symbols similar (but not identical) to those in KZM. Let us denote the light curve of 2 N data points by {xn}, n = 1 ...N, and their respective zero-mean 0 { } and normally distributed errors
sn . The noise is accounted for by = −2 N −2 −1 assigning weights wm sm [ n=1 sn ] . It is further assumed 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 that {wnxn} have zero arithmetic average. As explained above, we know exactly which points are in transit in each of the test orbits: Frequency [d ] {x } are all points in transits of the primary star, {x } are all points i j 8 BLS in transits of the secondary star, and {xk} are all points out of transit. As in KZM, we sum of all weighted squared deviations 6    D = w (x − L )2 + w (x − L )2 + w (x − H )2. 4 i i 1 j j 2 k k (1) i j k 2

Minimizing D gives simple arithmetic weights as the best value 0 = = foreachofthelevelsL1, L
2 and H: L1
s1/r1, L2 s2/r
2 and −(s1+s2) H = ,wheres1 = xi wi ,s2 = xj wj ,r1 = wi 1−(r1
+r2) i j i = 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 and r2 j wj . Substituting into equation (1) gives   Frequency [d ] N 2 2 2 (s1 + s2) s s D = w x2 − + 1 + 2 . (2) Figure 3. An example of the periodograms of CB-BLS (top panel) and n n 1 − (r + r ) r r n=1 1 2 1 2 BLS (bottom panel) for one realization of System 1j (the Default System Minimizing D does not depend on the first term of the right-hand with 1 per cent added white noise). The CB-BLS peridogram was generated as described in Section 4.2. The CB-BLS periodogram has no significant side of equation (2), so the CB-BLS statistics is aliasing since the model fitted is not periodic. Note that the CB-BLS was (s + s )2 s2 s2 created just at the correct sampling limit, meaning that a denser sampling CB-BLS = 1 2 + 1 + 2 (3) 1 − (r + r ) r r or applying a non-linear search as described in Section 3.3, step (vi), will 1 2 1 2 somewhat increase the CB-BLS signal. On the other hand, the BLS signal Its maximum corresponds to the best-fitting planetary orbital is already oversampled because of the binning employed. model. One example of a CB-BLS periodogram compared to a BLS periodogram is shown in Fig. 3. It is evident that CB-BLS found the correct frequency with high significance, while BLS did better described with Roche lobe geometry. Still, this approximation not. is well suited for the current implementation of the algorithm since We note that the algorithm will work well even if the third body at the analysis stage (when it is determined for each point whether is a luminous star and not a (dark) planet since this information is it is in transit or not) it is assumed that the stellar radii are constant. already encoded in the binary model as ‘third-light’. We also note Therefore, the simulated data and the analysis method match in the that in the current implementation of CB-BLS the CB planet is sense explained in Section 3.2, step (iii), and Section 3.3, step (v). assumed to be a test mass that does not influence the binary, while For real data, while preparing the data one can calculate the different exactly this influence is the basis of both eclipse timing and RV. projected shapes of the binary components at each binary phase – This simplification is a source of noise for CB-BLS. and thus follow the algorithm (step v): at each data point one will still be able to determine whether the planet is transiting one of the binary components or not. In the end, pure Gaussian noise was 4 TESTS ON SIMULATED DATA added to the data. Since good modelling of EBs is not the topic of this paper, we use 4.1 Simulated data generation the same procedure that generated the data light curve to generate We integrated the three-dimensional motion of three point bodies the binary model with exactly the same input values – only with the under mutual gravitational interaction for ∼150 d, and generated transit signal excluded from the output. In essence this is the perfect simulated light curve for that period (more below). The uniform model – and modelling errors will indeed be a limitation to CB-BLS time-steps (50 s) were far smaller than the typical exposure time of (see also discussion on Section 5). We also choose not to simulate photometric surveys and continuous so only every eighth simulated limb darkening (although the Mandel and Agol formalism allows point was used to simulate a 400-s duty cycle. Next we removed for limb darkening) since later, at the analysis stage, these effects all points meeting modulu(JD) < 0.8 − sin (π JD/150)/8, (where should be anyway modelled out by the binary model and will not JD is the simulated time in days) simulating the lengthening and add new information on the accuracy of the proposed algorithm. On shortening of nights during the 150 d observing season. All the the other hand, purely geometrical transits allow fewer distracting light curves below are therefore almost 9000 data points long. The effects when introducing a new algorithm as in this paper. For a light curves are generated from the 3D positions using the Mandel graphical illustration of the effects of limb darkening, see fig. 1 & Agol (2002) formalism, so their main limitation is that the stars of Deeg et al. (1998). Finally, using the Mandel & Agol formalism are assumed spherical. This spherical model will probably be only prevented us from computing accurately the geometrically complex approximately true for such short-period binaries since they are case of the planet partially transiting both stars simultaneously (see

C 2008 The Author. Journal compilation C 2008 RAS, MNRAS 387, 1597–1604 Identification of circumbinary planets 1601 a) b) Search grid density. Since in-transit points are only a few per cent

1 of the planetary orbit the density of points in the f p axis has to 0.9 0.9 be smaller than a few per cent of the Nyquist resolution (∼1/span), 0.8 0.8 = 0.7 0.7 so we set f 1/span/100, where span is the time-span of the 0.6 0.6 data, ∼150 d in the simulations. For the semimajor axis factor a 0.5 0.5 0.4 0.4 any significant deviation from unity has a physical meaning so a 0.3 0.3 first guess of a = 1 may not be bad at all. We note that a range of 0.2 0.2 0.1 0.95–1.07 can be derived for several systems simulated by Holman 0 0 0.5 1 & Wiegert (1999) (last three columns of their table 4). The last step is to straighten the periodogram (remove the typical Figure 4. Geometrically complex relative positions where it is difficult to long-periods rise). We iteratively fit a low-order polynomial and account for the contribution of the transit of the occulted star. Panel (a): part clip to 2σ , which finds the ‘backbone’ of the periodogram. The of the planet’s disc transits both stars, and the rest is not transiting either resultant polynomial is subtracted from the periodogram, and the star; we avoided this rare position. Panel (b): all the planet’s disc transits result is divided by the σ of the last iteration, effectively making both stars: in the uniform-disc simulations this case is treated well, but the treatment is only approximated if limb darkening is included. the periodogram values equivalent to the signal detection efficiency metric (SDE) from KZM. This procedure allows direct comparison between different period-searching algorithms. Fig. 4, panel a). Being quite rare, this configuration was simply The tests begin with measuring the binary period Pb (using avoided in the simulations. AoV Schwarzenberg-Czerny 1989) and T0 (weighted average of the times during one eclipse weighted by the depth). We then use the model values for the orbital elements and R1,2 to complete the 4.2 Tests CB-BLS inputs about the binary. The frequency range searched = We simulated several systems varying different system parameters for is between f p 0.02 (to allow three full periods within the = in order to explore the properties of CB-BLS. We tabulate the data time-span) and f p 0.2. The latter is approximately four times the sets used in this paper in Table 1, and use the data set names binary period, which translates to ∼2.5 times the binary semimajor mentioned there in the following text. Each system was realized axis – close to acrit for a stable orbit for a CB planet (Holman & 50 times with random white noise and, unless specified otherwise, Wiegert 1999). We measure the performance of CB-BLS and BLS the results below are the median result of 50 similar realizations. by a correctness statistic: the fraction of realizations that had the The Default System is the ‘easiest’ since it is very close to the highest peak of their periodogram within a small region around the circular, coplaner model this implementation of CB-BLS searches correct value. for. The Default System is a binary made from two equal total luminosity stars – a primary with mass of 1.1 M, and radius of 1.1 R and a secondary with mass and radius of 0.9 M and 0.9 R 4.2.1 Changing signal-to-noise ratio (i.e. the latter has higher surface brightness). The system centre of Systems 1a–1t are the Default Systems with added white noise with mass is at the origin. The binary orbit is circular with period P = b an amplitude of σ = 0.1–2 per cent, respectively. Fig. 5 shows the 1.234 56 d. correctness as a function of the amplitude of the added white noise. The Default CB planet has mass of 0.001 M and radius of Clearly, BLS finds the correct frequency only for the very high- 0.1 R, and a period of P = 7.890 12 d. The photometric signals p est quality light curves – with correct identification falling below are therefore ∼0.4 per cent and ∼0.6 per cent deep for the transit of 50 per cent already at noise levels of ∼0.8 per cent, while CB-BLS the primary and secondary components, respectively. P specifies p maintains that performance through noise levels of ∼1.6 per cent both the distance and velocity of the planet at T = 0: at that instant a or more (to be compared with the ∼0.4 and ∼0.6 per cent transits). point mass at the origin with the combined mass of the binary would Since in a typical survey there are many more targets with mediocre induce a circular planetary motion with period P . All three object p quality than there are with the highest, millimag-precision targets – are on the X-axis at initialization, and the planet is on the positive the impact on the possible CB planet yield is significant. X side and moving towards the observer, so the initial planetary orbital phase ϕ0 ≈ 0.75. Note that the planet does not move in a circular orbit since it is pulled by two moving bodies. Correctness vs. Noise Level (Systems 1) 1 Most of the tests below are two-dimensional searches on fp and = BLS ϕ0, where the mass ratio is set on its correct value of q 0.45, 0.8 and the semimajor axis factor is at the default value of a = 1 (for more details on the dependence of CB-BLS on q, a,andϕ0,see 0.6 Section 4.4). We did not try to look for the absolute maximum using non-linear searches. 0.4

0.2 Table 1. Simulated systems. Fraction of correct detections Fraction 0 −3 ◦ System name Noise (10 ) Pp (d) i ( ) 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Noise level Default 0 7.890 12 90 1a–1t 1–20 7.890 12 90 Figure 5. For 50 realizations of each of Systems 1a–1t, and for a small 2a–2f 10 [9–19].890 12 90 region around the correct frequency (0.129 < f p < 0.131), we plot the 3a–3h 10 7.890 12 89.75, 89.5–88 correctness versus the amplitude of added white noise for CB-BLS (solid blue line) and BLS (red dashed line).

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Correctness vs. P (Systems 2) 4.3 Short comparison with algorithm by the TEP network p 1 The anonymous referee correctly pointed out that a comparison with BLS 0.8 the transit detection algorithm used by the TEP project (Doyle et al. 2000 – hereafter the TEP algorithm) is needed. Since a thorough 0.6 comparison with the TEP algorithm is beyond the scope of this paper, we only list a few points in lieu. 0.4 (i) Both algorithms assume for each test orbit a planet in a circu- 0.2 lar, edge-on and coplanar orbit with the binary. Fraction of correct detections Fraction (ii) In the TEP algorithm, transit events are fitted individually on 0 6 8 10 12 14 16 18 20 each night’s data, which is reliable only for relatively strong transit P [d] p signals – a limitation not present in CB-BLS. (iii) The TEP algorithm requires multiple fits – as many fits as Figure 6. For 50 realizations of each of Systems 1j, 2a–2f, we plot the correctness statistic versus planetary period. The reason for the reduced there are transit events in each test orbit – and these will add noise to the detection statistic. CB-BLS requires only a single fit for each performance of both BLS and CB-BLS at the Pp = 13.890 12 d is that this period happens to have a particularly bad window function with less than test orbit. one-third of the in-transit points relative to the Default System. (iv) In the TEP algorithm, each test orbit is used to produce a model light curve which is then matched to the data. This requires additional modelling (e.g. planetary radius, limb darkening, etc.) – again adding noise to detection statistic. In CB-BLS no further 4.2.2 Changing Pp modelling is required, and the depth(s) are analytically found from Systems 2a–2f are based on the Default System with 1 per cent the data. added white noise, but with different planetary periods such that (v) In-transit data points carry far more information about the for System 2a Pp = 9.890 12 d, and each subsequent System Pp is planet than out-of-transit points. However, the TEP algorithm can- longer by 2 d. These systems, together with System 1j (which has not handle the longest transits if there are not enough out-of-transit the same noise level and the a 7.89012 d period) – are plotted in points in a given night (e.g. see events 2, 7, 9, 14 and 19 in Fig. 1). Fig. 6. The main effect of the increased period is the reduction of Since these events contain numerous data points and are in part the total number of in-transit points, making the signal detection also deeper than other in-transit points, the TEP algorithm therefore more difficult. Still, CB-BLS is superior to BLS and maintains a gives up on a very valuable portion of the in-transit points. This ∼50 per cent correct detection ratio all the way to Pp ≈ 20 d. limitation is not present in CB-BLS. It should be noted, however, that the TEP algorithm was adapted to process a fairly inhomo- geneous data set originating from several different telescopes, and with strong extinction effects due to the red colour of their target 4.2.3 Changing i star (CM Dra) relative to all available comparison stars. Systems 3a–3h are based on the Default Systems with 1 per cent To summarize, the TEP algorithm can be applied to the detec- added white noise, only with different inclinations of the planetary tion of transiting planets around single stars, and it was already orbit between 90◦ and 88◦ (while transits no longer occur at ∼87◦.5 rigorously compared to other such algorithms (Tingley 2003a, and and ∼87◦ for the smaller and larger binary components, respec- especially Tingley 2003b) and was found to be inferior to BLS. tively). The binary star is still exactly edge-on in these systems. Since CB-BLS and BLS have very similar statistical properties, we Fig. 7 depicts the correctness for these systems and one can see that believe that the TEP algorithm will be inferior to CB-BLS when CB-BLS almost always find the correct period even when the fitted applied to CB planets. model becomes increasingly inaccurate with decreasing inclination. On the other hand, BLS never finds more than half of the systems. 4.4 Other results and notes We observed the following properties and results of CB-BLS. (i) To show the behaviour of the CB-BLS statistic along the other Correctness and Significance vs. Inclination (Systems 3) axes: q, a and ϕ , we used one realization of the Default System 1 0 with 1 per cent added white noise. CB-BLS produces a very sharp peak on the ϕ0 axis, and the global maximum indeed corresponds 0.8 BLS to the correct ϕ0, q and a with good precision (see Fig. 8). Note that no error analysis was carried out and the quoted uncertainties are 0.6 only a very rough estimate. (ii) CB-BLS takes about 10 times longer to execute (for every 0.4 value of q) than BLS. While BLS can be implemented with a com- putational shortcut (binning in phase) that shortcut is useless for Fraction of correct detections Fraction CB-BLS since the analysis is performed in time, not phase. There- 0.2 90 89.8 89.6 89.4 89.2 89 88.8 88.6 88.4 88.2 88 fore, binning the light curve in time is indeed possible, but it will Inclination [deg] cause correlated noise to have increased effect on CB-BLS, and it Figure 7. For 50 realizations of each of Systems 1j, 3a–3h, we plot the may cause high dilution of some of the shorter transit events. correctness statistic versus planetary orbital inclination. Note that edge-on (iii) Since some of the transits of a CB planet are be extremely is to the left-hand side. long we noticed that in the Default System in-transit points make

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x 10 large number of test orbits are fitted to the data there is a nonvan- 1.2 ishing probability that even good candidates may be consequences

0.8 1 of random sequences of transit-like noise features. (iv) Spectroscopic confirmation of a candidate transiting CB 0.8 0.6 planet is expected to be relatively expensive in telescope time since

q 0.6 one should follow the system long enough to allow for the three 0.4 orbits to be disentangled. The lower false positives fraction will 0.4 allow this high cost to be tolerable. 0.2 0.2 (v) Following up on CB planet may be particularly interesting

0 since these systems have orbital evolution on relatively short time- 0.8 1 1.2 0 0.5 1 scales (a few 100 s of days e.g. Schneider 1994), and they produce a phase not one but four distinct Rossiter-McLaughlin effects (e.g. Gaudi Figure 8. Left-hand panel: contours of CB-BLS in the mass ratio – semima- & Winn 2007): whenever star 1 occults star 2 and vice verse, and = +1 = +0.04 jor axis plane. The peak is at q 0.48−11 and a 1.07−0.15 (where the error whenever the planet transits either one of the stars. ranges are at 90 per cent the peak level), while the correct values are 0.45 and 0.99, respectively. The nine contours are linearly spaced, so the error ranges are approximately at the boldfaced contour. For illustrative purposes, both 5 DISCUSSION parameters were sampled at a high resolution of 0.01. Right-hand panel: a We have presented a modified version of the popular BLS algorithm cut of CB-BLS in the ϕ0 axis and through the global maximum. The peak is at the correct value 0.75. tailored for the detection of CB planets. We have shown that it is superior to BLS for this task, and that using this algorithm it is possible to find CB planets in the residuals of EBs that have noise up 3.5 per cent of the data points (Including ingress and egress). levels that are routinely achieved by current ground-based transit Note that this fraction is almost twice as high as the correspond- surveys. ing fraction for a planet around a single star with the same pe- The algorithm is based on fitting planetary orbits to the data riod – alleviating the difficulty of finding planets with longer and then applying the CB-BLS statistic. Although more general periods. in principle, we have shown that the simplest edge-on, coplanar (iv) As illustrated in the left-hand panel of Fig. 8, the CB-PER and circular model is rather effective as an identification tool (i.e. statistic is somewhat convoluted on small scales, but the main struc- versus characterization). We have shown that CB-BLS maintains tures are relatively apparent on large scales. This means that while high correct identification rate even when the noise level increases, caution will be needed, sampling CB-BLS on larger scales first or the planetary period increases, or when the planetary orbital (the resolutions recommended and used in this paper) to find the re- inclination is no longer edge-on. gion(s) of promising maxima, and then zooming-in on these regions On the limitations side, the simple fact that the transits need to be seems like a good way to perform a more efficient search. discerned against the background of two stars can not be changed. Another possible limitation is EB modelling: since CB planets are We list below a few notes and expectations about CB-BLS. found in the residuals of EB light curves, the modelling must be (i) CB planets generate signals in a wide range of durations of very high quality to allow for the detection of the added weak and depths, possibly reducing effects of red noise (Pont, Zucker signal. & Queloz 2006) and so false detection rates. Detecting CB planets will have significant impact on the field (ii) By looking at eclipse time variation one may deduce infor- of extrasolar planets studies as it will expand the possible environ- mation similar to RV measurements. In principle, such a signal will ments for planet formation significantly. Issues such as migration, allow to obtain all the information available in photometery and stability and planet-disc interaction will have to be further investi- RV from the same single light curve. One important consequence gated in the context of close binaries. Moreover, since the objects in of the above is the ability to reduce the false-positives fraction of question are short-period binary stars, detecting such planets may the final candidates list: while CB planets can produce only very have repercussion on the much more established field of close bi- small eclipse time variation signal, systems with heavier substellar nary stars (for the closest of which the formation process still not or low-mass stellar tertiaries may produce much larger signal, and well understood even without the added complexity of planets). so may be identified as such already from the initial light curve. We If orbital near-coplanarity is common, then EBs are already pre- comment that such detected systems, with three massive objects in selected to be near edge-on. This means that, keeping all things very tight configuration, are interesting systems in their own right. equal, the specific ‘value’ of an EB for the planet hunter is much We note that light time effect was not included in the current imple- higher that of a single star. Thus, if one needs to select targets mentation of CB-BLS and a different analysis tool will be needed (e.g. the Kepler and CoRoT space missions) and one aims to find as for that task. many planets as possible – one may wish to monitor as many EBs (iii) An important source of difficulty for transit surveys is the as possible. presence of a number of transit-mimicking phenomena, causing the So far, no wide-scale searches for transiting CB planets were candidate list to be contaminated by a large fraction of false pos- conducted. We believe the null result of the TEP project is partly itives. We believe that CB-BLS will have a lower yield of false due to the fact that it preceded many important advances in the field positives than searches on single stars from two reasons: firstly, of transiting exoplanets (the Sysrem, TFA and BLS algorithms to the model we fit is very specific and will probably not fit systems name a few). Later, the same data was used to look for variation in that are not truly three-bodied. Secondly, some of the mimicking eclipse times minima of CM Dra (Deeg et al. 2000, 2008). Since in systems may be identified as such already from the discovery data this technique one observes accelerations along the line of sight, it thanks to light time effects (see above). However, one should re- is much more closely related to RV than to transit searches and so member the TEP project’s warning (Doyle et al. 2000) that when a is quite distinct from transit searches.

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In recent years the rate of transiting planets detection increased Deeg H. J., Ocana˜ B., Kozhevnikov V. P., Charbonneau D., O’Donovan dramatically because of the experience gained in doing high rela- F. T., Doyle L. R., 2008, A&A, 480, 563 tive precision wide-field photometeric surveys. Using CB-BLS will Doyle L. R. et al., 2000, ApJ, 535, 338 allow to easily harness these massive ground- and space- based Ducheneˆ G., McCabe C., Ghez A. M., Macintosh B. A., 2004, ApJ, 606, surveys to look for transiting CB planets. 969 Duquennoy A., Mayor M., 1991, A&A, 248, 485 Gaudi B. S., Winn J. N., 2007, ApJ, 655, 550 ACKNOWLEDGMENTS Holman M. J., Wiegert P. A., 1999, AJ, 117, 621 Kovacs´ G., Zucker S., Mazeh T., 2002, A&A, 391, 369 (KZM) I thank the anonymous referee for the constructive comments that Kovacs´ G., Bakos G., Noyes R. W., 2005, MNRAS, 356, 557 improved the paper. I Acknowledge support from Tsevi Mazeh Mandel K., Agol E., 2002, ApJ, 580, L171 during earlier stages of work in this field. I Acknowledge using the Monin J.-L., Clarke C. J., Prato L., McCabe C., 2007, in Reipurth B., Jewitt freely available3 N-body integrator by Howard E. Motteler. D., Keil K., eds, Protostars and Planets V. Univ. Arizona Press, Tuscon, 395 Mugrauer M., Neuhauser¨ R., Mazeh T., 2007, A&A, 469, 755 REFERENCES Pierens A., Nelson R. P., 2007, A&A, 472, 993 Pont F., Zucker S., Queloz D., 2006, MNRAS, 373, 231 Albrow M. D. et al., 2000, ApJ, 534, 894 Quintana E. V., Lissauer J. J., 2007, in Haghighipour N., ed., Planets in Bennett D. P. et al., 1999, Nat, 402, 57 Binary Star Systems. Springer, Heidelberg, in press (arXiv:0705.3444) Bonnell I. A., Bate M. R., 1994, MNRAS, 269, L45 Schneider J., 1994, Planet. Space Sci., 42, 539 Correia A. C. M., Udry S., Mayor M., Laskar J., Naef D., Pepe F., Queloz Schwarzenberg-Czerny A., 1989, MNRAS, 241, 153 D., Santos N. C., 2005, A&A, 440, 751 Tamuz O., Mazeh T., Zucker S., 2005, MNRAS, 356, 1466 Deeg H. J. et al., 1998, A&A, 338, 479 Tingley B., 2003a, A&A, 403, 329 Deeg H. J., Doyle L. R., Kozhevnikov V. P., Blue J. E., Mart´ın E. L., Tingley B., 2003b, A&A, 408, L5 Schneider J., 2000, A&A, 358, L5 Wilson R. E., 1979, ApJ, 234, 1054 Wilson R. E., 1990, ApJ, 356, 613 Wilson R. E., Devinney E. J., 1971, ApJ, 166, 605

3 http://www.csee.umbc.edu/∼motteler/teaching/courses/parallel prog/01a/nbody/nbody.html This paper has been typeset from a TEX/LATEX file prepared by the author.

C 2008 The Author. Journal compilation C 2008 RAS, MNRAS 387, 1597–1604 A&A 506, 445–453 (2009) Astronomy DOI: 10.1051/0004-6361/200911861 & c ESO 2009 Astrophysics The CoRoT space mission: early results Special feature

Searching for transiting circumbinary planets in CoRoT and ground-based data using CB-BLS

A. Ofir1,H.J.Deeg2, and C. H. S. Lacy3

1 School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel e-mail: [email protected] 2 Instituto de Astrofisica de Canarias, C. via Lactea S/N, 38205 La Laguna, Tenerife, Spain 3 Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA

Received 17 February 2009 / Accepted 20 May 2009

ABSTRACT

Aims. Already from the initial discoveries of extrasolar planets it was apparent that their population and environments are far more diverse than initially postulated. Discovering circumbinary (CB) planets will have many implications, and in this context it will again substantially diversify the environments that produce and sustain planets. We search for transiting CB planets around eclipsing binaries (EBs). Methods. CB-BLS is a recently-introduced algorithm for the detection of transiting CB planets around EBs. We describe progress in search sensitivity, generality and capability of CB-BLS, and detection tests of CB-BLS on simulated data. We also describe an analytical approach for the determination of CB-BLS detection limits, and a method for the correct detrending of intrinsically-variable stars. Results. We present some blind-tests with simulated planets injected to real CoRoT data. The presented upgrades to CB-BLS allowed it to detect all the blind tests successfully, and these detections were in line with the detection limits analysis. We also correctly detrend bright eclipsing binaries from observations by the TrES planet search, and present some of the first results of applying CB-BLS to multiple real light curves from a wide-field survey. Conclusions. CB-BLS is now mature enough for its application to real data, and the presented processing scheme will serve as the template for our future applications of CB-BLS to data from wide-field surveys such as CoRoT. Being able to put constraints even on non-detection will help to determine the correct frequency of CB planets, contributing to the understanding of planet formation in general. Still, searching for transiting CB planets is still a learning experience, similarly to the state of transiting planets around single stars only a few years ago. The recent rapid progress in this front, coupled with the exquisite quality of space-based photometry, allows to realistically expect that if transiting CB planets exist – then they will soon be found. Key words. methods: data analysis – stars: variables: general – stars: planetary systems – occultations – binaries: eclipsing

1. Introduction binaries in about 1% of the stars surveyed (Almenara et al. 2009), leading to a sample of about 300 close binaries from its Bound binary stars are one of the most common environments first year of operation. Assuming that a planetary orbit would be in the Galaxy. Studying planet formation and evolution without roughly aligned with a binary component’s orbital plane, EBs accounting for binary (and multiple) star systems is surely in- constitute a sample with planetary orbits being preferentially complete – so we aim to try to fill-in observational data on these aligned to display transits across the host stars. types of systems. To help achieve this goal, a Binaries Working Group was formed within CoRoT Exoplanets Science Team of There are many detection techniques for planets in bina- ries: some are common to planets around single stars (such the CoRoT space mission (Baglin et al. 2006) to coordinate the different searches for planets in binary systems, and we report on as: radial velocity (RV), transits, astrometry and microlensing, one of the activities within the Working Group, namely – tran- Muterspaugh et al. 2007; Lee et al. 2008) and some are unique to binaries (such as: eclipse timing, Deeg et al. 2000, Lee et al. sit searches using the CB-BLS algorithm (Ofir 2008, hereafter Paper I). These efforts are now all the more relevant following 2009; and gravitational waves, Seto 2008). Generally speak- the recent detection by Lee et al. (2009) of an eclipse-timing ing, in each geometry (i.e., circumstellar or circumbinary orbits) techniques that are in principle the same take on different em- signal compatible with two circumbinary planets around HW phasizes. Virginis. Planets around eclipsing binaries may be expected in sig- In this paper we will focus on transits of CB planets, nificant numbers, since CoRoT finds close and deeply eclipsing and specifically transiting CB planets around eclipsing bina- ries (EBs). The transit signal from CB planets is not periodic, Based on observations obtained with CoRoT, a space project op- hence common techniques searching such signals are of low ef- erated by the French Space Agency, CNES, with participation of the ficiency and special search algorithms have to be employed, such Science Programme of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, as CB-BLS (Paper I) or TDA (Doyle et al. 2000). In the follow- Germany and Spain. ing we list the accumulated additions to CB-BLS since Paper I

Article published by EDP Sciences 446 A. Ofir et al.: Searching for transiting circumbinary planets using CB-BLS in Sect. 2, describe blind tests to CB-BLS in Sect. 3, and show 2.1. CB-BLS with a single depth examples from the first application of CB-BLS to real data in Sect. 4, and conclude. If the EB surface brightness ratio J is known (and J is a natural output of most, if not all, EB modeling tools) then the depth ratio between transits in front of the primary and the secondary 2. Accumulated additions to CB-BLS EB components will also be J, and Eq. (1) in Paper I can then be re-written with just a single fitted depth as (note the last term): The following describe additions to the CB-BLS implementation   starting from the version used to generate the results of Paper I 2 2 D = wk(xk − H) + wi(xi − L) (internally designated as version 0.51) till now (version 0.83). k i While the basic idea of orbit fitting remains unchanged, the spe-  + w − 2. cific implementation has improved significantly in search sensi- j(x j JL) (1) tivity, generality, speed and results analysis. To avoid extensive j repetitions, we assume in the following that the reader is familiar Here we approximate L2 from Paper I to JL, which is an approx- with Paper I. We note that we plan to release the CB-BLS source imation to the correct value of J(L + H). The approximation is MATLAB code (written in ) in the future. CB-BLS now: good as long as |H||L|, which is the case for low duty-cycle – Allow the inclusion of the surface brightness ratio (J)inthe signals such as transits. As in BLS (Kovács et al. 2002, hereafter input, which increases sensitivity. See more in Sect. 2.1. KZM) and CB-BLS Paper I, minimization allows to analytically – Allows natural use of the more accurate Roche-lobe geome- compute H (unchanged) and L (revised):

try. All the user has to do is to specify the surface potentials −(s1 + s1) s1 + Js2 Ω , – which are the direct outputs of EB modeling – in- H = , L = (2) 1 2 1 − (r + r ) r + J2r stead of the radii. CB-BLS then computes the 3D shape of 1 2 1 2 the surface, rotates the shape to the binary inclination, and where the r1,2 and s1,2 are simple sums of the data and the computes the silhouette of the sky-projected shape at each weights as in Paper I. Plugging these to D gives: binary phase. CB-BLS allows single-surface binaries (con-  (s + s )2 (s + Js )2 tact binaries) too – which are common. We note that this fea- D = w x2 − 1 2 − 1 2 · (3) n n − r + r + 2 ture was forecasted in Paper I (Sect. 3.2) and is implemented n 1 ( 1 2) r1 J r2 along these lines. We comment that using this feature slows CB-BLS significantly. Similarly to BLS and to paper I, the first term on the right hand side is constant, leaving the rest as SR – the new CB-BLS statis- – Accounts for EB inclination. The EB orbital inclination − is calculated anyhow during the EB modeling, so the 2D tic (times 1): (instead of 1D, as in Paper I) sky-projected orbit for each (s + s )2 (s + Js )2 component is computed – and the 2D distance from the test SR= 1 2 + 1 2 · (4) − + + 2 planetary model found. The planetary orbit is still assumed 1 (r1 r2) r1 J r2 edge-on, but this is a good approximation since the planet is The use of J, together with the use of Roche geometry, EB incli- farther away from the baricenter than the EB components, nation and the directional correction, are all attempts to use all and so it’s alignment requirements are more stringent to be- available knowledge about the host EB and the expected tran- gin with. sit signal shape to reduce the number of free parameters. For – Enables the simultaneous solution of multiple light curves of this reason CB-BLS uses the simplest possible box-like tran- the same system, each with it’s own EB model – which also sit model and concisely avoids even slightly more complicated allows one to use multi-band data in a single run. Since after models that requires an additional free parameter (such as the regularization (see Paper I Sect. 3.3) the transit signal should trapezoidal transit model, limb darkening, or the other effects be nearly achromatic – the CB-BLS statistic can be calcu- mentioned at the end of the previous section). Note however, lated using all the regularized residuals – regardless of band. that the EB model itself can be as complicated as needed – as We note that performing a multi-band solution and using the long as it stays a pre-processing step to CB-BLS it does not add (single) surface brightness ratio J are mutually exclusive. free parameters to the CB-BLS fitting process. – Includes the directional correction (Tingley 2003) – ignores negative depths. – Includes a set of utilities: detection limits estimator (see 2.2. Estimating CB-BLS detection limits Sect. 2.2), CB transit predictor, non-linear optimization. Giving robust estimates for detection limits of CB planets is dif- – Has better visualization of results for analysis, and has im- ficult. A full analysis needs to account for all the effects known proved robustness, better speed optimization, more input from planets around single stars, and for a number of additional control, bug fixes etc. significant sources of noise, for example: EB modeling errors, – Allows one to output all the computed CB-BLS values (and which are system-dependant and introduce systematic errors of not just the maximal one for each orbital period) to properly unknown magnitude. We believe that such a full analysis can account for the sample of fitted models (Ofir, in prep.). only be done with extensive simulations on a system-by-system We stress that CB-BLS is a detection algorithm, and as such – basis. Still, as long as the approximations assumed in Paper I concisely avoids many complicating elements that are known still hold, especially that the CB planet moves in a circular and to affect the shape of the transit light curve, including: stellar edge-on orbit and that the noise is purely Gaussian, one can for- limb darkening, motion of EB components along the line of mulate an analytic detection limit. Figure 1 shows the side- and sight (the very basis of RV and eclipse timing techniques), plane- front- (or observers-) views of the geometry of one component tary orbital eccentricity and obliquity, non-Keplerian (especially of an EB, explaining the different symbols used below. Newtonian) motions, etc. The reason none of these is accounted We begin by considering the effective transit√ Signal/Noise δ for is discussed in the last paragraph of the following section. ratio for single stars defined by KZM: αsingle = σ Nd where δ A. Ofir et al.: Searching for transiting circumbinary planets using CB-BLS 447

that L can vanish completely when a cos(ib) > R (i.e., the planet passes above/below the binary component without transiting it). We note that a should scale differently for the primary and sec- ondary components according to their mass ratio q,andthata is itself a function of binary phase: each component will have the maximum chord length of 2R at the orbital nodes (where a = 0), and lower values – as low as L of Eq. (7) – at other times. To bet- ter estimate L the time-averagea ¯ for each component should be Fig. 1. Geometrical layout of one component (marked “Secondary”) of determined, which for circular orbits (and L > 0 at all times) is  2/3 an EB for the estimation of CB-BLS detection limits. The Primary is 2 ap Pp a¯ = ab. Using Kepler’s third law = and substituting shown only for easyer understanding of the layout. Symbols used are: π ab Pb ib for the binary orbital inclination, a for the radial projection of the back one finds that: component’s distance from the center-of-mass, h for the maximum pro-    /   jected distance of the component above the line sight (or more exactly: R P 2 3 a¯ cos(i ) 2 d = b 1 − b · (8) above the plane containing both the line of sight and the line of nodes), πa P R and the angle β between a stellar radius and the chord L across the stel- b p lar disk cut by the above plane (boldfaced). For each of the binary components the R anda ¯ will be different, so Eq. (8) can give both d1 and d2 – to be substituted back into is the transit depth, σ is the dispersion of the LC, N is the num- Eq. (6). ber of data points and d is the transit duty cycle – the fraction of Since i, J, Pb, N,σand the ratios: R/ab and R/a¯ are all given in-transit data points. If the surface brightness ratio J is known by the EB model and the LC, we now have a detection limit δ then one can extended α to transiting CB planets; we remind the as a function of only our empirical choice of αCB and the EB reader that after regularization the transit depths are only two geometry model – depending only on the planetary period Pp. discrete√ values with a ratio of J. We therefore rearrange to get We note that the derived detection limit is for the best-detectable δ Nd = ασ. In order to account for the√ fact that two stars can be configuraton of planetary orbits, which are those that are copla- nar with the line of sight and at the same position angle as the transited, we change the left side to δ N(d1 + d2)whered1, d2 are the individual on-transit duty cycles of the components, and EB’s orbit. Finally, we remark that relaxing the Gaussian noise requirement may be achieved by quatifiying the correlated noise in order to account for the different depths of the two compo- (e.g. as σ in Pont et al. 2006) and adding it to the σ used in the δ2 + δ2 r nents, we make the following changes: N(d1 1 d2 2), to give formulation above. a final definition of δ  α = + 2 3. Blind tests to CB-BLS CB σ N(d1 d2J )(5) where δ is the regularized depth of the primary transit. When CB-BLS was subsequently blind-tested using a detached EB ob- investigating detection limits one must first define what “detec- served during the initial run of CoRoT (CoRoT ID 102806577). Note that the data were not detrended in any way. Notably, tion” is. Using the general guidance of Fig. 6 on KZM for αsingle, corrobated by our experience from the Blind Tests of Sect. 3, CoRoT’s orbital period was not removed from the data. (where e.g. “Test3” with α = 11 was near the limit of detectabil- Therefore, the tests are done in the presence of strong systematic ity, see Fig. 4), we estimate that robust detections usually have noises. The “examiner” (HD) created the test data in four steps: α ≥ 10−12. We then use the α definition to get (1) removal of a constant slope apparent in the data and conver- CB F − F /F F σα sion to relative flux units ( 0) 0,where 0 is an average of δ =  CB (6) the out-of eclipse flux. The test LCs contain 7213 data points. (2) 2 N(d1 + d2 J ) generation of a model light curve (LC) of the EB and removal of , this model from the data; (3) on the residuals, suppression of the we now need to find d1 d2. For a particular system the duty cy- noise1 in a band-pass of periods between 5 h and 12 h. Random cles depends significantly on the exact relation between the or- noise of similar amplitude was then inserted in that band-pass. bits of the two binary components and the CB planet – a small / This band-pass corresponds to periods a few times longer than change in the ephemeris can lead to the drastically longer and or the typical duration of transits events; their detectability should shorter transits. We therefore wish to avoid this problem and therefore not be affected. Also, periodograms of the lightcurves consider only the average detection power at a particular plane- before and after this operation were compared in order to assure tary orbital period. In analogy to the transit duration calculation that the overall noise characteristics did not change significantly; around single stars, the average duty cycle for each of the two L (4) adding to the previous data a model LC that consists of the components is d = π where L is the transit chord lenght of a 2 ap EB model of step (2) together with a simulated circumbinary planet whose orbital plane is spanned by the line of sight (i.e., planet, using the UTM transit simulator (Deeg 2009). Steps (3) = ◦ ip 90 ) and the line of the component’s nodes, as shown in and (4) were repeated six times, simulating different planets in Fig. 1. step (4). Since in Fig. 1 the height h can be found from both the side The CB-BLS “solver” (AO) then received the six test LCs = h β = h view as: cos(ib) a and from the front view as: sin( ) R one designated Test0 through Test5, and parameters of the physi- obtains the relation:  cal model of the system. The solver then independently solved   the LC using JKTEBOP (Southworth et al. 2004a,b) and applied a cos(i ) 2 L = 2R cos(β) = 2R 1 − b (7) R 1 This step disables “detections” based on simple subtractions between the various test light curves, all of which had been generated from the where a is the radial projection of the component’s distance from same original. For test-sets based on different originals, this step would the center-of-mass (for the definition of a, β, h see Fig. 1). Note not be necessary. 448 A. Ofir et al.: Searching for transiting circumbinary planets using CB-BLS

1.02 A B

1 0.05

0.98 0.04

0.96

0.94 0.03

0.92 0.02 Relative flux variation 0.9

0.01 0.88

0.86 0

0.84 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2595 2600 2605 2610 2615 2620 2625 2630 2635 2640 2645 Phase CoRoT date Fig. 2. Panel A): LC of the EB used in the blind tests (dots) and its JKTEBOP model (line). This LC is the Test5 LC which has no planet added to it. Panel B): the residuals of the six test LCs from Test0 (top) to Test5 (bottom). Each successive residuals LC was shifted by 1% to aid visibility.

Table 1. Main EB- and CB planet-parameters that affect the planet’s for limb darkening – but since these none of these features are transit. derivable from CB-BLS they are not given in this comparison. While simple phase-folding the LC will not separate well Parameter Value Unit in- and out- of transit points (which is the motivation behind Period 3.6670288245 [d] CB-BLS), a “folded” graphical representation of the CB planet’s Inclination 86.6699982 [deg] transits is possible (and instrumental for signal analysis): in- R1 1.856 [R] transit points are expected when the sky-projected distance be- R2 0.6838 [R] tween the planet and one of the components is closer than L1 14.620 [L] that component’s radius. For that reason the data can be folded L2 0.2500 [L] against the minimum distance of the planet from each of the EB RMS of residuals ∼1.3 [mmag] components – and that distance is scaled by that (i.e., the closer) star’s radius. The result is that all in-transit points are expected Test0 Rp 1.09 [RJ] below scaled-distance of 1, and all out-of-transit points are ex- Test1 Rp 0.95 [RJ] Test2 R 0.78 [R ] pected at scaled-distances grater than 1. Figure 5 shows the LC p J of Test3 folded in this way, which can also serve as an illustration Test3 R 0.79 [R ] p J for the ability of CB-BLS to detect even shallow transits signifi- Test4 R 0.95 [R ] p J cantly. Note that this simulated planet caused only three primary R R Test5 p none [ J] transit events, where a primary transit is only ∼1.4 mmag deep (to be compared with rms dispersion of 1.3 mmag). Scaling this depth to 1 R (and ignoring the much-fainter secondary compo- nent) gives 0.39 RJ – smaller than all known transiting planets CB-BLS. For the CB-BLS analysis, only the mass ratio was used but the unique super-Earth CoRoT-7b (Léger et al. 2009). As out of the full physical model. As written in Paper I, if the mass seen in Fig. 3 the Test3 LC is significantly detected, but is not ratio is not known – it can simply be searched-on as a free pa- far from the limit of reliable detection. Indeed, one can also ap- rameter. Figure 2 depicts the EB itself with the JKTEBOP model ply the detection limits procedure (Sect. 2.2) to the CoRoT test (from the Test5 LC), and also the six residuals LCs. Note that the LC too – and Fig. 4 shows these for various αCB values with residuals have some structure, meaning, they have some corre- the detected signal for reference – and the detected signal is in- lated noise – as expected in real data. In Table 1 we list some of deed just above or just below the detection limit, depending on the EB’s and simulated planets’ physical model parameters that the choice of αCB. With the successful detection on all test sig- most affect transit detection. Note that the RMS of the residu- nals and the agreement between the theoretical detection limits als is about 1.3 mmag. We comment that each of these CB-BLS and actual detection, we conclude that CB-BLS passed the blind analyses take approximately 2 min on a 3 GHz PC (using the tests successfully and is ready for use on real data. natural parameter resolutions presented in Paper I), so process- ing time is neglible, given the small number of targets relative to constant stars. 4. Application of CB-BLS to real data The six tests signals were such that Test0 was relatively 4.1. TrES Lyr1 field easy and not blind (it was used primarily to make sure the test The photometry of the TrES survey Lyr1 field (O’Donovan procedures are working) – but still the simulated system was et al. 2006; Dunham et al. 2004) is freely available at the a physically-possible system, while Tests 1–5 were completely NASA NStED website2, but this photometry is after TrES’s blind. Figure 3 shows the resultant CB-BLS periodograms and Table 2 gives the resultant best CB-BLS fits values. All six test 3 The possible detection levels are: “+++” (Strong and secure), “++” LCs were correctly identified, where notably Test5 was correctly (Probable. Noisy), “+” (Weak detection) and “no planet”. identified only when the single-depth SR of Sect. 2.1 was used. 4 The depth of the secondary transit is omitted since it is simply J Note that the simulated planets had their the inclination and po- times the primary transit. sition angle varied to some extent and that their LCs also account 2 http://nsted.ipac.caltech.edu/ A. Ofir et al.: Searching for transiting circumbinary planets using CB-BLS 449

SDE of Test0 SDE of Test1 SDE of Test2 10 10 10

8 8 8

6 6 6

4 4 4

2 2 2

0 0 0

−2 −2 −2 0.04 0.06 0.08 0.1 0.12 0.14 0.04 0.06 0.08 0.1 0.12 0.14 0.04 0.06 0.08 0.1 0.12 0.14

SDE of Test3 SDE of Test4 SDE of Test5 10 10 10

8 8 8 no planet

6 6 6

4 4 4

2 2 2

0 0 0

−2 −2 −2 0.04 0.06 0.08 0.1 0.12 0.14 0.04 0.06 0.08 0.1 0.12 0.14 0.04 0.06 0.08 0.1 0.12 0.14 Orbital frequency Fig. 3. The straightened periodograms of the blind tests – to be read together with the input and output values specified on Table 2. The correct frequency is marked with a dashed vertical line. The highest frequency ( f ∼ 0.136 d−1) corresponds to a period just twice that of the binary – near the instability limit. The periodograms are normalized to the their own rms (as described in Paper I) – thus, a value of 5 is a 5σ detection of a certain period.

Test LC Detection Limits For Different α −3 contributes ∼11 000 data points of the total ∼15 000 of the TrES x 10 CB 1.8 Lyr1 dataset. 1.7 12 Here we present our first application of CB-BLS to pho- tometry from a real wide-field survey and the following pre- 1.6 11 processing scheme is the template for our future applications of 1.5 CB-BLS. The main difference between the scheme below and the corresponding pre-processing steps of other transit searches 1.4 10 is the ability to not only detrend intrinsically-constant stars but 1.3 also to detrend variable stars by iteratively detrending their resid-

1.2 uals. This approach was first proposed by Kovács et al. (2005) for their reconstructive TFA algorithm of transit signals, but here 1.1

detection limit (rel. flux) we aim to de-trend EBs, which show large variety of variations, 1 and so – the bin-averaging method proposed by Kovács et al. (2005) is ill-suited for the current problem. The pre-processing 0.9 has four main stages: 0.8 5 10 15 20 25 30 Planetary period (d) 1. Determination of the systematic effects: This is very simi- α = , , lar to what is done routinely on transit surveys. Firstly, out- Fig. 4. Detection limits for 10 11 12 of the CoRoT test LC (sold lier data points are removed form all light curves by sigma lines) and the Test3 signal as it was detected (from Table 2). clipping each light curve around a small-window (5 points) median filter. Next, we wish to determine a few SYSREM effects (Tamuz et al. 2005) – but we must make sure that variable stars are not part of the set of stars that is used detrending, and so can’t be used as-is for our purpose. We there- to determine the effects. To that end we use the Alarm fore asked the above authors for the raw photometry of the same statistic (Tamuz et al. 2006) as a general variability statis- data, and we process below only the raw Sleuth data – which tic (used similarly to the Stetson J statistic, Stetson 1996)in 450 A. Ofir et al.: Searching for transiting circumbinary planets using CB-BLS

Table 2. The input values of the simulated CB planets (“Examiner” rows) and their respective solution (“Solver” rows).

3 Test Attribute Detection Period Baricenter Depth In-transit αsingle Comment dataset [d] crossing (primary4) points [CoRoT JD] [mmag] Examiner 13.54 2594.54 4.683 Test0 Solver +++ 13.545 2594.525 4.768 148 44.0 Not blind. Examiner 12.673 2563.567 2.749 Test1 Solver +++ 12.667 2595.251 2.494 145 22.8 A bug (since then fixed) caused the detected reference time to be when the planet crossed the baricenter behind the EB system, causing a half-integer difference (2.5 periods) from the correct one. Examiner 13.08 2594.54 1.853 Test2 Solver +++ 13.091 2594.513 1.560 248 18.6 Examiner 17.748 2597.54 1.901 Test3 Solver +++ 17.738 2597.571 1.349 132 11.7 Examiner 12.673 2563.567 2.749 Test4 Solver +++ 12.652 2595.295 2.579 143 23.4 See comment to Test1 Examiner no planet – – – Test5 Solver no planet – – – 0 0 A very weak signal was ini- tially suspected before using the single-depth analysis. That pe- riodogram peak completely dis- appeared when this feature was added and used.

−3 x 10 4

3

2

1

0

−1 normalized LC, binned −2

−3 0 10 20 30 40 50 60 minimum (d1,d2)/R(star @ min d) Fig. 5. The Test3 LC residuals folded against scaled-distance for the best-fit model (see text for details). Readers who are familiar with phase- folded LCs can view of this figure as yet another fold of the LC about the center of the transit, so that both ingress and egress fall on scaled-distance ∼1, and all in-transit points are expected below scaled-distance of 1 (to the left of the vertical dashed line). To aid visibility the data is binned to 0.1 units of this scaled-distance. Despite the fact that Test3 was the shallowest signal in this blind tests series CB-BLS clearly separates in-transit from out-of-transit points.

the following manner (Note that in general Alarm will have in each iteration the effects must be always computed from a smaller value for less-systematic input): 1) we compute the same raw data and not from the SYSREM-corrected data. Alarm for all stars; 2) we determine the sub-set of constant This procedure also improves the signal-to-noise ratio of the stars using an Alarm maximal value that corresponds to the SYSREM effects. For the TrES Lyr1 data we used the final bulk of the stars (i.e., many stars that change similarly, so set of constant stars to calculate the three SYSREM effects, they probably don’t have intrinsic variability). See Fig. 6 for with ultimate precision similar to that of the TrES survey. an example; 3) the SYSREM effect(s) are computed using 2. Detrending variable stars: The constant stars allowed us only this subset of constant stars (one effect in the above ex- to determine the systematic effects well – and from now ample) and the correction is applied to all the stars, 4) alarm on the effects are assumed known and will not be changed. is re-computed. Since now the bulk Alarm distribution is nar- To correct variable stars for these systematic effects we rower (e.g., main panel of Fig. 6) it allows to better filter true will have to apply the same correction determined above variables – so using a lower Alarm maximal value the set to the residuals around the smoothed LC of the target vari- of constant stars is re-determined. Steps 2–4 can be repeated able star by iteratively smoothing the target LC, detrend- several times till the set of constant stars converges. Note that ing the residuals, adding back the corrected residuals to the A. Ofir et al.: Searching for transiting circumbinary planets using CB-BLS 451

250 80 TrES Lyr1 02432

13.3 60 13.35 200 40 13.4 13.45

20 13.5 150 13.55

0 Magnitude 13.6 0 20 40 60 80 100 13.65 No. of objects 100 13.7

13.75

13.8 50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Phase Fig. 7. Two light curves of star 02432 from the TrES Lyr1 field. Bottom, 0 0 10 20 30 40 50 60 70 80 Red LC: the light curve as posted on the public NStED database: it was Alarm detrended with no special care for intrinsic variability. Top,BlueLC: Fig. 6. Histogram of the Alarm statistic for 1000 objects (all objects the same raw data processed as described in the text – with cleaning in some magnitude range) of the TrES Lyr1 dataset. The insert shows procedures applied only to the residuals. Note that transit detection in the lower part of the Alarm distribution before the first iteration for LCs such as the red LC is nearly impossible. variable-stars filtering (see text). After we used only stars with Alarm < 35 to calculate one SYSREM effect – the Alarm distribution of the same objects looked as shown on the main panel.

previous smooth and then re-smoothing the LC, till conver- gence While this procedure is sensitive to the exact smooth- ing technique, when the smoothing parameters fit well for a given LC the results are quite significant for transit detec- tion (see Fig. 7), and allow us to reduce the scatter of the LC around the model to the same level as the scatter of LCs of constant stars of similar brightness. 3. EB solution: Light curves for eclipsing binaries in the Lyr1 field were analyzed by the NDE model. Errant observa- tions were picked out by eye and eliminated before analysis. Accurate dates on minima were determined from the data by using the method of Kwee & van Woerden (1956). The re- sulting periods and zero epochs are listed in Table 3, along with the fitted orbital parameters. In most cases, the fitted light curves were relatively insensitive to the assumed values of the limb-darkening coefficients (xp and xs) and to the mass ratio (q), which was guessed based on preliminary values of Fig. 8. More examples of the EBs from the TrES Lyr1 field. These the light ratio. 5 of the 17 light curves showed significant EB LCs were generated using the process discussed in the text for the eccentricity. proper detrending of variable stars. This, together with good model- 4. Generation of final EB LC: Almost identically to the ing, resulted in extremely small systematics in the residuals across the > “Detrending variable stars” step – the raw LC is detrended 11 000 data points. The object ID at the top of each panel is the NStED using the solved EB model. Now the model is final so multi- designation. ple iterations are not needed.

Figure 8 depicts further examples of EBs from the TrES Lyr1 field, showing that the generation of multiple near-systematics- free EB light curves from wide-field transit surveys using the We comment that since there were about 7000 objects in the procedure above is indeed possible. The low level of systematics relevant magnitude range one may expect about 70 EBs to be will help CB-BLS to be less likely to find spurious signals. All in present in the data, and thus a yield of two dozen EBs may seem all, about two dozen detached or semi-detached EBs were bright too low. However, a similar number of EBs were actually iden- enough (similarly-bright constant stars had ultimate precision of tified but prioritized very low and not processed further (such ∼ 2%) to be processed as above. Of the two dozen EBs identified as EBs with long periods, grazing EBs, EBs with low SNR, 17 were fitted, and for 8 of them planet detection seemed possi- EBs with additional signals overlaid, non-eclipsing contact EBs, ble (the other EBs exhibit either low inclination angles, evidence etc.). Considering that further EB’s were missed due to the win- of spots or period change), and CB-BLS was applied – but we dow function – the total fraction of EBs seems roughly compat- α = did not detect any significant signal. The CB 12 detection ible with CoRoT’s ∼1% above. limits for each of the objects are given in Fig. 9.

5 The other columns are: the period P and reference epoch E0 (in HJD-2 453 000), the surface brightness ration Js, the primary, secondary light, primary and secondary components L3, Lp and Ls, the linear limb- darkening coefficients x = x , the mass ratio q = ms , the rms of the data radii and their ratio rp, rs and k, the orbital eccentricity, inclination and p s mp argument of periastron passage i, e and ω, the light fraction of third around the model σ, and the number of data points used in the fit N. 452 A. Ofir et al.: Searching for transiting circumbinary planets using CB-BLS

Table 3. Results of fitting light curves of bright EBs from the TrES Lyr1 field. Boldfaced star names (NStED ID) indicate that CB-BLS was subsequently applied.

Star ID 5 PE J r r kieω L L L x , x q = ms σ N 0 s p s 3 p s p s mp [d] [JD-2 453 000] [ab][ab] [deg] [deg] [mmag] 00442 1.0620113 544.9157 0.577 0.252 0.180 0.714 85.3 0.045 -90.3 0.042 0.775 0.225 0.60 0.863 7.255 11011 00822 2.42759 562.8633 1.03 0.157 0.190 1.21 79.6 0.004 -100.0 0 0.397 0.603 0.60 1.0 7.112 11028 01199 2.696428 555.7985 0.374 0.174 0.083 0.477 90 0.003 -63.0 0.032 0.922 0.078 0.60 0.5 7.804 10997 01679 1.401052 551.8386 0.103 0.292 0.216 0.74 66.5 0 0 0.239 0.947 0.053 0.60 0.67 7.288 11151 02303 1.387197 546.7336 0.049 0.280 0.100 0.358 79.6 0.072 83.8 0 0.994 0.006 0.60 0.368 7.978 11074 03705 4.703549 560.7989 0.793 0.113 0.071 0.63 85.5 0 0 0 0.760 0.240 0.60 0.95 10.146 11072 03708 0.428355 552.7032 0.95 0.377 0.354 0.94 60.9 0 0 0 0.55 0.45 0.60 0.95 14.256 11087 03793 3.472262 545.7911 1.005 0.113 0.100 0.88 87.4 0 0 0.32 0.56 0.44 0.48 0.95 9.754 11148 04063 0.876825 549.8667 0.000 0.398 0.179 0.45 69.7 0 0 0.153 1.000 0.000 0.60 0.29 11.848 11096 04826 1.25042 596.8055 0.302 0.240 0.155 0.65 80.8 0 0 0.20 0.89 0.11 0.60 0.85 10.674 10410 05140 0.903320 554.9364 0.010 0.339 0.203 0.714 84.8 0 0 0.249 0.996 0.004 0.60 0.65 24.129 10214 05911 0.2932419 545.7257 0.66 0.395 0.355 0.90 58.4 0 0 0.625 0.656 0.344 0.60 0.95 14.555 10679 05926 0.7085494 545.8493 0.075 0.455 0.329 0.72 55.4 0 0 0 0.964 0.036 0.60 0.80 14.249 10597 06613 0.7445117 546.8838 0.54 0.55 0.44 0.80 41.8 0 0 0 0.75 0.25 0.60 0.80 16.191 11095 06825 1.801803 551.9185 0.133 0.264 0.242 0.917 88.9 0.205 88.6 0 0.887 0.100 0.40 0.70 18.272 10647 07919 6.5233411 549.9007 0.272 0.260 0.249 0.956 67.3 0 0 0 0.792 0.208 0.60 0.40 18.067 10426 08329 1.322684 593.8688 0.090 0.302 0.186 0.615 89.3 0 0 0 0.967 0.033 0.60 0.60 17.262 9690

CB planets Detection limits − TrES Lyr1 0.022 08329 0.02 06825 0.018

0.016 03705 0.014 04826 04063 0.012

0.01 03793 02303 0.008 01199 detection limit (rel. flux)

0.006

0.004

0.002 0 5 10 15 20 25 30 35 40 Planetary period (d) α = Fig. 9. The CB 12 detection limits for each of the TrES EBs marked Fig. 10. Some of the open literature EBs to which the CB-BLS analysis in Table 3 – i.e., the smallest depth of primary transits caused by a was applied. Each EB light curve is phased to it’s orbital period with hypothetical CB planet in the systems that is expected to be reliably the best-fit model over plotted and the model residuals drawn below. detected with CB-BLS. The detection limit was calculated as explained in Sect. 2.2. The planetary periods used are from twice the host EB period to half the survey time span. Light curves of WW Cam (Lacy et al. 2002) and V1061 Cyg (Torres et al. 2006) were taken from the literature and fitted by 4.2. Other targets the NDE model (Etzel 1981; Popper & Etzel 1981) as described While wide-field transit surveys such as CoRoT will probably be above. LC parameters for those stars are listed in the referenced the main source of EBs for future CB-BLS analyses (as demon- articles. Light curves of V432 Aur (Siviero et al. 2004)and strated above), there are currently a number of open literature pa- BP Vul (Lacy et al. 2003) were also taken from the literature pers on EBs that have a long enough and accurate enough LCs and fitted with JKTEBOP – giving LC parameters similar to the to possibly allow the detection of transiting planets. These pa- ones listed in the referenced articles. In Fig. 10 we plot the above pers focus on the EBs and so have the added benefit of having LCs together with their best-fitting model and model residuals. the EBs (usually) fully analyzed – including spectroscopic de- We applied CB-BLS to these systems too but did not detect any termination of the mass ratio q (which allows us to remove one significant signal. free parameter, and shorten the CB-BLS run time). Note that for some of these objects the new multi-band CB-BLS feature is re- 5. Conclusions quired. Also note that while the blind test were conducted on a ∼50d long LC, these other targets were observed over much We presented a number of improvements to the CB-BLS al- longer periods – typically several years. This necessitates a cor- gorithm that allow CB-BLS to improve it’s sensitivity to shal- respondingly higher frequency resolution, and consequently – low transits, correctly model distorted close binary stars, use longer CB-BLS run time. multi-band photometric data, and more. We also presented an A. Ofir et al.: Searching for transiting circumbinary planets using CB-BLS 453 analytical approach for the determination of detection limits for respectively, and, for e.g., 2–1 stand for the spectroscopic CB-BLS. The resultant implementation of CB-BLS was blind- eclipse of component 1 by component 2). tested using five test light curves derived from CoRoT data – all five were correctly and strongly identified, and the theoreti- Specifically, using CB-BLS to look for transiting CB planets is cal prediction for the detection limit was in line with the actual especially useful since: results. We also presented an example of a procedure for the – CB-BLS allows to find shallow transiting CB planets in the correct detrending of variable stars from wide-field surveys that residuals of EBs. results in far less systematic input light curves for CB-BLS, and – CB-BLS can naturally include Roche geometry – and there a subsequent first application of CB-BLS to real LCs from both are many EBs that require that. targeted observations and a wide-field survey. – CB-BLS can simultaneously fit multi-band data. Looking for transiting CB planets requires good understand- – CB-BLS allows to harness existing datasets to the detection ing of several issues: how to generate good photometry of of transiting CB planets with no further inputs. Medium (or intrinsically-constant stars (now well understood), how to gen- maybe even low) resolution spectroscopic input can allow to erate good photometry of intrinsically-variable stars (for e.g., eliminate the mass ratio as free parameters and to reduce the as explained above: iterative detrending of the residuals), high- required CPU time, but this is not mandatory. quality EB modeling, and finally - the actual search for transiting – CB-BLS source code and documentation are planned to be CB planets (e.g., the CB-BLS algorithm). While the above gen- made freely available. The source code is almost entirely in eral description will probably remain correct, we are still in the MATLAB and so easily portable. process of learning the details of the process – as exemplified by the still-evolving CB-BLS. Still, we feel that the experience of the single-stars transit surveys allows for an even steeper learn- Acknowledgements. We thank Francis O’Donovan and the rest of the TrES team ing curve (and we remind the reader that single-stars transit sur- for making the Lyr1 raw data available to us. A.O. is supported by the European Helio- and Asteroseismology Network (HELAS), a major international collab- veys had their own learning curve: more than 80% of the known oration funded by the European Commission’s Sixth Framework Programme. transiting planets today were not known only three years ago). H.D. acknowledges support by grant ESP2007-65480-C02-02 of the Spanish Looking for CB planets around EBs is advantageous since Ministerio de Ciencia e Inovación. EBs are already well-aligned to our line of sight. Since theo- retical models predict that CB planets will be, at least initially, aligned with their host EB – the chances that CB planets will References transit in front of the EB components are relatively high. CB Almenara, J. M., Deeg, H. J., Aigrain, S., et al. 2009, A&A, 506, 337 planets in general and transiting CB planets in particular are ex- Baglin, A., Auvergne, M., Boisnard, L., et al. 2006, 36th COSPAR Scientific pected to be particularly beneficial for the general study of ex- Assembly, 36, 3749 trasolar planets: Deeg, H. J. 2009, IAU Symp., 253, 388 Deeg, H. J., Doyle, L. R., Kozhevnikov, V. P., et al. 2000, A&A, 358, L5 – Binaries are a very significant fraction of the total stellar pop- Doyle, L. R., Deeg, H. J., Kozhevnikov, V. P., et al. 2000, ApJ, 535, 338 ulation. Studying planet formation and evolution without in- Dunham, E. W., Mandushev, G. I., Taylor, B. W., & Oetiker, B. 2004, PASP, 116, 1072 cluding the formation and evolution of planets in binary star Etzel, P. B. 1981, Photometric and Spectroscopic Binary Systems, 111 systems is surely incomplete. Gaudi, B. S., & Winn, J. N. 2007, ApJ, 655, 550 – The frequency of CB planets depend on assumed planetary Gillon, M., Smalley, B., Hebb, L., et al. 2009, A&A, 496, 259 formation mechanism, and may allow to distinguish between Johnson, J. A., Winn, J. N., Cabrera, N. E., & Carter, J. A. 2009, ApJ, 692, L100 competing theories. The detection limits formalism intro- Kovács, G., Zucker, S., & Mazeh, T. 2002, A&A, 391, 369 duced here will allow us to give meaningful constrains on Kovács, G., Bakos, G., & Noyes, R. W. 2005, MNRAS, 356, 557 the frequency of CB planets by correctly accounting for null Kwee, K. K., & van Woerden, H. 1956, Bull. Astron. Inst. Netherlands, 12, 327 results. Lacy, C. H. S., Torres, G., Claret, A., & Sabby, J. A. 2002, AJ, 123, 1013 – After the initial surprises of close-in giant planets and plan- Lacy, C. H. S., Torres, G., Claret, A., & Sabby, J. A. 2003, AJ, 126, 1905 Lee, D.-W., Lee, C.-U., Park, B.-G., et al. 2008, ApJ, 672, 623 ets in eccentric orbits, detecting CB planets will again sub- Lee, J. W., Kim, S.-L., Kim, C.-H., et al. 2009, AJ, 137, 3181 stantially diversify the environments that produce and sus- Léger, A., Rouan, D., Schneider, J., et al. 2009, A&A, 506, 287 tain planets. Muterspaugh, M. W., Konacki, M., Lane, B. F., & Pfahl, E. 2007, – Understanding very high precision LCs of transiting plan- [arXiv:0705.3072] O’Donovan, F. T., Charbonneau, D., Mandushev, G., et al. 2006, ApJ, 651, L61 ets around single stars is limited by the uncertainty of stellar Ofir, A. 2008, MNRAS, 387, 1597 parameters (e.g., Johnson et al. 2009; Gillon et al. 2009, Pont, F., Zucker, S., & Queloz, D. 2006, MNRAS, 373, 231 and discussion therein). EBs allow to us significantly in- Popper, D. M., & Etzel, P. B. 1981, AJ, 86, 102 crease stellar parameters accuracy, so resultant fits to plan- Seto, N. 2008, ApJ, 677, L55 etary structure models will have smaller error bars. Siviero, A., Munari, U., Sordo, R., et al.2004, A&A, 417, 1083 Southworth, J., Maxted, P. F. L., & Smalley, B. 2004a, MNRAS, 351, 1277 – Follow up will be interesting for several reasons: I) close-in Southworth, J., Zucker, S., Maxted, P. F. L., & Smalley, B. 2004b, MNRAS, 355, CB planets can show orbital evolution on short time scales 986 (even 100s of days); II) higher chances of finding resonant Stetson, P. B. 1996, PASP, 108, 851 systems and/or chaotic systems; III) CB planet systems Tamuz, O., Mazeh, T., & Zucker, S. 2005, MNRAS, 356, 1466 Tamuz, O., Mazeh, T., & North, P. 2006, MNRAS, 367, 1521 produce four distinct Rossiter-McLaughlin (e.g., Gaudi & Tingley, B. 2003, A&A, 408, L5 Winn 2007)effects: 1-2, 2-1, p-1 and p-2 (where 1, 2 and Torres, G., Lacy, C. H. S., Marschall, L. A., Sheets, H. A., & Mader, J. A. 2006, p designate the two binary components and the CB planet ApJ, 640, 1018 Mon. Not. R. Astron. Soc. 404, L99–L103 (2010) doi:10.1111/j.1745-3933.2010.00843.x

The SARS algorithm: detrending CoRoT light curves with Sysrem using simultaneous external parameters

Aviv Ofir,1 Roi Alonso,2,3 Aldo Stefano Bonomo,2 Ludmila Carone,4 Stefania Carpano,5 Benjamin Samuel,6 Jorg¨ Weingrill,7 Suzanne Aigrain,8,9 Michel Auvergne,10 Annie Baglin,10 Pierre Barge,2 Pascal Borde,6 Francois Bouchy,11,12 Hans J. Deeg,13,14 Magali Deleuil,2 Rudolf Dvorak,15 Anders Erikson,16 Sylvio Ferraz Mello,17 Malcolm Fridlund,18 Michel Gillon,3,19 Tristan Guillot,20 Artie Hatzes,21 Laurent Jorda,2 Helmut Lammer,7 Alain Leger,6 Antoine Llebaria,2 Claire Moutou,2 Marc Ollivier,6 Martin Paetzold,¨ 4 Didier Queloz,3 Heike Rauer,16,22 Daniel Rouan,2 Jean Schneider23 and Guenther Wuchterl21 1School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel 2LAM, UMR 6110, CNRS/Univ. de Provence, 38 rue F. Joliot-Curie, 13388 Marseille, France 3Observatoire de Geneve,` UniversitedeGen´ eve,` 51 chemin des Maillettes, 1290 Sauverny, Switzerland 4Rheinisches Institut fur¨ Umweltforschung an der Universitat¨ zu Koln,¨ Aachener Strasse 209, 50931, Koln,¨ Germany 5RSSD, ESTEC/ESA, PO Box 299, 2200 AG Noordwijk, the Netherlands 6Institut d’Astrophysique Spatiale, Universite Paris XI, F-91405 Orsay, France 7Space Research Institute, Austrian Academy of Science, Schmiedlstr. 6, A-8042 Graz, Austria 8School of Physics, University of Exeter, Exeter EX4 4QL 9Oxford Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH 10LESIA, Observatoire de Paris-Meudon, 5 place Jules Janssen, 92195 Meudon, France 11Institut d’Astrophysique de Paris, UMR7095 CNRS, Universite´ Pierre & Marie Curie, 98 bis boulevard Arago, 75014 Paris, France 1222 Observatoire de Haute-Provence, CNRS/OAMP, 04870 St Michel l Observatoire, France 13Instituto de Astrof´ısica de Canarias, E-38205 La Laguna, Tenerife, Spain 14Dept. de Astrof´ısica, Universidad de La Laguna, Tenerife, Spain 15Institute for Astronomy, University of Vienna, Turkenschanzstrasse¨ 17, 1180 Vienna, Austria 16Institute of Planetary Research, DLR, 12489 Berlin, Germany 17IAG Universidade de Sao Paulo, Sao Paulo, Brazil 18Research and Scientific Support Department, European Space Agency, Keplerlaan 1, NL-2200AG, Noordwijk, the Netherlands 19IAG UniversiteduLi´ ege,` Alleedu6ao´ utˆ 17, Liege` 1, Belgium 20Universit de Nice Sophia Antipolis, CNRS, Observatoire de la Cte d’Azur, BP 4229, 06304 Nice, France 21Thuringer¨ Landessternwarte, 07778 Tautenburg, Germany 22TU Berlin, Zentrum fur¨ Astronomie und Astrophysik, Hardenbergstr. 36, 10623 Berlin, Germany 23LUTH, Observatoire de Paris-Meudon, 5 place Jules Janssen, 92195 Meudon, France

Accepted 2010 March 1. Received 2010 March 1; in original form 2010 February 9

ABSTRACT Surveys for exoplanetary transits are usually limited not by photon noise but rather by the amount of red noise in their data. In particular, although the CoRoT space-based survey data are being carefully scrutinized, significant new sources of systematic noises are still being discovered. Recently, a magnitude-dependant systematic effect was discovered in the CoRoT data by Mazeh et al. and a phenomenological correction was proposed. Here we tie the observed effect to a particular type of effect, and in the process generalize the popular Sysrem algorithm to include external parameters in a simultaneous solution with the unknown effects. We show that a post-processing scheme based on this algorithm performs well and indeed allows for the detection of new transit-like signals that were not previously detected. Key words: methods: data analysis – techniques: photometric – planetary systems.

E-mail: avivofi[email protected]

C 2010 The Authors. Journal compilation C 2010 RAS L100 A. Ofir et al.

(hereafter LC) its mean or median m¯ we are left with the matrix 1 INTRODUCTION i of residuals rij . In the original Sysrem, the residuals of intrinsically The limiting factor for most planetary transit surveys is not the constant stars are modelled using two contributions: theoretical photon noise but rather the practically achieved red noise r = A C + noise, (1) from non-astrophysical sources (Pont, Zucker & Queloz 2006). The ij j i 1 most capable transit surveys are the space-based surveys CoRoT where Aj is the effect in each exposure and Ci is the effect’s coeffi- and Kepler because their stable environments allow for minimal red cient for each star. We note that since the data are in the magnitude noise (and other benefits – such as continuous observations). Still, system the effects found in this manner are relative in flux. In order no instrument is perfect and the CoRoT light curves are known to to test out hypothesis that the magnitude-dependent effects stem show a number of significant effects that hinder transit detection, from something that is additive in flux, we introduce the SARS such as discontinuities of arbitrary magnitude due to high energetic model: proton flux near the South Atlantic Anomaly (SAA), residuals at rij = Aj xij CA,i + Rj CR,i + noise. (2) the CoRoT orbital period, spacecraft jitter, CCD long-term aging and more. Many of these effects are correctable to satisfactory level Here the second term is exactly the usual Sysrem effect were at post-processing, but not for all stars and at all times. we simply change the letter from Aj to Rj to designate that it On top of these effects, Mazeh et al. (2009) (hereafter M09) is a relative effect. The first term stands for the additive effect = 0.4mij recently discovered that there are significant magnitude-dependant by introducing xij 10 which makes sure that the effect is systematic effects in the CoRoT light curves, and they developed a stronger for faint stars and weaker for bright stars – and in the correct phenomenological algorithm to correct for them. In this Letter we tie functional form expected from additive flux effects. In practice, we − = 0.4(mij mrel) the above observation to a particular type of effect: added/subtracted use xij 10 ,wheremrel is a constant number (e.g. the linear flux, and are thus able to improve on their correction. In the median of all the stars on all the exposures) to avoid overly large or process we generalize the Sysrem algorithm (Tamuz, Mazeh & small values for xij . As in Sysrem, minimizing the sum of squared Zucker 2005) to include arbitrary external parameters and show residuals S,   the benefits of using this modified version. In the following, we 2  r − model formulate the Sysrem generalization in Section 2, which is part of a S = ij . (3) complete post-processing scheme presented in Section 3, and then σij conclude. Given the best-fitting effects R and A, and the corresponding coefficients C R and C A:   2 THE SARS CORE rij xij CA,i − R CR,ixij CA,i i σ 2 j i σ 2 = ij ij Aj  2 2 , (4) xij CA,i 2.1 Algorithm i 2 σij M09 first noted that there are magnitude-dependent systematic ef-   fects in the CoRoT data. They proposed to correct for the effects rij CR,i − A CR,ixij CA,i i σ 2 j i σ 2 = ij ij by fitting a parabola to the residuals of each exposure – but this Rj  2 , (5) CR,i correction is a purely phenomenological correction since there is i 2 σij no identified cause for the effects, and thus no explanation as to   why a parabola is the best functional form. We hypothesize that the r x A A x R ij ij j − C j ij j j σ 2 R,i j σ 2 underlying physical mechanism M09 were trying to correct for is = ij ij CA,i  2 2 , (6) a constant flux that is either added or subtracted from all the light xij Aj j 2 curves due to calibration errors, scattered light or other causes. Such σij an additive effect will create a large magnitude difference on faint   stars, and small magnitude difference on bright stars, as M09 had rij Rj − C Aj xij Rj j σ 2 A,i j σ 2 = ij ij originally observed. Indeed, the original authors had also consid- CR,i  2 . (7) Rj ered this option (Tsevi Mazeh, personal communication) but they j σ 2 chose to use a more phenomenological correction rather than to tie ij the correction to this proposed physical mechanism. Since detrend- As in Sysrem, the values of Aj ,Rj ,CA,i ,CR,i are iteratively ing algorithms cannot a priori disentangle additive from relative refined until convergence is achieved. We found it important that in effects, we choose to simultaneously correct both types of effects, each iteration the new values of the effects are used to calculate the and so developed ‘Simultaneous Additive and Relative Sysrem’ – coefficients, and not the values of the previous iteration. or the SARS algorithm – described below. = Suppose a matrix of photometric measurements of N stars (i 2.2 Further generalization 1,...,N)onM measurements (j = 1,...,M)isgiven,sothat The formulae (4)–(7) do not ‘know’ that x is meant to scale mag- the magnitude value of the ith star on the jth frame is mij and its ij nitude data to create flux-based correction – they only know that x associated error is σi,j . After removing from each stellar light curve ij depends on external information not present in the original matrix of residuals. In this, SARS presents a significant departure from 1 The CoRoT space mission, launched on 2006 December 27, has been de- the original Sysrem by allowing for the detrending against any ex- veloped and is operated by CNES, with the contribution of Austria, Belgium, plicitly known external parameters as long as their effect can be Brazil, ESA, Germany and Spain. CoRoT data become publicly available encapsulated in some xij . For example, these can be distance from one year after release to the Co-Is of the mission from the CoRoT archive: the centre of the CCD or pixel phase (or otherwise location based), http://idoc-corot.ias.u-psud.fr/ CCD temperature (or otherwise weather related) or Moon phase (or

C 2010 The Authors. Journal compilation C 2010 RAS, MNRAS 404, L99–L103 The SARS algorithm L101 otherwise temporal effects), etc. It is thus easy to include multiple (3) Subtract a running median with a window the size of three external effects in the detrending model (e.g. the SARS model of CoRoT orbital periods, and reject outliers. equation 2), and by minimizing the sum of squared residuals S to (4) Choose a ‘learning set’ to calculate the effects with. establish their effect on the data simultaneously with the effects of (5) Apply the effects to all stars (we used three pairs of effects). unknown sources. (6) Reset errors and reject bright outliers. However, in order to achieve full automation we elaborate below 2.3 Suggested good practices on steps that were either unspecified or human dependant on M09. Below we describe what we think are good practices when using (7) Outliers rejection is done in three tiers: SARS: (i) Removal of solitary outliers that are far from a small- (i) Starting point: we note that already the Sysrem ‘search space’ window (five-point) median filter. was very large: as many parameters to adjust as there are stars + ex- (ii) Further outliers must meet two criteria: (1) that frame has posures. By simultaneously fitting more than one effect in SARS – anomalously high median absolute deviation (usually SAA-affected we further enlarge this search space greatly. In the original Sysrem frames) and (2) the data point is far from a three-orbit median. the starting point was deemed to be unimportant since Tamuz et al. (iii) Before SARS-core application, frames must have a min- (2005) claimed that in their simulations no matter what initial val- imum number of valid learning-set stars (we used at least 100). ues were used, the same effect and coefficients were obtained. We (8) Automatic choosing of the learning set aims to isolate the believe that these simulations were somewhat lacking in that they intrinsically and instrumentally constant stars. These stars are as- used white noise only, with no red noise component, which allowed sumed to be numerous and similarly variable in the raw data. An them to always find the (unique) global χ 2 minimum with no lo- initial learning set is chosen by multiple criteria: cal minima to be avoided. We have also performed a similar test – but on real data, rather than simulated data, and found that some- (i) the alarm statistic of the LC (Tamuz, Mazeh & North times (a few per cent of the runs) the global minimum was indeed 2006) must be part of the bulk of alarms; missed. Fearing that the enlarged SARS search space would worsen (ii) the alarm statistic of the residuals must be part of the bulk the problem, we choose to start the iterations from a deterministic of alarms; point. Assuming that the median of photometric measurements is (iii) the locus of constant stars on the log(rms) versus magni- rather robust, we start by finding a proxy to the relative and additive tude plot is along a straight line. Learning-set stars must not be far effects by Rj = median(rij )andAj = median(rij xij ), respectively. from that locus. We set all C R and C A to unity since we wish to find effects that Next, the learning set is refined by a procedure inspired by tech- affect many (if not all) stars. niques originally developed for photometric follow-up of transiting (ii) Convergence criteria: the convergence criteria for the above planets (Holman et al. 2006) and is aimed at delivering the best iterations was unspecified in Tamuz et al. (2005). We define it as comparison signal (lowest relative noise). the iteration when the maximal absolute value of total correction abs(Aj xij CA,i + Rj CR,i) is smaller than some fraction f of the (i) Given a set of N stars, calculate relative error on the total flux standard deviation of that particular object. We used f = 0.5inour for all N subsets of (N − 1) stars. processing. (ii) Compare the best subset (having the lowest relative flux error) (iii) Once either additive or relative effects show no further corre- with the relative flux error of the sum of N stars. lation, one can use the regular Sysrem to look for additional effects (a) If error reduced: repeat from step (i) with (N − 1) stars. of the other type since one may have different number of relative (b) If error increased: optimal set reached. and additive effects – until no effects of either type are identified. (iv) Bright stars both make planetary transits easier to detect, and This procedure guarantees that a local minimum in relative error is are more susceptible to relative effects [which are later corrected reached. We opt not to search for the global optimum since this is by Sysrem/TFA (Kovacs,´ Bakos & Noyes 2005)/other]. For these deemed too difficult (testing all subgroups of N stars require testing reasons some of the transit surveys intentionally monitor only the N! configurations, where N is in the order several thousands). We relatively bright stars in their field of view. On the other hand, fainter note that the resultant learning set preferentially includes faint stars stars more readily show additive effects. We therefore propose to (see Fig. 1) which at least partially is because any variability is easier add more faint stars to the data of such surveys when using SARS to spot on brighter stars. Interestingly, Fig. 1 and panel 2 of Fig. 2 as they might hold the key to better correct all stars. show that despite the fact that faint stars are preferentially selected as learning-set stars – bright stars are better corrected, showing that indeed something was learned from the fainter objects and was well 3 THE SARS POST-PROCESSING SCHEME applied to the brighter stars.

3.1 Post-processing steps (9) We use the SARS core three times. The above SARS core is just one element of the SARS post- (i) Use on the learning set only – used to recalibrate the errors processing scheme. We were able to achieve complete automation only (see below). with no human input from CoRoT N2 FITS files to clean LCs. (ii) Use on the learning set only (now with calibrates errors) The post-processing global structure was similar to the one used by – to calculate the effects. M09. (iii) Use on the whole data set – apply the already calculated effect to all the LCs. (1) Resample to 512s: resampling is done for each CoRoT colour separately, if available. (10) Errors resetting is done by (2) Divide to ∼10 d blocks, process blocks individually. ExpErr(j) err = StarErr(i) , (8) ij median(ExpErr) C 2010 The Authors. Journal compilation C 2010 RAS, MNRAS 404, L99–L103 L102 A. Ofir et al.

where StarErr is estimated from the star’s LC and ExpErr is 0.7 estimated from the distribution of magnitude residuals of each

0.6 exposure.

0.5 3.2 Results 0.4 A comparison of the performance of SARS-cleaned and M09- 0.3 cleand LCs (the later sometimes dubbed ‘CleanSet’) of one random field (LRc02) is shown in Fig. 2: the SARS post-processing deliv- 0.2 ers lower LC dispersion than in M09’s CleanSet for about 65 per

Fraction of learning–set stars Fraction 0.1 cent of the stars, while keeping at least the same number of valid data points M (CCD E2) if not more (CCD E1).√ If we compare the 0 detection power, which is defined as DP ∼ M/σ, we find that it 11 12 13 14 15 16 17 18 Magnitude is higher in SARS than in CleanSet for up to 80 per cent of the stars. We note that there is a small trend in the relative performance: the Figure 1. A representative plot of the fraction of learning-set stars in several brighter the stars are the better SARS is relative to CleanSet. This is magnitude bins (data here are from the example presented in Section 3.2, the expected result of the approximated functional form of the M09 for the learning set of the first effects-pair in the first block of LRc02). correction: since there are many more faint stars in the data than bright stars, the parabolic least-squares correction of M09 tends to Ratio of LC dispersion better suite the numerous faint ones, and so less fitting (due to the A 400 –3 x 10 E1 4619 phased to 1.69383d –1

# of stars 200

0 0 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 σ / σ SARS CleanSet 1 Ratio of LC dispersion vs. R magnitude

1.4 B 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

CleanSet 1.2 –3 σ x 10 E1 1715 phased to 2.0361d / –1 1 SARS

σ –0.5 0.8 11 12 13 14 15 16 0 R mag

0.5 Number of images: Cleanset (blue) and SARS (red)

1 C 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1000 E1 1475 phased to 2.11853d 500 1.001

0 1 1.7 1.8 1.9 2 2.1 2.2 4 0.999 M x 10 0.998 Relative discovery power 0.997 D 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 600

–3 x 10 E2 4502 phased to 9.69826d 400 –4

200 –2 0 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0 DP / DP SRAS CleanSet 2 Figure 2. Comparison between SARS and CleanSet for one random field 4 (CCD E1 of LRc02). Panel A: histogram of the ratio of LC dispersion in 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SARS and CleanSet. Note σSARS/σCleanSet < 1 for most stars. Panel B: the above ratio of LC dispersion versus R magnitude: the observed trend is Figure 3. Example of four CoRoT LRa02 candidates that were not detected explained in the text. Panel C: histogram of the number of remaining data by any of the detection teams before the application of the SARS post- points after outlier rejection in SARS and CleanSet. Panel D: histogram of processing, and which are currently being followed up. The light curves are the ratio of detection power (DP) between SARS and CleanSet. folded and binned to aid visibility.

C 2010 The Authors. Journal compilation C 2010 RAS, MNRAS 404, L99–L103 The SARS algorithm L103 approximated functional form) to the bright stars. Thus our initial spurious signals in the BLS spectra (Kovacs,´ Zucker & Mazeh 2002) hypothesis that the effects are additive seems even more robust. and thus the detection of shallower signals. This global statistics is also translated to specific detections: We were able to achieve good performance and complete au- so far we have SARS-analysed three long runs (LRc02, LRa02 tomation which allows us to now process the entire mission data, and LRa01) and found about 10 new transit-like signals that were and to look for – and find – ever shallower transit-like signals. For not detected before in each field. For example in Fig. 3 we show example on LRc02 target CoRoT ID 0105842933 we were able four such LRa02 new transit candidates that were also chosen for to clearly detect a very shallow signal, only 10−4 mag deep, in a follow-up. P = 1.08 085 d period. Not only that, but we were also able to show that this is an eclipsing binary since at the double period the odd and even eclipses have different depths, with the secondary eclipse still 4 DISCUSSION visible (on a binned LC) while having a depth below the 84 ppm At the start of the CoRoT mission the CoRoT Exoplanets Science depth of an exo-Earth around a Sun-like star. Team (CEST) made the strategic choice of having multiple team We will make the SARS-cleaned light curves available for the analysing the exact same input data. By cross-checking each detec- CoRoT community, and it is our intention that when the proprietary tion with different tools and cleaning techniques (e.g. Cabrera et al. period is over to make data generally available (upon request). We 2009; Carpano et al. 2009) the CEST hoped to achieve the best pos- note that we have also allowed for the application of SARS to sible transit candidates list for follow-up observations by the limited the residuals of astrophysically variable stars (pulsators, eclipsing ground-based telescope resources. Here we present yet another step binaries, etc.) which will allow to better clean them too – as part of in the journey to clean photometric data sets in general and CoRoT a parallel CEST effort to look for transiting circumbinary planets data in particular: we generalize the popular and efficient Sysrem (Ofir 2008; Ofir, Deeg & Lacy 2009). algorithm to include external parameters in a simultaneous solution, together with the unknown effects. This allows us to show that data from CoRoT is probably contaminated with additive, rather than relative, systematic effects – and that these effects are the probable REFERENCES cause behind the phenomenological observation of M09. The size Cabrera J. et al., 2009, A&A, 506, 501 of the additive correction abs(Aj xij CA,i ) is comparable to that of the Carpano S. et al., 2009, A&A, 506, 491 relative correction abs(Rj CR,i), with a median additive-to-relative Holman M. J. et al., 2006, ApJ, 652, 1715 ratio of about 0.5, but with a large scatter – making the additive Kovacs´ G., Zucker S., Mazeh T., 2002, A&A, 391, 369 correction larger than the relative correction for ∼1/3 of the data Kovacs´ G., Bakos G., Noyes R. W., 2005, MNRAS, 356, 557 points. Additive effects can arise from scattered light or erroneous Mazeh T. et al., 2009, A&A, 506, 431 (M09) bias or background subtraction, and we believe that the additive Ofir A., 2008, MNRAS, 387, 1597 Ofir A., Deeg H. J., Lacy C. H. S., 2009, A&A, 506, 445 effects can be used just as the regular Sysrem effects to help to trace Pont F., Zucker S., Queloz D., 2006, MNRAS, 373, 23 down the origin of the systematics and thus to avoid them in the Tamuz O., Mazeh T., Zucker S., 2005, MNRAS, 356, 1466 first place. Tamuz O., Mazeh T., North P., 2006, MNRAS, 367, 1521 We believe that the main advantage of SARS is not in a dramatic change in the standard deviation σ of the LCs, but rather in the whiter colour of their noise, which in turn allows for lower background of This paper has been typeset from a TEX/LATEX file prepared by the author.

C 2010 The Authors. Journal compilation C 2010 RAS, MNRAS 404, L99–L103

Part 3: Conclusions

− 69 − 1. Summary

Most of the stars in the Galaxy form in groups and about half of them have one or more bound stellar companions. The presence of a stellar companion does not forbid the formation of sub-stellar and planetary companions, but it certainly affects it. Indeed, it was already found that despite biases against detecting planets in binaries a large fraction of the known planets are part of binary systems, and that the closer stellar components do affect the mass distribution of the planets. I therefore proposed to further investigate the relation between stellar- and substellar- multiplicities. This observational effort is worthwhile because this relation sheds light on the formation process of the whole system and may allow us to discriminate between competing and otherwise degenerate theories of planet formation.

I presented an array of techniques for the photometric detection of planets in eclipsing binary systems covering almost every configuration of such systems. One of these techniques (called CB-BLS) is original and was developed during this thesis. Using two other techniques (timing and background objects) resulted in actual signal detection. I also presented a technique for the improved de-trending of all light curves of a photometric survey called SARS that was also developed during this thesis. This technique is useful for all subsequent studies – and not just for planets in binaries – and was indeed successfully incorporated in a search for planets around single stars in the CoRoT data (see Figure 21 ). All of the above was published during this thesis in 3 first-author papers in refereed journals (including one as a single author), 6 papers in refereed journals as co-author, one single-author paper in a non-refereed journal, and one conference proceeding.

Figure 21. A gallery of four transiting planets and one transiting brown dwarf detected during my PhD studies. Left: CoRoT-12b (top), CoRoT-13b (bottom). Right: CoRoT-14b (top), CoRoT-15b (middle) and HAT-P-5b (bottom). (Papers #8, # 9, # 11, #10 and # 4, respectively)

− 70 − 2. Current Status and Future development

In this thesis I wanted to look for planets in EB systems, and so far the results on this core subject are very preliminary: one stellar-mass object detected by eclipse timing, one background transit-like signal (of unknown nature), and a null result on looking for transiting CB planets on a 12 EBs. I note that this null is still insignificant: Even in the ideal case of 100% detection efficiency, the best limit I can put is that CB planets' frequency is less than roughly 1/12. However, this is a gross approximation: neglecting the different orbital inclinations of the systems, the probed planetary periods, and the high noise values (all light curves are ground-based). These will make the overall detection efficiency <<100% and the null - insignificant.

The cause for the small number of objects that were found – or even just searched – is because the largest fraction of my time during the thesis was spent actually taking advantage of the unexpected (and successful) development of SARS by applying it to the entire CoRoT mission data, and not using CB-BLS or timing. This meant that the original intent of looking for CB planets had to be somewhat postponed. Still, despite this postponing, this thesis is already represents the widest published photometric search for transiting CB planets ever conducted. Also, SARS itself was quite successful and resulted in participation in a number of detection papers on new transiting planets and a transiting brown dwarf.

Importantly, this research program of looking for planets in binaries is larger than the PhD thesis and I plan to continue working on looking planets in binaries during my upcoming postdoc: • I recently finished SARS-processing all the CoRoT mission data, and can now return to all the fields and apply the corrections derived from the single stars to the EBs as originally intended. • Both CB-BLS and eclipse timing are particularly powerful when applied together to SARS-processed space-based data – but this was yet to happen. The entire CoRoT data will soon be put to such processing. • In the near future I will also be able to use Kepler data for these purposes: already large amounts of data (>150,000 light curves) are publicly available.

Recently, a new technique by Deeg & Doyle (2010) for the photometric detection of non- transting close-in CB planets was developed using the EB eclipses reflected off the face of the planets. This technique hold great promise since it does not rely on the occurrences of transits. This means that even if one down-selects from the few thousands of Kepler and CoRoT EBs only a few hundred objects that are particularly sensitive to this technique (problems-free short period EBs, but not over-contact systems) even a null result will be significant in constraining the frequency of short-period giant CB planets. When combined with transit searches, this will further enhance the statistical significant of any result.

Using all available techniques, at the end of the research program I will be able to compare the populations of planets around single stars and planets that revolve around one binary component in more depth than was possible before. I will also try to either detect the first close-in circumbinary planet, or give a significant limit to such a population in case of a null detection.

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− 75 − 4. Table of Acronyms

ADI - Angular Differential Imaging AO - Adaptive Optics AU - Astronimical Unit BD - Brown Dwarf BLS - Box Least Squares CB - Circum Binary CB-BLS - Circum Binary Box Least Squares CP - Circum Primary DEBiL - Detached Eclipsing Binaries Light curve EB - Eclipsing Binary EBOP - Eclipsing Binary Orbit Program FOV - Field Of View FU - Follow-up HST - Hubble Space Telescope JWST - James Webb Space Telescope LC - Light Curve LOCI - Locally Optimized Combination of Images MMR - Mean Motion Resonance PSF - Point Spread Function RM - Rossiter-McLaughlin (effect) RV - Radial Velocity SARS - Simultaneous Additive and Relative Sysrem SDI - Spectral Differential Imaging SNR - Signal-to-Noise Ratio SysRem - Systematics Removal TDuV - Transit Duration Variations TFA - Trend Filtering Algorithm TTV - Transit Time Variations WD - Willson-Devinney (code) VLT - Very Large Telescope

− 76 − − 77 − תקציר

כוכבי ם כפולים הם אחת מהסביבות הנפוצות ביותר בגלקסיה . לימוד של תהליכי יצירה והתפתחות פלנטות מבלי לכלול את יצירת והתפתחות הפלנטות במערכות כוכבים כפולים הינו בוודאי לוקה ב חסר . כבר ידוע שפלנטות נוצרות בקלות בכוכבים כפולים רחבים ( כלומר , רחוקים זה מזה ) למרות הטיות תצ פיתיות קשות נגד תגליות שכאלה : לפחות 17% מהפלנטות המוכרות סובבות סביב מרכיב אחד של כוכב כפול רחב . מצד שני , כמעט ואין אילוצים תצפיתיים על יצירת פלנטות בכוכבים כפולים קרובים . תכנית המחקר הנוכחית מכוונת להשלים את הפער התצפיתי הקיים ב מערכות כוכבים אלו . .

סקרים ל מציאת פלנטות מלקות , גם מה קרקע וגם מהחלל , אוספים כמויות גדולות מאוד של נתונים פוטומטריים שגם כוללים כוכבים כפולים מלקים ( "ככ מ ) רבים . מכיוון שפלנטות במערכות ככ" מים צפויות להיות ( לפחות בהתחלה ) באותו המישור של ככ" -מ האם , אני השתמשתי ב קרבה של הככ" מים לקו הראייה "ע( י בחירתם כמלקים ) כדי להגדיל את הסיכוי הגיאומטרי של פלנטות במערכת להלקות כל אחד ממרכיבי הככ" .מ .מ

השתמשתי בנתונים פוטומטריים בעיקר מן החללית CoRoT . התחלתי מן הנתונים הגלמיים יוח סר תי מגמות ב נתונים על מנת להימנע מרעשים סיסטמטיים . אני מרחיב על טכניקה מיוחדת ש פותחה במהלך העבודה הנקראת "SARS" שאפשרה לי לנקות את הנתונים עד כדי שאצליח לגלות אותות רבים דמויי- ליקויים שלא התגלו קודם לכן . עבור כוכבים משתנים , כמו ככ" מים , אני מראה כיצד ניתן לחסר מגמות מהנתונים מבלי ל פגוע ב השתנות הפנימית . אני מתאר גם שיטה חדשה לחיפוש שפו תחה במהלך העבודה הזו שנקראת "CB-BLS" שנועדה לחפש פלנטות בנתונים פוטומטריים של ככ" מים לאחר שאלו נוקו. כל אלו אפשרו לי לחפש פלנטות כמעט בכל קונפיגורציה אפשרית : פלנטות מלקות סביב אחד או שני המרכיבים של הככ"מ , פלנטות שאי נן מלק ות מסביב לשני מרכיבי הככ"מ , פלנטות מלקות באובייקטי רקע , וגם – כתוצר לוואי ( אך מוצלח למדי –) חיפוש משופר לפלנטות מלקות " רגילות " סביב כוכבים בודדים . .

בתיזה זו אני מציג את התוצאות המשמעותיות הראשונות של תכנית המחקר , הכוללות את גילויין של ארבע פלנטות מלקות , ננס- חום מלקה , וגילוי של אותות מאובי יקט רקע ומתזמון ככ" מים . אלו הן רק תוצאות ראשוניות : תכנית המחקר הזו בוודאי תמשיך אל תוך הפוסט- דוקטורט העתידי שלי , כך שעד סיום התכנית אני אוכל להשוות באופן ניסיוני את קצב יצירת הפלנטות בככ" מים קרובים לזה של פלנטות סביב כוכבים בודדים , "וע י כך אספק אילוץ חשוב לתיאוריות אודות יצירת פלנטות וכוכבים – אילוץ שלא קיים כיום . .

− 78 −

הפקולטה למדעים מדויקים RAYMOND AND BEVERLY SACKLER "ע ש ריימונד ובברלי סאקלר FACULTY OF EXACT SCIENCES בית הספר לפיסיקה ולאסטרונומיה SCHOOL OF PHYSICS & ASTRONOMY

חיפוש אחר פלנטות במערכות כוכבים כפולים לוקים

תזה לתואר " דוקטור לפילוסופיה"

אביב אופיר

עבודה זו נעשתה בה רד כתם :של :של פרופ ' Artie Hatzes ( מכון TLS , גרמניה ) ופרופ ' שרה בק

הוגש לסנאט של אוניברסיטת תל אביב טבת התשע"א