Microlensing Search for Planets with Two Simultaneously Rising Suns

a r X i v :0801.4828v 1 [a s t r o -p h ] 31 J a n 2008

D RAFT VERSION F EBRUARY 3,2008

Preprint typeset using L A T E X style emulateapj v.10/09/06

MICROLENSING SEARCH FOR PLANETS WITH TWO SIMULTANEOUSLY RISING SUNS

C HEONGHO H AN

Program of Brain Korea 21,Department of Physics,Chungbuk National University,Chongju 361-763,Korea;cheongho@astroph.chungbuk.ac.kr

Draft version February 3,2008

ABSTRACT

Among more than 200extrasolar planet candidates discovered to date,there is no known planet orbiting around normal binary stars.In this paper,we demonstrate that microlensing is a technique that can detect such planets.Microlensing discoveries of these planets are possible because the planet and host binary stars produce perturbations at a common region around center of mass of the binary stars and thus the signatures of both planet and binary can be detected in the light curves of high-magni?cation microlensing events.The ranges of the planetary and binary separations of systems for optimal detection vary depending on the planet mass.For a Jupiter-mass planet,we ?nd that high detection ef?ciency is expected for planets located in the range of ～1AU –5AU from the binary stars which are separated by ～0.15AU –0.5AU.Subject headings:gravitational lensing –planets and satellites:general

1.INTRODUCTION

Since the ?rst discovery by Wolszczan &Frail (1992),more than 200extrasolar planet candidates have been discov-ered.Among the currently known extrasolar planet-hosting stars,approximately 20%are members of binaries or multi-ple systems (Haghighipour 2006).Nearly all of the planets in these systems revolve around only one of the stars.The only exception is the planetary system PSR B1620-26(Lyne et al.1988;Backer et al.1993),but this system consists of not nor-mal stars but a pulsar and a white dwarf.

Besides the orbital con?guration of the known planets in binaries where the planet revolves around one of the widely separated binary members,a planet can stay in a stable orbit if the planet is located well outside the binary stars and thus seeing the two stars as approximately a single object.How-ever,such planets,which were imagined as a planet with two simultaneously rising suns in the Star Wars saga (Tatooine),have not been seen in planet searches using the radial veloc-ity technique because the search programs avoid short-period binary stars.The chance to detect such planets via the transit technique is also very low because these planets tend to have wide orbits.

Planets in binary stellar systems can be detected by us-ing the microlensing technique.Such a possibility was ?rst mentioned by Bennett et al.(1999).They reported a can-didate planet orbiting around a binary system from the ob-servation and light-curve modeling of a microlensing event MACHO-97-BLG-41.However,their interpretation of this event is very special in the sense that the source trajectory is precisely aligned with the line connecting the planet and the center of mass of the binary.Besides,the interpretation of the signal was rejected because a rotating binary-lens model provides an excellent ?t to the observed data (Albrow et al.2000).Lee et al.(2008)also investigated the lensing signal of planets in binary systems.However,their analysis is re-stricted to planets orbiting around one of the binary members.In this paper,we investigate the feasibility of detecting planets with two simultaneously rising suns by using the microlens-ing technique.

2.LENSING BEHA VIOR

The general geometry of a planet revolving around the stars of a close binary is such that the separation between the stars

F I

G .1.—Lensing geometry of a planet revolving around close binary stars.The big dashed circle represents the Einstein ring of a mass corresponding to the total mass of the binary stars.The angle φdenotes the position angle of the planet as measured counterclockwise from the binary axis and d b and d p denote the projected separations between the binary stars and between the planet and the binary center of mass,respectively.The right panel shows the enlarged view of the region around the binary stars.The ?gure drawn in red color represents the lensing caustic produced by the lens system.

is much smaller than the star-planet separation (see Figure 1).Under this geometry,the lensing behavior of the triple lens system can be greatly simpli?ed because the close stellar bi-nary pair and the planet can be separately treated.

The lensing behavior of the close stellar binary pair is mostly described by the single mass lens located at the center of the mass of the binary system with a mass equal to the total mass of the binary.A small deviation occurs around the caus-tic which forms close to the center of mass.The caustic repre-sents the set of source positions at which the magni?cation of a point source becomes in?nite.For a close binary,the caustic has the shape of an asymmetric hypocycloid with four cusps and the asymmetry increases as the mass ratio between the stars,q b =m 2/m 1,decreases.Here m 1and m 2represent the masses of the heavier and lighter binary components,respec-tively.The caustic size depends weakly on the mass ratio,but it decreases rapidly with the decrease of the stellar separation.For a close binary,then,the perturbation region is con?ned to a small region around the center of mass of the binary.

The planet,on the other hand,causes formation of two sets of disconnected caustics.One set is located away from the host star.The other set is located close to the planet-hosting star,which coincides with the region of the binary-induced perturbation.The latter caustic (central caustic)has an elon-gated wedge-like shape.The size of the planet-induced cen-

2PLANETS WITH TWO SUNS

F IG.2.—Lensing magni?cation patterns of triple lens systems composed of a planet revolving around binary stars.The labels above and on the right represent the projected separations between binary stars(d b)and between the planet and the center of mass of the binary(d p),respectively.In each map,the coordinates are centered at the position of the center of mass of the binary stars and the x-axis is aligned with the binary axis.The heavier star is on the right.The planets have a common position angle ofφ=45?as measured counterclockwise from the binary axis(see Figure1).The grey-scale is drawn such that brighter tone represents the region of higher magni?cation.The?gures drawn in solid curves represent the lensing caustics.The presented patterns are for a Saturn-mass planet revolving around binary stars with a total mass of0.5M⊙and a companion/primary mass ratio of0.5.The light curves resulting from the source trajectories marked by straight lines with arrows in the individual panels are presented in the corresponding panels of Figure3(thick solid curves in black color).The panels blocked by thick black solid lines show the cases where the planet dominates the perturbation pattern,while the panels blocked by thick white solid lines show the opposite cases where the binary stars dominate the pattern.

tral caustics depends both on the star-planet separation and the planet/star mass ratio(Chung et al.2005).The planet-induced caustic is small due to the small mass ratio of the planet.How-ever,its size becomes non-negligible when the planetary sep-aration is equivalent to the Einstein radius(Mao&Paczy′n ski 1991;Gould&Loeb1992).

The small sizes of the deviation regions induced by the planet and the host binary stars greatly simplify the descrip-tion of the lensing behavior of the system.This is because each deviation can be treated as a perturbation and thus the lensing behavior of the triple lens system is approximated as the superposition of those of the two sets of binary lenses composed of the binary star pair and the pair composed of the planet and a virtual star located at the center of the mass of the binary stars with a mass equal to the total mass of the binary.In addition,the coincidence of the individual pertur-bation regions might enable to detect both signatures of the planet and host binary stars from high magni?cation events for which the source trajectory passes close to the common region of perturbation.

3.MAGNIFICATION PATTERN

With the possible approximation of binary superposition in mind,we investigate the magni?cation pattern in the central region of various triple lens systems composed of a planet around binary stars.For this,we construct magni?cation map,which represents the map of lensing magni?cation as a function of the source star position.For the construction of the map,we use the ray-shooting method.We choose this method because it allows not only simple procedure of multiple-lensing magni?cation computation but also easy in-corporation of the?nite-source effect.

Figure2shows the maps for a Saturn-mass planet revolv-ing around binary stars with a total mass of M=0.5M⊙and a mass ratio of q b=0.5.The labels above and on the right side of the?gure represent the projected separations between binary stars(binary separation,d b)and between the planet and the center of mass of the binary(planetary separation, d p),respectively.In each map,the coordinates are centered at the position of the center of mass of the binary stars and the x-axis is aligned with the binary axis,where the heav-ier star is on the right.For all tested cases,the planets have a common position angle ofφ=45?as measured counter-clockwise from the binary axis(see Figure1).The grey-scale is drawn such that brighter tone represents the region of higher magni?cation.The?gures drawn in solid curves rep-resent the caustics.Since the caustics induced by the planet and binary stars are small,?nite-source effect would be im-portant in magni?cation pattern(Bennett&Rhie1996).We consider the effect by assuming that the source star has a ra-dius equivalent to that of the Sun.We assume that events are observed toward the Galactic bulge?eld and the dis-tances to the lens and source are D L=6kpc and D S=8kpc, respectively,by adopting those of a typical Galactic bulge event(Han&Gould1995).Then,the corresponding Ein-stein radius is r E=(4GM/c2)1/2[D L(D S?D L)/D S]1/2～2.5

TABLE1

O PTIMAL S EPARATION R ANGES

planet planetary binary

type separation separation Jupiter-mass1.0AU d p 5.0AU0.15AU d b 0.5AU Saturn-mass1.6AU d p 3.8AU0.15AU d b 0.5AU Uranus-mass2.0AU d p 3.0AU0.15AU d b 0.5AU AU and the source size normalized by the Einstein radius is ρ=1.5×10?3.

In Figure3,we also present the light curves resulting from the source trajectories marked by straight lines on the maps. In each panel,there exist three light curves.The thick solid light curve is for the triple-lens event,while the curves drawn in red and blue colors are for the cases where there is no planet and the planet-hosting star is a single object,respectively. From Figure2and3,we?nd that the in?uence of the planet and binary stars on the pattern of perturbation varies depend-ing on the binary and planetary separations.When the binary separation is small and the planetary separation is equivalent to the Einstein radius,the planet dominates the perturbation pattern.These correspond to the cases blocked by thick black solid lines in Figure2.On the contrary,the binary dominates the perturbation pattern when the binary separation is consid-erable and the planetary separation is either too large or too small compared to the Einstein radius.These correspond to the cases enclosed by thick white solid lines in Figure2.For events produced by these lens systems,then,the resulting per-turbation would be well described by a binary lens of either star-planet or binary star pair.However,for lens systems with separations located in the neutral region of the d b–d p param-eter space,the in?uences of the planet and stellar binary are equivalent and thus it would be possible to detect both signals of the planet and binary stars.

4.OPTIMAL BINARY AND PLANETARY SEPARATIONS Then,what are the optimal ranges of the binary and plane-tary separations for which the microlensing technique is sen-sitive to the detections of planets orbiting around binary stars. In this section,we investigate these optimal ranges.

The size of the perturbation region is proportional to the size of the caustic.We,therefore,determine the optimal re-gion in the d b–d p parameter space as the one within which the sizes of the planet and binary-induced caustics become equivalent.Figure4shows the regions found under this ap-proximation for three different types of Jupiter,Saturn,and Uranus-mass planets.For lens systems with planetary and binary separations located in the shaded region,the size ra-tio between the two types of caustic is in the range of1/5≤?ξp/?ξb≤5.0,where?ξp and?ξb represent the sizes of the planet and binary-induced caustics,respectively.We ap-ply two exceptions to this rule.The?rst is that if both caus-tics are too small,we assume that the signal detection would be dif?cult due to severe?nite-source effect.To account for the?nite-source effect,we set the lower limit of the caustic

HAN

3

F IG.3.—Light curves of lensing events caused by triple lens systems composed of a planet revolving around binary stars.The lens system geometry and the source star trajectories responsible for the individual events are presented in the corresponding panels of Figure2.In each panel,there exist three light curves. The thick black solid light curve is for the triple-lens event,while the curves drawn in red and blue colors are for the cases where there is no planet and the planet-hosting star is a single object,respectively.

F IG. 4.—The optimal ranges of binary and planetary separations for which microlensing technique is sensitive to the detections of planets orbiting around binary stars.

size for signal detection as two times of the source size.The second exception is that if both caustics are greater than a cer-tain value,we assume that the chance to detect both planet and stellar binary is not small.We set this threshold caustics size as10times of the source size.From the comparison of the optimal ranges determined in this way with those of the neutral region judged based on eye inspection of the maps in Figure2,we?nd good agreement.The optimal ranges vary depending on the planet mass.For a Jupiter-mass planet,we ?nd that high detection ef?ciency is expected for planets lo-cated in the range of1AU d p 5AU orbiting around bina-ries with separations of0.15AU d b 0.5AU.The range of the planetary separation shrinks as the planet mass decreases. However,the range of the binary separation remains nearly the same regardless of the planet mass.In Table1,we sum-marize the optimal ranges for various types of planets.

It might be that planets located in some portions of the tested d b–d p parameter space might be dynamically unstable and thus the estimated optimal region is overestimated.At present,however,the possible extent of the planet separation around stars of a close binary system is an open question and is subject to be tested from observation.In this sense,the con-straint of the stable region of the planetary separation that will be provided by the microlensing method is very important.

5.DISCUSSION

Interpreting the signals of triple-lens systems is not an easy task.With more complete understanding of lensing behavior and the development of ef?cient modelling codes,however, such analysis is being started for the analysis of observed lens-ing events(A.Gould private communication).Not long ago,binary-lens modelling was considered to be a dif?cult task, but now it is routinely conducted for binary events.Consid-ering this,triple-lens modelling would be possible in future lensing analysis.

Nevertheless,one might think of several possible degener-ate cases to the signal of the planet orbiting a close binary stars.One possible case is a triple lens system where a planet orbits around one of widely separated binary stars.In this case,the binary-produced caustic is located also close to the planet-induced caustic,causing potential degeneracy.How-ever,the caustic produced by the wide-separation binary has a very symmetric hypocycloid shape,while the shape of the caustic produced by close binary stars is in general asym-metric.Therefore,the resulting patterns of the two cases are different and thus it would not be dif?cult to distinguish the two cases.Another possible case is a star with multi-ple planets(Gaudi et al.1998).Here the perturbations in the central region are produced by the individual planets.The planet-induced caustics are much more elongated than binary-induced caustic.Therefore,it would not be dif?cult to distin-guish this case,either.

Planets around close binary stars will be detected through the channel of high-magni?cation events.Current microlens-ing follow-up observations(Beaulieu et al.2006;Gould et al. 2006)are focusing on these events due to their high ef?ciency in planet detections(Griest&Sa?zadeh1998).By using mul-tiple telescopes located at different locations,these observa-tions enable dense and continuous coverage of events which is required to detect the short-lasting signature of the planet in binary stars.In addition,greatly enhanced source bright-ness of high-magni?cation events enables precision photome-try which is essential for the characterization of the signature. Therefore,we predict that planets with two simultaneously

4PLANETS WITH TWO SUNS

rising suns would be detected in the near future.

6.CONCLUSION

We investigated the feasibility of detecting planets orbit-ing close binary stars by using the microlensing technique. We presented the channel for which one can identify the sig-natures of such planetary systems.We illustrated the signa-tures for various planet-binary con?gurations and explained the tendencies of the signatures.We also estimated the ranges of the binary and planetary separations for which the mi-crolensing method is ef?cient in detecting these planetary sys-tems.Discovering planets orbiting around close binary stars is dif?cult by using the radial velocity or transit technique. Therefore,microlensing is an important technique that can provide information about these planetary systems,which is very important for our understanding of planet formation.

This work was supported by the Science Research Center (SRC)program.

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