1. (Recent Results on Circumbinary Planets)
The KEPLER Circumbinary Systems
(Recent Results on Circumbinary Planets)
Jerome A. Orosz
with thanks to
Bill Welsh, Don Short, Gur Windmiller, Dan Fabrycky, Josh Carter, Laurance Doyle, The Kepler EB and TTV Working Groups

2. Importance of binaries
Detection methods
Results published to date
Summary
Future work

3. Importance of Binaries
Binaries and higher-order multiple systems are common.
Raghavan et al. (2010) found 54% ± 2% of nearby solar-type stars are single
Many of the target stars in large surveys will be binaries

4. Importance of Binaries
There are two “classes” of binaries with planets:
S-type where the planet orbits one of the stars in a wide binary
P-type or circumbinary where the planet both stars
Several S-type systems are known, mainly from radial velocity surveys where the star with the RV variations has a resolved companion
The first clear detections of circumbinary planets has come from the Kepler data

5. Detection Methods Use eclipse timing variations (ETVs):
The binary system orbits the system center of mass (COM), resulting in a displacement along the line of sight
Variations in the eclipse arrival times of order a few seconds or less might be expected in favorable situations
Variations in the eclipse arrival times of order a few minutes might be expected in cases where there are dynamical interactions

6. Detection Methods Use eclipse timing variations (ETVs):
Most claimed detections based on light travel time (LTT) effects have been controversial. The best case is NN Ser, where two planets with periods of 7.9 and 15.3 years can explain the ETVs

7. Detection Methods Use eclipse timing variations (ETVs):
Most claimed detections based on light travel time (LTT) effects have been controversial. The best case is NN Ser, where two planets with periods of 7.9 and 15.3 years can explain the ETVs
Note that the length of time over which the measurements have been made is about 17 years…

8. Detection Methods
Use transits:

9. Detection Methods Use transits:
Borucki & Summers (1984) argued that one should look at eclipsing binaries (EBs) to find transiting planets: if the orbits are coplanar the probability of a transit is increased around an EB where the orbit is viewed close to edge-on
Schneider & Chevreton (1990) and Deeg et al. (1994) showed that transits in a circumbinary system should have unique signatures

10. Detection Methods Use transits:
Borucki & Summers (1984) argued that one should look at eclipsing binaries (EBs) to find transiting planets: if the orbits are coplanar the probability of a transit is increased around an EB where the orbit is viewed close to edge-on
Schneider & Chevreton (1990) and Deeg et al. (1994) showed that transits in a circumbinary system should have unique signatures
One should use caution, however…

11. The Kepler Mission
The Kepler spacecraft is in an Earth-trailing orbit, which allowed it to observe the same region of the sky nearly continuously for about 4 years
Extremely precise photometry was obtained for nearly 200,000 stars, including about 3000 EBs

12. Here is KOI-28, which has periods of 4.049729 days and 4.100871 days
Such a circumbinary configuration would be unstable, so this must be a blend of two EBs (e.g. two EBs landed on the same pixel)

13. This is KIC 7622486, which has periods of 2. 279996 days and 40
This is KIC , which has periods of days and days
A circumbinary configuration would be stable, so how do we tell if this is a blend?

14. In a triple system, the three bodies move about the system COM
If the third body is planetary, the COM is essentially the binary COM
Stellar eclipses, if the orbit is seen roughly edge on, occur at the stellar conjunctions
At the time of the inferior conjunction of the planet, the stars are not necessarily along the same line-of-sight…

15. The conjunction is when x=0 for the planet
The conjunction is when x=0 for the planet. Chances are the star is not at x=0, and the transits may be early or late relative to a linear ephemeris.

16. The deep events with the 40 day period in KIC do not show significant variations from a linear ephemeris, so they must be due to a blended EB

17. Here is Kepler-16. The orbital period is 41. 0777 days
Here is Kepler-16. The orbital period is days. Note the extra transit in Q1.

18. Here is Kepler-16. The orbital period is 41. 0777 days
Here is Kepler-16. The orbital period is days. Note the extra transit in Q1. Also in Q4.

19. Here is Kepler-16. The orbital period is 41. 0777 days
Here is Kepler-16. The orbital period is days. Note the extra transit in Q1. Also in Q4. And in Q6

20. There are 7 such events through Q16, with a rough period of 221 days

21. There are transit timing variations (TTVs) of up to 6 days, which indicates that this is not a blend
The dips are caused by the third body transits of the primary

22. We also see transits of the secondary star, which completely rules out a blended EB

23. We also see ETVs
The primary O-C curve has a different slope than the secondary O-C curve, which in an indication the primary and secondary eclipse periods are different.
In this case, the two periods differ by seconds

24. Each curve shows a periodicity of about 112 days, which is roughly half of the mean period of the transits.

25. The big arrow is how the planet pulls on the COM of the binary
The small arrows are the tidal force the planet puts on the stars
The m=2 tidal pattern rotates at the planet’s orbital period, and every half an orbit the stars have to climb up and down the tidal potential

26. Their phases are successively delayed and advanced every period of the planet, so the observed effect is twice the planet’s frequency

27. Here is an other example (Kepler-38)
Here is an other example (Kepler-38). Note the transit duration variations

28. In general, the TTVs and the durations of circumbinary transits vary cyclically with the binary phase, which can be understood analytically

30. Near the phase of the primary eclipse, the planet and the star are moving in opposite directions, hence the transits are shorter
Near the phase of the secondary eclipse, the planet and the star are moving in the same direction, hence the transits are longer

31. What We Have Learned So Far
Given enough events, the transits of a circumbinary body will show large TTVs, which can rule out a blend
The circumbinary body can transit both stars, and if the primary and secondary eclipses are not equal, the transits across the primary and secondary will likewise be unequal---this also rules out a blend
Under certain conditions, the circumbinary body can perturb the binary, leading to observable effects

32. Details, Details
Since the binary is not a point mass, the planet’s orbit is not exactly Keplerian
Since the planet may perturb one or both stars, their orbits may not be strictly Keplerian
Given the above, the standard codes to model eclipsing binaries need to be modified to account for the gravitational interactions
The first such code was devised by Josh Carter
My ELC code has been modified to include the necessary dynamical effects

33. Details, Details
The transit depths give you the ratio of the planet’s radius to the stellar radius
The eclipses give you the ratio of the stellar radii
The radial velocity curve of at least one star is needed to establish the scale of the system
If the scale of the system is known, the actual radii of the stars and the planet can be found
If ETVs are observed, then mass of the planet can be found

34. Initial Discoveries
Between October, 2011 and October, 2013 we announced the discovery of five EBs with circumbinary planets:
Kepler 16 (Doyle et al. 2011)
Kepler 34, 35 (Welsh et al. 2012)
Kepler 38 (Orosz et al. 2012a)
Kepler 47 (Orosz et al. 2012b)

35. Kepler 16
We have 7 primary transits observed with Kepler, plus one additional one from the ground. The planet’s period is days

36. Kepler 34
Transits of both stars are evident. The planet’s period is 289 days.

37. Kepler 35
Transits of both stars are evident. The planet’s period is 132 days.

38. Kepler 38
Transits of only the primary are evident. The planet’s period is 106 days.

39. Kepler 47
The first planet transited the primary 24 times. That planet’s period is 49.5 days.

40. Kepler 47
The second planet transited the primary 6 times. That planet’s period is 187 days.

41. Kepler 47
The third planet transited the primary 4 times. That planet’s period is 303 days.

42. Additional Systems
Kepler-64 (aka Planet Hunters-1, Schwamb et al. 2013)
Kepler-413 (Kostov et al. 2014)
Kepler-453 (Welsh et al. 2015)
Kepler-1647 (Kostov et al. 2016)

43. Kepler 453
Three transits of the primary are evident, starting in Q9. The planet’s period is 241 days.

44. Kepler-1647 Brightness Time Primary Eclipse 20% loss Secondary Eclipse
Planet Transit
0.2% loss

45. View from Earth
Image: Lynette Cook

46. The Big Picture The score so far:
11 planets in 9 eclipsing binaries published
3 more eclipsing binaries with a single planet each in the works:
KOI 3152 (Socia et al submitted)
KIC (Orosz et al. in prep)
TIC (Kostov et al. in prep)

47. KOI 3152
Three transits of the primary are evident, starting in Q9. The planet’s period is 175 days.

48. KIC
Two pairs of primary+secondary transits are seen, starting in Q13. The planet’s period is 260 days.

49. TIC
Three transits of the primary are seen (it is in the TESS CVZ). The planet’s period is 95 days.

50. TIC
This SB1 was observed as part of the BEBOP program. The binary has P=14.61 days and e=0.16

51. TIC
The R-M effect was observed with CORALIE. The errors on the HARPS data are about 5 m/sec

52. The Big Picture The developing picture, based on all systems:
The primary star masses range from 0.69 to 1.53 solar masses (Kepler-16, Kepler-64)
The eccentricities of the binaries range from to (Kepler-47, Kepler-34)
The periods of the binaries range from 7.49 to days (Kepler-47, Kepler-16)
All systems are within a few degrees of being coplanar
The stellar spin axis of Kepler-16 and Kepler-47 are roughly aligned with the orbital angular momentum

53. The Big Picture The developing picture, based on all systems:
With three exceptions (two outer planets in Kepler-47 and Kepler-1647), the planets orbit very close to the critical radius for stability

54. The Big Picture

55. The Big Picture

56. The Big Picture The developing picture, based on all systems:
With three exceptions (two outer planets in Kepler-47 and Kepler-1647), the planets orbit very close to the critical radius for stability
With one exception (Kepler-1647), all planets have radii much smaller than Jupiter (keep in mind larger planets are easier to detect owing to deeper transits)

57. The Big Picture

58. The Big Picture The developing picture, based on all systems:
With three exceptions (two outer planets in Kepler-47 and Kepler-1647), the planets orbit very close to the critical radius for stability
With one exception (Kepler-1647), all planets have radii much smaller than Jupiter (keep in mind larger planets are easier to detect owing to deeper transits)
With one exception (Kepler-1647), the planets with reliable measurements all have masses between Neptune’s and Saturn’s

59. The Big Picture

60. The Big Picture

61. The Big Picture
Precession of the planet’s orbit is usually results in limited “windows” of “transitability”
-- For example, KOI-3152 transits about 7% of the time

62. The Big Picture
Precession of the planet’s orbit is usually results in limited “windows” of “transitability”
-- For example, Kepler-453 transits about 8% of the time

63. The Big Picture Planet Time scale (yr) Transit % Kepler-16 ~40 40
~50
Kepler-35
~20
Kepler-47
~10
100
~245 23
~738 12
Kepler-413
~11
Kepler-453
~103 8
Kepler-1647
~7041 6
KOI-3152
~35 7
TESS 2601
~23 61

64. The Big Picture
Precession of the planet’s orbit is usually results in limited “windows” of “transitability”

65. The Big Picture The developing picture, based on all systems:
The planet with the largest mass and radius (Kepler-1647) has the orbit that is by far the largest---the other planets with lower mass orbit very near the stability limit
Pierens & Nelson (2008) predicted such a tendency, based on simulations of orbital evolution of planets in a circumbinary disk (Jupiter-mass planets tend to be unstable)

66. The Big Picture The developing picture, based on all systems:
About half of the EBs in the Kepler sample have periods of a few days or less
The shortest period circumbinary system has a period of 7.5 days (Kepler-47), and typical periods are 20 days or more

67. vertical lines show EBs that host planets.
Note: very incomplete at long periods.
median
period
= 2.30 d

68. The Big Picture The developing picture, based on all systems:
About half of the EBs in the Kepler sample have periods of a few days or less
The shortest period circumbinary system has a period of 7.5 days (Kepler-47), and typical periods are 20 days or more
Is this an observational bias?
Short-period systems should have more transits, and should be easier to detect
On the other hand, shorter-period systems tend to have more stellar activity and other “complications”

69. The Big Picture The developing picture, based on all systems:
About half of the EBs in the Kepler sample have periods of a few days or less
The shortest period circumbinary system has a period of 7.5 days (Kepler-47), and typical periods are 20 days or more
Is this an observational bias?
The apparent lack of planets around short-period binaries may be related to the mechanism that removed the angular momentum from the stellar orbit and allowed the stars to orbit so closely

70. Future Work
All of the Kepler CBPs were found visually. Is there a better way?

71. Future Work
All of the Kepler CBPs were found visually. Is there a better way?

72. Future Work
All of the Kepler CBPs were found visually. Is there a better way?

73. Future Work
What about TESS?

74. Future Work
What about TESS?

75. Future Work What about TESS?
Can see ~100 systems using the “1-2 punch” technique where two or more transits occur at one conjunction

76. Future Work What about TESS?
TESS observed the Kepler field the summer of 2019, so update all solutions using new stellar eclipses

77. Questions?