INFLUENCE OF STELLAR MULTIPLICITY ON PLANET FORMATION. IV. ADAPTIVE OPTICS IMAGING OF KEPLER STARS WITH MULTIPLE TRANSITING PLANET CANDIDATES

The sample of MTPSs remains the same as that in Wang et al. (2014b). From the NASA Exoplanet Archive⁵ , we select Kepler objects of interest (KOIs) that satisfy the following criteria: (1) disposition of either Candidate or Confirmed; (2) with at least two planet candidates; (3) Kepler magnitude (K_P) brighter than 13.5. The above selection criteria resulted in 138 MTPSs in Wang et al. (2014b). With the updated Exoplanet Archive, the selection criteria resulted in 208 MTPSs. In this paper, we focus on the 138 MTPSs to be consistent with previous work. Their stellar and orbital parameters can be found in Tables 2 and 3 in Wang et al. (2014b).

Most MTPSs in our sample are true planetary systems based on a statistical analysis by Lissauer et al. (2012). Subsequent papers on Kepler MTPS validated 851 planet candidates in 340 systems (Lissauer et al. 2014; Rowe et al. 2014), 66 MTPSs in our sample are included in those validated systems. Furthermore, 25 additional MTPSs in our sample are confirmed planetary systems, and the remaining 47 MTPSs have the disposition of a planet candidate according to the latest NASA Exoplanet Archive. Therefore, the false-positive rate for the MTPS sample studied in this paper should be extremely low.

2.2.1. Archival AO Data for Follow-up Observations

2.2.2. AO Imaging with PHARO at Palomar

2.2.3. AO Imaging with NIRC2 at Keck II

The raw data were processed using standard techniques to replace bad pixels, subtract dark, flat-field, subtract sky background, align, and co-add frames. We constructed a bad pixel map using dark frames. Pixels with dark currents that deviated more than 5σ from their surrounding pixels were recorded as bad pixels. Their values were replaced with the median flux of surrounding pixels. Dark frames were obtained with the exact same setting as the science frames, e.g., exposure time, co-adds, and readout mode. After dark subtraction, each science frame was corrected for flat fielding. The dithered science frames provided an estimate of the sky background that was subtracted off from the science frames. The dark-subtracted, flat-fielded, sky-removed science frames were then co-added, resulting in a single frame for subsequent analyses.

We calculated 5σ detection limit as follows. We defined a series of concentric annuli centering on the star. For the concentric annuli, we calculated the median and the standard deviation of flux for pixels within these annuli. We used the value of five times the standard deviation above the median as the 5σ detection limit. The detection limits at different angular separations are reported in Table 1. We developed an automatic program to detect stellar companions whose differential magnitudes are brighter than the 5σ detection limit. The program recorded the differential magnitude, position, position angle, and detection significance of each detection. All detections were then visually checked to remove confusions such as speckles, background extended sources, and cosmic-ray hits. In total, 42 stellar companions were detected within 5'' around 35 KOIs. Their properties are summarized in Table 2. Figure 1 shows nine KOIs with newly detected stellar companions within 2''.

Zoom In Zoom Out Reset image size

Table 2.  Visual Companion Detections with AO Data for Kepler MTPS

KOI	Star#	Telescope	Filter	Δ Maga	Separationb		Distancec		PA	Associationd	Ref.e
							Primary	Secondary		Probability
				(mag)	(arcsec)	(AU)	(pc)	(pc)	(deg)
K00005	1	Keck	K	2.20	0.14	40.12	${286.6}_{-15.8}^{71.1}$	...	307.4	>0.90	CFOP
K00070	1	Palomar	J	4.41	3.77	1052.60	${279.5}_{-23.6}^{25.3}$	...	51.8	0.52	A12
K00102	1	Palomar	J	1.12	2.84	934.31	${329.4}_{-30.5}^{75.0}$	...	222.2	>0.90	A12
K00108	1	Palomar	J	5.71	2.51	891.07	${354.6}_{-39.2}^{45.4}$	...	285.2	0.48	A12
K00108	2	Palomar	J	5.60	3.23	1145.12	${354.6}_{-39.2}^{45.4}$	...	100.8	0.30	A12
K00108	3	Palomar	J	6.60	5.00	1773.09	${354.6}_{-39.2}^{45.4}$	...	112.5	0.00	A12
K00115	1	MMT	K	5.06	4.00	2168.27	${542.1}_{-97.0}^{140.6}$	...	89.7	0.33	A12
K00119	1	Palomar	J	0.16	1.05	327.89	${313.0}_{-62.2}^{106.8}$	${380.8}_{-154.5}^{499.6}$	119.1	>0.90	this work
K00119	1	Palomar	K	0.22	1.04	326.17	${313.0}_{-62.2}^{106.8}$	${380.8}_{-154.5}^{499.6}$	120.2	>0.90	this work
K00148	1	Palomar	J	4.75	2.51	775.44	${308.7}_{-17.2}^{27.0}$	...	245.6	0.78	A12
K00148	2	Palomar	J	3.14	4.43	1368.74	${308.7}_{-17.2}^{27.0}$	...	220.4	0.73	A12
K00279	1	Keck	K	2.35	0.92	247.44	${268.6}_{-46.3}^{187.6}$	...	247.3	>0.90	CFOP
K00282	1	Palomar	K	3.86	4.16	1408.24	${338.8}_{-26.5}^{16.9}$	...	210.3	0.84	CFOP
K00284	1	Palomar	J	0.24	0.87	229.45	${264.7}_{-39.4}^{34.4}$	${339.5}_{-146.8}^{347.4}$	95.8	>0.90	A12
K00284	1	Palomar	K	0.24	0.86	226.48	${264.7}_{-39.4}^{34.4}$	${339.5}_{-146.8}^{347.4}$	96.7	>0.90	A12
K00285	1	Palomar	J	4.19	1.50	676.86	${452.7}_{-47.0}^{18.4}$	${3855.9}_{-3163.9}^{2632.5}$	137.7	>0.90	CFOP
K00285	1	Palomar	K	4.08	1.50	677.09	${452.7}_{-47.0}^{18.4}$	${3855.9}_{-3163.9}^{2632.5}$	137.7	>0.90	CFOP
K00298	1	Palomar	J	0.24	2.00	581.07	${290.2}_{-54.4}^{300.0}$	${247.2}_{-68.1}^{335.0}$	272.8	>0.90	this work
K00298	1	Palomar	K	0.08	1.96	570.05	${290.2}_{-54.4}^{300.0}$	${247.2}_{-68.1}^{335.0}$	272.5	>0.90	this work
K00312	1	Palomar	K	6.67	3.01	950.62	${316.1}_{-25.9}^{33.3}$	...	104.4	0.34	this work
K00312	2	Palomar	K	5.84	4.97	1569.91	${316.1}_{-25.9}^{33.3}$	...	121.7	0.33	this work
K00326	1	Palomar	K	1.03	3.49	27865.11	${7989.4}_{-1200.3}^{1953.2}$	...	269.4	0.89	this work
K00353	1	Palomar	K	3.07	1.04	820.45	${789.7}_{-103.2}^{151.9}$	...	23.0	>0.90	this work
K00353	2	Palomar	K	4.15	1.43	1131.97	${789.7}_{-103.2}^{151.9}$	...	236.3	>0.90	this work
K00354	1	Palomar	K	4.83	3.73	1425.50	${382.1}_{-25.5}^{29.8}$	...	210.1	0.36	this work
K00626	1	Palomar	K	5.30	2.75	1463.00	${532.3}_{-43.4}^{39.1}$	...	167.9	0.21	this work
K01151	1	Palomar	K	2.25	0.76	316.71	${419.5}_{-50.0}^{53.7}$	...	306.6	>0.90	this work
K01316	1	MMT	K	5.81	2.78	1249.69	${449.6}_{-96.3}^{185.2}$	...	4.8	0.68	CFOP (Dupree)
K01613	1	Keck	K	1.00	0.22	79.49	${364.3}_{-19.1}^{21.7}$	...	184.6	>0.90	CFOP
K01613	1	Palomar	K	1.16	0.21	75.31	${364.3}_{-19.1}^{21.7}$	...	183.4	>0.90	CFOP
K01692	1	Palomar	K	6.36	3.17	841.66	${265.4}_{-19.8}^{14.6}$	...	337.2	0.31	this work
K01781	1	Keck	J	2.71	3.48	607.66	${174.8}_{-14.8}^{10.7}$	${508.7}_{-178.8}^{569.0}$	332.4	>0.90	this work
K01781	1	Keck	K	2.35	3.47	606.92	${174.8}_{-14.8}^{10.7}$	${508.7}_{-178.8}^{569.0}$	332.2	>0.90	this work
K01781	1	Palomar	K	2.29	3.43	599.24	${174.8}_{-14.8}^{10.7}$	${508.7}_{-178.8}^{569.0}$	332.4	>0.90	this work
K01806	1	Palomar	K	1.45	3.43	2096.38	${612.1}_{-70.2}^{62.3}$	...	249.7	0.90	this work
K01929	1	Palomar	K	4.86	1.37	835.32	${608.8}_{-162.1}^{64.2}$	...	163.0	>0.90	this work
K01932	1	Keck	J	4.08	0.54	1165.27	${2171.2}_{-885.7}^{444.3}$	${10489.3}_{-10378.5}^{2415.5}$	116.6	>0.90	this work
K01932	1	Keck	H	3.37	0.52	1129.01	${2171.2}_{-885.7}^{444.3}$	${10489.3}_{-10378.5}^{2415.5}$	115.3	>0.90	this work
K01932	1	Keck	K	3.12	0.52	1138.78	${2171.2}_{-885.7}^{444.3}$	${10489.3}_{-10378.5}^{2415.5}$	115.1	>0.90	this work
K01932	2	Palomar	K	4.12	4.57	9928.21	${2171.2}_{-885.7}^{444.3}$	...	312.9	0.51	this work
K02011	1	Palomar	K	2.73	4.95	2312.74	${467.1}_{-68.5}^{59.2}$	...	292.1	0.82	this work
K02059	1	Keck	K	0.14	0.39	92.93	${238.4}_{-15.7}^{13.8}$	...	289.5	>0.90	this work
K02059	1	Palomar	K	0.14	0.38	91.43	${238.4}_{-15.7}^{13.8}$	...	289.0	>0.90	this work
K02169	1	Palomar	K	2.74	3.49	1026.94	${294.1}_{-29.0}^{97.4}$	...	289.0	>0.90	this work
K02289	1	Palomar	K	2.78	0.94	535.74	${570.5}_{-67.8}^{99.2}$	...	221.2	>0.90	this work
K02672	1	Palomar	K	3.46	0.65	152.28	${236.0}_{-46.5}^{126.7}$	...	305.5	>0.90	CFOP
K02672	2	Palomar	K	6.04	4.62	1090.18	${236.0}_{-46.5}^{126.7}$	...	310.5	0.26	this work
K02949	1	Palomar	K	3.86	2.35	1442.31	${613.1}_{-111.5}^{598.6}$	...	311.0	0.81	this work
K03158	1	Palomar	J	2.39	1.83	54.30	${29.6}_{-3.1}^{1.4}$	${78.8}_{-64.7}^{53.8}$	253.3	>0.90	C15
K03158	1	Keck	K	2.21	1.86	55.05	${29.6}_{-3.1}^{1.4}$	${78.8}_{-64.7}^{53.8}$	252.8	>0.90	C15
K03158	1	Palomar	K	2.13	1.83	54.35	${29.6}_{-3.1}^{1.4}$	${78.8}_{-64.7}^{53.8}$	253.1	>0.90	C15
K03500	1	Palomar	K	3.35	2.53	1150.97	${455.2}_{-44.7}^{60.4}$	...	140.0	0.90	this work
K04021	1	Palomar	K	0.33	1.74	1886.56	${1085.2}_{-221.0}^{303.3}$	...	115.8	>0.90	this work
K04288	1	Palomar	K	6.59	2.93	1039.80	${354.8}_{-37.1}^{61.1}$	...	279.8	0.03	this work

Notes.

^aTypical ΔMag uncertainty is 0.1 mag. The uncertainty is estimated from the companion injection simulation described in Section 3.3. ^bTypical angular separation uncertainty is 005. The uncertainty is estimated from the companion injection simulation described in Section 3.3. ^cDistance is estimated based on stellar properties of primary stars (Huber et al. 2014) and color information of secondary stars (see Section 4.1 in Wang et al. 2015 for more details). ^dAssociation probability has 10% uncertainty due to statistical error in simulation. ^eAO images from CFOP are provided by David Ciardi unless otherwise noted.

References. A12—Adams et al. (2012); C15—Campante et al. (2015).

Download table as:  ASCIITypeset images: 1 2

For stellar companions detected by imaging techniques, we need to check whether they are optical doubles/multiples, which will systematically increase the stellar multiplicity rate. To test physical association, Ngo et al. (2015) obtained multiple-epoch AO images and measured common proper motion. In our case, Kepler stars are generally farther away and common proper motion is more difficult to measure. Given only one epoch of observation, we can use color information of detected stellar companions and assess the probability of their physical association to primary stars (Lillo-Box et al. 2014; Wang et al. 2014a, 2015). The color information provides an estimate of the stellar properties, which can then be used to estimate distance for consistency check between the primary and the secondary stars. Any inconsistent distance would be an indication that the primary and the secondary stars are optical doubles. For stellar companions with only single-band observations, color information is not available. We can assess the probability with a galactic stellar population simulation. This method is described in detail in Wang et al. (2015), and the physical association probabilities of each detected stellar companions are given in Table 2.

Following the method described in Wang et al. (2015), we conduct simulations to estimate the search completeness for the AO observations. In these simulations, we use the AO contrast curve as a threshold for detection. In practice, however, not all stars above the AO contrast curve are detected by our pipeline, so we run another simulation to test the goodness of using the contrast curve as a threshold. The simulation is identical to other studies (Lillo-Box et al. 2014; Gilliland et al. 2015; Ngo et al. 2015) that artificially inject companion stars with the same PSF at random separations, differential magnitudes, and position angles. The results are shown in Figure 2 for two examples, one for a Palomar AO image and the other one for Keck. For the Palomar AO image, 94.7% of injected companion stars above the contrast curve are successfully recovered by our detection pipeline and 88.2% of injections below the contrast curve are missed. For the Keck image, 90.7% of injections are recovered above the contrast curve and 88.4% are missed below the contrast curve. The simulation shows that using the contrast curve as a detection threshold is a reasonable assumption. The resulting AO search completenesses are within a few percent for the case of using the AO contrast curve as a hard limit for detection and for the case using the artificial PSF injection result (Lillo-Box et al. 2014; Gilliland et al. 2015; Ngo et al. 2015). The comparable results are due to a relatively smooth distribution of masses and separations of stellar companions, which translates to a smooth distribution on the ΔMag—angular separation plane as shown in Figure 2. The hard-edge effect of using the AO contrast curve is averaged out and becomes comparable with a more realistic artificial PSF injection simulation.

Zoom In Zoom Out Reset image size

Since AO imaging technique is not sensitive to stellar companions within or close to the diffraction limit of a telescope, we use other techniques to constrain the presence of stellar companions, i.e., the RV technique and the dynamical analysis (Wang et al. 2014b). There are 22 KOIs in our sample with at least three epochs of RV observation. Following the description of Wang et al. (2014a), we use the Keplerian Fitting Made Easy package (Giguere et al. 2012) to analyze the RV data. Among 22 KOIs with RV data, only KOI-5 exhibits an RV trend. The stellar companion that can potentially induce the trend is constrained to be beyond 7 AU (Wang et al. 2014a). More recent RV data suggest that in addition to two transiting planet candidates, two more distant components exist in the KOI-5 system (H. Isaacson 2015, private communication). One is a sub-stellar companion with a period of ∼2700 days and the other one is the AO-imaged stellar companion. Therefore, we consider the closest stellar companion to KOI-5 to have a projected separation of 40.12 AU (Table 2).

Besides RV and AO observations, we can use dynamical analysis to put additional constraints on potential stellar companions. This dynamical analysis makes use of the coplanarity of MTPSs discovered by the Kepler mission (Lissauer et al. 2011). A stellar companion with high mutual inclination to the planetary orbits would have perturbed the orbits and significantly reduced the coplanarity of planetary orbits, and hence the probability of multi-planet transits (see Section 2.6 in Wang et al. 2014b). Therefore, the fact that we have observed multiple transiting planet helps to exclude the possibility of a highly inclined stellar companion. The dynamical analysis is complementary to the RV technique because it is sensitive to stellar companions with large mutual inclinations to the planetary orbits. For systems with no stellar companions detected by the AO and/or RV method, an isolation probability can be calculated based on the search completeness of AO and RV observations and the constraints from the dynamical analysis (Wang et al. 2015). The isolation probability is a measure of how likely a star is isolated from other stellar companions within a certain distance. The isolation probabilities within 2000 AU for KOIs with non-detections of stellar companions are given in Table 1.

The stellar multiplicity rate for MTPSs (5.2 ± 5.0%) is 2.8σ lower than that for stars in the solar neighborhood (21.1 ± 2.8%) for 1 AU < a < 100 AU. The difference may result from two possible origins that are not mutually exclusive. First, MTPSs occur less frequently in multiple stellar systems. Suppressive planet formation in multiple stellar systems has been noted in previous observational works on both RV and transiting planet samples (e.g., Eggenberger et al. 2011; Roell et al. 2012; Wang et al. 2014b) and recently a theoretical work (Touma & Sridhar 2015). However, other works suggest that the influence of a stellar companion may not be significant (Horch et al. 2014; Gilliland et al. 2015) or may be facilitative depending on the stellar separation and planetary mass (Ngo et al. 2015; Wang et al. 2015).

If suppressive planet formation does not play a role, there may be another origin for the low stellar multiplicity rate: MTPSs are less likely to be observed in multiple stellar systems (Wang et al. 2014b). Coplanarity of MTPSs can be affected by an additional stellar component. Thus, the likelihood of observing multiple transiting planets is reduced.

If suppressive planet formation plays a major role, then our measurements of stellar multiplicity rates indicate that within 100 AU, MTPSs occur less frequently due to the influence of stellar companions. For 100 AU < a < 2000 AU, since the stellar multiplicity rates are comparable (0.9σ difference) between MTPSs (8.0 ± 4.0%) and the control sample (12.5 ± 2.8%), we conclude that the influence of stellar companions, if any, is too small to be observed.

If coplanarity is responsible for the observed low stellar multiplicity rate for MTPSs, then we should expect a difference of stellar multiplicity rate between MTPSs and STPSs. Note that the influence of stellar companions on coplanarity depends on stellar separations. If stellar separations are beyond ∼100 AU, their influence on coplanarity is negligible (Wang et al. 2014a, 2014b). Therefore, any difference of the stellar multiplicity rate beyond 100 AU is more likely to be due to the origin of planet formation rather than the companions' influence on coplanarity.

In Section 5.1, we show that beyond 100 AU, the stellar multiplicity rates are comparable between MTPSs and the control sample. Here, we compare MTPSs to STPSs. Since these two populations likely have different dynamical histories (Morton & Winn 2014; Xie et al. 2014), the comparison allows us to study whether the difference is related to stellar multiplicity.

From CFOP, we select 89 Kepler STPSs. The selection criteria are the same as described in Section 2 with two exceptions: (1) the number of transiting planets is equal to one; (2) they must have AO images. The stellar properties of these STPSs are given in Table 3. The sample of these STPSs is a subsample of Kepler stars with high-resolution imaging observations from CFOP (D. Ciardi 2015, in preparation). Out of these 89 Kepler stars, only 6 have RV observations. Since the RV technique is sensitive to close-in stellar companions, obtaining the statistics for stellar companions within 100 AU is difficult. Therefore, we focus on 100 AU < a < 2000 AU. The AO detections are listed in Table 4. Following the same method in Wang et al. (2015), we find that the stellar multiplicity rate is 6.4 ± 5.8% for STPSs for 100 AU < a < 2000 AU. The value is consistent with that for MTPSs, i.e., 8.0 ± 4.0%. Therefore, we find no evidence that stellar companions between 100 and 2000 AU are responsible for the difference of orbital configuration between MTPSs and STPSs. However, the difference may be caused by stellar companions within 100 AU, for which we do not have adequate observational constraints.

Table 4.  Visual Companion Detections with AO Data for Kepler STPS

KOI	Star#	Telescope	Filter	Δ Maga	Separationb		Distancec		PA	Associationd	Ref.e
							Primary	Secondary		Probability
				(mag)	(arcsec)	(AU)	(pc)	(pc)	(deg)
K00118	1	Palomar	J	3.94	1.24	583.76	${470.3}_{-24.4}^{18.8}$	${1152.1}_{-605.8}^{878.0}$	214.3	>0.90	CFOP
K00118	1	Palomar	K	3.65	1.23	578.94	${470.3}_{-24.4}^{18.8}$	${1152.1}_{-605.8}^{878.0}$	214.6	>0.90	CFOP
K00268	1	MMT	J	3.03	1.57	372.64	${238.1}_{-7.1}^{32.6}$	${305.4}_{-274.7}^{116.2}$	179.7	>0.90	CFOP
K00268	1	MMT	K	2.52	1.65	392.07	${238.1}_{-7.1}^{32.6}$	${305.4}_{-274.7}^{116.2}$	174.8	>0.90	CFOP
K00268	1	Palomar	K	2.47	1.75	415.62	${238.1}_{-7.1}^{32.6}$	${305.4}_{-274.7}^{116.2}$	267.3	>0.90	CFOP
K00268	2	MMT	J	4.37	2.34	556.29	${238.1}_{-7.1}^{32.6}$	${305.4}_{-274.7}^{116.2}$	128.1	>0.90	CFOP (Dupree)
K00268	2	MMT	K	3.87	2.33	554.58	${238.1}_{-7.1}^{32.6}$	${305.4}_{-274.7}^{116.2}$	132.0	>0.90	CFOP (Dupree)
K00268	2	Palomar	K	3.72	2.49	593.65	${238.1}_{-7.1}^{32.6}$	${305.4}_{-274.7}^{116.2}$	309.9	>0.90	CFOP
K00273	1	MMT	J	4.75	0.51	122.11	${239.0}_{-12.0}^{11.5}$	${25619.3}_{-14890.6}^{15172.9}$	152.4	>0.90	CFOP (Dupree)
K00273	1	MMT	K	5.31	0.55	131.77	${239.0}_{-12.0}^{11.5}$	${25619.3}_{-14890.6}^{15172.9}$	152.4	>0.90	CFOP (Dupree)
K00306	1	Palomar	J	2.27	2.08	473.60	${228.2}_{-8.6}^{9.2}$	${400.2}_{-348.9}^{189.0}$	245.4	>0.90	CFOP
K00306	1	Palomar	K	1.95	2.08	475.48	${228.2}_{-8.6}^{9.2}$	${400.2}_{-348.9}^{189.0}$	245.3	>0.90	CFOP
K00344	1	Palomar	K	3.53	4.13	2465.18	${597.5}_{-126.2}^{290.0}$	...	178.8	0.76	this work
K00344	2	Palomar	K	5.30	3.57	2132.69	${597.5}_{-126.2}^{290.0}$	...	210.5	0.39	this work
K00374	1	Palomar	J	6.03	1.76	643.62	${366.6}_{-28.1}^{124.0}$	${20614.0}_{-12594.6}^{4747.0}$	88.3	0.69	CFOP
K00374	1	Palomar	K	6.32	1.85	676.52	${366.6}_{-28.1}^{124.0}$	${20614.0}_{-12594.6}^{4747.0}$	87.4	0.67	CFOP
K01311	1	Palomar	K	4.20	0.44	284.23	${648.2}_{-111.1}^{483.8}$	...	175.9	>0.90	this work
K01537	1	MMT	K	0.13	0.09	45.56	${522.5}_{-56.1}^{28.3}$	...	64.5	>0.90	CFOP (Dupree)
K01615	1	Palomar	K	6.60	2.98	610.53	${205.1}_{-11.7}^{13.5}$	...	357.8	0.18	CFOP
K01619	1	Keck	K	2.00	2.09	265.00	${126.8}_{-10.9}^{4.3}$	...	226.7	>0.90	CFOP
K01808	1	Palomar	K	3.30	4.69	1991.97	${424.4}_{-70.8}^{177.3}$	...	162.9	0.66	this work
K01890	1	Keck	K	2.02	0.41	181.54	${443.0}_{-45.5}^{13.5}$	...	145.4	>0.90	CFOP
K01964	1	Palomar	J	2.09	0.40	51.28	${129.2}_{-13.0}^{14.4}$	${186.2}_{-152.8}^{127.1}$	0.4	>0.90	CFOP
K01964	1	Palomar	K	1.83	0.40	51.28	${129.2}_{-13.0}^{14.4}$	${186.2}_{-152.8}^{127.1}$	0.9	>0.90	CFOP
K02032	1	Palomar	K	0.40	1.10	311.71	${283.8}_{-27.0}^{19.2}$	...	311.4	>0.90	CFOP
K02324	1	Palomar	K	0.48	4.73	7271.72	${1537.1}_{-258.9}^{1574.8}$	...	353.4	0.73	CFOP
K02706	1	Palomar	K	5.37	1.66	455.08	${273.7}_{-21.3}^{27.1}$	...	165.8	>0.90	CFOP
K02754	1	Palomar	K	1.55	0.79	231.80	${294.9}_{-35.4}^{296.7}$	...	260.4	>0.90	CFOP
K02790	1	Keck	K	0.48	0.26	88.75	${341.5}_{-28.8}^{16.7}$	...	134.6	>0.90	CFOP
K02904	1	Palomar	K	2.16	0.69	264.31	${383.2}_{-27.2}^{33.8}$	...	226.4	>0.90	CFOP
K03168	1	Palomar	J	3.78	0.80	192.09	${239.4}_{-22.9}^{8.0}$	${379.0}_{-334.5}^{132.3}$	332.6	>0.90	CFOP
K03168	1	Keck	K	3.37	0.81	193.33	${239.4}_{-22.9}^{8.0}$	${379.0}_{-334.5}^{132.3}$	332.3	>0.90	CFOP
K03168	1	Palomar	K	3.33	0.81	192.81	${239.4}_{-22.9}^{8.0}$	${379.0}_{-334.5}^{132.3}$	332.2	>0.90	CFOP
K03190	1	Palomar	K	3.96	2.38	954.33	${401.7}_{-57.8}^{56.7}$	...	188.4	0.90	CFOP
K03245	1	Palomar	K	1.84	1.54	590.39	${384.0}_{-27.1}^{54.1}$	...	185.1	>0.90	CFOP
K03248	1	Palomar	K	4.76	3.98	1332.34	${334.7}_{-37.3}^{53.4}$	...	242.5	0.48	CFOP
K04329	1	Keck	K	2.89	1.84	625.41	${340.0}_{-33.3}^{26.0}$	...	118.6	>0.90	CFOP
K04407	1	Palomar	K	1.99	2.46	616.94	${251.0}_{-37.6}^{193.0}$	...	299.9	>0.90	CFOP
K04407	2	Palomar	K	4.91	2.65	665.76	${251.0}_{-37.6}^{193.0}$	...	311.2	0.84	CFOP
K05236	1	Palomar	K	6.01	1.93	966.01	${500.5}_{-41.8}^{41.3}$	...	281.9	0.44	CFOP
K05556	1	Palomar	K	2.70	3.33	1300.46	${391.1}_{-48.8}^{54.3}$	...	162.7	>0.90	CFOP
K05556	2	Palomar	K	3.97	3.15	1233.77	${391.1}_{-48.8}^{54.3}$	...	248.6	0.83	CFOP
K05665	1	Palomar	K	2.27	2.08	847.21	${407.2}_{-54.6}^{12.6}$	...	94.1	>0.90	CFOP
K05949	1	Palomar	K	3.06	0.69	415.34	${600.9}_{-86.5}^{74.7}$	...	255.3	>0.90	CFOP

Notes.

^aTypical ΔMag uncertainty is 0.1 mag. The uncertainty is estimated from the companion injection simulation described in Section 3.3. ^bTypical angular separation uncertainty is 005. The uncertainty is estimated from the companion injection simulation described in Section 3.3. ^cDistance is estimated based on stellar properties of primary stars (Huber et al. 2014) and color information of secondary stars (see Section 4.1 in Wang et al. 2015 for more details). ^dAssociation probability has 10% uncertainty due to statistical error in simulation. ^eAO images from CFOP are provided by David Ciardi unless otherwise noted.

Download table as:  ASCIITypeset images: 1 2

The same sample of 138 MTPSs were studied in Wang et al. (2014b). They found evidence of suppressive planet formation in tight binary stellar systems with a < 20 AU. This finding is consistent with the finding in this paper that the stellar multiplicity rate for MTPSs is lower than the control sample within 100 AU at the 2.8σ level. However, we cannot rule out another possibility that may cause the low stellar multiplicity, i.e., the influence of stellar companions on coplanarity of planetary orbits.

Combining newly obtained AO imaging data with archival RV data, we improve the statistics of stellar companions of planet host stars at large semimajor axes. For example, in Wang et al. (2014b), stellar multiplicity rate can only be constrained within ∼100 AU because of a lack of AO imaging data. In this work, we extend the constraints to 2000 AU. Even within 100 AU, the stellar companion statistics is improved by the AO imaging data. This is because the AO imaging technique complements the RV technique at semimajor axes at which the dynamical signals are difficult to detect. The combination of AO and RV data enables the detection of a deficit of stellar companions to MTPSs within 100 AU.

Wang et al. (2014a) combined RV and AO data for 56 Kepler planet host stars. The stellar multiplicity rate for a < 2000 AU was 43.2 ± 5.7%, which is a factor of three higher than what we reported in this paper, i.e., 13.3 ± 5.7%. The discrepancy is due to two reasons. First, we exclude optical doubles, whereas Wang et al. (2014a) included both optical doubles and physically associated companions. Physical separation of 2000 AU roughly corresponds to 3''–6'' angular separation (for the typical distances to these Kepler stars), at which the physical association probability is ∼50%. Therefore, roughly half of the visual companions are expected to be optical doubles around 2000 AU. Second, we considered statistics of stellar companions to planet host stars when calculating the incompleteness of the companion search (Wang et al. 2015). In comparison, Wang et al. (2014a) considered statistics of stellar companions for stars in the solar neighborhood. The companion search incompleteness was overestimated in Wang et al. (2014a) because the stellar multiplicity rate for planet host stars is generally lower than that for stars in the solar neighborhood, especially for small semimajor axes. Therefore, the correction factor due to search incompleteness is smaller, resulting in a lower stellar multiplicity rate.

We study the influence of stellar companions on MTPSs using a sample of 138 Kepler MTPSs. We search for stellar companions to these planet host stars with AO images and archival RV data. In total, we detected 42 stellar companions within 5'' around 35 multi-planet host stars. The properties of detected stellar companions are summarized in Table 2. We also provide detection limits for all stars in our sample in Table 1.

We compare the stellar multiplicity rate between MTPSs and a control sample, i.e., stars in the solar neighborhood. For semimajor axes 1 AU < a < 2000 AU, the stellar multiplicity rate is 13.3 ± 5.7% for MTPSs, which is 3.2σ lower than 33.6 ± 2.8% for the control sample, i.e., the field stars in the solar neighborhood (Raghavan et al. 2010). The deficit of stellar companions to MTPSs can be a result of two origins, a suppressive planet formation and the disruption of coplanarity due to stellar companions. Since the latter may only be effective within 100 AU, we divide the semimajor axes into two ranges, 1 AU < a < 100 AU and 100 AU < a < 2000 AU. The stellar multiplicity rate of MTPSs for 1 AU < a < 100 AU is lower (2.8σ) than that for the control sample. The stellar multiplicity rates are comparable between MTPSs and the control sample for 100 AU < a < 2000 AU.

We also compare the stellar multiplicity rates for MTPSs and STPSs. No quantitative difference is found between MTPSs and STPSs for 100 AU < a < 2000 AU. For 1 AU < a < 100 AU, our data are insufficient for comparative study between MTPSs and STPSs because of a lack of RV data for STPSs. Based on these results, we cannot distinguish the two origins that could be responsible for the low stellar multiplicity rate for MTPSs for 1 AU < a < 100 AU. Future AO and RV follow-up observations for a larger sample are needed for such a comparative study between MTPSs and STPSs.