SOAR TESS Survey. I. Sculpting of TESS Planetary Systems by Stellar Companions

The hosts of TESS planet candidates (TESS objects of interest, or TOIs) were selected from the data releases available online at the TESS data release portal.⁷ Faint stars (typically, T_mag > 13 mag) that are not well suited for speckle observations were not targeted; this limit reduces the number of late-type stars that are observed in this survey. Previously confirmed planet hosts, primarily from the WASP (Street et al. 2003) and HATS (Bakos 2018) surveys, were excluded from the target selection, as these systems have been heavily studied in the past (e.g., Ngo et al. 2015; Evans et al. 2016, 2018). Seventeen community-detected TESS planet candidates⁸ were also observed but were not used in the subsequent analysis in this work. To increase observing efficiency, target acquisition was improved using precise target coordinates, determined for each night with proper motions from Gaia DR2 (Gaia Collaboration et al. 2018), when available, and the TIC (Stassun et al. 2019) otherwise. As previously noted in Arenou et al. (2018), we find that many targets with only two-parameter astrometric solutions in Gaia DR2 are actually close binaries.

The properties of the host stars and planet candidates observed are plotted in Figure 1.

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We observed 542 TESS planet candidate hosts with the high-resolution camera (HRCam) imager on the 4.1 m SOAR telescope over 7 nights in 2018–2019. The observation procedure and data reduction are described in Tokovinin (2018). Briefly, each observation consists of 400 frames split into two data cubes, typically consisting of a 200 × 200 binned pixels region of interest centered on the target star (63 on a side at the pixel scale of 001575 and 2 × 2 binning) taken in approximately 11 s with an Andor iXon-888 camera. The resulting data cube is processed by a custom IDL script, which computes the power spectrum, in which a resolved multiple stellar system will appear as characteristic fringes. Binary parameters (separation, position angle, and magnitude difference) are determined from modeling the power spectrum. Secondary stars will appear as mirrored peaks in the speckle autocorrelation function (ACF), the Fourier transform of the power spectrum, at the separation and position angle of the companion. To remove the 180° ambiguity inherent to the classical speckle interferometry, our pipeline also computes the shift-and-add (SAA) images, centered on the brightest pixel in each frame (this is sometimes called "lucky imaging"). Relatively bright binaries with Δm > 0.5 mag often have their companions visible in the SAA images, allowing us to select the correct quadrant (these measurements are marked by the flag "q" in Table 6 in the Appendix). In all other cases, the position angles are determined with a 180° ambiguity. Figure 4 in Tokovinin (2018) gives an example of typical speckle data, including the SAA image. Observations were taken in the I band (λ_cen = 824 nm, Δλ = 170 nm), which is approximately centered on the TESS bandpass. Four resolved systems (TOI 123, 131, 138, and 146) were also imaged in the V band in preparation for a future association analysis.

The detection limits are estimated from the rms fluctuations σ of the ACF computed in annular zones of increasing radii; peaks exceeding the 5σ level are assumed to be detectable. This has been verified by injecting simulated binary companions into the real ACFs (see, e.g., Figure 9 in Tokovinin et al. 2010). Moreover, for each target, we require detection of the companion in both data cubes. Our procedure practically excludes false detections at separations larger than ∼01. At closer separations, however, the faint and persistent ACF details of instrumental origin, such as vibration or the optical ghosts described in Tokovinin (2018), can mimic real close binaries with a large Δm. We intercompare the ACFs and power spectra of sequentially observed targets to identify such artifacts. Finally, the estimated detection limits are verified by comparing with the (ρ, Δm) of actually measured companions, and a good agreement is always found.

The pixel scale and orientation are calibrated by observing several wide binaries with a well-modeled motion, as explained in Section 4.2 of Tokovinin (2018). The rms agreement between the measured calibrator positions and their models is typically from 1 to 3 mas in separation and better than 02 in angle. The pixel scale is therefore established with an accuracy of better than 0.5%. The calibration of HRCam was checked by comparing the positions of wider calibrators predicted by their models for 2015.5 with their relative positions in Gaia DR2.

We detail the observations in Table 6 in the Appendix. The cumulative 5σ detection sensitivities are plotted in Figure 2.

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The additional flux from a nearby star will dilute the transit depth in the TESS light curves, resulting in an underestimated radius for the planet candidate. We compute correction factors to the radius estimates derived from the TESS light curves for two scenarios: (1) the planet orbits the target star and (2) the planet orbits the secondary star, which is bound to the primary star.⁹

For the first scenario, we use the relation from Law et al. (2014) to derive a radius correction factor,

where is the corrected radius of the planet orbiting the primary star, is the original planetary radius estimate based on the diluted transit signal, and F_A is the fraction of flux within the aperture from the primary star.

For the case where the planet candidate is bound to the secondary star, we use the relation for the radius correction factor,

where is the corrected radius of the planet orbiting the secondary star bound to the primary star; R_B and R_A are the stellar radii of the secondary and primary star, respectively; and F_B is the fraction of flux within the aperture from the secondary star.

We use the stellar radius estimates from the TIC (Stassun et al. 2019) when available for the primary stars. The radii of secondary companions in the scenario where they are bound to the target star were estimated using the observed contrast ratio in the TESS band (approximated using the I bandpass of SOAR) and finding the radius of an appropriately fainter star within the Dartmouth stellar models (Dotter et al. 2008).

The TIC includes a contamination ratio that takes into account stars within 10 TESS pixels of the target. This includes stars typically down to the limiting magnitude of the 2MASS (Skrutskie et al. 2006) and APASS (Henden et al. 2009) catalogs (T ∼ 17–19). Using the list of detected close binaries to TESS planet candidate hosts and their binary parameters, a custom Python script crossmatched each of their coordinates to stars in the TIC catalog. We find that 31 stars in the TIC had similar positions relative to the primary as was found in SOAR imaging (Δρ < 05 and Δθ < 20°, or [Δθ ± 180°] < 20°). The properties of these systems are available in Table 2 in the Appendix. One notable resolved binary in our survey is the pair TOI 658 and TOI 659. The magnitude differences in the TESS bandpass for wide binaries in the TIC are generally similar to that measured from the SOAR observations, supporting our use of I-band observations as a proxy for the TESS observations. A similar crossmatch was performed with Gaia DR2 (Gaia Collaboration et al. 2018), yielding 38 matches to SOAR detected companions. These companions were all widely separated (ρ > 1''). The separations measured by SOAR have a mean and median difference of 15 and 6 mas, respectively, compared to those reported in Gaia DR2. The average difference in magnitude differences between SOAR and Gaia DR2 is 0.16 mag and likely due to the different passbands. The properties of these systems are available in Table 4 in the Appendix.

We provide a correction factor for hosts, as in some cases the crossmatch between the TIC and the SOAR binary is ambiguous; however, we caution that the correction should be used judiciously. For all other systems, the contamination ratios reported should be used in addition to the TIC contamination ratio. In practice, the reported radius estimates of TESS planet candidates on the TESS data release portal and Exoplanet Follow-up Observing Program (ExoFOP) typically take into account flux contamination. The additional correction due to binaries detected by SOAR is the product of the original radius estimate and the radius correction factor reported in this work.

A relatively large number of companions detected near Kepler planet candidates were unassociated, especially at separations greater than 1'' (Horch et al. 2014; Ziegler et al. 2018c). The TESS targets are spread across the sky, in regions of low and high stellar density, but generally at higher Galactic latitudes than the Kepler field. In addition, the targets are typically bright (T_mag < 12 mag), and subsequently, the detectable stars near them are several magnitudes brighter than the Kepler stars, given approximately equal contrast sensitivity. It is likely, then, that the number of detected field stars will be reduced in the TESS sample.

We use the stellar densities in the region of sky around each target in Gaia DR2 (Gaia Collaboration et al. 2018) to estimate the likelihood of a field star being detected near a TESS star. Gaia DR2 is essentially complete for sources down to G = 17 mag, or G = 19 mag in noncrowded fields (Gaia Collaboration et al. 2018). For our typical target with I = 12 mag and a contrast sensitivity of 5 mag, the faintest detectable companions will have I ≈ 17 mag, comparable to the Gaia completeness limit.

For each target, we begin by performing a cone search in DR2 to search for all stars within 05. The cone search was done using the Astropy affiliated package astroquery (Price-Whelan et al. 2018) to search the Gaia DR2 catalog hosted by the Barbara A. Mikulski Archive for Space Telescopes (MAST). We use the number of sources in DR2 within the 05 circular field to determine the source density (i.e., number of sources per arcsec²) as a function of G magnitude, ρ_source[G]. For each target, we determine the limiting magnitude of detectable secondary stars (G_limit) within separation increments of 05. We then use these limiting magnitudes and the DR2 source density () to determine the probability of detecting an unassociated field star within that separation range (e.g., 1''–15). The cumulative probability for all separations out to 315 provides the number of field stars we can expect to find near that target (see Figure 3). Typically, targets near the galactic plane and the Small and Large Magellanic Clouds are far more likely to have a field companion due to the high local source density.

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We perform a Monte Carlo analysis using these probabilities and the distribution of contrast sensitivity to simulate 10⁴ surveys and find that, on average, we should detect 3.2 ± 0.5 field stars within 315 of the observed TESS targets. The field companions are nearly always high contrast (with a large ΔI). Therefore, we expect the impact on the subsequent analysis due to unassociated asterisms of field stars to be negligible.

Nine targets are resolved triples with two companions in the SOAR images. For TOIs 378, 183, 487, 952, and 909, both companions are paired to the main star. In contrast, close pairs in TOI 455, 697, and 612 belong to the secondary components. Finally, in TOI 141, both separations are comparable, 12 and 044. For the resolved triples, the positions and magnitude differences refer to pairs of stars (e.g., Aa,B and Aa,Ab), as indicated in Column 3 of Table 6 in the Appendix, not the merged inner pairs like A,B.

As discussed in Section 2.3, the additional flux from a stellar companion will dilute the transit signal in the TESS light curves, resulting in an underestimated planetary radius. We report the radius correction factors for planet candidates hosted in resolved binaries in our survey in Table 1.

In general, the identity of the host star for an S-type planet in a close binary is ambiguous (Horch et al. 2014), although there is evidence that typically, the primary is more likely to be the planet host (Gaidos et al. 2016). Therefore, we report correction factors for each host scenario. Overall, we find a mean correction factor of 1.11 in the cases where all of the planets orbit the primary stars. This is similar to the factor of 1.08 found for Kepler planets (Ziegler et al. 2018b) under the same assumption. Likewise, if all planets orbit the secondary stars that are bound to the primary,¹¹ the radii of the planets will increase by a factor of 2.55, on average. This is slightly less than the 3.29 found for Kepler planets by Ziegler et al. (2018b), which is likely due to the lower number of field stars detected in the TESS sample (see Section 2.4). Indeed, if a faint field companion is considered as bound, its estimated radius is small, and the resulting correction factor for the radius of a planet orbiting this companion becomes large.

In perhaps a more realistic scenario, where planets are equally likely to orbit the primary or secondary star, we find an average correction factor of 1.82. This again is slightly lower than the correction factor of 2.18 found with similar assumptions in the Kepler survey.

We can restrict our separation range to reduce the fraction of unassociated stars in our sample. Within 1'', we find mean correction factors of 1.14, 1.90, and 1.55 under the assumptions that all primary stars host the planets, all secondary stars host the planets, and either star is equally likely to host the planet, respectively. The latter figure, more probable than either of the other cases, is in agreement with the radius corrections of 1.6, 1.64, and 1.54 found for the Kepler planets by Ciardi et al. (2015), Hirsch et al. (2017), and Ziegler et al. (2018b), respectively.

While Gaia DR2 typically cannot resolve binaries with separations less than approximately 07 (Ziegler et al. 2018a), the additional source does often result in spurious astrometric solutions. The reliability of the Gaia astrometry is quantified by the renormalized unit weight error (RUWE),¹² which is near 1.0 for single sources, with a greater value (for instance, >1.4) indicating a nonsingle or otherwise extended source. Sources with only a two-parameter astrometric solution have null RUWE values.

We find that for the 135 observed TESS planet candidate hosts observed with SOAR with RUWE values >1.4, 114 had resolved companions. Twelve of the observed targets had null RUWE values, and all 12 had bright, close companions (Δmag < 2 and 01 < ρ < 05). For the observed targets with either high or null RUWE values, approximately 86% had companions, typically within the Gaia DR2 binary resolution limit of 07. The median RUWE value for resolved close binaries (ρ < 075) is 5.56, compared to 1.04 for wider binaries (ρ > 075) and 1.03 for single targets. Only six targets with close binaries have RUWE values less than 1.4, five (TOIs 264, 476, 575, 609, and 640) of which have high contrasts (Δmag > 4) and one (TOI-379) of which has a very low separation (ρ = 003). The RUWE values and properties of resolved systems are plotted in Figure 4.

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It is unclear why some single stars (21 out of 412 observed) have high RUWE values. One possibility is the number of Gaia observations of each star. Gaia uses a scanning law that passes through the north and south ecliptic poles every 6 hr, resulting in approximately twice as many observations at mid-ecliptic latitudes as near the ecliptic plane or poles (Gaia Collaboration et al. 2016). A Kolmogorov–Smirnov test, however, finds the distribution of ecliptic latitudes for single stars with high and low RUWE values to be similar. The distribution of Gaia magnitudes and nearby stellar densities (determined in Section 2.4) of single stars with high and low RUWE values was also similar.

It is also possible that the anomalously high RUWE values for single stars are a result of binaries not detected by the SOAR speckle observations, such as those with close separations or high magnitude differences outside the sensitivity of SOAR. Further observations with larger-aperture telescopes and laser guide star AO could confirm whether these single stars have companions. Of the 21 single stars with high RUWE values, five have the results of additional high-resolution imaging available on ExoFOP.¹³ None of the five targets had a detected companion star.

Checking for a high or null RUWE value can serve as an excellent first check for potential companion stars in TESS systems, although further high-resolution observations would still be required to determine the properties of a purported companion. The clustering of binary systems with null RUWE values in a region of similar separation and magnitude difference, however, could even be used to infer the vague properties of a subset of the unresolved stars in Gaia DR2.

To facilitate an analysis of the multiplicity of our observed targets, some sample preparation was required.

The speckle imaging is a snapshot of the host systems, providing an on-sky angular separation between the primary and secondary star. To determine the projected physical separations, the distance to each system is required. We collect distances to each of these targets from Gaia DR2 (Bailer-Jones et al. 2018), when available. However, Gaia can provide spurious astrometric solutions in the case of close, unresolved binaries (Arenou et al. 2018). So, when the Gaia distance errors are large (greater than 20%), we use the distances reported in the TIC (Stassun et al. 2019), which were derived using inverse Stefan–Boltzmann relations based on V magnitudes. The distances used for each target in this analysis are available in Table 1.

We prepare our sample by removing stars with T_eff in the TIC inconsistent with an FGK-type star (i.e., T_eff > 7200 and <3900 K) using the relations of Pecaut et al. (2012). We also remove binaries with contrasts indicating mass ratios q < 0.4. These systems, with high magnitude differences, are significantly more likely to be chance alignments based on the analysis in Section 2.4, and their exclusion enables comparisons between the Kepler (Kraus et al. 2016) and TESS sample. We determine q by finding the mass of the primary star based on its likely spectral type estimated using the T_eff reported in the TIC and the secondary star based on the magnitude difference with the primary (Kraus & Hillenbrand 2007). We also remove systems with a TESS follow-up disposition of false positive and only a single transit detected by TESS. After these cuts, our sample includes 455 stars observed with SOAR.

To improve our coverage of wide binaries, we include companions to these 455 SOAR targets found in Gaia DR2 (Gaia Collaboration et al. 2018) with proper motions and distance estimates (Bailer-Jones et al. 2018) consistent at 2σ. We search out to an on-sky angular radius equivalent to a 5000 au projected separation based on the Gaia distance estimate. El-Badry & Rix (2018) found that the proper motion of wide binaries can vary significantly because of orbital motion. For each star, we calculate the maximum Keplerian orbital on-sky motion as a function of projected separation. The proper motion of each nearby Gaia star is allowed to vary by this orbital motion in our binary detection. The Gaia DR2 binaries used are listed in Table 5 in the Appendix. Only pairs of stars with contrasts consistent with mass ratios q > 0.4 were included. Ziegler et al. (2018a) provided the binary recovery sensitivity of Gaia DR2.

Close binaries can provide many potential obstacles to planet formation and evolution. In a large survey of Kepler planets, Kraus et al. (2016) found that far fewer planets were detected around stars with companions at solar system scales within approximately 50 au. The TESS sample is quite disparate in several ways from the Kepler sample, as shown in Figure 1. In general, the TESS planets are somewhat larger and at shorter periods than the Kepler planets, a consequence of the TESS photometric precision and survey strategy. Unlike Kepler, the TESS planets are spread across the sky and sample a more diverse set of the Galactic stellar population, providing an opportunity to confirm and characterize the effect of binaries

To understand how binaries impact planetary systems, we compare our sample to a simulated survey of field solar-type stars. We use the field binary statistics of Raghavan et al. (2010), who found a flat eccentricity distribution, a lognormal period distribution (with a mean of log P = 5.03, corresponding to an orbital semimajor axis of approximately 50 au, and σ_{log P} = 2.28), and a nearly uniform mass ratio distribution (with a sharp increase near-equal-mass ratio) in the population of solar-type field binaries. We follow the procedures of Kraus et al. (2016) to account for projection effects, Malmquist bias, and the detection limits of our survey. We also account for the reduced sensitivity of TESS to planet transits due to dilution by the stellar companion.

For each solar-type star observed in our survey, a Monte Carlo model was constructed to determine the expected number of binary companions at a range of projected separations between 1 and 5000 au. In each of 10⁵ iterations, there was a 33% ± 2%, 8% ± 1%, and 3% ± 1% probability that one, two, or three companion stars would be populated, respectively (the observed multiplicity of solar-type stars). Since binaries are overrepresented in flux-limited surveys (Schmidt 1968), we correct for Malmquist bias by adjusting this probability by an additional factor equal to the fractional volume excess in binaries due to their relative brightness, . The period, eccentricity, and mass ratio of these binaries were drawn from the distributions reported in Raghavan et al. (2010). The period was converted to a semimajor axis using the TIC estimated stellar masses. We select uniformly distributed values for the cosine of inclination, the position angle of the ascending node, the longitude of periastron, and the time of periastron passage. Finally, the instantaneous separation was projected to the distance to the primary star as reported in Gaia DR2. The mass ratio was converted to an approximate magnitude contrast using the relations in Kraus & Hillenbrand (2007), and possible detection by SOAR speckle imaging and Gaia DR2 was determined using the measured sensitivity limits and the companion's contrast and separation. We use the ratio of nondetected binaries to the total number of binaries at each separation to determine a completeness correction due to limitations in the ability to resolve close or wide companions.

The resulting observed binaries of TESS planet candidate hosts from SOAR and Gaia compared to the expected number derived for field stars are shown in Figure 5. The uncertainty in the expected number of observed binaries at each separation range is derived from the spread of binaries in the simulated surveys, which propagates the field binary rate uncertainties reported by Raghavan et al. (2010). The observed companion rate to the TESS planet candidates as a function of projected separation was determined by dividing the number of observed binaries by the total number of stars observed. The companion rate in each separation bin was then corrected for survey completeness using our measured sensitivity limits. The companion rates for the TESS planet candidate hosts and field solar-type stars are shown in Figure 6. The distributions differ substantially, both at close and wide separations, which we will address in turn.

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4.2.1. Bias against Planet Detection in Binaries

The additional flux from a companion star reduces the depth of the transit, making planet detection more difficult, and the TIC (Stassun et al. 2019) was constructed without consideration for potential stellar multiplicity. Left uncorrected, this observational bias would result in fewer binaries being detected among planet hosts, as transiting planets are easier to detect around single stars with no flux dilution.

We quantify the magnitude of this bias using the methods of Wang et al. (2015), adapted for the TESS sample. The planet search pipeline for TESS, run by the Science Processing Operations Center (SPOC; Jenkins et al. 2016), flags a potential transit candidate if the signal-to-noise ratio (S/N) is greater than 7.1. The S/N can be calculated by the equation

where δ is the transit depth, CDPP_eff is the effective combined differential photometric precision per transit, and N_transits is the number of observed transits. In the presence of a companion star, the transit depth is reduced due to the additional flux by a factor X given in Equations (1) and (2), depending on the identity of the host star, which likewise reduces the S/N of the detection.

We estimate the detection bias using a simulation for each of the TESS systems observed with no binary companion. For every single system, we choose the planet that has the highest S/N and add a companion star, whose mass is drawn randomly from the binary mass distribution described in Raghavan et al. (2010; e.g., uniform with a spike near unity). The transit depth of the planet is calculated for one of two randomly selected scenarios: (1) the planet orbits the primary star with reduced transit depth from the second star, or (2) the planet orbits the secondary with updated transit depth due to the different stellar radius and dilution from the primary star. For the selected scenario, the S/N of the detection is calculated using the new transit depth, and, if greater than 7.1, it was determined that the planet could still be detected by TESS with the companion star. This procedure is repeated 10⁵ times for each observed TESS system to determine α, the probability of a planet detection in that system if a stellar companion is present. The distribution of α for the observed systems is an indication of the magnitude of the binary detection bias (i.e., if most of the observed planets in single systems would still be detectable even with a binary companion, then it is likely that a few additional planet signals were not detected by TESS due to dilution from a second star). Relevant data and α-values for each system are provided in the Appendix in Table 3.

We find that most of the TESS systems would still be detectable even with an equal-mass companion, with median and mean α-values of 1.0 and 0.97. Significantly more TESS planets are detectable with companions compared to the Kepler sample of Wang et al. (2015), who found a median value of α = 0.89. This is likely due to the larger radii and lower periods of the TESS planets, which result in higher S/N. We would expect that 9 ± 2 of the 416 observed single systems (2.1% ± 0.4%) would not have planets detected by TESS if each were in stellar binaries. Therefore, the number of potential TESS planets that were not detected due to binary dilution is likely to be small relative to the number of systems observed, and we expect that the detection bias against planets in binary systems does not significantly impact the subsequent analysis.

In the simulations, the stellar radii are from the TIC. The stellar radii of secondary stars were determined using the mass–radius relationship of Feiden & Chaboyer (2012). The CDPP_eff was estimated from the TESS-band magnitude of the primary and the photometric precision model of Stassun et al. (2018), interpolated based on the transit duration.

4.2.2. Suppression of Planet-hosting Close Binaries

We find significantly fewer binaries in the TESS sample with projected separations of less than 100 au than would be expected for a similar survey of field stars (44 observed binaries compared to an expectation of 124 ± 8,¹⁴ a 9.0σ discrepancy). We find a completeness-corrected companion rate for TESS planet hosts of at projected separations of less than 100 au and larger than 1 au. For comparison, we estimate for field stars a companion rate at similar projected separations of using the binary statistics of Raghavan et al. (2010). TESS planet hosts are therefore approximately 3× less likely to have a close binary companion compared to field stars.

Similar to Kraus et al. (2016), the dearth of close binaries for planet hosts can be modeled by a simple two-parameter model using a suppression factor, S_bin, that cuts on at some semimajor axis value, a_cut. We performed a Markov Chain Monte Carlo (MCMC) analysis to explore 10⁶ possible values for S_bin and a_cut, seeking to reduce the χ² goodness of fit to the observed distribution. The resulting distributions are shown in Figure 7. We find the optimal values for the suppression with 68% credibility ranges to be S_bin = 24 and a_cut = 46 au, shown in Figure 5. These values are in agreement with those found by Kraus et al. (2016) for Kepler planet candidates (S_bin = 34 and a_cut = 47 au), and again, the null hypothesis (i.e., the field and planet candidate host distribution are similar with no binary suppression occurring) is strongly disfavored at 9.8σ.

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4.2.3. Enhancement of Wide Binaries in Systems with Large Planets

At wide separations, more binaries were detected around the TESS planet candidate hosts compared to the field stars: 119 observed binaries with projected separations greater than 100 au, compared to an expected number of 77 ± 7, a 4.9σ discrepancy.

The wide binaries being detected are almost exclusively those hosting the large planet candidates. This is readily apparent if we split our sample into two bins using a radius cut of 9 R_⊕ (approximately the size of Saturn), as shown in Figure 8. We find that both populations of 244 small and 199 large planets exhibit a paucity of systems in close binaries. At wide separations, however, the companion rates for the two populations diverge: at projected separations greater than 200 and 10³ au, large planet hosts have completeness-corrected companion rates of 47.8% ± 3.8% and 30.4% ± 3.4%, respectively. For small planet hosts, the companion rates for similar projected separation ranges are and , respectively. Thus, the two populations have discrepant companion rates for projected separations greater than 200 and 10³ au with significances of 9.8σ and 8.1σ, respectively.

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The companion rates for the small and large planets at wide separations are also both significantly divergent from that of field stars. We estimate from the distribution of Raghavan et al. (2010) that field stars have a companion rate of 13.7% and 5.3% at projected separations greater than 200 and 10³ au, respectively. Therefore, large TESS planets are approximately a factor of 3.5 more likely to be hosted in a wide binary than would be expected. Conversely, small TESS planets are 2× less likely to be found in a wide binary system than would be expected from field star statistics.

We observed 44 planet candidate hosts with T_eff estimates in the TIC consistent with an M dwarf (T_eff < 3900 K; Pecaut et al. 2012). We detected companions to 16 of these hosts, for a multiplicity fraction of 36% ± 9%. This is consistent with the field star M dwarf multiplicity fraction of 26.8% ± 1.4% found by Winters et al. (2019).

To compare the separation distribution of planet candidate M dwarf hosts to the field star population, we use the companion fraction, the lognormal projected separation distribution (peaking at 20 au with σ_{log a} = 1.16), and the uniform mass ratio distribution (with a slight increase in near-equal-mass binaries) found by Winters et al. (2019). The resulting distribution is shown in Figure 9.

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We find fewer close binaries than would be expected for the M dwarf planet candidate hosts: two observed compared to approximately 11 expected at projected separations of less than 100 au. We also find a large number of companions at wider separations: 14 observed companions at projected separations between 100 and 5000 au, compared to approximately five that would be expected.

Both of these results mirror those found with the solar-type sample. We do not see a large number of companions at very wide projected separations (s > 1000 au). This may, in part, be due to the M dwarf projected separation distribution peaking at lower separations (∼20 au rather than ∼50 au) and with lower variance than the solar-type sample. Also, as shown in Section 4.2.3, the widest binaries typically host Jupiter-sized planets, which are inherently rare around M dwarfs (Dressing & Charbonneau 2013).

The mass ratio, or q, distribution of solar-type binary systems was found to be nearly uniform by Raghavan et al. (2010), with an increase for near-equal-mass binaries. Winters et al. (2019) found a similar distribution at high-q for M dwarfs. Ngo et al. (2016) found that the mass ratio distribution for hosts of hot Jupiters was heavily weighted toward low-q companions.

The mass ratio distribution of resolved TESS planet candidate hosts may vary significantly from that of field stars. To compare the two populations, we use the mass ratios derived from the observed magnitude difference, as described in Section 4.1, for the SOAR binaries, while for the field stars, we use the mass ratios from the simulation described in Section 4.2, which takes into account our survey sensitivity.

The observed and expected mass ratio distribution of binaries to TESS planet candidate hosts is shown in Figure 10. The mass ratio distribution of observed binaries is consistent with being uniform for q > 0.4; for lower mass ratios, the SOAR sensitivity is low. There is no significant difference in the distribution for small and large planets (cut at 9 R_⊕). Compared to the expected number based on field star statistics, we find slightly fewer high-q binaries, due in part to binary suppression at low separations, and slightly more low-q binaries, which is likely to be, at least in part, a consequence of unassociated field star contamination as the companions with large magnitude differences are at wide separations.

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