Speckle Observations of TESS Exoplanet Host Stars: Understanding the Binary Exoplanet Host Star Orbital Period Distribution

We present high-resolution speckle interferometric imaging observations of TESS exoplanet host stars using the NN-EXPLORE NESSI instrument the at the 3.5-m WIYN telescope. Eight TOIs, that were originally discovered by Kepler, were previously observed using the Differential Speckle Survey Instrument (DSSI). Speckle observations of 186 TESS stars were carried out and 45 (24%) likely bound companions were detected. This is approximately the number of companions we would expect to observe given the established 46% binarity rate in exoplanet host stars. For the detected binaries, the distribution of stellar mass ratio is consistent with that of the standard Raghavan distribution and may show a decrease in high-q systems as the binary separation increases. The distribution of binary orbital periods, however, is not consistent with the standard Ragahavan model and our observations support the premise that exoplanet-hosting stars with binary companions have, in general, wider orbital separations than field binaries. We find that exoplanet-hosting binary star systems show a distribution peaking near 100 au, higher than the 40-50 au peak that is observed for field binaries. This fact led to earlier suggestions that planet formation is suppressed in close binaries.


INTRODUCTION
Our team has been carrying out high resolution speckle imaging of stars for which transit-like signals have been detected by the planet-finding missions Kepler (Borucki et al. 2011), K2 , and TESS (Ricker et al. 2015). High resolution imaging has proven useful for determining whether the signals are produced by planets or one of the various "astrophysical false positives" that plague wide-field transit surveys (Howell et al. 2011). For those stars that do turn out to have transiting planets, high-resolution imaging also helps to characterize the basic system properties. Our decade-long program has provided high spatial resolution observations of thousands of exoplanet host stars. The final reduced data products are deposited in the public NASA Exoplanet Archive ExoFOP 1 .
The ongoing TESS mission, and its predecessors Kepler and K2, identify planet candidates by simultaneously staring at many stars in the sky, collecting highly precise photometric time series for each star. For TESS, the light curves have either 2-min or 30-min sampling, depending on whether the star was prioritized by the TESS Science Team or the Guest Investigator program. The light curves are searched for transit-like dips in brightness, tell-tale signatures of exoplanets orbiting across the face of their alien sun. An ideal photometer would be able to isolate the light from each and every target star, in which case the observed fractional loss of light would be (R p /R ) 2 , the area of the planet's silhouette divided by the area of the stellar disk. However, because of the limited angular resolution of the telescopes, this simple interpretation is often not appropriate. Each TESS camera pixel subtends about 20 arcseconds, and the digital apertures that are defined to produce the photometric time series consist of many pixels. Multiple stars may be present in the aperture, one or more of which may be, for example, variable or an eclipsing binary. The signal of a deep eclipse, when combined with the constant light from the target star, may mimic an exoplanet-like signal. This and other stellar configurations can be troublesome (Brown et al. 2011), requiring follow-up observations to confirm or validate transiting planets.
Given that about half of the stars harboring exoplanets are in binary or multiple star systems, knowledge of bound companions is critical in allowing a complete and proper characterization of the exoplanet properties as well as providing robust tests of planet formation and evolution scenarios. Matson et al. (2019) used such information to make discovery predictions for high resolution imaging detections of bound companions for the TESS mission. "Third light" contamination within the aperture reduces the transit depth, causing the analysis to yield an exoplanet of a smaller radius than it really is (Ciardi et al. 2015). Other effects as well come into play which can produce incorrect characterization of both the host star's properties (Furlan & Howell 2020) and, with the incorrect planet radius, a skewed planet radius distribution and occurrence rates (Teske et al. 2018;Bouma et al. 2018) as well as improper mean density and atmospheric values (Howell 2020).
Several studies of Kepler and K2 exoplanet host stars have found companion fractions of 40-50% (e.g. Horch et al. 2014;Deacon et al. 2016;Matson et al. 2018;Ziegler et al. 2018), consistent with solar-type stars in the solar neighborhood (Raghavan et al. 2010). However, other studies find fewer close binary companions around Kepler exoplanet host stars ) and TESS planet candidate host stars (Ziegler et al. 2020). These studies find a deficit of close binary systems with projected separations less than ∼40 au. Matson et al. (2018) identified exoplanet candidate host stars from K2 that have stellar companions within 40 au based on the projected separation of the detected companion and the estimated distance to the system. To date, it has remained unclear if close binaries are able to host exoplanets and whether the formation and survival of a planetary system is possible under such conditions. For instance, planet formation in close binaries may depend not only on the presence of a stellar companion, but also on orbital parameters such as eccentricity and mutual inclination between the planetary system and the binary . Discovering exoplanets that form and evolve in diverse physical characteristics which provide different dynamic interactions compared to our own Solar System pose many questions for the leading planet formation theories, especially for exoplanets residing in binary star systems (Thebault & Haghighipour 2015).
TESS was launched in April 2018. After a few months of on-orbit check-out, it began to observe the southern sky in July 2018. Northern sky observations began in July 2019, and thus ground-based observations of northern sky TESS targets only began in earnest in late fall 2019. We present herein, the results of our first year of TESS high resolution speckle imaging follow-up using the NN-EXPLORE NESSI instrument at the WIYN 3.5-m telescope.

Target Selection
Starting in June 2019, we began follow-up observations of stars believed to host exoplanets discovered by the NASA TESS satellite during its second year of operation, a time period in which it surveyed the northern sky. A few preliminary equatorial targets were observed in June 2019 with the majority of the northern sky TESS targets being observed in October and November 2019.
Using the mission's list of TESS Objects of Interest (TOIs) that are made public on ExoFOP 2 , stars with robust software pipeline vetted transit-like signals, and additional community discovered exoplanet candidate host stars (known by their TESS Input Catalogue (TIC) designation) we observed 186 targets with NESSI at WIYN during the Figure 1. Properties of the TESS stars in our sample using ExoFOP TOI database values. Referenced to the DR2 Gaia apparent magnitude, these plots show the distribution of the distance and effective temperature within the sample. Most stars are near 10-11th magnitude, closer than 500 pc, and cooler than 7000K. A few more distant and hotter stars are not shown (See Table 1).
summer and fall of 2019. Our observation time was obtained through the NN-EXPLORE program 3 , we ran a queue at WIYN, reduced the speckle interferometric data, and placed all our reduced data products, without a proprietary period, into the NASA ExoFOP.

WIYN Observations and Data Reduction
Speckle observations presented in this paper were accomplished using the NESSI high resolution speckle imaging instrument (Scott et al. 2018) mounted on the 3.5-m WIYN telescope located at Kitt Peak National Observatory. NESSI is a dual-channel imager using high-speed readout EMCCD detectors with plate scales of 0.0182 arcsec/pixel and a dichroic to split the optical light at ∼700 nm. Speckle images are obtained in a shutterless stream of 1000 images per set, each image being 40 ms in duration. Depending on the target brightness, 3 or more sets are obtained in a row, each producing a simultaneous pair of blue and red images. The NESSI observations used a 562/40 nm blue filter and a 832/40 nm red filter. The speckle images are stored as multi-extension FITS files (data cubes) of 1000, 40 ms images each.
Resolved star systems produce a characteristic interferometric fringe pattern from which the separation, position angle, and delta magnitude can be determined through a modeling procedure. The raw FITS files are passed through our standard Fourier analysis pipeline (Horch et al. 2009) in which the average power spectrum for each image is computed and summed. We next deconvolve the speckle transfer function through division by the power spectrum of a point source standard star (a nearby star that is observed at a similar time as the target star) and compute a weighted least-squares fit of a fringe pattern to the result. During this step, pixels in the Fourier plane that have low signal-to-noise and low-frequency values judged to be in the seeing disk are set to zero. In order to determine the highest probability quadrant location of the companion star, we compute a reconstructed image via bispectral analysis (Lohmann et al. 1983). Details of our data reduction techniques and error assessments are given in Horch et al. (2011) and Howell et al. (2011). Table 1 lists the TESS targets we observed and which will be discussed in this paper. In order to characterize each star we list in Table 1 some relevant stellar parameters; the Gaia magnitude, effective temperature of the star, and the  Gaia determined distance as obtained from the ExoFOP archive TESS TOI table in October 2020. In all cases, we used the well-vetted "default" or "preferred" stellar parameters as given in the ExoFOP archive. Column 5 gives the date of observation, with the remaining four columns being the 5σ ∆mag contrast limit obtained in the observation at 0.2 and 1.0 arcsec in each band-pass.
Gaia parallaxes can be unreliable for close binaries as described in Arenou et al. (2018) with a good discussion related to Gaia parallexs and high-resolution imaging presented in Ziegler et al. (2020). Close binaries resolved by Gaia, usually having separations of 0.7 arcsec or larger, are somewhat large by our standards. For unresolved binaries, Arenou et al. (2018) states ". . . the astrometric quality of unresolved binaries with a small magnitude difference is not significantly different from that of single stars." The uncertainties in the Gaia parallax values for resolved close binaries (≥0.7 arcsec) manifest themselves in cases such as faint stars (fainter than G=∼17), crowded sources (leading to duplicate entries), diffuse objects, and nearly resolved binaries spatially close to bright stars. We have six stars in Table 1 ( TOIs 523, 1152TOIs 523, , 1162TOIs 523, , 1163TOIs 523, , 1172TOIs 523, , and 1393 which fall into the duplicate and crowded/nearby bright star categories (See note to Table 1). Only three of these, those in italics in the above list, revealed a nearby star in our observations which Gaia also resolved. In all three cases, the companions are widely separated from the primary star at 1.5 arcsec. While the distances to these three stars may have a larger than average parallax uncertainty, none of these wide companions are considered in the detailed analysis of this paper nor do they have any effect on its conclusions.
Speckle imaging provides angular resolutions to the diffraction limit of the telescope. For NESSI at WIYN, the inner working angle yields angular resolutions of 39 and 64 mas, providing spatial resolutions of 4-20 au (at 100-500 pc, 562 nm) and 6.2-31 au (at 100-500 pc, 832 nm). Eight of the 186 TESS TOIs presented herein were observed years ago at WIYN, as they were first detected as exoplanet host stars by the Kepler mission. These stars (identifiable in Table  1 by their date of observation) were observed using the Differential Speckle Survey Instrument (DSSI, Horch et al. 2009), which was the speckle imager used at WIYN from 2008 until NESSI was commissioned in 2016. The use of DSSI for exoplanet host star follow-up observations is described in Howell et al. (2011). DSSI used similar filters to NESSI but with slightly different central wavelengths, 692 nm and 880 nm. All observing and reduction procedures were similar to those described above for NESSI. Figure 1 shows two relevant properties of the TESS targets we have observed in this work, the distance and effective temperature of the sample as a function of the Gaia magnitude. Note that the stars cluster near 10-11th magnitude, 80% are closer than 500 pc, and 75% are cooler than 7000K. The closest stars (d<100 pc) represent the faintest and coolest stars in the sample. Figure 2 shows the contrast range of the observations obtained for our targets as a function of their Gaia magnitude. For each band-pass, we note that the total range in contrast narrows, that is the delta magnitude limits become shallower, as the target star becomes fainter. This is a function of S/N in the Fourier summed images and why our standard observing practice is to use 3 or more images sets per observation depending on the target star magnitude 4 . Seeing too can have a similar effect in lowering the contrast of the final image. While the resolution of speckle imaging does not decrease with bad seeing, spreading the light out over a larger area both decreases the correlation of individual speckles across the image (having a correlation size of about 1 arcsec; Howell et al. 2019) as well as making individual speckles harder to detect above any background sky noise during the 40 ms observation time. Both of these effects will reduce the interferometric signal in the data due to a lowering of the S/N in the final image 5 . For the observations presented here, the majority were observed in seeing of 1.1 arcsec or better.
Examining Figure 2, it can be seen that the 562 nm bandpass keeps approximately the same sensitivity difference (∼1 mag) between 0.2 and 1.0 arcsec over the entire magnitude range providing a contrast limit of 4-5 magnitudes at the bright end and 3-4 magnitudes near G=13. The 832 nm band-pass has deeper contrast limits at both reference angular separations. These observations reach a contrast of 7 magnitudes at the bright end (with a range of 2 magnitudes) and reach a contrast limit near 6 magnitudes with a range of 1 magnitude, near G=13. Even though our EMCCDs have 10% less detector QE at 832 nm vs. 562 nm, the atmospheric effects and speckle correlations for each target star are better at redder wavelengths. Greater contrast limits (up to 8 magnitudes) have been achieved at WIYN by obtaining more sets of speckle images because, to no one's surprise, the more time spent on a target the better S/N of the observation. Figure 2. Speckle imaging contrast limits as a function of target star Gaia magnitude. The ∆ magnitude contrast obtained at reference angular separations of 0.2" and 1.0" are shown as a function Gaia magnitude for our TESS sample. Note that the contrast obtained is both larger and extends to greater ∆ magnitudes at 832 nm while both filters show a convergence in overall contrast range toward fainter stars.

DETECTED COMPANIONS
As an example of one of our speckle imaging reduced data products, Figure 3 presents typical contrast curves we obtain with NESSI observations at WIYN. The field of view of NESSI in speckle mode (0.018 arcsec/pixel) is 19 X 19 arcsec, however we typically only read out a 256 X 256 pixel subsection region of interest centered on the target star yielding a final image of 4.6 arcsec on a side. However, as mentioned earlier, speckle decorrelation occurs within the atmosphere outside of ∼1 arcsec; therefore, we only use the robust Fourier analysis and speckle reconstruction techniques, as well as determine the 5σ contrast limits (blue points) and our fit to them (red curve) for an angular size patch of sky of 1.2 arcsec on a side, beyond which decorrelation occurs, becoming worse with increasing separation . Figure 3, showing the binary exoplanet host star TOI 894, reveals the detected close companion as a "+" sign below the 5σ contrast curves as well as displaying the companion star (located to the upper right) in the speckle reconstructed image insets displayed under each curve. Table 2 lists the companion stars we have detected, many seen in both band-passes with fainter and/or redder companions detected only in the 832nm observation. The table gives the target name, angular separation, position angle, and ∆magnitude within each respective band-pass with global internal uncertainties near ±6 mas, ±2 degrees, and ±0.2 magnitudes, respectively. Similar values for "Sep" and "PA" between the two filters provide additional confirmation of the goodness of fit of the Fourier analysis. The last column presents an estimate of the orbital separation of the two stars, in au, using the distance given in Table 1 and assuming that the instantaneous spatial separation detected in our imaging is approximately the orbital semi-major axis. Thirteen stars have companions beyond 1.25 srcsec, four of which, TOI851, TOI944, TOI994, and TOI1162, have fairly wide separated companions in Figure 3. Speckle imaging contrast curves and reconstructed images for TOI 894. The red curve in each plot is a fit to 5σ blue points measured at various annuli. The black + signs and filled square symbols are background measurements of the limiting contrast in the reconstructed image; + sign being points above the mean "sky". Note the detection of the companion star at ∼0.5 arcsec separation, well beyond the 5σ limit. The companion is also seen in the approximate 1 arcsec square inset images which have N up and E to the left.
the "speckle world" (well beyond ∼1.25 arcsec), thus their ∆mag values will not be as accurate as the rest, perhaps being overestimated and with an additional uncertainty of ±0.5 magnitudes (Howell et al. 2011). Stars with companions within ∼30 au will have binary orbital periods of decades and be systems that will reveal orbital motions within only a few years (See Colton et al., 2020 submitted). Two TOIs, 1163 & 1228 are shown to be triple systems having a close companion with a wider tertiary.  Ziegler et al. (2020) and the WIYN 832 nm curve is from Scott et al. 2018. The two contrast curves essentially match near the diffraction limit of the telescopes (SOAR is 4.1-m and WIYN is 3.5-m), with the WIYN 832 nm contrast limit being deeper at all separations. The stellar companions detected at WIYN inside 1.2 arcsec are shown including four inside 0.1 arcsec that would not be detected at SOAR. Ziegler et al. (2020) recently published a paper describing TESS TOIs observed by speckle interferometry at the 4.1-m SOAR telescope in Chile. SOAR and WIYN have similar apertures, so a comparison of any common systems is useful. Not many TOIs were common between the SOAR program and ours at WIYN as TESS surveyed the southern sky in year 1 and the northern sky in year 2. However, five TOIs with detected companions (123,172,462,851,952) were observed by both telescopes/instruments and in all cases the derived parameters for the detected companions were in complete agreement. Figure 4 compares the 5σ contrast curves for NESSI at WIYN and the speckle imager at SOAR. The curves roughly match near the diffraction limit of these similar size telescopes while the WIYN 832-nm contrast curve limit is deeper at all separations. The companions detected at WIYN inside 1.2 arcsec (the range of good speckle interferometric correlation) are also shown in Figure 4, including four very close companions that would be undetectable at SOAR. These four exoplanet host star bound companions orbit very close to the primary star (35, 35, 16, and 7 au) and contain planetary systems with close-in (periods of 1 to 5 days), Neptune-size (radii of 5 to 9 R e ) planets.
Of the 186 TESS exoplanet host stars (TOIs) discussed in this paper, 45 total companions were found, 36 are within 1.2 arcsec. More interestingly, 21 of the companions are within 0.5 arcsec and 9 are inside 0.25 arcseccompanions difficult to impossible to detect by other means. Our speckle imaging program is aimed at the detection of companions that can cause validation and exoplanet characterization problems and can cause spectral modeling to produce incorrect values for the host star properties (Furlan & Howell 2020). We are particularly interested in finding true, bound companions, stars that generally lie inside 0.25 arcsec (Matson et al. 2018), which are hard or impossible to discover with other instruments or other means. These true bound companions are the stars which will provide detailed robust information for exoplanet formation, dynamics, and evolution. Finally, our simultaneous two-color observations allow us to not only detect companions, but also gain some astrophysical knowledge for them in terms of the companion spectral type (i.e., mass, see below).

DISCUSSION
Speckle interferometry has become one of the leading ground-based telescope follow-up resources in the study of exoplanets. Such observations are critical to obtaining correct stellar and exoplanet properties. While both the Kepler and K2 mission exoplanet host stars yielded a similar percentage of binaries (near 40-50%; Horch et al. (2014); Deacon et al. 2016;Matson et al. 2018;Ziegler et al. 2018), the missions sampled different regions of the sky (single field of view at mid-galactic latitude vs. multiple ecliptic fields of view) as well as having different observing strategies and photometric precision levels.
The TESS survey affords us with an opportunity to directly compare the observed stellar companion detection fractions and binary host star properties for nearly equal surveys in the southern and northern sky. We acknowledge that the speckle interferometric observed companion stars have a bias (as is true of any observational campaign) and do not not represent the full story. The companions that are missing could be those with large magnitude differences (below the contrasts available), orbital locations which place them inside even the resolution of speckle imaging (very close binaries), companions of very red color (very faint in the optical band-pass), and companions at separations outside the field of view (i.e., outside the angular distance for speckle correlation, near 1.2"). In our speckle imaging program, we concentrate on nearby companions (<1.2 arcsec), stars with a high probability of being true bound companions and essentially undetectable by other means. In our analysis, we account for possible "missing" companions in a statistically probabilistic manner (see below).
Using <1.2 arcsec as a guide, we find that 24 out of our total of 186 stars show a detected companion, giving a detection fraction of 13%. Ziegler et al. (2020) find 67 stars (out of 542 total stars they observed) with detected companions within 1 arcsec or 12.5%. This is gratifying to see as it lends credence to the fact that the exoplanet host stars which are binaries seem to yield the same observed percentage in both hemispheres when using comparable (but different) instruments and telescopes. It is interesting to note that the observed percentage of 13% is roughly twice that seen for Kepler and K2 exoplanet host stars observed with speckle imaging at the WIYN telescope, 7% (Horch et al. 2014) and 6% (Matson et al. 2018), but are not unexpected based on the observed 46% true binary fraction and the generally much closer and brighter stars being observed by TESS. See Matson et al. (2019) and §4.1 below. Figure 5 shows the relation between the angular separation in arcsec of our detected companions and their projected physical separations in au. We can see in the figure the existence of a near-linear cutoff line for the minimum spatial separation observable as a function of the angular separation available for the TESS targets. Outside of 0.6 arcsec, we see a falloff in the number of detected companions perhaps signaling a true drop-off in bound companions vs. line- Figure 5. The relationship between angular separation (arcsec) and spatial separation (au) of the detected companions within a projected distance of 200 au (1.6"). We note that the closest spatial separations make up the majority of the closest physical separations. There is a dropoff in the frequency of detected companions outside of ∼0.6 arcsec, possibly representing the transition from mostly bound to mostly line-of-sight companions.
of-sight companions (See Matson et al. 2018). Of course, gravitationally bound systems do indeed exist at larger separations than 0.6 arcsec (e.g., Common proper motion pairs), however they are increasingly rare to detect as the separation becomes larger than our field of regard. Using Figure 5, we note that for a typical TESS star (<500 pc), the contrast curves in Figure 4 begin to turn over at their inner working angle at values of ∼46 au (0.2") at SOAR and ∼14 au (0.1") with NESSI at WIYN.

Predictions of Stellar Companions
Matson et al. (2019) used predicted distributions of TESS exoplanet host stars to examine the population of stellar companions detectable with speckle imaging. Here we use the same techniques to compare our observed companions to expectations and estimate the stellar parameters for the companion stars. We begin by considering all possible bound companions for a given TOI using the Modern Mean Dwarf Stellar Color and Effective Temperature Sequence Table based on Pecaut & Mamajek (2013) to assign stars with later spectral types (cooler effective temperatures) as possible companions. For each possible companion we then calculate a V −band delta magnitude (∆m) and mass ratio (q = M 2 /M 1 ) relative to the primary (TOI) star. Because we assign companions based on spectral types, which are discrete and unevenly spaced in mass, we fit a seventh order polynomial to the mass ratios as a function of delta magnitudes for each TOI and then determine the fraction of companions that fall within the 562 nm speckle contrast limit of ∆m ≤ 6. We also weight the likelihood of each companion by the mass ratio distribution of Raghavan et al. (2010), such that companions with mass ratios of 0.1 ≤ q ≤ 0.95 are equally likely and those with q > 0.95 are enhanced by 2.5×. Figure 6 shows possible companions for select TOIs, with the spectral type of the TOI indicated by the solid line color and the spectral types of the individual possible companions indicated by the color of the points. The dashed line highlights the speckle detection limit at ∆m = 6, and small vertical lines indicate where the mass ratio is equal to 0.1 for each TOI. The fractions of detectable companions for all TOIs in our sample are listed in Table 3 under "Comp. Frac.", with a mean of 0.57 for the sample. Table 3 also shows the stellar parameters used in our predictions as well as the spectral type of potential companions at ∆m = 4 and ∆m = 6 for all TOIs observed at WIYN. Two stars without distances are listed for completeness, but no analysis of possible companions is included.  Since the separation of the components must also be considered when evaluating which companions speckle imaging is sensitive to, we use the binary orbital period distribution for solar-type stars (Raghavan et al. 2010) to determine the fraction of possible companion separations that can be detected. For each TOI we use a log-normal period distribution parameterized by the mean semi-major axis in au and standard deviation in log P based on the mass of the primary (See Table 3 of Sullivan et al. 2015). The angular resolution limits of NESSI (0.04 -1.2" at 562nm) are then converted to period space using the mass and distance of each TOI via Kepler's third law. The binary period distributions and portions of log P space that are detectable using speckle imaging for TOIs with a range of spectral types are shown in Figure 7 (shaded regions). The speckle limits in au and the fraction of each binary distribution, "Distr. Frac.", that falls within those limits (converted to log P ) are listed in Table 3. The mean "Distr. Frac." for all TOIs observed at WIYN is 0.34. Taking the mean value for "Distr. Frac." times the mean value for "Comp. Frac." (0.57 from above), we should expect to actually observe bound companions around ∼19% of our stars, a value comparable to our observed value of 13%.
Figures 6 and 7 also show where observed companions from this study were detected in relation to our predictions. As in the predictions, we assigned the spectral type of the primary star based on the T eff reported in Table 1, and then determine the spectral type of the secondary using the observed delta magnitude. For systems with small separations and small delta magnitudes, such as TOI 890, 979, 1008, and 1267, the reported effective temperature will be a combination of both stars. While disentangling the temperatures of the two components in these systems does not impact our overall results, it should be considered for detailed analysis of the individual systems. The 562 nm delta magnitude of companions observed around the TOIs in Figure Raghavan et al. (2010). The shaded regions (color coded by spectral type of the primary as in Figure 6) show the orbital periods corresponding to projected separations at which speckle imaging at WIYN (562nm) can detect companions. The dashed lines correspond to the separation of observed companions converted to log P space using the distance and mass of the primary star. See the Appendix for a plot of all binary period distributions.
predictions and the observed delta magnitudes and separations for all TOIs with detected companions are given in the Appendix (Figures 11-14).
Similar to Figure 4, the plot of delta magnitude vs. mass ratio illustrates that most companions detected at WIYN have ∆mag ≤ 3 − 4 and have companions of the same or slightly cooler spectral types. We estimate the mass ratio for each observed system by converting the predicted V −band delta magnitude to a TESS delta magnitude (via Stassun et al. 2018) and fitting a polynomial to the possible mass ratios as a function of ∆m T ESS . We then use the observed 832nm ∆m values for each TOI (since all companions were detected in that filter) to determine the mass ratio from the polynomial fit.
A histogram of the mass ratios for all detected companions is shown in Figure 8, with the companions detected within 1.2" shown as hatched bars. The mass ratio distribution shows an increase in the number of high-q systems with a uniform distribution at lower-q, in agreement with Raghavan et al. (2010). The drop off at the lowest q-values (≤0.4) is where our sensitivity to faint, red companions decreases. Figure 8 also shows the mass ratios as a function of separation in au, with the companions detected within 1.2" shown as solid points. While the lack of low-q systems at smaller separations could be taken as an observational bias (and likely is), the relative lack of close (<1.2") highq systems at larger separations is indeed interesting and suggestive. Similarly, Raghavan et al. (2010) opined that short-period systems prefer higher mass ratios, that is, like-mass pairs (q>0.95) prefer relatively short orbital periods. Likewise, Moe & Di Stefano (2017) noted that the "twin fraction" significantly decreases with orbital period. We also see a slight preference for the hotter stars to be in high-q systems whereas the cooler stars tend toward low-q systems.
For the stars shown in Figure 8, we examined in detail possible connections of planet radius or orbital period with the stellar properties. Neither exoplanet orbital period (ranging from <1 to 15 days, well within even our closest binary systems at <10 au) nor exoplanet radius (<1 to 30 R e ) showed a meaningful correlation with the stellar or binary properties in this relatively small sample. Nine of the 25 exoplanets in these binaries are larger than 10R e and generally belong to wider separated pairs (>200 au). TOI 1191 6 is a notable exception harboring a planet of radius 25.4R e , orbital period of 15.7 days, and residing in a binary system separated by only 16 au. Figure 7 confirms that observed companions also fall within our expected separation/period ranges and highlights our sensitivity to the peak of the expected binary period distribution for most TOIs, making speckle imaging ideal for companion searches. While further information is needed to robustly prove whether the observed companions are truly bound, the fact that the delta magnitudes and separations we measure correspond to realistic binary parameters gives us confidence that most close companions are likely to be physically bound.
We also use our fraction of possible companions ("Comp. Frac.") and fraction of each binary period distribution ("Distr. Frac.") that NESSI can detect to estimate the number of companions we expect to observe around the 186 TOIs observed at WIYN. For each TOI we determine the "Comp. Frac." and "Distr. Frac." in separation bins of width=0.01" from 0.04 to 0.24" and bins of width=0.2" from 0.24 to 1.24", to account for the rapidly changing delta magnitude detection limits at close separations (see Fig. 4). We then multiply the "Comp. Frac." by the "Distr. Frac." for each TOI (see "Speckle Frac." in Table 3), and sum the fraction of companions in each separation bin to determine the total number of companions we expect to detect with speckle imaging. Assuming 46% of the TOIs have true bound companions, we multiply the total number of detectable companions by 0.46 to get ∼ 17 expected companions within 1.2". The results are plotted in Figure 9, with the expected number of companions shown in separation bins of 0.2" as yellow bars, and the observed companions within 1.2" plotted as blue-hatched bars. The error bars on the expected companions reflect the minimum and maximum total number of expected companions determined by randomly selecting which 46% of the TOIs have companions for 100,000 random iterations. While our calculations only expect ∼ 17 companions compared to the 29 we observe within 1.2" of 28 TOIs, the number of companions observed matches the model predictions given the sizable uncertainties in each bin (See Figure 9).
To further examine the population of observed companions and determine whether we see any indication of binary suppression (inside of ∼40 au) among close binaries with exoplanets as suggested by Kraus et al. (2016) and Ziegler et al. (2020), we convert the projected separation in arcseconds to au using the distance of each TOI for both the observed and expected companions. Figure 10 shows the separation in au of observed companions within 1.2" in logarithmic bins of 0.5 dex (hatched blue bars).
However, the two left most bins are underrepresented in our sample not due to binary suppression, but due to the speckle contrast curve becoming steep and shallow at small separations. This is a property of every high-resolution imaging instrument, with the inner working angle efficiency falling off at ∼14 au at WIYN and ∼40 au at SOAR. Given this increased incompleteness at small separations (See Figure 4) we estimate a "correction" factor based on a convolution of the inner contrast curve, that is the steep change in magnitude averaged over the corresponding broad bins in au (taking min au vs. separation as a metric for minimum separations observable at each bin of arcsec, see Fig. 5). This correction increases the left most bins by 0.6 and 2.1 stars, respectively (unfilled hatched bars in Fig. 10). Fitting a Gaussian to the corrected distribution (solid red line) shows that the TESS companion sample peaks at ∼ 100 au with a width of 0.75 au. The Gaussian distribution was determined using a non-linear least squares fit to the "corrected" bins, but is consistent with the fit determined from a maximum likelihood estimate on the unbinned data. Figure 10 also shows the expected number of companions (solid yellow bars) based on the Raghavan distribution convolved with the NESSI contrast curve as described previously. A Gaussian fit to the expected companions, using a non-linear least squares fit to the binned data, (solid black line) peaks at a separation of only 26 au, a value biased toward close separations given the NESSI contrast curve convolution with the distribution of Raghavan et al. (2010, peak ∼ 50 au, σ ∼ 1.1). The uncertainties on the expected companion bins, however, allow the distribution to be statistically consistent with the Raghavan distribution, shown in Figure 10 as a dashed yellow line, which has been scaled to the expected number of companions (17) and bin widths.
We also present the unbinned cumulative distribution of detected companions within 1.2 arcsec in Figure 11. The (binned) expected companion distribution from Figure 10 is shown for comparison.
Based on Figures 10 and 11, we note that our distribution of observed companion separations does not match that of Raghavan et al. (2010). While we have only a modest sample of binary exoplanet host star companions, there is evidence in Figures 8-10 that binary stars which host exoplanets have a "Raghavan-like" mass distribution but have a larger mean orbital separation (∼100 au) with a slightly narrower breadth in their distribution. Companion stars can eject planets from stellar systems (Haghighipour 2006), perturb proto-planetary disks (Jang-Condell 2015), and create planetesimals through gravitational interactions (Rafikov & Silsbee 2015). The wider mean separation of exoplanet hosting binaries is likely needed to permit proto-planetary disk formation and planetary evolution without disruption by the stellar companion.
Thus, discussions of close binary star "suppression" might indeed be real, but not because of a fall-off of systems within the Raghavan distribution at close separation period, but rather due to exoplanet host star binaries having a different orbital period distribution all together, one with a larger mean separation. Detected Companions <1.2" Expected Companions Figure 10. Histogram of projected separation in logarithmic bins of au for companions detected within 1.2" of a TOI at WIYN (solid blue bars). The unfilled hatched bars represent a 'correction' factor based on our mean contrast curve range in delta magnitude over the separation bins in au (see Figure 4 and text for more details). A Gaussian fit to the 'corrected' companion distributions is shown in red, which is narrower and peaks further out than the distribution of Raghavan et al. (2010). Also plotted is the expected number of companions (solid yellow bars) as determined from the "Comp. Frac." and "Distr. Frac" of 46% of the TOIs (see text for details). The Gaussian fit to the expected companion distribution is shown in black, while the Raghavan distribution, scaled to the expected number of companions and bin width, is plotted as a yellow dashed line. Detected Companions < 1.2" Expected Companions Figure 11. Cumulative distribution for projected separations of companions detected within 1.2" of exoplanet candidate host stars using speckle imaging at WIYN. The expected companion distribution based on the Raghavan distribution convolved with the NESSI contrast curve (see text for details) is shown for comparison. The expected companion distribution is in logarithmic bins of 0.5 dex as in Figure 10. The Y-axis is the number of companions.
We have presented the first year of high-resolution speckle imaging observations for TESS stars using the NN-EXPLORE NESSI instrument at the 3.5-m WIYN telescope. Speckle observations of 186 TESS exoplanet host stars were carried out, the majority of which were brighter than 12th magnitude, closer than 500 pc, and solar-like. Of the TESS stars observed, 45 (13%) revealed a close companion. This number is consistent with the expected 19% value based on our models. The distribution of stellar mass ratios in exoplanet binary star systems seems to match that of the Raghavan field binary distribution, perhaps presenting some common aspect of binary star formation, while there may be a lack of high-q binaries at wider separations. Our measured orbital separation distribution, however, does not match the expectation. Our observations support the fact that exoplanet hosting binary stars have, in general, wider separations (longer orbital periods) than field binaries. Thus, the suggested close binary suppression is really not "missing" short period systems from a normal Raghavan-like distribution, but instead is a feature of a wider separation population of binaries, those that host exoplanets.
Additional observations of binary exoplanet host stars are needed in order to build up the sample. A control sample, that is a sample of similar TESS stars not seen to show a transit event, are also needed in order to help vet observational biases. Higher contrast, higher resolution speckle imaging observations will be presented in an upcoming study of TESS exoplanet host stars using 2 years of speckle interferometric observations from the 8-m Gemini North and Gemini-South telescopes.
Note added in Proof: After our analysis was finished and this paper submitted, Gaia EDR3 was released, providing refined parallax values. These improved values, essentially all within ±10% for our stars with companions of 1.2 arcsec or less, produce only small bimodel changes to the distances and are inconsequential in relation to the main results presented in this paper.            a This value is calculated using spectroscopic parallax estimated from the Table 1 stellar parameters. b The filters used were 'r' and 'i', instead of 562 nm and 832 nm, respectively. Two companions were detected c These TOIs were observed multiple times in which the companion was detected. Variations between filters & observations were: TOI 1163 (9 times) Sep±0.042;PA ±0.041; ∆Mag±0.52 (the ranges given include both companion stars). TOI 1387(2 times) Sep±0.021;PA ±0.053; ∆Mag±0.45. TOI 1324(4 times) Sep±0.009;PA ±3.29; ∆Mag±0.13.       1.067 · · · · · · · · · · · · · · · · · · · · ·   · · · K1V 0.853 · · · · · · · · · · · · · · · · · · · · ·       Raghavan et al. (2010). The shaded regions (color coded by spectral type of the primary as in Figure 6) show the orbital periods corresponding to projected separations at which speckle imaging at WIYN can detect companions (0.04 − 1.2"). The dashed lines correspond to the separation of observed companions converted to log P space using the distance and mass of the primary star.  Raghavan et al. (2010). The shaded regions (color coded by spectral type of the primary as in Figure 6) show the orbital periods corresponding to projected separations at which speckle imaging at WIYN (0.06 − 1.2") can detect companions. The dashed lines correspond to the separation of observed companions converted to log P space using the distance and mass of the primary star.