Dynamical Architectures of S-type Transiting Planets in Binaries I: Target Selection using Hipparcos and Gaia proper motion anomalies

The effect of stellar multiplicity on planetary architecture and orbital dynamics provides an important context for exoplanet demographics. We present a volume-limited catalog up to 300 pc of 66 stars hosting planets and planet candidates from Kepler, K2 and TESS with significant Hipparcos-Gaia proper motion anomalies, which indicate the presence of companions. We assess the reliability of each transiting planet candidate using ground-based follow-up observations, and find that the TESS Objects of Interest (TOIs) with significant proper motion anomalies show nearly four times more false positives due to Eclipsing Binaries compared to TOIs with marginal proper motion anomalies. In addition, we find tentative evidence that orbital periods of planets orbiting TOIs with significant proper motion anomalies are shorter than those orbiting TOIs without significant proper motion anomalies, consistent with the scenario that stellar companions can truncate planet-forming disks. Furthermore, TOIs with significant proper motion anomalies exhibit lower Gaia differential velocities in comparison to field stars with significant proper motion anomalies, suggesting that planets are more likely to form in binary systems with low-mass substellar companions or stellar companions at wider separation. Finally, we characterize the three-dimensional architecture of LTT 1445 ABC using radial velocities, absolute astrometry from Gaia and Hipparcos, and relative astrometry from imaging. Our analysis reveals that LTT 1445 is a nearly flat system, with a mutual inclination of 2.88 deg between the orbit of BC around A and that of C around B. The coplanarity may explain why multiple planets around LTT 1445 A survive in the dynamically hostile environment of this system.


INTRODUCTION
Radial velocity (RV, Cumming et al. 2008;Fulton et al. 2021) surveys and space-based transit searches such as Kepler (Borucki et al. 2010;Howard et al. 2012) and TESS (Ricker et al. 2014) have revolutionized our understanding of exoplanet demographics.However, the process of confirming exoplanets is biased against stars in multiple systems, since close companions complicate the observations and analysis.Although one third of nearby solar-type stars have at least one companion (Raghavan et al. 2010), the effects of stellar multiplicity on planetary architecture and orbital dynamics are still poorly understood.In addition, unknown stellar companions can cause inaccuracy for estimating planet radius by diluting the measured transit depths (Furlan et al. 2017;Teske et al. 2018;Sullivan et al. 2023).Planet properties may also be inaccurate if the planet is actually orbiting the secondary star.Thus, identifying the stellar companions of transiting planets helps to obtain more accurate planet parameters and characterize the demographics of planets in binaries (Fontanive & Bardalez Gagliuffi 2021;Cadman et al. 2022).By analyzing large samples of planets in binaries and comparing them to single systems, we can gain insights into the factors that shape the the formation and evolution of exoplanets.
Close companions are expected to have a deleterious influence on planet formation, through disk truncation (Artymowicz & Lubow 1994;Jang-Condell et al. 2015) or dynamical stirring of planetesimals (Quintana et al. 2007).Recent ALMA observations show that disks in binaries have lower masses (Akeson et al. 2019) and smaller radii (Cox et al. 2017;Manara et al. 2019), supporting the disk truncation scenario.Kraus et al. (2016) used high-resolution adaptive optics (AO) imaging of 382 Kepler Objects of Interest (KOIs) to show that planet occurrence rate in close binaries (< 47 AU) is only 0.34 times that of single stars or wide binaries.Ziegler et al. (2020Ziegler et al. ( , 2021)); Howell et al. (2021); Lester et al. (2021) performed similar searches for stellar companions to TESS Objects of Interest (TOIs) and also found a deficit of close binaries (< 100 AU).For giant planets discovered by RV observations, Hirsch et al. † NASA FINESST Fellow (2021) reported that the planet occurrence rate in binaries with a separation < 100 AU is significantly smaller than those in binaries with a separation > 100 AU or single stars.Additionally, Fontanive & Bardalez Gagliuffi (2021) presents a volume-limited sample of companions from tens of AU out to 20000 AU in the literature and Gaia DR2 to exoplanet host stars.They found giant planets with masses above 0.1 M J are more frequently seen than small sub-Jovian planets in binary systems, which is supported by the simulations from Cadman et al. 2022.However, some planets survive in such dynamically challenging environments for reasons that are still unclear (Hatzes et al. 2003;Correia et al. 2008;Kane et al. 2015;Dupuy et al. 2016).Close binary companions could induce gravitational perturbations on their orbits, causing the migration or spin-orbit misalignment of planets.Furthermore, close companions may torque the protoplanetary disks where planets form, and therefore shape the architecture of the planet systems.Studying the architecture of planets in close binary systems will shed light on the planet formation and evolution in these systems.
Transit surveys including TESS, Kepler and K2 offer an unbiased planet sample in terms of stellar multiplicity.The coarse spatial resolution of TESS (21 ′′ /pixel) and Kepler (4 ′′ /pixel) makes it essential to conduct ground-based follow-up observations to resolve close binary systems.Previous studies have used adaptive optics (AO) and speckle imaging to search for stellar companions to planet candidate hosts discovered by Kepler and TESS missions (Kraus et al. 2016;Ziegler et al. 2020Ziegler et al. , 2021;;Howell et al. 2021;Lester et al. 2021).Gaia mission's Renormalised Unit Weight Error (RUWE) is also an indicator for companions, as RUWE values are sensitive to the deviation from the single-star astrometic model.However, RUWE values are most effective for detecting binaries with separations from 0 ′′ .1 to 0 ′′ .6 (Lindegren et al. 2018;Ziegler et al. 2020).The companions located outside of the range might be overlooked.
In this paper, we use Gaia (Gaia Collaboration et al. 2022) and Hipparcos (ESA 1997) proper motion anomalies (Kervella et al. 2019;Brandt et al. 2019) to identify close companions hiding in the large pixels of TESS or Kepler.The method takes advantage of ∼ 25 years time baseline between the two missions, and is sensitive to companions with orbital periods from decades to centuries (Kervella et al. 2019).Furthermore, the combination of Gaia and Hipparcos astrometry, radial velocities (RVs) and imaging astrometry makes it possible to determine the 3D orbits of the companions and obtain their dynamical masses (Brandt et al. 2019;Xuan & Wyatt 2020).In this paper, we characterized the 3D orbits of companions in the proof-of-concept system LTT 1445 ABC with the method.It's important to note that our emphasis here is on the orbit parameters of stellar companions with orbital periods in years, rather than on transiting planets with much shorter orbital periods in the order of days.Finally, By obtaining the inclinations of the companion orbits, we can constrain the mutual inclinations between the orbital plane of the companion and that of the transiting planet.This information can provide insight into the system's dynamical history.

HIPPARCOS-GAIA PROPER MOTION ANOMALIES
The Gaia spacecraft (Gaia Collaboration et al. 2022) measures the position and proper motion of nearly 1.7 billion stars since 2014.Its predecessor Hipparcos (Perryman et al. 1997) also provides precise astrometric measurements of nearby stars from 1989 to 1993.The measurements have a time baseline of nearly 25 years and can detect the effect of unresolved binaries since a companion would cause the primary to wobble around the barycenter on the sky plane (Brandt et al. 2019;Kervella et al. 2019).Specifically, we use Hipparcos and Gaia EDR3 proper motions and their uncertainties from the Hipparcos-Gaia Catalog of Accelerations (HGCA, Brandt 2021).The catalog provides three proper motions for every star: (1) the Hipparcos proper motion µ H at an epoch near 1991.25;(2) the Gaia EDR3 proper motion µ G at an epoch near 2016.01;(3) long-term proper motion µ HG given by position difference between Hipparcos and Gaia divided by the 25 years baseline.
These proper motions are in units of mas yr −1 .The proper motions are given in right ascension (RA, α) and declination (DEC, δ) direction.For simplicity, we use the total proper motion combined from the two directions and omit the subscript for RA and DEC in this paper.The long-term proper motion µ HG can be used to estimate the velocity of celestial linear motion across the sky plane over nearly 25 years.We subtracted the long-term proper motion µ HG from Hipparcos and Gaia proper motions as follows: The two residuals represent the proper motion anomalies at the Hipparcos and Gaia epochs, respectively (Kervella et al. 2019).Note that these anomalies are also known as astrometric accelerations (Brandt 2021).We use the terminology of "proper motion anomalies" to prevent confusion with the general concept of "acceleration," as the residuals are measured in the unit of mas year −1 .As shown in Figure 1, a significant proper motion anomalies reveals a deviation from the linear stellar motion, possibly caused by a gravitationally bound companion.We calculate the signal-to-noise ratio of proper motion anomalies at Hipparcos and Gaia epochs using the calibrated uncertainties of Hipparcos and Gaia measurements from Brandt (2021): where σ[µ] represent the uncertainties.Next, we convert the proper motion anomalies in the unit of mas yr −1 into the differential velocities in the unit of m s −1 as follows (Kervella et al. 2019): where ϖ is the parallax in units of mas.For a binary system, the differential velocity is approximately the projected tangential velocities of the primary's orbital motion on the sky plane (Kervella et al. 2019).Based on Kepler's law, the differential velocities are proportional to the companion masses (m c ) and inversely proportional to the square root of orbital distances (r): ∆v ∝ mc √ r .Due to the observing window smearing effect (for details see Kervella et al. 2019), the proper motion anomalies method is most sensitive to companions with orbital periods longer than observing windows of Hipparcos and Gaia (δ H = 1227 days, Perryman et al. 1997, δ G,DR3 = 1038days, Gaia Collaboration et al. 2022).On the other hand, the efficiency of the proper motion anomalies method drops for companions at orbital periods much longer than the 25-year baseline between the two missions.For instance, the efficiency is reduced to ∼ 30% when the orbital period is ten times the time baseline (∼ 250 years) (Kervella et al. 2019).Therefore, the sweet spot of proper motion anomalies is for companions at orbital periods from ∼ 3 years up to ∼ 250 years, corresponding to a few AU to dozens of AU in terms of the semi-major axis.Multiple studies have found a deficiency of planets in close binaries with separation below 100 AU, supporting the theory of close companions disturbing and preventing planet formation (Kraus et al. 2016;Ziegler et al. 2020;Hirsch et al. 2021;Fontanive & Bardalez Gagliuffi 2021;Cadman et al. 2022).Hipparcos and Gaia astrometry thus offers an efficient way to search for planets in binaries that have separation of < 100 AU, with which we can study the effect of companions on planet formation and evolution.
2. We calculated the distance of targets with Gaia DR3 parallax and selected stars with distances smaller than 300 pc.
3. We calculated the signal-to-noise of Gaia proper motion anomalies of every star from the last step.We selected those showing Gaia proper motion anomalies with ≥ 3σ significance (SNR G ≥ 3) into our target sample.Hereafter, we refer to our sam-ple as HGCA-high-SNR stars or stars with significant proper motion anomalies.
4. We also constructed a control sample of TOI stars with SNR G < 3. Hereafter, we refer to the control sample as HGCA-low-SNR stars or stars with marginal proper motion anomalies.
There are a total of 66 systems (58 TOIs, 4 KOIs, and 4 K2 planet candidates) in our target sample with high-SNR proper motion anomalies (see Table 1).We also identified 254 TOIs with low-SNR proper motion anomalies in the control sample and list them in Appendix C. The HGCA provides a parameter called χ 2 , which represents the chi-squared value obtained from fitting a constant proper motion to the more precise pair of µ HG −µ G and µ H −µ HG proper motion measurements (Brandt 2021).This parameter is also helpful in evaluating the significance of proper motion anomalies.For instance, a χ 2 value of 11.8 corresponds to a 3σ evidence for proper motion anomalies.We compare the output samples using criteria of χ 2 ≥ 11.8 and SNR G ≥ 3. The two criteria are nearly equvalent, resulting in comparable samples.
Some targets in our sample have been investigated before.The triple system Kepler-444 consists of a primary star with five transiting Mars-sized and Mars-mass planets.Dupuy et al. (2016) and Mills & Fabrycky (2017) characterized the Kepler-444 BC companion pair as orbiting the primary A in a highly eccentric orbit (e ∼ 0.864, a ∼ 5 AU) using RVs and relative astrometry from imaging.Recently, Zhang et al. (2022) improved the constraints on the orbit of the Kepler-444 BC pair (e ∼ 0.55, a ∼ 36 AU, i ∼ 85.4 deg) using a longer time baseline of RVs and the proper motion anomalies data from the Hipparcos and Gaia missions.Both studies suggest that Kepler-444 BC may have truncated the protoplanetary disk of the primary, resulting in the small sizes of the system's five planets.Zhou et al. (2022) characterizes the 3D orbit of an M-dwarf companion to TOI-4399 (HIP 94235), which hosts a mini-Neptune with an orbital period of 7.1 days.Their results show that the companion has a semi-major axis of ∼ 60 AU and an inclination of ∼ 67.8 • , indicating a modest misalignment between the companions and the transiting planet.Furthermore, previous studies have identified that the Hipparcos and Gaia proper motion anomalies of TOI-144 (π Men, Xuan & Wyatt 2020;De Rosa et al. 2020;Damasso et al. 2020), TOI-1144(HAPT-11, Xuan & Wyatt 2020) and TOI-1339(HD 191939, Lubin et al. 2022) are from giant planets at a few AU.By combining the proper motion anomalies and RVs, these studies obtained a constraint on the semi-major axis, orbital inclination and mass of the giant planets.
Among the sample of 66 targets with high proper motion anomalies, 33 systems have confirmed companions from previous surveys using AO/speckle imaging, mostly at separations from 0.1 ′′ to 2 ′′ .We list the companion separations in Table 1 from published papers (Mason et al. 2001;Kraus et al. 2016;Ziegler et al. 2020Ziegler et al. , 2021;;Winters et al. 2019;Howell et al. 2021;Lester et al. 2021) and TESS Follow-up Observing Program (TFOP).Additional AO imaging using Keck/NIRC2 and Subaru/SCExAO will be presented in a follow-up paper.We first analyzed the fraction of false positives of the transiting detections in the sample.
Table 1 lists the NASA Exoplanet Archive dispositions that classify TOIs/KOIs/K2 candidates, including Confirmed/Known Planet (CP/KP), Planet Candidate (PC), Ambiguous Planetary Candidate (APC), False Positive (FP), and False Alarm (FA).We also present different reasons for the false positive/false alarm dispositions in Table 1.A false positive or false alarm flag is assigned in several situations.The first scenario is Eclipsing Binaries (EBs), in which the secondary stars graze the edge of primaries, and the reduction in brightness is indistinguishable from transits of smaller planets.The second scenario is the contamination by a Nearby Eclipsing Binary (NEB) as multiple stars are unresolved due to the large pixel scale of Kepler and TESS (4 ′′ for Kepler and 21 ′′ for TESS ).In this case, the bright primary star dilutes the light of a nearby, dimmer, eclipsing binary pair to the point at which the eclipses seem as shallow as a planetary transit.In addition, stellar variation (SV) and spacecraft systematics errors (SSE) can also mimic the dips in light curves similar to those from transiting planets.
To break down the FP into the EB/NEB/SV flag, we refer to the TESS Follow-Up Observing Program Sub-Group 1&2 (TFOP SG1 & SG2) disposition and notes as a guide for TOIs.TFOP SG1 performs seeing-limited imaging of the TOIs using ground-based telescopes with higher spatial resolution to check whether the transits occur on target.They detected four TOIs (TOI-2118, TOI-1665, TOI-909, TOI-1946) in our sample as NEB.In addition, TFOP SG2 identified 8 EBs based on oddeven transit difference (TOI-394, TOI-1124,TOI-575, ) or RVs from TRES+FIES (TOI-953, TOI-1837, TOI-2017, TOI-2666,TOI-222).In our sample, the majority of KOIs and K2 transiting signal are from EBs based on the results from Kepler/K2 EB catalogs (Slawson et al. 2011;Armstrong et al. 2015;Rizzuto et al. 2017;Kruse et al. 2019).We present the details of each FP in our sample in Appendix A.
The left panel in Figure 3 presents the fraction of confirmed planets, planet candidates, eclipsing binaries, nearby eclipsing binaries, and other false positives in TOIs with significant proper motion anomalies (58 TOIs).We have chosen to only present the results of TOIs for a homogeneous comparison, because follow-up observations for candidates of TOI, KOI, and K2 are conducted through various projects, and the majority of KOIs and K2 targets in our sample are eclipsing binaries (EBs).For comparison, we show a control sample from TOIs with SNR G < 3 and distances smaller than 300 pc (254 TOIs).We also break down the false positives in the HGCA-low-SNR sample into the same categories as our targets based on the TFOP SG1 disposition.The HGCA-high-SNR TOIs contain a higher fraction of false positives (up to 21.8% compared to the 14.4% of HGCAlow-SNRs TOIs).The difference is mainly from the excess of EBs among the HGCA-high-SNR TOIs, taking up ∼ 11.6% of the sample.The EB false positives result from contamination of triple systems with close-in eclipsing binaries.Due to the dilution of light curves by multiple sources in the same pixel, the transit depth appears comparable to planetary transits around single stars.Our finding agrees with previous studies.Ziegler et al. (2020) presents that hot Jupiters are more common in binaries with wide companions compared to field stars.But Ziegler et al. (2021) argues that these findings can be attributed to false positive contamination arising from tertiary companions to closely orbiting eclipsing binaries.In contrast, other false positives, including NEB, stellar variability, and spacecraft false alarms, account for a similar share in the two samples.

Orbital period of TOIs with significant proper motion anomalies
In this section, we compare the orbital periods of planets around TOIs with significant Hipparcos-Gaia astrometric acceleration and those with marginal astrometric acceleration.Figure 4a presents the planet orbital periods and the Gaia differential velocities of TOIs with high-SNR and low-SNR proper motion anomalies, respectively.The Gaia differential velocities are defined in Section 2 (see Eqn. 3) We exclude systems with false positive and false alarm dispositions.We do not include the eight KOIs and K2 targets because seven of   Figure 4a shows a tentative inverse correlation between the orbital period of transiting planets and the Gaia differential velocities of their host stars.The planet periods of TOIs with differential velocities > 1000 m s −1 are all shorter than ten days.Figure 4b displays the distributions of planet orbital periods of HGCA-high-SNR and HGCA-low-SNR TOIs.We include 53 HGCA-high-SNR TOIs and 200 HGCA-low-SNR TOIs.We can see that orbital periods of transiting planets in HGCA-high-SNR TOIs are generally shorter than in HGCA-low-SNR TOIs.A Kolmogorov-Smirnov test shows that the difference between two samples' planet orbital period distributions is statistically significant (p-value = 9.7×10 −3 ).
To explore whether the trend found in Figure 4 et al. (2021).In Figure 5c, we include 138 and 296 confirmed planets in binary and single KOIs from Kraus et al. (2016).To rule out the influence of EBs that usually have short periods, we only select confirmed planets (CP) or known planets (KP) from their sample.We also removed duplicate TOIs resulting from the overlap between different surveys.We did not apply a distance cutoff to their sample, as such an approach would have resulted in a further decrease in the size of the sample.But most of their targets are within 400 pc, with a small fraction extending beyond 800 pc (See Figure 1 in Kraus et al. 2016 andZiegler et al. 2021).We find that TOIs in binaries have orbital periods statistically shorter than those in single systems (p-value = 0.0016).However, we do not see a significant difference between confirmed Kepler planets in binaries and singles (p-value=0.82).
A few possibilities can explain the different results in the TOI and KOI samples.First, the difference in sensitivity between the two missions may explain the observed disparity, as TESS detected more short-period planets within ten days but fewer at longer periods than Kepler.However, this explanation alone cannot account for the shorter orbital periods of planets in binary TOIs, since TESS searches for planets without considering the binarity of the targets.The second possibility is that stellar companions in KOI sample have relatively larger separations as they are generally more distant and fainter than TOIs.Therefore, companions in KOI sam-ple are less influential in shaping the planets' orbital periods.Ziegler et al. (2020Ziegler et al. ( , 2021) ) and Kraus et al. (2016) both present stellar companions to KOIs/TOIs at separation from a few AU to a few thousand AU.However, Figure 5d illustrates that the distributions of stellar companion separations in the TOI and KOI samples do not exhibit a significant difference (p-value=0.20).Thirdly, the difference between binary and single TOIs might potentially be attributed to the relatively small size of TOIs in binary systems.Therefore, a larger sample of TOIs in binaries is required to reach a more decisive conclusion.Finally, the disparity in planet periods observed between the TOI and KOI samples may be due to the fact that Kepler has higher precision and is thus more sensitive to smaller planets than TESS .Consequently, the two missions may be observing different populations of planets.To test the hypothesis, we need to revise the radii of planets orbiting TOIs/KOIs in binary systems by accounting for the flux dilution.
In short, the reason why the TESS bias affects binary and single systems differently is not yet understood, and a larger sample of TOIs is needed to draw a more definitive conclusion.If the TOIs in binaries do have shorter orbital periods (<10 days), they might form in truncated disks by the companions.Besides, planets' survival probability is likely higher at close-in orbits because the host stars provide more shield to resist the gravitational disturbance from the companions.

Differential velocity distribution of TOIs vs. field stars
As detailed in section 2, the differential velocities can be approximately seen as the projected orbital velocities of the primary stars around the system barycenter, which increases with the companion masses and decreases with orbital distances.In this section, we compare the Gaia differential velocities of HGCA-high-SNR TOIs with field stars, which consists of all stars exhibiting significant proper motion anomalies from HGCA within 300 pc. Figure 6 presents the results.The differential velocities of field stars exhibit a peak around 3000 m s −1 and a broader bump centered at ∼ 200m s −1 to the left.The velocity magnitude at the peak is consistent with differential velocities caused by stellar companions with orbital periods from a few years to a few hundred years (sensitive range for Hipparcos-Gaia proper motion anomalies method).For example, a solar mass star would have a differential velocity of around 4400 m s −1 with a 0.5 M ⊙ companion at an orbital period of approximately 25 years, assuming a face-on orbit.As the orbital periods increase or companion masses decrease, the stellar companions' velocities produce a tail at lower velocities.For example, a 0.01 M ⊙ companion would cause a velocity of around 100 m s −1 for a solar mass star at 25 years period.
Compared to field stars, the distribution of HGCAhigh-SNR TOIs displays a higher peak at velocities around 100 m s −1 with a shortfall at high differential velocities.These distributions suggest that transiting planets are more likely to form in binaries when the companions have lower masses or are at wider separations.Our results are compatible with the previous studies that planets are less common in close binary systems compared to single systems or wide binaries (Wang et al. 2015;Kraus et al. 2016;Ziegler et al. 2020Ziegler et al. , 2021;;Hirsch et al. 2021;Moe & Kratter 2021).In a recent study, Moe & Kratter (2021) finds that the occurrence rate of planets in binaries with a < 10 AU is roughly 15% of that in single systems, while wide binaries with a > 200 AU have similar planet occurrence rates as single stars.The recent ALMA high-resolution surveys also find that disks in multiple systems are smaller, fainter, and less long-lived than those in singles (Cox et al. 2017;Akeson et al. 2019;Manara et al. 2019;Zurlo et al. 2020;Zagaria et al. 2023).These findings support the theory

ORBIT CHARACTERIZATION OF BENCHMARK SYSTEM: LTT 1445 ABC
In the section, we present the results of proof-ofconcept system LTT 145 ABC, for which we characterize the three dimensional orbits of the companion pair BC around A with RVs, Hipparcos-Gaia astrometric acceleration and relative astrometry from AO imaging.

Background
LTT 1445 ABC (TOI-455) is the closest M dwarf triple known to harbor multiple planets at a distance of 6.86 pc (Rossiter 1955;Luyten 1957Luyten , 1980;;Winters et al. 2019Winters et al. , 2022))  of ∼ 36 years (e C,B = 0.5 ± 0.11, i C,B = 89 • .64 ± 0.13, a C,B = 8.1 ± 0.5AU, Ω C = 137.63• ± 0.19).However, it is unclear how the companion pair orbit around the primary.Therefore, we utilized the Hipparcos-Gaia proper motion anomalies, combined with primary RVs and relative astrometry to characterize the orbit of LTT1445 BC pair around the primary A. Furthermore, we constrain the mutual inclination between orbital plane of C around B and that of the subsystems around the primary.LTT 1445 A is targeted by James Webb Space Telescope Cycle 1 GO Program 2708 (PI Z. Berta Thompson) to investigate the presence of an atmosphere of the planet b.
Our characterization of the companion pair's orbit provides context for the dynamical stability of the system.

Orbit Fitting
We use 9 archival RVs of LTT1445 A taken with HARPS between 2004 and 2013 from Trifonov et al. (2020) and 136 published RVs from 2019 to 2021 taken with 5 high-precision spectrographs including the W. M. Keck Observatory echelle spectrograph HIRES, ESPRESSO, HARPS, MAROON-X and PFS from Winters et al. (2022).We also include 5 RVs we newly collected between Sep. 2021 and Jan. 2023 using HIRES (see Table 2).The proper motion anomalies of LTT 1445 A at Hipparcos and Gaia epoch are from HGCA.Finally, we adopt two published relative astrometric measurements taken at 2003 and 2010 from Dieterich et al. (2012) and Rodriguez et al. (2015) (see Table 3).We consider BC pair as one object and use the relative astrometry of mass center of BC subsystem to primary A. We use open source package orvara (Brandt et al. 2021), which performs a parallel-tempering Markov Chain Monte Carlo (MCMC) fitting.In total, our analysis uses 15 free parameters.Two of them are the masses of the host star (M A ) and combined mass of companion pair (M BC ).Six orbital parameters define the orbit of companion pair, including semi-major axis (a), inclination (i), longitude of the ascending node (Ω), mean longitude at a reference epoch (t ref ) of 2455197.5 JD (λ ref ), and the eccentricity (e) and the argument of periastron (ω) in the form of e sin ω and e cos ω.We also included six parameters to fit the zero-point for RV data from different instruments.As there was a fiber exchange for HARPS in 2015, we use different RV zero points for HARPS RVs taken before and after 2015.The last parameter is the intrinsic jitter of RV data.We ignore the transiting planets because their RVs amplitudes are expected to be smaller than the stellar jitter.The proper motion anomalies from inner planets are also nearly zero because signals cancel out when the orbital periods are much shorter than the observing window duration of Hipparcos and Gaia .We use the primary mass and companion masses from Winters et al. (2019) as priors in our fitting and bound the jitter between 0 to 10 m s −1 .The likelihood is calculated by comparing the measured separations, position angles, absolute astrometry, and radial velocities to those of a synthetic orbit and assuming Gaussian errors (Brandt et al. 2021).
We use 100 walkers to sample our model and the chains converge after 2.5 × 10 5 steps.We discarded the first 30% as burn-in portion.Figure 7 shows the best-fit orbit (black lines) from our MCMC chains, including fitted astrometric orbit, RVs and Hipparcos- Gaia proper motions.The reduced χ 2 of RVs indicates a good fit and accurate measurement errors,with values of 0.97.We obtain a dynamical mass of M A = 0.251 +0.010 −0.010 M ⊙ for primary A and mass of M BC = 0.39 0.009 −0.009 M ⊙ for BC subsystem, which agree with published values from Winters et al. (2022) within 1σ.Our best-fit model shows that the subsystem BC orbits around primary A in an eccentric and edge-on orbit (a BC,A = 58 −20 +16 AU, e BC,A = 0.375 +0.037 −0.064 , i BC,A = 88 • .5 +1.3  −1.4 , Ω BC,A = 135.15• ± 0.28, see Table 4 for other parameters).We compute the mutual inclination ∆I between orbital plane of BC around A and that of C around B with their inclination (i C,B , i BC,A ) and longitude of ascending node (Ω C,B , Ω BC,A ): (4) We obtained the mutual inclination ∆i = 2 • .88±0.63.Therefore, LTT 1445 ABC is a flat system where the subsystem BC orbits around A in nearly the same plane as their orbit around each other.Because the LTT 1445 A is a slow rotator (P tot ∼ 84 days, Winters et al. 2019), we are not able to measure the spin-orbit angle of two transiting planets b and c relative to the primary through Rossiter-MacLauglin effect.However, the probability of observing the two transiting planets and companion pair BC all have edge-on orbits is notably low, if we assume their orbits are independent.Specifically, if the cos(i) values of planet b, c, and companion pair BC are drawn randomly from a uniform distribution between 0 and 1, the probability of observing all these bodies to have inclinations within the range of 87 • to 90 • is only 0.014%.Therefore, it is highly likely that the transiting planet orbits are coplanar with the orbit of the BC companions.Meanwhile, the alignment of the non-transiting planet LTT 1445 Ad with the inner planets is subject to significant uncertainty.Located at a distance of 0.09 AU, the angle range for a transiting configuration is only 1.6 • .A plausible scenario is that LTT 1445 Ad is aligned with the inner planets but is located outside the transiting configuration.A detailed dynamical study might yield interesting constraints on the possible orbits of planet d, but is outside the scope of this paper.

Implication for planet formation
One piece that needs to be added to understand the effect of companions on planet formation is the inclination of the companion orbits.Inclination plays a vital role in the dynamic interaction between the companions and inner planets or the protoplanetary disks.For example, the Kozai-Lidov effect (Kozai 1962;Lidov 1962) occurs when the mutual inclination between two objects is greater than ∼ 40 • , causing the inner objects to be unstable.Previous studies have also found that an inclined outer companions may misaligned the orbit of inner planets (Huber et al. 2013;Zhang et al. 2021).Fortunately, the combination of Hipparcos and Gaia astrometry and RVs allow us to characterize the threedimensional orbits of the companions.In this work, we present the results of triple system LTT 1445, in which LTT 1445 BC orbit around the primary A with a semimajor axis of ∼ 58AU.The LTT 1445 system bears a remarkable resemblance to the Kepler-444 triple system, where Kepler-444 BC orbits around A in an edge-on orbit and is likely to be aligned with the orbit of five transiting planets around the primary A (Dupuy et al. 2016;Zhang et al. 2022).LTT 1445 and Kepler-444 both agree with the statistical results reported by Dupuy et al. (2022), which concludes that low mutual inclinations between planets and companions are required to explain the observed orbital arcs in 45 binary systems containing Kepler planet candidates.One may ponder whether the coplanarity of the systems relates to the planet's formation in a dynamically hostile environment.
Zanazzi & Lai (2018) investigated the evolution of disk inclinations in binary systems and found that effective realignment between the circumstellar disks around the primary star and companions tends to occur when the companions are closer than 200 AU.Considering that LTT1445 BC has a semi-major axis of ∼ 58 AU, it is plausible that the companions were initially misaligned with the primary disk but later underwent realignment during their evolution.Another close binary HIP94235 (a ∼ 50AU ) is consistent with the possibility in which the primary hosts a transiting mini-Neptune.The companion HIP94235B exhibits an inclination of around 68 • (Zhou et al. 2022), which suggests a minimum misalignment of 22 • between the companions and the transiting planet.Given that HIP94235 is part of a young comoving group (∼ 120 Myr, Zhou et al. 2022), it is possible that the realignment between the companion and the disk is still ongoing.Alternatively, it is also possible that the LTT 1445 BC were initially aligned with the primary disk from the onset.In this case, the fully con-planar configuration and close separation of LTT 1445 triples are consistent with the disk fragmentation scenario that gravitational instability in a shearing disk might produce multiples stars (Adams et al. 1989;Moe & Kratter 2018;Offner et al. 2022).In either possibility, although the companions likely truncated the primary's circumstellar disk, there was still enough disk material remaining to form multiple planets.In short, constraining the mutual inclination between planets and stellar companions in more systems is needed to understand the mechanisms behind planet formation in close binary systems.

CONCLUSIONS
We have presented a study of transiting planets with systems that show significant Gaia-Hipparcos accelerations.Our conclusions are as follows: 1. We presented a catalog of 66 transiting planet hosts (58 TOIs, 4 KOIs, and 4 K2 planet candidates) within a 300 pc volume limit with significant Hipparcos and Gaia proper motion anomalies through cross-matching the TOI/KOI/K2 catalogs with HGCA.The parameters of these targets are presented in Table 1.Among these targets, 33 have directly imaged stellar companions, either from published papers or the ExFOP website.
2. For transiting planet candidates identified by TESS, we evaluated the reliability of the transits based on the radial velocities obtained with Keck/HIRES and the TESS Follow-Up Observing Program.We found that TOIs with high proper motion anomalies have nearly four times more eclipsing binary classifications than TOIs with insignificant proper motion anomaliess.The excess of EBs in HGCA-high-SNR TOIs might be from the contamination of triple systems.Note-The χ 2 of relative astrometry is 0.09 for separations and 0.06 for PAs, with 2 measurements for each.The χ 2 of the Hipparcos and Gaia proper motion differences is 2.64 for four measurements.The χ 2 of RV is 146.80 for 150 measurements.
3. We translated the proper motion anomalies into differential velocities between the epochs of Hipparcos and Gaia, expressed in units of ms −1 .We observe a tentative inverse correlation between transiting planet orbital periods and Gaia differential velocities, with short planet periods occurring preferentially with more massive and closer companions.Additionally, our findings suggest a possible trend of shorter planet periods in binaries, although this could be an artifact of the TESS observation bias.If the trend is genuine, it supports the theory that planets in binaries form in smaller protoplanetary disks truncated by their companions.
4. We observe that HGCA-high-SNR TOIs exhibit lower differential velocities than the entire population of significant proper motion anomalies stars within 300 pc in HGCA catalog.This comparison indicates that planets are more likely to persist in systems with low-mass companions or wider stellar companions.
5. We determined the three-dimensional orbit of the companion pair BC around the primary star A in the triple system LTT 1445, which also hosts two transiting planets.Our analysis indicates that LTT 1445 is a flat system, with the orbital plane of BC around A being almost coplanar with the orbital plane of the outer planet c around B (∆i ∼ 2.88 • ).This coplanarity may account for the survival of multiple planets in an otherwise dynamically challenging environment.
Future observations will provide opportunities to confirm potential companions in systems with no reported companions.Our next paper in the series will feature AO images and astrometric measurements.We will also constrain the companion mass and separation for low-mass companions below the detection limit.Additionally, we will identify the host stars based on transit duration and stellar density and recalculate planet radii by estimating the contrast between the two stars.Observatory from telescope time allocated to the National Aeronautics and Space Administration through the agency's scientific partnership with the California Institute of Technology and the University of California.The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community.We are most fortunate to have the opportunity to conduct observations from this mountain.• HIP15053 (TOI-394): TFOP SG1 identified different odd-even depth in TESS QLP light curve, which indicates that TOI394.01 is an EB.The RVs at two quadrature time collected using Keck/HIRES from the primary don't show a RV difference consistent with a stellar mass object.So it is likely that the primary is orbited by a close EB companion and the transit is from the companion pair instead of the primary.
• HIP98516 (TOI-1124): TFOP SG1 detected event on target.But TFOP SG1 also detected strong chromaticity of the transit depth and odd-even depth in TESS light curve, which indicates TOI-1124.01 is a blend.
• HIP28122 (TOI-896): TFOP SG1 evaluated it as false alarm because of marginal signal.No transiting events are detected in sector 33, therefore TOI-896.01 retired as false alarm.
• HIP58234 (TOI-680): SG1 clears the field of NEBs, and detects a 1ppt event arriving a little early.Additional transits show chromaticity, and HIRES RVs show no convincing variation phased to the ephemeris.This is likely a blend or a planet around the compaion.
• HIP45621 (TOI-2666): TOI2666.01 is a single transit.Keck/HIRES spectra show that the star is a spectroscopic binary(SB).The companion is 18.5% the brightness of the secondary and separated by 35 km/s.
• HIP57386 (TOI-5521): There are no SG1 results available for this system.However, two TRES observations indicate a velocity offset of 29.5 km/s that is out of phase with the photometric ephemeris.This strongly suggests the presence of a stellar companion in the system, although it cannot be responsible for the shallow transits observed.This is consistent with the WDS catalog, which presents a companion at 0.7 ′′ to TOI-5521.
• HIP93711 (TOI-2299): Possible on target.SG1 detected the transit, but it is unclear whether it originated from the target or a neighbor at 3.6 arcsec to the west.In addition, spoc-s14-s60 detects two TCEs at 214 and 246 days instead of a single TCE at 165 days.But they may not be reliable.
• HIP65205 (TOI-1831): It's a large star with a close companion at 0.66 arcsecs.The transit shows a slight odd-even transit depth difference, which could possibly come from an EB.SG1 clears the field of NEBs.But TRES observation does not find a large RV variation, so it retired as an APC/EB?/CRV in SG1.However, as there is a very close companion at 0.66 arcsec from the star, it is also possible that the transit event is occurring at the companion, which could explain why large RV variations were not seen in the primary star.We plan to investigate this system further in our project.
• HIP24718 (TOI-128): TFOP SG1 finds no NEBs beyond 2 ′′ but they cannot rule out the close companion at ∼ 2 ′′ .If the signal originates from either the primary star or companion, it could still be a planet.
• HIP41849 (TOI-575): TFOP SG1 notes additional TESS data reveal this to be an EB, with primaries and secondaries both visible.Probably on a 0.6" companion seen in high-resolution imaging.
• HIP74685 (TOI-2017): TFOP SG1 detects event on target.But TOI2017.01 is an F+M EB with an orbital solution from TRES and the CfA Digital Speedometers.

Figure 1 .
Figure 1.Principle of Hipparcos Gaia proper motion anomalies.µH and µG represent the proper motions of the same star measured by Hipparcos and Gaia with a time baseline of around 25 years.µHG is the stellar long-term velocity across the sky plane.If we subtract µHG from µH and µG, the residuals are the proper motion anomalies at Hipparcos and Gaia epochs, respectively.(a) A star with marginal proper motion anomalies: if µH and µG are similar to the long-term velocity µHG, the star moves across the sky plane in a linear motion.(b) A star with significant proper motion anomalies: a significant residual indicates the star not only moves linearly but also orbits around the system barycenter due to the gravitational pull from a companion.

Figure 2 .
Figure 2. Gaia color-absolute magnitude diagram for our targets (star signs) and stars in HGCA within 300 pc (grey dots).TOI/KOI/K2 planet candidate hosts with significant proper motion anomalies are color-coded by the signal-tonoise ratio of their proper motion anomalies at Gaia epoch (SNRG).

Figure 3 .
Figure 3. Right panel: the fraction of confirmed planets, planet candidates, and several false positives of TOIs in our high SNR sample.Left panel: the fraction of the same categories but for low SNR TOIs.The two samples are both limited to 300 pc.We only present TOIs in this figure because the majority of KOI/K2 targets in our sample are EBs.

Figure 4 .
Figure 4. Panel a: planet orbital period vs. differential velocities at Gaia epoch of TOIs with significant proper motion anomalies (color-coded by their Gaia DR3 RUWE) and TOIs with marginal proper motion anomalies (grey).We exclude TOIs with FP/FA dispositions.High-SNR TOIs with RUWE ≥ 1.4 are in red, whereas those with RUWE < 1.4 are in blue.Panel b: marginalized distribution of planet orbital periods of high (orange) and low (grey) SNR TOIs overlapped with the cumulative distribution function.We exclude TOIs with FP/FA dispositions.them are false positives.We colored HGCA-high-SNR TOIs by their Gaia DR3 Renormalised Unit Weight Error (RUWE).A RUWE value greater than 1.4 usually indicates that the source is non-single and the two components are too close to be fully resolved by Gaia (Lindegren et al. 2018).The HGCA-high-SNR TOIs with high RUWE mostly have differential velocities beyond one thousand m s −1 , including TOI-271, TOI-680, TOI-930, TOI-1719, and TOI-1131.The high differential velocities are consistent with these TOIs having close stellar companions with separations below 1 ′′ (see Table1) 2 .In compari- motion anomalies reveal the existence of giant planets at a few au in TOI-144(π Men), TOI-1144(HAPT-11), and TOI-1339 systems.
Figure 5a presents the stellar companion separations and planet orbital periods of these TOIs and KOIs.In Figure 5b, We include 265 and 56 confirmed planets in binary and single TOIs from Ziegler et al. (2020, 2021); Howell et al. (2021); Lester

Figure 5 .
Figure 5. Panel a: planet orbital period vs. stellar companion separations of TOIs (green, Ziegler et al. 2020, 2021; Lester et al. 2021; Howell et al. 2021) and KOIs (purple,Kraus et al. 2016) in binary systems.We only include confirmed planets (CP) or known planets (KP).Panel b: marginalized distribution of planet orbital periods of TOIs in binaries (green) and singles (grey).Panel c: same as panel b but for KOIs in binary (purple) and single (grey) systems.Panel d: marginalized distribution of stellar companion separations of TOIs (green) and KOIs (purple) in binaries.

Figure 6 .
Figure 6.Gaia differential velocity distribution of TOIs with significant proper motion anomalies (red) compared to field stars (blue).The field star sample consists of all stars with significant proper motion anomalies from HGCA within 300 pc.The differential velocity are in log scale.We exclude TOIs with FP/FA disposition.

Figure 7 .
Figure 7. Orbit characterization of LTT 1445 BC mass center around A using RVs, relative astrometry and absolute astrometry from Hipparcos and Gaia.(a): relative astrometry orbits of LTT 1445 BC pair around A. The blue filled circles are two observed relative astrometry used in our analysis.(c): Observed and fitted RVs of LTT 1445 from HARPS, HIRES, ESPRESSO, MAROON-X, PFS.(d)-(e): Observed and fitted Hipparcos and Gaia proper motion of LTT 1445 A in right ascension and declination.In all of above panels, the thicker black lines represent the best-fit orbit in the MCMC chain while the other 50 lines represent random draws from the chain; (b): relative astrometry orbits of LTT 1445 C around B from Winters et al. (2019).
made use of the High-Resolution Imaging instruments 'Alopeke and Zorro and were obtained under Gemini LLP Proposal Number: GN/S-2021A-LP-105.'Alopeke and Zorro were funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quigley.Alopeke was mounted on the Gemini North telescope of the international Gemini Observatory, a program of NSF's OIR Lab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. on behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovaes e Comunicaes (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).Funding for the TESS mission is provided by NASA's Science Mission Directorate.This research has made use of the Exoplanet Follow-up Observation Program website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.This research has made use of the NASA Exoplanet Archive and ExoFOP, which are operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.

Table 1 )
2. In comparison, HGCA-high-SNR TOIs with low RUWE have differential velocities from dozens to a few hundred m s −1 .In some systems, the velocities in the middle range are from stellar companions at relatively wider separation.2Except for TOI-510 which has a companion at 5.5 ′′ reported from WDS catalog.The Hipparcos Gaia acceleration indicates there might be another unresolved companion at a closer separation.
. The hierarchical system consists of a primary LTT 1445 A (0.268 R ⊙ , 0.257 M ⊙ ) orbited by a M dwarf pair BC at a separation of ∼ 7 Winters et al. (2019)rometry from Fourth Interferometric Catalog (FIC) and Differential Speckle Survey Instrument (DSSI),Winters et al. (2019)found that LTT 1445 C orbits around B in an eccentric and edge-on orbit with a period

Table 3 .
Relative Astrometry used in the Orbit Characterization for LTT 1445BC around A

Table 5 .
TOIs with low-SNR proper motion anomalies a The flags come from NASA Exoplanet Archive.CP: Confirmed Planet, PC: Planet Candidate, APC: Ambiguous Planet Candidate, FP: False Positive, FA: False Alarm.