CD –27°11535: Evidence for a Triple System in the β Pictoris Moving Group

Observations of CD-27 that were made between 2006 May 27 and 2009 June 1 with the NaCo instrument were obtained from the ESO Science Archive Facility. ²⁹ Two data sets were obtained with the S27 camera (27 mas pixel⁻¹) and the IB2.27 intermediate-band filter, and one was obtained with the S13 camera (13 mas pixel⁻¹) and the K_s broadband filter. These data were obtained under program IDs 077.C-0483, 081.C-0825, and 083.C-0659. The first two epochs were originally published in Elliott et al. (2015); however, the large uncertainty of their separation measurements motivated us to reanalyze their observations.

We used a standard near-infrared data reduction process to reduce and analyze each data set using associated calibrations obtained from the archive. The dark current was measured by finding the median of several exposures of the same exposure time taken while the instrument light path was blocked. This combined frame was then subtracted from each raw image. We created a flat field and bad pixel map using pairs of lamp-on and lamp-off exposures obtained during the day. These were used to perform the flat-field correction of the raw images and to correct for bad pixels. We did not apply any distortion correction to the image, as the effect of distortion over such a small angular separation between the two resolved components of the CD-27 system is negligible. The thermal background within each image was estimated using a median combination of all images, which was then subtracted from each image.

Relative astrometric and photometric measurements were made by fitting the point-spread function (PSF) of both components with that of a single star observed on the same (or neighboring) night with the same instrument configuration. We searched the archive for suitable observations for each of our three data sets. Unlike for CD-27, the individual images for the reference stars were aligned and combined to create a high signal-to-noise ratio (S/N) PSF that could be used for PSF fitting. The centroid of the star in each image was calculated by fitting a two-dimensional Gaussian within a region of 4 pixels centered on an initial guess for the location of the star. This process was repeated using the result of the first iteration as the guess position for the second.

A model of the two components of the CD-27 system was constructed using two copies of the model PSF interpolated to the positions (x₀, y₀) and (x₁, y₁) and multiplied by scaling factors f₀ and f₁. A background term (A) was added to account for any residual background signal present in the image. We used the implementation of Powell's method within the scipy.optimize package to find the optimal set of parameters that minimized the residuals after model subtraction in two 1.5λ/D apertures centered on the positions of the two components. This was repeated for each of the potential PSF calibrator stars. The PSF star that resulted in the smallest-amplitude residuals was used to measure the relative astrometry and photometry between the resolved components.

The pixel positions of the two components were converted into an angular separation and position angle using the plate scale and orientation of the detector given in Table 5. Magnitude differences were calculated from the ratio of the two scaling factors. This process was repeated for each image of the CD-27 system, yielding an average and standard deviation for each value that are given in Table 5. The reduced images, the best-fit PSF model, and the corresponding residuals are shown in Figure 1.

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The system was observed on six separate epochs over the course of 11 yr with Keck/NIRC2 through seven different filters (z, J, H, K_s , $K^{\prime}$, $L^{\prime}$, BrG). A single star was observed with the same filter that could act as a PSF reference in all but the last epoch in 2021 June. For that epoch, a PSF was constructed using the binary 1RXS J195602.8–320720 after digitally masking the fainter secondary. The observations were reduced using a standard near-infrared reduction pipeline similar to that employed to reduce the NaCo data. The raw images were dark subtracted, divided by a flat field, and cleaned of bad pixels using outlier rejection. The geometric distortion of the detector was corrected using a flux-conserving algorithm (Yelda et al. 2011; Service et al. 2016). The relative position and brightness of the two resolved components of the CD-27 system were calculated using the same PSF fitting approach used for both the NaCo and GPI data sets. This process was repeated for each image, yielding an average value and standard deviation for the pixel offsets and flux ratio. These were converted into on-sky separations and position angles using the calibration values listed in Table 5. The reduced images, the best-fit PSF model, and the corresponding residuals for a subset of the observations of the system are shown in Figure 1.

CD-27 was observed with GPI on 2018 August 15 and 2019 August 05 alongside the PSF calibrator HD 153318 (see Table 4). The GPI images were all processed and reduced with the GPI Data Reduction Pipeline (DRP) v1.5.0 (Perrin et al. 2014). After dark current subtraction and bad pixel interpolation, microspectra within the raw 2D image were extracted to create an (x, y, λ) data cube (Maire et al. 2014). An image of an argon arc lamp was taken immediately before the data to calibrate the wavelength axis of the data cube. Bad pixels were corrected using outlier rejection both before and after the data cube construction step. The system was clearly resolved into two components within the reduced image (Figure 2), at an angular separation far beyond what is typically explored with the nonredundant mask (NRM) technique. These observations were scheduled prior to a reliable determination of the orbit of the system.

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Rather than using a specialized pipeline to reduce these observations (e.g., Greenbaum et al. 2019), we instead used a similar approach to that for the NaCo observations described in the previous section because of the large angular separation between the two components (Figure 2). Observations of the single calibrator star HD 153318 were reduced and used to construct a model of the PSF. Two copies of this PSF were shifted and scaled to fit the two resolved components of the CD-27 system. This process was repeated using the central wavelength slice of each observation from each epoch (19 in 2018, 16 in 2019) yielding an average and standard deviation for each measurement. On-sky separations and position angles were calculated using the relevant calibration measurements given in Table 5. The reduced images, the best-fit PSF model, and the corresponding residuals are shown in Figure 2.

We obtained optical echelle spectra of CD-27 at the Apache Point Observatory (APO) 3.5 m telescope with the ARCES instrument (Wang et al. 2003) on five epochs in 2021. Given the seeing-limited conditions and the close separation of the system, we obtained a blended spectrum of the entire system. The observations were reduced using a standard spectroscopic reduction pipeline that performs bias and flat-field correction, measures and corrects the continuum, and derives a wavelength solution from observations of a ThAr calibration lamp.

Figure 3 shows the region surrounding the Li λ6707.79 line for the CD-27 system taken on 2021 June 20 and for our RV standard HIP 23311 with a spectral type of K3 taken on the same night. Despite the near-equal visual magnitude of A and B, we do not observe double lines in our spectrum, but rather broad lines, suggesting that some or all of the components are rapid rotators. No significant RV shift is measured over our 4 months of data. We confirm the strong lithium absorption observed by Torres et al. (2006), though with these unresolved spectra we cannot determine how much lithium corresponds to each component of the system. Nevertheless, given the late spectral types of the components, with a K5 spectral type assigned to the system, this strong lithium absorption is a clear sign of youth, consistent with β Pictoris moving group membership.

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With the astrometry for each epoch collected, we proceed with fitting a Keplerian orbit to the relative astrometry of B with respect to A. To do so, we use a parallel-tempered Markov Chain Monte Carlo (MCMC) procedure (Foreman-Mackey et al. 2013), implemented within the orbit fitting software orbitize! (Blunt et al. 2017). In total, 256 chains are run in parallel at 16 temperatures to sample the posterior distribution of the following eight parameters: semimajor axis (a), eccentricity (e), inclination angle (i), argument of periastron (ω), position angle of nodes (Ω), normalized epoch of periastron passage (τ), parallax (π), and total mass (M_tot). Here τ is the fraction of the orbit past a given reference date (in our case 2020 January 1) and is parameterized by the period (Blunt et al. 2020).

To ensure rapid convergence of the chains, the walkers are initialized from an optimized starting position found using a rejection sampling algorithm (OFTI) to find 256 potential orbits based on the first three NaCo epochs. For the OFTI algorithm, we employ a uniform prior in total mass between 0.5 and 5 M_⊙. The semimajor axis prior is a log uniform distribution with a minimum value of 1 × 10⁻³ au and a maximum of 1 × 10⁷ au. Eccentricity and epoch of periastron are given uniform priors between 0.0 and 1.0. The argument of periastron and position angle of nodes also have uniform priors between 0.0 and 2π, but the inclination angle makes use of a sine prior. Finally, we use a Gaussian prior on the parallax from the parallax and error of 12.0040 ± 0.2854 mas (DR2; Gaia Collaboration et al. 2018). The priors used in the MCMC analysis were identical, other than that of the semimajor axis, which had a log uniform prior between 1 × 10⁻¹ au and 1 × 10³ au.

Posteriors from the MCMC fit are given in Table 2, and the orbit is plotted in Figure 4 and 5. The astrometric measurements span almost a complete orbital period, resulting in a very well constrained orbit with a reduced χ² of 9.8. We find a fairly low eccentricity of 0.2394 ± 0.0005 and an inclination of 141.27° ± 0.15°. The semimajor axis of the orbit is 9.8 ± 0.2 au, with a period of 19.83 ± 0.02 yr, giving a total mass of ${2.36}_{-0.16}^{+0.17}$ M_⊙.

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Table 2. Best-fit Orbital Parameters and Corresponding Median and 1σ Confidence Intervals for the CD-27 System

Parameter	Unit	${\chi }_{\min }^{2}$ Orbit	Median, 1σ CI	Bonavita et al. (2022)
a	au	9.7	${9.8}_{-0.2}^{+0.2}$	9.73 ± 0.15
e	⋯	0.2396	${0.2394}_{-0.0005}^{+0.0005}$	0.264 ± 0.026
i	deg	141.39	${141.27}_{-0.15}^{+0.15}$	147.2 ± 5.9
ω	deg	11.0	${11.6}_{-0.4}^{+0.5}$	12.8 ± 8.8
Ω	deg	218.1	${218.4}_{-0.2}^{+0.2}$	35.3 ± 4.8
T0	yr	2029.03	${2029.06}_{-0.03}^{+0.03}$	2009.35 ± 0.24
P	yr	19.81	${19.83}_{-0.02}^{+0.02}$	20.78 ± 0.84
Mtot	M⊙	2.35	${2.36}_{-0.16}^{+0.17}$	2.14 ± 0.27

Note. Values from Bonavita et al. (2022) given for comparison.

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Recently, the CD-27 system was included in a sample of binaries characterized with VLT/SPHERE by Bonavita et al. (2022), who presented an initial determination of the orbit of this system. With our improved coverage of the orbit, we are able to further constrain the orbital parameters. Although we find similar values for the orbital period and eccentricity (see Table 2), the orbit appears rotated by 180° on the sky. This discrepancy is due to the difference between the studies for which component in the system is designated the primary. Bonavita et al. (2022) report an ambiguity in which of the two components is brightest in the near-IR, whereas we are able to differentiate which of the two resolved components is the brightest at a very high confidence (∼100σ in the 2019 August 26 epoch).

We compare the total system mass from the visual orbit to the masses predicted from four evolutionary model grids. As we do not have a measurement of the mass ratio of the system, we assume a mass ratio of q = 1, a reasonable assumption given the near-equal flux ratio. The absolute magnitude of each component was estimated from the apparent magnitude of the blended system reported in the Two Micron All Sky Survey (2MASS) catalog (Cutri et al. 2003), the flux ratio measured in the corresponding filter reported in Table 5, and the distance derived from the Gaia DR2 parallax measurement. We generated mass−magnitude relations from four evolutionary models between 10 and 40 Myr: Siess (Siess et al. 2000), BHAC15 (Baraffe et al. 2015), Yonsei−Yale (Spada et al. 2013), and Padova PARSEC (Bressan et al. 2012). These models are compared to the mass and absolute magnitudes of the two components of CD-27 in Figure 6.

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Given the expected age of 26 ± 3 Myr for the system, the two components appear either underluminous or too massive when compared to the evolutionary models. Such a discrepancy is difficult to explain without invoking a systematic error in either—or both—of the component masses or absolute magnitudes. If the two stars were instead above the zero-age main sequence, that could more easily be explained by a different age of the system. This discrepancy is not sensitive to our assumed mass ratio, as changing this simply shifts the components in opposite directions horizontally relative to the model tracks. This would indeed move one of the two stars closer to the main sequence, but the other would become an even greater outlier.

A low-mass third companion to either of the two resolved components of the system could explain the discrepancy between the total mass from the orbit and the mass predicted from the absolute magnitude of each component. We test this hypothesis by simultaneously fitting the visual orbit and the spectral energy distribution of both of the resolved components under various assumptions regarding the system architecture. Specifically, we investigate a binary (AB) and a triple with the additional companion around either the primary (AaAb-B) or the secondary (A-BaBb). We also test the effect of removing the Gaia DR2 parallax constraint on the quality of the fit. We use Metropolis−Hastings MCMC implemented within the emcee package (Foreman-Mackey et al. 2013) to simultaneously fit the visual orbit, the flux ratios between the two resolved components, and the total near-infrared flux of the system. The visual orbit is fit as before (Section 3). The flux ratios and total flux of the system are estimated from the four aforementioned evolutionary models, with an independent fit performed per model grid. Due to the 2.9-day variability of the system (Kiraga 2012), we only use flux ratio measurements taken on 2020 July 24 that were taken in five different bands within an hour and, consequently, would be less affected by variability. For each fit, we run 128 chains in parallel for 10⁴ steps. The walkers are initialized with uniform distributions, centered at the values reported in Section 3. At each step in the fit, the flux of each constituent star is generated using an interpolating function given its age, mass, and the evolutionary model, from which the flux ratio between the two resolved components is determined. The absolute magnitude of the blended system is calculated and converted into an apparent magnitude using the parallax, which is then compared to the 2MASS measurements for the system (Cutri et al. 2003). We use priors to keep the age between 10 and 100 Myr (consistent with the amount of lithium absorption observed), the parallax positive, and the mass of the constituent stars between 0.1 and 1.5 M_⊙. The priors on the orbital parameters are as used in Section 3. The lower bound on the star mass prior was set by the minimum mass reported in the evolutionary models.

The results of our experiment are reported in Table 3. A representative example of the model fluxes (in an AaAb-B configuration), their flux ratio and our data points is included in Figure 7. We find a best fit to the BHAC15 and Padova model grids in the AaAb-B configurations, with a minimum χ² of 2.8, excluding the contribution from the visual orbit fit, compared with ∼5 for the A-B configuration and 10–12 for the A-BaBb configuration. The Seiss and Yonsei−Yale models show similar goodness of fit for the A-B and AaAb-B configurations, with the A-BaBb configuration being more strongly disfavored. The fits with and without a prior on the parallax give a generally similar goodness of fit, due in part to the relatively large uncertainty of the Gaia DR2 parallax measurement. This joint fit of the astrometric and photometric measurements of the CD-27 system provides some evidence of an unresolved companion to the A component within the CD-27 system, although the improvement in the goodness of fit does depend on which evolutionary model is used. We compute the component masses for the AaAb-B system architecture by taking the weighted average of the four model-dependent results and find M_Aa = 0.923 ± 0.008 M_⊙, M_Ab = 0.177 ± 0.055 M_⊙, and M_B = 0.903 ± 0.009 M_⊙. The age of the system with this method is 24.1 ± 1.9 Myr, and the parallax is 12.61 ± 0.13 mas.

Table 3. Possible Configurations of CD-27

Configuration	Prior on Parallax	Evolutionary Model	Min χ2	Age (Myr)	Parallax (mas)	M1 (M⊙)	M2 (M⊙)	M3 (M⊙)
AaAb-B	Flat	BHAC15	2.8	${23.6}_{-1.9}^{+1.9}$	${12.72}_{-0.13}^{+0.11}$	${0.906}_{-0.007}^{+0.006}$	${0.881}_{-0.008}^{+0.009}$	${0.171}_{-0.046}^{+0.056}$
		Padova	2.8	${22.8}_{-1.8}^{+1.8}$	${12.66}_{-0.12}^{+0.11}$	${0.916}_{-0.008}^{+0.008}$	${0.888}_{-0.008}^{+0.008}$	${0.181}_{-0.046}^{+0.051}$
		Seiss	5.9	${24.5}_{-1.8}^{+1.8}$	${12.41}_{-0.13}^{+0.10}$	${0.984}_{-0.010}^{+0.009}$	${0.955}_{-0.009}^{+0.009}$	${0.169}_{-0.047}^{+0.062}$
		Yonsei−Yale	6.3	${25.9}_{-1.9}^{+2.0}$	${12.69}_{-0.20}^{+0.16}$	${0.905}_{-0.011}^{+0.009}$	${0.875}_{-0.019}^{+0.016}$	${0.193}_{-0.062}^{+0.083}$
	Gaia DR2	BHAC15	2.7	${23.4}_{-1.8}^{+1.8}$	${12.59}_{-0.11}^{+0.12}$	${0.907}_{-0.007}^{+0.006}$	${0.888}_{-0.009}^{+0.008}$	${0.222}_{-0.051}^{+0.051}$
		Padova	2.7	${22.8}_{-1.7}^{+1.7}$	${12.57}_{-0.10}^{+0.11}$	${0.916}_{-0.007}^{+0.008}$	${0.893}_{-0.008}^{+0.008}$	${0.218}_{-0.047}^{+0.047}$
		Seiss	5.5	${24.4}_{-1.8}^{+1.7}$	${12.34}_{-0.13}^{+0.12}$	${0.984}_{-0.010}^{+0.009}$	${0.958}_{-0.009}^{+0.009}$	${0.200}_{-0.057}^{+0.061}$
		Yonsei−Yale	6.6	${25.4}_{-1.8}^{+1.9}$	${12.48}_{-0.12}^{+0.15}$	${0.906}_{-0.010}^{+0.008}$	${0.888}_{-0.014}^{+0.011}$	${0.276}_{-0.065}^{+0.056}$
A-B	Flat	BHAC15	5.8	${23.7}_{-1.7}^{+1.8}$	${13.16}_{-0.04}^{+0.04}$	${0.904}_{-0.007}^{+0.006}$	${0.862}_{-0.006}^{+0.006}$	⋯
		Padova	5.1	${22.2}_{-2.0}^{+2.0}$	${13.13}_{-0.04}^{+0.04}$	${0.915}_{-0.008}^{+0.008}$	${0.866}_{-0.007}^{+0.007}$	⋯
		Seiss	5.9	${24.1}_{-1.7}^{+1.7}$	${12.79}_{-0.04}^{+0.04}$	${0.984}_{-0.009}^{+0.009}$	${0.939}_{-0.007}^{+0.007}$	⋯
		Yonsei−Yale	6.9	${26.7}_{-1.9}^{+1.8}$	${13.24}_{-0.07}^{+0.06}$	${0.897}_{-0.012}^{+0.011}$	${0.840}_{-0.011}^{+0.015}$	⋯
	Gaia DR2	BHAC15	5.5	${23.2}_{-1.7}^{+1.7}$	${13.14}_{-0.03}^{+0.04}$	${0.907}_{-0.006}^{+0.006}$	${0.865}_{-0.006}^{+0.006}$	⋯
		Padova	5.2	${21.9}_{-1.9}^{+1.8}$	${13.10}_{-0.04}^{+0.04}$	${0.918}_{-0.008}^{+0.008}$	${0.870}_{-0.007}^{+0.007}$	⋯
		Seiss	5.9	${23.8}_{-1.6}^{+1.6}$	${12.78}_{-0.04}^{+0.04}$	${0.987}_{-0.009}^{+0.008}$	${0.941}_{-0.007}^{+0.007}$	⋯
		Yonsei−Yale	7.2	${25.4}_{-1.8}^{+1.8}$	${13.17}_{-0.06}^{+0.06}$	${0.907}_{-0.011}^{+0.009}$	${0.853}_{-0.014}^{+0.014}$	⋯
A-BaBb	Flat	BHAC15	10.6	${22.9}_{-1.7}^{+1.7}$	${12.86}_{-0.05}^{+0.04}$	${0.916}_{-0.006}^{+0.007}$	${0.861}_{-0.006}^{+0.006}$	${0.113}_{-0.010}^{+0.020}$
		Padova	11.8	${20.3}_{-2.1}^{+2.4}$	${12.84}_{-0.05}^{+0.04}$	${0.929}_{-0.007}^{+0.008}$	${0.865}_{-0.008}^{+0.008}$	${0.108}_{-0.006}^{+0.013}$
		Seiss	10.9	${23.6}_{-1.6}^{+1.6}$	${12.51}_{-0.06}^{+0.05}$	${0.998}_{-0.008}^{+0.008}$	${0.940}_{-0.006}^{+0.006}$	${0.119}_{-0.014}^{+0.028}$
		Yonsei−Yale	10.6	${26.0}_{-1.7}^{+1.7}$	${12.84}_{-0.11}^{+0.08}$	${0.920}_{-0.010}^{+0.009}$	${0.847}_{-0.011}^{+0.013}$	${0.132}_{-0.024}^{+0.047}$
	Gaia DR2	BHAC15	12.4	${22.7}_{-1.7}^{+1.7}$	${12.83}_{-0.07}^{+0.05}$	${0.918}_{-0.006}^{+0.007}$	${0.862}_{-0.006}^{+0.006}$	${0.121}_{-0.015}^{+0.028}$
		Padova	11.3	${20.2}_{-2.0}^{+2.3}$	${12.82}_{-0.05}^{+0.04}$	${0.932}_{-0.007}^{+0.008}$	${0.867}_{-0.008}^{+0.008}$	${0.111}_{-0.008}^{+0.018}$
		Seiss	9.6	${23.4}_{-1.7}^{+1.6}$	${12.49}_{-0.07}^{+0.05}$	${1.000}_{-0.008}^{+0.008}$	${0.941}_{-0.006}^{+0.006}$	${0.125}_{-0.019}^{+0.034}$
		Yonsei−Yale	12.0	${25.5}_{-1.6}^{+1.6}$	${12.71}_{-0.16}^{+0.13}$	${0.928}_{-0.010}^{+0.010}$	${0.849}_{-0.011}^{+0.013}$	${0.183}_{-0.054}^{+0.071}$

Note. M₁ is A or Aa, M₂ refers to B or Ba, while M₃ is the mass of Ab or Bb.

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Estimating the system mass and absolute magnitudes of both components requires a reliable measurement of the system parallax. The discrepancy between measured and predicted system mass could be explained by decreasing the distance to the star. This would cause a decrease in the system mass due to a decrease in the semimajor axis, and it would decrease the absolute magnitudes of the two components. This scenario was considered in Section 4.1, where we found no significant difference in the goodness of fit when comparing fits where the parallax was constrained based on the Gaia DR2 measurement to those where it was allowed to float freely. Nevertheless, the large uncertainty on the parallax measurement suggests that this is a plausible explanation for the observed discrepancy.

The astrometric parameters of the CD-27 system reported in Gaia DR2 are derived from a five-parameter astrometric fit (position, proper motion, parallax) based on 111 measurements taken over the course of almost 2 yr. All of the sources within Gaia DR2 were treated as single stars, assuming constant linear motion over the time span of the mission. Stars that deviate from linear motion for whatever reason will still be fit using the same five-parameter model, but the goodness of fit will suffer owing to the incorrect assumption of linear motion. For CD-27, Gaia DR2 reports a unit weight error of u = 4.8, well above the typical value of u = 1.4 for stars with G ∼ 10 (Gaia Collaboration et al. 2018). This poor goodness of fit is reflected in the unusually large uncertainties on the five fitted astrometric parameters. The goodness of fit is significantly worse in the subsequent Gaia Data Release 3 (DR3; Gaia Collaboration et al. 2021), as shown in Figure 8, and only a two-parameter solution was presented. The star was not listed in the nonsingle star supplement in DR3, suggesting that an astrometric binary solution was attempted but rejected.

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We consider two plausible causes for this apparent deviation from linear motion that could explain the poor goodness of fit in both Gaia DR2 and DR3 and that could have biased the parallax measurement reported in Gaia DR2. We first consider the effect of orbital motion of the two known components over the course of the Gaia observations. We use the orbit fit presented in Section 3 and the flux ratios in Table 5, under the assumption that ΔG ∼ Δz, to predict the motion of the photocenter as observed by Gaia from 2014 July 25 to 2016 May 23. We predict almost linear motion in the decl. direction with little change in R.A. This would manifest itself as a small change to the measured proper motion of the system rather than inducing significant nonlinear motion. It is unlikely that the orbital motion of the two resolved components could explain the poor goodness of fit in Gaia DR2.

Another source of nonlinear astrometric motion in long-period binary systems is the variability of one or both of the components. So-called variability-induced movers (VIMs; Wielen 1996) are systems in which the periodic variability of an unresolved binary causes the photocenter to move in a characteristic fashion. Several examples have been identified in the Hipparcos and Gaia DR3 catalogs. Using the measured ∼15% amplitude of the V-band variability of this system (Kiraga 2012), we estimate that the variability can shift the Gaia photocenter relative to the barycenter by as much as 10 mas between minima and maxima if the variability is confined to one component. Given that this is comparable to the amplitude of the parallax signal, it is likely that significant variability could significantly bias the parallax measurements. Unfortunately, without access to the individual Gaia measurements, it is not possible to attempt to fit the parallax while simultaneously modeling this effect. CD-27 is not flagged as a VIM in Gaia DR3, and it is not possible to ascertain whether such a solution was attempted.

Our spectroscopic measurements can be used to place a lower limit on the orbital period of an additional companion within the system. A low-mass companion on a very short orbital period would induce a significant change of the RV of the star it orbits, so long as the orbit is not face-on. We search for the effects of a third component within the ARCES spectra by cross-correlating each with the spectrum of HIP 41277, a K8 star with a comparable $v\sin i$ to CD-27. We use eight orders of the ARCES spectrum covering ∼5500−6700 Å, each with several lines and high S/N. The resulting cross-correlation function has a single peak for each epoch, and we do not measure a significant variation of the RV. To explore the effects of relative RV and rotational broadening on the cross-correlation function, we generate a synthetic binary spectrum with varying RV offsets and rotational velocities that we cross-correlate with the spectrum of HIP 41277. We generate the simulated binary by combining two copies of a spectrum of a K5 star we observed as an RV standard (HIP 48331; Soubiran et al. 2013). Each spectrum is rotationally broadened and scaled based on the predicted optical flux ratio for the two stars. We sum and normalize the blended spectrum, which is then cross-correlated with HIP 41277. This process is repeated for a grid of RV offsets (six between 0 and 40 km s⁻¹) and $v\sin i$ (four between 5 and 20 km s⁻¹). The resulting cross-correlation functions are shown in Figure 12. At small delta RV (≲25 km s⁻¹) and $v\sin i$ (≲5 km s⁻¹), the cross-correlation function has a single peak. When lines are broadened by rotation ($v\sin i\gtrsim 20$ km s⁻¹), a larger delta RV (≳40 km s⁻¹) is required to resolve them. We identify the delta RV at which we detect two visually distinct peaks in the cross-correlation function, indicating a detectable separation between the primary and secondary absorption lines. Typical $v\sin i$ for K-type stars in the β Pic moving group are 10−13 km s⁻¹ (Zuckerman et al. 2001). For $v\sin i=10$ km s⁻¹, the smallest delta RV at which we see two distinct peaks is ∼25 km s⁻¹. For $v\sin i=13$ km s⁻¹, the smallest delta RV at which we see two distinct peaks is ∼30 km s⁻¹. The predicted delta RV from our orbit fit for A and B alone is ∼5 km s⁻¹. Thus, there can be an additional delta RV ≳25 km s⁻¹ caused by the orbit of a companion around either component that would remain undetectable in our ARCES spectra. This upper limit on the RV, assuming zero eccentricity, a 90° inclination angle, and the masses given in row 2 of Table 3, corresponds to a semimajor axis larger than 0.04 au (orbital period >0.01 yr).

As there is no obvious Keplerian signal in the residuals of the orbit fit to our astrometric measurements (Figure 5, second and fourth panels), we can place an upper limit on the semimajor axis of an inner binary. We make the conservative assumption that an orbit with a photocenter semiamplitude of 2 mas in the near-infrared would have easily been detected. Using the predicted masses and fluxes of the three components given for the AaAb-B configuration in Table 3, we convert this maximum photocenter semimajor axis into an upper limit on the total semimajor axis of the inner subsystem. We compute the reduced mass $B={M}_{2}/\left({M}_{1}+{M}_{2}\right)$ and reduced flux $\beta ={F}_{2}/\left({F}_{1}+{F}_{2}\right)$, from which we can calculate the total semimajor axis as a = a_p /(B − β). We find a conservative upper limit for the semimajor axis of the inner binary of ∼1.6 au (orbital period <2.0 yr). The allowed phase space for the semimajor axis of an inner binary is shown in Figure 9.

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