Evidence of a Substellar Companion to AB Dor C

Stellar evolution models are essential to infer star fundamental parameters such as radius, mass, and/or age. Their reliability has long been tested and validated by the general good agreement between predictions and measurements. However, only recently have accurate measurements of stellar masses and radii become accessible in the case of low- and very low-mass stars, thus allowing more stringent tests on stellar models. In the particular case of pre-main-sequence (PMS) stars, the models show an increasing difficulty in accurately reproducing some of the characteristics of a star with masses below 1.2 M_⊙ (see, e.g., Hillenbrand & White 2004; Gennaro et al. 2012; Stassun et al. 2014).

Only stellar systems with dynamically determined masses can effectively be used to test and check the predictions of the models (see recent works of Dupuy & Liu 2017 and Mann et al. 2019). AB Doradus (AB Dor) represents one such case. It is a PMS quadruple system formed by two pairs of stars separated by $9^{\prime\prime}$, AB Dor A/C and AB Dor Ba/Bb (Close et al. 2005; Guirado et al. 2006), giving name to the AB Doradus moving group (AB Dor-MG). The main star of this system, the K0 dwarf AB Dor A (K_s = 4.686) has been extensively studied at all wavelengths, from the UV to radio (Gómez de Castro 2002; Guirado et al. 1997). Precise Hipparcos and very long baseline interferometry (VLBI) observations provided an accurate distance measurement (d = 15.06 ± 0.07 pc) and revealed the presence of AB Dor C, a low-mass companion with 0.090 M_⊙, orbiting AB Dor A at an average angular distance of 02 (Guirado et al. 1997). The pair AB Dor A/C has also been observed by different near-infrared instruments at the Very Large Telescope (VLT; Close et al. 2005, 2007; Boccaletti et al. 2008), allowing independent photometry of AB Dor C (K_s = 9.5), which, along with the dynamical mass determination, served as a benchmark for young, low-mass stellar evolutionary models (Azulay et al. 2017 and references therein).

Previous comparisons of observed magnitudes with theoretical mass–luminosity relationships suggested that the models tend to underpredict the mass of AB Dor C or, equivalently, overpredict the flux of the object, especially at the J and H bands (Close et al. 2005). This disagreement was also noted in studies of the other pair of the system, AB Dor Ba/Bb (Wolter et al. 2014; Janson et al. 2018). The authors argued that theoretical models tend to be consistent in the case of young moving groups but not in older associations such as the AB Dor moving group. This tendency was reinforced by the study of other members of this moving group, such as GJ 2060 AB (Rodet et al. 2018) or LSPM J1314+1320 AB (Dupuy et al. 2016). In the case of AB Dor C, most of the difficulty in validating the model predictions comes from the uncertainty in age and the possible binary nature of the object. Regarding the latter, Marois et al. (2005) pointed out that if AB Dor C were a binary brown dwarf, the overluminosity shown by the models, including the permanent disagreement in the J and H filters, could easily be corrected assuming reasonable mass ratios. Indeed, the determination of the possible binary nature of AB Dor C is an important issue for an object acting as calibrator of young, low-mass objects that needs to be addressed.

In this Letter we present interferometric evidence of the presence of a low-mass companion to AB Dor C from VLT Interferometer (VLTI) observations performed with the Astronomical Multi-BEam combineR (AMBER) focal instrument (Petrov et al. 2007), installed at the ESO facilities in Cerro Paranal, Chile. Attempts to observe this object with the GRAVITY instrument are also reported. We describe the observations and data reduction in Section 2. The analysis is presented in Section 3 and the comparison with stellar models and discussion are presented in Section 4. Finally, in Section 5 we present our conclusions.

The observations of AB Dor C were performed with the VLTI using the AMBER instrument with the external fringe tracker Fringe-Tracking Instrument of NIce and TOrino (FINITO) in low-resolution mode at the J, H, and K bands (programme 090.C-0559(A)). However, due to a technical problem, the J band did not perform well and was not used in our analysis. The H band was tested but finally also discarded in the analysis, as discussed below. The observations were performed on 2012 December 28 from 02:40 to 04:40 UT using the 8.2 m unit telescopes (UT) with the configuration UT1-UT2-UT4. Due to the faint magnitude of AB Dor C (K_s = 9.5), we used a nonstandard observing configuration that consisted of using AB Dor A as a fringe tracker to increase the integration time on AB Dor C. To achieve this, first we set AMBER in low-resolution mode with a DIT of 0.1 s; second, we found and locked the fringes of AB Dor A in the fringe tracker FINITO; and third, we offset AMBER (through tip/tilt correction) to find the fringes of AB Dor C. This "off-axis" fringe tracking allowed an exposure time on AB Dor C longer than that imposed by the atmospheric piston. Fringes were seen in every single frame (see Figure 1), which could be properly averaged to obtain the visibility data. The procedure above benefited from (i) a precise knowledge of the orbit of AB Dor C (Guirado et al. 2006), which allowed us to predict with milliarcsecond precision the relative position AB Dor A/C; (ii) an optimum observing epoch, 2012 December, with AB Dor C near apoastron (042 separated from A; see Figure 2), thus minimizing the possible contamination from the brighter star AB Dor A; and (iii) good atmospheric conditions with a seeing of ∼07. The star HD 35199 (disk-equivalent diameter of 0.86 mas; Mérand et al. 2006) was also observed to calibrate the AB Dor C visibilities. The logs of these observations are shown in Table 1.

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Table 1.  Observation Log of AB Dor C and Calibrators

Obs. Time	Target	Triplet	Mode	Seeing
2012 Dec 28 02:40	HD 35199	U1-U2-U4	Low JHK	079
2012 Dec 28 03:17	AB Dor C	U1-U2-U4	Low JHK	063
2012 Dec 28 03:43	AB Dor C	U1-U2-U4	Low JHK	072
2012 Dec 28 04:17	AB Dor C	U1-U2-U4	Low JHK	074
2012 Dec 28 04:40	AB Dor A	U1-U2-U4	Low JHK	074

Note. Due to the nonstandard observing configuration (see the text), HD 35199 could only be observed at the beginning of the observation.

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In addition to the AMBER data, 4 hr of VLTI/GRAVITY time were allocated (program 0102.C-0297, with the telescopes UT1-UT2-UT3-UT4) and scheduled on 2017 December 9 to confirm our findings. However, the proximity of the much brighter AB Dor A (located at 02 from C) during the observing epoch prevented AB Dor C to be properly identified in the GRAVITY acquisition camera, therefore making the observation technically unfeasible.

We obtained the raw visibility data using the software package amdlib v.3.0.8⁷ (Tatulli et al. 2007; Chelli et al. 2009). We selected and averaged the resulting visibilities of each frame using different criteria for the baseline flux and for the fringe signal-to-noise ratio (S/N; for more information see the AMBER Data Reduction Software User Manual⁸ ). In particular, (i) we selected frames having a baseline flux with an S/N larger than 1, 2, 3, 4, 5, 6, 7, 10, 15, and 20; (ii) for each of these selections, we kept 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 100% of the remaining frames with the highest fringe S/N, which effectively created a grid of 10 × 10 reduced data sets with different selection criteria; (iii) we made extensive tests to determine the robustness and consistency of each one of the data sets above (basically, we compared each data set to simulated visibilities of different source geometries, discarding those data sets producing unacceptable fits); and (iv) based on the previous tests, we selected the data set containing 5% of the frames with highest fringe S/N chosen from those with a baseline flux S/N larger than 6. The calibration of the transfer function was made using the calibrator star HD 35199.

The values of the squared visibilities panel (Figure 3, left) are far from corresponding to those of a pointlike source; rather, they indicate either the presence of an extended structure around AB Dor C, and/or the binary nature of the object. Actually, the sinusoidal behavior seen in the visibilities is a typical signature of a binary system (e.g., Millour et al. 2009). Supporting the previous statement, the closure phase (Figure 3, right) displays a nonnegligible departure from the null value, indicating that the contrast between binary components should be relatively high (Monnier 2003). The fact that the visibilities do not decrease with baseline suggests, in principle, that the components are not resolved.

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We performed an exhaustive and systematic search for companions to AB Dor C using the software CANDID⁹ (Gallenne et al. 2015). CANDID performs a least-squares fit of both the companion position and flux ratio at each starting position of a 2D grid using the interferometric observables, the squared visibilities, and the closure phases. We first used CANDID with only K-band data, revealing a companion to AB Dor C at a level of 24σ with separation and flux ratio detailed in Table 2, where the number of sigmas indicates how significant the binary model is compared to a single star and is computed using formula (8) in Gallenne et al. (2015). In agreement with this, the calculation of the corresponding χ² for both the single and binary scenarios yields a clear preference for the presence of a companion: ${\chi }_{\mathrm{single}}^{2}$=14.07 and ${\chi }_{\mathrm{binary}}^{2}=2.60$.

On the other hand, the quality of the fit is degraded (from 24σ to 16σ) when using both the K and H bands, adding, at least, another spurious solution. Moreover, no detection is found with CANDID when using only the H band. Given the results above, we conservatively restricted our interferometric data set to K band only.

To assess the validity of the CANDID results, we also fitted the observed visibilities with the Lyon Interferometric Tool prototype (LITpro), developed by the Jean-Marie Mariotti Center (JMMC; Tallon-Bosc et al. 2008). We used a simple two-point model to simulate the suspected binary nature of AB Dor C. In contrast to the CANDID procedure, LITpro does not perform a systematic search of the parameters; therefore, aiming at identifying the best model, we initialized the fitting program with different sets of values for the free parameters, namely: flux ratio, binary separation, and position angle. In practice, we explore the following parameter space around the CANDID position: flux ratio between 2% and 8% in steps of 0.5%, separation between 25 and 50 mas in steps of 0.5 mas, and P.A. between 140° and 220° in steps of 05. We selected as plausible fits the range of χ² values that correspond to a 95% confidence interval. The results of this parameter search are given in Table 2, and coincide, within uncertainties, with the position found with the CANDID software and the K band, strengthening the validity of our binary hypothesis for AB Dor C. Given the plausibility of the results obtained with this binary model (and, admittedly, to avoid a possible overinterpretation of the data), we did not explore more complicated geometries with LITpro (i.e., binary with disks or envelopes).

From the analysis above, we conclude that AB Dor C is a binary system with components separated by 38 ± 1 mas, and a flux ratio at the K band of 5% ± 1%, where the uncertainties have been conservatively enlarged to cover the results of both software.

The interferometric results presented allow us to characterize the components of the tentative binary in AB Dor C (AB Dor Ca/Cb). The combination of the flux ratio (Cb/Ca), 5% ± 1%, with the total (Ca+Cb) K_s absolute magnitude of 8.38 ± 0.16 (Boccaletti et al. 2008) implies a binary with magnitudes K_s = 8.43 ± 0.16 and K_s = 11.7 ± 0.3 for Ca and Cb, respectively.

4.1. Comparison with Evolutionary Models

With the individual magnitudes of the components, an estimate of the individual masses can be obtained by using PMS evolutionary models. We computed the models using the Pisa stellar evolutionary code (Tognelli et al. 2018) for masses in the range 0.01–0.4 M_⊙ and solar metallicity ([Fe/H] = 0). We also used an interpolation of the DUSTY models (Chabrier et al. 2000) and BHAC15 models (Baraffe et al. 2015) to infer the dependence of the derived parameters on the adopted evolutionary tracks. The boundary between DUSTY and BHAC15 models was based on mass, with each model covering the ranges of 0.001–0.1 M_⊙ for the former and 0.01–1.4 M_⊙ for the latter.

Following the procedure described in Section 4.2 of Liu et al. (2008), we used these evolutionary models and our inferred magnitudes of Ca and Cb to estimate the mass of each one of the components; the sum of these masses is the the total mass of the system, which is represented against the age in Figure 4. The shadowed gray area indicates the possible combinations of masses for Ca and Cb accomplishing that the total mass of the system lies within the measured dynamical mass of 0.090 ± 0.008 M_⊙ for AB Dor C (Azulay et al. 2017). This implies masses of 0.072 ± 0.013 M_⊙ and 0.013 ± 0.001 M_⊙ for each one of the components of the binary, which interestingly lie near the hydrogen-burning limit for the case of AB Dor Ca, and near the deuterium-burning limit, straddling the boundary between brown dwarfs and giant planets, for the case of AB Dor Cb. Given the relatively large mass ratio between AB Dor Ca/Cb, we notice that the tentative binarity of AB Dor C would not result in a substantial change in the age range when compared with previous estimates based on the same evolutionary models (Azulay et al. 2017). Likewise, the presence of AB Dor Cb does not affect the age determinations based on model isochrones fitting to the members of the AB Dor moving group (Bell et al. 2015).

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4.2. Binary Hypothesis and Photometry

How is the interpretation of published AB Dor C photometry affected by our binary hypothesis? In Figure 5 we represent the cooling curves of AB Dor Ca/Cb (models by Tognelli et al. 2018) compared with published AB Dor C photometric measurements (Close et al. 2005, 2007; Luhman & Potter 2006; Boccaletti et al. 2008) for the two scenarios considered: (1) the (old) single-object scenario (with AB Dor C as a single object of 0.090 M_⊙) and (2) the (new) binary scenario resulting from our detection (with AB Dor C as a binary with estimated masses of 0.072 M_⊙ and 0.013 M_⊙, according to the parameters given in Table 2). Published magnitudes at the J, H, and K bands are shown for the two most-considered age ranges in the literature: 75 ± 25 Myr (Janson et al. 2007; Boccaletti et al. 2008) and 120 ± 20 Myr (Luhman et al. 2005; Ortega et al. 2007), the latter being favored by the recent works of Bell et al. (2015) and Gagné et al. (2018).

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For the discussion that follows we use solely the fact that AB Dor C may be a binary system with masses 0.072 M_⊙ and 0.013 M_⊙ (as obtained in Section 4.1) and previously reported photometric measurements. As we can see in Figure 5, for an age of 75 Myr (left column plots), the binary hypothesis produced an overall better agreement considering all the three bands than the single-object hypothesis. In fact, the binary tracks are compatible (to within 1.2σ of the showed uncertainties), with all the photometric measurements, slightly favoring those reported by Close et al. (2007) and Luhman & Potter (2006). Turning to the age of 120 Myr (right column plots in Figure 5), we found that the binary track nicely reproduces the J-band measurements; however, the tracks for this older age range seems to underestimate some of the H- and K-band measurements (especially those from Boccaletti et al. 2008). The most relevant result of the comparisons above is that the small disagreements in the J and H bands reported by Luhman & Potter (2006) and Close et al. (2007) are partially alleviated (for an age of 75 Myr), or completely removed (for an age of 120 Myr), considering AB Dor C as a binary system.

We also estimated the bolometric luminosity (L_bol) using the photometric published measurements and the bolometric corrections found in Pecaut & Mamajek (2013) and Filippazzo et al. (2015). Both corrections produce very similar results and are consistent within the errors. Conservatively we adopt the bolometric correction value of 3.10 ± 0.13 from Filippazzo et al. (2015) for an M7 dwarf. Differences in bolometric luminosity or in magnitudes could highlight two scenarios. On one hand, a discrepancy in luminosity would suggest problems in the fundamental physics used to compute very low-mass stars models, in particular due to the adopted equation of state, outer boundary conditions, magnetic fields, and surface spots (Siess 2001; Chabrier et al. 2007; di Criscienzo et al. 2010; Feiden & Chaboyer 2013; Somers & Pinsonneault 2015; Tognelli et al. 2018). On the other hand, a difference visible only in magnitudes should point out the need for more accurate synthetic spectra, which, especially in the case of low- and very low-mass stars, still represents a challenging task. The top panels of Figure 5 show that the binary scenario produces a slightly better agreement with the estimated bolometric luminosities. This is especially notable at the younger age of 75 Myr. Although small, this effect may be pointing to a problem in the fundamental physics used in very low-mass stars models, as previously stated.

Regarding the spectral type of AB Dor C, and according to the binary scenario, the M5.5 ± 1 classification reported by Luhman & Potter (2006) should be assigned to the heavier component of the system, AB Dor Ca. To obtain an estimate of the spectral features of the weaker component Cb we used the color–magnitude calibration provided by Zapatero Osorio et al. (2014), in turn based on the least massive population, brown dwarfs, and giant planets, belonging to the Pleiades cluster (age 120 Myr). Following this calibration, and for a K_s magnitude of 11.7 ± 0.3 (Section 4), a spectral type of L4–6 could be expected for component AB Dor Cb.

4.3. Orbit and Stability of AB Dor Ca/Cb

We present interferometric evidence that AB Dor C is not a single pointlike star but most likely a binary system of very low-mass objects. Our results show that both squared visibilities and closure phases are in good agreement with a binary system of ∼38 mas separation between the components and a K-band flux ratio of ∼5%. This configuration implies masses for the tentative binary AB Dor Ca/Cb of 0.072 ± 0.013 M_⊙ and 0.013 ± 0.001 M_⊙, according to the PMS evolutionary models of Chabrier et al. (2000), Baraffe et al. (2015), and Tognelli et al. (2018). It is worth noting that, with these masses, one of the objects would lie near the hydrogen-burning limit (AB Dor Ca), while AB Dor Cb would lie at the frontier between brown dwarfs and planets. The binarity of AB Dor Ca/Cb may have gone unnoticed in previous observations given the three-magnitude difference between Ca and Cb and the great difficulty of discerning AB Dor C itself from the nearby, five-magnitude brighter AB Dor A. However, the binary hypothesis would alleviate the disagreement between observed magnitudes and theoretical mass–luminosity relationships. We considered the two most frequently used scenarios (75 ± 25 Myr and 120 ± 20 Myr) and found that especially at the J and H bands the binary hypothesis produces a better agreement than a single 0.090 M_⊙ object.

The perturbation caused by the more massive AB Dor A would destabilize a binary system of separation larger than 50 mas. With a separation of about 38 mas, the newly discovered binary AB Dor Ca/Cb appears stable under such perturbation. Yet, although our result defines a very plausible scenario for AB Dor C, it is based on a limited number of visibilities taken near the performance limit of AMBER and, therefore, further confirmation of our findings would be convenient. Advanced instrumentation (i.e., GRAVITY dual-field on-axis mode observations) will help to clarify the nature of this remarkable system.

Authors thank the anonymous referee for useful suggestions that improved the manuscript. J.B.C., J.C.G., and J.M.M. were partially supported by the Spanish MINECO projects AYA2012-38491-C02-01, AYA2015-63939-C2-2-P, PGC2018-098915-B-C22 and by the Generalitat Valenciana projects PROMETEO/2009/104 and PROMETEOII/2014/057. I.M.-V. is a fellow of the GenT program (Generalitat Valenciana) under the Project Grant CIDEGENT 2018/021.