Non-confirmation of the Astrometric Binary Candidate HD 113283 Using FEROS Radial Velocities

Among the products of Gaia DR3 (Gaia Collaboration et al. 2016, 2022) are 169,227 non-single stars with solutions by the astrometric pipeline presented in Halbwachs et al. (2022) and by the refined "exoplanet pipeline" (Holl et al. 2022a). The latter is run on "stochastic" sources labeled as "OrbitalAlternative*" and on 19,845 preselected stars labeled as "OrbitalTargetedSearch*" within the nss_two_body_orbit table.

The 533 stars with solutions in the "OrbitalTargetedSearch*" sample include the nearby and bright (ϖ = 40.476 ± 0.015 mas, G = 6.9540 ± 0.0028 mag, Gaia Collaboration et al. 2022) G5 dwarf HD 113283 (=HIP 64690 = GJ 11909 = Gaia DR3 5765846127180770432). The astrometric two-body solution has period P = 20.025 ± 0.013 days, eccentricity e = 0.737 ± 0.097, and significance ${a}_{0}/{\sigma }_{{a}_{0}}=4.705$ (Holl et al. 2022a).

Using nsstools ⁴ (Halbwachs et al. 2022) we converted the Thiele-Innes coefficients to Campbell elements (a₀ = 0.84 ± 0.18 mas, i = 548 ± 43, ω = 771 ± 65, Ω = 1680 ± 65). Using

$$\begin{eqnarray}&&{f}_{{ \mathcal M }}=\displaystyle \frac{{({m}_{2}\,\sin \,i)}^{3}}{{({m}_{1}+{m}_{2})}^{2}}=\displaystyle \frac{{(2\pi )}^{2}{({a}_{1}\,\sin \,i)}^{3}}{{\mathrm{GP}}^{2}}\end{eqnarray} \tag{ 1 }$$

we derive the mass function ${f}_{{ \mathcal M }}=0.0016\,{M}_{\odot }$ assuming equality between the semimajor axes of photocenter and host star, a₀ = a₁. The host mass m₁ = 0.9 M_⊙ (Mortier et al. 2013) yields a companion mass m₂ > 0.15 M_⊙, which is a lower limit due to the stellar companion's non-negligible luminous contribution. Therefore, radial velocity (RV) variations with semi-amplitude K₁ > 13.5 km s⁻¹ are expected.

To confirm the astrometric candidate fifteen spectra were taken using FEROS (Kaufer et al. 1999) mounted on the MPG/ESO 2.2 m telescope in La Silla. The spectra were extracted using CERES ⁵ (Brahm et al. 2017) and reduced using both CERES and SERVAL (Zechmeister et al. 2018). ⁶ Both results, with the respective means subtracted (${\overline{\mathrm{RV}}}_{\mathrm{CERES}}=-4.789\pm 0.002\,\mathrm{km}\,{{\rm{s}}}^{-1}$), are presented in Figure 1 (top) along with the GLS periodograms (middle) (Zechmeister & Kürster 2009). The CERES and SERVAL results have standard deviations of 7.2 m s⁻¹ and 7.4 m s⁻¹ respectively and no significant periodicity. Therefore, the RV data indicate that the Gaia two-body solution is spurious.

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The solution's significance ${a}_{0}/{\sigma }_{{a}_{0}}=4.705$ is on the lower end of the distribution of the "OrbitalTargetedSearch*" sample (Holl et al. 2022a) and would be discarded for the "OrbitalAlternative*" sample and in the standard astrometric pipeline (Halbwachs et al. 2022), which uses a selection criterion ${a}_{0}/{\sigma }_{{a}_{0}}\gt 158/\sqrt{P\,[\mathrm{day}]}$ (≈35.3 for HD 113283). More stringent selection criteria would result in a cleaner "OrbitalTargetedSearch*" final sample.

Furthermore, we calculated the semimajor axis of the apparent orbit ${\tilde{a}}_{0}\approx 498\,\mu \mathrm{as}$ following Appourchaux et al. (2015). Comparing this to the one-body Gaia solution (astrometric_excess_noise = 122.86 μas), it is apparent that the astrometric signature of the two-body solution is much larger than expected. After the two-body solution by Holl et al. (2022a) is subtracted, an excess noise (astrometric_jitter in the nss_two_body_orbit table) of 113.24 μas remains, a reduction of merely 9.62 μas, which further indicates a discrepancy between the one- and two-body solutions. By comparison, the validated sources in Holl et al. (2022a) show much larger reductions of the excess noise.

Holl et al. (2022b) show that spurious solutions caused by Gaia's scan angle and scanning law cluster at periods following 365.25/P[days] = m5.8 + n, where m and n are the number of cycles per precession period (∼63.0 days) and per year, respectively. Figure 1 (bottom) shows a GLS periodogram of the star's observation times according to the Gaia DR3 nominal scanning law calculated using the scanninglaw package (Green 2018). ⁷ A significant peak at P = 19.73 days close to the 20.025 days period is apparent, which is likely linked to an overdensity of spurious solutions at P = 19.9 days (m = 3, n = 1). This finding casts serious doubts on the nature of the Gaia solution. One can also identify a strong peak at 31.46 days which coincides with the second harmonic of the precession period (m = 2, n = 0). Holl et al. (2022b) propose that most spurious solutions are caused by optical pairs with fixed orientation and separation <05 (background stars or long-period binaries). Archival images reveal no background objects in the immediate vicinity of HD 113283. RV variations at a long orbital period remain possible when including three archival spectra, however, no significant proper motion anomaly based on Hipparcos and Gaia EDR3 astrometry was detected (Kervella et al. 2022).

In any case, HD 113283 advocates for a more stringent filtering of the Gaia two-body solutions.

D.S. and S.R. acknowledge support by DFG priority program SPP 1992 (RE 2694/7-1). TT acknowledges support by DFG Research Unit FOR 2544 (KU 3625/2-1). This work was supported by the International Max Planck Research School for Astronomy and Cosmic Physics at the University of Heidelberg. This work has made use of data from the ESA mission Gaia, processed by the Gaia Data Processing and Analysis Consortium. This research has made use of VizieR and SIMBAD, operated at CDS. We acknowledge the use of MPIA DDT at FEROS and thank the observers. Based on ESO programs 092.A–9002(A), 095.A–9029(C), and 0109.A–9032(A).

Facility: Max Planck:2.2m(FEROS). -