The Kinematic and Chemical Properties of the Close-in Planet Host Star 8 UMi

In this study, the astrometric parameters and the broadband photometry of 8 UMi are retrieved from Gaia DR3 ¹² (Gaia Collaboration et al. 2023). The derived distance of 8 UMi is 163.7 ± 0.4 pc, measured from the Gaia parallax with the zero-point corrected (Lindegren et al. 2021; Huang et al. 2021a). To correct for the reddening, the value of extinction E(B − V) = 0.02 is taken from the reddening map of Schlegel et al. (1998), with systematics corrected. The extinction coefficients of the three Gaia bands are taken from Table 1 of Huang et al. (2021b). The intrinsic color and absolute magnitude of 8 UMi are thus ${({B}_{{\rm{P}}}-{R}_{{\rm{P}}})}_{0}=1.13\pm 0.03$ and M_G = 0.45 ± 0.05, respectively. The uncertainties are from the photometric errors and the reddening correction by assuming a constant error of 0.02 in E(B − V).

Analysis of a high-resolution spectrum is required to accurately infer the elemental-abundance ratios of 8 UMi. We searched for observation records in public spectral data archives, and retrieved the high-resolution spectrum of 8 UMi from the SOPHIE archive. This spectrum was obtained with the 1.93 m telescope at Haute Provence Observatory equipped with the SOPHIE échelle spectrograph. The downloaded spectrum is processed through the standard data reduction pipeline of SOPHIE. First, a two-dimensional spectrum (E2DS) is obtained after optimal order extraction, cosmic-ray extraction, wavelength calibration, and spectral flat-field correction to the raw data. Second, the pipeline merges the 39 spectral orders after correction of the blaze function, yielding a one-dimensional spectrum (S1D; Bouchy et al. 2009). The observation mode employed for 8 UMi was the high-resolution mode (HR mode), with a spectral resolution of R ∼ 75,000, covering the wavelength range from 3872 to 6943 Å. The signal-to-noise ratio (S/N) of this spectrum is generally above 100 (peak S/N ∼350 at around 6300 Å), except at the very blue edge (≤4050 Å), which is excluded in the following analysis.

For the downloaded spectrum, we use the cross-correlation function method to calculate its line-of-sight velocity v_los = −9.58 ± 0.03 km s⁻¹. The spectrum is corrected to the rest frame using the derived v_los, and then is normalized locally by division with a pseudo-continuum defined manually. To derive atmospheric parameters (i.e., effective temperature T_eff, surface gravity log g, and metallicity [Fe/H]) of 8 UMi, we employ the equivalent width (EW) method with the MOOG radiative transfer code (Sneden et al. 2012). The MARCS atmospheric model (Gustafsson et al. 2008), the line list compiled from Chen et al. (2000) and Sitnova et al. (2015), and the solar abundance of Grevesse et al. (2007) are adopted. All of these processing steps are combined in the integrated software package iSpec (Blanco-Cuaresma 2019). The EWs of the atomic iron lines are measured, based on the compiled line list mentioned above. Specifically, a Gaussian function is adopted to fit unblended single atomic absorption lines. Ultimately, the EWs of 30 Fe i lines and 7 Fe ii well separated and weak to mild-strength lines (20–100 mÅ) are measured in this way.

The measured EWs, using T_eff = 4847 K, [Fe/H] = −0.03, and v_mic = 1.30 km s⁻¹ from Hon et al. (2023) as an initial guess, are employed to derive the atmospheric parameters of 8 UMi using the nonlinear least-squares fitting algorithm installed in iSpec, which considers both excitation equilibrium and ionization balances. For surface gravity, we have two estimates: one, log g = 2.57, is from the asteroseismologic scaling relation (Kallinger et al. 2018) with maximum power ${\nu }_{\max }$ measured by Hon et al. (2023) from TESS, with a correction for a ∼4% systematic offset found in Stello et al. (2022); another, log g = 2.63, is from isochrone fitting based on the Bayesian technique (see Section 3.1 for details). A mean value of log g = 2.60 is the input value in iSpec for log g; it changes slightly with the changes of T_eff and [Fe/H] during the iteration. Finally, the atmospheric parameters are found to be T_eff = 4897 ± 100 K, log g = 2.60 ± 0.07, [Fe/H] = −0.05 ± 0.07, and v_mic = 1.48 ± 0.10 km s⁻¹. Figure 1 shows the [Fe/H] estimates as a function of reduced EWs and excitation potential. The slopes between [Fe ii and i/H] and reduced EW/excitation potential are both flat. ¹³ The difference between [Fe i/H] and [Fe ii/H] is smaller than 0.01 dex. In general, the derived atmospheric parameters are consistent with those from Hon et al. (2023), as well as those estimated in the original discovery paper (Lee et al. 2015).

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Based on the estimated atmospheric parameters, the chemical abundances for a total of 23 elements are measured using the software packages SIU (Reetz 1991) and TAME (Kang & Lee 2012) by the spectrum-synthesis method with the assumption of LTE. A differential analysis is adopted when deriving abundances. The original atomic parameters are from different sources for different elements. The atomic parameters for the CH molecular lines are taken from Masseron et al. (2014). The line list is generated using LINEMAKE (Placco et al. 2021) around 4215 Å for deriving the abundance of N. For other elements, the atomic parameters are drawn from several studies including Neves et al. (2009), Zhao et al. (2016), and Sitnova et al. (2022). We refine the $\mathrm{log}{gf}$ values of each atomic line to make sure they well reproduce atomic absorption-line profiles in the solar spectrum of Kurucz et al. (1984). The refined $\mathrm{log}{gf}$ values, excitation potentials, EWs observed in the solar spectrum, EWs measured in 8 UMi, and the corresponding abundances calculated for 8 UMi of individual lines are presented in Table A1. Synthetic line-fitting examples for CH, CN, Mg, and Y in 8 UMi are shown in Figure 1. For the solar spectrum, the synthetic line-fitting results are presented in Figure A1.

To derive the mass and age of 8 UMi, we adopt a conventional Bayesian method, similar to that developed in Huang et al. (2022), by matching the observed stellar parameters with theoretical isochrones. The theoretical isochrones are taken from PARSEC (Bressan et al. 2012), with [M/H] from −0.12 to +0.02 in steps of 0.01 dex, and age from 0.5 to 4.5 Gyr in steps of 0.05 Gyr. The full grids include over 540,000 individual models. The input observable constraints are intrinsic color ${({B}_{{\rm{P}}}-{R}_{{\rm{P}}})}_{0}$ and absolute magnitude M_G (see Section 2.1). As an example, Figure 2 compares 8 UMi to model isochrones in the M_G –${({G}_{\mathrm{BP}}-{G}_{\mathrm{RP}})}_{0}$ diagram (left panel), and presents the posterior probability distribution function (PDF) of age yielded by the Bayesian estimate (right panel). Based on the PDF, the age of 8 UMi is found to be $\tau ={1.9}_{-0.3}^{+1.2}$ Gyr. The upper and lower uncertainties correspond to the 16% and 84% percentiles of the resulting PDF. This suggests 8 UMi is a young star, if it has evolved as a single star.

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The isochrone fitting yields a mass of ${1.70}_{-0.25}^{+0.15}\,{M}_{\odot }$ for 8 UMi. This is consistent with the stellar mass derived in a similar way by the original planet discovery paper (Lee et al. 2015), but larger by 13% than the asteroseismic measurement (1.51 ± 0.05 M_⊙) of Hon et al. (2023). We do not attempt to resolve this discrepancy here, but note that the asteroseismic measurements on 8 UMi by two different studies, Hon et al. (2023) and Hatt et al. (2023), are inconsistent with each other in the oscillation frequency at the maximum power, ${\nu }_{\max }$, which is the key parameter that determines the stellar mass. These two studies both used TESS data, although they differ in the number of sectors (8 versus 12). According to Hatt et al. (2023), the oscillation frequency at the maximum power, ${\nu }_{\max }$, is determined to be 50.8 ± 2.4 μHz, which would suggest a host mass of about 2 M_⊙.

The value of the host star mass may be the key to resolve the puzzle of 8 UMi b. A higher host mass means that the planetary orbit is slightly wider at a given orbital period. In the mass range 1.5–2.0 M_⊙, a higher mass also produces a smaller stellar size at the tip of red giant branch. The latter is best illustrated in the panel (b) of Figure 3 in Hon et al. (2023) for the case of the 8 UMi system. As a consequence, the impact of the tidal effect also sensitively depends on the host star mass, and a slightly higher mass can reduce the chance of planet engulfment during the red giant branch (RGB) and helium-flash phases, as theoretical studies have shown (e.g., Kunitomo et al. 2011).

The Gaia DR3 astrometric information and distance estimate (see Section 2.1), as well as the radial velocity measured from the SOPHIE spectrum (see Section 2.2), are adopted to derive space velocities with the galpy python package (Bovy 2015). For this calculation, the solar motions are set to be (U_⊙, V_⊙, W_⊙) = (−7.01, 10.13, 4.95) km s⁻¹ (Huang et al. 2015), and the circular speed at the solar position set to be V_c (R₀) = 234.04 km s⁻¹ from Zhou et al. (2023). For the solar positions, we adopt a value of R₀ = 8.178 kpc (GRAVITY Collaboration et al. 2019) for the Galactocentric distance, and a value of Z₀ = 25 pc (Bland-Hawthorn & Gerhard 2016) for the vertical offset. The resulting space velocity components of 8 UMi are (U, V, W) = (−10.28 ± 0.20, 10.92 ± 0.12, −7.61 ±0.09) km s⁻¹ in a Cartesian coordinate system centered on the Sun and (V_R , V_ϕ , V_Z ) = (−10.28 ± 0.20, 244.96 ± 0.19, −7.61 ± 0.09) km s⁻¹ in Galactocentric cylindrical coordinates. The three-dimensional positions of 8 UMi are R = 8.228 ± 0.035 kpc, ϕ = 0809 ± 0004, and Z = 129.7 ± 0.5 pc. Errors in the space velocities and positions are calculated by 20,000 Monte Carlo simulations by sampling the measurement errors (assuming Gaussian distributions). Figure 3(a) shows the location of 8 UMi in the Toomre diagram. For comparison, the background shows the distribution of field red clump giant stars (sample taken from Huang et al. 2020) color coded by median age. In Huang et al. (2020), the ages of these red clump stars are estimated from LAMOST spectra, using machine-learning techniques, with the ages calibrated using asteroseismic masses from Kepler. The typical age uncertainty is 20%. In this figure, we also show density contours of the thin-disk population selected from the field red clump sample with the criteria from Chen et al. (2021). 8 UMi falls on the typical position of members of the thin-disk population with young median ages.

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To provide a quantitative estimate of the kinematic age for 8 UMi, red clump stars with 3D space velocities similar to 8 UMi (i.e., V between 5 and 15 km s⁻¹ and $\sqrt{{U}^{2}+{W}^{2}}$ between 5 and 20 km s⁻¹) are selected. The right panel of Figure 3 shows the age distribution of those selected red clump stars. This leads to an kinematic age estimate ${\tau }_{\mathrm{kinematic}}={3.5}_{-2.0}^{+3.0}$ Gyr for 8 UMi.

Table 1 presents the chemical-abundance pattern for 8 UMi determined using the methods described in Section 2.2. The errors of the derived abundances are also provided in Table 1. The values of σ represent the statistical uncertainties in measurements, while the δ[X/Fe] represents the systematic error estimated from changes of abundances by individually varying T_eff, log g, [Fe/H], and v_mic according to the 1σ parameter uncertainties. Overall, the chemical results indicate that 8 UMi, with [Fe/H] = −0.05 ± 0.07 and [α/Fe] = + 0.01 ± 0.03, is a typical thin-disk star. In addition, four intriguing features are also seen in the chemical-abundance pattern of 8 UMi. First, the lithium abundance is significantly enhanced, with A(Li) ≈ 1.94, which is consistent with previous measurements of A(Li) = 2.0 ± 0.2 from Kumar et al. (2011) and Charbonnel et al. (2020). Possible origins of this enhanced Li abundance are discussed in the next section. Second, the carbon abundance is relatively low for such a solar-metallicity star. It may be attributed to extra mixing through the CNO cycle (aka the first dredge-up process) during the RGB phase (e.g., Boothroyd & Sackmann 1999). Third, [Zn/Fe] = −0.29 is slightly lower than the solar value. Note that Sitnova et al. (2022) reported a median [Zn/Fe] ≈ −0.10, with a lower boundary extending as low as −0.30, for thin-disk stars with solar metallicity. This suggests that subsolar zinc abundances are quite common for solar-metallicity stars. Finally, the s-process elements (Ba, La, Nd) exhibit slightly higher abundances, with an average value of [X/Fe] ≈ +0.20 to +0.30. This supersolar abundance is additional evidence for the genuinely young age for 8 UMi, since the fraction of s-process elements increases with time in the Universe (Spina et al. 2018).

As mentioned above, the [C/N] ratio at the stellar surface is potentially influenced by the CNO cycle during the first dredge-up, which is correlated with the stellar mass. Thus, [C/N] is a good age indicator for giants because of the mass–age relation in stellar evolution. The left panel of Figure 4 shows the [C/N]-age distribution, using red clump stars again from Huang et al. (2020). The [Fe/H] range of this sample is from −1.0 to +0.5. Their [C/H] and [N/H] are derived from LAMOST low-resolution spectra by adopting a machine-learning method using the LAMOST-APOGEE stars in common as a training sample. The typical precision of the derived [C/H] and [N/H] is about 0.1 dex. We determine ${\tau }_{[{\rm{C}}/{\rm{N}}]}={3.3}_{-1.5}^{+2.5}$ Gyr for 8 UMi based on the age distribution of red clump stars with [C/N] ranging from −0.67 to −0.23, the 1σ interval on [C/N] measured for 8 UMi (see Table 1). The systematic error of [C/N] measurement is about 0.15 dex; its effect on age estimate is around 1.5 Gyr.

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Over the last decade, the ratios between s-process and α-elements have been found to be chemical clocks for solar-metallicity stars. Among all the ratios, the [Y/Mg]–age relation is tight and applicable for both dwarf and giant stars (e.g., Nissen et al. 2020; Casamiquela et al. 2021). By fitting a linear relation ¹⁴ for age–[Y/Mg] based on a nearby sample ¹⁵ from Nissen et al. (2020), the age inferred from [Y/Mg] for 8 UMi is τ_[Y/Mg] = 3.5 ± 2.0 Gyr. The uncertainty is given by the 1σ uncertainty of the linear relation and the measurement error of [Y/Mg]. The systematic error, resulting from varying stellar atmospheric parameters and v_mic (see Table 1), amounts to 0.09 dex, corresponding to an uncertainty of 2.5 Gyr in age. Moreover, we investigate the NLTE effects on Mg and Y. In the model atmosphere of 4897/2.60/−0.05, the NLTE calculations were conducted for Mg i and Y ii using the model atoms detailed in Alexeeva et al. (2018, 2023). The NLTE abundance corrections, represented as Δ_NLTE = log _NLTE − log _LTE, for the Mg I lines at 5528 and 5711 Å are 0.00 and +0.03 dex, respectively. Similarly, for the Y ii lines at 5289 and 5402 Å, the corrections are +0.01 and 0.00 dex, respectively. Thus, the systematic error induced by NLTE effects (−0.01 dex) is negligible comparing to the one caused by errors in the stellar atmospheric parameters and v_mic.

In summary, the ages of 8 UMi derived from the two chemical clocks agree very well with each other. The chemical ages are also consistent with that derived from the kinematic estimate in Section 3.2.

According to Hon et al. (2023), an old age ¹⁶ is required for the binary-merger formation channel of 8 UMi. However, the above kinematic and chemical results show that the true age of this system is 3.25–3.50 Gyr, with a 1σ statistical uncertainty of 1.50–3.00 Gyr. This is consistent with the isochrone-fitting age of ${1.9}_{-0.3}^{+1.2}$ Gyr derived under the single-star assumption.

Another argument that was used in Hon et al. (2023) to support the binary-merger scenario is that such a formation channel can explain the Li enhancement of 8 UMi. Previous studies have shown that most recognized Li-rich giants are found among the red clump stars (e.g., Yan et al. 2021). To explain this Li enhancement in red clump stars, one possible scenario is the merger of a HeWD and an RGB that triggers a convection shell to synthesize Li, leading to Li-rich red clump stars (Zhang et al. 2020). However, other competing models that do not invoke binary mergers can also produce Li-rich red clump stars, such as planet engulfment (Aguilera-Gómez et al. 2016) and the lithium enhancement in the tip of the RGB process or in the helium flash (Silva Aguirre et al. 2014). Given that there is another giant planet with a relatively wide orbit in 8 UMi, the chance is high that one or several small planets may have existed on inner orbits (Zhu & Dong 2021), and the ingestion of such close-in planets would be sufficient to explain the observed Li abundance (e.g., Aguilera-Gómez et al. 2016).

In summary, the binary-merger formation channel of 8 UMi proposed by Hon et al. (2023) is not supported by our kinematic and chemical analysis of 8 UMi. Alternative models are required to explain the existence of the close-in planet Halla orbiting 8 UMi.