Pulsational Velocity Variations of the Radial Mode sdBV Star BPM 36430

Hot subdwarf B (sdB) stars are the leftover He–fusing cores of red giants that were stripped of their outermost H layers due to interactions with a nearby companion. They are located on the extreme horizontal branch, have a canonical mass of 0.47 M_⊙ (Fontaine et al. 2012), and display effective temperatures ranging from T_eff = 20,000–40,000 K (Heber 2016). Hot subdwarfs are almost always found in binaries, and studying their period and mass distributions can shed light on the common envelope and Roche lobe overflow processes that produce them. Luckily, many sdBs pulsate with slow gravity-mode (g-mode) pulsations (sdBV_s stars), rapid pressure-mode (p-mode) pulsations (sdBV_r stars), or hybrid pulsations (sdBV_rs stars). Asteroseismology analysis of their pulsation properties can reveal numerous fundamental parameters like rotation rates, masses, and radii (Lynas-Gray 2021).

Using TESS photometry, Smith et al. (2022) recently discovered the sdB star BPM 36430 to be a hybrid sdBV_rs pulsator as it exhibits many small–amplitude g-mode pulsations and a single, high–amplitude p-mode pulsation. Through a careful pulse timing study of the p-mode, Smith et al. (2022) determined BPM 36430 is in a 3.12465 ± 0.00018 d binary with a white dwarf companion. Given the period (342 s) and large amplitude (∼2%) of the p-mode oscillation, it is likely an l = 0 radial mode with a significant velocity variation. If so, one could apply the Baade–Wesselink method and obtain precise mass and radius measurements of the sdB primary. Here, we present radial velocity measurements for BPM 36430 from time-series spectroscopy and demonstrate that the mode is consistent with a radial pulsation.

Using the Goodman spectrograph on the 4.1 m SOAR telescope in Chile, we took 549 consecutive spectra of BPM 36430 over a 6 hr period on 2023 June 9. We used a 1'' slit and the 930 mm⁻¹ grating to cover the spectral range 3600–5300 Å with a resolution of R ∼ 1400 at 4000 Å. Integration times were 30 s, less than 10% of the pulsation period. The position angle was set to 34135 East of North so that we could place a second, nearby star on the slit to track and correct for any drifts in the wavelength solution due to instrumental flexure. Comparison spectra of an FeAr lamp were obtained at the end of the time series for wavelength calibration.

In order to extract radial velocities from the BPM 36430 spectra, we fit slanted inverse Lorentzian functions (Equation (1)) to the H Balmer lines Hβ to H7 to determine their centroid values.

$$\begin{eqnarray}&&f(\lambda )=\displaystyle \frac{A}{\pi }\displaystyle \frac{\tfrac{{\rm{\Gamma }}}{2}}{{\left(\lambda -{\lambda }_{0}\right)}^{2}+{\left(\tfrac{{\rm{\Gamma }}}{2}\right)}^{2}}+m\lambda +b\end{eqnarray} \tag{ 1 }$$

We adopt as the final velocity for each spectrum, the weighted average of all of the individual H Balmer line measurements. The top panel of Figure 1 presents the resulting radial velocity curve. We then computed the discrete Fourier transform (DFT) of the RV curve using Period04 (Lenz & Breger 2014). The DFT shown in the bottom panel of Figure 1 reveals a strong peak at around 252 day⁻¹ with an amplitude just above 4 km s⁻¹. The period of this RV signal is in agreement with the photometric period of the p-mode pulsation reported by Smith et al. (2022). To determine the amplitude of the RV variation, we used SciPy's curve_fit routine to perform a nonlinear least–squares fit of a sinusoid to the RV curve. The period was fixed to the value previously found by Smith et al. (2022) during this process. We report a best–fitting semi–amplitude of 4.4 ± 0.4 km s⁻¹.

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Using time-series spectroscopy from SOAR/Goodman, we detect a clear radial velocity variation in the sdBV_rs star BPM 36430 at a period consistent with its strong p-mode pulsation at 342 s. The atmospheric parameters of BPM 36430 determined by Smith et al. (2022), the period & photometric amplitude of the 342 s mode, and the strength of the velocity variation are all consistent with other known sdBV radial mode pulsations (e.g., Baran et al. 2008; Barlow et al. 2010). Thus, we conclude that the 342 s pulsation is likely radial in nature. In the future, we plan to use additional follow–up photometry and spectroscopy to apply the Baade–Wesselink method to this mode and determine the mass and radius of BPM 36430.

B.K. would like to thank his parents for instilling curiosity and a strong work ethic in him and his grandparents for always believing in him. B.K., B.S., and B.B. acknowledge support from the National Science Foundation through grant AST #1812874.

Facility: SOAR (Goodman) - .

Software: Astropy (Astropy Collaboration et al. 2013, 2018), SciPy (Virtanen et al. 2020), Period04 (Lenz & Breger 2014).