Rotation period of the O giant xi Persei: Coexistence of cyclic and periodic variability. A weakly magnetic candidate star

The gist The low-velocity absorption part of the N iv λ1718 Å line of ξ Persei has been shown to contain a prominent sinusoidal signal with a period of 2.040514 ± 0.000020 d, which is identified as the stellar rotation period The most likely origin of the rotational modulation is the presence of a weak (presumably) dipolar magnetic field, which has nonetheless remained undetected thus far

How it works

The researchers searched for periodicity in spectral regions probing the region around the star very close to the surface, specifically focusing on low-velocity wind regions They identified the low-velocity wind region probed by the N iv λ1718 Å line as a most uncontaminated spectral region for which a large and homogeneous dataset is available from 307 IUE spectra over 12 years and 11 STIS spectra taken 21 years later They also studied time-resolved He ii λ4686 Å spectra Furthermore, they searched for periodicities in high-precision space photometry (MOST, BRITE, and TESS), covering a time span of 13 years

Period Analysis and Results

The CLEAN analysis and subsequent weighted least-squares fit of the flux in the N iv line region resulted in a unique period of 2.040514± 0.000020 d, attributed to rotation The phase of maximum flux in the N iv, Si iv, Hα, and He ii line profiles coincided with results from X-ray variability studies They also found this period with low amplitude in photometric data, albeit with large intrinsic scatter, and with a deviating maximum phase The analysis of the N iv flux using weighted least-squares fit of the IUE + 4w STIS data yielded a best period of 2.040514 d with a formal 1-σ uncertainty of 0.000020 d This result is in opposition to earlier conclusions favouring a rotation period of ∼4 d, which was based on the assumption of a much larger stellar radius than they adopted in this work

Interpretation and Physical Model

The coherent periodic behaviour of several observables probing the wind nearest the stellar surface suggests that ξ Per has an as-yet undetected weak global surface magnetic field The sinusoidal behaviour suggested that only one magnetic pole is visible, implying an inclination of i ∼ 51◦, and therefore β ≲ 90◦ −i = 39◦ for the magnetic obliquity They propose a conceptual framework where weak wind confinement by a global magnetic field can create a small magnetospheric disc, while allowing for the formation of more classic ‘corotating interaction regions’ at higher magnetic latitudes The periodic variations are then understood to result from the changing projected area of the magnetospheric disc as a function of rotational phase, both along the line of sight and off the stellar limb

Coexistence of Variability Drivers

The study distinguishes between two types of variability: a strict periodicity seen in N iv low-velocity flux variations and an apparently cyclic nature found in Si iv doublet DACs, especially at high velocities The strict periodicity is consistent with the presence of a stable, large-scale magnetic field on the surface of ξ Per The cyclic nature of the Si iv DACs is still considered consistent with the prevalent CIR model, proposing that spots driving these CIRs originate from moderate-to-high magnetic latitudes This leads to a toy model involving both a magnetospheric disc with a varying projected area and the aforementioned CIRs, all contributing to the variability seen across multiple observational diagnostics

Magnetic Field Constraints

Assuming the star hosts a magnetic dipole field, calculations based on adopted stellar parameters and an upper limit on polar field strength of 59 G yield a wind magnetic confinement parameter η∗ = 0.16 This value corresponds to a magnetic field strength of Beq ≈ 23 G, which is below the upper limit reported by David-Uraz et al. (2014) The results indicate that any large-scale magnetic field below this limit would only produce weak wind confinement

Conclusion

The paper concludes that the rotation period of 2.040514 ± 0.000020 d is the stellar rotation period, and it provides a stable clock for strictly periodic variations in the wind near the stellar surface The authors suggest that while stochastic low-frequency (SLF) variability may be present, the periodicity observed in N iv lines points to a stable, large-scale magnetic field Highly sensitive magnetic measurements in the future might eventually prove or disprove their conjecture that ξ Per hosts a magnetic field

Data Availability

Tables 2 and 3 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 26555 for HST The paper includes data collected with the TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI) The funding for the TESS mission is provided by the NASA Explorer Program Parts of Sect. 6 are based on data collected by the BRITE Constellation satellite mission, designed, built, launched, operated and supported by the Austrian Research Promotion Agency (FFG), the University of Vienna, the Technical University of Graz, the Canadian Space Agency (CSA), the University of Toronto Institute for Aerospace Studies (UTIAS), and the Foundation for Polish Science & Technology (FNiTP MNiSW), and the National Science Centre (NCN) The paper includes data collected with TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI) The funding for the TESS mission is provided by the NASA Explorer Program Parts of Sect. 6 are based on data collected by the BRITE Constellation satellite mission, designed, built, launched, operated and supported by the Austrian Research Promotion Agency (FFG), the University of Vienna, the Technical University of Graz, and the Canadian Space Agency (CSA), and the University of Toronto Institute for Aerospace Studies (UTIAS), and the Foundation for Polish Science & Technology (FNiTP MNiSW), and the National Science Centre (NCN) The paper includes data collected with TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI) The funding for the TESS mission is provided by the NASA Explorer Program Parts of Sect. 6 are based on data collected by BRITE Constellation satellite mission, designed, built, launched, operated and supported by the Austrian Research Promotion Agency (FFG), the University of Vienna, the Technical University of Graz, and the Canadian Space Agency (CSA), and the University of Toronto Institute for Aerospace Studies (UTIAS), and the Foundation for Polish Science & Technology (FNiTP MNiSW), and the National Science Centre (NCN) The paper includes data collected with TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI)

Acknowledgements

The authors are very grateful to the observers who contributed to this project, in particular to Douglas Gies at Kitt Peak and Regina Zwarthoed at Calar Alto during the 1989 campaign Special thanks go to Katie Gordon and Douglas Gies for providing the angular diameter of ξ Per, and to Tahina Ramiaramanantsoa for helpful discussions and comments regarding results of MOST and BRITE photometry They gratefully acknowledge insightful discussions with Lex Kaper, Henk Spruit, Asif ud-Doula, Alex de Koter, Zsolt Keszthelyi, Sarah Brands, and David Cohen They are also much indebted to Stan Owocki for helpful correspondence and reading a first version of the manuscript Jari van Opijnen kindly provided the corrected Gaia distance value They gratefully thank the late Derck Massa for his generous comments on the analysis of STIS spectra

References

(1) Sota et al. (2011) (2) Maíz-Apellániz et al. (2004) (3) Gaia DR3 Bailer-Jones et al. (2021) (4) Martins et al. (2017) (5) Markova et al.

1. Based on Section 4, an improved AI system can perform robust period analysis by implementing a weighted least-squares cosine fit with four free parameters: f(a, b, P, t0) = b + a cos (2π/P) (t − t0). This allows the system to systematically compare results across different datasets (IUE vs. IUE + STIS), as shown in Table 4.

2. The AI can be trained to critically assess the impact of data sampling irregularity on periodogram analysis, specifically by comparing the generalised Lomb-Scargle (GLS) periodogram results with a fine frequency grid versus a grid that includes the known period from CLEAN, as detailed in Fig. 6c.

3. The system can be engineered to differentiate between periodic and cyclic variability by analyzing the phase dependency of different spectral line regions; for instance, it can compare the strict periodicity seen in the N iv low-velocity flux variations with the apparently cyclic nature of the DACs found in the Si iv doublet, as discussed in Section 9.

4. The AI should be capable of calculating and interpreting wind confinement parameters like η∗ = B2eqR2/Ṁv∞, using adopted stellar parameters from Table 1 to determine the resulting Alfvén radius relative to the Keplerian corotation radius, as described in Section 8.3.

5. The system can integrate multi-wavelength data by comparing phase relationships between different diagnostics, such as correlating the phase corresponding to maximum Hα emission is typically referred to as the high state with the phases of N iv, Si iv, and He ii flux maxima in Fig. 17.

6. The AI can evaluate the physical implications of magnetic obliquity by using stellar parameters to predict inclination angles, concluding that for a radius of 11.2 R⊙, the inclination angle is expected to be 51◦ based on Fig. 12 and Section 5.