THE STELLAR-ACTIVITY–ROTATION RELATIONSHIP AND THE EVOLUTION OF STELLAR DYNAMOS

By N. Wright, J. Drake, Eric Mamajek, G. Henry. 2011

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We present a sample of 824 solar and late-type stars with X-ray luminosities and rotation periods. This is used to study the relationship between rotation and stellar activity and derive a new estimate of the convective turnover time. From an unbiased subset of this sample the power-law slope of the unsaturated regime, LX/Lbol∝Roβ, is fit as β = −2.70 ± 0.13. This is inconsistent with the canonical β = −2 slope to a confidence of 5σ, and argues for an additional term in the dynamo number equation. From a simple scaling analysis this implies ΔΩ/Ω∝Ω0.7, i.e., the differential rotation of solar-type stars gradually declines as they spin down. Supersaturation is observed for the fastest rotators in our sample and its parametric dependencies are explored. Significant correlations are found with both the corotation radius and the excess polar updraft, the latter theory providing a stronger dependence and being supported by other observations. We estimate mass-dependent empirical thresholds for saturation and supersaturation and map out three regimes of coronal emission. Late F-type stars are shown never to pass through the saturated regime, passing straight from supersaturated to unsaturated X-ray emission. The theoretical threshold for coronal stripping is shown to be significantly different from the empirical saturation threshold (Ro < 0.13), suggesting it is not responsible. Instead we suggest that a different dynamo configuration is at work in stars with saturated coronal emission. This is supported by a correlation between the empirical saturation threshold and the time when stars transition between convective and interface sequences in rotational spin-down models.

Subfields: Astronomy and Astrophysics

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Citations in the corpus

• The Extreme Ultraviolet and X-Ray Sun in Time: High-Energy Evolutionary Tracks of a Solar-Like Star (2015, background): “Magnetic activity is strongly coupled to rotation via a stellar dynamo, such that the total X-ray luminosity decays with increasing rotation period,P, asLX ∝ P−3 to ∝ P−2; for small P, LX saturates atLX ≈ 10−3Lbol (Lbol being the stellar bolometric luminosity; see Wright et al. 2011=W11).”
• The stellar rotation–activity relationship in fully convective M dwarfs (2018, methodology): “3 shows the standard rotation–activity diagram with the fractional X-ray luminosity, LX/Lbol, plotted against the Rossby number, Ro = Prot/τ , for all the fully convective stars in our sample, both new targets and those presented by Wright et al. (2011).”
• The coronal X-ray - age relation and its implications for the evaporation of exoplanets (2011, methodology): “We also point the reader towards the complementary study of the activity-rotation relation by Wright et al. (2011) that waspublished while this work was in the refereeing process.”
• Origin and evolution of the atmospheres of early Venus, Earth and Mars (2018, background): “This suggests that the internal dynamo strongly relates to the surface rotation period (e.g., Pallavicini et al. 1981, Walter 1981, Maggio et al. 1987, Güdel et al. 1997, Ayres 1997, Wright et al. 2011).”
• THE Hα EMISSION OF NEARBY M DWARFS AND ITS RELATION TO STELLAR ROTATION (2016, methodology): “This has been demonstrated using coronal (x-ray) emission (e.g. Pallavicini et al. 1981; Vilhu 1984; Pizzolato et al. 2003; Wright et al. 2011), chromospheric (Hα and Ca II) emission (e.g. Wilson 1966; Noyes et al. 1984; Soderblom et al. 1993), and radio emission from accelerated electrons (e.g.…”
• Stellar magnetism: empirical trends with age and rotation (2014, methodology): “0.1 (e.g., James et al. 2000; Pizzolato et al. 2003; Wright et al. 2011).”
• MAGNETIC WREATHS AND CYCLES IN CONVECTIVE DYNAMOS (2012, background): “…between rotation and magnetic activity, as inferred from proxies such as X-ray and chromospheric emission (Saar & Brandenburg 1999; Pizzolato et al. 2003; Wright et al. 2011), however superimposed on this trend is considerable variation in the presence and period of magnetic activity cycles.”
• A BCool magnetic snapshot survey of solar-type stars (2013, neutral): “Ser., 358, 362 Eddy J. A., 1976, Science, 192, 1189 Fares R., Donati J.-F., Moutou C., et al., 2012, MNRAS, 423, 1006 Fernandes J., Lebreton Y., Baglin A., Morel P., 1998, A&A, 338, 455 Fossati L., Kochukhov O., Jenkins J. S., Stancliffe R. J., Haswell C. A., Elmasli A., Nickson E., 2013, A&A, 551, ”
• MAGNETIC BRAKING FORMULATION FOR SUN-LIKE STARS: DEPENDENCE ON DIPOLE FIELD STRENGTH AND ROTATION RATE (2012, background): “…2010; Mamajek & Hillenbrand 2008; Meibom et al. 2011; Epstein & Pinsonneault 2012); and the correlation of stellar activity with rotation, as well as the “saturation” of this activity in fast rotators (e.g., Saar & Brandenburg 1999; Pizzolato et al. 2003; Reiners et al. 2009; Wright et al. 2011).”
• THE KEPLER CATALOG OF STELLAR FLARES (2016, methodology): “X-ray luminosity for lowmass stars saturates at rotation periods of a few days (Pizzolato et al. 2003; Wright et al. 2011).”
• THE MASS-DEPENDENCE OF ANGULAR MOMENTUM EVOLUTION IN SUN-LIKE STARS (2014, background): “Observations of various indicators of magnetic activity (Noyes et al. 1984a; Reiners et al. 2009; Pizzolato et al. 2003; Mamajek & Hillenbrand 2008; Wright et al. 2011; Vidotto et al. 2014), as well as theoretical models for magnetic field generation (Durney & Latour 1978; Noyes et al. 1984b;…”
• THE SOLAR NEIGHBORHOOD. XXXVII. THE MASS–LUMINOSITY RELATION FOR MAIN-SEQUENCE M DWARFS (2016, background): “Magnetic properties are generally explored via measurements of chromospheric ac- tivity (flaring, x-ray emission, spots) and are correlated with rapid rotation (Wright et al. 2011; Stelzer et al. 2013), attributes that are all typically seen in young M dwarfs.”
• Improved angular momentum evolution model for solar-like stars II. Exploring the mass dependence (2015, neutral): “96 (Wright et al. 2011; Oglethorpe & Garaud 2013).”
• Planetary evaporation by UV and X‐ray radiation: basic hydrodynamics (2012, background): “Furthermore, this high-energy radiation falls off with age (e.g. Jackson et al. 2012) in association with stellar spin-down (e.g. Hempelmann et al. 1995; Güdel 2004; Wright et al. 2011).”
• STELLAR DIAMETERS AND TEMPERATURES. II. MAIN-SEQUENCE K- AND M-STARS (2012, background): “…a more thorough literature search to gather a range of temperature estimates for these stars to make this comparison (the additional references include Eggenberger et al. 2008 and Luck & Heiter 2005 for GJ 702B, and Morales et al. 2008, Demory et al. 2009, and Wright et al. 2011 for GJ 551).”
• Stellar winds on the main-sequence - II. The evolution of rotation and winds (2015, methodology): “18? from Wright et al. (2011) gives FX ∝ t−1.23, which combined with Eqn.”