Colder and Hotter: Interferometric Imaging of Β Cassiopeiae and Α Leonis

Abstract

Near-infrared interferometers have recently imaged a number of rapidly rotating A-type stars, finding levels of gravity darkening inconsistent with theoretical expectations. Here, we present new imaging of both a cooler star β Cas (F2IV) and a hotter one α Leo (B7V) using the CHARA array and the MIRC instrument at the H band. Adopting a solid-body rotation model with a simple gravity darkening prescription, we modeled the stellar geometric properties and surface temperature distributions, confirming both stars are rapidly rotating and show gravity darkening anomalies. We estimate the masses and ages of these rapid rotators on L-R pol and HR diagrams constructed for non-rotating stars by tracking their non-rotating equivalents. The unexpected fast rotation of the evolved subgiant β Cas offers a unique test of the stellar core-envelope coupling, revealing quite efficient coupling over the past ∼ 0.5 Gyr. Lastly we summarize all our interferometric determinations of the gravity darkening coefficient for rapid rotators, finding none match the expectations from the widely used von Zeipel gravity darkening laws. Since the conditions of the von Zeipel law are known to be violated for rapidly rotating stars, we recommend using the empirically-derived β = 0.19 for such stars with radiation-dominated envelopes. Furthermore, we note that no paradigm exists for self-consistently modeling heavily gravity-darkened stars that show hot radiative poles with cool convective equators.

Interferometric observations of rapidly rotating stars

“…This lower value is consistent with trends toward a lower expected value for a star with lower surface temperature (see Fig. 9 of Che et al 2011, andClaret 2000), although it is not nearly as small as would be expected for a fully radiative photosphere (β = 0.08).…”

“…Also as with Altair, Regulus has now been imaged by CHARA-MIRC Che et al (2011) (Table 1), but further rich detail has been added from the imaging. In particular, a much tighter constraint on inclination is now available (i = 7 In addition to its close companion, Regulus has a wide companion α Leo B at a separation of ∼175 , also a binary.…”

“…Observationally, β Cas presents itself nearly pole-on, with i = 19.9 ± 1.9 • , indicating a significant rotation rate (v = 206 km s −1 , P = 1.12 +0.03 −0.04 days). As with Regulus, Che et al (2011) also fit for β, finding a value of 0.146 +0.013 −0.007 . This lower value is consistent with trends toward a lower expected value for a star with lower surface temperature (see Fig.…”

On the deviations of the classical von Zeipel’s theorem at the upper layers of rotating stars

“…By using interferometric techniques, some very rapid isolated rotating stars were also investigated, opening a new window on the stellar rotation (van Belle et al 2001(van Belle et al , 2006Domiciano de Souza et al 2003;Aufdenberg et al 2006;Peterson et al 2006;Monnier et al 2007;Zhao et al 2009). In Che et al (2011) the predicted theoretical transition zone between radiative/convective envelopes (Claret 1998) was confirmed by using rapid rotators, some of them near the breakup velocities.…”

“…3 in Claret 2003). However, some discrepancies are present too, as such Che et al (2011), who studied the hot star α Leo and found β 1 = 0.75, significantly lower than the value predicted by von Zeipel's theorem (β 1 = 1.0). On the other hand, the detected scattering of the semi-empirical values of β 1 around the theoretical values of double-lined eclipsing binaries also demand a theoretical explanation.…”