Hideyuki Saio

Accreting supermassive stars of ≳10⁵ M_⊙ will eventually collapse directly to a black hole via the general-relativistic (GR) instability. Such direct collapses of supermassive stars are thought to be a possible formation channel for supermassive black holes at z > 6. In this work, we investigate the final mass of accreting Population III stars with constant accretion rates between 0.01 and 1000 M_⊙ yr⁻¹. We determined the final mass by solving the differential equation for GR linear adiabatic radial pulsations. We find that models with accretion rates ≳0.05 M_⊙ yr⁻¹ experience the GR instability at masses depending on the accretion rates. The critical masses are larger for higher accretion rates, ranging from 8 × 10⁴ M_⊙ for 0.05 M_⊙ yr⁻¹ to ∼10⁶ M_⊙ for 1000 M_⊙ yr⁻¹. The 0.05 M_⊙ yr⁻¹ model reaches the GR instability at the end of the core hydrogen burning. The higher-mass models with higher accretion rates reach the GR instability during the hydrogen burning stage.

Betelgeuse is a well known bright red supergiant that shows semi-regular variations with four approximate periods of 2200, 420, 230, and 185 days. While the longest period was customarily regarded as LSP (long secondary period) of unknown origin, we identify the ∼2200-d period as the radial fundamental mode, and the three shorter periods as the radial first, second, and third overtones. From a linear nonadiabatic pulsation analysis including the pulsation/convection coupling, we have found that these radial pulsation modes are all excited in the envelope of a model in a late stage of the core-carbon burning. Models with similar pulsation property have masses of 11 ∼ 12 M_⊙ (19 M_⊙ at ZAMS) with luminosities (log L/L_⊙ = 5.27 ∼ 5.28) and effective temperatures (log T_eff ≈ 3.53) that are consistent with the range of the observational determinations. We also find that a synthetic light curve obtained by adding the fundamental and the first-overtone mode is comparable with the light curve of Betelgeuse up to the Great Dimming. We conclude that Betelgeuse is likely in the late stage of core carbon burning, and a good candidate for the next Galactic Type II supernova.

Betelgeuse is a well known bright red supergiant that shows semi-regular variations with four approximate periods of 2200, 420, 230, and 185 days. While the longest period was customarily regarded as LSP (long secondary period) of unknown origin, we identify the ~2200-d period as the radial fundamental mode, and the three shorter periods as the radial first, second, and third overtones. From a linear nonadiabatic pulsation analysis including the pulsation/convection coupling, we have found that these radial pulsation modes are all excited in the envelope of a model in a late stage of the core-carbon burning. Models with similar pulsation property have masses of 11~12 M_\odot (19M_\odot at ZAMS) with luminosities (log L/L_\odot =5.27~5.28) and effective temperatures (log T_{eff}\approx 3.53) that are consistent with the range of the observational determinations. We also find that a synthetic light curve obtained by adding the fundamental and the first-overtone mode is comparable with the light curve of Betelgeuse up to the Great Dimming. We conclude that Betelgeuse is likely in the late stage of core carbon burning, and a good candidate for the next Galactic Type II supernova.

We propose a helium nova model for the Large Magellanic Cloud (LMC) supersoft X-ray source (SSS) [HP99]159. This object has long been detected as a faint and persistent SSS for about 30 yr, and recently been interpreted to be a source of steady helium-shell burning, because no hydrogen lines are observed. We find that the object can also be interpreted as in a decaying phase of a helium nova. The helium nova is slowly decaying toward the quiescent phase, during which the observed temperature, luminosity, and SSS lifetime (≳30 yr) are consistent with a massive white dwarf model of ∼1.2 M_⊙. If it is the case, this is the second discovery of a helium nova outburst after V445 Pup in our Galaxy, and also the first identified helium nova in the LMC. We also discuss the nature of the companion helium star in relation to Type Ia supernova progenitors.

R-mode oscillations in a rotating star produce characteristic signatures in a Fourier amplitude spectrum at frequencies related with the rotation frequency, which can be, in turn, used to obtain the surface rotation rate of the star. Some binary stars observed by Kepler indicate the presence of r modes that are probably excited by the tidal effect. In this paper, we have obtained stellar rotation periods in 20 eccentric (heartbeat) binaries with r-mode signatures. The majority of the rotation periods are found to be comparable to pseudo-synchronous periods, in which the angular velocity of rotation is similar to the angular orbital motion of the companion at periastron. In particular, for the heartbeat stars with orbital periods longer than about 8 d, all but one agree with pseudo-synchronous rotation. In contrast to a previous investigation by Zimmerman et al., our result supports the pseudo-synchronisation theory developed by Hut.

R-mode oscillations in a rotating star produce characteristic signatures in a Fourier amplitude spectrum at frequencies related with the rotation frequency, which can be, in turn, used to obtain the surface rotation rate of the star. Some binary stars observed by Kepler indicate the presence of r~modes that are probably excited by the tidal effect. In this paper, we have obtained stellar rotation periods in 20 eccentric (heartbeat) binaries with r-mode signatures. The majority of the rotation periods are found to be comparable to pseudo-synchronous periods, in which the angular velocity of rotation is similar to the angular orbital motion of the companion at periastron. In particular, for the heartbeat stars with orbital periods longer than about 8\,d, all but one agree with pseudo-synchronous rotation. In contrast to a previous investigation by Zimmerman et al., our result supports the pseudo-synchronisation theory developed by Hut.

The relation of period spacing (ΔP) versus period (P) of dipole prograde g modes is known to be useful to measure rotation rates in the g-mode cavity of rapidly rotating γ Dor and slowly pulsating B (SPB) stars. In a rapidly rotating star, an inertial mode in the convective core can resonantly couple with g-mode propagative in the surrounding radiative region. The resonant coupling causes a dip in the P – ΔP relation, distinct from the modulations due to the chemical composition gradient. Such a resonance dip in ΔP of prograde dipole g modes appears around a frequency corresponding to a spin parameter 2f_rot(cc)/ν_co-rot ∼8–11 with f_rot(cc) being the rotation frequency of the convective core and ν_co-rot the pulsation frequency in the co-rotating frame. The spin parameter at the resonance depends somewhat on the extent of core overshooting, central hydrogen abundance, and other stellar parameters. We can fit the period at the observed dip with the prediction from prograde dipole g modes of a main-sequence model, allowing the convective core to rotate differentially from the surrounding g-mode cavity. We have performed such fittings for 16 selected γ Dor stars having well-defined dips, and found that the majority of γ Dor stars we studied rotate nearly uniformly, while convective cores tend to rotate slightly faster than the g-mode cavity in less evolved stars.

We discuss low-frequency g modes excited by resonant couplings with weakly unstable oscillatory convective modes in the rotating convective core in early-type main-sequence stars. Our non-adiabatic pulsation analyses including the effect of Coriolis force for 2M(circle dot) main-sequence models show that if the convective core rotates slightly faster than the surrounding radiative layers, g modes in the radiative envelope are excited by a resonance coupling. The frequency of the excited g mode in the inertial frame is close to vertical bar m Omega(c)vertical bar with m and Omega(c) being the azimuthal order of the g mode and the rotation frequency of the convective core, respectively. These g-mode frequencies are consistent with those of photometric rotational modulations and harmonics observed in many early-type main-sequence stars. In other words, these g modes provide a non-magnetic explanation for the rotational light modulations detected in many early-type main-sequence stars.