Astroseismology of a  -Cephei star Nick Cowan April 2006 Nick Cowan April 2006

Motivation: Blowing up Stars O & B stars die in spectacular explosions known as Type II SN. Try as they may, theoreticians are unable to properly model these explosions. Astroseismology allows us to map out the interior of such stars and understand how they die.

 -Cephei Stars Late O to early B variable stars at the end of their MS life. Periods of a few hours. Mostly have radial modes, though some have more complex vibrations.

Fe-Peak  -Mechanism The opacity of stellar gas typically decreases as the temperature increases. The trend reverses at temperatures where H or He ionize, and the later is thought to cause the oscillations in classical Cepheids and RR- Lyrae. In the case of  -Cephei stars, the ionization of Fe-peak elements (Sc through Cu) results in an opacity reversal for T > 10 5 K. The opacity of stellar gas typically decreases as the temperature increases. The trend reverses at temperatures where H or He ionize, and the later is thought to cause the oscillations in classical Cepheids and RR- Lyrae. In the case of  -Cephei stars, the ionization of Fe-peak elements (Sc through Cu) results in an opacity reversal for T > 10 5 K.

More on the  -Mechanism If energy is being transported radiatively at one of these reversal layers, the star may be unstable to pulsations. If a layer is compressed, its temperature increases and so does its opacity. This leads to an increase in the restoring radiative pressure and an overshoot in the decompression. The resulting pulsations have periods which scale roughly with the star’s density: P  (G  ) -1/2 If energy is being transported radiatively at one of these reversal layers, the star may be unstable to pulsations. If a layer is compressed, its temperature increases and so does its opacity. This leads to an increase in the restoring radiative pressure and an overshoot in the decompression. The resulting pulsations have periods which scale roughly with the star’s density: P  (G  ) -1/2

Pulsation Modes

HD B0.5 III B = 8.33, V = 8.53 log T eff = 4.47 log g = 3.9 Vsini = 200 km/s M = 14 M sun Parallax is inconclusive (0.5-3 kpc) 6.02 cd -1 frequency (4 hr period) based on HIPPARCOS photometry.

Critical Rotation If a star spins sufficiently rapidly, material at its equator is simply in orbit around the star. Even below the critical velocity, serious deformation of the star may occur. HD rotates at about 40% v crit.

Periodogram of HD

Aliases & Prewhitening Aliases –If the frequency of variations are integer or half- integer multiples of the frequency of your observations, you may not be observing the true frequency, but merely its alias. –HIPPARCOS was capable of continuous observations and so was impervious to aliasing. Prewhitening –Removes any previously known correlations from data. –Essentially subtract the frequencies you know so that you may better see other frequencies. Aliases –If the frequency of variations are integer or half- integer multiples of the frequency of your observations, you may not be observing the true frequency, but merely its alias. –HIPPARCOS was capable of continuous observations and so was impervious to aliasing. Prewhitening –Removes any previously known correlations from data. –Essentially subtract the frequencies you know so that you may better see other frequencies.

Phase Diagrams for HD

Theoretical Codes Code Liegeois d’Evolution Stellaire (CLES) –Modeled the MS evolutionary track for B stars with a variety of masses MAD –Modeled the non-adiabatic oscillations –Did not take into account rotation, even though second-order rotational effects shift the frequency of pulsations. Code Liegeois d’Evolution Stellaire (CLES) –Modeled the MS evolutionary track for B stars with a variety of masses MAD –Modeled the non-adiabatic oscillations –Did not take into account rotation, even though second-order rotational effects shift the frequency of pulsations.

Amplitude Ratios of HD

Frequency Spectra of HD

Summary HD exhibits at least two non-radial pulsation modes. The primary mode has a frequency of 6 cd -1 and is unambiguously identified as a dipole oscillation. It is responsible for the ~0.5 mag variations of the star in the visible. At least one weaker mode is present but the nature of the oscillation could not be determined from the data. What this means about the star’s interior is completely beyond me! HD exhibits at least two non-radial pulsation modes. The primary mode has a frequency of 6 cd -1 and is unambiguously identified as a dipole oscillation. It is responsible for the ~0.5 mag variations of the star in the visible. At least one weaker mode is present but the nature of the oscillation could not be determined from the data. What this means about the star’s interior is completely beyond me!