_This is the author’s version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science on Vol. 350 no. 6259 pp. 423-426 , DOI: 10.1126/science.aac6933_ Internal stellar magnetic fields are inaccessible to direct observations and little is known about their amplitude, geometry and evolution. We demonstrate that strong magnetic fields in the cores of red giant stars can be identified with asteroseismology. The fields can manifest themselves via depressed dipole stellar oscillation modes, which arises from a magnetic greenhouse effect that scatters and traps oscillation mode energy within the core of the star. The _Kepler_ satellite has observed a few dozen red giants with depressed dipole modes which we interpret as stars with strongly magnetized cores. We find field strengths larger than $\sim\! 10^5 \,{\rm G}$ may produce the observed depression, and in one case we infer a minimum core field strength of $\approx \! \! 10^7 \,{\rm G}$.

Recent asteroseismic analyses have revealed the presence of strong (B≳10⁵ G) magnetic fields in the cores of many red giant stars. Here, we examine the implications of these results for the evolution of stellar magnetic fields, and we make predictions for future observations. Those stars with suppressed dipole modes indicative of strong core fields should exhibit moderate but detectable quadrupole mode suppression. The long magnetic diffusion times within stellar cores ensure that dynamo-generated fields are confined to mass coordinates within the main sequence convective core, and the sharp increase in dipole mode suppression rates above 1.5 M⊙ may be explained by the larger convective core masses and faster rotation of these more massive stars. In clump stars, core fields of $\sim 10^5 \, {\rm G}$ can suppress dipole modes, whose visibility should be equal to or less than the visibility of suppressed modes in ascending red giants. High dipole mode suppression rates in low-mass (M ≲ 2 M⊙) clump stars would indicate that magnetic fields generated during the main sequence can withstand subsequent convective phases and survive into the compact remnant phase. Finally, we discuss implications for observed magnetic fields in white dwarfs and neutron stars, as well as the effects of magnetic fields in various types of pulsating stars.

_This is the author’s version of the work. It is posted here for personal use, not for redistribution. The definitive version was published in Nature on 04 January 2016, DOI:10.1038/nature16171_ Magnetic fields play a role in almost all stages of stellar evolution . Most low-mass stars, including the Sun, show surface fields that are generated by dynamo processes in their convective envelopes . Intermediate-mass stars do not have deep convective envelopes , although 10% exhibit strong surface fields that are presumed to be residuals from the stellar formation process . These stars do have convective cores that might produce internal magnetic fields , and these might even survive into later stages of stellar evolution, but information has been limited by our inability to measure the fields below the stellar surface . Here we use asteroseismology to study the occurrence of strong magnetic fields in the cores of low- and intermediate-mass stars. We have measured the strength of dipolar oscillation modes, which can be suppressed by a strong magnetic field in the core , in over 3,600 red giant stars observed by . About 20% of our sample show mode suppression but this fraction is a strong function of mass. Strong core fields only occur in red giants above 1.1 solar masses (1.1), and the occurrence rate is at least 60% for intermediate-mass stars (1.6–2.0), indicating that powerful dynamos were very common in the convective cores of these stars.

The core rotation rates of massive stars have a substantial impact on the nature of core collapse supernovae and their compact remnants. We demonstrate that internal gravity waves (IGW), excited via envelope convection during a red supergiant phase or during vigorous late time burning phases, can have a significant impact on the rotation rate of the pre-SN core. In typical (10 M⊙ ≲ M ≲ 20 M⊙) supernova progenitors, IGW may substantially spin down the core, leading to iron core rotation periods $P_{\rm min,Fe} \gtrsim 50 \, {\rm s}$. Angular momentum (AM) conservation during the supernova would entail minimum NS rotation periods of $P_{\rm min,NS} \gtrsim 3 \, {\rm ms}$. In most cases, the combined effects of magnetic torques and IGW AM transport likely lead to substantially longer rotation periods. However, the stochastic influx of AM delivered by IGW during shell burning phases inevitably spin up a slowly rotating stellar core, leading to a maximum possible core rotation period. We estimate maximum iron core rotation periods of $P_{\rm max,Fe} \lesssim 10^4 \, {\rm s}$ in typical core collapse supernova progenitors, and a corresponding spin period of $P_{\rm max, NS} \lesssim 400 \, {\rm ms}$ for newborn neutron stars. This is comparable to the typical birth spin periods of most radio pulsars. Stochastic spin-up via IGW during shell O/Si burning may thus determine the initial rotation rate of most neutron stars. For a given progenitor, this theory predicts a Maxwellian distribution in pre-collapse core rotation frequency that is uncorrelated with the spin of the overlying envelope.

MLT These notes are mostly inspired from reading Cox & Giuli (“Principles of stellar structure”); some insights are from A.Maeder (“Physics, formation and evolution of rotating stars”) and Kippenhahn & Weigert (“Stellar Structure and Evolution”) Pressure Scale Height In hydrostatic equilibrium we can define the total pressure scale height, $\hp$, as -{\D r} \equiv {\hp} = {\p} where $\p$ is the total pressure ($ + $). The pressure scale height is a measure of the distance over which the pressure changes by an appreciable fraction of itself.

Asteroseismology of 1.0 − 2.0M⊙ red giants by the _Kepler_ satellite has enabled the first definitive measurements of interior rotation in both first ascent red giant branch (RGB) stars and those on the Helium burning clump. The inferred rotation rates are 10 − 30 days for the ≈0.2M⊙ He degenerate cores on the RGB and 30 − 100 days for the He burning core in a clump star. Using the MESA code we calculate state-of-the-art stellar evolution models of low mass rotating stars from the zero-age main sequence to the cooling white dwarf (WD) stage. We include transport of angular momentum due to rotationally induced instabilities and circulations, as well as magnetic fields in radiative zones (generated by the Tayler-Spruit dynamo). We find that all models fail to predict core rotation as slow as observed on the RGB and during core He burning, implying that an unmodeled angular momentum transport process must be operating on the early RGB of low mass stars. Later evolution of the star from the He burning clump to the cooling WD phase appears to be at nearly constant core angular momentum. We also incorporate the adiabatic pulsation code, ADIPLS, to explicitly highlight this shortfall when applied to a specific _Kepler_ asteroseismic target, KIC8366239.

Thermohaline mixing has recently been proposed to occur in low-mass red giants, with large consequence for the chemical yields of low-mass stars. We investigate the role of thermohaline mixing during the evolution of stars between 1$\mso$ and 3$\mso$, in comparison with other mixing processes acting in these stars. We use a stellar evolution code which includes rotational mixing, internal magnetic fields and thermohaline mixing. We confirm that during the red giant stage, thermohaline mixing has the potential to decrease the abundance of ³He, which is produced earlier on the main sequence. In our models we find that this process is working on the RGB only in stars with initial mass $ \le 1.5\mso$. Moreover we report that thermohaline mixing is also present during core He-burning and beyond, and has the potential to change the surface abundances of AGB stars. While we find rotational and magnetic mixing to be negligible compared to the thermohaline mixing in the relevant layers, the interaction of thermohaline motions with the differential rotation may be essential to establish the timescale of thermohaline mixing in red giants. To explain the surface abundances observed at the bump in the luminosity function, the speed of the mixing process needs to be more than two orders of magnitude higher than in our models. However it is not clear if thermohaline mixing is the only physical process responsible for these surface-abundance anomalies. Therefore it is not possible at this stage to calibrate the efficiency of thermohaline mixing against the observations.

We study the convection zones in the outer envelope of hot massive stars which are caused by opacity peaks associated with iron and helium ionization. We determine the occurrence and properties of these convection zones as function of the stellar parameters. We then confront our results with observations of OB stars. A stellar evolution code is used to compute a grid of massive star models at different metallicities. In these models, the mixing length theory is used to characterize the envelope convection zones. We find the iron convection zone (FeCZ) to be more prominent for lower surface gravity, higher luminosity and higher initial metallicity. It is absent for luminosities below about $10^{3.2}\lso$, $10^{3.9}\lso$, and $10^{4.2}\lso$ for the Galaxy, LMC and SMC, respectively. We map the strength of the FeCZ on the Hertzsprung-Russell diagram for three metallicities, and compare this with the occurrence of observational phenomena in O stars: microturbulence, non-radial pulsations, wind clumping, and line profile variability. The confirmation of all three trends for the FeCZ as function of stellar parameters by empirical microturbulent velocities argues for a physical connection between sub-photospheric convective motions and small scale stochastic velocities in the photosphere of O- and B-type stars. We further suggest that clumping in the inner parts of the winds of OB stars could be caused by the same mechanism, and that magnetic fields produced in the FeCZ could appear at the surface of OB stars as diagnosed by discrete absorption components in ultraviolet absorption lines.