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# Angular momentum transport within evolved low-mass stars

Abstract

Asteroseismology of $$1.0-2.0M_\odot$$ 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 $$\approx 0.2M_\odot$$ 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.

# Introduction

Stellar rotation and the resulting internal rotational profile, together with the mechanisms that contribute to angular momentum transport, remain poorly probed. Different classes of transport mechanisms have been proposed, in particular hydrodynamical instabilities and circulations induced by rotation (see Maeder et al., 2000, for a review), magnetic torques (Gough et al., 1998; Spruit, 1999; Spruit, 2002; Spada et al., 2010) and internal gravity waves (see e.g., Charbonnel et al., 2005). In the absence of strong mass loss, the bulk of the redistribution of angular momentum is expected to occur when shearing is generated during evolutionary episodes of expansion or contraction.

Most stars ignite hydrogen in a shell at the end of the main sequence. Above this shell the star begins to expand, while the core contracts. In the absence of a strong coupling between the core and the envelope, conservation of angular momentum requires that the core spins up while the envelope spins down. This implies very rapidly rotating stellar cores and a shear layer between core and envelope. Evolutionary calculations that include angular momentum transport from rotational instabilities and circulations also predict rapidly rotating stellar cores at the end of stellar evolution (e.g., Heger et al., 2000; Suijs et al., 2008; Eggenberger et al., 2012; Marques et al., 2013). This is at odds with the observed rotation rate of white dwarfs (WD) and neutron stars (NS). This can be somewhat remedied by including angular momentum transport due to magnetic torques in radiative regions (Tayler-Spruit dynamo (TS) Spruit, 2002; Heger et al., 2005; Suijs et al., 2008).

In the era of space asteroseismology, the Kepler satellite enabled the measurement of the core rotation in many red giant branch (RGB) stars using the splitting of mixed modes (Beck et al., 2012; Deheuvels et al., 2012; Mosser et al., 2012; Deheuvels et al., 2014). Mixed modes are oscillations that have an acoustic component (p-mode) in the envelope and are g-modes (restoring force is buoyancy) in the stellar core (see e.g., Beck et al., 2011). Mosser et al. (2012); Mosser et al. (2012)a showed that it is the rotation rate of the material below the active hydrogen burning shell that is most directly inferred from the splitting of mixed modes (see also Marques et al., 2013). This measurement of the interior rotational state of an evolved star provides a new test for theoretical ideas of angular momentum transport. Similar to the case of compact remnants, models solely including angular momentum transport due to rotational mixing and circulations predict rotation rates 2 to 3 orders of magnitude higher than observed (Eggenberger et al., 2012; Marques et al., 2013; Ceillier et al., 2013). While the adopted treatment of angular momentum transport is a crude approximation, Marques et al. (2013) have shown that even the most extreme of the physically motivated hydrodynamic mechanisms included in their code cannot yield the observed slow rotation.

Our goal is to assess whether models including transport due to TS magnetic fields agree more closely with the observations. While the physics of the Tayler instability is secure, the existence of the Tayler-Spruit dynamo loop is debated on both analytical and numerical grounds (Braithwaite, 2006; Zahn et al., 2007). However observations of the spin rates of compact objects (WDs and NSs) are in much better agreement with models including this angular momentum transport mechanism (Heger et al., 2005; Suijs et al., 2008), which has also been discussed in the context of the rigid rotation of the solar core (Eggenberger et al., 2005), but see also Denissenkov et al. (2010). In Sec. \ref{stev} we present the stellar evolution calculations and the details of the implemented physics. Results for the evolution of core rotation during the early RGB are shown in Sec. \ref{earlyrgb} for different angular momentum transport mechanisms. Results are compared to Kepler asteroseismic observations of mixed modes in RGB stars. In Sec. \ref{splittings} we show how the rotational splittings of mixed modes are calculated from the stellar evolution models using ADIPLS(Christensen-Dalsgaard, 2008). Sec. \ref{beyond} presents the angular momentum evolution of our models beyond the early RGB. Predictions for the core rotation rates past the luminosity bump (Sec. \ref{bump}), during core He-burning (Sec. \ref{clump}) and in the WD stage (Sec. \ref{wd}) are shown and compared to the asteroseismically derived values. In Sec. \ref{conclusions} we draw our conclusions and discuss possible future work.