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  • The spin rate of pre-collapse stellar cores: wave driven angular momentum transport in massive 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 (\(10 \, M_\odot \lesssim M \lesssim 20 \, M_\odot\)) 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, stochastic influxes of AM delivered by IGW during shell burning phases also entail a maximum 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 ordinary pulsars. 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.



    Rotation is a key player in the drama that unfolds upon the death of a massive star. The angular momentum (AM) contained in the iron core and overlying layers determines the rotation rate at core collapse (CC), which could have a strong impact on the dynamics of CC and the subsequent supernova (See e.g MacFadyen et al., 1999; Woosley et al., 2002; Woosley et al., 2006; Yoon et al., 2006). Rotation may help determine the nature of the compact remnant, which could range from a slowly rotating neutron star (NS) to a millisecond magnetar or rapidly rotating black hole (See e.g. Heger et al., 2000; Heger et al., 2005). The former may evolve into an ordinary pulsar, while the latter two outcomes offer exciting prospects for the production of long gamma-ray bursts (GRB) and superluminous supernova. In each of these phenomena, rotating central engines are suspected to be the primary source of power (Woosley, 1993; Kasen et al., 2010; Metzger et al., 2011).

    Despite rotation being recognized as an important parameter controlling the evolution of massive stars (Maeder 2000), little is known about the rotation rates of the inner cores of massive stars nearing CC. The best observational constraints stem from measurements of the rotation rates of the compact remnants following CC. For instance, a few low-mass black hole X-ray binary systems have been measured to have large spins that can only be accounted for by high spins at birth (Axelsson et al., 2011; Miller et al., 2011; Wong et al., 2012). However, the rotation rates of young NSs show little evidence for rapid rotation (\(P \lesssim 10 \, {\rm ms}\)) at birth. The most rapidly rotating young pulsars include PSR J0537-6910 (\(P=16\,{\rm ms}\)) and the Crab pulsar (\(P=33\,{\rm ms}\)), whose birth periods have been estimated to be \(P_i \lesssim 10\,{\rm ms}\) (Marshall et al., 1998) and \(P_i \sim 19 \, {\rm ms}\) (Kaspi et al., 2002), respectively. Many young NSs appear to rotate much more slowly, with typical periods of hundreds of ms (Lai, 1996; Gotthelf et al., 2013; Dinçel et al., 2015). In general, pulsar observations seem to indicate a broad range of initial birth periods in the vicinity of tens to hundreds of milliseconds (Faucher-Giguère et al., 2006; Popov et al., 2010; Gullón et al., 2014). Hence, rapidly rotating young NSs appear to be the exception rather than the rule.

    Theoretical efforts have struggled to produce slow rotation rates. In the absence of strong AM transport mechanisms within the massive star progenitor, NSs would invariably be born rotating near break-up (Heger 2000). Heger et al. (2005) and Suijs et al. (2008) examined the effect of magnetic torques generated via the Tayler-Spruit (TS) dynamo (Spruit, 2002), and found typical NS spin periods at birth (assuming AM conservation during core-collapse and the ensuing supernova) of several milliseconds. Wheeler et al. (2014) implemented magnetic torques due to MRI and the TS dynamo, and were able to reach iron core rotation rates of \(P_{c} \sim 500 \, {\rm s}\), corresponding to NS spin periods of \(P \sim 25 \, {\rm ms}\). These efforts are promising, but the operation of both mechanisms within stars has been debated (e.g. Zahn et al., 2007), and theoretical uncertainties abound.

    Recent asteroseismic advances have allowed for the measurement of core rotation rates in low-mass red giant stars (Beck et al. 2012; Beck et al. 2014; Mosser et al. 2012; Deheuvels et al. 2012; Deheuvels et al. 2014). In these stars, the core rotates much faster than the surface and one cannot assume nearly rigid rotation as suggested in Spruit et al. (1998). However, the cores of low-mass red giants rotate much slower than can be explained via hydrodynamic AM transport mechanisms or magnetic torques via the TS dynamo (Cantiello et al., 2014). If similar angular momentum transport mechanisms operate in more massive objects, this suggests that the pre-collapse cores of massive stars may rotate slower than predicted by many previous theoretical investigations.

    Internal gravity waves (IGW) constitute a powerful energy and AM transport mechanism in stellar interiors. Several studies (Kumar et al. 1997; Zahn et al. 1997; Kumar et al. 1999;