Angular momentum evolution: an observational perspective

forming regions revealed bimodal rotation period distributions (Attridge & Herbst 1992; Bouvier et al. 1993; Edwards et al. 1993; Bouvier et al. 1995; Eaton et al. 1995; Choi & Herbst 1996). These results were later reinforced by larger ONC and Taurus-Auriga samples (e.g. Herbst et al. 2000b, 2002; Rodr´ıguez-Ledesma et al. 2010). Similar results

1.4. Avoiding break-up: the angular momentum problem

have also been observed in other young star forming regions such asρOph, IC 348, Lupus,

NGC 2264, NGC 6530, and the Upper Scorpius OB association (e.g. Shevchenko & Herbst 1998; Wichmann et al. 1998b; Herbst et al. 2000a; Cohen et al. 2004; Lamm et al. 2005; Cieza & Baliber 2007; Dahm et al. 2012; Henderson & Stassun 2012).

The longer period peak in the bimodal distribution was found to be populated by

accreting PMS stars (indicated by e.g. strong Hα; see Section 1.3.3) or disc-hosting PMS

stars (indicated by e.g. a significant IR excess; see Section 1.3.1) while the shorter period peak consisted mainly of non-accretors or disc-less PMS stars. The peak of slower rotators was interpreted as indicating accretion disc-regulated angular momentum removal. Then, following the dissipation of (at least the inner regions of) its disc, the star spins up as it contracts, conserving angular momentum as it does so, and is observed in the peak of more rapid rotators.

Accretion disc-regulated angular momentum evolution has not found unanimous sup- port, however. Certain studies did not observe a relationship between stellar rotation and accretion disc indicators or found that the distribution of rotation periods in their sample was unimodal, rather than bimodal (e.g. Stassun et al. 1999; Rebull 2001; Makidon et al. 2004). However, these contrasting findings could be explained in terms of a variety of biases which mask the underlying relationship between the presence of accretion discs and PMS stellar rotation. These include (e.g. Herbst et al. 2002; Littlefair et al. 2005; Lamm et al. 2005; Cieza & Baliber 2007)

• contamination by aliasing and beat periods;

• inclusion of non-member stars at a variety of ages;

• unreliable indicators of accretion discs;

• an underlying relation between rotation and stellar mass.

Beats and aliasing

If the rotation period is measured using ground-based photometry, a sampling interval of 1 day is introduced. If the true rotation period is close to 1 day, one may measure the

beat period, rather than the true rotation period. In addition, the variability which allows

starspots on the stellar surface. If multiple spots are present, one may measure aharmonic

period rather than the true rotation period. These effects are considered in more detail in Section 2.3.2.

Age dependence

The rotation rates of PMS stars in older star forming regions are observed to be more rapid (e.g. Irwin & Bouvier 2009). As such, inaccurately identifying members of a star forming region can blur the distributions of accretion disc-hosting stars and disc-less stars. Thus, the distribution of rotation periods can appear more unimodal.

Accretion-disc indicators

As discussed in Sections 1.3.1 and 1.3.3, accretion disc indicators based on Spitzer IRAC

colours and Ca ii EWs are more reliable than those based on NIR excess and Hα EWs.

If one cannot reliably separate accretion disc-hosting YSOs from disc-less YSOs, the dis- tributions of what are believed to be Class II and III YSOs or CTTS and WTTS will be contaminated. As a result, one may not recover the observed relationship between rotation and disc presence.

Mass dependence

An underlying relationship between rotation rate and stellar mass has been uncovered with

the rotation period distribution of low mass stars (M? .0.35−0.5 M, depending on the

adopted PMS evolutionary model) appearing unimodal (e.g. Herbst et al. 2002; Cieza & Baliber 2007). Studies which failed to separate the “high” and “low” mass TTSs failed to recover the previously observed bimodal rotation period distributions (e.g. Stassun et al. 1999).

This mass effect is partially attributable to the comparative sizes of “high” and “low” mass TTSs. For a sample of stars of a given age and specific stellar angular momentum,

j?, those with lower masses will have smaller radii, R?. Consequently, as j? ∝R2?/P, the

rotation periods,P, of the lower mass sample will be shorter than the higher mass sample

(Herbst et al. 2001). Thus, the lower mass slow rotators are shifted towards the peak of rapid rotators, blurring the bimodality found for the higher mass sample.

1.4. Avoiding break-up: the angular momentum problem

Figure 1.12: Representation of the magnetic interaction between a PMS star and the inner regions of its accretion disc under the disc-locking framework, based on figure 1 of Matt & Pudritz (2005b). The closed stellar- and disc-magnetic field lines are represented by red and blue lines, respectively. The black lines represent open stellar-magnetic field lines. Accretion of disc material onto the star occurs along closed stellar magnetic field lines, as indicated by the arrow. Three important regions of the disc are also noted: the truncation radius,Rtrunc; the co-rotation radius,Rco;

and the radial extent of the closed stellar magnetic field, Rout.

severely affected by even a small contamination of stars with spectral types later than M2. The difference in size between the higher and lower mass stars is not sufficient to explain this on its own and the location of this boundary remains poorly understood. The most promising underlying physical explanation relates to changes in the strength and geometry of the large-scale stellar magnetic field around this spectral type (Lamm et al. 2005).