DISK BRAKING IN YOUNG STARS: PROBING ROTATION IN CHAMAELEON I AND TAURUS-AURIGA

One of the major outstanding issues in star formation theory is the regulation of angular momentum in young stars. The specific angular momentum of young single stars at ∼1 Myr is about 4 orders of magnitude lower than in molecular cloud cores, from which the stars formed, indicating efficient rotational braking in the early phases of stellar evolution (Bodenheimer 1995). In this context, a large number of studies have explored the connection between the presence of disks and rotation (Herbst et al. 2007).

Disk braking is defined here as a process that provides rotational braking based on magnetic coupling between the star and the disk. One possible theoretical scenario for disk braking is "disk locking," originally proposed for T Tauri stars by Camenzind (1990), Koenigl (1991), and Shu et al. (1994). In that case, the magnetic connection between the star and the disk produces a torque onto the star, transferring angular momentum to the disk (presumably, from where it is eventually removed by, e.g., magnetically driven winds). An alternative scenario for disk braking is stellar winds powered by accretion, as recently modeled by Matt & Pudritz (2005). For a more detailed overview of the theoretical work on disk braking, see, for example, the review by Matt & Pudritz (2008).

If disk braking is at work, we expect to observe three kinds of stars: slow rotators with disks, slow rotators without disks, and fast rotators without disks. This distribution corresponds to the following evolutionary sequence: while stars are coupled to their disks, they will rotate slowly; once stars lose their disks, they will continue to rotate slowly for some time but gradually spin up as they contract toward the main sequence, with some stars eventually becoming fast rotators. Thus, rapidly rotating stars with disks should not exist in an ideal disk braking scenario.

Observationally, the evidence for disk braking is confusing. Some photometric studies found a correlation between rotational properties and near-infrared color excess suggestive of disks (e.g., Edwards et al. 1993; Herbst et al. 2002), whereas others have not (e.g., Stassun et al. 1999; Makidon et al. 2004). The photometric monitoring program of Lamm et al. (2005) observed disk braking in ∼2–3 Myr NGC 2264, but with the effect less pronounced for low-mass stars. Recent studies using Spitzer mid-infrared observations of the ∼1 Myr Orion Nebula Cluster (ONC) and NGC 2264 support a disk-rotation connection: stars with longer rotation periods were found to be more likely than those with short periods to have IR excesses (Rebull et al. 2006; Cieza & Baliber 2007). However, the mid-infrared study by Cieza & Baliber (2006) of IC 348 did not find the preferential distribution of rotation with disk presence.

While both near-infrared and mid-infrared signatures indicate the presence of a dusty disk, they do not prove the coupling between star and disk as required by the disk braking scenario. To demonstrate a direct link between the inner disk and the central star, a better diagnostic for disk braking may be ongoing accretion. For strongly active accretors, rotation periods are difficult to determine since period measurements rely on the presence of stable starspot regions; therefore, period samples may be biased toward weakly accreting stars. In some respects, it is advantageous to use projected rotational velocity (vsin i) instead of rotation periods.

A recent spectroscopic study of disk accretion in low-mass young stars by Jayawardhana et al. (2006) found evidence of a possible accretion–rotation connection in the η Cha (∼6 Myr) and TWA (∼8 Myr) associations. All accretors in their sample of 41 stars were slow rotators, with vsin i ≲ 20 km s⁻¹, whereas the non-accretors showed a large span in rotational velocities, up to 50 km s⁻¹. However, given the small number of accretors, they caution that those results should be checked with larger samples. A larger study of solar-like mass stars in NGC 2264 by Fallscheer & Herbst (2006) found disk braking signatures in using UV excess indicative of accretion. For a review of recent observational studies on rotation and angular momentum evolution of young stellar objects and brown dwarfs, see Herbst et al. (2007).

As part of a comprehensive, multi-epoch spectroscopic survey, we present here a study of rotation and disk braking at ages of ∼2 Myr in the star-forming regions Taurus-Auriga and Chamaeleon I. This study comprises 144 stars, which significantly enlarges the previously available sample of spectroscopic data in those two regions (see the summary by Rebull et al. 2004 for currently available rotational data). From the spectra, we extract vsin i, and, as accretion indicators, the full width of Hα at 10% of the peak (hereafter, Hα 10% width) and Ca ii fluxes. We investigate the distribution of vsin i, estimate angular momentum values, and test for the signature of disk braking.

We used 572 high-resolution optical spectra of 144 members in the ∼2 Myr old Chamaeleon I and Taurus-Auriga star-forming regions obtained with the echelle spectrograph MIKE (Bernstein et al. 2003) on the Magellan Clay 6.5 meter telescope at the Las Campanas Observatory, Chile. The data were collected on 15 nights during four observing runs between 2006 February and 2006 December. We complemented our optical spectra with infrared measurements from the InfraRed Array Camera (IRAC; Fazio et al. 2004) aboard the Spitzer Space Telescope. For Cha I, we used the results of Damjanov et al. (2007), and for Tau-Aur we analyzed publicly available images obtained between 2004 September and 2007 March, using the methods described in detail by Damjanov et al. (2007). Our results are listed in Tables 1 and 2.

Our sample consists of a magnitude-limited subset (R ⩽ 17.6 for Cha I; R ⩽ 13.4 for Tau-Aur) of targets from Leinert et al. (1993), Ghez et al. (1993), Simon et al. (1995), Kohler & Leinert (1998), Briceño et al. (2002), and Luhman (2004a, 2004b). To isolate the possible influence of binarity on disk braking in this study, we excluded from our sample unresolved wide binaries and double-lined spectroscopic binaries. Our targets span the spectral type range from F2 to M5 based on published classifications. In addition, we observed a sample of 25 slowly rotating velocity standard stars selected from the list of Nidever et al. (2002); these cover the same spectral range as our targets. We determined the spectral type for 13 targets without prior classification by fitting their spectra against those of the standard stars, and identifying the best fits.

MIKE is a slit-fed double echelle spectrograph with blue and red arms. For this study, we used only the red spectra, which cover the range of 4900–9300 Å in 34 spectral orders. The 035 slit was used with no binning to obtain the highest possible spectral resolution, R∼ 60,000. The pixel scale was 014 pixel⁻¹ in the spatial direction, and approximately 0.024 Å pixel⁻¹ at 6500 Å in the spectral direction. In MIKE, the spatial direction of the projected slit is wavelength dependent, and not aligned with the CCD columns. To extract these slanted spectra, we used customized routines running in the ESO-MIDAS environment (described in detail in A. Brandeker et al. 2009, in preparation). Integration times were chosen such that we obtained signal-to-noise ratios (S/N) >30 per spectral resolution element at 6500 Å; they typically ranged from 60 to 1200 s depending on seeing.

3.1. Accretion Signatures

3.2. Projected Rotational Velocity

4.1. Accretion and Disk Presence

To examine the correlation between disk presence and accretion, we show in Figure 1 the 8 μm excess against Hα 10% widths for those targets for which both measurements are available. (The error bars on the Hα 10% width refer to the standard deviation of the estimates over epochs.) Out of the 67 objects in this subsample, 22 show evidence of both accretion and disk presence (see the upper right regions in Figure 1), implying that gas from the inner disk is still being channeled onto the star, and 41 objects have neither infrared excess nor signs of accretion. Thus, in nearly all cases (63/67), the accretion signature is well correlated with disk presence.

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Of the four exceptions, the three non-accretors with infrared excess, all in Cha I, are CHXR 20, Hn 18, and ISO 52. For these objects, accretion rates may have dropped below measurable levels in Hα 10% width even though the disks persist. The Ca ii-λ8662 flux of Hn 18 is detectable and indicates a negligible accretion rate of 4.4 × 10⁻¹¹ M_☉ yr⁻¹. Also, accretion may be variable on short timescales (Nguyen et al. 2009). For CHXR 20, Ca ii-λ8662 emission was undetected at one epoch, and is present at two other epochs with a suggested small accretion rate of 2.6 × 10⁻¹⁰ M_☉ yr⁻¹. The only accretor without infrared excess, LkCa 21, was observed on a single epoch with a Hα 10% width of 277 km s⁻¹; this value includes a contribution from rotational broadening of 46 km s⁻¹. The net 10% width is below the threshold for accretors originally set out by (White & Basri 2003). In addition, Ca ii-λ8662 emission was not observed in LkCa 21 implying that it likely is not an accretor.

4.2. Stellar Mass and Rotational Velocity

Rotational velocity is known to vary as a function of stellar mass in young stars, likely because the efficiency of angular momentum removal depends on magnetic activity, which in turn depends on stellar mass (see Scholz et al. 2007). To probe the rotation–mass dependence, we show the projected rotational velocity as a function of spectral type in Figure 2. Here late-K spectral type corresponds to ∼1 M_☉ (Baraffe et al. 1998). The results are similar to what was found previously (e.g., Scholz et al. 2007; Rebull et al. 2002). Higher mass stars tend to have faster projected rotational velocity overall than their lower mass counterparts.

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To examine this rotation–mass trend further, we divided our targets into two mass bins consisting of F–K type stars, and M type stars. In Figure 3, we show boxplots of vsin i for the two mass bins: the horizontal lines inside the rectangles indicate the median values. Clearly, in both Cha I and Tau-Aur, the median vsin i for the higher mass bins, 26 km s⁻¹ and 24 km s⁻¹, are significantly faster than those of the lower mass bins, both at 11 km s⁻¹.

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To get a quantitative sense of the difference in rotational velocity between the high and low mass stars, we applied the Kolmogorov–Smirnov (K–S) test. This analysis shows there is a probability of only ∼0.5% for Cha I, and ∼0.1% for Tau-Aur that the vsin i for the two mass bins were drawn from the same distribution.

When interpreting this finding, one should take into account that the stars in our sample assuming an age of ∼2 Myr span roughly a range of 1–4 R_☉ in stellar radii. To gauge the contribution of stellar radius on vsin i, we evaluated the specific angular momentum in our sample as follows. First, we converted spectral type to effective temperature by looking up and interpolating values from Sherry et al. (2004). Second, we used the effective temperature to obtain estimates of mass M, radius R, and moment of inertia I from the models of D'Antona & Mazzitelli (1997). Third, we combined these values with our vsin i estimates to compute the projected specific angular momentum using the relation jsin i = (vsin i)I/MR. In Figure 4, we show jsin i as a function of stellar mass. From the best linear fit to the upper envelope of the data points, we find by eye that j ∝ M^0.5. Indeed, there is an increase in specific angular momentum with increasing stellar mass.

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4.3. Accretion and Rotational Velocity

To check for a connection between accretion and rotation, in Figures 5 and 6, we show vsin i as a function of Hα 10% width and of 8 μm excess for our targets. In addition, the figures show both the intrinsic contribution of rotation to the line widths, and the separation between accretors and non-accretors.

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We compared the distribution of vsin i for accretors and non-accretors using a number of K–S tests. To account for the rotation-mass dependence (see Section 4.2), we carried out these tests for the two mass bins (F–K type and M type) separately. The probability that the vsin i of accretors and non-accretors were drawn from the same distribution in Cha I is 6% for the high-mass targets, and 50% for the low-mass ones. The probabilities for high- and low-mass targets in Tau-Aur are 8% and 10%, respectively. For the entire sample, the corresponding probabilities for high- and low-mass targets is 30% and 7%, respectively. Thus, any connection between accretion and projected rotational velocity is at best marginally significant. The vsin i distributions are shown in Figure 7.

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Since the presence of dusty disks is strongly correlated with accretion in our targets, it is not surprising there is, for high and low mass stars in Tau-Aur respectively, a 9% and 13% probability that the vsin i for stars with and without disks were drawn from the same distribution. It would appear that the presence of ongoing accretion or a disk has no significant effect on the rotation in our sample. This is contrary to the standard disk braking scenario, as outlined in Section 1.

One particular reason for the negative test results is the presence of a significant number of rapidly rotating accretors, as seen in Figure 5. Based on Spitzer data, Rebull et al. (2006) find that the fraction of stars with disks is very low for rotation periods P < 1.8 d (see their Figure 3). For a radius of 1 R_☉ and an average sin i, this period corresponds to a projected rotational velocity of 22 km s⁻¹. This value scales linearly with stellar radius. In our sample, we see 5–10 objects rotating faster than this threshold, where the exact number depends on the inclinations and stellar radii. This type of objects is not expected in the evolutionary sequence for the standard disk braking scenario described in Section 1.

Previous studies drew conclusions about the disk-braking scenario based on rotation periods from photometric data, while we use projected rotational velocity. To check whether this makes a difference, we ran Monte Carlo simulations based on published data from previous photometric studies, e.g., Stassun et al. (1999), Herbst et al. (2002) surveys in the ONC. In the simulations, rotation periods were converted to vsin i by selecting random viewing angles and using uniformly distributed stellar radii of 1–4 R_☉. In the case of Herbst et al. (2002), where there was previous indication of disk braking, we found probabilities of <1% that diskless stars have the same distribution of vsin i as disk harboring stars, hence we recovered their evidence for disk braking. Furthermore, for data from Stassun et al. (1999), where disk braking was not observed, we found that the simulated vsin i distributions for diskless and disk-harboring stars were similar, with probabilities consistently >10%. We conclude that our results are insensitive to our use of projected rotational velocity to probe disk-braking scenarios.

We present a comprehensive study of projected rotational velocities and Hα 10% widths for young stars in Taurus-Auriga and Chamaeleon I. Our three main results are as follows.

• 1.  
  Indicators for accretion and inner disks agree for >94% of our total sample. For nearly all objects, the dissipation of the dusty inner disk and the drop in accretion rate below measurable levels occur simultaneously. Consequently, the lifetimes of inner disks are similar to the timescales of gas accretion. Based on our large sample, systems with inner disk clearings and ongoing gas accretion are rare (1/67); the same holds for systems with nonaccreting inner disks (3/67). This consistency shows that timescales for inner disk clearing and accretion decline are much shorter than typical disk lifetimes (∼10⁵ years instead of several 10⁶ years).
• 2.  
  F–K stars have on average of 2–2.5 times larger rotational velocities than M stars. Although rotational velocity is proportional to stellar radius, from the models of D'Antona & Mazzitelli (1997) at 2 Myr, the typical radius of our F–K stars is less than 1.5 times that of the M stars in our sample. Moreover, the specific angular momentum is proportional to M^0.5. This mass dependence complements findings in Orion of Wolff et al. (2004) where the upper envelope of the observed values of angular momentum per unit mass varies as M^0.25 for stars on convective tracks (∼1 Myr) with a break in the power law with a sharp decline in j with decreasing mass for stars with M < 2 M_☉ for slightly older stars on radiative tracks (see their Figure 3). They posit that these broad trends can be accounted for by simple models where stars lose angular momentum before they are deposited on the birth line, plausibly through star–disk interaction, and for stars with M < 2M_☉, the amount of braking increases with time spent evolving down their convective tracks. Our analysis of ∼2 Myr old T Tauri stars in Cha I and Tau-Aur showed an angular momentum mass trend in between that of the two age groups studied in Orion for the same mass regime. This intermediate result could hint at only the beginning stages of disk braking, a significant age spread, or both.
• 3.  
  The presence of accretion or an inner disk does not significantly affect the distribution of rotational velocities in Taurus-Auriga and Chamaeleon I. This finding adds to the ongoing debate on disk braking in young stars, as it is in stark contrast to recent studies in the ONC and NGC 2264 (e.g., Rebull et al. 2006; Cieza & Baliber 2007), where a clear increase in disk fraction is found with increasing rotation period.

Part of the explanation may be that the stars have had insufficient time to brake. Hartmann (2002) estimate a disk-magnetosphere braking timescale τ_DB ≳  4.5 ×  10⁶ yr $M_{0.5}\;\dot{M}^{-1}_{-8} f$, where M_0.5 is the stellar mass in units of 0.5 M_☉, $\dot{M}_{-8}$ is the mass accretion rate in units of the typical value of 10⁻⁸ M_☉ yr⁻¹(M/0.5 M_☉), and f is the stellar rotation as a fraction of breakup velocity, then τ_DB for our sample (typically ∼5 Myr) is somewhat larger than the estimated age of the stars (∼2 Myr). Adopting the accretion and rotation results of Rebull et al. (2000) and Clarke & Bouvier (2000), we find a shorter typical τ_DB of ∼1 Myr for the ONC where disk braking is observed. Therefore, disk-locking in Cha I and Tau-Aur may be ineffective overall.

In addition, there is evidence for spin-down not involving accretion from the inner disk. The specific angular momentum values for ∼10 Myr solar-like mass stars in Orion, where strong braking is observed (Wolff et al. 2004), are typically lower than those found in our sample of similar mass non-accretors (where disk-locking should have expired) by a factor of ∼5. In contrast, the j values for ∼1 Myr solar-like mass stars in Orion are similar to those of our non-accretors. These measurements could imply another braking mechanism is at work after disks have dissipated. Of course, this indication for another braking mechanism relies on accurate age estimates.

Another possible explanation for the lack of strong disk braking in our sample is age spread, which might be larger in Taurus-Auriga and Chamaeleon I than in the cluster cores of ONC and NGC 2264. Covering objects in varying stages of their rotational history could dilute a disk braking signature. In addition, the contrast between our results and those of previous studies that find strong evidence of disk braking may stem from different initial conditions at evolutionary stages before the stars became optically observable, e.g., at the birth line. The initial rotational velocity distributions for dense star-forming regions like ONC and NGC 2264 could be very different from Tau-Aur and Cha I where star formation has occurred in an environment with much lower stellar density. Future investigation of a similar kind should aim to take into account a more complete understanding of stellar properties when looking at correlations between rotation and disk/accretion signatures. In combination with previous results in other young clusters, our data will serve as an empirical basis for future studies on the timescales and efficiency of disk braking mechanisms.

We thank the anonymous referee for helpful comments that improved the clarity of the paper. We thank David Lafrenière and Nairn Baliber for useful suggestions relating to the work presented in this paper. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. We would also like to thank the Magellan staff for their tireless effort and patience in accommodating our aggressive observing program. This work was supported in part by NSERC grants to R.J. and M.H.vK., and an Early Researcher Award from the province of Ontario to R.J.