Observable Consequences of Rotation for Stars, Brown Dwarfs, and Star Clusters
It is reasonable to suppose that a typical newborn star or brown dwarf inherits much of its progenitor molecular cloud’s angular momentum. This leads to the suggestion that such an object ought to have a rotational velocity that is close to the Keplerian breakup limit, resulting in significant centrifugal expansion at the equator. According to models of internal energy transport, this expansion ought to make the poles of a rotator significantly hotter than its equator, so that the inclination of its rotational axis greatly affects both the shape of its observed spectrum and its total observed flux. These predictions are consistent with the interferometric and spectroscopic observations of stellar and sub-stellar objects whose rotational speeds are frequently at appreciable fractions of the Keplerian limit.
In particular, the oblate shapes, surface temperature variations, and spectral line broadening of many early-type stars indicate large rotational velocities. Via its effects on surface temperature and shape, rotation has a significant effect on these stars’ spectra. Thus, in order to infer the structural and life history parameters of these objects from their spectra, one must carefully integrate specific intensity over the two-dimensional surfaces of corresponding stellar models. Toward this end, in Chapter 2, we offer PARS (Paint the Atmospheres of Rotating Stars) – an integration scheme based on models that incorporate solid body rotation, Roche mass distribution, and collinearity of gravity and energy flux (Lipatov & Brandt, 2020a). The scheme features a closed-form expression for the azimuthal integral, a high-order numerical approximation of the longitudinal integral, and a precise calculation of surface effective temperature at rotation rates up to 99.9% of the Keplerian limit. Extensions of the scheme include synthetic color-magnitude diagrams and planetary transit curves. An important input to PARS in Chapter 2 is a grid of specific intensities for stellar plane-parallel atmosphere models, ATLAS9.
Much like the observations of early-type stars, spectroscopy and time-resolved photometry of brown dwarfs are frequently indicative of rotational velocities that are comparable to the breakup limit. Accordingly, in Chapter 3, we apply PARS to parameter inference in the case of rotating brown dwarfs, exploring the dependence of these sub- stellar objects’ observables on rotational speed and axis inclination. In this case, instead of specific intensities for stellar atmosphere models, we feed PARS an intensity grid that is appropriate for brown dwarfs, computed by PICASO (a Planetary Intensity Code for Atmospheric Spectroscopy Observations) from Sonora brown dwarf 1D climate and chemistry models. We find that the specific flux of a typical fast-rotating brown dwarf can increase by as much as a factor of 1.5 with movement from an equator-on to a pole-on view. On the other hand, the distinctive effect of rotation on spectral shape increases toward the equator-on view. The latter effect also increases with lower effective temperature. The bolometric luminosity estimate for a typical fast rotator at extreme inclinations has to be adjusted by as much as ∼ 20% due to the anisotropy of the object’s observed flux. We provide a general formula for the calculation of the corresponding adjustment factor in terms of rotational speed and inclination.
Rotation does not only directly affect the spectra of present-day stars, it also significantly alters the evolution of stars throughout their lives, chiefly via its effect on stellar internal transport. By means of both the direct and the evolutionary effects, stellar rotation is possibly responsible for the fact that the color-magnitude diagrams (CMDs) of intermediate-age star clusters (≲2 Gyr) are much more complex than those predicted by coeval, non-rotating stellar evolution models. The clusters’ observed extended main sequence turnoffs (eMSTOs) could result from variations in stellar age, stellar rotation, or both. The physical interpretation of eMSTOs is largely based on the complex mapping between stellar models—themselves functions of mass, rotation, orientation, and binarity—and the CMD. In Chapter 4, we compute continuous probability densities in three-dimensional color, magnitude, and vsini (i.e., projected equatorial velocity) space for individual stars in a cluster’s eMSTO, based on a rotating stellar evolution model. These densities enable the rigorous inference of cluster properties from a stellar model, or, alternatively, constraints on the stellar model from the cluster’s CMD. We use the MIST stellar evolution models to jointly infer the age dispersion, the rotational distribution, and the binary fraction of the Large Magellanic Cloud cluster NGC 1846. We derive an age dispersion of ∼ 70 − 80 Myr, approximately half the earlier estimates due to non-rotating models. This finding agrees with the conjecture that rotational variation is largely responsible for eMSTOs. However, the MIST models do not provide a satisfactory fit to all stars in the cluster and achieve their best agreement at an unrealistically high binary fraction. The lack of agreement near the main-sequence turnoff suggests specific physical changes to the stellar evolution models, including a lower mass for the Kraft break and potentially enhanced main sequence lifespans for rapidly rotating stars.