3,218 research outputs found

    Nonlinear Galactic Dynamos and the Magnetic Pitch Angle

    Get PDF
    Pitch angles pp of the large-scale magnetic fields B\overline{\bf{\it{B}}} of spiral galaxies have previously been inferred from observations to be systematically larger in magnitude than predicted by standard mean-field dynamo theory. This discrepancy is more pronounced if dynamo growth has saturated, which is reasonable to assume given that such fields are generally inferred to be close to energy equipartition with the interstellar turbulence. This 'pitch angle problem' is explored using local numerical mean-field dynamo solutions as well as asymptotic analytical solutions. It is first shown that solutions in the saturated or kinematic regimes depend on only five dynamo parameters, two of which are tightly constrained by observations of galaxy rotation curves. The remaining 3-dimensional (dimensionless) parameter space can be constrained to some extent using theoretical arguments. Predicted values of p|p| can be as large as 40\sim40^\circ, which is similar to the largest values inferred from observations, but only for a small and non-standard region of parameter space. We argue, based on independent evidence, that such non-standard parameter values are plausible. However, these values are located toward the boundary of the allowed parameter space, suggesting that additional physical effects may need to be incorporated. We therefore suggest possible directions for extending the basic model considered.Comment: 11 pages, 5 figures, 1 table, edited to match ApJ versio

    Estimation of nonseparable models with censored dependent variables and endogenous regressors

    Get PDF
    In this article we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalize the identification argument put forward in Altonji, Ichimura, and Otsu (2012 Altonji, J. G., Ichimura, H., Otsu, T. (2012). Estimating derivatives in nonseparable models with limited dependent variables. Econometrica 80:1701–1719. [CrossRef], [Web of Science ®] ), construct a nonparametric estimator, characterize its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. Identification is constructive and is achieved through a control function approach. We show that the estimator is consistent and asymptotically normally distributed. The Monte Carlo results are encouraging
    corecore