We forecast parameter uncertainties on the mass profile of a typical Milky Way dwarf spheroidal (dSph) galaxy using the spherical Jeans Equation and Fisher matrix formalism. We show that radial velocity measurements for 1000 individual stars can constrain the mass contained within the effective radius of a dSph to within 5%. This is consistent with constraints extracted from current observational data. We demonstrate that a minimum sample of 100,000 (10,000) stars with both radial and proper motions measurements is required to distinguish between a cusped or cored inner slope at the 2-sigma (1-sigma) level. If using the log-slope measured at the half-light radius as a proxy for differentiating between a core or cusp slope, only 1000 line-of-sight and proper motions measurements are required, however, we show this choice of radius does not always unambiguously differentiate between core and cusped profiles. Once observational errors are below half the value of the intrinsic dispersion, improving the observational precision yields little change in the density profile uncertainties. The choice of priors in our profile shape analysis plays a crucial role when the number of stars in a system is less than 100, but does not affect the resulting uncertainties for larger kinematic samples. Our predicted 2D confidence regions agree well with those from a full likelihood analysis run on a mock kinematic dataset taken from the Gaia Challenge, validating our Fisher predictions. Our methodology is flexible, allowing us to predict density profile uncertainties for a wide range of current and future kinematic datasets.
We re-examine the possibility of ultrahigh energy cosmic rays being accelerated in nearby dormant quasars. We particularize our study to heavy nuclei to accommodate the spectrum and nuclear composition recently reported by the Pierre Auger Collaboration. Particle acceleration is driven by the Blandford-Znajek mechanism, which wires the dormant spinning black holes as Faraday unipolar dynamos. We demonstrate that energy losses are dominated by photonuclear interactions on the ambient photon fields. We argue that the local dark fossils of the past quasar activity can be classified on the basis of how source parameters (mass of the central engine and photon background surrounding the accelerator) impact the photonuclear interaction. In this classification it is possible to distinguish two unequivocal type of sources: those in which nuclei are completely photodisintegrated before escaping the acceleration region and those in which photopion production is the major energy damping mechanism. We further argue that the secondary nucleons from the photodisintegrated nuclei (which have a steep spectral index at injection) can populate the energy region below "the ankle" feature in the cosmic ray spectrum, whereas heavy and medium mass nuclei (with a harder spectral index) populate the energy region beyond "the ankle", all the way to the high energy end of the spectrum. In addition, we show that five potential quasar remnants from our cosmic backyard correlate with the hot-spot observed by the Telescope Array.
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