Elliptical galaxies are systems where dark matter is usually less necessary to explain observed dynamics than in the case of spiral galaxies, however there are some instances where Newtonian gravity and the observable mass are insufficient to explain their observed structure and kinematics. Such is the case of NGC 4649, a massive elliptical galaxy in the Virgo cluster for which recent studies report a high fraction of dark matter, 0.78 at 4R e . However this galaxy has been studied within the MOND hypothesis, where a good agreement with the observed values of velocity dispersion is found. Using a MONDian gravity force law, here we model this galaxy as a self-consistent gravitational equilibrium dynamical system. This force law reproduces the MOND phenomenology in the a < a 0 regime, and reduces to the Newtonian case when a > a 0 . Within the MONDian a < a 0 scales, centrifugal equilibrium or dispersion velocities become independent of radius, and show a direct proportionality to the fourth root of the total baryonic mass, V 4 ∝ (M Ga 0 ). We find that the recent detailed observations of the surface brightness profile and the velocity dispersion profile for this galaxy are consistent with the phenomenology expected in MONDian theories of modified gravity, without the need of invoking the presence of any hypothetical dark matter.
Understanding the observations of dynamical tracers and the trajectories of lensed photons at galactic scales within the context of General Relativity (GR), requires the introduction of a hypothetical dark matter dominant component. The onset of these gravitational anomalies, where the Schwarzschild solution no longer describes observations, closely corresponds to regions where accelerations drop below the characteristic a 0 acceleration of MOND, which occur at a well established mass-dependent radial distance, R c ∝ (GM/a 0 ) 1/2 . At cosmological scales, inferred dynamics are also inconsistent with GR and the observed distribution of mass. The current accelerated expansion rate requires the introduction of a hypothetical dark energy dominant component. We here show that for a Schwarzschild metric at galactic scales, the scalar curvature, K, multiplied by (r 4 /M ) at the critical MOND transition radius, r = R c , has an invariant value of κ B = K(r 4 /M ) = 28Ga 0 /c 4 . Further, assuming this condition holds for r > R c , is consistent with the full spacetime which under GR corresponds to a dominant isothermal dark matter halo, to within observational precision at galactic level. For a FLRW metric, this same constant bounding curvature condition yields for a spatially flat spacetime a cosmic expansion history which agrees with the ΛCDM empirical fit for recent epochs, and which similarly tends asymptotically to a de Sitter solution. Thus, a simple covariant purely geometric condition identifies the low acceleration regime of observed gravitational anomalies, and can be used to guide the development of extended gravity theories at both galactic and cosmological scales.
Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counterintuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfvén waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, α = 2 as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed >600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: preflare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that α = 1.63 ± 0.03. This is below the critical threshold, suggesting that Alfvén waves are an important driver of coronal heating.
We have developed a laboratory exercise designed to help students translate between different field representations. It starts with students qualitatively mapping field lines for various bar magnet configurations and continues with a Hall probe experiment in which students execute a series of scaffolded tasks, culminating in the prediction and measurement of the spatial variation of magnetic field components along a line near magnets. We describe the experimental tasks, various difficulties students have throughout, and ways this lab makes even their incorrect predictions better. We suggest that developing lab activities of this nature brings a new dimension to the ways students learn and interact with field concepts.
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