Imaging Optically-Thin Hot Spots Near the Black Hole Horizon of Sgr A* at Radio and Near-Infrared Wavelengths

Sub milli-arcsecond astrometry and imaging of the black hole Sgr A* at the Galactic centre may become possible in the near future at infrared and sub-millimetre wavelengths. Motivated by observations of short-term infrared and X-ray variability of Sgr A*, in a previous paper we computed the expected images and light curves, including polarization, associated with an compact emission region orbiting the central black hole. We extend this work, using a more realistic hot-spot model and including the effects of opacity in the underlying accretion flow. We find that at infrared wavelengths the qualitative features identified by our earlier work are present, namely it is possible to extract the black hole mass and spin from spot images and light curves of the observed flux and polarization. At radio wavelengths, disk opacity produces significant departures from the infrared behaviour, but there are still generic signatures of the black hole properties. Detailed comparison of these results with future data can be used to test general relativity and to improve existing models for the accretion flow in the immediate vicinity of the black hole.Comment: 13 pages, 26 figures, submitted to MNRA

A simpler characterization of Sheffer polynomial

We characterize the Sheffer sequences by a single convolution identity $$F^{(y)} p_{n}(x) = \sum _{k=0}^{n}\ p_{k}(x)\ p_{n-k}(y)$$ where $F^{(y)}$ is a shift-invariant operator. We then study a generalization of the notion of Sheffer sequences by removing the requirement that $F^{(y)}$ be shift-invariant. All these solutions can then be interpreted as cocommutative coalgebras. We also show the connection with generalized translation operators as introduced by Delsarte. Finally, we apply the same convolution to symmetric functions where we find that the ``Sheffer'' sequences differ from ordinary full divided power sequences by only a constant factor