4,881 research outputs found
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 where is a
shift-invariant operator. We then study a generalization of the notion of
Sheffer sequences by removing the requirement that 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
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