5,293 research outputs found
Smooth critical points of planar harmonic mappings
In a work in 1992, Lyzzaik studies local properties of light harmonic
mappings. More precisely, he classifies their critical points and accordingly
studies their topological and geometrical behaviours. We will focus our study
on smooth critical points of light harmonic maps. We will establish several
relationships between miscellaneous local invariants, and show how to connect
them to Lyzzaik's models. With a crucial use of Milnor fibration theory, we get
a fundamental and yet quite unexpected relation between three of the numerical
invariants, namely the complex multiplicity, the local order of the map and the
Puiseux pair of the critical value curve. We also derive similar results for a
real and complex analytic planar germ at a regular point of its Jacobian
level-0 curve. Inspired by Whitney's work on cusps and folds, we develop an
iterative algorithm computing the invariants. Examples are presented in order
to compare the harmonic situation to the real analytic one.Comment: 36 pages, 5 figure
Stability of an Ultra-Relativistic Blast Wave in an External Medium with a Steep Power-Law Density Profile
We examine the stability of self-similar solutions for an accelerating
relativistic blast wave which is generated by a point explosion in an external
medium with a steep radial density profile of a power-law index > 4.134. These
accelerating solutions apply, for example, to the breakout of a gamma-ray burst
outflow from the boundary of a massive star, as assumed in the popular
collapsar model. We show that short wavelength perturbations may grow but only
by a modest factor <~ 10.Comment: 12 pages, 3 figures, submitted to Physical Review
Las Vegas Academy Jazz Band III: A Celebration of Black History Month
Program listing performers and works performed
Measuring the 3D Clustering of Undetected Galaxies Through Cross Correlation of their Cumulative Flux Fluctuations from Multiple Spectral Lines
We discuss a method for detecting the emission from high redshift galaxies by
cross correlating flux fluctuations from multiple spectral lines. If one can
fit and subtract away the continuum emission with a smooth function of
frequency, the remaining signal contains fluctuations of flux with frequency
and angle from line emitting galaxies. Over a particular small range of
observed frequencies, these fluctuations will originate from sources
corresponding to a series of different redshifts, one for each emission line.
It is possible to statistically isolate the fluctuations at a particular
redshift by cross correlating emission originating from the same redshift, but
in different emission lines. This technique will allow detection of clustering
fluctuations from the faintest galaxies which individually cannot be detected,
but which contribute substantially to the total signal due to their large
numbers. We describe these fluctuations quantitatively through the line cross
power spectrum. As an example of a particular application of this technique, we
calculate the signal-to-noise ratio for a measurement of the cross power
spectrum of the OI(63 micron) and OIII(52 micron) fine structure lines with the
proposed Space Infrared Telescope for Cosmology and Astrophysics. We find that
the cross power spectrum can be measured beyond a redshift of z=8. Such
observations could constrain the evolution of the metallicity, bias, and duty
cycle of faint galaxies at high redshifts and may also be sensitive to the
reionization history through its effect on the minimum mass of galaxies. As
another example, we consider the cross power spectrum of CO line emission
measured with a large ground based telescope like CCAT and 21-cm radiation
originating from hydrogen in galaxies after reionization with an interferometer
similar in scale to MWA, but optimized for post-reionization redshifts.Comment: 21 pages, 6 figures; Replaced with version accepted by JCAP; Added an
example of cross correlating CO line emission and 21cm line emission from
galaxies after reionizatio
Event-Horizon-Telescope Evidence for Alignment of the Black Hole in the Center of the Milky Way with the Inner Stellar Disk
Observations of the black hole in the center of the Milky Way with the Event
Horizon Telescope at 1.3 mm have revealed a size of the emitting region that is
smaller than the size of the black-hole shadow. This can be reconciled with the
spectral properties of the source, if the accretion flow is seen at a
relatively high inclination (50-60 degrees). Such an inclination makes the
angular momentum of the flow, and perhaps of the black hole, nearly aligned
with the angular momenta of the orbits of stars that lie within 3 arcsec from
the black hole. We discuss the implications of such an alignment for the
properties of the black hole and of its accretion flow. We argue that future
Event-Horizon-Telescope observations will not only refine the inclination of
Sgr A* but also measure precisely its orientation on the plane of the sky.Comment: To appear in the Astrophysical Journa
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