5,193 research outputs found
Real rank boundaries and loci of forms
In this article we study forbidden loci and typical ranks of forms with
respect to the embeddings of given by the line
bundles . We introduce the Ranestad-Schreyer locus corresponding to
supports of non-reduced apolar schemes. We show that, in those cases, this is
contained in the forbidden locus. Furthermore, for these embeddings, we give a
component of the real rank boundary, the hypersurface dividing the minimal
typical rank from higher ones. These results generalize to a class of
embeddings of . Finally, in connection with real
rank boundaries, we give a new interpretation of the
hyperdeterminant.Comment: 17 p
Cross section, final spin and zoom-whirl behavior in high-energy black hole collisions
We study the collision of two highly boosted equal mass, nonrotating black
holes with generic impact parameter. We find such systems to exhibit zoom-whirl
behavior when fine tuning the impact parameter. Near the threshold of immediate
merger the remnant black hole Kerr parameter can be near maximal (a/M about
0.95) and the radiated energy can be as large as 35% of the center-of-mass
energy.Comment: Rearranged results section; accepted for publication in Phys. Rev.
Let
Testing general relativity and probing the merger history of massive black holes with LISA
Observations of binary inspirals with LISA will allow us to place bounds on
alternative theories of gravity and to study the merger history of massive
black holes (MBH). These possibilities rely on LISA's parameter estimation
accuracy. We update previous studies of parameter estimation including
non-precessional spin effects. We work both in Einstein's theory and in
alternative theories of gravity of the scalar-tensor and massive-graviton
types. Inclusion of non-precessional spin terms in MBH binaries has little
effect on the angular resolution or on distance determination accuracy, but it
degrades the estimation of the chirp mass and reduced mass by between one and
two orders of magnitude. The bound on the coupling parameter of scalar-tensor
gravity is significantly reduced by the presence of spin couplings, while the
reduction in the graviton-mass bound is milder. LISA will measure the
luminosity distance of MBHs to better than ~10% out to z~4 for a (10^6+10^6)
Msun binary, and out to z~2 for a (10^7+10^7) Msun binary. The chirp mass of a
MBH binary can always be determined with excellent accuracy. Ignoring spin
effects, the reduced mass can be measured within ~1% out to z=10 and beyond for
a (10^6+10^6) Msun binary, but only out to z~2 for a (10^7+10^7) Msun binary.
Present-day MBH coalescence rate calculations indicate that most detectable
events should originate at z~2-6: at these redshifts LISA can be used to
measure the two black hole masses and their luminosity distance with sufficient
accuracy to probe the merger history of MBHs. If the low-frequency LISA noise
can only be trusted down to 10^-4 Hz, parameter estimation for MBHs (and LISA's
ability to perform reliable cosmological observations) will be significantly
degraded.Comment: 13 pages, 4 figures. Proceedings of GWDAW 9. Matches version accepted
in Classical and Quantum Gravit
Algebraic lattice constellations: bounds on performance
In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain. Furthermore, we discuss constructions, minimum product distance, and bounds for full-diversity complex rotated Z[i]/sup n/-lattices for any dimension n, which avoid the need of component interleaving
Profiling of berries by comprehensive two-dimensional gas chromatography/time-of-flight mass spectrometry (GCxGC/TOF-MS)
poster C149, Proceedings Annual Biomedical Research Conference for Minority Students (ABRCMS 2011), November 9 - 12, 2011, Americaâs Center, St. Louis, MO, US
Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
We study the inspiral, merger and ringdown of unequal mass black hole
binaries by analyzing a catalogue of numerical simulations for seven different
values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and
Post-Newtonian results by projecting the waveforms onto spin-weighted spherical
harmonics, characterized by angular indices (l,m). We find that the
Post-Newtonian equations predict remarkably well the relation between the wave
amplitude and the orbital frequency for each (l,m), and that the convergence of
the Post-Newtonian series to the numerical results is non-monotonic. To leading
order the total energy emitted in the merger phase scales like eta^2 and the
spin of the final black hole scales like eta, where eta=q/(1+q)^2 is the
symmetric mass ratio. We study the multipolar distribution of the radiation,
finding that odd-l multipoles are suppressed in the equal mass limit. Higher
multipoles carry a larger fraction of the total energy as q increases. We
introduce and compare three different definitions for the ringdown starting
time. Applying linear estimation methods (the so-called Prony methods) to the
ringdown phase, we find resolution-dependent time variations in the fitted
parameters of the final black hole. By cross-correlating information from
different multipoles we show that ringdown fits can be used to obtain precise
estimates of the mass and spin of the final black hole, which are in remarkable
agreement with energy and angular momentum balance calculations.Comment: 51 pages, 28 figures, 16 tables. Many improvements throughout the
text in response to the referee report. The calculation of multipolar
components in Appendix A now uses slightly different conventions. Matches
version in press in PR
Reconstructing the massive black hole cosmic history through gravitational waves
The massive black holes we observe in galaxies today are the natural
end-product of a complex evolutionary path, in which black holes seeded in
proto-galaxies at high redshift grow through cosmic history via a sequence of
mergers and accretion episodes. Electromagnetic observations probe a small
subset of the population of massive black holes (namely, those that are active
or those that are very close to us), but planned space-based gravitational-wave
observatories such as the Laser Interferometer Space Antenna (LISA) can measure
the parameters of ``electromagnetically invisible'' massive black holes out to
high redshift. In this paper we introduce a Bayesian framework to analyze the
information that can be gathered from a set of such measurements. Our goal is
to connect a set of massive black hole binary merger observations to the
underlying model of massive black hole formation. In other words, given a set
of observed massive black hole coalescences, we assess what information can be
extracted about the underlying massive black hole population model. For
concreteness we consider ten specific models of massive black hole formation,
chosen to probe four important (and largely unconstrained) aspects of the input
physics used in structure formation simulations: seed formation, metallicity
``feedback'', accretion efficiency and accretion geometry. For the first time
we allow for the possibility of ``model mixing'', by drawing the observed
population from some combination of the ``pure'' models that have been
simulated. A Bayesian analysis allows us to recover a posterior probability
distribution for the ``mixing parameters'' that characterize the fractions of
each model represented in the observed distribution. Our work shows that LISA
has enormous potential to probe the underlying physics of structure formation.Comment: 24 pages, 16 figures, submitted to Phys. Rev.
When the tale comes true: multiple populations and wide binaries in the Orion Nebula Cluster
The high-quality OmegaCAM photometry of the 3x3 deg around the Orion Nebula
Cluster (ONC) in r, and i filters by Beccari et al.(2017) revealed three
well-separated pre-main sequences in the color-magnitude diagram (CMD). The
objects belonging to the individual sequences are concentrated towards the
center of the ONC. The authors concluded that there are two competitive
scenarios: a population of unresolved binaries and triples with an exotic mass
ratio distribution, or three stellar populations with different ages. We use
Gaia DR2 in combination with the photometric OmegaCAM catalog to test and
confirm the presence of the putative three stellar populations. We also study
multiple stellar systems in the ONC for the first time using Gaia DR2. We
confirm that the second and third sequence members are more centrally
concentrated towards the center of the ONC. In addition we find an indication
that the parallax and proper motion distributions are different among the
members of the stellar sequences. The age difference among stellar populations
is estimated to be 1-2 Myr. We use Gaia measurements to identify and remove as
many unresolved multiple system candidates as possible. Nevertheless we are
still able to recover two well-separated sequences with evidence for the third
one, supporting the existence of the three stellar populations. We were able to
identify a substantial number of wide binary objects (separation between
1000-3000 au). This challenges previously inferred values that suggested no
wide binary stars exist in the ONC. Our inferred wide-binary fraction is approx
5%. We confirm the three populations correspond to three separated episodes of
star formation. Based on this result, we conclude that star formation is not
happening in a single burst in this region. (abridged)Comment: Astronomy and Astrophysics (A&A) accepted. 12 pages, 9 figures +
appendix. New version with language corrections and new ID values in Tab.A.
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