1,721 research outputs found
On the inspiral of Massive Black Holes in gas-rich galaxy mergers
We present a study on the dynamics of massive BHs in galaxy mergers, obtained
from a series of high-resolution N-Body/SPH simulations. The presence of a
gaseous component is essential for the rapid formation of an eccentric
(Keplerian) BH binary, that resides at the center of a massive (~10^9 Msun)
turbulent nuclear disc. Using physically and/or numerically motivated recipes,
we follow the accretion history of the BHs during the merger. The mass of the
BHs increases as large central inflows of gas occur inside each galaxy, and
their mass ratio varies with time. Given the encountered strong degeneracy
between numerical resolution and physical assumptions, we suggest here three
possible paths followed by the galaxies and the BHs during a merger in order to
fulfill the M-sigma relation : Adjustment, Symbiosis, and BH Dominance. In an
extremely high resolution run, we resolved the turbulent gas pattern down to
parsec scales, and found that BH feedback is expected to be effective near the
end of the merger. We then trace the BH binary orbit down to a scale of 0.1 pc
modeling the nuclear disc as an equilibrium Mestel disc composed either of gas,
gas and stars, or just stars. Under the action of dynamical friction against
the rotating gaseous and/or stellar background the orbit circularizes. When
this occurs, each BH is endowed with its own small-size (~0.01 pc) accretion
disc comprising a few percent of the BH mass. Double AGN activity is expected
to occur on an estimated timescale of ~10 Myrs, comparable to the inspiral
time. The double nuclear point--like sources that may appear have typical
separations of ~10 pc, and are likely to be embedded in the still ongoing
starburst.Comment: 10 pages, 5 figures, Proceedings of the Conference "The Multicoloured
Landscape of Compact Objects and their Explosive Origins", Cefalu` 200
Birth of massive black hole binaries
If massive black holes (BHs) are ubiquitous in galaxies and galaxies
experience multiple mergers during their cosmic assembly, then BH binaries
should be common albeit temporary features of most galactic bulges.
Observationally, the paucity of active BH pairs points toward binary lifetimes
far shorter than the Hubble time, indicating rapid inspiral of the BHs down to
the domain where gravitational waves lead to their coalescence. Here, we review
a series of studies on the dynamics of massive BHs in gas-rich galaxy mergers
that underscore the vital role played by a cool, gaseous component in promoting
the rapid formation of the BH binary. The BH binary is found to reside at the
center of a massive self-gravitating nuclear disc resulting from the collision
of the two gaseous discs present in the mother galaxies. Hardening by
gravitational torques against gas in this grand disc is found to continue down
to sub-parsec scales. The eccentricity decreases with time to zero and when the
binary is circular, accretion sets in around the two BHs. When this occurs,
each BH is endowed with it own small-size (< 0.01 pc) accretion disc comprising
a few percent of the BH mass. Double AGN activity is expected to occur on an
estimated timescale of < 1 Myr. The double nuclear point-like sources that may
appear have typical separation of < 10 pc, and are likely to be embedded in the
still ongoing starburst. We note that a potential threat of binary stalling, in
a gaseous environment, may come from radiation and/or mechanical energy
injections by the BHs. Only short-lived or sub-Eddington accretion episodes can
guarantee the persistence of a dense cool gas structure around the binary
necessary for continuing BH inspiral.Comment: To appear in "2007 STScI Spring Symposium: Black Holes", eds. M.
Livio & A. M. Koekemoer, Cambridge University Press, 25 pages, 12 figure
The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity
The coupled equations for the scalar modes of the linearized Einstein
equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1
wave equation with a potential , on a field . For smooth metric
perturbations is singular at , the
mode harmonic number, and has a second order pole at . This is
irrelevant to the black hole exterior stability problem, where , and
, but it introduces a non trivial problem in the naked singular case
where , and the singularity appears in the relevant range of
. We solve this problem by developing a new approach to the evolution of the
even mode, based on a {\em new gauge invariant function}, -related
to by an intertwiner operator- that is a regular function of the
metric perturbation {\em for any value of }. This allows to address the
issue of evolution of gravitational perturbations in this non globally
hyperbolic background, and to complete the proof of the linear instability of
the Schwarzschild naked singularity, by showing that a previously found
unstable mode is excitable by generic initial data. This is further illustrated
by numerically solving the linearized equations for suitably chosen initial
data.Comment: typos corrected, references adde
Unstable fields in Kerr spacetimes
We show that both the interior region of a Kerr black
hole and the Kerr naked singularity admit unstable solutions of the
Teukolsky equation for any value of the spin weight. For every harmonic number
there is at least one axially symmetric mode that grows exponentially in time
and decays properly in the radial directions. These can be used as Debye
potentials to generate solutions for the scalar, Weyl spinor, Maxwell and
linearized gravity field equations on these backgrounds, satisfying appropriate
spatial boundary conditions and growing exponentially in time, as shown in
detail for the Maxwell case. It is suggested that the existence of the unstable
modes is related to the so called "time machine" region, where the axial
Killing vector field is time-like, and the Teukolsky equation, restricted to
axially symmetric fields, changes its character from hyperbolic to elliptic
On the orientation and magnitude of the black hole spin in galactic nuclei
Massive black holes in galactic nuclei vary their mass M and spin vector J
due to accretion. In this study we relax, for the first time, the assumption
that accretion can be either chaotic, i.e. when the accretion episodes are
randomly and isotropically oriented, or coherent, i.e. when they occur all in a
preferred plane. Instead, we consider different degrees of anisotropy in the
fueling, never confining to accretion events on a fixed direction. We follow
the black hole growth evolving contemporarily mass, spin modulus a and spin
direction. We discover the occurrence of two regimes. An early phase (M <~ 10
million solar masses) in which rapid alignment of the black hole spin direction
to the disk angular momentum in each single episode leads to erratic changes in
the black hole spin orientation and at the same time to large spins (a ~ 0.8).
A second phase starts when the black hole mass increases above >~ 10 million
solar masses and the accretion disks carry less mass and angular momentum
relatively to the hole. In the absence of a preferential direction the black
holes tend to spin-down in this phase. However, when a modest degree of
anisotropy in the fueling process (still far from being coherent) is present,
the black hole spin can increase up to a ~ 1 for very massive black holes (M >~
100 million solar masses), and its direction is stable over the many accretion
cycles. We discuss the implications that our results have in the realm of the
observations of black hole spin and jet orientations.Comment: 14 pages, 7 figures, accepted for publication in Ap
The Effects of Class Size on Student Performance in Reading in the Primary Grades
The purpose of this study was to examine the effect of class size on reading achievement of primary grade students in the Bismarck (North Dakota) Public Schools. Data for the study included using scores from the Gates-MacGinitie Reading Test (Fourth Edition). The results on the Gates-MacGinitie Reading Test were analyzed according to grade, gender, socioeconomic status, race, and class size. Students in the study were identified as having been in either small classes (17 or less) or large classes (22 or more). Three years of data (1999–2002) were analyzed as part of the small class study. A second source of data was gathered from a teacher survey instrument that was distributed to all teachers employed by the Bismarck Public Schools for the 2001–2002 school year who taught in classrooms identified as small or large. This survey measures teachers\u27 perceptions regarding instructional practices, classroom management, and time allotment.
Results indicated that there was no significant difference in reading achievement scores of first grade, second grade, or third grade students who were placed in small compared to large classrooms. There was a significant difference in female students\u27 reading achievement when they were placed in small sized classrooms. When the achievement of Native American students was compared to Caucasian students, there was a significant different in reading achievement scores by Caucasian students in small sized classrooms. There was also a significant difference in reading achievement scores by students not on free-reduced meal plans. Consequently, this study does not suggest that small class size is an equalizer for Native American students, males, or students who are economically disadvantaged. The major finding from the teacher survey showed that teachers in large sized classrooms had more current professional development on reading strategies, which may have contributed to the class size achievement showing no significance when in small sized classrooms. By using analysis of variance (ANOVA), the study found that the following items were significantly different when teachers in small sized and large sized classrooms were compared: teaching leans toward students as individuals rather than towards the class in general (.016), time spent on disciplining the class (.008), time working with small groups (.041), time spent with students one on one (.017), time spent working with students on special projects (.004), and time spent developing creative projects for the class (.008)
Nonmodal linear stability of the Schwarzschild black hole
A proof is given that the space L of solutions of the linearized vacuum Einstein equation around a Schwarzschild black hole is parametrized by two scalar fields, which are gauge invariant combinations of perturbed algebraic and differential invariants of the Weyl tensor and encode the information on the odd (−) and even (+) sectors L. These fields measure the distortion of the geometry caused by a generic perturbation and are shown to be pointwise bounded on the outer region r ≥ 2M.publishedVersionFil: Dotti, Gustavo Daniel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Dotti, Gustavo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física Enrique Gaviola; Argentina.Física de Partículas y Campo
Hyperk\"ahler torsion structures invariant by nilpotent Lie groups
We study HKT structures on nilpotent Lie groups and on associated
nilmanifolds. We exhibit three weak HKT structures on which are
homogeneous with respect to extensions of Heisenberg type Lie groups. The
corresponding hypercomplex structures are of a special kind, called abelian. We
prove that on any 2-step nilpotent Lie group all invariant HKT structures arise
from abelian hypercomplex structures. Furthermore, we use a correspondence
between abelian hypercomplex structures and subspaces of to
produce continuous families of compact and noncompact of manifolds carrying non
isometric HKT structures. Finally, geometrical properties of invariant HKT
structures on 2-step nilpotent Lie groups are obtained.Comment: LateX, 12 page
Maternal employment : enabling factors in context
Maternal employment is still below the overall EU recommended level of 60% in many European
countries. Understanding the individual, household and contextual circumstances under which
mothers of children of different ages are likely to be employed is crucial to develop strategies
capable of increasing maternal employment. This article takes a comparative approach to
investigating the characteristics associated with maternal employment in the presence of children
aged 0\u20132, 3\u20135, 6\u20139 and 10\u201312 years. We model the probability of being employed full-time, parttime
or being a homemaker using EU-SILC data (2004 to 2007) from Germany, Italy, Norway
and the United Kingdom \u2013 four countries belonging to different gender and welfare regimes. The
results indicate that individual and household characteristics are more relevant in determining
mothers\u2019 employment in countries where the state is less supportive towards maternal
employment: Italy and to a lesser extent Germany and the UK \u2013 for the period observed
Instability of the negative mass Schwarzschild naked singularity
We study the negative mass Schwarzschild spacetime, which has a naked
singularity, and show that it is perturbatively unstable. This is achieved by
first introducing a modification of the well known Regge - Wheeler - Zerilli
approach to black hole perturbations to allow for the presence of a
``kinematic'' singularity that arises for negative masses, and then exhibiting
exact exponentially growing solutions to the linearized Einstein's equations.
The perturbations are smooth everywhere and behave nicely around the
singularity and at infinity. In particular, the first order variation of the
scalar invariants can be made everywhere arbitrarily small as compared to the
zeroth order terms. Our approach is also compared to a recent analysis that
leads to a different conclusion regarding the stability of the negative mass
Schwarzschild spacetime. We also comment on the relevance of our results to the
stability of more general negative mass, nakedly singular spacetimes.Comment: 15 page
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