26,150 research outputs found
Robust Simulations and Significant Separations
We define and study a new notion of "robust simulations" between complexity
classes which is intermediate between the traditional notions of
infinitely-often and almost-everywhere, as well as a corresponding notion of
"significant separations". A language L has a robust simulation in a complexity
class C if there is a language in C which agrees with L on arbitrarily large
polynomial stretches of input lengths. There is a significant separation of L
from C if there is no robust simulation of L in C. The new notion of simulation
is a cleaner and more natural notion of simulation than the infinitely-often
notion. We show that various implications in complexity theory such as the
collapse of PH if NP = P and the Karp-Lipton theorem have analogues for robust
simulations. We then use these results to prove that most known separations in
complexity theory, such as hierarchy theorems, fixed polynomial circuit lower
bounds, time-space tradeoffs, and the theorems of Allender and Williams, can be
strengthened to significant separations, though in each case, an almost
everywhere separation is unknown.
Proving our results requires several new ideas, including a completely
different proof of the hierarchy theorem for non-deterministic polynomial time
than the ones previously known
On relaxation processes in collisionless mergers
We analyze N-body simulations of halo mergers to investigate the mechanisms
responsible for driving mixing in phase-space and the evolution to dynamical
equilibrium. We focus on mixing in energy and angular momentum and show that
mixing occurs in step-like fashion following pericenter passages of the halos.
This makes mixing during a merger unlike other well known mixing processes such
as phase mixing and chaotic mixing whose rates scale with local dynamical time.
We conclude that the mixing process that drives the system to equilibrium is
primarily a response to energy and angular momentum redistribution that occurs
due to impulsive tidal shocking and dynamical friction rather than a result of
chaotic mixing in a continuously changing potential. We also analyze the merger
remnants to determine the degree of mixing at various radii by monitoring
changes in radius, energy and angular momentum of particles. We confirm
previous findings that show that the majority of particles retain strong memory
of their original kinetic energies and angular momenta but do experience
changes in their potential energies owing to the tidal shocks they experience
during pericenter passages. Finally, we show that a significant fraction of
mass (~ 40%) in the merger remnant lies outside its formal virial radius and
that this matter is ejected roughly uniformly from all radii outside the inner
regions. This highlights the fact that mass, in its standard virial definition,
is not additive in mergers. We discuss the implications of these results for
our understanding of relaxation in collisionless dynamical systems.Comment: Version accepted for Publication in Astrophysical Journal, March 20,
2007, v685. Minor changes, latex, 14 figure
Close Pairs as Proxies for Galaxy Cluster Mergers
Galaxy cluster merger statistics are an important component in understanding
the formation of large-scale structure. Unfortunately, it is difficult to study
merger properties and evolution directly because the identification of cluster
mergers in observations is problematic. We use large N-body simulations to
study the statistical properties of massive halo mergers, specifically
investigating the utility of close halo pairs as proxies for mergers. We
examine the relationship between pairs and mergers for a wide range of merger
timescales, halo masses, and redshifts (0<z<1). We also quantify the utility of
pairs in measuring merger bias. While pairs at very small separations will
reliably merge, these constitute a small fraction of the total merger
population. Thus, pairs do not provide a reliable direct proxy to the total
merger population. We do find an intriguing universality in the relation
between close pairs and mergers, which in principle could allow for an estimate
of the statistical merger rate from the pair fraction within a scaled
separation, but including the effects of redshift space distortions strongly
degrades this relation. We find similar behavior for galaxy-mass halos, making
our results applicable to field galaxy mergers at high redshift. We investigate
how the halo merger rate can be statistically described by the halo mass
function via the merger kernel (coagulation), finding an interesting
environmental dependence of merging: halos within the mass resolution of our
simulations merge less efficiently in overdense environments. Specifically,
halo pairs with separations less than a few Mpc/h are more likely to merge in
underdense environments; at larger separations, pairs are more likely to merge
in overdense environments.Comment: 12 pages, 9 figures; Accepted for publication in ApJ. Significant
additions to text and two figures changed. Added new findings on the
universality of pair mergers and added analysis of the effect of FoF linking
length on halo merger
Comparing Simulations and Observations of the Lyman-Alpha Forest I. Methodology
We describe techniques for comparing spectra extracted from cosmological
simulations and observational data, using the same methodology to link
Lyman-alpha properties derived from the simulations with properties derived
from observational data. The eventual goal is to measure the coherence or
clustering properties of Lyman-alpha absorbers using observations of quasar
pairs and groups. We quantify the systematic underestimate in opacity that is
inherent in the continuum fitting process of observed spectra over a range of
resolution and signal-to-noise ratio. We present an automated process for
detecting and selecting absorption features over the range of resolution and
signal-to-noise of typical observational data on the Lyman-alpha "forest".
Using these techniques, we detect coherence over transverse scales out to 500
h^{-1}_{50} kpc in spectra extracted from a cosmological simulation at z = 2.Comment: 52 pages, includes 14 figures, to appear in ApJ v566 Feb 200
On the Clustering of Sub-millimeter Galaxies
We measure the angular two-point correlation function of sub-millimeter
galaxies (SMGs) from 1.1-millimeter imaging of the COSMOS field with the AzTEC
camera and ASTE 10-meter telescope. These data yields one of the largest
contiguous samples of SMGs to date, covering an area of 0.72 degrees^2 down to
a 1.26 mJy/beam (1-sigma) limit, including 189 (328) sources with S/N greater
than 3.5 (3). We can only set upper limits to the correlation length r_0,
modeling the correlation function as a power-law with pre-assigned slope.
Assuming existing redshift distributions, we derive 68.3% confidence level
upper limits of r_0 < 6-8 h^-1 Mpc at 3.7 mJy, and r_0 < 11-12 h^-1 Mpc at 4.2
mJy. Although consistent with most previous estimates, these upper limits imply
that the real r_0 is likely smaller. This casts doubts on the robustness of
claims that SMGs are characterized by significantly stronger spatial
clustering, (and thus larger mass), than differently selected galaxies at
high-redshift. Using Monte Carlo simulations we show that even strongly
clustered distributions of galaxies can appear unclustered when sampled with
limited sensitivity and coarse angular resolution common to current
sub-millimeter surveys. The simulations, however, also show that unclustered
distributions can appear strongly clustered under these circumstances. From the
simulations, we predict that at our survey depth, a mapped area of two
degrees^2 is needed to reconstruct the correlation function, assuming smaller
beam sizes of future surveys (e.g. the Large Millimeter Telescope's 6" beam
size). At present, robust measures of the clustering strength of bright SMGs
appear to be below the reach of most observations.Comment: 23 pages, 8 figures, accepted for publication in The Astrophysical
Journa
Not Alone: Tracing the Origins of Very Low Mass Stars and Brown Dwarfs Through Multiplicity Studies
The properties of multiple stellar systems have long provided important
empirical constraints for star formation theories, enabling (along with several
other lines of evidence) a concrete, qualitative picture of the birth and early
evolution of normal stars. At very low masses (VLM; M <~ 0.1 M_sun), down to
and below the hydrogen burning minimum mass, our understanding of formation
processes is not as clear, with several competing theories now under
consideration. One means of testing these theories is through the empirical
characterization of VLM multiple systems. Here, we review the results of
various VLM multiplicity studies to date. These systems can be generally
characterized as closely separated (93% have projected separations Delta < 20
AU) and near equal-mass (77% have M_2/M_1 >= 0.8) occurring infrequently
(perhaps 10-30%). Both the frequency and maximum separation of stellar and
brown dwarf binaries steadily decrease for lower system masses, suggesting that
VLM binary formation and/or evolution may be a mass-dependent process. There is
evidence for a fairly rapid decline in the number of loosely-bound systems
below ~0.3 M_sun, corresponding to a factor of 10-20 increase in the minimum
binding energy of VLM binaries as compared to more massive stellar binaries.
This wide-separation ``desert'' is present among both field (~1-5 Gyr) and
older (> 100 Myr) cluster systems, while the youngest (<~10 Myr) VLM binaries,
particularly those in nearby, low-density star forming regions, appear to have
somewhat different systemic properties. We compare these empirical trends to
predictions laid out by current formation theories, and outline future
observational studies needed to probe the full parameter space of the lowest
mass multiple systems.Comment: 16 pages, 7 figures, contributed chapter for Planets and Protostars V
meeting (October 2005); full table of VLM binaries can be obtained at
http://paperclip.as.arizona.edu/~nsiegler/VLM_binarie
Merger rates of double neutron stars and stellar origin black holes: The Impact of Initial Conditions on Binary Evolution Predictions
The initial mass function (IMF), binary fraction and distributions of binary
parameters (mass ratios, separations and eccentricities) are indispensable
input for simulations of stellar populations. It is often claimed that these
are poorly constrained significantly affecting evolutionary predictions.
Recently, dedicated observing campaigns provided new constraints on the initial
conditions for massive stars. Findings include a larger close binary fraction
and a stronger preference for very tight systems. We investigate the impact on
the predicted merger rates of neutron stars and black holes.
Despite the changes with previous assumptions, we only find an increase of
less than a factor 2 (insignificant compared with evolutionary uncertainties of
typically a factor 10-100). We further show that the uncertainties in the new
initial binary properties do not significantly affect (within a factor of 2)
our predictions of double compact object merger rates. An exception is the
uncertainty in IMF (variations by a factor of 6 up and down). No significant
changes in the distributions of final component masses, mass ratios, chirp
masses and delay times are found.
We conclude that the predictions are, for practical purposes, robust against
uncertainties in the initial conditions concerning binary parameters with
exception of the IMF. This eliminates an important layer of the many uncertain
assumptions affecting the predictions of merger detection rates with the
gravitational wave detectors aLIGO/aVirgo.Comment: Accepted for publication in Ap
The Formation of Low-Mass Binary Star Systems Via Turbulent Fragmentation
We characterize the infall rate onto protostellar systems forming in
self-gravitating radiation-hydrodynamic simulations. Using two dimensionless
parameters to determine disks' susceptability to gravitational fragmentation,
we infer limits on protostellar system multiplicity and the mechanism of binary
formation. We show that these parameters give robust predictions even in the
case of marginally resolved protostellar disks. We find that protostellar
systems with radiation feedback predominately form binaries via turbulent
fragmentation, not disk instability, and we predict turbulent fragmentation is
the dominant channel for binary formation for low-mass stars. We clearly
demonstrate that systems forming in simulations including radiative feedback
have fundamentally different parameters than those in purely hydrodynamic
simulations.Comment: 11 pages, 10 figures, accepted to Ap
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