1,842 research outputs found
Lensing and high-z supernova surveys
Gravitational lensing causes the distribution of observed brightnesses of
standard candles at a given redshift to be highly non-gaussian. The
distribution is strongly, and asymmetrically, peaked at a value less than the
expected value in a homogeneous Robertson-Walker universe. Therefore, given any
small sample of observations in an inhomogeneous universe, the most likely
observed luminosity is at flux values less than the Robertson-Walker value.
This paper explores the impact of this systematic error due to lensing upon
surveys predicated on measuring standard candle brightnesses. We re-analyze
recent results from the high-z supernova team (Riess et al. 1998), both when
most of the matter in the universe is in the form of compact objects
(represented by the empty-beam expression, corresponding to the maximal case of
lensing), and when the matter is continuously distributed in galaxies. We find
that the best-fit model remains unchanged (at Omega_m=0, Omega_Lambda=0.45),
but the confidence contours change size and shape, becoming larger (and thus
allowing a broader range of parameter space) and dropping towards higher values
of matter density, Omega_m (or correspondingly, lower values of the
cosmological constant, Omega_Lambda). These effects are slight when the matter
is continuously distributed. However, the effects become considerably more
important if most of the matter is in compact objects. For example, neglecting
lensing, the Omega_m=0.5, Omega_Lambda=0.5 model is more than 2 sigma away from
the best fit. In the empty-beam analysis, this cosmology is at 1 sigma.Comment: 11 pages, 3 ps figures. uses aaspp4.sty. accepted to ApJ Letters.
includes analysis of lensing due to matter continuously distributed in
galaxie
Localizing coalescing massive black hole binaries with gravitational waves
Massive black hole binary coalescences are prime targets for space-based
gravitational wave (GW) observatories such as {\it LISA}. GW measurements can
localize the position of a coalescing binary on the sky to an ellipse with a
major axis of a few tens of arcminutes to a few degrees, depending on source
redshift, and a minor axis which is times smaller. Neglecting weak
gravitational lensing, the GWs would also determine the source's luminosity
distance to better than percent accuracy for close sources, degrading to
several percent for more distant sources. Weak lensing cannot, in fact, be
neglected and is expected to limit the accuracy with which distances can be
fixed to errors no less than a few percent. Assuming a well-measured cosmology,
the source's redshift could be inferred with similar accuracy. GWs alone can
thus pinpoint a binary to a three-dimensional ``pixel'' which can help guide
searches for the hosts of these events. We examine the time evolution of this
pixel, studying it at merger and at several intervals before merger. One day
before merger, the major axis of the error ellipse is typically larger than its
final value by a factor of . The minor axis is larger by a factor
of , and, neglecting lensing, the error in the luminosity distance is
larger by a factor of . This large change over a short period of
time is due to spin-induced precession, which is strongest in the final days
before merger. The evolution is slower as we go back further in time. For , we find that GWs will localize a coalescing binary to within $\sim 10\
\mathrm{deg}^2$ as early as a month prior to merger and determine distance (and
hence redshift) to several percent.Comment: 30 pages, 10 figures, 5 tables. Version published in Ap
Cosmology from supernova magnification maps
High-z Type Ia supernovae are expected to be gravitationally lensed by the
foreground distribution of large-scale structure. The resulting magnification
of supernovae is statistically measurable, and the angular correlation of the
magnification pattern directly probes the integrated mass density along the
line of sight. Measurements of cosmic magnification of supernovae therefore
complements galaxy shear measurements in providing a direct measure of
clustering of the dark matter. As the number of supernovae is typically much
smaller than the number of sheared galaxies, the two-point correlation function
of lensed Type Ia supernovae suffers from significantly increased shot noise.
Neverthless, we find that the magnification map of a large sample of
supernovae, such as that expected from next generation dedicated searches, will
be easily measurable and provide an important cosmological tool. For example, a
search over 20 sq. deg. over five years leading to a sample of ~ 10,000
supernovae would measure the angular power spectrum of cosmic magnification
with a cumulative signal-to-noise ratio of ~20. This detection can be further
improved once the supernova distance measurements are cross-correlated with
measurements of the foreground galaxy distribution. The magnification maps made
using supernovae can be used for important cross-checks with traditional
lensing shear statistics obtained in the same fields, as well as help to
control systematics. We discuss two applications of supernova magnification
maps: the breaking of the mass-sheet degeneracy when estimating masses of
shear-detected clusters, and constraining the second-order corrections to weak
lensing observables.Comment: 4 pages, 2 figures, ApJL submitted; "Signal" discussed here is the
extra covariance in astro-ph/050958
Problems with Pencils: Lensing Covariance of Supernova Distance Measurements
While luminosity distances from Type Ia supernovae (SNe) provide a powerful
probe of cosmological parameters, the accuracy with which these distances can
be measured is limited by cosmic magnification due to gravitational lensing by
the intervening large-scale structure. Spatial clustering of foreground mass
fluctuations leads to correlated errors in distance estimates from SNe. By
including the full covariance matrix of supernova distance measurements, we
show that a future survey covering more than a few square degrees on the sky,
and assuming a total of ~2000 SNe, will be largely unaffected by covariance
noise. ``Pencil beam'' surveys with small fields of view, however, will be
prone to the lensing covariance, leading to potentially significant
degradations in cosmological parameter estimates. For a survey with 30 arcmin
mean separation between SNe, lensing covariance leads to a ~45% increase in the
expected errors in dark energy parameters compared to fully neglecting lensing,
and a ~20% increase compared to including just the lensing variance. Given that
the lensing covariance is cosmology dependent and cannot be mapped out
sufficiently accurately with direct weak lensing observations, surveys with
small mean SN separation must incorporate the effects of lensing covariance,
including its dependence on the cosmological parameters.Comment: 4 pages, 2 figures, PRL submitted; "Noise" discussed here is the
"signal" in astro-ph/050957
Model-Independent Constraints on Dark Energy Density from Flux-averaging Analysis of Type Ia Supernova Data
We reconstruct the dark energy density as a free function from
current type Ia supernova (SN Ia) data (Tonry et al. 2003; Barris et al. 2003;
Knop et al. 2003), together with the Cosmic Microwave Background (CMB) shift
parameter from CMB data (WMAP, CBI, and ACBAR), and the large scale structure
(LSS) growth factor from 2dF galaxy survey data. We parametrize as
a continuous function, given by interpolating its amplitudes at equally spaced
values in the redshift range covered by SN Ia data, and a constant at
larger (where is only weakly constrained by CMB data). We
assume a flat universe, and use the Markov Chain Monte Carlo (MCMC) technique
in our analysis. We find that the dark energy density is constant
for 0 \la z \la 0.5 and increases with redshift for 0.5 \la z \la 1 at
68.3% confidence level, but is consistent with a constant at 95% confidence
level. For comparison, we also give constraints on a constant equation of state
for the dark energy.
Flux-averaging of SN Ia data is required to yield cosmological parameter
constraints that are free of the bias induced by weak gravitational lensing
\citep{Wang00b}. We set up a consistent framework for flux-averaging analysis
of SN Ia data, based on \cite{Wang00b}. We find that flux-averaging of SN Ia
data leads to slightly lower and smaller time-variation in
. This suggests that a significant increase in the number of SNe Ia
from deep SN surveys on a dedicated telescope \citep{Wang00a} is needed to
place a robust constraint on the time-dependence of the dark energy density.Comment: Slightly revised in presentation, ApJ accepted. One color figure
shows rho_X(z) reconstructed from dat
Lensing and Supernovae: Quantifying The Bias on the Dark Energy Equation of State
The gravitational magnification and demagnification of Type Ia supernovae
(SNe) modify their positions on the Hubble diagram, shifting the distance
estimates from the underlying luminosity-distance relation. This can introduce
a systematic uncertainty in the dark energy equation of state (EOS) estimated
from SNe, although this systematic is expected to average away for sufficiently
large data sets. Using mock SN samples over the redshift range
we quantify the lensing bias. We find that the bias on the dark energy EOS is
less than half a percent for large datasets ( 2,000 SNe). However, if
highly magnified events (SNe deviating by more than 2.5) are
systematically removed from the analysis, the bias increases to 0.8%.
Given that the EOS parameters measured from such a sample have a 1
uncertainty of 10%, the systematic bias related to lensing in SN data out to can be safely ignored in future cosmological measurements.Comment: 5 pages, 4 figures; one figure and references added; minor
modifications to text; reflects version accepted for publication in Ap
Future Type Ia Supernova Data as Tests of Dark Energy from Modified Friedmann Equations
In the Cardassian model, dark energy density arises from modifications to the
Friedmann equation, which becomes H^2 = g(\rhom), where g(\rhom) is a new
function of the energy density. The universe is flat, matter dominated, and
accelerating. The distance redshift relation predictions of generalized
Cardassian models can be very different from generic quintessence models, and
can be differentiated with data from upcoming pencil beam surveys of Type Ia
Supernovae such as SNAP. We have found the interesting result that, once
is known to 10% accuracy, SNAP will be able to determine the sign of
the time dependence of the dark energy density. Knowledge of this sign (which
is related to the weak energy condition) will provide a first discrimination
between various cosmological models that fit the current observational data
(cosmological constant, quintessence, Cardassian expansion). Further, we have
performed Monte Carlo simulations to illustrate how well one can reproduce the
form of the dark energy density with SNAP.
To be concrete we study a class of two parameter (,) generalized
Cardassian models that includes the original Cardassian model (parametrized by
only) as a special case. Examples are given of MP Cardassian models that
fit current supernovae and CMB data, and prospects for differentiating between
MP Cardassian and other models in future data are discussed. We also note that
some Cardassian models can satisfy the weak energy condition even with a
dark energy component that has an effective equation of state .Comment: revised version accepted by Ap
Reduced convergence and the local smoothness parameter: bridging two different descriptions of weak lensing amplification
Weak gravitational lensing due to the inhomogeneous matter distribution in
the universe is an important systematic uncertainty in the use of standard
candles in cosmology. There are two different descriptions of weak lensing
amplification, one uses a local smoothness parameter , the
other uses reduced convergence (where
is convergence). The description involves Dyer-Roeder distance
( corresponds to a smooth universe);
it is simple and convenient, and has been used by the community to illustrate
the effect of weak lensing on point sources such as type Ia supernovae. Wang
(1999) has shown that the description can be made realistic by
allowing to be a local variable, the local smoothness
parameter. The description has been used by Wang, Holz, & Munshi (2002)
to derive a universal probability distribution (UPDF) for weak lensing
amplification. In this paper, we bridge the two different descriptions of weak
lensing amplification by relating the reduced convergence and the local
smoothness parameter . We give the variance of
in terms of the matter power spectrum, thus providing a quantitative guidance
to the use of Dyer-Roeder distances in illustrating the effect of weak lensing.
The by-products of this work include a corrected definition of the reduced
convergence, and simple and accurate analytical expressions for
. Our results should be very useful in studying the weak
lensing of standard candles.Comment: Revised and expanded version. ApJ accepte
Large-Scale Bulk Motions Complicate the Hubble Diagram
We investigate the extent to which correlated distortions of the luminosity
distance-redshift relation due to large-scale bulk flows limit the precision
with which cosmological parameters can be measured. In particular, peculiar
velocities of type 1a supernovae at low redshifts may prevent a sufficient
calibration of the Hubble diagram necessary to measure the dark energy equation
of state to better than 10%, and diminish the resolution of the equation of
state time-derivative projected for planned surveys. We consider similar
distortions of the angular-diameter distance, as well as the Hubble constant.
We show that the measurement of correlations in the large-scale bulk flow at
low redshifts using these distance indicators may be possible with a cumulative
signal-to-noise ratio of order 7 in a survey of 300 type 1a supernovae spread
over 20,000 square degrees.Comment: 6 pages; 4 figure
A new measure of using the lensing dispersion in high- type Ia SNe
The gravitational lensing magnification or demagnification due to large-scale
structures induces a scatter in peak magnitudes of high redshift type Ia
supernovae (SNe Ia). The amplitude of the lensing dispersion strongly depends
on that of density fluctuations characterized by the parameter.
Therefore the value of is constrained by measuring the dispersion in
the peak magnitudes. We examine how well SN Ia data will provide a constraint
on the value of using a likelihood analysis method. It is found that
the number and quality of SN Ia data needed for placing a useful constraint on
is attainable with Next Generation Space Telescope.Comment: 9 pages, 3 figures. Accepted for publication in The Astrophysical
Journa
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