scholarly journals Measuring time delays: II. Using observations of the unresolved flux and astrometry

2021 ◽  
Author(s):  
Ofer M Springer ◽  
Eran O Ofek
Keyword(s):  
Time Delay ◽  
Measurement Errors ◽  
Time Delays ◽  
Cosmological Parameters ◽  
Power Spectra ◽  
Flux Ratio ◽  
Simulated Data ◽  
Real Data ◽  
New Method ◽  
Image Separation

Abstract Lensed quasars and supernovae can be used to study galaxies’ gravitational potential and measure cosmological parameters. The typical image separation of objects lensed by galaxies is of the order of 0.5″. Finding the ones with small separations, and measuring their time-delays using ground-based observations is challenging. We suggest a new method to identify lensed quasars and simultaneously measure their time-delays, using seeing-limited synoptic observations in which the lensed quasar images and the lensing galaxy are unresolved. We show that using the light curve of the combined flux, and the astrometric measurements of the center-of-light position of the lensed images, the lensed nature of a quasar can be identified, and its time-delay can be measured. We provide the analytic formalism to do so, taking into account the measurement errors and the fact that the power spectra of quasar light curves is red. We demonstrate our method on simulated data, while its implementation to real data will be presented in future papers. Our simulations suggest that, under reasonable assumptions, the new method has the potential to detect unresolved lensed quasars and measure their time delays, even when the image separation is about 0.2″, or the flux ratio between the faintest and brightest images is as low as 0.05. Python and MATLAB implementations are provided. In a companion paper, we present a method for measuring the time delay using the combined flux observations. This method may be useful in cases in which the astrometric information is not relevant (e.g., reverberation mapping).

scholarly journals Astrometric requirements for strong lensing time-delay cosmography

2019 ◽  
Vol 489 (2) ◽  
pp. 2097-2103 ◽  
Author(s):  
Simon Birrer ◽  
Tommaso Treu
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Direct Estimate ◽  
Strong Lensing ◽  
Image Separation ◽  
Modelling Techniques ◽  
Precision Time ◽  
Image Position

ABSTRACT The time-delay between the arrival of photons of multiple images of time-variable sources can be used to constrain absolute distances in the Universe, and in turn obtain a direct estimate of the Hubble constant and other cosmological parameters. To convert the time-delay into distances, it is well known that the gravitational potential of the main deflector and the contribution of the matter along the line of sight need to be known to a sufficient level of precision. In this paper, we discuss a new astrometric requirement that is becoming important, as time-delay cosmography improves in precision and accuracy with larger samples, and better data and modelling techniques. We derive an analytic expression for the propagation of astrometric uncertainties on the multiple image positions into the inference of the Hubble constant and derive requirements depending on image separation and relative time-delay. We note that this requirement applies equally to the image position measurements and to the accuracy of the model in reproducing them. To illustrate the requirement, we discuss some example lensing configurations and highlight that, especially for time-delays of order 10 d or shorter, the relative astrometric requirement is of order milliarcseconds, setting a tight requirement on both measurements and models. With current optical infrared technology, astrometric uncertainties may be the dominant limitation for strong lensing cosmography in the small image-separation regime when high-precision time-delays become accessible.

scholarly journals TDCOSMO

2020 ◽  
Vol 642 ◽  
pp. A194 ◽  
Author(s):  
D. Gilman ◽  
S. Birrer ◽  
T. Treu
Keyword(s):  
Dark Matter ◽  
Time Delay ◽  
Time Delays ◽  
Arrival Time ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Line Of Sight ◽  
Gravitational Lenses ◽  
Additional Source ◽  
Precision Limit

Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constant H0. The lens models used in time delay cosmography omit dark matter subhalos and line-of-sight halos because their effects are assumed to be negligible. We explicitly quantify this assumption by analyzing mock lens systems that include full populations of dark matter subhalos and line-of-sight halos, applying the same modeling assumptions used in the literature to infer H0. We base the mock lenses on six quadruply imaged quasars that have delivered measurements of the Hubble constant, and quantify the additional uncertainties and/or bias on a lens-by-lens basis. We show that omitting dark substructure does not bias inferences of H0. However, perturbations from substructure contribute an additional source of random uncertainty in the inferred value of H0 that scales as the square root of the lensing volume divided by the longest time delay. This additional source of uncertainty, for which we provide a fitting function, ranges from 0.7 − 2.4%. It may need to be incorporated in the error budget as the precision of cosmographic inferences from single lenses improves, and it sets a precision limit on inferences from single lenses.

scholarly journals Gravitational Lensing in the Clumpy Universe

1999 ◽  
Vol 183 ◽  
pp. 241-241
Author(s):  
Hideki Asada
Keyword(s):  
Time Delay ◽  
Gravitational Lensing ◽  
Cosmological Parameters ◽  
Cosmological Parameter ◽  
Accurate Estimation ◽  
Image Separation ◽  
Cosmological Tests ◽  
The Universe

Most of methods to determine the cosmological parameters by using the gravitational lensing are based on the following three typical observations; (1) the image separation, (2) the lensing statistics and (3) the time delay. For the accurate estimation of the cosmological parameter, it is of great importance to clarify the relation between the observation in the realistic universe and the determination of the cosmological parameters. In particular, it has been discussed by many authors that inhomogeneities of the universe may affect the cosmological tests.

scholarly journals Accurate cosmology from gravitational-lens time delays

2012 ◽  
Vol 8 (S289) ◽  
pp. 331-338
Author(s):  
S. H. Suyu
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Gravitational Lens ◽  
Current Status ◽  
Gravitational Lenses ◽  
Distance Measurements ◽  
One Step

AbstractThe time delays between the multiple images of a strong gravitational-lens system, together with a model of the lens-mass distribution, provide a one-step determination of the time-delay distance, and thus a measure of cosmological parameters, particularly the Hubble constant, H0. I review the recent advances in measuring time-delay distances, and present the current status of cosmological constraints based on gravitational-lens time delays. In particular, I report the time-delay distance measurements of two gravitational lenses and their implication for cosmology from a recent study by Suyuet al.

scholarly journals The redshift-space momentum power spectrum – I. Optimal estimation from peculiar velocity surveys

2019 ◽  
Vol 487 (4) ◽  
pp. 5209-5234 ◽  
Author(s):  
Cullan Howlett
Keyword(s):  
Power Spectrum ◽  
Measurement Errors ◽  
Cosmological Parameters ◽  
Power Spectra ◽  
Optimal Estimation ◽  
Peculiar Velocity ◽  
Optimal Weights ◽  
Peculiar Velocities ◽  
Redshift Surveys ◽  
The Galaxy

Abstract Low redshift surveys of galaxy peculiar velocities provide a wealth of cosmological information. We revisit the idea of extracting this information by directly measuring the redshift-space momentum power spectrum from such surveys. We provide a comprehensive theoretical and practical framework for estimating and fitting this from data, analogous to well-understood techniques used to measure the galaxy density power spectrum from redshift surveys. We formally derive a new estimator, which includes the effects of shot noise and survey geometry; we evaluate the variance of the estimator in the Gaussian regime; we compute the optimal weights for the estimator; we demonstrate that the measurements are Gaussian distributed, allowing for easy extraction of cosmological parameters; and we explore the effects of peculiar velocity (PV) measurement errors. We finish with a proof-of-concept using realistic mock galaxy catalogues, which demonstrates that we can measure and fit both the redshift-space galaxy density and momentum power spectra from PV surveys and that including the latter substantially improves our constraints on the growth rate of structure. We also provide theoretical descriptions for modelling the non-linear redshift-space density and momentum power spectrum multipoles, and forecasting the constraints on cosmological parameters using the Fisher information contained in these measurements for arbitrary weights. These may be useful for measurements of the galaxy density power spectrum even in the absence of peculiar velocities.

scholarly journals Limits between the Cosmological Parameters from Strong Lensing Observations for Generalized Isothermal Models

2009 ◽  
Vol 6 (2) ◽  
pp. 394-400
Author(s):  
Baghdad Science Journal
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Gravitational Lens ◽  
Angular Structure ◽  
Density Distributions ◽  
General Family ◽  
Strong Lensing ◽  
Elegant Form

This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time delay and by using the models of distances.

scholarly journals A New Mixed Estimator in Nonparametric Regression for Longitudinal Data

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Made Ayu Dwi Octavanny ◽  
I Nyoman Budiantara ◽  
Heri Kuswanto ◽  
Dyah Putri Rahmawati
Keyword(s):  
Longitudinal Data ◽  
Least Squares ◽  
Nonparametric Regression ◽  
Cross Validation ◽  
Weighted Least Squares ◽  
Simulated Data ◽  
Real Data ◽  
New Method ◽  
Mixed Estimator ◽  
Data Yield

We introduce a new method for estimating the nonparametric regression curve for longitudinal data. This method combines two estimators: truncated spline and Fourier series. This estimation is completed by minimizing the penalized weighted least squares and weighted least squares. This paper also provides the properties of the new mixed estimator, which are biased and linear in the observations. The best model is selected using the smallest value of generalized cross-validation. The performance of the new method is demonstrated by a simulation study with a variety of time points. Then, the proposed approach is applied to a stroke patient dataset. The results show that simulated data and real data yield consistent findings.

Evidence Evaluation for Bayesian Neural Networks Using Contour Monte Carlo

2005 ◽  
Vol 17 (6) ◽  
pp. 1385-1410 ◽  
Author(s):  
Faming Liang
Keyword(s):  
Neural Networks ◽  
Monte Carlo ◽  
Gaussian Approximation ◽  
Simulated Data ◽  
Real Data ◽  
New Method ◽  
Monte Carlo Algorithm ◽  
Multilayer Perceptrons ◽  
Nonlinear Phenomena ◽  
Bayesian Neural Networks

Bayesian neural networks play an increasingly important role in modeling and predicting nonlinear phenomena in scientific computing. In this article, we propose to use the contour Monte Carlo algorithm to evaluate evidence for Bayesian neural networks. In the new method, the evidence is dynamically learned for each of the models. Our numerical results show that the new method works well for both the regression and classification multilayer perceptrons. It often leads to an improved estimate, in terms of overall accuracy, for the evidence of multiple MLPs in comparison with the reversible-jump Markov chain Monte Carlo method and the gaussian approximation method. For the simulated data, it can identify the true models, and for the real data, it can produce results consistent with those published in the literature.

scholarly journals Constraining cosmology using galaxy position angle-only cosmic shear

2021 ◽  
Author(s):  
Lee Whittaker
Keyword(s):  
Cosmological Parameters ◽  
Power Spectra ◽  
Simulated Data ◽  
Image Data ◽  
Position Angle ◽  
Scale Factor ◽  
Weak Lensing ◽  
Measurement Information ◽  
Data Set ◽  
Shear Fields

Abstract We investigate cosmological parameter inference from realistic simulated weak lensing image data using only galaxy position angles, as opposed to full-ellipticity information. We demonstrate that input shear fields can be accurately reconstructed using only the statistics of source galaxy position angles and that, from these shear fields, we can successfully recover power spectra and infer the input cosmology. This paper builds on previous work on angle-only weak lensing estimation by extending the method to deal with variable and anisotropic point spread function (PSF) convolution and variable shear fields. Previous work employed a weighting scheme to downweight the contribution to shear estimates from sources aligned with the PSF. This work removes the need to downweight sources by convolving them with an image of the PSF rotated by 90○. We show that this successfully undoes the rotation caused by PSF convolution, assuming we have reliable images of the PSF. We find that we can accurately recover the input shear signal from simulated weak lensing data, based loosely on current Stage III missions, using only the position angles to within an overall scale factor, and that the scale factor can be determined using a cosmology independent simulation with noise, galaxy, and PSF properties that match those of the simulated data set. We then demonstrate that we can constrain cosmological parameters using angle-only shear estimates with a constraining power comparable to a basic application of IM3SHAPE, which provides full-shape measurement information.

scholarly journals Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Chun-xia Dou ◽  
Zhi-sheng Duan ◽  
Xing-bei Jia ◽  
Xiao-gang Li ◽  
Jin-zhao Yang ◽  
...  
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
Upper Bound ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Large System ◽  
Disturbance Attenuation ◽  
Robust Controller ◽  
Large Systems ◽  
Delay Dependent

A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribedH∞disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence ofH∞robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimizedH∞performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.

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