Tailoring - PowerPoint Presentation

Slide1

Tailoring Strong Lensing Cosmographic Observations

Eric V. Linder (

arXiv

: 1502.01353v1)Slide2

ContentsIntroductionMeasuring time delay distancesOptimizing Spectroscopic

followup

Influence of systematics

R

edshift distribution revisited

Model systematics

ConclusionSlide3

I. IntroductionWhat is the ‘Cosmography’?The science that maps the general features of the cosmos or universe, describing both heaven and Earthbeginning to be used to describe attempts to determine the large-scale

geometry and kinematics of the observable universe, independent of any specific cosmological theory or modelSlide4

1. Introduction – CosmographyDistance – redshift relationsType Ia

supernova luminosity distance - redshift relation

The cosmic microwave background radiation anisotropies/ baryon acoustic oscillations in galaxy clustering

Cosmic redshift drift

The strong

gravitational

lensing

time delay

distance - redshift

relation

(1964,

Refsdal

)Slide5

1. Introduction Strong lensing distanceWhy interesting?unlike the standard distance-redshift relations the measured time delay is a

dimensionful

quantity

the

time delay distance is comprised of the ratio of three

distances

sensitive

to the Hubble constant

H0

the

time delay distance has an unusual

dependence

on dark energy properties and has high

complementarity

with the usual distance probes

On-going & future surveys:

DES, LSST, Euclid, WFIRSTSlide6

1. IntroductionTwo aspects of implementation of time delay distances into surveysOptimization of spectroscopic resourcesThe role of systematicsSlide7

II. Measuring time delay distancesTime delay between two images of the source come from:The geometric path difference of the light propagation

The differing gravitational potential experienced

The time delay distance:

Δt

: the observed time delay

Δϕ

: the potential difference modeled from the observations such as image position, fluxes, surface brightnessSlide8

II. Measuring time delay distancesThe time delay distance:(surveys: DES, LSST, Euclid, WFIRST)

Δt

: the observed time delay

By monitoring the image fluxes over several years

Δ

ϕ

: the potential difference modeled from the observations such as image position, fluxes, surface brightness

constrained by the rich data of the images (HST, JWST)

lens mass modeling : galaxy velocity dispersion by through spectroscopy

Redshift of lens and sources : spectroscopySlide9

II. Measuring time delay distancesFor Δt

and

Δϕ

,

These essential

followup

must be sought in order to derive the strong lensing cosmological constraints from the wide field imaging survey (limitation on telescope time)

The optimization of cosmological

leverage

given a finite

followup

resources

Combine the strong

lesing

distances with CMB and supernovae distances to break degeneracies between parametersSlide10

II. Measuring time delay distancesEtc.Combine the strong

lesing

distances with CMB and supernovae distances to break degeneracies between parameters

Adopt a Planck quality constraint on the distance to last scattering (0.2%) and physical matter density (0.9%)

For supernovae, use a sample of the quality expected from ground based surveys

Perform a Fisher information analysis for (

Ωm

, w0,

wa

, h, Μ) with flat LCMD cosmologySlide11

III. Optimizing Spectroscopic FollowupSpectroscopic time is restricted

Optimization: maximize the cosmological leverage of the measured time delay distance given the constraint, fixed this (= limited source)

by examining the impact of sculpting the redshift distribution of the lenses to be followed up

especially, fix the spectroscopic time

for the sample of lenses

whose redshift or galaxy velocity dispersion are to be measured

with fixed signal-to-noiseSlide12

III. Optimizing Spectroscopic FollowupSpectroscopic time for lenses is restricted

fixed signal-to-noise

gives

Spectroscopic exposure time becomes increasingly expensive with redshift as roughly (1+z)^6

However, as exposure time gets smaller, other noise contributions enter as well as overheads (telescope slewing and detector readout time)Slide13

III. Optimizing Spectroscopic FollowupSpectroscopic time for lenses is restricted

Optimizing

procesure

Fix signal-to-noise to obtain constraint on the exposure time,

t_exp

Choose the quantity to optimize: dark energy figure of merit (FOM),

the area of a confidence contour in the dark energy equation of state plane, marginalized over all other parameters.

To optimize the redshift distribution, begin with a

uniform distribution in lens redshiftSlide14

III. Optimizing Spectroscopic FollowupSpectroscopic time for lenses is restricted

Optimizing

procesure

Fix signal-to-noise to obtain constraint on the exposure time,

t_exp

Choose the quantity to optimize: dark energy figure of merit (FOM)

To optimize the redshift distribution, begin with a

uniform distribution in lens redshift

Take 25 time delay systems of 5% precision in each bin of redshift width

dz

= 0.1 over the range z = 0.1~0.7, for a total of 150 systems

(fixed resource constraint, total spectroscopic time)Slide15

III. Optimizing Spectroscopic FollowupSpectroscopic time for lenses is restricted

Optimizing

procesure

F

ixe signal-to-noise to obtain constraint on the exposure time,

t_exp

Choose the quantity to optimize: dark energy figure of merit (FOM)

B

egin with a

uniform distribution in lens redshift

Perturb the initial uniform distribution by one system in each bin, one at a time (conserve the resources)

C

alculate resulting FOM

Iterate the last two processes

Round the numbers in each bin to the nearest integerSlide16

III. Optimizing Spectroscopic Followup

Optimization increases the FOM by almost 40%, keeping the spectroscopic time fixed.

Optimized

redshift dist.

Heavily weighted toward low redshift (less time burden)

The higher redshift bin is needed, but it does not seek to maximize the range by taking the highest bin (greatest time burden)

FOM becomes improved

Parameter estimationSlide17

IV. Influence of SystematicsDealing with systematic uncertaintiesInvestigate two impact of systematicsRedshift distribution revisited

Model systematicsSlide18

IV. Influence of SystematicsA. Redshift distribution revisitedThe effect of various levels of systematic uncertainties on the optimization in III.

On the optimized redshift distribution and the resulting cosmological parameter estimation.

Implementation of the systematic as a floor, added in quadrature to the statistical uncertainty:

ni

: the number in redshift bin

iSlide19

IV. Influence of SystematicsA. Redshift distribution revisited

O

ptimized lens redshift distribution, subject to resource constraint, for

different levels of systematicsSlide20

IV. Influence of SystematicsA. Redshift distribution revisitedOptimized lens redshift distribution, subject to resource constraint, for

different levels of systematicsSlide21

IV. Influence of SystematicsA. Redshift distribution revisitedOptimized lens redshift distribution, subject to resource constraint, for

different levels of systematics

reduced

hubble

constant, hSlide22

V. ConclusionThe strong gravitational lensing time delay distance – redshift relation : a geometric probe of cosmologyBeing dimensionful and hence sensitive to the Hubble constant, H0Being a triple distance ratio and hence highly complementary to other distance probesSlide23

V. ConclusionThe strong gravitational lensing time delay distance – redshift relation : a geometric probe of cosmologyOptimization of the lens system redshift distribution to give maximal cosmology leverage, given followup

resources do improve the result (FOM, parameter estimation,

etc

)