Tailoring Strong Lensing Cosmography Observations

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Eric V. Linder (arXiv: 1502.01353v1)
 
Contents
 
I.
Introduction
II.
Measuring time delay distances
III.
Optimizing Spectroscopic followup
IV.
Influence of systematics
A.
Redshift distribution revisited
B.
Model systematics
V.
Conclusion
 
 I. Introduction
 
What is the ‘Cosmography’?
The science that maps the general features
of the cosmos or universe, describing both
heaven and Earth
beginning 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 model
 
1. Introduction – Cosmography
Distance – redshift relations
 
Type 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)
 
1. Introduction
Strong lensing distance
 
Why 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, WFIRST
 
1. Introduction
 
Two aspects of implementation of time
delay distances into surveys
1.
Optimization of spectroscopic resources
2.
The role of systematics
 
II. Measuring time delay distances
 
Time 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 brightness
 
II. Measuring time delay distances
 
The 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 : spectroscopy
 
II. Measuring time delay distances
 
For 
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 parameters
 
II. Measuring time delay distances
 
Etc.
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
cosmology
 
III. Optimizing Spectroscopic Followup
 
Spectroscopic 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-noise
 
III. Optimizing Spectroscopic Followup
 
Spectroscopic 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)
 
III. Optimizing Spectroscopic Followup
 
Spectroscopic 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 redshift
 
III. Optimizing Spectroscopic Followup
 
Spectroscopic 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)
 
III. Optimizing Spectroscopic Followup
 
Spectroscopic time for lenses is 
restricted
Optimizing procesure
Fixe signal-to-noise to obtain constraint on the
exposure time, t_exp
Choose the quantity to optimize: dark energy figure
of merit (FOM)
Begin 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)
Calculate resulting FOM
Iterate the last two processes
Round the numbers in each bin to the nearest
integer
 
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 estimation
 
IV. Influence of Systematics
 
Dealing with systematic uncertainties
Investigate two impact of systematics
A.
Redshift distribution revisited
B.
Model systematics
 
IV. Influence of Systematics
A. Redshift distribution revisited
 
The 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 i
 
IV. Influence of Systematics
A. Redshift distribution revisited
 
Optimized lens
redshift distribution,
subject to resource
constraint, for
different levels of
systematics
 
IV. Influence of Systematics
A. Redshift distribution revisited
 
Optimized lens
redshift distribution,
subject to resource
constraint, for
different levels of
systematics
 
IV. Influence of Systematics
A. Redshift distribution revisited
 
Optimized lens
redshift distribution,
subject to resource
constraint, for
different levels of
systematics
 
reduced hubble
constant, h
 
V. Conclusion
 
The strong gravitational lensing time
delay distance – redshift relation : a
geometric probe of cosmology
Being dimensionful and hence sensitive to
the Hubble constant, H0
Being a triple distance ratio and hence
highly complementary to other distance
probes
 
V. Conclusion
 
The strong gravitational lensing time
delay distance – redshift relation : a
geometric probe of cosmology
 
Optimization of the lens system redshift
distribution to give maximal cosmology
leverage, given followup resources do
improve the result (FOM, parameter
estimation, etc)
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The exploration of cosmography involves mapping the general features of the universe to understand its large-scale geometry and kinematics. This study delves into measuring time delay distances, optimizing spectroscopic follow-up, and addressing systematics such as redshift distribution and model systematics in strong gravitational lensing. The time delay distance, a crucial aspect, is influenced by dark energy properties and complements traditional distance probes, making it an intriguing area for research and observations.

  • Cosmography
  • Time delay distances
  • Strong lensing
  • Dark energy
  • Observations

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  1. Eric V. Linder (arXiv: 1502.01353v1) Tailoring Tailoring Strong Lensing Cosmographic Strong Lensing Cosmographic Observations Observations

  2. Contents Introduction I. II. Measuring time delay distances III. Optimizing Spectroscopic followup IV. Influence of systematics A. Redshift distribution revisited B. Model systematics V. Conclusion

  3. I. Introduction What is the Cosmography ? The science that maps the general features of the cosmos or universe, describing both heaven and Earth beginning 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 model

  4. 1. Introduction Cosmography Distance redshift relations Type 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)

  5. 1. Introduction Strong lensing distance Why 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, WFIRST

  6. 1. Introduction Two aspects of implementation of time delay distances into surveys 1. Optimization of spectroscopic resources 2. The role of systematics

  7. II. Measuring time delay distances Time 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: t : the observed time delay : the potential difference modeled from the observations such as image position, fluxes, surface brightness

  8. II. Measuring time delay distances The time delay distance: (surveys: DES, LSST, Euclid, WFIRST) t : the observed time delay By monitoring the image fluxes over several years : 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 : spectroscopy

  9. II. Measuring time delay distances For t and , 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 parameters

  10. II. Measuring time delay distances Etc. 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 ( m, w0, wa, h, ) with flat LCMD cosmology

  11. III. Optimizing Spectroscopic Followup Spectroscopic 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-noise

  12. III. Optimizing Spectroscopic Followup Spectroscopic 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)

  13. III. Optimizing Spectroscopic Followup Spectroscopic 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 redshift

  14. III. Optimizing Spectroscopic Followup Spectroscopic 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)

  15. III. Optimizing Spectroscopic Followup Spectroscopic time for lenses is restricted Optimizing procesure Fixe signal-to-noise to obtain constraint on the exposure time, t_exp Choose the quantity to optimize: dark energy figure of merit (FOM) Begin 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) Calculate resulting FOM Iterate the last two processes Round the numbers in each bin to the nearest integer

  16. 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 estimation

  17. IV. Influence of Systematics Dealing with systematic uncertainties Investigate two impact of systematics A. Redshift distribution revisited B. Model systematics

  18. IV. Influence of Systematics A. Redshift distribution revisited The 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 i

  19. IV. Influence of Systematics A. Redshift distribution revisited Optimized lens redshift distribution, subject to resource constraint, for different levels of systematics

  20. IV. Influence of Systematics A. Redshift distribution revisited Optimized lens redshift distribution, subject to resource constraint, for different levels of systematics

  21. IV. Influence of Systematics A. Redshift distribution revisited Optimized lens redshift distribution, subject to resource constraint, for different levels of systematics reduced hubble constant, h

  22. V. Conclusion The strong gravitational lensing time delay distance redshift relation : a geometric probe of cosmology Being dimensionful and hence sensitive to the Hubble constant, H0 Being a triple distance ratio and hence highly complementary to other distance probes

  23. V. Conclusion The strong gravitational lensing time delay distance redshift relation : a geometric probe of cosmology Optimization of the lens system redshift distribution to give maximal cosmology leverage, given followup resources do improve the result (FOM, parameter estimation, etc)

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