The Alcock-Paczynski Probe of Cosmology

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The Alcock-Paczynski Probeof Cosmology

• Lyman-? forest, LSS,
• And Cosmic Consistency

Albert Stebbins Fermilab
Dark Energy Workshop Center for Cosmological
Physics University of Chicago 15 December 2001
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The Alcock-Paczynski TestAlcock Paczynski
(1979) An evolution free test for non-zero
cosmological constant Nature 281 358

• There are 2 directly observable measures of the
  size of an object expanding w/ cosmological
  flow
• Angular size
• Radial extent in redshift space
• If such objects are not preferentially aligned
  either along or perpendicular to our
  line-of-sight then, by requiring no such
  preferential alignment, one can determine the
  ratio of the conversion factors, angular distance
  to physical distance, to that from redshift
  distance to physical distance.
• i.e. one can determine ?z/??z.

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Observational Fundamentalism
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Different Tests - Different Combinations

• Examples of how these two functions are related
  to standard tests
• the apparent luminosity of standard candles
• (the K-correction, kz, includes
  (1z)4 surface brightness dimming and redshift
  of spectrum into /out of observational band)
• the cosmological volume element (? of objects)
  per unit redshift per unit solid angle
• the Alcock-Paczynski test
• N.B. in practice other cosmological dependencies
  tend to creep into these tests, e.g. the linear
  growth rate of perturbations, or more complicated
  things like the star formation rate.

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A-P Just Another Cosmological Test

• As with all such tests one must go to
  significant redshift to measure anything
  interesting. For zltlt0 you already know what the
  answer is.
• The AP test at lo-z quickly (zgt0.5) becomes
  sensitive to the presence of ?, but only at the
  20 level.
• It is insensitive to curvature at lo-z, rather
  like the SNeIa lz.
• At very hi-z it becomes most sensitive to the
  curvature at about the 70 level.
• At hi-z it is relatively insensitive to ?,
  rather like the CMB lpeak test.

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A-P Just The Same Cosmological Test
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Cosmological Consistency
As described, the results of different
cosmological tests are inter-related. Some of
these relationships are axiomatic, e.g.
Other relationship depend on the cosmic
consistency relation, e.g. Which relates
observables from an A-P test and a l-z (e.g.
SNeIa) test to Which probably isnt quite
measurable. However since the right-hand-side is
z-independent one can test cosmic consistency by
requiring that one infers the same ?0 at each z.
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Cosmological Inconsistency?

• These relations hold no matter how weird the dark
  energy is!
• Violation of an axiomatic relation probably
  indicates a measurement error or
  mis-interpretation of measurements.
• The cosmic consistency relations is a result of
  assumptions of the FRW (Friedmann-Robertson-Walker
  Cosmology - one of the fundamental tenets upon
  which interpretation of cosmological observations
  is based.
• Violation of cosmic consistency might indicate
• non-FRW geometry i.e. we live in the center of a
  spherically symmetric but non-homogeneous
  universe (violation of cosmological Copernican
  Principle)
• non-metric theory for propagation of light
  (post-modern tired light) - as we are in a sense
  measuring the metric with these tests.
• Measurement error or a problem with
  interpretation of measurements.
• As the relations combine different tests, and as
  it is unlikely that errors in one test would
  balance errors in another such as to satisfy the
  relations, this provides a powerful check of all
  tests involved!
• It is thus worthwhile to compare the AP test at
  the same redshifts as SNeIa

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Alcock-Paczynski Realities
As with all cosmological tests one must overcome
observational hurdles in order to make the test
a useful one.

• Systematics
• Since angular size is measure of physical size
  and radial size measure of velocity differences
  we do expect that the two are the same - there
  can be preferential alignment w.r.t.
  line-of-sight i.e. redshift space distortions.
• These distortions must be understood and taken
  into account.
• On small scales 1 Mpc astrophysical objects
  have separated from cosmic expansion and have
  little to do w/ cosmic expansion (fingers of
  God).
• On large scales gt20 Mpc (_at_z0) simple linear
  theory distortions (Kaiser effect) may suffice.

• Statistics
• If objects were truly round in redshift space
  then one need observe only one at each z to
  determine ?z/??z.
• More generally accuracy is given by ?
  ln(?z/??)e/v(8N) where N is the number of
  independent objects and e their RMS ellipticity.
  N.B. 0 e 1
• Statistical measurement errors decreases
  effective N.
• this result cribbed from weak lensing theory

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Large Scale Structure Voids, Filaments, etc.

• From galaxy redshift surveys one may identify
  structures such as voids (Ryden) or filaments
  (Möller Fynbo), measure their shapes and use
  these for the AP test
• As these are quasi-linear structures the redshift
  space distortions are non-trivial to correct for.
• At present surveys dense enough to identify
  structures are at lo-z where the AP is less
  useful.
• In the future DEEP and VIRMOS will provide dense
  surveys at z1.

SDSS Galaxy Redshift Survey Early DataStoughton
et al. (2001) Sloan Digital Sky Survey Early
Data Releasein preparation
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Large Scale Structure Sparse Sampling

• Sparse surveys efficiently measure the 2-pt
  statistics of clustering especially on large
  scales where the perturbations are linear.
• They are not useful for identifying individual
  structures.
• e.g. the BRG (Bright Red Galaxy) part of the SDSS
  redshift survey, or much of 2DF.

SDSS Galaxy Redshift Survey Early DataStoughton
et al. (2001) Sloan Digital Sky Survey Early
Data Releasein preparation
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Large Scale Structure QSOs

• Or the quasar redshift survey that is part of the
  SDSS (Calvão, De Mello Neto, Waga).

SDSS Galaxy Redshift Survey Early DataStoughton
et al. (2001) Sloan Digital Sky Survey Early
Data Releasein preparationSchneider et al.
(2001) The Sloan Digital Sky Survey Quasar
Catalog I Early Data Release astro-ph/0110629
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Composite Objects ?rp,?

• One may also use statistics of redshift space
  clustering in place of shapes of individual
  objects.
• In particular the redshift space 2-point function
  ?rp,? ?? ,?z
• This is a convenient way of combining all of the
  data w/o identifying objects.
• One can use this in cases where, say, the galaxy
  sampling is too sparse to allow accurate
  identification of objects.

SDSS Galaxy Redshift-Space CorrelationZehavi et
al. (2001) Galaxy Clustering in Early SDSS
Redshift Data astro-ph/0106476
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Alcock-Paczynski Redshift Space Distortions

• Redshift space distortions themselves give some
  clue as to the cosmological parameters c.f. the
  Kaiser effect
• Combining the AP test w/ theory for redshift
  space distortion (and to some extent bias) one
  can obtain a combined constraint on cosmological
  parameters (Matsubara Szalay). e.g. for SDSS
  Northern survey (Subbarao)

OTHERS FIXED ?m ?? ?b/?m h n ?8 b
Main 3 19 16 4 2 0.5 0.5
BRG 2 4 9 2 1 0.3 0.4
QSO 14 15 76 20 14 5 6
SDSS Parameter EstimationMatsubara Szalay
(2001) Constraining the Cosmological Constant
from Large-Scale Redshift-Space Clustering
astro-ph/0105493
MARGIN- ALIZED ?m ?? ?b/?m b
Main 14 57 51 2
BRG 9 10 33 0.9
QSO 170 75 360 69
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Alcock-Paczynski Redshift Space Distortions
Parameter Estimation for 1. (200h-1 Mpc)3 cube
2. ? ? survey Matsubara Szalay (2001)
Constraining the Cosmological Constant from
Large-Scale Redshift-Space Clustering
astro-ph/0105493
Shot Noise (20h-1 Mpc)3 n0.1, 0.3, 1, 3, 10, 8
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Lyman-? ForestStructure along line-of-sight to
QSOs
Continuum Fitting Systematic!
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The Ly-? Alcock-Paczynski Forest TestMcDonald
Miralda-Escudé (1999) Measuring the Cosmological
Geometry from the Ly? Forest Along Parallel Lines
of Sight Ap.J. 518 24 Hui, Stebbins, Burles
(1999) A Geometrical Test of the Cosmological
Energy Contents Using theLyman-alpha Forest Ap.J
Lett. 511 L5
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The Alcock-Paczynski Ly-? Forest Test

• The quality of the AP test depends on the QSO
  separation
• Too small
• Just right
• Too large

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First Try
In practice one cross-correlates the Ly-?
absorption e-? between the different
lines-of-sight. This can be done in ? space or
its Fourier transform. One expects the
correlation to be near perfect on z-scales larger
than the transverse separation, no correlation on
scales much larger than the separation, with
roughly an exponential falloff.
Alcock-Paczynski Test Applied to QSO Triplet
Burles, Stebbins, Hui (circa 1999, unpublished)
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Ly-? Forest Sensitivity

• McDonald (2001) has performed detailed modeling
  of expected SDSS QSOs, comparing w/ simulations
  to model redshift space distortions.
• With followup spectra (i.e. apart from SDSS
  spectroscopy) one can obtain a respectable limit
  on ?.

Cosmological Accuracy from SDSS QSOsMcDonald
(2001) Toward a Measurement of the Cosmological
Geometry at z2 Predicting Ly? Forest
Correlations in Three Dimensions, and the
Potential of Future Data Sets astro-ph/0108064
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Conclusions

• Alcock-Paczynski test - yet another cosmological
  test.
• Redundant with other tests in z ranges where they
  overlap.
• Implementations have been proposed up to QSO
  redshifts (z3) - perhaps further w/ IR
  spectroscopy.
• No useful applications have yet been carried out.
• For deep redshift surveys - and when combined
  with theory of redshift space distortion - can
  provide very tight constraints on at a.k.a.
  p?.
• Probably provides best probe of cosmology at z2
  through Ly-? Forest.