Observational constraints on dark energy

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Observational constraints on dark energy

• Robert Crittenden
• Institute of Cosmology and Gravitation
• University of Portsmouth

Workshop on High Energy Physics Phenomenology -
Bhubaneswar January 10, 2006
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SN fainter than expected!
Is this because the universe is accelerating or
due to a systematic? Dust, lensing, evolution
Confirmed by many varied observations What
drives it? Dark energy
What might this dark energy be and how can we
learn about it?
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What drives the acceleration?

• Cosmological constant

• Introduced by Einstein to make a static
  universe.
• Associated with a vacuum energy density,
  typically
• It could be the Planck mass, or the
  super-symmetry or electro-weak breaking mass
  scale, but it is BIG.
• Constant in space and time.
• Equation of state

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What drives the acceleration?

• Cosmological constant
• Quintessence models

• Motivated by models of inflation.
• Scalar field rolling down shallow potential
  well.
• Equation of state varies
• Smooth on small scales by repulsion, but
  clusters on scales larger than dark energy sound
  horizon scale.
• Naturalness issues
• Why now?

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Myriad of Quintessence models
The equation of state is dynamic and depends on
the precise choice of potential. Fundamental
physics has not determined the functional form of
the potential, much less the specific parameters.
Like inflation, no preferred model!
Albrecht Weller
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What drives the acceleration?

• Cosmological constant
• Quintessence models
• Phantoms and ghosts

• Any equation of state,
• Can lead to Big Rip divergences in finite
  times.
• Violates weak and dominant energy conditions,
  and has negative energy states.
• Classical and quantum instabilities.
• Very difficult to find a working physical model.

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What drives the acceleration?

• Cosmological constant
• Quintessence models
• Phantoms and ghosts
• Tangled defect networks

Tangled string or domain wall networks give very
specific predictions but are effectively ruled
out observationally
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What drives the acceleration?

• Cosmological constant
• Quintessence models
• Phantoms and ghosts
• Tangled defect networks
• Modification of gravity on large scales

Many possible ideas Branes, Brans-Dicke
theories, MOND, backreaction of fluctuations?
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What drives the acceleration?

• Cosmological constant
• Quintessence models
• Phantoms and ghosts
• Tangled defect networks
• Modification of gravity on large scales

What can the observational data tell us about the
dark energy properties its density, evolution
and clustering?
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Expansion rate H(z)

• We have no evidence that dark energy interacts
  other than gravitationally.
• It is believed to be smooth on small scales.
• Thus, virtually our only handle on its nature is
  through its effect on the large scale expansion
  history of the universe, described by the Hubble
  parameter, H(z), and things which depend on it.

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Observable effects of dark energy

• It contributes to the present energy density and
  thus to the Hubble expansion rate.
• It contributed to the past expansion rate, so
  affects the distance and time measurements to
  high redshifts.
• It affects the growth rate of dark matter
  perturbations in two ways
• A faster expansion rate in the past would have
  made it harder for objects to collapse.
• On large scales, the dark matter reacts to the
  perturbations in the dark energy.

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CMB and large scale surveys
What can these tell us about dark energy?
Virtually all of the information is in their two
point correlations, with themselves and with each
other.
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Power spectra
These spectra describe the statistical properties
of the maps and their features contain a great
deal of information about the universe.
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Weighing the universe

• There must be enough matter to explain the
  present expansion rate

Dark energy density were trying to determine
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Weighing the universe

• There must be enough matter to explain the
  present expansion rate

• Dark matter density constraints (25)
• CMB Doppler peak heights
• Position of LSS turnover

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Weighing the universe

• There must be enough matter to explain the
  present expansion rate

• Dark matter density constraints (20-25)
• Baryon/dark matter ratio in x-ray clusters
• Large scale velocities, mass/light ratio

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Weighing the universe

• There must be enough matter to explain the
  present expansion rate

• Baryon density constraints (4)
• Light element abundances
• CMB Doppler peak ratios

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Weighing the universe

• There must be enough matter to explain the
  present expansion rate

• Photon density constraint (0.004 )
• Observed CMB temperature

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Weighing the universe

• There must be enough matter to explain the
  present expansion rate

• Neutrino density constraints (lt 1)
• Small scale damping in LSS
• Overall neutrino mass limits

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Weighing the universe

• There must be enough matter to explain the
  present expansion rate

• Curvature of universe constraint (lt 2)
• Angular size of CMB structures

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Weighing the universe

• There must be enough matter to explain the
  present expansion rate

• Critical density constraint
• Measurement of Hubble constant
• Biggest source of possible systematic errors

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Weighing the universe

• There must be enough matter to explain the
  present expansion rate

Assuming value measured by Hubble Key Project,
70-75 of matter not observed. H0 72-8
km/s/Mpc
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Evolution of the expansion rate H(z)

• Evolution of dark energy determined by its
  equation of state

While the dark energy density is larger than the
other components, it can be constrained by
measuring the evolution of H(z). Changing H(z)
effects distances and times to high redshifts.
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Evolution of the expansion rate

• Cosmic clocks

Age of objects, now and at high redshifts
Weak constraints from globular cluster ages.
Use luminous red galaxies as clocks if they
evolve passively? Not all formed at the same
time, so requires many high redshift galaxies to
find the oldest.
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Evolution of the expansion rate

• Cosmic clocks
• Co-moving volume

If objects have constant co-moving density, then
their number counts can constrain the expansion
evolution
Requires many high redshift galaxies and no
density evolution. Constraints from strong
gravitational lensing.
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Evolution of the expansion rate

• Cosmic clocks
• Co-moving volume
• Angular distance relation

Angular size of distant objects can tell you how
far away they are
Requires large yardstick of known size.
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The baryon yardstick

• Before electrons and protons combined, they were
  tightly coupled to photons and so the density
  fluctuations oscillated acoustically.
• The largest scales which had time to compress
  before recombination were imprinted on the CMB
  and LSS power spectra

Given ??and its angular size, we can find dA if
we know the curvature!
Flat
Closed
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CMB as cosmic yardstick
Both the curvature and the dark energy can change
the scale of the Doppler peaks. We used the
position of the Doppler peaks to determine the
curvature, assuming a cosmological
constant. However, if we assume a flat universe,
we can turn this around to find a constraint on
the equation of state.
WMAP compilation
Angular distance to last scattering surface
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CMB angular distance
Degeneracy needs to be broken by other data, like
Hubble constant or SN data. Present data is
consistent with w-1, so we cannot change w too
much, unless we compensate it by changing the
curvature.
Small amount of curvature keeps peak position
unchanged
Flat universe Recall DE slightly changes peak
position
Single integrated constraint on w and present
density from the shape of CMB spectrum w lt
-0.8.
Lewis Bridle 03 MCMC results
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LSS as a cosmic yardstick

• Imprint of oscillations less clear in LSS
  spectrum unless high baryon density
• Detection much more difficult
• Survey geometry
• Non-linear effects
• Biasing

Big pay-off Potentially measure dA(z) at many
redshifts!
Eisenstein et al. 98
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Baryon oscillations detected!
SDSS data
SDSS and 2dF detect baryon oscillations at 3-4
sigma level. SDSS detection in LRG sample z
0.35 Thus far, fairly weak constraints on
equation of state.
Future many competing surveys KAOS -
Kilo-Aperture Optical Spectrograph, SKA 106
galaxies at z 0.5-1.3, z 2.5-3.5
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Evolution of the expansion rate

• Cosmic clocks
• Co-moving volume
• Angular distance relation
• Alcock-Paczynski tests

Compare dimensions of objects parallel and
perpendicular to the line of sight and ensure
that they are the same on average.
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Evolution of the expansion rate

• Cosmic clocks
• Co-moving volume
• Angular distance relation
• Alcock-Paczynski tests
• Luminosity distance relation

Use supernovae (or perhaps GRBs) as standard
candles and see how their brightness changes with
their redshift.
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Recent supernovae constraints
Gold data has best 150 SN and includes high
redshift SN discovered with the Hubble
telescope. Rules out grey dust models.
Residuals relative to an empty universe Riess et
al. 2004
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Recent supernovae constraints
Limits on density and equation of state Riess et
al. 2004
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SNLS results

• New independent sample of 71 supernovae Astier
  et al. 2005

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SNLS baryon oscillations
Combining data sets indicates close to
cosmological constant with about 70 of the
present density.
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Growth rate of structure
Accelerated expansion makes gravitational
collapse more difficult
Normalized to present, dark energy implies
fluctuations were higher in the past
This ignores d.e. clustering, reasonable on small
scales.
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Probes of ?(z)

• Difficult to measure, even its present value
  (parameterized in ?8) is subject to some debate
  (0.6 - 1.0?).
• CMB amplitude provides early point of reference.
• Gravitational lensing (Jain talk.)
• Evolution of galaxy clustering, though tied up
  with bias!
• Controls the number of collapsed objects, like
  clusters.

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Cluster abundances
If the statistics are Gaussian, the number of
collapsed objects above a given threshold depends
exponentially on the variance of the field.
Press-Schecter
Thus, the growth factor controls the number of
clusters at a given redshift.
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Cluster abundances
We can observe these in x-rays or the CMB via the
Sunyaev-Zeldovich effect.
Normalizing to the present, a dark energy
dominated universe will have many more objects at
high redshifts. Unfortunately, we dont measure
the masses directly, which can complicate the
cosmological interpretation.
XCS clusters from K. Romer
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Probes of ?(z)

• Difficult to measure, even its present value
  (parameterized in ?8) is subject to some debate
  (0.6 - 1.0?).
• CMB amplitude provides early point of reference.
• Gravitational lensing (Jain talk.)
• Evolution of galaxy clustering, though tied up
  with bias!
• Controls the number of collapsed objects, like
  clusters.
• Induces very recent CMB anisotropies!

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Recent CMB anisotropies

• While most CMB fluctuations are created at last
  scattering, some can be generated at low
  redshifts gravitationally via the ISW (linear)
  and Rees-Sciama (non-linear) effects

potential depth changes as cmb photons pass
through
gravitational potential traced by galaxy density
The potential is constant for a matter dominated
universe, but begins to evolve when the two dark
energy effects modify the growth rate of the
fluctuations.
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Two uncorrelated CMB maps
The CMB fluctuations we see are a combination of
two uncorrelated pieces, one induced at low
redshifts by a late time transition in the total
equation of state.
Early map, z1000 Structure on many scales
ISW map, zlt 4 Mostly large scale features
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large scale correlations
ISW fluctuations tend to be on the very largest
scales
On small scales, positive and negative ISW
effects will tend to cancel out. This leads to
an enhancement of the large scale power spectrum
The early and late power is fairly weakly
correlated, so the power spectra add directly
WMAP best fit scale invariant spectrum
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Observing the ISW effect
in the cmb map, additional anisotropies should
increase large scale power

• Not observed in WMAP data
• In fact, decrease is seen

• why might this be?
• cosmic variance
• no ISW, still matter dominated
• accidental cancellation
• drop in large scale power
• simple adiabatic scenario wrong

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Correlations with the galaxy distribution
The gravitational potential determines where the
galaxies are and where the ISW fluctuations are
created! Thus the galaxies and the CMB should be
correlated. Most of the cross correlation arises
on large or intermediate angular scales
(gt1degree). The CMB is well determined on these
scales by WMAP, but we need large galaxy surveys.
Can we observe this?
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cmb sky
S. Boughn, RC 2004
WMAP
Galactic plane, centre removed most aggressive
WMAP masking 68 of sky
WMAP internal linear combination map (ilc) also
Tegmark, de Oliveira-Costa Hamilton map (no
significant differences in resulting
correlations)
dominant source of noise to cross correlation is
accidental correlations of cmb map with other maps
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hard x-ray background
HEAO-1 x-ray satellite
3 degree resolution 3-17 keVs Flown in 1970s

• Removed nearby sources
• Cuts (leaving 33 of sky)
• Galactic plane, centre removed
• brightest point sources removed
• Fits
• monopole, dipole
• detector time drift
• Galaxy
• local supercluster

Virtually all visible structures cleaned out
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x-ray cmb correlation
compare observed correlation to that with Monte
Carlo cmb maps with WMAP power spectrum correlatio
n detected at 2.5-3 sigma level, very close to
that expected from ISW.
dots observed thin Monte Carlos thick ISW
prediction (WMAP best fit model) errors highly
correlated
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Correlations seen in many frequencies!

• X-ray background
• Radio galaxies
• NVSS confirmed by Nolta et al (WMAP
  collaboration)
• Wavelet analysis shows even higher significance
  (Vielva et al.)
• FIRST radio galaxy survey (Boughn student)
• Infrared galaxies
• 2MASS near infrared survey (Afshordi et al.)
• Optical galaxies
• APM survey (Folsalba and Gaztanaga)
• Sloan Digital Sky Survey (Scranton et al., FGC)
• Band power analysis of SDSS data (N. Pamanabhan,
  et al.)

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Dark energy clustering and ?(z)

• The ISW probes the fluctuations on very large
  scales, where we cannot ignore the clustering of
  dark energy
• If it is not a cosmological constant, the dark
  energy clusters on large scales, while remaining
  smooth on smaller scales.
• The dark energy sound horizon divides smooth and
  clustered regimes quintessence type models have
  large sound speeds (cs 1) and the transition
  occurs near the horizon scale, but it can be
  smaller.
• Failing to include the clustering makes a big
  difference in ISW predictions.
• If the sound speed is large, the ISW effect is
  one of the few ways we can see its affects.

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dark energy sound speed
The ISW signal can reflect the clustering of dark
energy
The ISW signal changes dramatically when dark
matter clustering is included (Caldwell, Dave
Steinhardt Bean Dore Hu Scranton) Without
clustering, dark energy increases the ISW effect,
since the dark energy becomes important
earlier However, the dark energy clustering
helps aids the collapse of dark matter, which
suppresses the ISW effect.
The isw contribution with and without including
clustering of dark energy (Weller Lewis 03)
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ISW summary

• Independent confirmation of need for dark
  energy.
• Many observations at 2-3 ??level in many
  frequencies, but these are not entirely
  independent -- same CMB sky!
• All consistent with predictions for cosmological
  constant model, given uncertainties in source
  redshift distributions.
• Ideally want surveys with full sky coverage and
  known source distribution in redshift out to z
  2-3 (depending on dark energy model.)
• Fundamentally limited by noise of CMB, 7-10?
  level.
• Potentially only probe of dark energy sound
  speed.

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Conclusions

• Probing the expansion history and growth of
  density perturbations illuminate different
  aspects of dark energy its density, equation of
  state, and sound speed.
• Many independent indications that dark energy is
  70-80 of critical density and w lt -0.8.
• Everything we have seen seems consistent with a
  cosmological constant.
• Improvements are expected on many fronts,
  particularly as large scale structure
  observations get bigger and better.

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Future prospects
Microwave background Future WMAP
data Planck QUAD, other polarized CMB
missions Large scale structure Sloan DSS Dark
Energy Survey, SALT? Lyman alpha
studies DEEP2 Astro-F KAOS, LSST,
SKA Supernovae Nearby SN factory SNLS, Essence
w-project SDSS SNAP/JDEM
SZ clusters AMI Amiba OCRA Planck South Pole
Telescope Weak lensing Megacam DarkCam
(VISTA) PanSTARRS, LSST JDEM DUNE X-ray
clusters XMM Cluster survey MACS REFLEX2 DUET
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Avoiding dark energy

• Blanchard et al have investigated what is
  necessary to have a cosmological model without
  dark energy.
• Briefly, they must discard
• Hubble constant measurements
• High redshift SN observations
• Baryon oscillation data
• ISW correlations
• Strong gravitational lensing data
• To fit the remaining data, they must
• Add a particular feature to the primordial
  spectrum
• Add a massive neutrino to suppress small scale
  power
• Any one of these is very reasonable, but it is
  difficult to justify all of them.

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CMB frequency dependence
X-ray and radio cross correlations for ILC and
various WMAP bands There appears to be no strong
frequency dependence
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How good will it get?
For the favoured cosmological constant the best
signal to noise one can expect is about 7.
This requires significant sky coverage, surveys
with large numbers of galaxies and some
understanding of the bias. The contribution to
(S/N)2 as a function of multipole moment. This
is proportional to the number of modes, or the
fraction of sky covered, though this does depend
on the geometry somewhat.
RC, N. Turok 96 Peires Spergel 2000
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could it be a foreground?

• insensitive to level of galactic cuts
• insensitive to point source cuts
• comparable signal in both hemispheres
• correlation on large angular scales

in addition, the contribution to the correlation
from individual pixels is consistent with what is
expected for a weak correlation NOT dominated by
a few pixels blue product of two Gaussians red
product of two weakly correlated Gaussians
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2MASS data
Afshordi, Loh Strauss Near infrared Full sky,
but low redshift
2.5 sigma detection of ISW 3 detection of SZ
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radio galaxies
NRAO VLA Sky Survey (NVSS)
flux limited at 1.4 GHz 82 of the sky 1.8
million sources 50 per square degree
nearby objects and Galaxy removed (leaving 56 of
sky) declination dependent banding
corrected redshift distribution somewhat
uncertain correlated with x-rays!!!
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radio cmb correlation
Radio galaxies are also correlated at 2.0-2.5
sigma level, again consistent with ISW origin
dots observed thin Monte Carlos thick ISW
prediction (WMAP best fit value) errors highly
correlated
Not independent of x-ray signal, but agreement
suggests its not due to systematic of maps
Independent WMAP analysis confirmation (Nolta et
al.)
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SDSS data (Scranton et al.)
Luminous red galaxies 3400 square degrees
Significant (gt90) detections in all bands
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Signal to Noise
A good fraction of the signal comes from low
redshifts, so a signal is possible with low
redshift surveys
(S/N)2 as a function of redshift and wavenumber
(Afshordi 04)
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Bennett et al comparison
Differences appear fairly consistent with COBE
noise level, apart from near galaxy
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COBE WMAP comparison
Why wasnt a correlation seen using the COBE
map? This was previously used to put bounds on a
cosmological constant COBE 53 90 map was used
to minimize detector noise, but still most of the
pixel variance was noise Correlations seem to
agree on large scales, but cosmic variance is
large there. Cosmic variance is smallest at
small separations, but noise is largest
Were we just unlucky that the noise cancelled the
correlations?
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isw vs anisotropies from last scattering
isw fluctuations are basically uncorrelated with
those produced earlier
The quadrupole primarily arises from modes on the
scale of the horizon The ISW anisotropies are
created nearer to us, and are generated by
smaller modes (larger wave number)
Highest correlations are for the quadrupole, but
it is still very weak
Contribution to the quadrupole power as a
function of wave number, the oscillations at high
k alternatively constructively or destructively
interfere, effectively cancelling out