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Power spectrum of the Lyα forest
Since the spatial distribution of the baryons in the
Intergalactic Medium is determined by the gravitational amplification
of density fluctuations of the dark matter, it is natural to examine
whether the matter density fluctuations could be measured through
fluctuations
in the distribution of baryons. The Cosmic Microwave Background
contains
a clear imprint of the matter fluctuations when still in the linear
regime of gravitational amplification. The baryons in the IGM represent
the quasi-linear regime intermediate between the CMB fluctuations and
the highly non-linear fluctuations leading to galaxy formation. It may
therefore be hoped that the baryons may be used to trace the evolution
of the baryon fluctuations at intermediate redshifts and scales. Such
measurements would in principle provide independent constraints on the
primordial power spectrum P(k) and the geometry of the Universe, and
may
even provide evidence for novel physics should distortions in the power
spectrum from the behaviour expected at the intermediate length scales
probed by the baryons be discovered.
Uncertainties
Several uncertainties, however, complicate any attempt to
determine the primordial power spectrum using the baryons:
1. Only the 1D power spectrum is measured
Only 1D power spectra may be directly measured, not the full
3D power spectrum. This is because currently the only means of
inferring the baryonic density fluctuations is through measurements of
the Lyα forest. In the future, this difficuly may be
circumvented if the 3D distribution of the baryons may be measured
through radio tomography using the
21cm line. Until then, efforts must be limited to the
fluctuations in the measured flux levels in the spectra of QSOs.
2. The 1D power spectrum is difficult to predict
The 1D matter power spectrum is a convolution over all
scales of the underlying 3D matter power spectrum. Since the 3D matter
spectrum is non-linear at small scales, predictions for the 1D matter
spectrum require high resolution N-body computations. As a result,
computations of the 1D
matter power spectrum are poorly converged. This effect, however,
is much ameliorated by the coherence in the flux measurements
resulting from the finite widths of the Lyα absorption
features. As a result, the power spectrum of the QSO flux smooths over
the most strongly non-linear scale. This more readily allows a
converged flux
power spectrum on large scales.
3. The QSO flux power spectrum is difficult to
predict
The scale of smoothing of the underlying matter
fluctuations in the QSO flux fluctuations depends on the dispersion
velocity of the baryons and the temperature of the IGM, which is
currently unknown. A reliable computation of the IGM temperature
requires reionisation
simulations . The unknown process by which the Universe was
reionised
precludes a definitive temperature prediction. Detailed numerical
computations are also required to determine the turbulent velocity
field broadening the absorption lines. Such computations are
expensive, as they require solving the fluid equations along with the
gravity equations for the dark matter. In lieu of this, attempts have
been made to artificially smooth the matter density fluctuations to
mimic these effects in N-body simulations for the dark
matter, and
dispense with solutions of the fluid equations. The resulting
estimates for the
smoothed flux power spectrum , however, depend on the smoothing
scheme, which is inevitably in part ad hoc.
4. The flux
power spectrum is difficult to measure
Uncertainties in
the varying continuum of the QSO through the Lyα forest result in
uncertainties in the flux power spectrum. The limited number of modes
probed is another limitation. While a large number of modes are
available at large wavevectors, these are the ones most affected by
the smoothing uncertainties. Fewer modes, and consequently larger
errors, are available at the smaller wavevectors, hindering precise flux P(k)
comparisons between models and observations.
Continued measurement efforts
None of
these uncertainties are insurmountable in principle. Efforts are
being made by various groups to develop the flux power spectrum into a
precise tool for inferring the underlying matter power spectrum. These
efforts are particularly interesting since they offer the best promise
for measuring the power spectrum on intermediate length scales,
amenable neither to Cosmic Microwave Background experiments, which
probe the larges scales, nor galaxy surveys, which probe the smallest.
For further information...
A review of
recent efforts to infer the matter power specturm from measurements of
the Lyα forest in the QSO spectra of the
Sloan Digital Sky Survey is found here. |
