Optimizing the Precision of Velocity Widths from HI Spectra
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**Session 3 -- Galaxy Surveys**
*Display presentation, Wednesday, January 12, 9:30-6:45, Salons I/II Room (Crystal Gateway)*

## [3.05] Optimizing the Precision of Velocity Widths from HI Spectra

*J. M. Anderson and B. M. Lewis (Arecibo Obs.)*
The rotation velocities of galaxies are estimated from their HI profile
widths at a percentage of their peak intensities. While smoothing low S/N
ratio spectra improves widths estimated from them, binning usually limits
the attainable precision from well observed spectra. Two effects occur.
The first comes from the finite resolution of a bin, and is ameliorated by
higher resolution; the second comes from the exact positioning of a set of
bins with respect to the signal, and dominates estimation errors for the
50% (20%) width of the usual 8 km/s resolution spectra at a S/N >30 (5),
though its influence is easily removed by rebinning.

We simulate the estimation process in the presence of noise, and use a FT
rebinning algorithm to find that the resulting variance of a width estimate
is proportional to (N/S) down to a precision ³10E-5 of a bin at a S/N
Å10E6: the exact numerical factors depend on both resolution and the
functional form of the spectral edge. The question then arises, as to the
optimal resolution needed to observe galaxy widths to resolution indep-
endent precisions of 1 and 0.1 km/s. The most demanding spectra come
from Sc galaxies, such as UGC5646, with narrow, intense peaks. These
exhibit rounded peaks at a 2 km/s resolution, with about 5 channels across
their tops: used as kernels with a rebinning algorithm these show that an
8 km/s resolution suffices to determine unbiased widths to <1 km/s, but 4
km/s resolution is needed to reliably reach a precision of <0.1 km/s. This is
in practise the resolution needed to Nyquist sample the intrinsic shape of
an integrated HI profile. However, an observer retains greater flexibility if
all precision observations are made at about 2 km/s resolution. This allows
(i) unexpected discontinuities in profile edges to be detected; (ii) the use
of smoothing operations over the likely range of S/N ratios to completely
restore channel to channel precision lost in the use of a higher resolution;
(iii) surety that integration time gives the only limit to achieved precision.

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