217 research outputs found
The Tully-Fisher relation : Correspondence between the Inverse and Direct approaches
In a previous paper, we have demonstrated the importance to define a
statistical model describing the observed linear correlation between the
absolute magnitude and the log line width distance indicator of
galaxies (the Tully-Fisher relation). As long as the same statistical model is
used during the calibration step of the relation and the step of the
determination of the distances of galaxies, standard statistical methods such
as the maximum likelihood technic permits us to derive bias free estimators of
the distances of galaxies. However in practice, it is convenient to use a
different statistical model for calibrating the Tully-Fisher relation (because
of its robustness, the Inverse Tully-Fisher relation is prefered during this
step) and for determining the distances of galaxies (the Direct Tully-Fisher
relation is more accurate and robust in this case). Herein, we establish a
correspondence between the Inverse and the Direct Tully-Fisher approaches.
Assuming a gaussian luminosity function, we prove that the ITF and DTF models
are in fact mathematically equivalent (i.e. they describe the same physical
data distribution in the TF diagram). It thus turns out that as long as the
calibration parameters are obtained for a given model, we can deduce the
corresponding parameters of the other model. We present these formulae of
correspondence and discuss their validitity for non-gaussian luminosity
functions.Comment: 10 pages, uuencoded en compressed Postscript file, figures avaible
under requests. To be published in A\&
On the motion of the Local Group and its substructures
The problem of the relative motion of the substructures of the Local Group of
galaxies revealed via S-tree method, as well as of the velocity of the Local
Group itself, is considered. The existence of statistically significant bulk
flow of the Milky Way subsystem is shown via 3D reconstruction procedure, which
uses the information on the radial velocities of the galaxies, but not on their
distances. Once the bulk motion of substructures is estimated, in combination
with the observed CMB dipole we also consider the mean velocity of the Local
Group itself. Assigning the Local Group the mean motion of its main
substructures we evaluate its peculiar velocity in Milky Way frame V(LG->MW)=
(-7 \pm 303,-15 \pm 155 ,+177 \pm 144) or 178 km/s toward galactic coordinates
l=245 and b=+85. Combined with CMB dipole V(MW->CMB), we obtain Local Group
velocity in CMB frame: V(LG->CMB) = (-41\pm 303,-497\pm 155,445 \pm 144) or 668
km/s towards l=265 and b=42. This estimation is in good agreement, within 1
sigma level, with the estimation of Yahil et al (1977).Comment: To be published in MNRA
On the 3D Velocity Reconstruction of Clusters of Galaxies
The problem of reconstruction of the 3D velocities of clusters of galaxies
from the redshift distribution of galaxies of the cluster is formulated. Though
numerical simulations show the impossibility of direct use of Ambartsumian's
formula derived for the stellar systems because of the small number of objects
in the clusters, an additional physical assumption on the form of the searched
velocity distribution can lead to the possibility of obtaining the transverse
velocity of the cluster. The accuracy of the proposed reconstruction procedure
is estimated.Comment: to appear in Astrofizika, vol.40, 1997; LaTex, 4 pages, 1 figure,
*.ps figure can be obtained from the author
Cluster luminosity function and n^th ranked magnitude as a distance indicator
We define here a standard candle to determine the distance of clusters of
galaxies and to investigate their peculiar velocities by using the n^{th} rank
galaxy (magnitude m). We address the question of the universality of the
luminosity function for a sample of 28 rich clusters of galaxies () in order to model the influence on of cluster richness. This
luminosity function is found to be universal and the fit of a Schechter profile
gives and in the range
[-21,-17]. The uncorrected distance indicator is more efficient for the
first ranks n. With n=5, we have a dispersion of 0.61 magnitude for the
(m,5log(cz)) relation. When we correct for the richness effect and subtract
the background galaxies we reduce the uncertainty to 0.21 magnitude with n=15.
Simulations show that a large part of this dispersion originates from the
intrinsic scatter of the standard candle itself. These provide upper bounds on
the amplitude of cluster radial peculiar motions. At a confidence
level of 90%, the dispersion is 0.13 magnitude and is limited to
1200 km/s for our sample of clusters.Comment: 9 pages, 7 postscript figures, LateX A&A, accepted in A&
Calibration of the Tully-Fisher relation in the field
A new technique for calibrating Tully-Fisher like relations by using field
galaxies is proposed. Based on a null-correlation approach (NCA), the technique
is insensitive to the presence of selection effects on apparent magnitude
and on log line-width distance indicator . This interesting property is used
for discarding near by galaxies of the observed sample. It is shown that such a
subsampling allows in effect to attenuate biases on calibration parameters
created by the presence of radial peculiar velocities.Comment: 20 pages, 24 figures. To appear in A&A Supplement Serie
Wavelet Analysis of Inhomogeneous Data with Application to the Cosmic Velocity Field
In this article we give an account of a method of smoothing spatial
inhomogeneous data sets by using wavelet reconstruction on a regular grid in an
auxilliary space onto which the original data is mapped. In a previous paper by
the present authors, we devised a method for inferring the velocity potential
from the radial component of the cosmic velocity field assuming an ideal
sampling. Unfortunately the sparseness of the real data as well as errors of
measurement require us to first smooth the velocity field as observed on a
3-dimensional support (i.e. the galaxy positions) inhomogeneously distributed
throughout the sampled volume. The wavelet formalism permits us to introduce a
minimal smoothing procedure that is characterized by the variation in size of
the smothing window function. Moreover the output smoothed radial velocity
field can be shown to correspond to a well defined theoretical quantity as long
as the spatial sampling support satisfies certain criteria. We argue also that
one should be very cautious when comparing the velocity potential derived from
such a smoothed radial component of the velocity field with related quantities
derived from other studies (e.g : of the density field).Comment: 19 pages, Latex file, figures are avaible under requests, published
in Inverse Problems, 11 (1995) 76
A robust method for measuring the Hubble parameter
We obtain a robust, non-parametric, estimate of the Hubble constant from
galaxy linear diameters calibrated using HST Cepheid distances. Our method is
independent of the parametric form of the diameter function and the spatial
distribution of galaxies and is insensitive to Malmquist bias. We include
information on the galaxy rotation velocities; unlike Tully-Fisher, however, we
retain a fully non-parametric treatment. We find km/s/Mpc,
somewhat larger than previous results using galaxy diameters.Comment: 4 pages, 1 figure, Cosmic Flows Workshop, Victoria B.C. Canada, July
1999, ed. S. Courteau, M. Strauss & J. Willick, ASP conf. serie
The determination of by using the TF relation : About particular selection effects
This paper completes the statistical modeling of the Hubble flow when a
Tully-Fisher type relation is used for estimating the absolute magnitude
from a line width distance indicator . Our investigation
is performed with the aim of providing us with a full understanding of
statistical biases due to selection effects in observation, regardless of
peculiar velocities of galaxies. We show that unbiased -statistics
can be obtained by means of the maximum likelihood method as long as the
statistical model can be defined. We focus on the statistical models related to
the Direct, resp. Inverse, Tully-Fisher relation, when selection effects on
distance, resp. on , are present. It turns out that the use of the Inverse
relation should be preferred, according to robustness criteria. The formal
results are ensured by simulations with samples which are randomly generated
according to usual characteristics.Comment: 8 pages, Postscript compressed file, to be published in A\&
About the Malmquist bias in the determination of H0 and of distances of galaxies
We provide the mathematical framework which elucidates the way of using a
Tully-Fisher (TF) like relation in the determination of the Hubble constant
, as well as for distances of galaxies. The methods related to the
so-called Direct and Inverse TF Relations (herein DTF and ITF) are interpreted
as maximum likelihood statistics. We show that, as long as the same model is
used for the calibration of the TF relation and for the determination of ,
we obtain a coherent Hubble's constant. The choice of the model is motivated by
reasons of robustness of statistics, it depends on selection effects in
observation which are present in the sample. The difference on the distance
estimates when using either the ITF or the DTF model is only due to random
fluctuations. It is interesting to point out that the DTF estimate does not
depend on the luminosity distribution of sources. Both statistics show a
correction for a bias, inadequately believed to be of Malmquist type. The
repercussion of measurement errors, and additional selection effects are also
analyzedComment: 37 pages,cpt-93/p.2808,latex A&A,4fig available on cpt.univ-mrs.fr
directory ftp/pub/preprints/93/cosmology/93-P.280
A physical distance indicator for spiral galaxies
In this paper we derive a Tully Fisher relation from measured I band
photometry and H rotation curves of a large survey of southern sky
spiral galaxies, obtained in Persic \& Salucci (1995) by deprojecting and
folding the raw H data of Mathewson, Ford \& Buchhorn (1992). We
calibrate the relation by combining several of the largest clusters in the
survey, using an iterative maximum likelihood procedure to account for
observational selection effects and Malmquist bias. We also incorporate a
simple model for the line of sight depth of each cluster. Our results indicate
a Tully Fisher relation of intrinsic dispersion mag, corresponding to
a distance error dispersion of . Application of this relation to mapping
the large scale velocity field is underway.Comment: Plain TeX Version 3.0, 4 pages, to appear in `Astrophysical Letters
and Communications' - proceedings of the international workshop on
observational cosmology: `From Galaxies to Galaxy Systems', Sesto, July 199
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