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  • Print publication year: 2012
  • Online publication date: December 2012

16 - Statistical astrometry

from Part IV - From detected photons to the celestial sphere



The term “statistical astrometry” refers to the inference of astrophysical quantities from samples (i.e. collections) of stars or other sources. Often the mean value of the astrophysical quantity or a description of its distribution is sought. The applications are numerous and include luminosity calibration, star-cluster membership determination, separating the Galaxy's structural components, detecting low-contrast substructure in the Galactic halo, etc. These studies become especially interesting now that astrometric catalogs are available with large numbers of parallaxes. However, there are a number of effects that can lead to errors in the inference of astrophysical quantities and thus complicate the interpretation of astrometric data. This chapter is focused on discussing these complicating effects with the aim of providing guidance on the optimal use of astrometric data in statistical studies.

Effects complicating the interpretation of astrometric data

The main effects that can complicate the interpretation of astrometric data for samples of objects are summarized below.

Completeness and selection effects

Any sample chosen from an astrometric catalog will suffer from incompleteness in the data and selection effects. Both issues are related to the properties of the astrometric survey and how the sample is chosen. In addition, they may depend on the location on the sky or the source properties. Hence, the chosen sample almost never represents the true distribution of sources in the astrophysical parameter space. Ignoring this fact leads to biased results in the scientific interpretation of the data.

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Arenou, F. and Luri, X. (1999). Distances and absolute magnitudes from trigonometric parallaxes. ASP Conf. Ser., 167, p. 13.
Binney, J. (2011). Extracting science from surveys of our Galaxy. Pramana, 77, 39–52.
Binney, J. and Merrifield, M (1998). Galactic Astronomy. Princeton, NJ: Princeton University Press.
Brown, A. G. A., Arenou, F., van Leeuwen, F., Lindegren, L., and Luri, X. (1997). Some considerations in making full use of the Hipparcos Catalogue. In Hipparcos Venice '97. ESA SP-402, p. 63.
de Bruijne, J. H. J. (1999). Structure and colour–magnitude diagrams of Scorpius OB2 based on kinematic modelling of Hipparcos data. MNRAS, 310, 585.
de Bruijne, J. H. J., Hoogerwerf, R., and de Zeeuw, P. T. (2001). A Hipparcos study of the Hyades open cluster. Improved colour–absolute magnitude and Hertzsprung–Russell diagrams. A&A, 367, 111.
Butkevich, A. G., Berdyugin, A. V., and Teerikorpi, P. (2005). Statistical biases in stellar astronomy: the Malmquist bias revisited. MNRAS, 362, 321.
Dravins, D., Lindegren, L., and Madsen, S. (1999). Astrometric radial velocities. I. Nonspectroscopic methods for measuring stellar radial velocity. A&A, 348, 1040.
,ESA (1989). The Hipparcos Mission: Pre-launch Status. ESA SP-1111.
,ESA (1997). The Hipparcos and Tycho Catalogues. ESA SP-1200.
Feast, M.W. and Catchpole, R. M. (1997). The Cepheid period-luminosity zero-point from Hipparcos trigonometrical parallaxes. MNRAS, 286, L1–L5.
Gómez, A. E., Luri, X., Mennessier, M.O., Torra, J., and Figueras, F. (1997). The luminosity calibration of the HR Diagram revisited by HIPPARCOS. In Hipparcos Venice '97. ESA SP-402, p. 207.
Gould, A. (2004). v⊥ CMD. astro-ph/0403506.
Hanson, R. B. (1979). A practical method to improve luminosity calibrations from trigonometric parallaxes. MNRAS, 186, 875.
Lindegren, L., Madsen, S., and Dravins, D. (2000). Astrometric radial velocities. II. Maximum-likelihood estimation of radial velocities in moving clusters. A&A, 356, 1119.
Luri, X., Mennessier, M. O., Torra, J., and Figueras, F. (1996). A new maximum likelihood method for luminosity calibrations. A&AS, 117, 405.
Lutz, T. E. and Kelker, D. H. (1973). On the use of trigonometric parallaxes for the calibration of luminosity systems: theory. PASP, 85, 573.
Madsen, S., Dravins, D., and Lindegren, L. (2002). Astrometric radial velocities. III. Hipparcos measurements of nearby star clusters and associations. A&A, 381, 446.
Malmquist, K. G. (1922). Lund Medd. Ser.I, 100, 1.
Perryman, M. A. C., Brown, A. G. A., Lebreton, Y., et al. (1998). The Hyades: distance, structure, dynamics, and age. A&A, 331, 81.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge: Cambridge University Press.
Ratnatunga, K. U. and Casertano, S. (1991). Absolute magnitude calibration using trigonometric parallax: incomplete, spectroscopic samples. AJ, 101, 1075.
Smith, H. Jr., (2003). Is there really a Lutz–Kelker bias? Reconsidering calibration with trigonometric parallaxes. MNRAS, 338, 891.
Smith, H. Jr., and Eichhorn, H. (1996). On the estimation of distances from trigonometric parallaxes. MNRAS, 281, 211.
Turon, C. and Crézé, M. (1977). On the statistical use of trigonometric parallaxes. A&A, 56, 273.
Turon, C. et al. (1992). The HIPPARCOS Input Catalogue. I – Star Selection. A&A, 258, 74.
van Leeuwen, F. (2007). Hipparcos, the New Reduction of the Raw Data. Dordrecht: Springer.