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Statistical biases in extragalactic distance determinations.

This work examines the challenges of bias in extragalactic distance determinations, focusing on the Hubble constant (H₀) and various observable parameters. The paper discusses when biases arise, particularly in contexts like the Tully-Fisher and Cepheid Period-Luminosity relations, exploring classical Malmquist and incompleteness biases. Using simulations and existing data, it analyses how these biases can influence distance measurements and their implications for cosmological models. It emphasizes the need for careful evaluation of standard candles and their reliability in distance estimation.

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Statistical biases in extragalactic distance determinations.

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  1. Statistical biases in extragalactic distance determinations. G. Paturel, Observatoire de Lyon In collaboration with P. Teerikorpi IHP 28-29 Avril 2005

  2. The difficult problem of Ho

  3. When does a bias appear ? 1) When the absolute magnitude is expressed as a function of an observable parameter with a scatter Examples : Tully-Fisher Relation Period-Luminosity Relation 2) When the sample has a limiting apparent magnitude mlim

  4. Let us explain in a simple case The « sosie » method (e.g.for TF relation) We select galaxies with the same logVM Through they should constitute « Standard Candles » with the same absolute magnitude. Are standard candles free of bias ? No !

  5. Graphical explanation of two kinds of bias (1) Classical Malmquist bias

  6. Graphical explanation of two kinds of bias (2) Incompleteness bias (at a constant distance modulus)

  7. How Cepheid Period Luminosity relation looks like ? The Cepheid PL relation fill the conditions to have a bias at a constant distance

  8. Does the bias affect the Cepheid Period-Luminosity relation ? The bias should exist but it can be small due to the small scatter of the PL relation. How to test the existence of a possible bias in the PL relation ?

  9. A simple simulation shows that a bias can exist Is it possible to use redshift as a relative distance indicator ? YES

  10. The Hubble law: V= H.r The original discovery: V < 1200 km/s

  11. Small dispersion around the regular Hubble flow • In 1957 de Vaucouleurs noted that deviations from Hubble law are small (<100 km/s) • In 1972 Sandage and coworkers (ApJ 172, 253) found still maller value (<60 km/s) • In 1999 Ekholm et al. confirm that the Hubble law works at small scale • In 2001 Ekholm et al. and Karachentsev et al., independently found a still smaller dispersion (<40 km/s) of the very local expansion

  12. Comparison with models

  13. We have a tool to have accurate, relative distances

  14. Hubble diagram with Cepheid distances

  15. Use of the 2-parameter bias model by Teerikorpi (1975) to check a bias diagram

  16. A bias diagram When the absolute limiting Magnitude allows us to see faint Cepheids the bias is Negligible. The fit of the bias model Leads to : logH=1.76 ; H=56 (km/s)/Mpc

  17. Influence of the correlation of errors The fit of the bias model Leads to : logH=1.80 ; H=63 (km/s)/Mpc The reality could be H=60 (km/s)/Mpc

  18. Comparison of corrected and uncorrected distances, using HST anf ground-based Cepheid distances Ground-based HST

  19. How the Hubble diagram changes

  20. What about long range distances

  21. The final question by A.Blanchard : Are the SN- standard candle affected in a similar way The possibility exists because the reference sample is not similar to the distant one (mixing several luminosities) Another effect could be due to evolution effect

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