2005/06/20 | 距离尺度[Distance Scale]
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The distance scale to local and distant objects in the universe can be determined using a number of methods. For close objects, geometric parallax provides a rigorous and absolutely reliable distance (to within experimental measurement error). For more distant objects, "standard candles" (objects of a given class whose distance is computed by comparing the observed brightness to an assumed absolute luminosity).
Baade method: Uses the brightness of supernovae (see below).
Bappu-Wilson method: let be the width (in Hz) between the edges of the central peak of the re-emission H or K lines of Ca+ (which itself has a superimposed peak). Experimentally, it is found that

This method can be used to the distances to nearby globular clusters and distant stars (Harwit 1988).
Cepheid variable (Type I): measure the period of a variable star. This period is related to the intrinsic brightness (and is independent of distance). Determine the star's luminosity, then compute the distance required to account for the observed flux. Cepheid variables allow measurement of distances to nearby galaxies.
Cepheid variable (Type II): population II Cepheid variables which have a shorter period and lower luminosity than type I Cepheids.
cluster main sequence fitting: measure the flux from stars in a cluster. Line up the main sequence on a calibrated HR diagram (a cluster, like the Hyades, for which luminosity is known). Then determine the distance at which luminosity will match the observed flux. This technique works best for globular clusters.
Faber-Jackson law: the rms spread in the velocity dispersion of stars in an elliptical galaxy is related to the galaxies intrinsic luminosity.
galaxy brightness: assuming that identical galaxy types have roughly the same brightnesses, so the distances to nearby galaxies can be determined.
geometric construction: use simple geometric constructions to determine size scale of earth, sun, and moon. This technique works for nearby objects in the solar system.
H II regions: assuming that the diameters of H II regions are constant, the distance to nearby galaxies can be inferred.
Hubble method: measure the Doppler shift of an astronomical body and compute the radial velocity. Then use the Hubble expression to compute the corresponding distance,
This method is used for distant galaxies.
moving cluster method: measure the angular extent of a moving cluster at different times. Measure the cluster's Doppler shift, and compute the radial velocity.

and

Therefore,

and

This means that

Because the cluster must be close, this technique can only be applied to the Hyades Cluster.

novae: the absolute brightness is related to the decay rate of the brightness. This allows distances to be found for nearby galaxies.
O stars: all O stars have roughly the same brightnesses, so the distances to nearby galaxies can be determined.
parallax: the angular shift seen in nearby objects as the earth orbits around the sun. Parallax shift of 0.02 can be measured, corresponding to a distance of 50 pc. This method therefore works for solar system objects and nearby stars.
planetary nebula: the luminosity function of planetary nebula can be estimated (Jacoby 1989).
proper motion: real angular shift of objects against background stars (yields component of velocity perpendicular to line of sight).
radar: by bouncing radar of an object and accurately timing the transmission and reception, the distance to objects in the solar system can be determined.
RR Lyrae variable: measure the period of a variable star. This period is related to the intrinsic brightness (and is independent of distance). Determine the star's luminosity, then compute the distance required to account for the observed flux. RR Lyrae stars allow measurement of distances to globular clusters.
spectroscopic parallax: the distance obtained by observing a star's color, correcting for Doppler shift, inferring the star's luminosity from a calibrated HR diagram, and calculating distance based on the observed flux. This method works for nearby clusters.
supernova (Baade's Method): measure the flux from a supernova remnant and, from an estimate of its luminosity, compute the distance.
surface brightness fluctuations: The amplitude and brightness variations in elliptical and spiral galaxies depends on the density of giant stars (Tonry and Schneider 1988).
Tully-Fischer relationship:
variable star:
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