next up previous
Next: The Mass of the Up: No Title Previous: No Title

Cosmological Distances

Part A Cepheid Variables
As we've discussed in class there exists a relationship between the period of luminosity variation and average luminosity for pulsating stars known as Cepheids. If we can identify a Cepheid variable and measure the period of its brightness variation then we can infer its luminosity from this relation and in turn determine its distance. We accomplish this via the relation between brightness and luminosity given as


where b is brightness measured in tex2html_wrap_inline189 , L is luminosity typically measured in tex2html_wrap_inline191 where tex2html_wrap_inline193 , and d is distance to the star measured in parsecs, with tex2html_wrap_inline195 .

  1. The Hubble Space Telescope (HST) Key Project team has been searching for Cepheids in galaxies within the Virgo cluster. In the barred spiral galaxy NGC 4535, believed to be a Virgo cluster member, several Cephieds have been found. One of them has a period of 30 days and is measured to have a brightness at Earth, tex2html_wrap_inline197 . Use the period-luminosity relationship given in Figure 1 and calculate the distance to NGC 4535 in Mpc.

    Figure 1: The Period-Luminosity relationship for Cepheids. The shaded strip centered on the mean line indicates schematically that there are slight devaitions from a one-to-one relation, because of both theoretical reasons and observational uncertainties. (From Shu, Chapter 9)

  2. Consider a Cepheid with period of 100 days. If the limiting brightness that HST can see is tex2html_wrap_inline199 calculate the distance to which this Cepheid can be seen. In practice the limiting distance for Cepheids is right about at the distance of the Virgo cluster. What might be some reasons for this limitation?

Figure 2:

Part B Light Echoes
In 1987 a supernova exploded in the Large Magellanic Cloud, it was given the endearing name SN 1987A. When the Hubble Space Telescope (HST) observed the remanant of the supernova it observed several rings surrounding it (see figure 2). These are thought to be material thrown off by the progenitor star sometime before the explosion. The supernova heated the rings of gas causing them to glow like fiery goats. Let's consider the inner, bright ring. It is presumed to be circular but tilted from the perspective of Earth. It's projected semi-axes have dimensions 0.830'' and 0.605''. Because of the tilted geometry light was was received from the near side of the ring 340 days before light arrived from its far side.

  1. Determine the inclination angle, i, between the normal to the plane of the ring and the line of sight from Earth.
  2. Use the time delay to determine the radius, r, of the ring in parsecs.
  3. Use trigonometry to find the distance to SN 1987A.
  4. If HST can resolve a minimum angle of 0.100'' what is the maximum distance to which this method could be applied?

next up previous
Next: The Mass of the Up: No Title Previous: No Title

Astronomy 7
Thu Nov 11 17:12:29 PST 1999