University of California, San Diego
Center for Astrophysics & Space Sciences

Solar System Distances

Radar + Newton's laws determine the AU (Astronomical Unit = 149,597,900km ~ 93,000,000 miles).

Parallax - Nearby Stars/500ly

Cluster H-R Diagrams - Milky Way Clusters/100,000ly

Cepheid Variable Stars - Nearby Galaxies/50Mly

Variable stars have proven to be one of the most reliable types of "standard candles". Cepheid Variables are giant stars which have instabilities in their envelopes that cause them to pulsate in size, temperature and luminosity over timescales of a few days. Below is the light curve (brightness as a function of time) for Cephei, the variable star in the constellation Cepheus from which the stars derive their name. This Mpeg animation shows the pulsation of a cepheid.

Light Curve of Delta Cephei
(You can determine your own light curve from the AAVSO)

The pulsations of Cepheids are very regular; Cephei has a period of pulsation (time between maxima or minima) of 5.366341 days. Furthermore the period is directly related to the luminosity of the star as shown from the Period-Luminosity Relation.

This relationship was first discovered by Henrietta Leavitt at Harvard who noticed that Cepheids in the Magellanic Clouds hae a relationship between apparent brightness and period in the sense that brighter Cepheids have longer pulsation periods. Since all the stars in the Magellanic clouds are about the same distance, this relationship must be a relationship between luminosity and period as well. Cepheids exemplify the desirable characteristics of standard candles:

• Their luminosities may be determined from the P-L relationship which has very little scatter.
• They are giant stars so they are pretty luminous and can be seen out to relatively large distances. With HST Cepheids are being studied in galaxies in the Virgo Cluster. about 50 million light-years away.
• The variability of Cepheids makes them easy to pick out. Photographs (now digital images) are obtained of galaxies over several nights. When the images are compared, most stars don't change, but the Cepheids blink brighter and fainter and are easily distinguished from the billions of other "normal" stars.

Cepheid Variable in M100
(may also be seen in this MPEG animation)

Brightest Stars & HII Regions

Supernovae

Probably the most promising new distance determination technique involves the use of Type Ia Supernovae as "Standard Candles". Type Ia Supernovae are white dwarf stars in binary systems in which mass is being transferred from an evolving companion onto the white dwarf. If the amount of matter transferred is enough to push the white dwarf over the 1.4 M "Chandrasekhar limit" for electron-degeneracy support, the white dwarf will begin to collapse under gravity. Unlike massive stars with iron cores, the white dwarf will have a C/O core which can undergo further nuclear reactions. The collapse of the white dwarf liberates enough heat that nuclear reactions ignite and blow the remnant apart in a thermonuclear deflagration. These SNIa explosions have all the right characteristics for Standard Candles; they are:

• extremely bright, outshining the entire galaxy of stars in which they reside.
• easily detected, but very rare, occurring only about once every 500 years in our galaxy.
• very uniform in brightness at maximum light.

Doppler Shift/Hubble Law

The doppler shift is a shift in wavelength or frequency of a wave due to relative motion of the source and receiver. If the source of waves is moving toward the receiver (or vice versa) each successive wavecrest is emitted a small distance closer to the receiver, the wavecrests will be closer together and the wave will be"squashed as shown below (shorter wavelengths & higher frequency). Similarly, if the source of waves is moving away from the receiver each successive wavecrest is emitted a small distance further away, the wavecrests will be further apart and the wave will be"stretched" (longer wavelengths, lower frequency). This is the phenomenon that causes the apparent shift in pitch (from higher approaching to lower receding) as a train passes by sounding its whistle.

Because shorter wavelength is toward the blue and longer wavelengths are toward the red for visible light, approaching velocities are said to produce "blueshifts" and receding velocities produce redshifts. for speeds small compared to the velocity of light the shift is given by:

From the work of Slipher in the early part of the 1900's astronomers knew that most of the spiral nebulae (galaxies) are receding from us. Edwin Hubble demonstrated that there was a linear relationship between distance and velocity for galaxies.

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