PHY / The Cepheid Period-Luminosity Relation
Cepheid stars and RR Lyrae star are examples of pulsating variable stars. A plot of the period-luminosity relation for Cepheid variables (as. Printed in U.S.A. THE PERIOD-LUMINOSITY RELATION FOR CEPHEID VARIABLE STARS R. B. HINDSLEY AND R. A. BELL Astronomy Program, University of. Cepheid variable, one of a class of variable stars whose periods (i.e., the time for Classical Cepheids exhibit a relation between period and luminosity in the.
With a calibrated period-luminosity relation astronomers could use Cepheid variables as standard candles to determine the distances to distant clusters and even other galaxies.
Cepheids have pulsation periods of 1 to 50 days. In the 's astronomers found that there are two types of Cepheids: Below is the light curve the plot of brightness vs. W Virginis Cepheids are from older low-metallicity stars and are about 4 times less luminous than Type I.
Below is the light curve of a W Virginis Cepheid from the Hipparcos database of variable stars. Note the differences in the shape of the light curve. The two types of Cepheids are distinguished from each other by the shape of the light curve profile. In order to compare the shapes without having to worry about the pulsation periods, the time axis is divided by the total pulation period to get the "phase": Because the luminosity of Cepheids can be easily found from the pulsation period, they are very useful in finding distances to the star clusters or galaxies in which they reside.
By comparing a Cepheid's apparent brightness with its luminosity, you can determine the star's distance from the inverse square law of light brightness. Recall that brightnesses are specified in the magnitude system, so the calibration brightness absolute magnitude is the brightness you would measure if the Cepheid was at the calibration distance of 10 parsecs 33 light years. In some cases the calibration distance may be the already-known distance to another Cepheid with the same period you are interested in.
Cepheid variable stars are so important that being able to measure their distances in other galaxies was the main factor in determining the size of the Hubble Space Telescope mirror and the measuring distances to Cepheids in 18 galaxies was the "Key Project" of the Hubble Space Telescope for its first decade all of the other results and pretty pictures were bonuses!
Early measurements of the distances to galaxies did not take into account the two types of Cepheids and astronomers underestimated the distances to the galaxies. He found it was aboutlight years away. However, the Cepheids he observed were Type I classical Cepheids that are about four times more luminous. Later, when the distinction was made between the two types, the distance to the Andromeda Galaxy was increased by about two times to about 2.
Recent studies using various types of objects and techniques have given a larger distance of between 2. They are smaller than Cepheids and, therefore, have shorter periods and lower luminosities. Pulsations in an overtone higher than first are rare but interesting.
Stars pulsating in an overtone are more luminous and larger than a fundamental mode pulsator with the same period. When the helium core ignites in an IMS, it may execute a blue loop and crosses the instability strip again, once while evolving to high temperatures and again evolving back towards the asymptotic giant branch. The duration and even existence of blue loops is very sensitive to the mass, metallicity, and helium abundance of the star.
In some cases, stars may cross the instability strip for a fourth and fifth time when helium shell burning starts. More massive and hotter stars develop into more luminous Cepheids with longer periods, although it is expected that young stars within our own galaxy, at near solar metallicity, will generally lose sufficient mass by the time they first reach the instability strip that they will have periods of 50 days or less.
- Classical Cepheid variable
- PULSATING STARS
Very massive stars never cool sufficiently to reach the instability strip and do not ever become Cepheids. At low metallicity, for example in the Magellanic Clouds, stars can retain more mass and become more luminous Cepheids with longer periods.
Cepheid Variable Stars & Distance
This is due to the phase difference between the radius and temperature variations and is considered characteristic of a fundamental mode pulsator, the most common type of type I Cepheid. In some cases the smooth pseudo-sinusoidal light curve shows a "bump", a brief slowing of the decline or even a small rise in brightness, thought to be due to a resonance between the fundamental and second overtone.
Garlick Ellipsoidal variables are stars that are not round, and present different aspects to us as they rotate. Ellipsoidal variables are all in close binary systems, where they are tidally-distorted by their companions. Doppler image of AE Phe at four phases, from Barnes et al. Some the RV Tauri stars form dust shells as they expand, which then obscure the light of the star until they expand and become diluted.
Of these, only about 20 were Cepheids. Its light curve is shown in Figure 6. Since all the stars are in the LMC, and are at the same distance from us, the apparent magnitudes are an accurate measure of the true relative luminosities of the stars.
Interstellar Medium and the Milky Way
She found a relation similar to that shown in Figure 7. She actually used apparent magnitudes; the conversion to absolute magnitudes shown in Figure 7 requires an estimate of the distance to the LMC.
The Cepheid period-luminosity relation The importance of such a relation, once it is calibrated, is that it provides a simple way to determine the distance to a Cepheid variable and, hence, to the cluster or galaxy that contains it. One merely determines the period, and observes the mean magnitude m. One looks up the absolute magnitude M that corresponds to that period. The difference between the apparent and absolute magnitudes, m-M, knows as the distance modulus, is equal to 5 log D -5, where D is the distance in parsecs.
This relation is easily derived from the inverse-square law, knowing that magnitudes are log2. Hence a measure of the period directly yields the distance.
This is simply the time it takes a sound or pressure wave to cross the stellar diameter. An isothermal star of solar radii and 10 solar masses will have a pulse period of about 5.
Cepheid Variable Stars & Distance Determination
One can derive the period-luminosity law as follows: Assume a sample of stars of the same mass classical Cepheids have masses of solar massesand the same temperature the instability strip is approximately vertical in the H-R diagram.
The luuminosity then scales as R2. Luminosity is proportional to 2. As observed from the Earth, stars trace appear to trace out the motion of the Earth's orbit around the Sun. Trigonometric parallax is useful to distance of about 50 pc for ground-based optical observations, and a few hundred pc for space-based, or radio VLBI, observations.
The accuracy is limited by smallness of the motions. There are no Cepheids within this distance. Beyond distances of a few tens of parsecs, one must cobble together distances from a variety of techniques. One can use the trigonometric parallaxes to determine the luminosities of stars on the main sequence. Then, the color or spectral type and observed magnitude of a main sequence star is sufficient to determine its true distance this is called the spectroscopic parallax.
Cepheids are not main sequence stars. However, some galactic Cepheids are found in clusters of stars. Like the stars in the LMC, all the stars in these clusters are at the same distance from us. One can us the spectroscopic parallax of the main sequence stars in the cluster to determine the distance to the cluster, and the Cepheid. The distance and observed magnitude then directly give the luminosity of the Cepheid, and a calibration of the period-luminosity relation.
There are of course many complications, most of which are beyond the scope of this introduction. However, there is one very important caveat. This is because there is a large difference in mean metallicity between the two galaxies: This affects the opacity, and the periods. Population I consists of metal-rich stars, including the Sun. Population II is metal poor, representing a population of stars that formed from a less enriched interstellar medium.