The period lumosity relationship is useful in determining appropriate

Cepheid Variable Stars & Distance

the period lumosity relationship is useful in determining appropriate

Who first determined that the energy/sec emitted by (luminosity of) Cepheid variable .. If a star with a large peculiar proper motion and/or speed with respect a The period-luminosity relationship is primarily used for main sequence stars. T/F. determination of the zero point of the period-luminosity relation He used the same proper motion data as Hertzsprung but omitted x Pavonis and 1 Carinae. Once established, this period-luminosity relation obviously would provide a simple From the proper motions of 13 cepheids in the Boss Preliminary General a new determination of the zero point of the period-luminosity relation. 2 He used.

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.

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.

The bump is most commonly seen on the descending branch for stars with periods around 6 days e. As the period increases, the location of the bump moves closer to the maximum and may cause a double maximum, or become indistinguishable from the primary maximum, for stars having periods around 10 days e. At longer periods the bump can be seen on the ascending branch of the light curve e. X Cygnibut for period longer than 20 days the resonance disappears.

the period lumosity relationship is useful in determining appropriate

A minority of classical Cepheids show nearly symmetric sinusoidal light curves. These are referred to as s-Cepheids, usually have lower amplitudes, and commonly have short periods. The majority of these are thought to be first overtone e.

PHY / The Cepheid Period-Luminosity Relation

X Sagittariior higher, pulsators, although some unusual stars apparently pulsating in the fundamental mode also show this shape of light curve e. Stars pulsating in the first overtone are expected to only occur with short periods in our galaxy, although they may have somewhat longer periods at lower metallicity, for example in the Magellanic Clouds.

Higher overtone pulsators and Cepheids pulsating in two overtones at the same time are also more common in the Magellanic Clouds, and they usually have low amplitude somewhat irregular light curves.

the period lumosity relationship is useful in determining appropriate

However, the namesake for classical Cepheids is the star Delta Cephei, discovered to be variable by John Goodricke a few months later. Delta Cephei is also of particular importance as a calibrator for the period-luminosity relation since its distance is among the most precisely established for a Cepheid, thanks in part to its membership in a star cluster [17] [18] and the availability of precise Hubble Space Telescope and Hipparcos parallaxes.

Flaring is most noticeable in the X-rays and UV, and among the M stars, where contrast with the photosphere is enhanced. Explosive variables include novae. The buildup of hydrogen-rich matter on the surface of a white dwarf, drawn fron a Roche-lobe-filling companion, will undergo a runaway thermonuclear detonation once enough builds up on the surface so that the lower layers become degenerate.

period–luminosity relation

Novae occur irregulary, at intervals from millions of years to a few years, depending on the accretion rate and the mass of the white dwarf. Cataclysmic variables CVs are white dwarf binaries undergoing accretion. These vary by a few magnitudes irregularly due to changes in the mass accretion rate. In the Polars, or AM Her stars, the accretion stream impacts the surface of the white dwarf directly. Variations in the mass accretion rate lead directly to brightness changes as the gravitational potential energy released heats the accretion colun and the impact zone.

In the dwarf novae an accretion disk forms, and the brightness variations in the disk reflect the viscous heating of the disk. All CVs eventually become novae. In an analogous set of variables, the X-ray binaries, the white dwarf is replaced by a neutron star of stellar-mass black hole.

5-types of stars and mass luminosity relationship

Artist's conception of a Polar, showing the disruption of the accretion stream by the MG magnetic field of the white dwarf Image copyright M. 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.

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. 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.

the period lumosity relationship is useful in determining appropriate

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.

the period lumosity relationship is useful in determining appropriate

At a given period, W Vir stars are less luminous than are classical Cepheids. Inadvertent application of the classical Cepheid P-L relation to W Vir stars leads to a to a large overestimate of the distances. Cepheids in Modern Astrophysics The study of the phenomenology of variable stars reached its zenith in the early 20th century.

Of what use is the study of Cepheids today? Simply put, because of the elegance and simplicity of the period-luminosity relation, they form the principle rung in the cosmic distance ladder.

Classical Cepheid variable - Wikipedia

The Cepheids are giants and supergiants which lie in the instability strip. Because they are intrinsically luminous, they can be seen to great distances. One of the key projects in the early years of the Hubble Space Telescope was to find and measure the periods of Cepheids in nearby galaxies, out to distances of about 20 Mpc 6 x km.