Classical Cepheid variable - Wikipedia
as the period-luminosity relationship; He used his data on nearby Cepheids to. The radii of 28 variables are used to determine the period-radius relation. . calibrations of the Cepheid period-luminosity relations and will be derived in Section 5 of .. means, a correction which was found appropriate from tests on several. Who first used RR Lyrae variable stars to determine distances in our Milky Way Galaxy? . use the period-luminosity relationship of RR Lyrae variables to determine the If a star with a large peculiar proper motion and/or speed with respect a.
Recent investigations suggest that not only the zero-point but also the slope of the Milky Way PL relation differ significantly from that of the LMC, casting doubts on the universality of the Cepheid PL relation. We want to make a differential comparison of the PL relations in the two galaxies by delineating the PL relations using the same method, the infrared surface brightness method IRSBand the same precepts.
We furthermore extend the metallicity baseline for investigating the zero-point dependence, by applying the method to five SMC Cepheids as well. We present new and accurate radial velocity measurements for a sample of 22 LMC Cepheids, enlarging our earlier sample of 14 stars to include 36 LMC Cepheids.
In the J,K bands we find identical slopes for the LMC and Milky Way PL relations and only a weak letallicity effect on the zero points consistent with a zero effectmetal poor stars being fainter.
In the optical we find the Milky Way slopes are slightly shallower than the LMC slopes but again consistent with no difference in the slopes and small effects on the zero points. The K-band PL relation on the other hand is found to be an excellent extragalactic standard candle being metallicity insensitive in both slope and zero-point and at the same time being reddening insensitive and showing the least internal dispersion. Introduction The Cepheid period-luminosity PL- Relation is fundamental to the calibration of the extra-galactic distance scale and thus to the determination of the Hubble constant.
Modern reviews on the calibration of the Cepheid distance scale can be found in e. A dissenting view can be found e. The value of the PL relation rests with its universality, in particular that the PL relation slope and zero points are independent of metallicity.
However, the size and even the sign of the effect is still disputed.
Observationally, we are in the dilemma of either using a large sample of Cepheids, like in the Large Magellanic Cloud LMCwhich constrains very well the slope of the relation for a low metallicity sample of stars and which leaves the zero point to be determined from secondary indicators, or of using direct geometric distances parallaxes to a handful of nearby, solar metallicity, Milky Way Cepheids which constrain well the zero point of the PL relation but which do not constrain the slope very well.
Baade-Wesselink type methods which use the pulsational properties of the Cepheids to determine direct distances to individual Cepheids promise to resolve this dilemma by yielding direct individual distances to a large sample of Milky Way and Magellanic Cloud Cepheids spanning a significant range of metallicities.
A few years ago the IRSB method was re-calibrated using interferometrically measured, phase-resolved angular diameters of Cepheids by Kervella et al. We interpreted this as evidence for the existence of an as yet undetected period-dependent systematic error in the IRSB method, but the limited size of the LMC sample prevented firm conclusions.Luminosity of a Star
To put our previous analysis on a firmer basis, we present in the present paper new and very accurate radial velocity curves for 22 additional LMC Cepheids Sect. The atmosphere of the Sun oscillates with a fundamental period of about 5 minutes. The study of these periods helioseismology provides a probe of the interior of the Sun, and provides temperature and density profiles accurate to a few percent within the convective zone. Asteroseismology, now possible for some of the brighter stars, reveals their internal characteristics temperatures, densities, etc.
Intrinsic variables All convective stars spectral types F, G, K, Mincluding the Sun, display both periodic and irregular variability resulting from stellar magnetic activity in the outer atmosphere. Asymmetric distributions of starspots reveal themselves as periodic rotational modulation of the brightness, with amplitudes up to 0.
Flaring due to magnetic recombination is irregular, and is common among the younger, more rapidly rotating convective stars. 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.
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. 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.
Cepheid Variable Stars & Distance
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.
Cepheid Variable Stars & Distance Determination
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. The bump is most commonly seen on the descending branch for stars with periods around 6 days e.
Lecture Pulsating Stars
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. 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. 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.