PHY / The Cepheid Period-Luminosity Relation
The theoretical period-luminosity relation for Cepheids was deduced from stellar evolution and pulsation computations. Questions concerning the metallicity. The period-luminosity relation is a correlation between the periods and mean luminosities of Cepheid variables. Some types of pulsating variable stars such as Cepheids exhibit a definite relationship between their period and their intrinsic luminosity. Such period- luminosity.
To verify that the period does increase with increasing luminosity. Prior to starting this lab, you must understand the astronomy at the AST level. Check the referencesor other basic astronomy references you may find in the library. The introductory quiz will be at the AST level. You must also have read the IDL primer. This is a data intensive lab and you will not be able to waste much time the first period reading the notes. Grading Policy Grading is based on the quality of the data analysis, the discussion of the uncertainties, and the answers to the questions at the end of this page.
Introduction The state-of-the-art astronomical detector before the late 19th century was the human eyeball. The eyeball is a marvelous detector, with excellent dynamic range and color sensitivity, but it has limited sensitivity and poor recording ability. The refinement of telescopic technology helped with the sensitivity limitations, but it was the invention of the photographic plate that permitted one to amass and study large amounts of data in a coherent fashion.Astronomy - Ch. 17: The Nature of Stars (15 of 37) Comparing Luminosity
Large Magellanic Cloud Figure 2: It did so fairly regularly until about with some plates taken up to Over half a million of these plates are stored in the Harvard plate stacks. One of the early targets was the Large Magellanic Cloud LMC; see above left imagea nearby 65 kilo-parsecs dwarf irregular galaxy. Henrietta Leavitt right image above ; also see this sitewho held the position of "computer" at the Harvard College Observatory, began classifying the variable stars in the LMC in Stars were not well understood a century ago, and much of astronomy was devoted to discovering and characterizing the variables.
The astrophysical significance of studying variable stars in the LMC is that all the stars in the LMC are roughly the same distance from us.
Distances are one of the most fundamental, but most difficult to measure, quantities in astronomy. Therefore, one can compare distance dependent quantities like luminositieswhich one cannot do easily for the brighter stars in our own Milky Way galaxy. Most, if not all, stars are variable. Some, like the novae, are spectacularly variable, while others are barely noticeable even upon close inspection. Among the plethora of types of variables are: Eclipsing variables, which are binary systems we observe from in or close to the plane of the orbit.
They vary because one star gets in front to the other each orbit, thereby diminishing total brightness. This is simply a geometrical obscuration. Pulsating variables, which are stars that lie in the instability strip in the Hertzsprung-Russell H-R diagram a plot of luminosity or magnitude vs. Most stars are stable against adiabatic perturbations. Perturb the star to a larger radius. The temperature will fall and the opacity will increase. Then let the star contract under its gravity.
The enhanced opacity will result in an enhanced radiation pressure, and a damping of the oscillation. However, in the instability strip, hydrogen is partially ionized in the outer radiative envelope of the star. As gravity makes the star contract, the low opacity does not lead to an increased radiation pressure, so the oscillations do not damp out.
The instability strip runs diagonally through the H-R diagram, with temperatures near 10,K. All stars are natural pulsators at low amplitudes.
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.
Cepheid Variable Stars & Distance Determination
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.
Interstellar Medium and the Milky Way
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. Its light curve is shown in Figure 6.
The Danish astronomer, Ejnar Hertzsprung quickly realised the significance of this discovery. By measuring the period of a Cepheid from its light curve, the distance to that Cepheid could be determined.
He used his data on nearby Cepheids to calculate the distance to the Cepheids in the SMC as 37, light years away. From this he could infer the distance to globular cluster too distant to have visible Cepheids and realised that these clusters were all essentially the same size and luminosity. By mapping the distribution and distance of globular clusters he was able to deduce the size of our galaxy, the Milky Way. Using these he determined that their distances wereandlight years respectively.
He thus established conclusively that these "spiral nebulae" were in fact other galaxies and not part of our Milky Way. This was a momentous discovery and dramatically expanded the scale of he known Universe.
Hubble later went on to observe the redshift of galaxies and propose that this was due to their recession velocity, with more distant galaxies moving away at a higher speed than nearby ones. This relationship is now called Hubble's Law and is interpreted to mean that the Universe is expanding. Period-luminosity relationship for Cepheids and RR Lyrae stars. Let us now see how this relationship can be used to determine the distance to a Cepheid.
Photometric observations, be they naked-eye estimates, photographic plates, or photoelectric CCD images provide the apparent magnitude values for the Cepheid.
Plotting apparent magnitude values from observations at different times results in a light curve such as that below for a Cepheid in the LMC. From the light curve and the photometric data, two values can be determined; the average apparent magnitude, m, of the star and its period in days. In the example above the Cepheid has a mean apparent magnitude of Knowing the period of the Cepheid we can now determine its mean absolute magnitude, M, by interpolating on the period-luminosity plot.
The one shown below is based on Cepheids within the Milky Way. The vertical axis shows absolute magnitude whilst period is displayed as a log value on the horizontal axes. The log of 4. When this is plotted a value of about Once both apparent magnitude, m, and absolute magnitude, M are known we can simply substitute in to the distance-modulus formula 4.
More importantly, if we infer that the size of the LMC relative to its distance from us is small we have also found the distance to the LMC within which the Cepheid is located. In practice astronomers would try and observe as many Cepheids as possible in another galaxy in order to determine a more accurate distance. As the number of stars observed go up the uncertainties involved in calculations for individual stars can be statistically reduced.