Looking at the H-R Diagram, you will first note that numerous stars are plotted. Imagine millions of stars, that is what makes up the diagram itself. Image courtesy of Florida State College at Jacksonville. Langer The tracks are computed using the LMC initial composition and include those published in Brott et al. According to the definition of L in Sect.
Comparing the two diagrams in Fig. Equation 8 determines the gravities of stars near the Eddington-limit, as it transforms to 9 see Table 1.
For stars with a helium-enriched surface, Eq. Table 1 Surface gravity see Eq. An example of this is provided by Markova et al.
That this possibility has its limits when high- and low-mass stars are shown together is demonstrated in Fig. We thus note here that the use of the effective gravity in Sect. We note again that spectroscopic determinations of can be made with a precision of about 0.
Furthermore, it is interesting to compare the tracks of the stars in the three diagrams in Figs. However, it is predicted that a certain fraction of stars does evolve according to unusual evolutionary paths, in particular the close binary stars, which undergo mass transfer. Moreover, at high mass there is also the possibility of chemically homogeneously evolving stars as a consequence of rapid rotation Brott et al.
For comparison, the same tracks shown in Figs. Both situations can lead to stars that are overluminous, i. An overluminosity is thus related to a larger mean molecular weight in a star than expected for an ordinary star Langer We note that in practice the determination of the surface gravity of a rapidly rotating star may require a centrifugal correction Herrero et al.
We do not consider this here, but focus on the effect of the helium enrichment produced by the rapid rotation, which remains once the star has spun down.
We see the same behavior in mass donors of interacting close binary models. This is demonstrated by the evolutionary track of the mass donor of a close binary model with an initial period of 2. Its absolute and relative change in mass is similar to that of the mass gainer the binary evolution model is almost conservative.
This increases its average mean molecular weight to values which ordinary single stars could not achieve. For comparison, the tracks from Fig. The right ordinate scale is not valid for them. The labels give the initial masses for the tracks drawn as solid lines. Figure 4 shows that later, after the star returns from its minimum effective temperature, the effect becomes even more drastic.
The mass donor is by then reduced to a total mass of 2. Compared to an ordinary 2. A shift by 2. White Dwarf stars, on the other hand, are extremely hot and dense, but because of their small size, they are not very luminous.
As a result, they can be found below and to the left of the main sequence. Following that, they will either go supernova or become a white dwarf. If you follow the pink band for hot stars down to the bottom of the H-R diagram you will notice that it intersects another group of stars that includes Procyon B.
These are the white dwarfs. They are very hot about 10, K or hotter therefore emit a lot of energy per second for each square metre of their surface. The fact that they are so dim however, means that they must be extremely small and have a very low surface area. The terminology of white dwarf must not be confused with the old-fashioned term of dwarf stars that was applied to main sequence stars. White dwarfs are very different objects to main sequence stars as we shall see in a later page.
Technically they have a luminosity class of wd. If we compare the dimmest stars on the H-R diagram we can also make some inferences.
The following diagram shows the lower region of the H-R diagram. Procyon B however is much hotter than Barnard's Star thus emits much more energy per second per unit surface area.
Given that they have the same total power output Procyon B must therefore have less surface area than Barnard's Star, that is its radius is smaller. This points to an interesting and sometimes confusing feature of the H-R diagram - the scales on the axes.
If colour index B-V rather than effective temperature is used then it goes from negative blue on the left to positive red on the right. A third alternative along the horizontal axis is to use spectral class. Of course, all three quantities are essentially showing the same thing. The diagram below shows the possible axes for an H-R diagram. The vertical axis displays the luminosity of the stars. This is either as a ratio compared with that of the Sun or as absolute magnitude, M.
One point to be careful of when using absolute magnitude is to remember that the lower or more negative the absolute magnitude, the more luminous the star. The brightest stars therefore appear at the top of the H-R diagram with the vertical axis having the most negative value of M at the top.
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