In what ways, if any, does the distance to a star influence its position on an H-R diagram?
The distance to a star does not influence its position on the H-R diagram: photospheric temperature and luminosity are intrinsic properties of a star. However, we sometimes have to apply corrections to our observations, because of interstellar extinction, in order to obtain intrinsic properties.
The photospheric temperatures and luminosities of five stars that are visually fairly bright in the sky are given in Table 1.
|Alkaid(η UMa)||17000||6.1 × 1029|
|Alcyone (in the Pleiades)||12000||3.2 × 1029|
|ε Eridani||4700||1.4 × 1026|
|Propus (η Gem)||3000||4.2 × 1029|
|Suhail(λ Vel)||2600||1.8 × 1030|
(a) Plot these stars on an H-R diagram (such as Figure 5), and hence try to assign each star to one of the main stellar classes described in Section 2.2.
(b) Suppose that we were to compare stars by preparing an H-R diagram that includes only the stars with the greatest apparent visual brightness. Discuss why such a diagram would be unrepresentative of stars as a whole.
(a) Figure 22 shows the five stars plotted on an H-R diagram. By comparison with Figure 5, we can make the following assignments given in Table 2.
|Star||Main stellar class||Comment|
|ε Eridani||main sequence||a nearby (3.2 pc), solar-type star|
|Suhail||red giant/supergiant||some stars fall between the four main classes|
(b) Low luminosity stars can have a large apparent visual brightness only if they are particularly close to us. Thus, low-luminosity stars will be under-represented in an H-R diagram that contains only the stars with the greatest apparent visual brightness. (There is always a likelihood that low-luminosity stars will be under-represented, simply because any detection system will fail to detect stars that give too low a flux density at the detector. This is an example of a selection effect.)
In terms of photospheric temperature, luminosity and radius, compare the Sun with other main sequence stars.
From Figure 5 we see that the Sun's photospheric temperature, T⊙, luminosity, L⊙, and radius, R⊙, have the following relationships to the temperature T, luminosity L and radius R of stars near the upper and lower ends of the main sequence:
upper end: T~ 6T⊙, L ~106L⊙, R~10R⊙
lower end: T~0.3 T⊙, L~10−4L⊙, R~0.03R⊙
Thus, the Sun is a very modest main sequence star.
Given that T Tauri stars become main sequence stars with little change in photospheric temperature, discuss whether this transition is accompanied by a change in stellar radius.
The region where T Tauri stars are found on the H-R diagram is shown in Figure 7. Since the question states that T Tauri stars approach the main sequence with little change in temperature, they must follow vertical paths from this region to the main sequence. By inspection of Figure 5 it can be seen that by following a vertical track from the T Tauri region to the main sequence a small reduction in radius must occur.
Discuss whether we can rule out the evolution of red giants to form supergiants.
To evolve into a supergiant, the red giant would have to acquire a lot of mass: see Figure 8. However, observations suggest that red giants lose mass (in the form of stellar winds), and so we can rule out the scenario in which a red giant evolves into a supergiant.