3. In class, I mentioned how people like to confuse the terms "galaxy" and "universe." People also mix up the terms "solar system" and "galaxy," and that's the problem here. The statement should read:
"The Sun is in fact the only star in our solar system. All of the other stars in the sky are located in other solar systems."
Solar system: a star and all of the things that orbit it (like the Sun and its accompanying planets, asteroids, and comets).
Galaxy: a collection of billions of stars, held together by gravity (like the Milky Way).
Universe: everything that exists. It contains many different galaxies.
6. Spirals, barred spirals, and irregulars are likely to have new stars forming within them, while elliptical galaxies are not. There are many lines of evidence that point to on-going star-formation in all galaxies except ellipticals: an overall bluish color (signifying the presence of short-lived O and B stars), the presence of hydrogen gas (detected by radio 21-cm radiation), the presence of dust (detected using long-wavelength infrared observations, and/or seen silouhetted against background starlight), pinkish H II regions (emission nebulae made of hydrogen gas excited by nearby O and B stars), the detection of abundant metals in the spectrum of the galaxy (implying the presence of Population I stars).
8. Cepheid variable stars are useful for finding the distances to galaxies because they are standard candles. This means that they can be seen at great distances due to their high luminosity, that they are relatively common, that they are easily identifiable (because of the way that they vary in brightness), and, most importantly, that it is possible to deduce a Cepheid's average luminosity from the length of its period (due to the period-luminosity relationship for Cepheids). Knowledge of a Cepheid's average luminosity, combined with an observation of its average brightness, allows you to deduce its distance using the inverse square law of light.
Limitations: 1) If a galaxy is more than about 30 Mpc away, even the most luminous Cepheid residing in it will be too faint for our current telescopes to detect. 2) There are actually two different types of Cepheid variable stars: Pop I (metal-rich) and Pop II (metal-poor). The two types have different period-luminosity relationships, so you must be sure to know with which type you are dealing (this can be done fairly easily by looking for metal lines in its spectrum). 3) The Cepheid period-luminosity relationship must be calibrated by finding the distances to nearer stars using parallax and spectroscopic parallax. Errors in the distances to these nearer stars will degrade the accuracy of the Cepheid method.
10. The Hubble Law says that 1) most galaxies (with the exception of the nearest ones) are moving away from us, and 2) the velocity (v) with which a galaxy recedes from us is directly proportional to its distance (d): the farther away it is, the faster it recedes. In symbols: v = H0 d, where H0 is the Hubble constant.
Rearranging the formula, we find that if you know the value of the Hubble constant, and if you measure a galaxy's radial velocity using the Doppler effect, then you can deduce its distance: d = v / H0. (Of course, for this to work, you must know what the Hubble constant is, and this can only be determined by measuring the distances to many galaxies independently of their velocities: H0 = v / d.
12. Galaxies that are near to our own (like those in the Local Group) feel the gravitational pull of our Galaxy fairly strongly, and this gravitational attraction offsets (or outweighs) the pushing-away that the galaxy feels due to the expansion of space between us and it. Thus, nearby galaxies will not follow the Hubble Law, and may in fact be moving towards us -- causing a blueshift in their spectra.
19. Because of the way that the distance ladder is set up, techniques for measuring the distances to far-away galaxies are calibrated by techniques for measuring relatively nearby stars. In the end, all distance techniques (at least, all of the ones that we have talked about in this course) rely on parallax in some way, so when the Hipparcos space mission improved the parallaxes to nearby stars, all distance-measurements needed to be revised.
20. (a) Globular clusters, being in the halo, contain Pop II stars, while mostly Pop I stars are found in the disks of spiral galaxies. This is because metal-rich Pop I stars are partially made from the metals cooked up in the cores of previous metal-poor Pop II stars, implying that Pop I stars are younger than Pop II. And given the fact that there is active star-formation going on in the disks of galaxies but not in the haloes (see question 6 above for the evidence that leads us to this), we can only find Pop I stars in the disk. So we expect to find Type I (that is, Pop I) Cepheids in the disk, and Type II (or Pop II) Cepheids in the halo.
(b) Looking at Figure 21-15 (page 492), we see that if a Type I Cepheid has the same period as a Type II Cepheid, then the Type I will always be more luminous. Hubble measured the periods of Type I Cepheids in the disk of the galaxy M31, but he assumed that they were Type II Cepheids like the ones in our halo. Thus, he under-estimated the luminosities of the M31 Cepheids. He then compared their luminosities to their apparent brightnesses to derive their distances, using the inverse square law of light. So how would this mess up his estimation of their distances?
Imagine two Cepheids, a Type I and a Type II, with the same period. The Type I is therefore more luminous. Imagine that these two Cepheids appear to have the same average brightness. Which one is closer? The less luminous one -- the Type II (it has to be closer to make up for the fact that it's less luminous).
Now imagine that the less distant Type II Cepheid disappears, leaving only the more distant Type I. You look at this Cepheid and mistakenly think it's the Type II (like Hubble did). You therefore conclude that it's closer than it actually is (like Hubble did).
(Got that? Think hard about what the inverse square law of light means, and you should see that this is true. Alternatively, try solving the inverse square law of light for d, and see how it depends on L.)
24. (a)
v = H0 d
10,800 km/s = (70 km/s/Mpc)(d)
d = 154 Mpc
There are 3.26 x 106 light-years in 1 megaparsec.
d = (154 Mpc)(3.26 x 106 ly / 1 Mpc) = 5.02 x 108 ly
(b) Rearrange the Hubble law to solve for d:
d = v / H0
We see that d and H0 are inversely related. Therefore, if H0 was smaller, d would be larger, and vice versa.
25.
v = H0 d
H0 = v / d
So we just need to divide the velocity of the galaxy by its distance to get H0. However, since the usual units of the Hubble constant are km/s/Mpc, we should convert the distance into Mpc (otherwise we'd get H0 in km/s/pc). There are one million (106) parsecs in a megaparsec, so d = (1.4 x 108 pc)(1 Mpc / 106 pc) = 140 Mpc
H0 = (7,500 km/s) / (140 Mpc) = 53.6 km/s/Mpc
Last edited 04 May 04 M. A. Weinstein.