Comments on Homework 6

Part A

A1.	True
A2.	c.
A3.	a.
A4.	b.
A5.	The period-luminosity law for Cepheids (see b. under A4.) shows that the longer the period the more luminous the star. This means that the 100 day Cepheid is more luminous than the 10 day Cepheid. In order for a more luminous star to appear fainter than a less luminous star, it must be a greater distance. Would your answer have been different if the P-L law were selection a, c, or d under A4?
A6.	True.
A7.	False. Our galaxy is a spiral, probably a barred spiral.
A8.	The key here is that, if the Galactic rotation curve is flat (Seeds, Fig. 17-14, and text), the orbital velocity is the same at 16 kpc as at 8 kpc. But the length of the orbit at 16 kpc is TWICE that at 8 kpc. Twice the distance at the same speed takes twice as long to complete. Answer: 500 million years.
A9.	Primarily because they are not very luminous and, therefore, too faint to be detected beyond a short distance from Earth. Secondary reasons include the fact that (i) the luminosity of a WD declines as it ages/cools, and (ii) the luminosity at a given age/temperature depends on the WD's mass.
A10.	A key here is the massive stars (and their descendants) are exclusively members of Pop. II. Low mass stars (and their descendants) may belong to Pop. I and II. To resolve this ambiguity, we need additional pieces of information. - Type II SN - Pop. I - White Dwarfs - Pop. I or II. - dwarfs - Pop. I and II. - OB stars - Pop. I.
A11.	Pop. II
A12.	The star must be low mass, metal-poor and red.
A13.	Match the stellar population (I and II?) with the following:  ___I___young  ___I___Type II supernovae  ___II__metal poor  ___II___H I clouds  ___I___H II clouds  ___II___globular clusters  ___I___dark clouds  ___I___the Sun The numerals I and II are used in various and different ways. Population I and II are defined in the book. The labels I and II for supernovae, which were applied before the concept of stellar populations had been devised by Walter Baade, recognize whether or not the Balmer lines of hydrogen appear in the supernova spectrum: Type I do not have detectable Balmer lines, Type II have pronounced Balmer lines. We now recognize Type II as exploding massive stars ­ young, recently formed stars and therefore Pop. I. Type I SN are exploding WDs and, in general, low mass long lived old stars from Pop. II (or extreme Pop. I). These labels for SN are too ingrained in astronomy to be now reversed to consistent with the I and II of stellar populations. The I and II of H I and H II are the chemists I and II. I following the chemical symbol (here, H for hydrogen) denotes a neutral atom. II denotes an atom that has lost on electrons that it appears as a singly charged positive ion to an outsider. Since hydrogen has but one electron, H II is the end of the line. But carbon, for example, has 6 protons and its neutral atom has 6 electrons. Then, the full family of carbon ions is C I, C II, C III, C IV, C V, C VI, and the bare carbon nucleus would be C VII. From the point of view of the stellar populations, gas belongs to Pop. I. H I clouds, H II regions, and dark clouds are different manifestations of gas in the disk of the Galaxy. (In what ways are they different?)
A14.	atomic nucleus, H atom, centimeter, kilometer, neutron star, white dwarf, astronomical unit, light year, kiloparsec, our Galaxy.

Part B

B1.	a.	Seeds (pp. 210-211, Fig.s 11-10, 11) explains how a 21 cm photon is emitted when a H atom with parallel spins of the electron and proton spontaneously experiences a spin flip to end with anti-parallel spins. In order to emit another 21 cm photon this atom must be restored to its parallel state. This restoration is achieved through collisions with H and other atoms in the cloud. In fact, the collisions also include changes in the reverse direction (parallel antiparallel) that are more frequent than the spontaneous emission of 21 cm photon.
	b.	The sketch shows a galaxy seen side-on. The method works for galaxies seen at other angles but is less sensitive and loses all sensitivity for face-on spiral galaxies -- why? Point the radio telescope at the clouds near point A other at point B. For the indicated direction of rotation, the 21 cm signal from A will be Doppler-shifted (to higher or to lower frequencies?). The signals from point B will be Doppler shifted in the opposite sense. The sense of the shifts gives immediately the direction of the rotation. The radial velocities derived from the Doppler shifts give the speed of rotation on applying a correction for the tilt of the galaxy's disk with respect to our line of sight.
	c.	If dark matter were absent, the distribution of stars tells us that essentially all of the mass of the Galaxy is in and near the central bulge. Then, the velocity of distant stars and gas will decline with increasing distance for the simple reason that the gravitational force driving the motions falls off as l/d2. Thus, the galaxies with and without dark matter would have different rotation curves as shown in the diagram.
B2.	a.	Reddening of starlight is direct proof of the presence of small dust grains. It is a general property of small particles (grains, aerosols, or molecules) that they scatter short wavelength light very effectively and long wavelength light poorly. The boundary between 'short' and 'long' is the size of the grain. Consider now a hot (blue) star seen through a gas/dust cloud. As the starlight proceeds toward us, light is scattered by dust grains out of the path. More blue light is scattered out than red light. Thus, the scattering changes the apparent color of the star. If there is sufficient dust, so much blue light will be scattered out that there is more red light than blue light, i.e., the hot stars appear red.
	b.	Take a spectrum of the star. Go on to describe how you use the spectrum to indicate which of the 3 possibilities holds: a cool star will be betrayed by molecular bands seen in the spectrum; a hot star will show lines of helium in the spectrum; a hot star moving away at high speed will be revealed by the fact that the expected absorption lines of helium and hydrogen appear but at much longer wavelengths than usual.
	c.	One example: mapping of the stars in the disk using the method of spectroscopic parallax. Second example: understanding what goes in at the center of our Galaxy.
B3.	a.	See Seeds Sec. 16.2.
	b.	See Seeds on 'Formation of the Galaxy' (pp. 316-318).
B4.	a.	Miss (surely not a Ms in those long ago days) Leavitt examined plates (pictures) of the Magellanic Clouds taken with a telescope in Bolivia or Peru (I think) and operated by the Harvard College Observatory. These external galaxies are at such a large distance from us that we may suppose all stars in them to be at the same large distance. Her task was to search the plates for variable stars belonging to the Clouds. Cepheids variables are quite numerous and have a characteristic variation of brightness. She measured the average brightness and the period for lots of these Cepheid variables and noted that the longer the period the brighter the Cepheid. This, she realized, meant the stars obeyed a period-brightness relation and since the star were all at the same distance effectively this meant Cepheids could be used as distance indicators. But to covert her period-brightness relation to the much more useful period-luminosity relation required knowing the distance to the Clouds or to at least one local Cepheid. It took many years - Miss Leavitt was long dead - before we could turn her relation with confidence into the period luminosity relation. You will recall that the P-L relation is now established using a handful of Cepheids located in galactic (open) clusters whose distances are found from main-sequence fitting.
	b.	The key is that the HST has exquisite angular resolution because it is above the Earth's atmosphere. Recall our atmosphere blurs images. In a distant galaxy, stars appear packed tightly together. If star images are blurred, it becomes difficult to impossible to identify individual stars, and especially to spot the rare Cepheid in a crowd of stars. With its crisp images, HST allows us to spot the Cepheids in crowded fields of stars.
	c.
B5.		Not yet covered in class.
	a.	This calls for a discussion of the measurement of radial velocity and distance to a galaxy.
	b.	No! See Seeds.
		Hubble's law is