Comments on Quiz 3

Part A

A1.	d. The Earth and Sun are about 8000pc from the Galactic center.
A2.	A globular cluster contains 100,000+ stars. An open cluster contains a couple of hundred at most.
A3.	Recall the period-luminosity relation for Cepheids: the longer the period the more luminous the variable star. Stars in a cluster are presumed to be all at the same distance. Then, the more luminous the star the brighter it will appear. For the 3 Cepheids this means the order by increasing brightness is 5, 15, and 75 days.
A4.	b.
A5.	iv.
A6.	Well known examples should be our Galaxy, the Andromeda galaxy, and the Magellanic Clouds.
A7.	c.
A8.	a.
A9.	b.
A10.	iv. A black hole of stellar origin is likely to have a mass of greater than 2-3 solar masses. All other listed objects have a much smaller mass with the white dwarf most closely approaching the mass of the black hole. Recall MAXIMUM mass of a white dwarf is 1.4 solar masses. We presume that black holes of less than 2-3 solar masses are most unlikely because either degenerate electrons of neutrons can stabilize the collapse before the object shrinks to a size smaller than its Schwarzschild radius. The qualification `near the Sun' was included in order to exclude the much more massive black hole lurking in the very center of the Galaxy.
A11.	`observed from the McDonald Observatory' was not an irrelevant qualification. This means that objects located in the disk of the Galaxy must be near the Sun because dust in the disk prohibits us from seeing more than a few kiloparsecs out into the disk. And on the scale of this drawing, Mars and the Sun are coincident.  a - a globular cluster at a distance of 20 kpc from the Sun  b - a young open cluster  c - Mars   d - a very metal-poor star  e - an H II region   f - the Sun
A12.	Type II supernovae are exploding massive stars. These are short-lived stars formed `yesterday' from a gas cloud. Elliptical galaxies have no gas, cannot continue star formation and so lack massive stars.
A13.	Pulsars emit radio (and other) waves in a highly directional fashion, a narrow cone like a lighthouse beacon. If the cone never points in our direction as the pulsar spins, we'll never see the pulsar.
A14.	If all we know about the object is that it is a black hole, we cannot unambiguously assign it a population type of I or II. All we know is that it is a descendant of a massive star. If we are told its location, for example, then we should be able to resolve the ambiguity.
A15.	b. This reminds us of `look back time'. The question does presuppose an evolutionary universe.
A16.	The Cosmological Principle (NOT principal) is a building block (an assumption) for model universes. It asserts that on a large scale the universe appears the same to all observers at a given time.
A17.	Exercise involving V = H0D. Turning this around we get
A18.	Helium in astronomical objects is mostly a product of the Big Bang and NOT a product of stars. This may seem odd given that ALL stars burn H to He on the main sequence and also at later phases in their lives. Yet, the amount of He we see is too much to be attributable to production by stars. More directly, when we observed the helium content of gas clouds contaminated with products from stars (oxygen, for example), we see that clouds with essentially no oxygen have considerable amounts of helium. This tells us that much of the helium was not contributed by stars. In rough numbers, the local stars and gas are made of 90% H and 9% He, and 1% of other elements (by number of atoms). The 9% helium is made of 8% from the Big Bang and 1% from previous generations of stars. On Earth, helium is a product of radioactive decay of heavy elements such as uranium, which are made in stars. The original helium of the gas that led to the Earth has long since escaped the Earth.
A19.	By increasing mass, H atom, yourself, Sun, Betelgeuse (about 15 times the mass of the Sun), globular cluster (100,000+ stars each of a solar mass or a bit less), the Galaxy, and the Local Group of galaxies.

Part B

B1.	a.	See Comments on HW6
	b.	See Comments on HW6
	c.	Yes, this relation would be useful. It implies that ALL Cepheids, whatever their period, have the same luminosity. As long as we can infer the luminosity we can combine this with the observed brightness to infer the distance. One might argue that the relation is potentially more useful than the real period-luminosity relation in which luminosity increases with increasing period. IF - a big if, perhaps - we knew that luminosity was independent of period, we could calibrate the relation using any Cepheid. A single Cepheid with a very accurately known distance would suffice. This is in sharp contrast to our real situation where we have to calibrate the period-luminosity relation using Cepheids spanning the complete period range.
B2.	a.	Seeds
	b.	Seeds
	c.	To answer this, we need a discussion of the accretion disk that forms around and OUTSIDE a black hole that can accrete gas from a companion star. Be sure to explain the source of the energy that heats the disk. And to discuss why it is so hot - a million or so degrees in the inner regions. Accretion disks form around WDs and NSs as well as BHs as long as there is a companion star to donate gas to the disk. Disks around NS and BHs are virtually indistinguishable from their temperatures but a disk around a WD is considerably cooler - WHY? The acid test is to determine the mass of the object inside the accretion disk. This is not always possible. But in some cases, one can from the orbital motions of the normal companion star and other information infer the mass. If this mass clearly exceeds 2-3M, it can only be a BH. If the mass is between 1.4 M and 2-3M, we would suppose it most likely to be a NS. And if the mass is less than 1.4 M, we would identify it as a WD.
B3.		See HW5.
B4.	a.
	b.	Two measured quantities enter into the determination of the law: the expansion velocity and the distance of a sample of nearby and distant galaxies. A spectrum is needed in order to infer the expansion velocity. Hubble got the distances to his small sample of galaxies by taking photographs of generally the outer parts of the galaxies (why the outer parts?) and searching these for the few stars that varied in brightness in the way characteristic of Cepheid variables. Then, for these stars he measured the brightness on all photographs and estimated the periods and mean brightness. Seed's Fig. 17-11 shows a series of images of a Cepheid in a distant galaxy. This data for as many Cepheids as possible in a given galaxy, he consulted his period-luminosity relation to infer the luminosities. And finally, the combination of measured brightness and inferred luminosity gave him the galaxy's distance. Seeds reproduces what he claims is Hubble's first diagram.
	c.	Seeds.
B5.	a.	see Seeds. Point out that the Z of A is caused by the dust in our disk. Point out too that it is seen clearly when we map galaxies on the sky. Would a radio map of galaxies show a Z of A? NO!
	b.	A spectrum of the star would suffice to decide between these alternatives: i) A cool star? If so, the spectrum would show the absorption features of a low temperature atmosphere ­ TiO bands and the like. ii) A hot star reddened by dust? The spectrum of a hot star contains absorption lines of helium, for example. These would betray that the star is hot despite the conflict between the expected intrinsic color (blue) and the observed color (red). Be sure you understand how a hot star that is blue can appear red. Small dust grains along the line of sight scatter blue light more strongly than the red light. After passage through a gas/dust cloud, a higher fraction of the blue light than the red has been scattered out of the line of sight. This scattering then alters the ratio of the blue to red light in the starlight that reaches us. What started out a s blue (more blue than red) may well appear to us as red (more red than blue). This is not at all unusual for lines of sight in the plane of the Milky Way and especially for stars embedded in a cloud. iii) Again the spectrum provides the answer. We can measure the radial velocity from the spectrum.
	c.	The setting of the Sun is seen through a longer path in our atmosphere than the noonday Sun. Because of this longer path, aerosols and dust scatter more of the blue light so that we see the Sun as redder than at noon.
B6.	a.,b.	Seeds. We looked for evidence against evolution in either directions, that is E0 S(SB)c and S(SB)c E0.
B7.	a.	Seed's statement of the Cosmological Principle is INCOMPLETE. He writes 'Any observer in any galaxy sees the same general features of the universe'. It is incomplete because it lacks the phrase 'at a given time'. If 'at a given time' is replaced by 'at all times', we have the Perfect Cosmological Principle.
	b.	Given that the Universe is expanding, its appearance is evolving - galaxies are getting further apart. This is consistent with the cosmological principle. This change of appearance violated the perfect cosmological principle. To reconcile this observation and the perfect cosmological principle, continuous creation of matter must be invoked. Matter is created (you may well ask 'How?') at just such a rate that galaxies form to keep the appearance the same, as demanded by the PCP. This means that in what we call a Steady-state Universe neighboring galaxies are not all of the same age - some may be young and others may be old. When the Steady-state universe was proposed, there was a conflict between the age of the Earth as derived from the decay of uranium and the expansion age of the universe as derived from Hubble's law. The Earth was younger than the Universe! The SS universe resolved this apparent contradiction. Later however, it failed several tests and is now discarded by almost everyone. What happened to our estimate of the expansion age of the universe?
	c.	Seeds.