Astro 3- Chapter 16

Cepheids with longer periods have higher luminosities. The graph shows how the average luminosity of a Cepheid variable star depends on its period. Each dot represents a different Cepheid. The data points suggest a clear trend: The longer the period of a Cepheid, the higher its luminosity.

10,000. You can now see why the period-luminosity relation is so useful. It's relatively easy to measure a Cepheid's period, and once we've done that, we can use the period-luminosity relation to determine the Cepheid's average luminosity.

The Cepheid varies in radius, and its luminosity is greater when its radius is larger. As the animation shows, a Cepheid's apparent brightness varies as the Cepheid varies in size. Because a Cepheid is at a fixed distance from Earth, these changes in apparent brightness reflect changes in luminosity. This fact, along with the fact that all Cepheids have similar surface temperature, explains the period-luminosity relation: A larger Cepheid will be more luminous and will take longer to pulsate in size than a smaller Cepheid.

100 billion. This estimate is found by counting galaxies in this small piece of the sky, and multiplying by the number of such pieces it would take to fill the entire sky.

globular galaxies. There are objects that we call globular clusters, but they are not galaxies.

a light source of known luminosity. Standard candles have known luminosities.

A type of very luminous star that makes an excellent standard candle. Cepheids are pulsating variable stars for which we can infer the luminosity from the time between peaks of brightness, which makes them valuable as standard candles.

the period between its peaks of brightness and its luminosity. The period-luminosity relation allows us to determine its luminosity from the period between its peaks of brightness.

The more distant a galaxy, the faster it is moving away from us. From this fact, we infer that we live in an expanding universe.

They are rare events, so we have observed them in only a tiny fraction of all galaxies. A white dwarf supernova may occur on average only every few centuries in a particular galaxy, so we have to be "lucky" to have caught one in action in that galaxy during the time we have been monitoring galaxies with large telescopes. Of course, by monitoring thousands or millions of galaxies, we'll catch a number of them every year.

The inside of the balloon does not represent any part of our universe. The surface of the balloon represents all three dimensions of space in our universe.

its light traveled through space for 1 billion years to reach us. Lookback time is more meaningful than distance, because the galaxy's current distance is different from what it was at the time it emitted the light we now see (because the universe is expanding).

the cosmological horizon. It is a horizon in time, not in space. That is, there is no physical boundary at the cosmological horizon, but we cannot see beyond it because we'd be trying to look to a time before the universe was born. (See Figure 1.4 of The Essential Cosmic Perspective.)

the expansion of the universe. It differs from what we usually think of as a Doppler shift because the galaxies are not really moving through the universe; rather, they only appear to be moving away from us because space itself is growing between the galaxies.

14 billion years. More precisely, the current estimate is 13.7 billion years, give or take a few hundred million years.

infrared light. We must observe very distant galaxies to see how galaxies looked when they were very young, and these galaxies have such large redshifts that any light they emitted as visible or ultraviolet has been shifted into the infrared.

Some regions in the universe start out denser than others. These small density enhancements are the seeds around which galaxies form; without these "seeds," models indicate that galaxies could not yet have formed in a 14-billion-year-old universe.

hundreds of millions of years.Remember that typical galaxies are 100,000 light-years in diameter, so even at the speed of light a collision would take hundreds of thousands of years. Galaxies actually collide at relative speeds less than 1/1000 of the speed of light, so the collisions unfold over hundreds of millions of years.

may either be the result of conditions in the protogalactic cloud that formed it or the result of later interactions with other galaxies. Both processes probably shape galaxies.

Relative to their sizes, galaxies are closer together than stars. Remember that on a scale where the Sun is the size of a grapefruit (see Chapter 1), the nearest stars are thousands of kilometers away. In contrast, on a scale where the Milky Way is the size of a grapefruit, the other galaxies in the Local Group all lie within just a few meters.

They are often spiral galaxies. Central dominant galaxies are elliptical galaxies.

Galaxies were closer together in the past because the universe was smaller. As the universe expands, the average distance between galaxies increases, making collisions less likely (on average) as time passes. (Note that this does not affect the likelihood of collisions within clusters, since clusters are gravitationally bound and are not expanding with time.)

a rate of star formation that may be 100 or more times greater than that in the Milky Way. The term starburst refers to a burst of star formation.

active galactic nuclei. The power source for active galactic nuclei is thought to be accretion onto a supermassive black hole.

an active galactic nucleus that is particularly bright. Observations show that quasars lie in the centers of distant galaxies, indicating that they are very luminous active galactic nuclei.

the presence of globular clusters in the halos of galaxies. Globular clusters orbit in the halo, far from the supermassive black hole in the center, and are unlikely to be related to the black holes in any major way.

1 billion solar masses. Models show that the luminosity of a bright active galactic nucleus can be explained through the accretion of matter toward a 1 billion (or so) solar mass black hole.

light emitted by hot gas in an accretion disk that swirls around the black hole. As matter falls toward the black hole, as much as 40% of its mass-energy can be converted into thermal energy and radiation.

the galaxies that are farthest away. Remember that the farther we look into space, the farther back in time we are seeing. Thus the most distant galaxies are the ones we see in the most distant past, when both they and the universe were much younger.

elliptical galaxies lack anything resembling the disk of a spiral galaxy. In essence, elliptical galaxies are "all bulge and halo" with no disk, while spiral galaxies have a disk as well as a bulge and halo.

We can learn the distance to the galaxy. We will be able to use the Cepheid's period to determine its luminosity from the period-luminosity relation. Then we can calculate its distance by comparing its luminosity and its apparent brightness in our sky, using the inverse square law for light. This tells us the Cepheid's approximate distance, which is also approximate distance to its host galaxy.

By observing individual Cepheid variable stars in Andromeda and applying the period-luminosity relation. By measuring their periods, the period--luminosity told him their luminosities. He could then calculate their distances by comparing their luminosities and their apparent brightnesses with the inverse square law for light.

away from us at 2,200 km/s. Multiply 22 km/s/(million light-years) × 100 million light-years = 2,200 km/s.

White dwarf supernovae all have roughly the same true peak luminosity, while massive supernovae come in a wide range of peak luminosities. This allows white dwarf supernovae to be used as standard candles, since we can assume we know their true luminosities.

No, because galaxies in the Local Group are gravitationally bound together. The universe as a whole is expanding, but structures held together by gravity (or other forces) are not.

Take a spectrum of the galaxy, and measure the difference in wavelength of spectral lines from the wavelengths of those same lines as measured in the laboratory. Even if the redshift is cosmological, we still measure it just like a Doppler shift.

The faster the rate of expansion, the younger the age of the universe. If the universe is expanding relatively fast, then it did not take quite so long to reach its current size.

stretches its wavelength. The effect is essentially the same that occurs with a redshift from the Doppler effect, but the underlying cause is different.

Beyond the cosmological horizon, we would be looking back to a time before the universe was born. Review Figure 1.4 of The Essential Cosmic Perspective.

the farther away we look, the further back in time we see. The light from distant galaxies take a long time to get to us, so we see them as they were millions of years ago.

Gas contracted to form the disks of galaxies before any stars were born. This is not one of the starting assumptions, and probably is not even true.

a spiral galaxy. With a lot of angular momentum, the protogalactic cloud would spin more rapidly as it collapsed, leading to the formation of a disk - which makes it a spiral galaxy.

The fact that spiral galaxies have both disk and halo components. This can be explained by the basic galaxy formation process, and does not require any interaction with other galaxies.

The fact that more distant galaxies have larger redshifts. This fact comes simply from the expansion of the universe, and does not require any collisions for its explanation.

The observed features of the starburst are thought to be caused by the presence of a supermassive black hole in the galaxy's center. Starbursts are not related to active galactic nuclei, and it is the latter that are thought to involve supermassive black holes.

smaller and bluer to larger and redder. Over time, mergers tend to make more large, red, elliptical galaxies.

the distance to the quasar. Strong evidence supports the idea that quasar redshifts are due to the expansion of the universe, so the size of a redshift tells us the quasar's distance through application of Hubble's law.

Active galactic nuclei tend to become less active as they age. Remember that at large distances we are seeing into the past. The fact that active galactic nuclei are far away means that they are young. The galaxies we see nearby are older. We conclude that activity is more common among young galaxies than older ones.

The X-ray source is no more than a few light-days in diameter. As discussed in Chapter 15 of The Essential Cosmic Perspective, the period of variability sets a limit on the size of a source.

The most luminous active galactic nuclei have huge redshifts. The redshifts are a consequence of being at great distance from us in an expanding universe, and do not directly tell us anything about why the objects are so luminous.

gravitational potential energy released by matter that is falling toward the black hole. The matter loses gravitational potential energy as it falls inward.

Galaxy formation and supermassive black hole formation must be related somehow. We don't yet know exactly how, but that's what the data imply.