For the Love of Physics (37 page)

For simplicity I have been ignoring the Doppler shift, which will be enormous because of your ever-increasing speed as you approach the
event horizon. In fact, as you cross the event horizon, you will be moving with the speed of light. (For an observer on Earth, the effects of this Doppler shift will be similar to the effects of the gravitational redshift.)

After you have crossed the event horizon, when you can no longer communicate with the outside world, you will still be able to see out. Light coming from outside the event horizon would be gravitationally shifted to higher frequency and shorter wavelength, so you would see a blueshifted universe. (That would also be the case if you could stand on the surface of a neutron star as well, for the same reason.) However, since you are falling in at great speed, the outside world will be moving away from you, and thus the outside world will become redshifted as well (as a result of the Doppler effect). So what will be the result? Will the blueshift win or will the redshift win? Or will neither win?

I asked Andrew Hamilton at the University of Colorado, JILA, who is a world authority on black holes and, as I expected, the answer is not so simple. The blueshift and redshift more or less cancel for a free faller, but the outside world looks redshifted above, redshifted below, and blue-shifted in horizontal directions. (You may enjoy looking at his “Journey into a Schwarzschild black hole” movies to see what it’s like to be an object falling into a black hole:
http://jila.colorado.edu/~ajsh/insidebh/schw.html
.)

There wouldn’t be anyplace to stand, however, since there’s no surface. All the matter that created the black hole has collapsed into a point, a singularity. What about the tidal forces—wouldn’t you be torn to bits by the fact that there will be a difference between the gravitational force on your head and your toes? (It’s the same effect as the side of the Earth facing the Moon experiencing a larger attractive force than the side of the Earth that is farther away from the Moon; this causes tides on Earth.)

Indeed, you would be torn to bits; a Schwarzschild black hole of 3 solar masses would rip you apart 0.15 seconds before you crossed the event horizon. This phenomenon is very graphically called spaghettification and involves your body being stretched beyond imagining. Once you have crossed the event horizon, the various pieces of your body will
reach the singularity in about 0.00001 seconds, at which time you will be crushed into a point of infinite density. For a 4-million-solar-mass black hole, like the one at the center of our galaxy, you would safely cross the event horizon without having any problems at all, at least at first, but sooner or later you will be shredded spaghetti style! (Believe me, it will be “sooner,” because you have only about 13 seconds left before that happens and then, 0.15 seconds later, you will reach the singularity.)

The whole idea of black holes is truly bizarre for everyone, but especially for the many astrophysicists who observe them (such as my former graduate students Jeffrey McClintock and Jon Miller). We know that stellar-mass black holes exist. They were discovered in 1971 when optical astronomers demonstrated that Cyg X-1 is a binary star system and that one of the two stars is a black hole! I will tell you all about this in the next chapter. Ready?

CHAPTER 13

Celestial Ballet

I
t will come as no surprise to you by now that many of the stars you see in the heavens, with or without a telescope of any kind, are a lot more complicated than distant versions of our own familiar Sun. You may not know that about a third of what you see aren’t even single stars at all, but rather what we call binaries: pairs of stars that are gravitationally bound together, orbiting each other. In other words, when you look up at the night sky about a third of the stars you see are binary systems—even though they appear to you as a single star. There are even triple star systems—three stars orbiting one another—out there as well, though they are not nearly as common. Because many of the bright X-ray sources in our galaxy turned out to be binary systems, I had many dealings with them. They are fascinating.

Each star in a binary system travels around what we call the center of mass of the binary, a point located between the two stars. If the two stars have equal mass, then the center of mass is at equal distance from the center of both stars. If the masses are not the same, then the center of mass is closer to the more massive star. Since both complete an orbit
in exactly the same amount of time, the more massive star must have a lower orbital speed than the less massive one.

To visualize this principle, imagine a dumbbell with a bar connecting two ends of equal mass, rotating around its midpoint. Now imagine a new dumbbell, 2 pounds on one end, 10 pounds on the other. The center of mass of this dumbbell is quite close to the heavier end, so when it rotates you can see that the larger mass has a smaller orbit, and that the smaller mass has farther to go in the same time. If these are stars instead of weighted ends, you can see that the lower-mass star zooms around its orbit at five times the speed of its larger, clunkier companion.

If one of the stars is much more massive than its companion, the center of mass of the system can even lie within the more massive star. In the case of the Earth and Moon (which is a binary system), the center of mass is about 1,700 kilometers (a little more than a thousand miles) below the Earth’s surface. (I mention this in appendix 2.)

Sirius, the brightest star in the sky (at a distance from us of about 8.6 light-years), is a binary system made up of two stars known as Sirius A and Sirius B. They orbit their common center of mass about once every fifty years (we call this the orbital period).

How can we tell that we’re looking at a binary system? We can’t see binaries separately with the naked eye. Depending on the distance of the system and the power of the telescopes we’re using, we can sometimes get visual confirmation by seeing the two stars as separate.

The famous German mathematician and astronomer Friedrich Wilhelm Bessel predicted that the brightest star in the sky, Sirius, was a binary system, consisting of a visible and an invisible star. He had concluded this based on his precise astronomical observations—he was the first in 1838 to make parallax observations (he narrowly beat Henderson—see
chapter 2
). In 1844 he wrote a famous letter to Alexander von Humboldt: “I adhere to the conviction that the star Sirius is a binary system consisting of a visible and an invisible star. There is no reason to suppose that luminosity is an essential quality of cosmic bodies. Visibility of countless stars is no argument against the invisibility of
countless others.” This is a statement of profound depth; what we can’t see, we usually don’t believe. Bessel started what we now call the astronomy of the invisible.

No one actually
saw
the “invisible” companion (called Sirius B) until 1862, when Alvan Clark was testing a brand new 18.5-inch telescope (the largest one at the time, made by his father’s company) in my hometown, Cambridge, Massachusetts. He turned the telescope on Sirius as it was rising above the Boston skyline, for a test, and discovered Sirius B (it was ten thousand times fainter than Sirius A).

Thank Goodness for Stellar Spectroscopy: Blueshifts and Redshifts

By far the most common method of figuring out that stars are binaries, especially if they’re distant, is by using spectroscopy and measuring what’s known as the Doppler shift. There may be no more powerful astrophysical tool than spectroscopy, and no more important discovery in astronomy in the past several centuries than the Doppler shift.

You already know that when objects are hot enough they will emit visible light (blackbody radiation). By decomposing sunlight in the way a prism does, the raindrops that make up a rainbow (
chapter 5
) show you a continuum of colors from red at one end to violet at the other, called a spectrum. If you decompose the light from a star, you will also see a spectrum, but it may not have all the colors in equal strengths. The cooler the star, for example, the redder the star (and its spectrum) will be. The temperature of Betelgeuse (in the constellation Orion) is only 2,000 kelvin; it’s among the reddest stars in the sky. The temperature of Bellatrix, on the other hand, also in Orion, is 28,000 kelvin; it’s among the bluest and brightest stars in the sky and is often called the Amazon Star.

A close look at stellar spectra shows narrow gaps where colors are reduced or even completely absent, which we call absorption lines. The spectrum of the Sun shows thousands of such absorption lines.
These are caused by the many different elements in the atmospheres of the stars. Atoms, as you know, are made of nuclei and electrons. The electrons cannot just have any energy; they have discrete energy levels—they cannot have energies in between these distinct levels. Their energies, in other words, are “quantized”—the term that gives rise to the field of quantum mechanics.

Neutral hydrogen has one electron. If it is bombarded with light, this electron can jump from one energy level to a higher energy level by absorbing the energy of a light photon. But because of the quantization of the energy levels of the electron, this cannot happen with photons of just any energy. Only those photons that have just the right energy (thus exactly the right frequency and wavelength) for the electron to make the quantum jump from one level to another will do. This process (called resonance absorption) kills these photons and creates an absence at that frequency in the continuum spectrum, which we call an absorption line.

Hydrogen can produce four absorption lines (at precisely known wavelengths, or colors) in the visible part of a stellar spectrum. Most elements can produce many more lines, because they have lots more electrons than hydrogen. In fact, each element has its own unique combination of absorption lines, which amounts to a fingerprint. We know these very well from studying and measuring them in the laboratory. A careful study of the absorption lines in a stellar spectrum can therefore tell us which elements are present in the star’s atmosphere.

However, when a star moves away from us, the phenomenon known as the Doppler shift causes the star’s entire spectrum (including the absorption lines) to shift toward the red part of the spectrum (we call this redshift). If, by contrast, the spectrum is blueshifted, we know the star is moving toward us. By carefully measuring the amount of shift in the wavelength of a star’s absorption lines, we can calculate the speed with which the star is moving relative to us.

If we observe a binary system, for example, each star will move toward us for half of its orbit and away from us during the other half. Its companion will be doing exactly the opposite. If both stars are bright
enough, we will see redshifted
and
blueshifted absorption lines in the spectrum. That would tell us that we are looking at a binary system. But the absorption lines will be moving along the spectrum due to the orbital motion of the stars. As an example, if the orbital period is twenty years, each absorption line will make a complete excursion in twenty years (ten years of redshift and ten years of blueshift).

If we can see only redshifted (or only blueshifted) absorption lines, we still know it is a binary system if we see the absorption lines move back and forth in the spectrum; a measurement of the time it takes for a full cycle of the lines will tell us the orbital period of the star. When would this happen? In the event that one star is too faint to be seen from Earth in optical light.

Let’s now return to our X-ray sources.

Shklovsky and Beyond

Way back in 1967, the Russian physicist Joseph Shklovsky had proposed a model for Sco X-1. “By all its characteristics, this model corresponds to a neutron star in a state of accretion… the natural and very efficient supply of gas for such an accretion is a stream of gas which flows from a secondary component of a close binary system toward the primary component which is a neutron star.”

I realize these lines may not strike you as earthshaking. It doesn’t help that they are written in the rather dry technical language of astrophysics. But that’s the way professionals in just about any field talk to one another. My purpose in the classroom, and the main reason I’ve written this book, is to translate the truly astounding, groundbreaking, sometimes even revolutionary discoveries of my fellow physicists into concepts and language intelligent, curious laypeople can really get hold of—to make a bridge between the world of professional scientists and your world. Too many of us seem to prefer talking only to our peers and make it awfully difficult for most people—even those who really want to understand science—to enter our world.

So let’s take Shklovsky’s idea and see what he was proposing: a binary star system composed of a neutron star and a companion from which matter was flowing to the neutron star. The neutron star would then be “in a state of accretion”—in other words, it would be accreting matter from its companion, the donor star. What a bizarre idea, right?