ASTRO 801
Planets, Stars, Galaxies, and the Universe

Black Holes

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Additional reading from www.astronomynotes.com


Want to learn more?

Before we go any further, let me note that Penn State teaches an entire face-to-face course on black holes (ASTRO 130) at the University Park campus. While it is true that most of the topics we will cover in ASTRO 801 can be elaborated on much more than I have the time or space for in this course, I think this is especially true of the topic of black holes. So, while we are going to address them here, I think that, in particular with this topic, if you want more detail, you should consider following up with additional reading and study beyond what is in the course on this page.

On the ASTRO 130 website, Professor Brandt lists the required reading and suggested reading on this topic, and you can certainly do well starting there with his recommendations.

Observationally, we find most neutron stars are approximately 1.4 solar masses. Theoretically, neutron stars may exist up to about 3 solar masses. Why is there an upper limit?

Let us again consider a Type II, core-collapse supernova. The implosion of the star compresses the core until it becomes essentially one giant ball of neutrons with a density larger than any other material known. The neutron star is supported by neutron degeneracy pressure. The question is: How strong is neutron degeneracy pressure?

In the case of the most massive stars (maybe only stars more massive than say, 25 or even 50 solar masses), not even neutron degeneracy pressure can stop the collapse of the core. In this case, at least 3 solar masses worth of matter collapses into a single point with infinite density. This point is referred to as a singularity. At a distance of approximately 9 km from the singularity is a spherical region at which the escape velocity is exactly equal to the speed of light. What this means is that any object that reaches this distance from the singularity (usually referred to as the event horizon or Schwarzschild radius) can never escape, even if it were moving at the speed of light. Thus, even light cannot escape from this object, and it is for this reason we call it a black hole.

You can calculate the size of the event horizon for a black hole in the following way:

  1. The escape velocity for an object with mass M and radius R is: V esc  = 2GM/R This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.
  2. Set V esc  = c This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. , the speed of light, and solve for R
  3. R = 2GM/ c 2 This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. ; we call this the Schwarzschild radius or R s This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

For an object of mass 3 solar masses = 3 x (1.99 x  10 30  kg) = 5.97 x  10 30  kg This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. :

R s = 2 x (6.67 x  10 11   m 3 / s 2 kg) x (5.97 x  10 30  kg) /  (3.0 x  10 8  m/s) 2  = 8.8 x  10 3  m = 8.8 km  9 km This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

The Schwarzschild radius scales linearly with mass, so a 30 solar mass black hole will have a radius of 90 km, and a 300 solar mass black hole will have a radius of 900 km.

Watch out for this misconception!

If you have seen just about any science fiction movie that mentions black holes, you probably picture a giant space vacuum cleaner sucking material into some vast whirlpool. There is actually a nice short bumper sticker saying you should keep in mind from here on out: Black Holes don't suck!

Black holes have mass and exert gravitational force on their surroundings, just like every other mass in the Universe. They do not have some special force that allows them to suck nearby stars into their event horizon. What is peculiar about black holes is that they are the only objects where their event horizon is outside their physical boundary, and when you get near this boundary, strange physical effects occur because of the strong gravitational field associated with these objects.

For more, you can get the "Bad Astronomer's" (Phil Plait's) list of 10 things you don't know about black holes.

Let's momentarily review some of the most basic aspects of Einstein's theory of relativity. In order to understand how light behaves in the universe, we need to consider both Einstein's theory of special relativity and general relativity. These can be summarized quickly in two statements, but both statements have far reaching consequences.

  • Special relativity says that there is no experiment that can tell whether you are undergoing straight-line, constant velocity motion, or whether you are standing still and everyone else is moving.
  • General relativity says that there is no experiment that can tell whether you are standing in a gravitational field or are undergoing a constant, straight line acceleration.

One of the consequences of general relativity is that it requires that space be curved in the vicinity of large masses. This means that if a photon of light passes close to the Sun, for example, it will not continue in a straight line, but it will be deflected by a small amount (see www.astronomynotes.com for a more detailed explanation). Another prediction of general relativity is that when light is emitted by a massive object, it should be redshifted. That is, a photon of light feels a gravitational attraction to the massive object, and it must expend some of its energy in order to escape from the object. Because the energy of a photon is proportional to its wavelength or frequency (remember, UV photons carry more energy than IR photons, for example), when the photon loses energy, it gets redder. This is the gravitational redshift, and it is different from the Doppler effect redshift we have studied earlier.

General relativity predicts that these strange effects (such as the deflection of starlight near a massive object, or the gravitational redshift) will be stronger when a photon of light encounters a stronger gravitational field. Thus, it is difficult to measure these effects for the Sun, for example, but in theory they should be easier to measure in the vicinity of a black hole.

Watch this!

One of the astronomers responsible for Astronomy Picture of the Day has produced a number of simulations of what you might see near a black hole because of the strong relativistic effects, called Virtual Trips to Black Holes and Neutron Stars:

  1. Watch "Approaching the Black Hole" and "Circling the Black Hole".
  2. Read the explanation for both movies.
Can you see the "Einstein Ring" effect?

There are a number of additional effects that an observer investigating a black hole from near its event horizon will experience. Two of these include:

  1. If you could get close enough to a black hole, you would experience strong tides. The difference in the gravitational pull from one side of a person to another near a black hole can be enormous. It is so strong that a person (and actually, even a star) is likely to be torn apart. This is referred to as "spaghettification." At YouTube, you can watch Astronomer Neil DeGrasse Tyson describe this process.
  2. If you did take a trip to the event horizon of a black hole, what would an outside observer see happening to you? Any light you emit will be progressively redshifted the closer you get to the black hole, so the observer would see your light source (say you are shining a red laser pointer at them) first appear as IR, then as microwave, and then as radio light, the closer you got to the event horizon. A related effect is time dilation—that is, to you as you approach the black hole, your watch would continue to tick off every second at the same rate. However, an outside observer would see your watch tick slower and slower and slower the closer you got to the event horizon. Actually, a stationary observer would never be able to see you cross the event horizon, because time slows down so much that the moment of you crossing the event horizon would seem to take an infinite amount of time to the observer.

Want to learn more?

There are many additional questions you and your students are likely to have about black holes. For two excellent resources presented in FAQ format, see:

From an astronomer's point of view, beyond these thought experiments about the nature of black holes, the questions we are often more interested in are: How might we detect these objects and how do they influence their environments? The first question you might ask is, have we ever directly detected a black hole? Below is an artist's illustration of one of the primary candidates.

Artist's illustration of Cygnus X-1 black hole binary, which shows a massive star streaming matter onto a small, unseen companion, creating an accretion disk around the companion.  In this case, the companion is believed to be a black hole.
Figure 6.17: Illustration of Cygnus X-1 black hole binary

We have found binary star systems where an O star (with a mass of approximately 25 solar masses) is orbiting a companion that has a mass of 6 - 10 solar masses. However, the companion does not appear to emit any of its own light. Theoretically, neutron stars should not be able to survive with masses greater than about 3 solar masses. So, if a binary star system contains an unseen companion with a mass of more than 3 solar masses, it may be a black hole. A handful of such objects exist. The most famous is an object called Cygnus X-1 (shown in the illustration above), which has even had a song written in its honor ("A Farewell to Kings—Cygnus X-1" by Rush). To investigate Cygnus X-1 and some of the effects described previously, there is an online, interactive tool for younger students who want to investigate black holes: "Black Holes: Gravity's Relentless Pull," created by the folks at hubblesite.org.

Try this!

  1. Go to "Black Holes: Gravity's Relentless Pull."
  2. After watching (or skipping) the introduction, click on "Journey to a Black Hole."
  3. Click on "The Voyage" tab at the top of the window.
  4. After reading the info there, click on "Begin Your Voyage."
  5. Choose Cygnus X-1 for a short simulated trip to this binary star system.
  6. Click on the "Up Close and Personal" tab at the top of the window.
  7. Choose "Show Questions and Experiments" at the bottom of the window.
  8. Go through as many of the questions and experiments as you would like, but, in particular, choose "Drop a Clock into a Black Hole" and "Fall into a Black Hole."
How well were the concepts described above reproduced in these animations?