Saturday, September 22, 2012

How do We Know a Black Hole Lives at the Milky Way's Center?

People often wonder how science can get a handle on out-of-this-world things like the properties of the universe many light years away or the small-scale structure of space-time itself.  In 2005, I presented the distinguished faculty address to give my audience a sense of how this is done.  The title of my talk was, "From Black Holes to the Internet:  How We Use The Scientific Method To Understand the Mysteries of Things Unseen."  It was a very enjoyable hour with lots of wonderful audience participation.  Here I summarize one part of my talk on "how we know" that there is a black hole in the center of our galaxy.

Science often proceeds by taking small steps that together build a general understanding. Here I outline how experiments on the earth along with observations of our universe can lead to an amazing understanding of the natural world.

The outline below shows how simple experiments on the earth's surface can be used to detect a massive black hole at the center of our galaxy, the Milky Way.
  1.  Establish Newton's Theory of Gravity by measuring forces between hanging masses here on earth.
  2. Use Newton's Theory of Gravity to determine the mass of the earth and check if it is consistent with what we know about the earth's composition and size.
  3. Predict the orbital shape and period of the moon based on the earth's mass. It is found that the calculated period is consistent with the measured one and the shape of the orbit is accurately predicted (ellipse with the earth at the focus). This evidence suggests that gravity acts on lunar distances.
  4. From the orbits of the planets, the mass of the sun is determined. Every planetary orbit gives the same solar mass (with the sun at the focus of every ellipse), so gravity appears to work even on these larger scales. Furthermore, the density of the sun that is determined from its mass is consistent with what we know of the sun's composition from independent spectroscopic measurements.
  5. The orbital properties of all bodies in the solar system obey Newton's Theory of Gravity with impeccable precision. This includes comets, asteroids, moons, satellites, and space ships.
  6. Mercury's orbit is found to deviate ever so slightly from Newton's predictions. This irks physicists until Einstein formulates the General Theory of Relativity in 1918 which fully accounts for the small deviation. It turns out that Newton's Theory of Gravity is a special case of General Relativity, which predicts the possibility of the existence of black holes.
  7. Telescopes that view infrared light are able to penetrate the dust that obscures the center of the Milky Way to visible light to see stars at our galaxy's center.
  8. Astronomers measure the orbits of these stars over more than a decade. As predicted by Newton, the orbits of the stars are perfect ellipses. The foci of these ellipses all coincide with an invisible object.
  9. Using the orbital data, the calculated mass of the dark object is almost 4 million solar masses.
  10. Some of the stars get very close to the dark object, so an upper limit of the object's size is determined from the distance of closest approach.
  11. The dark object's mass and density fall in the range predicted by general relativity for a black hole.
The infrared observations of stellar orbits as described above do not prove the existence of a galactic black hole; but provide strong evidence. There are other independent measurements that all point to a black hole (see below). When the pieces of the puzzle are assembled, the picture that emerges is one of a huge black hole at the galactic center.

Incidentally, such massive black holes are found at the centers of other galaxies and even globular clusters. Since evidence of smaller black holes are routinely "observed" in binary star systems, it becomes clear that black holes are out there.

This journey illustrates something fundamental about nature, and about the breadth of physical laws. Richard Feynman said it best, "Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry."

A youtube video shows the motions of the stars around the central black hole that comes from direct telescopic observations.  The data covers over a decade of observations. A more dramatic version can be seen here.

Scientists are slow to accept a new idea or theory unless there are multiple pieces of supporting evidence.

The case for black holes is bolstered by X-ray observations of the hot gas surrounding the galactic black hole at the heart of our Milky Way. The observed X-ray spectrum can be used to determine the gas temperature using the same principles that betray the temperature of glowing orange embers in our fireplaces.

If the gas is to remain stationary, the inward gravitational tug of the black hole must be balanced by the outward pressure of the gas. The calculation is simple enough for a high school physics student, requiring only Newton's Universal Law of Gravity (see below) and the gas laws.

This simple calculation leads to a black hole mass of about 3.4 billion suns, in agreement with the observations of stellar orbits.

Newton's Universal Law of Gravity

Newton's Law of Universal Gravity

Newton's universal law of gravity states that the force of attraction between two objects is proportional to the product of the two masses and inversely proportional to the square of the distance between their centers. The constant of proportionality is G.

G can be determined be measuring the forces between masses that are measured with a torsion balance. This is a common experiment done in most physics departments by students, and even in high schools.

 Kepler's Laws (1571 - 1630)

Kepler's laws follow from Newton's theory of gravity.

 Elliptical orbit of planet about the sun

Kepler's Laws state that:

  1. Planets travel in elliptical orbits with the sun at one of the foci (shown above).
  2. Equal areas are swept in equal times (see diagram below).
  3. The time it takes to complete one orbit is proportional to d3/2
Kepler's law of equal areas

All objects in our solar system are observed to obey Kepler's Laws, and therefore confirm Newton's more general theory. Einstein's Theory of General Relativity is the most general theory that makes small corrections to the orbit of Mercury and is required to make the GPS system work.

But don't believe the authorities. Anyone can observe the motion of Jupiter's moons to determine the mass of the gas giant. I took the photo below of Jupiter and three of its moons. 
Jupiter and three of its moons

 Cutting Through the Dust

Raleigh found that the degree of scattering is proportional to the inverse of the fourth power of the wavelength of light. Blue light has a shorter wavelength than red light, so is more strongly scattered. Rayleigh scattering explains why the sky is blue.

Yellow fog lights work on the same principle. When white light is filtered to remove the blue light, what remains is green and red, which appears yellow. The longer wavelengths pass further through the fog and the scattered glare from the blue light is eliminated, making it easier to see.

The infrared range of the spectrum is made from light of even longer wavelengths, allowing telescopes to see through the muck. Special detectors are used to image the light. The image below is of the center of the Milky Way, taken by researchers at Max-Planck Intitut fur extraterrestrische Physik.
Center of Galaxy

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