Black Holes Black Holes Escape Velocity Escape Velocity

Black Holes

Black Holes

“Escape Velocity”

“Escape Velocity” Doesn’t depend on mass of object trying to escape

As r gets very small, and as M gets very large, ve can grow very large • Why do we care if ve gets very large? If ve reaches the speed of light, 3 x 105 km/s, the body will have very unusual properties: • Einstein’s Theory of Special Relativity, which is well-proven in the lab, says that nothing made of matter can travel fast than light speed. Nothing can escape from the body – a cosmic turnstile. • Einstein’s Theory of General Relativity shows that although light has no mass, it is still affected by very strong gravitational forces, as space itself is then warped. Thus no light can escape from the body – the object is invisible even if it generates light. A black hole.

The Schwarzschild Radius If we set ve = c and solve for r, we get rs = 2 GM/c 2 Schwarzschild Radius Karl Schwarzschild For any mass M, if the body has r ≤ rs, then it is a black hole

The Schwarzschild Radius Mass of object Schwarzschild Radius, rs 1 Mʘ 3 km 1 Mearth 1 cm 70 kg 10 -23 cm (10 -15 atomic radii) 2 x 1011 Mʘ 4, 000 A. U.

Some properties of Black Holes • Still a star! • Has a mass and a size (rs) • As soon as you are at r > rs, the gravitational attraction of a BH is identical to that of a star of the same mass • However, as you approach rs, the tidal forces are huge

Tidal Forces near a Black Hole

Do Black Holes Exist? • They are allowed by relativity, and their properties can be studied mathematically • However, this doesn’t mean that nature actually decides to make them! • Do we have reason to suspect BHs might exist? • Yes! There is a limit of about 3 Mʘ to the most massive allowed neutron star, but we know some stars have 100 Mʘ at the end of fusion

Discovering Black Holes • Recall that far from rs, the gravitational pull of a BH is exactly the same as an ordinary star of the same mass • Therefore single, isolated BHs could be very difficult to find • A better bet: BHs in binary systems • A specific case: X-ray stars

The X-ray Sky • X-rays don’t penetrate the Earth’s atmosphere • To look around the sky in X-rays must use special telescopes in orbiting satellites • Routine today, but not possible until the late 1960 s/early 1970 s Apollo-Soyuz Test Project (1975)

The X-ray Sky • Our Sun is a very weak source of X-rays • We can calculate how bright other nearby stars would be in X-rays as seen from Earth, and they are way too faint • Therefore we might guess the “X-ray” sky might look very different than the visible sky

The Visible Light Sky

The X-ray Sky

The X-ray Sky • Only a few hundred objects: clearly not “normal” stars • A few align on the sky with supernova remnants • Most line up with “innocent” looking visible stars: no obvious reason for them to emit Xrays • We can measure the distance to the visible star, and thus calculate the luminosity of the X -ray emission

The energy emitted in X-rays is 105 -106 greater than the total energy emitted at all wavelengths by normal stars! • Where does all that energy come from? • The spectrum of the normal star shows it is, well, normal! • Perhaps there is a second star also present that is making the X-rays, but too faint to see in visible light

Gas swirls in the “accretion disk, ” awaiting its turn to fall onto the compact star at the center Collisions in the disk make the gas extremely hot The temperature depends on the gravitational force of the small companion star Only white dwarfs, neutron stars, or something massive but smaller still can cause the gas to reach X-ray temperatures

X-ray Binary Stars • Two stars locked in orbit, one visible and normal, one tiny and too faint to see • Compact star pulls gas off of normal star, which heats in the accretion disk and glows in X-rays • But we only see one star in visible light: how can we check this explanation? • Does the star we do seem to be in motion?

The Doppler Effect Receding: frequency decreases, wavelength increases (“redshift”) Approaching: frequency increases, wavelength decreases (“blueshift”)

(suppose the yellow star is invisible!)

Cygnus X-1 • One of the first X-ray stars detected, and one of the brightest in our Galaxy • About 6, 100 lt-yr distant (not a neighbor!) • Location of the X-ray source is found to coincide with a normal star, cataloged a century ago, HDE 226868 • m=9

Cygnus X-1

Could Cygnus X-1 be a Black Hole? • The spectral lines of HDE 226868 are found to redshift and blueshift in a repeating pattern every 5. 6 days • It’s orbiting something not visible! • But we know that white dwarfs and neutron stars in binary systems can also make X-rays: how can we rule these out? • We need to estimate the mass of the unseen star • If M > 1. 4 Mʘ, it can’t be a white dwarf • If M > 3 Mʘ, it can’t be a neutron star

How can we weigh a star we cannot see? Suppose we watch a seesaw and see this: Now suppose we watch a different seesaw and see this:

And now this: The unseen rider must be heavier than the visible rider!

We can estimate the mass of the unseen companion in Cygnus X-1/HDE 226868 as M > 14 Mʘ This is too massive to be a white dwarf or neutron star, the only other objects compact enough to have an accretion disk hot enough to make X-rays Cygnus X-1 is likely a Black Hole!

• Most of the 100 bright X-ray sources in our Galaxy have white dwarf or neutron star companions • However there about a dozen other X-ray binary stars where the motion of the normal star suggests that the unseen star is a black hole