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>The astronomers who detected the echo think it indicates that the black hole consumed >a very large mass roughly the size of the planet Mercury.

Sounds like an astrophysical burp to me. Queue "I can't believe I ate the whole thing!"

I don't know why this never occurred to me till just now, but I seem to recall from the pop GR books I've read (Kip Thorne's Black Holes and Time Warps, for instance) that you never actually see anything fall into a black hole; time dilation stops it just above the event horizon. That being the case, how come we see these X-ray bursts? Is what we're actually seeing just the mass hitting the accretion disk?

I also heard about a fascinating acoustical effect that occurs with mugs of hot chocolate, ably demonstrated by Bradley Carroll of Weber State University with a packet of Swiss Miss instant cocoa. Tapping a spoon against the bottom of a mug of freshly made hot cocoa produces a tone of constantly rising pitch. If you stir the cocoa some more, the pitch will plunge before it starts rising again. And it's a significant increase: about three octaves, "an eightfold increase in frequency, twice the rise in pitch you encounter while singing the 'Star Spangled Banner,'" says Weber. Yet there is no noticeable change in the actual mug of cocoa.

A post-doc I knew in grad school recalled being given a variant of this question as part of his Ph.D. defense-- I think it was just stirring sugar into a cup of coffee, not hot cocoa. His guess was also that it had something to do with changing the speed of sound in the liquid, but he wasn't sure of the "right" answer. It was one of those questions they ask in order to see how well you think on your feet...

David's recollection of Thorne's book is correct: to an outside observer, a space craft at the brink of the event horizon will seem to be frozen in time. As I recall, the explanation is that light can't escape once it moves past the event horizon, and since we get our "information" from light (electromagnetic radiation), that's where our information ends. But there's been a lot of research into black holes since Thorne's book. They're bizarre objects, and we're only just beginning to understand their peculiarities. The question of whether anything can "escape" the gravitational pull is an especially knotty one -- it seems as if they DO give off some radiation. Stephen Hawking, for instance, has proposed "Hawking radiation" as a possible explanation.

Briefly, it goes something like this: empty space isn't really empty. There are "virtual particle" matter/antimatter pairs that continually pop into existence for fractions of a second before annihilating into radiation. (Google the Casimir Effect for an interesting experiment demonstrating this phenomenon.) If a particle pair pops out near a black hole, and one particle falls in, the black hole must emit the remaining particle's (tiny) mass as radiation in order for energy to be conserved. That's why black holes eventually evaporate over very long periods of time -- depending on their size. The mini-black holes that might be created in the Large Hadron Collider are so small, they would evaporate in fractions of a second... which is probably a very good thing. :)

I'm sure some of my readers/commenters can shed more light on this phenomenon, particularly the X-ray bursts, which are _not_ (I don't think) Hawking radiation -- they're too intense for that. The point of the above is that, where black holes are concerned, there's a great deal we don't know yet, and the crafty supermassve objects are constantly surprising us with new twists. I do know those x-rays are one of the ways we know there's a black hole at the center of the Milky Way, and probably most other galaxies, too.

And Chad, asking a poor post-doc to explain the hot chocolate effect on his toes is just, well, cruel. :)

X-ray bursts are indeed, as Jennifer Ouellette suspected, not Hawking radiation. They're an awful lot brighter than the Hawking radiation from a typical black hole, because the Hawking temperature of the hole depends inversely on the hole's mass. If you want the exact formula, it's equation 16.120 in Zwiebach's **First Course in String Theory**:

T = (hbar * c^3) / (8 * pi * k * G * M).

In this formula, "hbar" is Planck's constant, c is the speed of light, k is Boltzmann's constant, G is the strength of gravity (Newton's constant) and M is the black hole's mass. If you'd rather know the mass necessary to have a given Hawking temperature, just swap M and T in the formula. Doing a quick back-of-the-envelope calculation, I get that to be as warm as the cosmic microwave background (2.7 kelvins), a black hole must have a mass of about 4.6e22 kilograms, or 0.77% the mass of the Earth (2.3e-8 solar masses). A black hole formed by a collapsing star will be **much** bigger and hence much colder than this. If a black hole is sitting in otherwise empty space, with no matter to feed it, the only thing it has to eat is cosmic microwave background photons.

Just like a mug of hot chocolate on a cold day, a black hole will emit energy (via Hawking radiation) until it comes into thermal equilibrium with its surroundings. Imagine for a moment that no matter is falling into the hole, so we only have to consider the CMB. If the hole is hotter than the CMB, we'll see a net energy flow outward; in order to be this hot, the hole must be small (and the smaller it gets, the hotter it grows). However, a large hole is colder than its surroundings, so the energy flow will go the other way.

The X-ray emissions come from the matter falling into the hole. As the hole-food spirals inward, forming an accretion disk, it gets squeezed, and it heats up. Big gulps of matter lead to big flashes of X-rays. Let me see. . . aha, thank you NASA:

http://imagine.gsfc.nasa.gov/docs/science/know_l2/black_holes.html

I forgot to say:

If you want to figure out how long it takes for a hole of a given starting mass to go "boom", all you need to do is take the Hawking temperature, use the Stefan-Boltzmann Law to calculate the radiant power (which goes as the fourth power of the temperature), multiply that by the surface area given by the Schwarszchild radius and write a differential equation in terms of the black hole mass. Simple! :-)

Someone in the physics blogosphere, probably Jen-Luc, needs to comment on this:

http://www.edmundoptics.com/images/imagelib/UScatcover.gif

Yes, it's the latest cover of the Edmund Industrial Optics catalog, and it has a "hot" babe showing her legs on the front cover! Even though I just purchased a $2750 camera from Edmund, this one went right into the trash. Excuse me, isn't it 2007?

Phil may be using time travel to post. Has he responded to anyone since? Computers haven't passed the Turing test yet...

You could use time travel for the Seahawks. Best Buy sells camcorders and VCRs, for example.

This light echo thing is a way of doing time travel, for instruments like Chandra, and other scopes. And that's for instruments that always look into the past. A search for SN1987a light echoes turned up two or three other super nova light echoes. Very cool stuff.

I like this particular experiment. I'll have to try it. Then drink it. I've got a packet in my desk drawer. I can switch from my insulated mugs to one that rings.

Too bad for the Mercurians, though. I'd rather have a nearby event on the horizon than a nearby event horizon.

Thanks for the hot coffee pitch explanation . It was driving me nuts for several years. Let's have lots of physics --- can't get enough.

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    Physics Cocktails

    • Heavy G
      The perfect pick-me-up when gravity gets you down.
      2 oz Tequila
      2 oz Triple sec
      2 oz Rose's sweetened lime juice
      7-Up or Sprite
      Mix tequila, triple sec and lime juice in a shaker and pour into a margarita glass. (Salted rim and ice are optional.) Top off with 7-Up/Sprite and let the weight of the world lift off your shoulders.
    • Listening to the Drums of Feynman
      The perfect nightcap after a long day struggling with QED equations.
      1 oz dark rum
      1/2 oz light rum
      1 oz Tia Maria
      2 oz light cream
      Crushed ice
      1/8 tsp ground nutmeg
      In a shaker half-filled with ice, combine the dark and light rum, Tia Maria, and cream. Shake well. Strain into an old fashioned glass almost filled with crushed ice. Dust with the nutmeg, and serve. Bongos optional.
    • Combustible Edison
      Electrify your friends with amazing pyrotechnics!
      2 oz brandy
      1 oz Campari
      1 oz fresh lemon juice
      Combine Campari and lemon juice in shaker filled with cracked ice. Shake and strain into chilled cocktail glass. Heat brandy in chafing dish, then ignite and pour into glass. Cocktail Go BOOM! Plus, Fire = Pretty!
    • Hiroshima Bomber
      Dr. Strangelove's drink of choice.
      3/4 Triple sec
      1/4 oz Bailey's Irish Cream
      2-3 drops Grenadine
      Fill shot glass 3/4 with Triple Sec. Layer Bailey's on top. Drop Grenadine in center of shot; it should billow up like a mushroom cloud. Remember to "duck and cover."
    • Mad Scientist
      Any mad scientist will tell you that flames make drinking more fun. What good is science if no one gets hurt?
      1 oz Midori melon liqueur
      1-1/2 oz sour mix
      1 splash soda water
      151 proof rum
      Mix melon liqueur, sour mix and soda water with ice in shaker. Shake and strain into martini glass. Top with rum and ignite. Try to take over the world.
    • Laser Beam
      Warning: may result in amplified stimulated emission.
      1 oz Southern Comfort
      1/2 oz Amaretto
      1/2 oz sloe gin
      1/2 oz vodka
      1/2 oz Triple sec
      7 oz orange juice
      Combine all liquor in a full glass of ice. Shake well. Garnish with orange and cherry. Serve to attractive target of choice.
    • Quantum Theory
      Guaranteed to collapse your wave function:
      3/4 oz Rum
      1/2 oz Strega
      1/4 oz Grand Marnier
      2 oz Pineapple juice
      Fill with Sweet and sour
      Pour rum, strega and Grand Marnier into a collins glass. Add pineapple and fill with sweet and sour. Sip until all the day's super-positioned states disappear.
    • The Black Hole
      So called because after one of these, you have already passed the event horizon of inebriation.
      1 oz. Kahlua
      1 oz. vodka
      .5 oz. Cointreau or Triple Sec
      .5 oz. dark rum
      .5 oz. Amaretto
      Pour into an old-fashioned glass over (scant) ice. Stir gently. Watch time slow.