For an isotropic (i.e., in all directions equally) radiator we have:

F = P / (4*pi*r^2)

where F is power flux (watts per square meter), P is power (watts), and r is distance (meters)

For a tightly focused beam:

F = P / (Sigma*r^2)

where Sigma is the solid angle (steradians) of the beam. Or:

P = Sigma*F*r^2

Sigma = 2*pi*(1 – cos(0.5*theta))

where theta is the full beam width (radians)

For small theta we use a Taylor series approximation:

P = 0.25*pi*theta^2*F*r^2

Thus, if you cut the beam width in half the power needed to produce the given flux (i.e., brightness) goes down by a factor of four. So small beams are good to project power a long way. Hope that helps.

http://server6.sky-map.org/starview?object_type=1&object_id=1148174927

Although its true that GRBs are still poorly understood, as Phil states there are many phenomenological characteristics in GRB afterglows that point towards there being jets in the system.

I would point out that I am not a GRB theorist, but know many that are and the concept to beaming and jets in GRBs is non-controversial these days.

Better would have ben “civilization threatened by nearby star going supernova/GRB.” Then we could have our cake and nuke it, too!

(My coat? the liquid nitrogen one on the far end.
Man, that’s cool….)

“People talk as if it were a fact that GRBs give off their energy in beams (rather than in every direction). I know there was some evidence for beaming recently (I think it was a paper in Nature or Science), but my impression was that the evidence was somewhat sketchy. Has there more evidence generated for the hypothesis that GRBs give off their energy in beams? Just looking at the NASA photograph, it looks like the thing was giving off energy in every direction. Would it take a force much more powerful than the burst itself to direct all that energy into beams?
Thanks for any insight …”

Dr_LHA responded:
“Mark: GRBs basically have to be beamed, otherwise the amount of energy they give off would be too large to explain.”

Thanks for responding Dr. LHA. That’s the impression I’d gotten also, i.e. the evidence for beaming is scant, but they MUST be beamed otherwise we have no explanation for them. This is pet peeve of mine so excuse me while I climb onto my soapbox …

“Ahem … All conveyors of science to masses out there in world … PLEASE STOP DOING THIS!!” That is, please stop giving people the impression that we understand things that we don’t, and then add little qualifiers like “of course there are some details that haven’t been worked out yet …” This is a curiosity KILLER to aspiring future scientists. I remember asking probing questions about gravity and electons and such to my high school physics teacher. He gave the impression that all this stuff has been figured out but it was much too difficult for me to understand. That basically killed the curiosity and interest I had. If he had instead said something like, “nobody really understands these things at the most fundamental level, we need people with an interest in these things to study them and figure them out” who knows how my career would have been different. It seems apparent to me that all we have with regards to GRBs is a couple of barely tenable HYPOTHESES about what causes them. These hypotheses are probably totally unable to explain the beaming of GRBs (which everyone agrees must be occurring because otherwise we would have no explanation for these things – anybody spot the logical inconsistency here?)

So, if it is true, please just say, “We have no idea what can cause a burst of energy this big. We have a couple of seriously deficient hypotheses that people are working on.”

Again, I ask. If the amount of energy put out by these things is what makes them difficult to understand, then how does “beaming” solve the problem since it would take more energy to concentrate a beam than is in the beam itself?

I’ll shut-up now and let someone with more knowledge correct/enlighten me.

Thanks

The point is also put across eloquently in Terry Pratchett’s story “Hogfather” where towards the end of the book Death explains wearily:

“Take the universe and grind it down to the finest powder, and sieve it through the finest sieve, and then show me one atom of justice, one molecule of mercy. And yet, you try to act as if there is some ideal order in the world. As if there is some, some rightness in the universe, by which it may be judged.”

btw I also like the Twilight Zone version of Clarke’s story, in which some sort of poetic consolation is suggested to account for the tragedy of the event. Makes you think.

The Greatest SF Story Ever Told
(A Pantoum Tribute to “The Star” by Arthur C. Clarke)

They knew their time had come at last
They understood all things must cease
Their faithful sun was dying fast
They must resign themselves to peace.

They understood all things must cease
Their mighty empire would be lost
They must resign themselves to peace
There would be none to count the cost.

Their mighty empire would be lost
They hoped their art would all be saved
There would be none to count the cost
They locked their treasures deep in caves.

They hoped their art would all be saved
They held each other in their grasp
They locked their treasures deep in caves
Their star pulsed out its dying gasp.

They held each other in their grasp
They knew God would remember them
Their star pulsed out its dying gasp -
Its light was seen in Bethlehem.

© Elwood Herring 26 Feb 2000

i guess this has been a “rant”? But BA, thanks for bringing the wonder of this weird, wonderful, and seemingly infinite Universe home to us! I really appreciate your love of what you do! Thanks, from the bottom of my heart!

I’m not sure how, or if you celebrate Easter, but I hope the Easter Bunny drops many chocolate eggs on you, Mrs. BA, and the little BA!

But… when I read something like this, all I can say is, “Wow”! There are really no other words to describe the awesomeness of the Universe.
Many months ago I said that I looked at Saturn’s rings. We have Hubble’s pics. But, please, if you have even a small telescope, take the time to find Jupiter, or Saturn, or Mars….

A few years ago when Mars was at it’s closest, I took my then 5 or 6 year old daughter out and aimed my small Meade 3.5 inch scope at Mars. I could ACTUALLY see the Ice-caps! later I showed her Jupiter and her 4 moons, then Saturn…. Real time! I was able to show my daughter the wonders of the Universe. My ex is taking them to church and stuff, ( I used to be a minister, but have “fallen”. That’s fine. I have no problem teaching my daughter what I believe, yet respecting what her mother, who knows zilch about science anyway, believes. I have the unique advantage of knowing, in a limited sense, both sides of the coin. At this point my oldest is more interested in Hannah Montana than the latest Mars update! My youngest is developmentally delayed (Down syndrome).

I guess I want to thank BA for showing me, and in turn, through me, my kids the wonders of Space! BA you are one of my heroes!

And a question:
The NASA page, and the previous page it links to, both say that what’s visible is the afterglow caused by the high energy jets from the (supposed) collapsing star heating up the gas surrounding the GRB. I’d have thought that the afterglow would emit light in all directions, not just the directions of the jets.. is that wrong?

I see only two realistic explanations:

1. This is definitely the sign of the end times. All the previous ones didn’t work out I know – but this is CERTAINLY it.

2. It could be some Amanda Tapping type scientist chick blowing stars up to protect the Earth from alien invasion. I mean think about it. We just happen to see such a huge explosion at this point in history? What are the odds?

I think the SG-1 series is based on reality, and the show is a Wormhole X-treme style double-bluff by the government. And Wormhole X-treme itself a triple-bluff to throw us off the track. It’s the only reasonable explanation.

Phil is probably in on it, by the way. That’s why he goes to so much trouble to show photos of people with his books. We are supposed to believe that lots of people are buying them, and that’s where his money comes from – not a big fat cheque from NASA.