Are the interferometers focussed?
27 Dec 2006 4:50:21 UTC
Topic 192236
(moderation:
Does anyone know wether such an interferometer has a favourite direction?
Would they detect waves coming straight from above or is their sensitivity very much lower with angles towards 90 degrees?
The arrangement of the interferometers on the globe is not in a way that they could cover all three dimensions, if they were sensitive only when a pulse comes in in a low angle along the plane of the L.
(I hope I could explain what I mean, some English words didn't come to my mind)
Are the interferometers focussed?
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Here's a straight lift from Peter Saulson's book [ Fundamentals Of Interferometric Gravitational Wave Detectors - ISBN 981-02-1820-6 , $91.00 USD at Amazon :-) ], page 24:
there's no response if it comes along the bisector of X and Y axes ( ie. at 45 degrees looking into the space between the arms, but in the XY plane ). You see this as the puckered dimple in the face showing us in the diagram.
The maximum is along the Z axis , with a factor of twice the response compared to along either X or Y arm alone. This is why it looks peanut shaped.
It's better to think of it like a radio reciever, rather than a lens like in a telescope. One reason is that the wavelength of the gravity waves is very much longer than the LIGO detectors - as distinct from visible light where the wavelength is very much smaller than the optics ( where you could model with geometric rays ).
The rms average over all directions is ~ 0.45, and if you want the funky maths here 'tis:
with this co-ordinate key:
Now there is a rough 'alignment' between Hanford's X-arm ( going ~ NW ) and Livingston's Y-arm ( going ~ SE ), with Hanford's Y-arm and Livingston's X-arm both going ~ SW. So by rotating Hanford counterclockwise ~ 90 degrees, looking from above, you will get to Livingston's arrangement. The null for Hanford is just to the north of due West, and that for Livingston is just to the west of due South - hence they are about 90 degrees from one another. None-the-less they are around the curve of the Earth from one another, so this is approximate. Thus I think they sort-of 'cover' each others blind spots.... I recall this as being a deliberate design decision.
Assuming my spherical trigonometry is not crappy, then with a great circle separation of ~3050 km and radius of earth @ 6380km, that gives
3050 / 6380 = 0.478 radians = ( 360 * 0.478 ) / ( 2 * PI ) ~ 27 degrees
worth of angle between the normals ( Z-axes, straight up ) at each site.
You are right with your hint - it would be better to have more global coverage. This is precisely the purpose of GEO, VIRGO and TAMA ( and one day AIGO - go Aussie!! ). Not only do you have better confidence with believing ~co-incident data as representing real waves, but that then also leads to more directional confidence with the source in the sky.
Imagine, one day, that a GRB ( Gamma Ray Burst ) alarm, from mostly orbiting satellites, marks the data records - and subsequently the analysis leads to a confirmed event whose direction corresponds to that of the astronomers original report!! This is one of the dreams.... :-)
Cheers, Mike.
NB. Your English is fine!
( edit ) These GRB's indicate, probably:
(a) the birth of massive objects like black holes ( BH ) and neutron stars ( NS ) in supernovae ( SN ) - a relativistic fireball makes the gammas.
(b) the collision of such massive objects like a BH swallowing a NS - a short lived torus of material near the event horizon produces the gamma rays.
So you could 'hear' the 'bang' of a SN, or the 'gulp' from a BH 'swallowing' something.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
It needs a bit of
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It needs a bit of 3-dimensional imagination but I think I've got it (the picture and the theory more than the maths) :-)
Thanks a lot for taking the time and explaining it!
p.s.: there's some similarity with microphone characteristics
p.p.s.: I found AIGO I think.
RE: It needs a bit of
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I'll just annotate the drawing. Think of it like a hollow peanut shell. Put yourself inside and right at the origin - which is in that dimple :
Now look around ( with a torch? ), the distance to the inner side of the shell is a measure of the sensitivity. The bigger the room in a given direction, the more sensitive it is, or alternately the less spacetime disturbance is required to produce a given phase delay between the two arms ( which is our measure of distortion ). That's why there is a null along the 45 degree line - if a wave comes along from that direction then both arms will be identically distorted and no difference in phase/length will be apparent.
Absolutely right!! In fact sound is a real good analogy here, gravity waves are similiarly hard to localise with one 'ear' so you triangulate with two or more!
That's it all right. Only a corner station for now .... :-(
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
This one would be Ruthe I
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This one would be Ruthe I think.
I've researched a bit more on
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I've researched a bit more on the beam pattern, and discovered more on the 'peanut'. If you consider the 'base' polarities of the gravitational waves :
then each has the beam patterns as follows ( with the peanut being the sum ):
Any wave can be considered as some linear superposition of the F+ and Fx ( a proportional mix of the two ).
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Well, I guess parts of those
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Well, I guess parts of those differences can be equalized by the calculation.
The resulting peanut is a little surprising, shapes like those usually result from interferences - but in means of gravity that would mean you can have anti-gravity by applying another gravity in a different angle, so that comparison is sure not valid.
RE: Well, I guess parts of
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Quite right. Gravity radiation's 'lowest' mode is quadrupolar as 'monopolar' violates conservation of mass/energy, and dipolar violates conservation of momentum. That, plus the weakness of the coupling ( G is small ), gives low intensity vibes. Electromagnetism starts at dipolar, as monopolar violates charge conservation and there's no equivalent of momentum conservation ( conservation of current? ) to prevent dipolar. There's only one gravitational 'charge' but two electric ones.
While there's antimatter, that's a different quantum number(s), and there's no negative mass. Although there is the putative antigravity/repulsive effect of dark energy and negative vacuum pressure and such stuff .... for the life of me, I can't get my head around that. :-)
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Let's hope that installation
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Let's hope that installation in Ruthe is well protected against water, the Sarstedt fire fighters expect very high water on Leine and Innerste. On the arial map it looks quite flat there.