How can they "aim" a LIGO?

> I mean how do they know what part of the sky your currently analyzing? I
> realize the screen saver is more eye candy that anything else. But can they
> really determine that the data I'm crunching came from such an exact part of
> the sky?

Analyzing a specific part of the sky is in this post, an explanation by Ben Owen, specifically this part:
This is a systematic search of the sky, one location at a time, for any periodic gravitational wave coming from that location. It has to be done for each location because the frequency shifts (Doppler shifts) due to the Earth's motion are different for different sky locations.
I think the "crosshairs" in the screensaver shows this spot (it is moving all over the sphere).

So they take a bunch of LIGO readings, pick a spot on the sphere, apply corrections for the Doppler effect for that spot en start analyzing the corrected data for periodic waves. If something is found for a specific spot, I guess the source is somewhere in that "area", but I don't know how large that area is.

> I've read thru both the explanations, and even as a layman, I'm still not
> convinced those are sound answers. They appear even to be conflicting.
>
> A couple of things that don't seem to make sense when combined together:
>
> To say you're searching a particular point in the sky implies that you can
> actively "point" something at it (like a parabolic dish, or a mirror)

Let me explain how I understand this. Maybe one of the project team could put me right if I am off track. In contrast to SETI (where they do aim the receiver), I do not think there is the same issue of 'aiming' the hardware.

If you had a camera that takes holograms, you could take a picture of the sky and later on look at different pieces of sky as thay appeared from your camera at the time. Every part of a hologram contributes to every direction you look, and converesely to get the best view in that direction you need every part of the hologram.

You take the picture then, and only decide where to 'point' it now. Tomorrow, with the same picture you decide to look in another direction and you can see that as well.

In fact, what your eyes are doing is processing some of the light that passes through the hologram, and throwing away other parts of that light. The stuff your eyes keep is 'added up' by the lens in your eye, and some rays of light add together to make bright spots and others cancel out to make dark spots. Point your eye in a different direction 'through' the hologram and you see something else.

That is quite a fair analogy to what we are doing here. The LIGO numbers together are a very poor quality hologram (I mean the data is sparse compared to the amount of data represented by a hologram on ordinary photgraphic film, I don't mean to cast apsersions of the quality of the LIGO which is the best LIGO we've got so far)

When lots of WU have the same data file, they all have the same 'hologram' taken at the same time. Each different WU is applying the same maths but with different values of a few parameters, and this is 'aiming' where your client is looking.

That maths that is used to do this is based on Fourier analysis, and without having looked at any of the code I'd bet that our clients are stuffed full of Fast Fourier Transforms. It is the FFT that is 'aimed', not the hardware.

The reason that the eye analogy is such a good one is that the FFT can also be used in the design and analysis of lens systems. You could say that the lens in your eye, or in your camera, performs an Analogue Fourier Transform.

> Additionally... How is LIGO aiming at the southern celestial hemisphere? Do
> gravity waves even behave with a "field of view" like optics or radio waves to
> make "pointing" possible? How does one "block out" gravity waves from outside
> the "field of view"?

The LIGO is like a tiny cross shaped window, and each dataset can 'see' everything you could see looking through a cross shaped (or diamond shaped??) window at that point. It is how you process the data afterwards that makes the difference. Just like when you look through a fence you can choose to focus on the fence (and the background is a blur) or can choose to focus on the hills behind (and the fence goes blurry), you could do the same with a hologram of the fence and the background seen thropugh it, and to use the same analogy we do the same by tweaking the paramters for the FFT. It is not so much that you block one thing as you focus on another, and let the unwanted stuff blur out.

Just like with a camera, where the wider the aperture the smaller the depth of field, so too with a LIGO, the larger the physical device the more precisely the FFTs can home in on one particular feature and ignore the rest.

Sorry, haven't much time, but to give you a rough idea:

The method we are using is called "matched filering". In principle we generate a signal with the expected properties and search for it in the data. The gravity waves sent out by the pulsars should be pure sinosoids of a given frequency. Arriving at the detectors, however, they got modulated in amplitude as the sensitivity of the detectors varies with their orientation relative to the source, and in frequency because of doppler effects caused by the motion of the earth (again relative to the source). These two modulations have to be taken into account, on one hand making the calculations much more complicated, but on the other allowing us to look in a certain direction of the sky. Gravity waves are not affected by matter, so it doesn't matter from which side of the earth they arrive.

BM

Thanks, BM!

Let's see if I'm getting this, now.

> The method we are using is called "matched filering". In principle we
> generate a signal with the expected properties and search for it in the data.

So the LIGOs are essentially "omni-directional" and we're searching the LIGO's collected data for matches with data from a self-generated sample signal of gravity waves that we might expect to see from a given particular point in space. (Yikes! Talk about brute force calculation!) And I assume now this is mainly to prove that our sample signals are built correctly and validate LIGO (prove our theories) and therefore claim to be able to "detect" gravity waves?

> The gravity waves sent out by the pulsars should be pure sinosoids of a given
> frequency.

Hence the clear value of the FFT in visualizing the detection...

> Arriving at the detectors, however, they got modulated in amplitude as the
> sensitivity of the detectors varies with their orientation relative to the
> source,

"Losses" due to "antenna/signal polarization"? (Interesting! Is that indeed a feature of gravity waves?) Does that help locate the pulsar? and/or perhaps give you spin axis of the pulsar?

> and in frequency because of doppler effects caused by the motion of the
> earth (again relative to the source).

Doppler, as indicated... Used in similar fashion as the Frequency Difference of Arrival (FDOA) techniques for radio direction finding?... or (as Gravy points out) maybe more simply by determing at what point in the earth's rotation the doppler shift changes in acceleration as the LIGO passes "underneath" the pulsar? That would at least give you a rough estimate of right ascension, no?

> These two modulations have to be taken into account, on one hand making the
> calculations much more complicated, but on the other allowing us to look in
> a certain direction of the sky.

"... allowing us to look in a certain direction of the sky."... in a manner of speaking, as predetermined by the self-generated signal, correct?

> Gravity waves are not affected by matter, so it doesn't matter from which
> side of the earth they arrive.

That part I had assumed to be true, but wanted to confirm.

SO.... getting back to original post... the cross hair on the screen saver really is just eye candy :-) ... or at most just a representation of the "scanning" method.

Sorry for the continuing list of questions... but this is all very interesting to learn about. I appreciate the replies.

Thanks again!
Glenn

Hi folks,

I'm back after being tied up for a while. The forum just disconnected and ate a very long post I tried, so I'll just say quickly:

LIGO isn't physically aimed at all. The sites move only as the Earth moves. The orange marker on the screensaver is not eye candy; it's very real and determines the cost of the search in CPU cycles. But the aiming is done in software rather than hardware. LIGO picks up waves from (almost) the whole sky all the time. They go right through the Earth, so there's no worry about what hemisphere a detector is in. Triangulation is used for short-lived sources, but that doesn't give you the kind of position accuracy you see in the screensaver. Matched filtering is a math trick that lets you latch onto one signal out of all the signals (and noise) that may be present simultaneously in the data.

For long-lived periodic sources, which are the only ones Einstein@Home is looking for, triangulation isn't used. The directionality comes from the Doppler shifts a signal picks up as the detectors move around. The Doppler shifts depend on time and sky position. If you process the data for one sky position (which you do with Einstein@Home) it enhances anything that might be coming from that position and washes out anything coming from other sky positions. Einstein@Home picks the next sky position close enough that the "washing out" due to a signal possibly appearing between the processed sky positions is never worse than, say, five percent. (I forget exactly what the number is for this search.)

The smallness of the window someone was referring to earlier comes from the length of the data set analyzed. In the future the data sets are going to get longer and longer (don't worry, the individual WUs will stay manageable!), which means the gap between different sky positions (different locations for the orange marker) will get narrower and narrower.

A lot of the math tricks were originally developed for radio, but LIGO is taking them much further. A lot of the things (like aiming) that radio could mostly do in hardware and merely "top up" in software have to be done all or almost all in software for gravitational wave detectors. There are some tantalizing similarities to radio, but it's really a different game.

Hope this helps,
Ben