Detector Watch S6 V1

I know I've covered some of this stuff in the dim/distant past, but I'll review it for recent attendees.

The operation of the interferometers is associated with a massive monitoring system that covers all aspects of the day to day, shift to shift, happenings. If there's a device or component it will have a setting, an input, an output ....... something .... which is worth recording. That is not only useful on a realtime basis but also for later review. So those involved in LIGO can access this data, in addition to the 'science' data, for whatever purpose.

Now the logs contain what are called Figures Of Merit which are summary plots ( usually ) that reveal the overall performance of the interferometer. These are automatically generated by programmed scripts for inclusion into the logs. One of these scripts is called 'RoboSciFom' which I guess means 'robotic science figure of merit'. Check this one out from Livingston :

There's no science data in this picture per se. It indicates the 'response' of the interferometer at the time it was recorded. Think, for a moment, of the interferometer as an aerial or antenna just like a radio or TV one. You could measure the capability of such an antenna by how well it will pick up a given signal, and for various reasons this capability will depend on the frequency of the signal you are trying to listen to. Thus it is so for the interferometers, as they are gravity wave aerials.

This diagram shows several curves. The greeny-brown dotted one which dips downwards from the left to a minimum and then steadily rises to the right is the predicted ability of the interferometer based upon it's design. It's the theoretical best performance, if you like, calculated from principles, models and engineering.

What is indicated on the left sided vertical axis is a measure of the spacetime strain - how much in particular is the variation from 'flatness' that a wave is producing. This is in powers of ten ( hence is called a logarithmic scale ), and the lower we can go on that the better - the quieter will be the signal we can hear. The horizontal scale is also logarithmic and refers to received gravity wave frequency.

So at the minimum of the curve, around 200 Hz indicated by the red loop, is the 'sweet spot' where the 'hearing' of the interferometer is the best. If any of you have had formal hearing tests ( headphones on, press the button when you hear a sound .... ) then it is quite similiar to a curve you may have seen. Except that the sense of the vertical axis is reversed and better hearing is represented toward the top.

The part of this curve from the left axis down to the kink indicated at the blue loop is determined by the 'gravity gradient', which we really can't change much on this planet. You have to go into space to improve the hearing down that lower end of frequencies - indeed that is where LISA will be.

The part between the blue and the red loops is due to all manner of vibrations that can 'invade' the interferometer from the outside. This includes just about anything you can think of which is noisy or energetic in some way and covers lawnmowers to ocean tides. There has been a huge effort to diminish this by enclosing the working parts of the interferometer within structures that isolate that sort of energy.

Now the gentle slope from the red loop across to the right side is determined by the quantum mechanical nature of photons - a thing called 'shot noise'. I liken it to Melbourne trams. You're waiting at the tram stop for quite a while with no arrivals ( despite the timetable! ), and then all of a sudden 6 turn up at once. Hmmmmm ..... sound familiar? Well photons tend to do that : fluctuate around some average power and this type of variation affects higher frequencies more than lower.

The grey curve which is generally following the design curve is what ( on average ) was the best achieved for the S5 run. I'll talk about the spikes on that curve later.

As for the other coloured curves, well I guess you'd suspect all is not well at the time this snapshot was taken .... and you'd be right! This does not represent a 'locked' interferometer and it isn't taking science data. For whatever technical reasons/troubles the interferometer is 'deaf' at this point. So anyone looking at this FOM will immediately conclude that all is not well.

More later ...... :-)

Cheers, Mike.

( edit ) Here you go, a much better 'audiogram' to compare and contrast :

Where you'll note the blue curve is mostly under the best S5 performance, that is better, especially at the high frequency end.

Yeah, it's not off to a good start is it? Should be ~ 30 Mpc for the standard 1.4/1.4 ( solar mass ) NS pair inspiral in enhanced LIGO. S3 - S5 was ~ 14 Mpc on a good day, for the 4km arms ( 7 Mpc for H2 ) ..... :-0 [ aim for advanced LIGO is ~ 200 Mpc ]

I've been catching up reading the logs today ( busy w/end in real life ) and at Hanford at least there is a host of problems with several apparent threads/issues that don't seem to be connected. I'll get back on this but it looks like trouble with the Wave Front Sensor(s) may be responsible. WFS is essentially is a check on beam alignment, but it interacts with the Output Mode Cleaner apparently. The OMC is a method of excluding photons that have travelled in the interferometer but aren't sufficiently coherent with the main beam.

Cheers, Mike.

( edit ) Mind you, I'm not sure how much/many of the features of eLIGO are in place yet .....

( edit ) Here's a document which outlines the expectations for the LIGO phases.

Another FOM worth looking at is this one ( from Livingston ) :

Alas, 'state vector' makes it sound more mathematical than it is. It is simply a numerical system for classifying the readiness of the interferometers ( and I don't think they've updated the legend for the vertical axis ). So during this 12 hour period the Livingston IFO was well locked and collecting science data, whereas Hanford is up and down. The stepwise increments indicate progression of the interferometer configuration towards locking. Here's the inspiral range for that time which reflects this :

So while Hanford was up for a shorter time, it had the greater range when it was. What is really preferred of course apart from long locked stretches per se, is coincident stretches for both IFO's. That way when ( Yeah! ) a signal arrives we could well get two 'views' of it. This is a key feature for the project, not only can one have greater confidence in the fact of a detection with several interferometers ( and let's not forget Virgo data which is in our analysis pipelines as we speak ) but also the possibility of 'triangulation' from separated detection sites. That way one raises the chances of a correlation with other astronomy modes.

What I reckon would be real cool would be ( near ) simultaneous detections of a supernova, say, by : LIGO, electromagnetic astronomy modes and a neutrino detector!! See SN1987A ...... :-)

Cheers, Mike.

( edit ) I think you'd need four interferometers to localise in the sky, range included. Since they are as yet undetected then GW strength at source can only be estimated from other considerations. This is sort of but not quite equivalent to the intrinsic brightness of stars where we have plenty of examples around to calibrate some scale of luminosity. I think the GW perturbation subsides like inverse distance once you are outside of the nearby space of the source system. If you could be sure of source strength and the propagation decay of the strength then only three detectors ( all being well technically ) could give a unique solution back to the origin of the wave. You see, a single detector doesn't 'point' well due to it's angular variation of antenna response. It only varies by about a factor of two over most incident directions.

To understand much of what happens at the interferometers the idea of resonance needs discussion. Resonance is a general concept in physics and fortunately we usually have an intuitive/everyday idea of what it means.

Imagine a box of some sort. Let's call it black, meaning that we can't/don't/won't look inside to see it's internals. Also suppose there is a hole in the side into which we can throw energy, and out of which we can sense what comes back. After some experimenting we notice that if we throw certain types of energy into the box, then we get back larger amounts of energy than otherwise. Clearly there is something going on in the box that reflects or returns what we gave it on certain occasions. This behaviour is the guts of resonance ..... and there are other definitions too.

Set the Wayback Machine Mr Peabody : Imagine sitting with Galileo in church, both your minds wandering from the sermon. Watch the swinging of the candle holders that are attached to the high roof by ropes. Back and forth. Back and forth. Quite regular, which you can attest to by timing with respect to your own pulse. Presumably the swinging motion is generated by drafts of air up there, and this gives a characteristic frequency for the motion. On analysis it seems that the length of the rope is the main determinant of that frequency, with the strength of gravity also. This is typical of resonance - a physical length/size and a force strength.

Now get a really good singer and a really good grand piano. Open the lid and have the singer put out a strong pure note into the open top. The piano will respond with vibration of the string corresponding to the same frequency of the note sung. Which string responds will depend on it's length and tension. Experiment with different sung notes. You'll notice it won't likely be just one string, there will be some lesser response from several strings on each occasion. However for a given sung note those other strings will have some fraction or multiple frequency to which they would have been the main responder. In other words there is harmony.

Back to the present day. I'm going to be an annoying salesman. I will knock on your front door once every 12 hours. You wisely don't answer, but I keep persisting. How could you characterise this behaviour mathematically? Well you could rightly say that the frequency of my knocking is once per 12 hours. But you could also say it is once per day too, as every day at a given time I will knock ( just ignore the in between ones ). In fact for all you know there might be two annoying door-knockers each turning up once per day for a go at it, but we alternate our turns and keep synchronised at 12 hours apart. There is also a sense in which my rhythm is 6 hourly, but at half strength, as I could be turning up every 6 hours but only actually knocking on the door every second time.

I'm attempting to give a sense of the idea of what is called up-conversion ( multiple of a frequency ) and down-conversion ( fraction of a frequency ). This pretty well happens, whether you intend it or not, for all resonant phenomena. Jupiter is a good example of this. This planet has been labeled the Hoover of the solar system. It just clears the little bits of garbage out and collects the rest. So if an asteroid has the (mis)fortune to return to more-or-less the same orbital place & time as Jupiter they will interact. Might is Right in this situation. In time the asteroid will be either flicked out of the solar system to never return, be gobbled up, or transitioned to a new orbit that will 'park' it out of resonance with Jupiter's orbit. We are lucky to have a Jupiter about to do this for us.

Back to LIGO. The interferometers are exceedingly complicated. Energy wise you can think of them like those black boxes above. Some boxes are next to others. Some boxes are inside others. The boxes interact. Some we want to resonate. Some we don't. And all are getting jiggled by the outside world, or by their own inevitable internal energies. We want to find the jiggles that are due to specific astronomical events far and away. It is those jiggles that are the quietest of them all, which we want to enhance ( via resonance over those 4km 'cavities' ) in a reliable way. Even though we have yet to hit the exact mark on that, the operations so far have improved/refined understanding of the resonances that are inherent in the design of the machine. Now let's look again at this FOM :

Focus on the grey curve, which is a reference curve derived from the best S5 experience. The spikes in that curve, rising very much above the greeny-brown dashed ( design spec ) curve, are where the interferometer resonates - and this is largely due to it's design ( boxes & boxes .... ) and inevitable interactions with it's environment ( like the electricity power supply frequency ).

One particularly interesting point is that Advanced LIGO is going to have the ability to shift some resonances of the machine and thus 'tune' the hearing. While not eliminating the energy from the configuration all together, one can 'park' the energy elsewhere in the spectrum. Currently some modeling based upon the knowledge of the inteferometer has allowed effectively 'smoothing' of the spikes, that is assuming what would have happened had the resonance not been there.

( Sorry for the long post - it's a hard area )

Cheers, Mike.