Thursday, June 14, 2012

The Null Result: NOT Finding What You Were Looking For

I've written many times on this blog about why we are looking for gravitational waves and what we hope to learn from them.  I also get to tell real people about this all the time with the work I do at the observatory.  As they get excited, they want to know how many gravitational waves we've detected.  My standard response (as of this date, of course) is, "None, and we didn't expect to either."  And I say this with a smile on my face.  Cue the confused and disappointed expressions...

With Initial LIGO, we were hoping to maybe see a gravitational wave from a pair of dense stars merging together about every ten years or so (based on astronomers' estimates on how many of these system there are out there and what fraction of them will be in this merger stage).  While LIGO has been taking data on and off (we take breaks to improve the detector) since 2002, we only have about 2 years of data when both LIGO detectors (in Louisiana and Washington state) were collecting data at the same time (things like earthquakes, weather, etc. can put one or both offline temporarily).  This gives us about a 20% chance of detecting a gravitational wave with LIGO - not the best odds but better than humans have ever done before!  When the Advanced LIGO upgrades are done and the detectors are running at their design sensitivity, we expect to find one of these "merger" gravitational waves about once a month!

An artist's impression of two stars orbiting each other and progressing (from left to right) to merger with resulting gravitational waves. [Image: NASA]

So, what have we been doing with all this data that has no gravitational waves in it?  Some may think it is worthless but that is far from the truth!  Most people think that when you do an experiment and don't find the thing you are looking for (a null result), the experiment was a failure.  While that can be true if your experiment is inherently flawed, it can also tell you valuable information about the world and Universe around you; now you know how something doesn't work or how rare something is.

Since we know that gravitational waves exist from the observations of the Taylor-Hulse pulsar (1993 Nobel Prize in Physics), we know gravitational waves are real.  So we are left with knowledge on how rare gravitational waves are.  We estimate this by carefully studying how sensitive our detectors are and how well our data analysis methods perform.  Once you know these things, you can combine that with how long you looked for gravitational waves (how much data was taken) and estimate the highest rates that the different kinds of detectable gravitational waves pass by Earth.


THE UPPER-LIMIT FOR BURST GRAVITATIONAL WAVES

I am going to use the example of burst gravitational waves which are short duration gravitational waves from unanticipated sources or from known sources where we can't be sure what the gravitational waves will look like, e.g. supernovae, etc.  (The science summary for this work is here.)  I chose this example because this is the kind of gravitational waves I specialize in.

In order to determine the sensitivity of our data analysis method, we need to put fake signals into real data and measure how many of each kind and strength are found by our data analysis method.  This gives us our efficiency.  When combined with the amount of data collected (giving us a measure of how long we were sensitive to gravitational waves) we can estimate the maximum rate that we would expect a kind of gravitational wave to pass by Earth.  We used many different signals to test the data analysis method, but my favorite is called a sine-Gaussian and looks like this:

Sine-Gaussian signal: a sine-wave (trigonometry) multiplied by a bell-curve (Gaussian function).  The horizontal axis measures time in seconds and the vertical axis measures the strength of the signal.  The spacing between the waves provides a measure of frequency.

Using different strengths and frequencies of this signal, we were able to set an upper-limit on the rate of these kinds of gravitational-wave bursts:

Upper limits on the rate of gravitational wave bursts, determined using the LIGO and Virgo data. The different curves represent signals with different characteristic frequencies; the vertical position of each curve shows what rate should have given us at least one detectable burst with 90% probability, for different assumptions about the strength of the burst (horizontal axis). Since no signal was detected, higher rates are ruled out with good confidence.  [Source: S6 Burst Science Summary]

The current results for the burst upper-limits (from the plot above) are that we expect up to about 1.3 sine-Gaussian-like signals a year in LIGO's most sensitive frequency range (64-1600 Hz) with 90% confidence.  


RESTRICTING PARAMETERS ON OBSERVATIONS

Another thing you can do with data that doesn't contain gravitational waves is restrict the possibilities on how observed events happened.  In 2007, there was a strong gamma-ray burst (GRB) observed by the InterPlanetary Network (IPN).  The area that the source could have originated from also overlapped with an arm of the Andromeda Galaxy:


Bottom left corner box: possible area where GRB 070201 could have originated.  Remaining part of image: close-up of the part of the candidate source area that overlaps the Andromeda Galaxy.  An dwarf spheroidal galaxy, called M110, is also labeled.

This was very exciting to all of us at LIGO because one of the possible causes of gamma-ray bursts is the merger of two neutron stars (like in the first image in this post).  With the Andromeda Galaxy being only about 2.5 million light-years away (LIGO was sensitive to these merger gravitational waves all the way out to several hundred million light-years away), if it really was a merger that caused this GRB then we should have seen it!

After careful analysis of our data before, during, and after this GRB, we did not find any evidence of a gravitational wave.  While it would have been very exciting to see something, this null result tells us that:
  1. if the GRB was located in the Andromeda Galaxy, it was not caused by a neutron star pair merger, or
  2. if the GRB was created by a neutron star pair merger, it was located far behind the Andromeda Galaxy. 

A LOT FROM SEEMINGLY NOTHING...

As of today (14 June 2012), LIGO has submitted 64 papers for publication.  You can also read the public science summaries for the latest published papers here.  This a quite a lot of papers based on data without any gravitational waves!

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