The upper limit paper you can get here. This is Figure 5 from that paper :

The curly 'e' [ Greek epsilon ] is eccentricity, the measure of wobbliness. So the top curve for 10^(-6) means roughly it's out of kilter to one part in million. The lowest curve is to one part in a billion. The neutron star 'mountains' which would produce this aren't very high by the way, say around 10 centimeters maximum. The density of a neutron star is that of the atomic nucleus : a billion kilograms per cubic meter, with strength of gravity at the surface about a trillion times that here on Earth. Maybe you could fit a mountain in your fridge ?! :-)

Cheers, Mike.

( edit ) Sorry, I should mention that the straight horizontal dashed line in the upper part of Figure 5 refers to a previous model, of which the paper is refining. That is, the upper limits on gravitational strain have been reduced by closer examination of the mountain scenario.

( edit ) So a 1 cm mountain on a sphere 10 kilometers in radius is a ratio of one millionth [ epsilon = 10^(-2) / 10^(+4) = 10^(-6) ]

( edit ) Here's more exact readings from the modelling, the levels of the peaks for each curve :

TABLE II: Maximum values for the amplitude hmax of gravitational waves in dependence on the ellipticity in order of epsilon, hmax and frequency band

10^(-6) 1.6 x 10^(-24) [250 Hz; 680 Hz]
10^(-7) 6.6 x 10^(-25) [550 Hz; 1500 Hz]
10^(-8) 1.5 x 10^(-26) [1000 Hz; 2800 Hz]
10^(-9) 2.7 x 10^(-27) [1000 Hz; 2800 Hz]

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

After all my time here : It's just hit me ..... how ambitious we are!!! :-)

We are trying to find evidence of a feature smaller than my car's glove compartment ( well, not withstanding the mountain's breadth ), far down in some really, really deep gravity well and who knows how far away.

The numbers are quite staggering. Einstein knew this too. After calculating the probable size of the effect he promptly despaired of ever measuring it.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

After all my time here : It's just hit me ..... how ambitious we are!!! :-)

The numbers are quite staggering. Einstein knew this too. After calculating the probable size of the effect he promptly despaired of ever measuring it.

Keep your chin up! The LIGO instruments routinely measure separation changes in a 4-kilometer baseline which are one thousand times smaller than an atomic nucleus. That's also quite staggering!

Ah, I've had one of those epiphany moments in life! Deep breaths. Let us all still go for it though .... get those signals !! :-)

[ It is the comfortable trap of exponents and logarithms. It linearises multiplicative scaling so neatly that it can obscure the real spans. The other big number that I just stare at sometimes ( well, not literally ) is that ratio of EM to gravity coupling : 10 to the 40-ish !! My ears aren't far enough apart to squeeze in the full width of all those significant zeroes .... :-) ]

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

â€œhardware injections are not expected to be detected in this search, simply because they were inactive during a large fraction of the data analyzed.â€

A shame.

In the later part of S5 data that we are currently crunching thru, the HW injections seem to cover a greater share of the observation period. Here's a little visualization (scaled up and cropped for better visual impression) of intermediate data structures of the S5R5 app when analyzing data containing a HW injection (a pretty strong one, btw). What you see is the result of the "convolution" or F-statistics analysis that Mike mentioned: The Y axis represents frequency, the X axis segments of observation time. Bright pixels indicate a better fit between the signal template and the actual detector data for a given target frequency (Y) and observation segment (X).

The data is already "demodulated", that is the Doppler effect for the sky-position of the injection is already compensated for and that's why the signal appears as a horizontal line. In un-demodulated (?, well, in raw, Doppler modulated) form, the signal would appear as a sine like curve as the signal frequency at the detector varies over time. The same would happen if there were a mismatch between the sky-position of the template and the actual position of the source.

As you can see the signal is on for about 60% of the time. The Hough Transform pattern recognition that would then be applied to this data (after thresholding this picture to a b/w image, so to speak) by the S5R5 app is quite robust against intermittent loss of the signal, so I guess the S5R5 analysis will recover some HW injected signals.

Anyway, it's always nice to be able to actually "see" with your own eyes that the software is actually picking up signals :-)

So basically it looks like the instrument is working as expected and the result so fare indicates that the theory has a flaw?

Yes, and no respectively. The interferometers are working at their design specifications and are correctly reporting no detections above a certain level. It is operating just above the threshold of detection of the most 'obvious' or 'best case' continuous waves from the rotating neutron stars ( at the specified frequencies ). There is confidence in the data analysis, specifically :

Quote:

While no statistically significant signal was observed in this analysis, the results demonstrate the capability of public distributed computing to accomplish a sensitive periodic GW search for the benefit of future searches.

So I guess we await the Advanced LIGO implementation, which will probe strain another magnitude lower, and hope/expect that detections will occur then. Meanwhile we keep effort up! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

So I guess we await the Advanced LIGO implementation, which will probe strain another magnitude lower, and hope/expect that detections will occur then. Meanwhile we keep effort up! :-)

In the later part of S5 data that we are currently crunching thru, the HW injections ........ picking up signals :-)

That's cool, Bikeman! :-)

Nice to see that graphic, it's quite an obvious feature. So the Hough is robust against some patches of signal loss, eh? I wonder if some submarines are using that. Also :

Quote:

To achieve the maximum possible sensitivity, the template waveforms must match the source waveforms to within a fraction of a cycle over the entire observation time (months or years for current data samples).

Consider a single data segment. Now, for a ~ 200Hz waveform tracked over the maximum 40 hour span, say, that's to within a fraction of a cycle in ~ 29,000,000 cycles in toto [ 200 * 60 * 60 * 40 ]. Whew, you'd want to have a pretty robust time standard to stamp stuff with! :-)

Even after accounting for Doppler effects, there's still an intrinsic frequency change ( assumed to be caused by the astrophysical source ) within that. These are of the order of 10^(-9) Hz/sec ( that is, the frequency may change by about 10^(-9) Hz with each second that passes ). Over 40 hours that's about 1.5 x 10^(-4) Hz [ 40 * 60 * 60 * 10^(-9) ]. Thus for a ~ 200Hz signal that will accumulate to around a dozen cycles [ At 200Hz there are 28,800,000 cycles in 40 hours. At 200.00015 Hz there are 28,800,021.6 cycles in 40 hours. Take (21.6)/2 = 10.6 ]. This is the 'quasi-monochromatic' or 'frequency drift' aspect that the algorithms need to account for.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

Yeah, the "spin-down", I forgot to mention that, thanks. That is actually also accounted for together with the "Doppler demodulation" for the graphic I posted.

The distance between pixels in that graphic for the Y-axis must be about 7e-6 Hz, the simulated Pulsar in question has a spindown rate of -8.65e-9 Hz/sec. Every pixel on the X-axis corresponds to at least 25 h of real-time , so for every step in the X-direction the source signal frequency decreases for at least ~7,8e-6 Hz, or about one pixel in the Y direction. The spindown would be clearly visible in the diagram, if it weren't already compensated for.

## The improved analysis paper

)

The improved analysis paper you can get here.

The upper limit paper you can get here. This is Figure 5 from that paper :

The curly 'e' [ Greek epsilon ] is eccentricity, the measure of wobbliness. So the top curve for 10^(-6) means roughly it's out of kilter to one part in million. The lowest curve is to one part in a billion. The neutron star 'mountains' which would produce this aren't very high by the way, say around 10 centimeters maximum. The density of a neutron star is that of the atomic nucleus : a billion kilograms per cubic meter, with strength of gravity at the surface about a trillion times that here on Earth. Maybe you could fit a mountain in your fridge ?! :-)

Cheers, Mike.

( edit ) Sorry, I should mention that the straight horizontal dashed line in the upper part of Figure 5 refers to a previous model, of which the paper is refining. That is, the upper limits on gravitational strain have been reduced by closer examination of the mountain scenario.

( edit ) So a 1 cm mountain on a sphere 10 kilometers in radius is a ratio of one millionth [ epsilon = 10^(-2) / 10^(+4) = 10^(-6) ]

( edit ) Here's more exact readings from the modelling, the levels of the peaks for each curve :

TABLE II: Maximum values for the amplitude hmax of gravitational waves in dependence on the ellipticity in order of epsilon, hmax and frequency band

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## After all my time here : It's

)

After all my time here : It's just hit me ..... how ambitious we are!!! :-)

We are trying to find evidence of a feature smaller than my car's glove compartment ( well, not withstanding the mountain's breadth ), far down in some really, really deep gravity well and who knows how far away.

The numbers are quite staggering. Einstein knew this too. After calculating the probable size of the effect he promptly despaired of ever measuring it.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: After all my time here

)

Keep your chin up! The LIGO instruments routinely measure separation changes in a 4-kilometer baseline which are one thousand times smaller than an atomic nucleus. That's also quite staggering!

Director, Einstein@Home

## RE: Keep your chin

)

Ah, I've had one of those epiphany moments in life! Deep breaths. Let us all still go for it though .... get those signals !! :-)

[ It is the comfortable trap of exponents and logarithms. It linearises multiplicative scaling so neatly that it can obscure the real spans. The other big number that I just stare at sometimes ( well, not literally ) is that ratio of EM to gravity coupling : 10 to the 40-ish !! My ears aren't far enough apart to squeeze in the full width of all those significant zeroes .... :-) ]

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## So basically it looks like

)

So basically it looks like the instrument is working as expected and the result

so fare indicates that the theory has a flaw?

## RE: RE: â€œhardware

)

In the later part of S5 data that we are currently crunching thru, the HW injections seem to cover a greater share of the observation period. Here's a little visualization (scaled up and cropped for better visual impression) of intermediate data structures of the S5R5 app when analyzing data containing a HW injection (a pretty strong one, btw). What you see is the result of the "convolution" or F-statistics analysis that Mike mentioned: The Y axis represents frequency, the X axis segments of observation time. Bright pixels indicate a better fit between the signal template and the actual detector data for a given target frequency (Y) and observation segment (X).

The data is already "demodulated", that is the Doppler effect for the sky-position of the injection is already compensated for and that's why the signal appears as a horizontal line. In un-demodulated (?, well, in raw, Doppler modulated) form, the signal would appear as a sine like curve as the signal frequency at the detector varies over time. The same would happen if there were a mismatch between the sky-position of the template and the actual position of the source.

As you can see the signal is on for about 60% of the time. The Hough Transform pattern recognition that would then be applied to this data (after thresholding this picture to a b/w image, so to speak) by the S5R5 app is quite robust against intermittent loss of the signal, so I guess the S5R5 analysis will recover some HW injected signals.

Anyway, it's always nice to be able to actually "see" with your own eyes that the software is actually picking up signals :-)

CU

Bikeman

## RE: So basically it looks

)

Yes, and no respectively. The interferometers are working at their design specifications and are correctly reporting no detections above a certain level. It is operating just above the threshold of detection of the most 'obvious' or 'best case' continuous waves from the rotating neutron stars ( at the specified frequencies ). There is confidence in the data analysis, specifically :

So I guess we await the Advanced LIGO implementation, which will probe strain another magnitude lower, and hope/expect that detections will occur then. Meanwhile we keep effort up! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: So I guess we await

)

Even the current "Enhanced LIGO" upgrade (S6 run is supposed to start this summer) should help. The sensitivity should increase by a factor of 2, so the volume of space covered increases by a factor of 8. Not too bad.

CU

Bikeman

## RE: In the later part of S5

)

That's cool, Bikeman! :-)

Nice to see that graphic, it's quite an obvious feature. So the Hough is robust against some patches of signal loss, eh? I wonder if some submarines are using that. Also :

Consider a single data segment. Now, for a ~ 200Hz waveform tracked over the maximum 40 hour span, say, that's to within a fraction of a cycle in ~ 29,000,000 cycles in toto [ 200 * 60 * 60 * 40 ]. Whew, you'd want to have a pretty robust time standard to stamp stuff with! :-)

Even after accounting for Doppler effects, there's still an intrinsic frequency change ( assumed to be caused by the astrophysical source ) within that. These are of the order of 10^(-9) Hz/sec ( that is, the frequency may change by about 10^(-9) Hz with each second that passes ). Over 40 hours that's about 1.5 x 10^(-4) Hz [ 40 * 60 * 60 * 10^(-9) ]. Thus for a ~ 200Hz signal that will accumulate to around a dozen cycles [ At 200Hz there are 28,800,000 cycles in 40 hours. At 200.00015 Hz there are 28,800,021.6 cycles in 40 hours. Take (21.6)/2 = 10.6 ]. This is the 'quasi-monochromatic' or 'frequency drift' aspect that the algorithms need to account for.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## Yeah, the "spin-down", I

)

Yeah, the "spin-down", I forgot to mention that, thanks. That is actually also accounted for together with the "Doppler demodulation" for the graphic I posted.

The distance between pixels in that graphic for the Y-axis must be about 7e-6 Hz, the simulated Pulsar in question has a spindown rate of -8.65e-9 Hz/sec. Every pixel on the X-axis corresponds to at least 25 h of real-time , so for every step in the X-direction the source signal frequency decreases for at least ~7,8e-6 Hz, or about one pixel in the Y direction. The spindown would be clearly visible in the diagram, if it weren't already compensated for.

CU

Bikeman