<p><strong>How LIGO, LISA, etc. Detect Gravitational Waves</strong></p>

<p>The point of instruments like LIGO and LISA is to measure time-varying changes in the distance within different arms of the instrument. In the case of an arm oriented in the direction of an incoming gravitational wave (GW), the length of the arm will increase and  decrease, while an arm oriented perpendicular will remain unchanged.</p>

<p>The <a href="https://en.wikipedia.org/wiki/LIGO#Operation" rel="noreferrer">method for measuring this</a> is to split a laser beam, send each half down the different arms, and then recombine them and look at the interference pattern. If the arms have identical lengths, then the beams will destructively interfere. If, however, one of the arms becomes longer (or shorter), the recombined beams will be out of phase, and you will no longer have perfect destructive interference.</p>

<p>The key to being able to measure this sort of thing accurately is two things:</p>

<ol>
<li><p>Arm length, so the beam traveling down the altered-length path has time
to accumulate a large enough phase shift for the interference pattern to
change enough to be measured. Longer arms lead to larger phase shifts, 
which is why LISA aims to have arms that are 2.5 million km in length.</p></li>
<li><p>The wavelength of the light: the shorter the wavelength, the smaller the
actual shift in arm length needs to be to make the beam shift appreciably
in phase. If the recombined beams differ in phase by 0.001%, then the change
in the interference pattern will be very hard to detect and measure. But if they differ
in phase by 50%, then the difference will be obvious. Shorter wavelengths
make for larger phase shifts.</p></li>
</ol>

<p>If you want think of the interferometric measurement as a kind of timing measurement (that is, we are, in a sense, measuring the difference in time it takes light to travel down the two arms), then <em>optical light is vastly better than radio for "timing" measurements</em>.</p>

<p><strong>Pulsar Timing</strong></p>

<p>As you pointed out, there <em>are</em> projects that use pulsars to try to detect gravitational waves (e.g., <a href="https://en.wikipedia.org/wiki/Pulsar_timing_array" rel="noreferrer">pulsar timing arrays</a>).</p>

<p>These work by measuring time delays in the arrival of radio pulses from millisecond pulsars. However, it's important to note the limitations: in order to measure the arrival time accurately, you have to observe a pulsar over a period of several minutes (or more) and <em>add up</em> all the pulse arrivals to get a single, accurate value. (You are <em>not</em> measuring changes between the arrival of one single pulse and the next.) You then repeat this measurement several weeks or months later to get another arrival time. Since you're taking measurements weeks or months apart, you can only detect variations on that same time scale, which is why pulsar timing arrays are hoping to detect GWs with periods of months to years (e.g., from binary supermassive black holes). The kinds of GWs that LIGO detects -- with periods of <em>fractions of a second</em> -- are completely beyond what pulsar timing arrays can do.</p>

<p>We cannot use optical light from stars, because we know of no star that produces the exquisitely regular periodicity of a millisecond pulsar.</p>

<p>As a final comment, your scenario of photons that "arrive regularly at 15 photons every microsecond onto a CCD" has the problem that Poisson noise (a.k.a. <a href="https://en.wikipedia.org/wiki/Shot_noise" rel="noreferrer">"shot noise"</a>) means that you <em>wouldn't</em> actually get 15 photons every microsecond; you'd get <em>around</em> 15 every microsecond (a typical sequence might look like this: 16, 15, 18, 15, 14, 14, 15, 23, 16, 12, ...). With that much variation, it's really hard to detect subtle variations in intrinsic signal strength.</p>

CC BY-SA 4.0
2019-03-25T00:40:29.653Z
I've just asked [Would an X-ray-based pulsar timing array in orbit or on the Moon to study GW background be effective?](https://astronomy.stackexchange.com/q/30110/7982)
uhoh
CC BY-SA 4.0
2019-03-25T08:51:48.323Z
"The kinds of GWs that LIGO detects -- with periods of fractions of a second -- are completely beyond what pulsar timing arrays can do." The comparison is with LISA. Periods of $10^2$ to $10^{5}$ seconds, so measurements on few minute timescales would seem ok. I don't think this adequately answers the question. You need to explain why the frequency response of a PTA decreases with increasing frequency. It isn't "shot noise", because shot noise has a flat frequency spectrum.
ProfRob
CC BY-SA 4.0
2019-03-24T23:04:29.313Z
2019-03-24T23:21:29.317Z
2019-03-24T23:21:29.317Z
Peter Erwin
<blockquote>
  <p>Can't pulsars and stars be used for gravitational wave measurement?</p>
</blockquote>

<p>In theory, yes. See the 2017 NASA article <a href="https://www.nasa.gov/feature/jpl/listening-for-gravitational-waves-using-pulsars" rel="nofollow noreferrer">Listening for Gravitational Waves Using Pulsars</a>. </p>

<blockquote>
  <p>Suppose that we collected photons from a distant star, and they arrive regularly at 15 photons every microsecond onto a CCD, when a gravity wave bends space time, wouldn't the regular 15 photons graph wobble as a result of the gravitational wave?</p>
</blockquote>

<p>Kind of. When the gravitational wave is passing by, we'll be subject to a slight time dilation. So it would look as if the pulsar had speeded up. </p>

<blockquote>
  <p>Why does the LISA observatory have to compare laser timings, if pulsars can be as precise as atomic clocks, can't it just compare a bunch of pulsar signals? A single satellite that records 50 pulsars would move compared the pulsars and would have a frequency of 50Hz ticks with pulses which can be graphed at kHz frequencies.</p>
</blockquote>

<p>Sorry, I don't know the answer to that. But see the <a href="https://en.wikipedia.org/wiki/Laser_Interferometer_Space_Antenna" rel="nofollow noreferrer">Wikipedia article</a> on LISA and note that it's scheduled for the 2030s. A lot can happen between now and then. Maybe it won't go ahead.   </p>

CC BY-SA 4.0
2019-03-25T00:41:00.523Z
I've just asked [Would an X-ray-based pulsar timing array in orbit or on the Moon to study GW background be effective?](https://astronomy.stackexchange.com/q/30110/7982)
uhoh
CC BY-SA 4.0
2019-03-25T08:04:40.540Z
@Uhoh : noted. I'm afraid I have difficulty giving a useful answer to that one. I'd be saying "probably" or "maybe".
John Duffield
CC BY-SA 4.0
2019-03-25T09:39:27.290Z
I think that those types of answers are well received if they are based on citable facts, e.g. "seems likely considering", "plausible based on"
uhoh
CC BY-SA 4.0
2019-03-26T18:08:52.047Z
@uhoh : I don't understand the mechanism by which two black holes can fall towards one another, so I have some concerns about the LIGO results, so my answer might be more _maybe_ than _probably_. So I'm going to poass on that one I'm afraid.
John Duffield
CC BY-SA 4.0
2019-03-24T18:08:43.803Z
2019-03-24T18:08:43.803Z
John Duffield
<p>The other point to raise, is the expected frequency of the gravitational waves you detect varies between Lisa and pulsar timing systems. This then alters the types of systems you will detect. Pulsar timing arrays should find massive black hole mergers, while Lisa should find; stellar mass black holes years before they merge, white dwarf binaries in the galaxy (also not merging), as well as intermediate mass black holes (merging). So the different detectors have different uses, even if one could be made more accurate than the other.</p>

CC BY-SA 4.0
2019-03-25T08:43:18.567Z
The point would be to explain why the frequency ranges differ.
ProfRob
CC BY-SA 4.0
2019-03-25T07:55:21.797Z
2019-03-25T07:55:21.797Z
Rob
<p>Suppose that we collected photons from a distant star, and they arrive regularly at 15 photons every microsecond onto a CCD, when a gravity wave bends space time, wouldn't the regular 15 photons graph wobble as a result of the gravitational wave?</p>

<p>Why does the LISA observatory have to compare laser timings, if pulsars can be as precise as atomic clocks, can't it just compare a bunch of pulsar signals? A single satellite that records 50 pulsars would move compared the the pulsars and would have a frequency of 50Hz ticks with pulses which can be graphed at kHz frequencies.</p>

CC BY-SA 4.0
2019-03-23T07:12:36.257Z
I could see two potential issues: precision of satellite orbits (it’s difficult to keep an exact orbit since earths gravity is not perfectly symmetric) and precision of measuring pulsars (interference in laser beams is easier to measure than changes in pulsar rates from 100hz to 100,00000001hz)
tuomas
CC BY-SA 4.0
2019-03-23T07:23:27.553Z
Yes, there is also the option of binary and variable stars, because their light can be sampled by a CCD to a precise graph at 10kHz and higher, so if there were multiple graphs at that precision coming from different directions in space, a gravity wave would cause the graphs to vary in time.
bandybabboon
CC BY-SA 4.0
2019-03-23T09:19:03.457Z
Probably didn't research the field enough, there is research from Arxiv about Pulsar Timing Arrays to find GW's.
bandybabboon
CC BY-SA 4.0
2019-03-23T09:20:05.577Z
Interesting indeed. Mind to share the article(s)?
tuomas
CC BY-SA 4.0
2019-03-23T09:26:58.097Z
https://arxiv.org/abs/1004.3602
bandybabboon
CC BY-SA 4.0
2019-03-23T19:16:48.307Z
The PDF file is here. https://arxiv.org/pdf/1004.3602.pdf I don't even understand why they want to use lasers in space, because radio waves travel at the same speed and can transmit better clock signals.
bandybabboon
CC BY-SA 4.0
2021-03-07T23:56:23.777Z
"if pulsars can be as precise as atomic clocks" It's because they aren't, not at averaging times below months at any rate.
alessandro
CC BY-SA 4.0
2021-03-08T03:07:37.290Z
Some researchers are studying pulsars to measure gravity waves: https://physicsworld.com/a/pulsar-timekeepers-measure-up-to-atomic-clocks/
bandybabboon
<astrophysics><gravitational-waves><pulsar><photons><lisa>
Can't pulsars and stars be used for gravitational wave measurement?
bandybabboon
# Can't pulsars and stars be used for gravitational wave measurement?

(Asked by: username_0 on 2019-03-23)

Suppose that we collected photons from a distant star, and they arrive regularly at 15 photons every microsecond onto a CCD, when a gravity wave bends space time, wouldn't the regular 15 photons graph wobble as a result of the gravitational wave?

Why does the LISA observatory have to compare laser timings, if pulsars can be as precise as atomic clocks, can't it just compare a bunch of pulsar signals? A single satellite that records 50 pulsars would move compared the the pulsars and would have a frequency of 50Hz ticks with pulses which can be graphed at kHz frequencies.

**Tags:** astrophysics, gravitational-waves, pulsar, photons, lisa

> **Comments:**
> **username_1**: I could see two potential issues: precision of satellite orbits (it’s difficult to keep an exact orbit since earths gravity is not perfectly symmetric) and precision of measuring pulsars (interference in laser beams is easier to measure than changes in pulsar rates from 100hz to 100,00000001hz)  
> **username_0**: Yes, there is also the option of binary and variable stars, because their light can be sampled by a CCD to a precise graph at 10kHz and higher, so if there were multiple graphs at that precision coming from different directions in space, a gravity wave would cause the graphs to vary in time.  
> **username_0**: Probably didn't research the field enough, there is research from Arxiv about Pulsar Timing Arrays to find GW's.  
> **username_1**: Interesting indeed. Mind to share the article(s)?  
> **username_0**: https://arxiv.org/abs/1004.3602  
> **username_0**: The PDF file is here. https://arxiv.org/pdf/1004.3602.pdf I don't even understand why they want to use lasers in space, because radio waves travel at the same speed and can transmit better clock signals.  
> **username_2**: "if pulsars can be as precise as atomic clocks" It's because they aren't, not at averaging times below months at any rate.  
> **username_0**: Some researchers are studying pulsars to measure gravity waves: https://physicsworld.com/a/pulsar-timekeepers-measure-up-to-atomic-clocks/  

---

## 3 answers

### Answer by username_3 on 2019-03-24. Score: 5

**How LIGO, LISA, etc. Detect Gravitational Waves**

The point of instruments like LIGO and LISA is to measure time-varying changes in the distance within different arms of the instrument. In the case of an arm oriented in the direction of an incoming gravitational wave (GW), the length of the arm will increase and decrease, while an arm oriented perpendicular will remain unchanged.

The [method for measuring this](https://en.wikipedia.org/wiki/LIGO#Operation) is to split a laser beam, send each half down the different arms, and then recombine them and look at the interference pattern. If the arms have identical lengths, then the beams will destructively interfere. If, however, one of the arms becomes longer (or shorter), the recombined beams will be out of phase, and you will no longer have perfect destructive interference.

The key to being able to measure this sort of thing accurately is two things:

1. Arm length, so the beam traveling down the altered-length path has time
   to accumulate a large enough phase shift for the interference pattern to
   change enough to be measured. Longer arms lead to larger phase shifts,
   which is why LISA aims to have arms that are 2.5 million km in length.
2. The wavelength of the light: the shorter the wavelength, the smaller the
   actual shift in arm length needs to be to make the beam shift appreciably
   in phase. If the recombined beams differ in phase by 0.001%, then the change
   in the interference pattern will be very hard to detect and measure. But if they differ
   in phase by 50%, then the difference will be obvious. Shorter wavelengths
   make for larger phase shifts.

If you want think of the interferometric measurement as a kind of timing measurement (that is, we are, in a sense, measuring the difference in time it takes light to travel down the two arms), then *optical light is vastly better than radio for "timing" measurements*.

**Pulsar Timing**

As you pointed out, there *are* projects that use pulsars to try to detect gravitational waves (e.g., [pulsar timing arrays](https://en.wikipedia.org/wiki/Pulsar_timing_array)).

These work by measuring time delays in the arrival of radio pulses from millisecond pulsars. However, it's important to note the limitations: in order to measure the arrival time accurately, you have to observe a pulsar over a period of several minutes (or more) and *add up* all the pulse arrivals to get a single, accurate value. (You are *not* measuring changes between the arrival of one single pulse and the next.) You then repeat this measurement several weeks or months later to get another arrival time. Since you're taking measurements weeks or months apart, you can only detect variations on that same time scale, which is why pulsar timing arrays are hoping to detect GWs with periods of months to years (e.g., from binary supermassive black holes). The kinds of GWs that LIGO detects -- with periods of *fractions of a second* -- are completely beyond what pulsar timing arrays can do.

We cannot use optical light from stars, because we know of no star that produces the exquisitely regular periodicity of a millisecond pulsar.

As a final comment, your scenario of photons that "arrive regularly at 15 photons every microsecond onto a CCD" has the problem that Poisson noise (a.k.a. ["shot noise"](https://en.wikipedia.org/wiki/Shot_noise)) means that you *wouldn't* actually get 15 photons every microsecond; you'd get *around* 15 every microsecond (a typical sequence might look like this: 16, 15, 18, 15, 14, 14, 15, 23, 16, 12, ...). With that much variation, it's really hard to detect subtle variations in intrinsic signal strength.

> **Comments:**
> **username_4**: I've just asked [Would an X-ray-based pulsar timing array in orbit or on the Moon to study GW background be effective?](https://astronomy.stackexchange.com/q/30110/7982)  
> **username_5**: "The kinds of GWs that LIGO detects -- with periods of fractions of a second -- are completely beyond what pulsar timing arrays can do." The comparison is with LISA. Periods of $10^2$ to $10^{5}$ seconds, so measurements on few minute timescales would seem ok. I don't think this adequately answers the question. You need to explain why the frequency response of a PTA decreases with increasing frequency. It isn't "shot noise", because shot noise has a flat frequency spectrum.  

---

### Answer by username_6 on 2019-03-24. Score: 1

> Can't pulsars and stars be used for gravitational wave measurement?

In theory, yes. See the 2017 NASA article [Listening for Gravitational Waves Using Pulsars](https://www.nasa.gov/feature/jpl/listening-for-gravitational-waves-using-pulsars).

> Suppose that we collected photons from a distant star, and they arrive regularly at 15 photons every microsecond onto a CCD, when a gravity wave bends space time, wouldn't the regular 15 photons graph wobble as a result of the gravitational wave?

Kind of. When the gravitational wave is passing by, we'll be subject to a slight time dilation. So it would look as if the pulsar had speeded up.

> Why does the LISA observatory have to compare laser timings, if pulsars can be as precise as atomic clocks, can't it just compare a bunch of pulsar signals? A single satellite that records 50 pulsars would move compared the pulsars and would have a frequency of 50Hz ticks with pulses which can be graphed at kHz frequencies.

Sorry, I don't know the answer to that. But see the [Wikipedia article](https://en.wikipedia.org/wiki/Laser_Interferometer_Space_Antenna) on LISA and note that it's scheduled for the 2030s. A lot can happen between now and then. Maybe it won't go ahead.

> **Comments:**
> **username_4**: I've just asked [Would an X-ray-based pulsar timing array in orbit or on the Moon to study GW background be effective?](https://astronomy.stackexchange.com/q/30110/7982)  
> **username_6**: @username_4 : noted. I'm afraid I have difficulty giving a useful answer to that one. I'd be saying "probably" or "maybe".  
> **username_4**: I think that those types of answers are well received if they are based on citable facts, e.g. "seems likely considering", "plausible based on"  
> **username_6**: @username_4 : I don't understand the mechanism by which two black holes can fall towards one another, so I have some concerns about the LIGO results, so my answer might be more _maybe_ than _probably_. So I'm going to poass on that one I'm afraid.  

---

### Answer by username_7 on 2019-03-25. Score: 0

The other point to raise, is the expected frequency of the gravitational waves you detect varies between Lisa and pulsar timing systems. This then alters the types of systems you will detect. Pulsar timing arrays should find massive black hole mergers, while Lisa should find; stellar mass black holes years before they merge, white dwarf binaries in the galaxy (also not merging), as well as intermediate mass black holes (merging). So the different detectors have different uses, even if one could be made more accurate than the other.

> **Comments:**
> **username_5**: The point would be to explain why the frequency ranges differ.  

---

