# How is distance to pulsars measured ?

AgentB
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I guess most pulsars are not visible, in the usual optical wavelengths.

Are the radio telescopes able to measure parallax angles with the same degree of accuracy as the current crop of optical telescopes?

Mike Hewson
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### How is distance to pulsars measured ?

For distance as a base estimate one has the dispersion of the signal. For a broadband signal ( ie. composed of many frequencies ) travelling through the interstellar medium there is a delay induced that is frequency dependent. Lower frequencies arrive later and higher frequencies earlier. You may be aware that this effect is factored into the searches at E@H.

Basically there are positive and negative charges ( plasma ) 'soaking' to various degrees the path between Earth and some source of interest. The positive charges are essentially protons and the negative charges are electrons ( ionised hydrogen if you like ). There is an effect from both but much less for the proton due to it's ~ 2000x greater mass than the electron. So one speaks of electron column density which represents the sum of all such photon/electron interactions along a very long cylinder b/w here and the pulsar. A photon's interaction with these electrons diminishes the more energetic the photon is, and hence higher frequency photons are less delayed.

So that regresses your question as to how this electron column density varies with actual distance to source. That would/could/does depend upon direction now. There will be more of this plasma in the centre bulk of the galaxy and less towards the edge. So the special question becomes : what is the direction to source from Earth's situation in the galaxy ? To my knowledge there are studies and methods orthogonal to the dispersion which enable a map to be formulated for the plasma density ( electrons per volume now ) across the galaxy. But there could be other information per instance like a clear association of a pulsar with an object or system for which the distance is well known/estimated on other grounds*.

Radio parallax is performed but the greater wavelength compared with optical light naturally prejudices the angular resolution ( all other things held constant ). As a very general rule for any photon collection system you may care to name, the angular discrimination** goes directly like wavelength and inversely with the diameter of the aperture of the 'bucket' used. Hence the design idea of , say, the Square Kilometer Array is to attempt to get ~ equivalent resolution to the optical telescopes by having continental dimensions for aperture. But there are also other arrangements to yield similiar benefits, relying crucially on very accurate timing and position information amongst the components. That way several devices can act as one.

Cheers, Mike.

* Globular clusters come to mind as a great scenario for this.

** Any depth perception measurement like parallax is directly dependent on angular discrimination. Heisenberg got into strife during his doctoral thesis defence because he could not derive an expression for the angular resolution of a microscope ! This from a man who subsequently re-based the topic entirely from a quantum viewpoint. For that matter he was unaware that with his approach to the correlation of findings before and after measurements, leading to his uncertainty principle, he had re-invented for himself the mathematical topic of matrices. In particular for a general matrix product AB is not the same result as BA. This had been known for ages but he re-derived the behaviours anyway. So there is hope for the rest of us .... :-)

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

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

AgentB
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### RE: For distance as a base

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For distance as a base estimate one has the dispersion of the signal. For a broadband signal ( ie. composed of many frequencies ) travelling through the interstellar medium there is a delay induced that is frequency dependent. Lower frequencies arrive later and higher frequencies earlier. You may be aware that this effect is factored into the searches at E@H.

Thanks Mike, I needed a few days to think about this. I did not know of that dispersion effect and that it needed to be be sought for, and sorted out.

I guess this same effect, electrons slowing down photons, which makes a prism split daylight?

If you had radio eyes, far pulses would be violet at the start and redder at the end of a pulse. Near pulses more green then yellow.

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... So the special question becomes : what is the direction to source from Earth's situation in the galaxy ? To my knowledge there are studies and methods orthogonal to the dispersion which enable a map to be formulated for the plasma density ( electrons per volume now ) across the galaxy.

I had to think a bit about what orthogonal meant. Hope you are saying we have 3D maps of plasma density for galaxy, so you can work what the number of interactions should be to get the dispersion you find.

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As a very general rule for any photon collection system you may care to name, the angular discrimination** goes directly like wavelength and inversely with the diameter of the aperture of the 'bucket' used.

So that is quite a few orders of magnitude, Arecibo has a 300m dish, but optical wavelengths is about a million times smaller roughly.

So I guess this means my 3mm eyes unaided are better at angular discrimination?!

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* Globular clusters come to mind as a great scenario for this.

Is that because there is a lot of stuff near the pulsar, so likely to see some optical evidence, or something else?

Every day at E@H a school day.

Odysseus
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### RE: I guess this same

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I guess this same effect, electrons slowing down photons, which makes a prism split daylight?

If you had radio eyes, far pulses would be violet at the start and redder at the end of a pulse. Near pulses more green then yellow.

Yes; in radio the phenomenon is often referred to as â€œchirpingâ€.

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* Globular clusters come to mind as a great scenario for this.

Is that because there is a lot of stuff near the pulsar, so likely to see some optical evidence, or something else?

I believe that itâ€™s because all the stars in a given globular are at about the same distance, so if it includes any cepheids or other members whose distance can be measured, e.g. from the difference between their absolute and apparent magnitudes, the results apply equally to all the rest.

Mike Hewson
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### RE: Thanks Mike, I needed a

Quote:

Thanks Mike, I needed a few days to think about this. I did not know of that dispersion effect and that it needed to be be sought for, and sorted out.

I guess this same effect, electrons slowing down photons, which makes a prism split daylight?

If you had radio eyes, far pulses would be violet at the start and redder at the end of a pulse. Near pulses more green then yellow.

The basic mechanism is electrons and photons mugging each other, as it were, for energy. A chap called Compton worked out what happens when a photon and an electron come across each other in the absence of other effects. So what is relevant here ( for the dispersion being looked at here ) is not the description of electrons bound to nuclei of atoms then being hit by photons. We're talking out and about in 'free space' with just two players. This is of course a quantum mechanical discussion in detail, but to a good approximation one can analyse it rather like billiard ball encounters. What could be your outcomes here when an electron and a photon come by each other ?

- they continue on each unaffected by the other.

- they exchange some of both energy and momentum, thus possibly altering direction and/or speed.

Now as a generality which way this goes depends on what they had before they met. The more energetic particle typically transfers some to the lesser one. So the lesser energetic particle 'mugs' the other.

The Compton Effect label ( also called Compton Scattering ) is reserved for the case where the more energetic photon hits a dawdling electron, which in turn leaves with more energy/momentum. Now the greater excess energy the photon has, for a given electron initial state, the less energy ( fractionally ) that it will lose. However all photons traversing the plasma will be robbed of energy, but the higher frequency/energy ones are less scattered. Scattering implies deflection from straight line travel, thus a scattered photon is delayed compared to a counterpart that wasn't.

There is Inverse Compton Effect/Scattering where the energy transfer goes the other way ie. more energetic electrons getting mugged by the photon. It doesn't have to be an electron, some other charged particle will do. This would happen, say, if a cosmic ray ( extremely high power proton ) gets 'touched' by the very low energy photons that bathe the universe ( cosmic microwave background ). In addition neither particle is truly free. There is at least galactic magnetic fields, so one phrase used is 'quasi-free'.

Be aware though that the word 'dispersion' means many things/mechanisms under many situations. The idea is of spreading of frequencies/wavelengths. Yes, prisms etc do that but now you are talking of electrons modeled not as free agents. There is some context/forces under which they oscillate and that gives rise to all manner of optical stuff.

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I had to think a bit about what orthogonal meant. Hope you are saying we have 3D maps of plasma density for galaxy, so you can work what the number of interactions should be to get the dispersion you find.

Sorry. I meant orthogonal as in 'by independent means'. So yes a free electron density map of the galaxy, if good enough ( ongoing research here ), allows one to begin with a dispersion modulus as recorded for a given direction from Earth and turn that into a distance away from Earth along that line.

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As a very general rule for any photon collection system you may care to name, the angular discrimination** goes directly like wavelength and inversely with the diameter of the aperture of the 'bucket' used.

So that is quite a few orders of magnitude, Arecibo has a 300m dish, but optical wavelengths is about a million times smaller roughly.

So I guess this means my 3mm eyes unaided are better at angular discrimination?!

That's the idea indeed. I use the phrase 'angular discrimination' here in the sense of : what is the smallest angle two sources can be separated by and still be marked as distinct ? There are nuances here though, because two point-like sources if close enough look as one ellipsoidal source.

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* Globular clusters come to mind as a great scenario for this.

Is that because there is a lot of stuff near the pulsar, so likely to see some optical evidence, or something else?

This is more or less what is meant by a globular cluster :

Richard Feynman once commented upon a photo similar to this by saying : "if you look at this and can't see gravity acting, then you have no soul". By that it is meant that each white dot is a star ( system ) and they are all circling their mutual common centre. One can be more precise though. There is a proposition called The Virial Theorem ( not viral ) which when applied to this circumstance can predict the averages of measurable things like velocities and whatnot, again based on the assumption that they are an interacting group. Globular clusters are well described by this and so we have high confidence that these stars are not just fluke projections onto an image plane but all reside at more-or-less the same galactic address.

Naturally the next question will be : how do you know if pulsar X is part of the cluster, or in fact a fluke projection along that direction ? I can't help with that one.

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Every day at E@H a school day.

Same here. Always somethin' new to discover. :-)

Cheers, Mike.

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

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

Mike Hewson
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### RE: So I guess this means

Quote:
So I guess this means my 3mm eyes unaided are better at angular discrimination?!

You can generalise this line of thinking. Take any biological being. Find the greatest and least extents of a sense organ that it could have. Now you have lower and upper bounds for the wavelength of disturbance that it can discriminate for direction.

Obviously an upper bound on sense organ size would be some greatest span of it's body along some traversing line. The least bound on sense organ size would refer to, probably, cellular dimensions now. You could hypothecate a sense organ that could register almost any physical event - "ooh, I've been hit by a cosmic ray !" or "it's getting warmer in here" - but that's not the same as knowing the direction to source. For that you need a differential across a distance.

Cheers, Mike.

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

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

Odysseus
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### A bit of a tangent, not

A bit of a tangent, not applicable to wavelengthsâ€¦

Given a brain capable of correlating a sequence of inputs with kinÃ¦sthesia or other positional data, the resolution of some senses can be extended beyond that implied by the size of the organ. A couple of examples occur to me offhand: many animals (especially predators) will bob their heads to obtain or refine the distance to a target by means of parallax, and dogs will range back and forth to detect gradients in airborne scents so as to determine the general direction or motion of the source.

Mike Hewson
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### RE: A bit of a tangent, not

Quote:

A bit of a tangent, not applicable to wavelengthsâ€¦

Given a brain capable of correlating a sequence of inputs with kinÃ¦sthesia or other positional data, the resolution of some senses can be extended beyond that implied by the size of the organ. A couple of examples occur to me offhand: many animals (especially predators) will bob their heads to obtain or refine the distance to a target by means of parallax, and dogs will range back and forth to detect gradients in airborne scents so as to determine the general direction or motion of the source.

Absolutely. The platypus moves it's electrostatic field sampler ( it's bill ) side to side through river bed debris rather like a mine sweeper. The hammerhead shark likewise scans it's nose side to side as it swims. Sucking insects will follow a carbon dioxide concentration gradient to find you within your house, and once in your bedroom use an infrared receptor on it's forehead to locate you asleep. The same receptor then discriminates the heat in detail of the skin surface to deduce the line & location of superficial blood vessels for the best test tap. We have a wombat with regular habits coming past our bedroom window around 3am, I will hear him if I am awake. He hits every bloody object in his way along the small creek that goes by our house. A wombat would not recognise itself in a mirror but they have a brilliant olfactory system ( yet to be forensically exploited for airport luggage surveillance ), mooted to be superior to even the best sniffer dogs. Behavioural studies ( which are difficult to perform ) indicate the production of quite detailed chemical maps of the districts they live in, and that guides the night-time activities.

The list is long and distinguished. You don't have to have waves and frequencies etc, but you can certainly get about and about to produce survey maps of 3D scalar and vector fields. Or failing that have search algorithms that target acquire.

Cheers, Mike.

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

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

AgentB
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### RE: The list is long and

Quote:

The list is long and distinguished. You don't have to have waves and frequencies etc, but you can certainly get about and about to produce survey maps of 3D scalar and vector fields. Or failing that have search algorithms that target acquire.

Thanks Mike and Odysseus, only at E@H can we see applied the scientific method to get from pulsars, the densest of all matter to wombats, the densest or all marsupials!

Again a few days thinking about dispersion...you mentioned here is a delay induced that is frequency dependent.

Is that delay caused by the photons travelling further - as they have not travelled a straight(er) line? Or does the interaction itself also take time and so cause the delay when the photon and electron exchange pleasantries?

I was not clear if the frequency would change as a result of an interaction, i expected it should. So not only delayed, the frequency has changed ?

Mike Hewson
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### RE: RE: The list is long

Quote:
Quote:

The list is long and distinguished. You don't have to have waves and frequencies etc, but you can certainly get about and about to produce survey maps of 3D scalar and vector fields. Or failing that have search algorithms that target acquire.

Thanks Mike and Odysseus, only at E@H can we see applied the scientific method to get from pulsars, the densest of all matter to wombats, the densest or all marsupials!

Again a few days thinking about dispersion...you mentioned here is a delay induced that is frequency dependent.

Is that delay caused by the photons travelling further - as they have not travelled a straight(er) line? Or does the interaction itself also take time and so cause the delay when the photon and electron exchange pleasantries?

I was not clear if the frequency would change as a result of an interaction, i expected it should. So not only delayed, the frequency has changed ?

Well ..... strictly speaking it's the frequency dependence of group velocity and this is ultimately the quantum mechanical bit applying to large numbers of quanta. That is, how does the cold plasma ( containing ions but not with much energy ) change the refractive index of the medium compared to vacuum ? So I am havering somewhat as to whether you call that a particle or wave aspect. I have been a bit remiss in trying to approximate by presenting the classical cut-down version which has holes in it - that you have found ! The issue with QM is that you are summating possible histories of photons, and thus include those where the photon sails through unaffected mixed in with those where it is interrupted. The nett effect may be interpreted in a classical sense as a delay at a given frequency .....

ASIDE : There's a thing called the plasma frequency which is the 'natural mode' of oscillation of the plasma all on it's lonesome. If you try to fire in radio waves then the plasma will absorb that which is below the plasma frequency and allow passage if greater, with less retardation the higher the signal frequency. We are are dealing with pulsar signals in the MHz range with plasma frequencies in the KHz.

Cheers, Mike.

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

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal