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Suppose we have some radio astronomy data for some specific moment (not a time series). Can we, using some computer program, filter out and get, say, only the data (EM radiation), whose sources are at a specific distance (e.g., 1 light year or 10 light years, etc)? I hope I put it more or less clearly. Sorry if the question is stupid:-). Thanks in advance!

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While @planetmaker has given the "simple answer"

The simple answer is: not without further knowledge as you have 2D data (the image) and want to derive 3D data (the objects and their coordinates).

which can't be argued with, I will anyway because things aren't always simple.

The question asks:

Suppose we have some radio astronomy data for some specific moment... (c)an we, using some computer program, filter out and get, say, only the data... whose sources are at a specific distance?

cosmic redshift and corresponding distances are inferred from "snapshots" of spectra all the time!

For large distances, due to metric expansion of the universe there is a shift in wavelength between what's radiated by a distant object and what's recorded by the observer. This shift is believed to be proportional to the distance, and referred to as Hubble's law. That constant of proportionality is also referred to as the Hubble constant. Now this is a hot topic in Astrophysics (are there any cold topics?) because determining the Hubble constant's value has some small disagreements. This disagreement is called "Hubble tension". But the number is roughly 70 (km/s)/Mpc meaning if an object has a red shift of say 1 part per thousand (the wavelength observered is 0.999 times the wavelength of that same spectral line measured in a lab on Earth or nearby star) then that's equivalent to a velocity of about 300 km/s (1/1000 the speed of light) and so one would estimate the distance to be ~4.3 Mpc (megaparsecs) or ~14,000,000 light years.

In reality (because nothing is simple) you have to be careful because objects also have their own real, individual velocities so conventional Doppler shift happens and there are other, smaller effects as well.

**But single snapshot of a spectrum from a spectrometer at a moment in time can certainly be used to infer a distance, so if you use a very narrow wavelength filter for a very common, strong spectral line, it will indeed produce a very rough "distance filter" for the objects that have strong emission of that line. Of course there will be a lot of noise from light NOT from that line, but it's a sort-of gedankeneperimental filter.

Fast radio burst dispersion

@jstarke's answer to Just how fast is a Fast Radio Burst thought to be? (see below) gives an excellent example of how the "chirp" of a fast radio bust (the high frequency components arrive first, the lower frequency components milliseconds or seconds later) can be folded back into a single pulse by undoing the dispersion of the waves due to free electrons in the super low density plasma of interstellar space.

See also:

According to Wikipedia's Fast Radio Bursts; Features are recorded they

The component frequencies of each burst are delayed by different amounts of time depending on the wavelength. This delay is described by a value referred to as a dispersion measure (DM). This results in a received signal that sweeps rapidly down in frequency, as longer wavelengths are delayed more.

Read more at Wikipedia's Dispersion_(optics); Pulsar emissions Unlike the Hubble constant where space is assumed to expand roughly uniformly everywhere (I said roughly) over large distances, the dispersion effect depends on the distance to the event and the average electron density along that path, or more simply said, the total integrated electron areal density along the path. You have to assume an average electron density before you can use the time difference between the "ping" at two different frequencies to infer a distance.

Astronomers do this all the time, they have established models for those electron densities, so they will regularly quote an inferred distance to an FRB (fast radio burst) event based on frequency.

So if you limit yourself to monitoring FRBs and your "moment in time" happens to be one second when an FRB happened, you can take that broadband radio measurement and apply a filter to it that lines up the various frequencies based on different dispersions from different total, integrated electron densities. The burst will become the narrowest, sharpest peak for the best integrated electron density, and that can be convered, using other models, to a distance.


From @jstarke's answer to Just how fast is a Fast Radio Burst thought to be?:

From Lorimer et al. (cited above):

Figure 2 from Lorimer et al. https://arxiv.org/abs/0709.4301

Figure 2: Frequency evolution and integrated pulse shape of the radio burst. The survey data, collected on 2001 August 24, are shown here as a two-dimensional ‘waterfall plot’ of intensity as a function of radio frequency versus time. The dispersion is clearly seen as a quadratic sweep across the frequency band, with broadening towards lower frequencies. From a measurement of the pulse delay across the receiver band using standard pulsar timing techniques, we determine the DM to be 375±1 cm−3 pc. The two white lines separated by 15 ms that bound the pulse show the expected behavior for the cold-plasma dispersion law assuming a DM of 375 cm−3 pc. The horizontal line at ∼ 1.34 GHz is an artifact in the data caused by a malfunctioning frequency channel. This plot is for one of the offset beams in which the digitizers were not saturated. By splitting the data into four frequency sub-bands we have measured both the half-power pulse width and flux density spectrum over the observing bandwidth. Accounting for pulse broadening due to known instrumental effects, we determine a frequency scaling relationship for the observed width W = 4.6 ms (f/1.4 GHz)−4.8±0.4 , where f is the observing frequency. A power-law fit to the mean flux densities obtained in each sub-band yields a spectral index of −4 ± 1. Inset: the total-power signal after a dispersive delay correction assuming a DM of 375 cm−3 pc and a reference frequency of 1.5165 GHz. The time axis on the inner figure also spans the range 0–500 ms.

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    $\begingroup$ A great answer; thanks for investing your time and effort! A big piece of knowledge to my knowledge base:-). $\endgroup$
    – avpol
    Sep 16, 2023 at 21:27
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Essentially you are asking "I do have an image. Can I tell which objects or pixels are in the foreground and which are in the background? At which distance is the object situated the light comes from?".

The simple answer is: not without further knowledge as you have 2D data (the image) and want to derive 3D data (the objects and their coordinates).

More complicated answers might involve a 'possibly' if you add knowledge about the type of objects, their typical sizes, maybe colour/wavelength and other knowledge which will give you distance information

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  • $\begingroup$ Very informative! I appreciate; thanks a lot! The data is scarce, and I will need more of them (of a different kind at that). $\endgroup$
    – avpol
    Sep 10, 2023 at 18:27

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