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Space radio interferometers could have a baseline of millions of kilometers, but is there a point where a larger baseline doesn't improve the resolution anymore because the photons observed are distorted before they arrive? This question deals with technological limits of resolution. I'm instead asking about cosmic limitations due to for example interstellar and extragalactic gas which scatters light.

This paper about results from the RadioAstron space/Earth interferometer is well above my pay grade, but it seems to be about this problem. The executive summary says:

At longer baselines of up to 235,000 km, where no interferometric detection of the scattering disk would be expected, significant visibilities were observed with amplitudes scattered around a constant value. These detections result in a discovery of a substructure in the completely resolved scatter-broadened image of the pointlike source, PSR B0329+54. They fully attribute to properties of the interstellar medium.

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  • $\begingroup$ If such a limit exists, it should definitely depend on frequency. Radio photons are pretty different from gamma photons, for example. $\endgroup$ – Florin Andrei Jan 26 '15 at 18:58
  • $\begingroup$ @FlorinAndrei And higher frequencies are more vulnerable to distortion than low frequencies, right? But the paper I saw talked about radio. Or is scattering discrete like something of the Lyman-Alpha Forest kind? There's much talk about the optical distortions through Earth's atmosphere, but maybe there's "a cosmic atmosphere" too through long distances. $\endgroup$ – LocalFluff Jan 26 '15 at 19:25
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    $\begingroup$ I would expect them to simply respond differently to different factors, that's all. Something that stops X rays altogether (lead glass) allows lower frequency visible photons to pass through unharmed. $\endgroup$ – Florin Andrei Jan 26 '15 at 19:34
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    $\begingroup$ I'd suggest we still know very little about the interstellar/intergalactic media and so while the answer to your bald question would be "yes", we probably don't know what that limit is - eg, what if there were balls of WIMPs out there? $\endgroup$ – adrianmcmenamin Jan 31 '15 at 15:44
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Q: "Is there a cosmic, rather than technological, upper limit to what a telescope can resolve?

Space radio interferometers could have a baseline of millions of kilometers, but is there a point where a larger baseline doesn't improve the resolution anymore because the photons observed are distorted before they arrive?'

Deviation of the wavefront from a blackbody spectrum and the processes that create them is reasonably well understood, the phases of the incoming wavefronts can be measured to enhance the directionality and reduce the distortion. Correlation of the different frequencies allows detection of even small amounts of distortion.

See: "The evolution of CMB spectral distortions in the early Universe" (29 Sept 2011), by J. Chluba, R.A. Sunyaev and the Video: "Spectral distortions of the CMB and what we might learn about the early universe", by Jens Chluba, and "Science with CMB spectral distortions" (27 May 2014), by Jens Chluba.

The method is explained in the paper "Cosmic Microwave Background constraint on residual annihilations of relic particles" (9 Aug 2000), by McDonald, Scherrer, and Walker, page 2:

"In this paper we compute the energy injected into the CMB by annihilating particles as a function of their mass and annihilation rate (i.e., the product of cross section and abundance squared). We derive constraints on the particle properties by comparison with the observed limits on chemical potential ($\mu$) distortions, and Compton-$y$ distortions (§II). We compare these constraints to similar constraints obtained from the production of deuterium by photodissociation of primordial helium (§III.A), and from the diffuse photon background produced after recombination by extragalactic annihilations (§III.B), and annihilations in the Milky Way halo (§III.C).

II. DISTORTIONS OF THE CMB ENERGY SPECTRUM

We consider first the effect of annihilation products on the CMB energy spectrum. The distortion of the spectrum takes place in two steps: first the high energy annihilation products rapidly dissipate their energy into the background photons and electrons, and then the low energy background evolves more slowly in an effort to restore the Planck spectrum. The permanence of distortions produced after $z ≃ 10^6$ is simple to understand in the following way: A Planck spectrum with a given photon number density must have a specific energy density. For $z ≃ 10^6$, photon nonconserving processes (double Compton scattering and bremsstrahlung) are inefficient in the background plasma. Therefore, if energy is injected into the CMB but not the the correct number of photons, a Planck spectrum cannot be restored. We now discuss in more detail the form of the distortions pro- duced in different redshift intervals. ...'.

See: "New Technology Offers to Broaden Vision for Radio Astronomy". Even a tiny antenna is very capable, this tiny antenna can see in seven directions simultaneously:

19 Element Phased Array Feed [Click image to zoom]

Adaptive optics are used with some optical telescopes, no reason not to apply the same algorithm to VLBI.

"Adaptive Optics: ESO's Very Large Telescope sees four times first (laser) light" (07/11/2016):

"... even at the best optical sites on Earth such as the 2600 m summit of Cerro Paranal or the 4205 m summit of Mauna Kea in Hawaii, refractive-index variations in the atmosphere lead to a seeing-limited resolution of 0.4 arcsec in contrast to the theoretical diffraction-limited resolution of less than 0.02 arcsec for the 8.2 m VLT telescopes.

"PKS 1954-388: RadioAstron Detection on 80,000 km Baselines and Multiwavelength Observations" (5 May 2017), by Edwards, Kovalev, Ojha, An, Bignall, Et al.:

"1 INTRODUCTION

A major challenge in astronomy is the struggle to observe objects with an angular resolution sucient to probe the underlying physical mechanisms. The longer wavelengths of radio-astronomy initially made the quest for high angular resolution more difficult, but the relative ease of preserving phase information enabled the technique of Very Long Baseline Interferometry (VLBI). Intercontinental VLBI routinely achieves milliarcsecond-scale angular resolutions, and extending the baselines between telescopes into space, with satellitebased telescopes, currently yields the highest angular resolution achieved in astronomy.".

There's a newer paper than the one you linked to, using a longer baseline, with better results. See: "PSR B0329+54: Substructure in the scatter-broadened image discovered with RadioAstron on baselines up to 330,000 km" (13 Sept 2016), by Popov, Bartel, Gwinn, Johnson, Andrianov, Fadeev, Et al., the conclusion on page 8:

"7 SUMMARY AND CONCLUSIONS

Here we summarize our observations and results and give our conclusions.

(i) We made VLBI observations of PSR B0329+54 with RadioAstron at 324 MHz on projected baselines up to 330,000 km or 350 M$\lambda$. Our goal was to investigate scattering properties of the ISM which affect radio observations of all celestial sources. While the results of such observations are in general influenced by the convolution of source structure with the scattering processes, pulsars are virtually point-like sources and signatures in the observational results can be directly related to the ISM scattering properties.

(ii) Visibility function at short ground-ground baselines manifests a single bright spike in delay-rate space that vanishes on long space-ground baselines. Thus, the scattering disk of PSR B0329+54 was completely resolved on ground-space baselines of 15,000 to 30,000 km. The FWHM of the angular diameter is 4.8 ± 0.8 mas at 324 Hz.

(iii) The diffractive length scale or size of the diffraction spot near Earth is 17, 000 ± 3, 000 km.

(iv) With the assumption of turbulent and large-scale irregularities in the plasma, the effective scattering screen is located at d/D = 0.6 ± 0.1 or somewhat more than half of the distance from Earth to the pulsar.

(v) At longer projected baselines, up to 330,000 km, significant visibility amplitudes were detected, although none were expected from the scattering disk. They are scattered around a mean which stays approximately constant up to the longest baselines. This result indicates that substructure was discovered in the scatter-broadened image of PSR B0329+54.".

Your last question:

Q: "I'm instead asking about cosmic limitations due to for example interstellar and extragalactic gas which scatters light."

Because you are looking at so many frequencies from so many angles for an extended period of time it's possible to use a supercomputer to see through (around) atoms, fog, dust.

Here are some layperson's explanations:

Ted Talks video: "See invisible motion, hear silent sounds"

CNN YouTube: "New technology makes troops invisible"

Ascendent Technology YouTube "Thermal Infrared & Visible CCTV PTZ Camera Fire Monitoring & Detecting See Through Smoke & Haze"

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