Noise in Maps of the Solar at Radio Wavelengths by T. S. Bastian et al. – Group of European Photo voltaic Radio Astronomers

The Solar is a robust supply of radio emissions, a lot in order that – in contrast to most celestial sources – this emission dominates the system noise of many radio telescopes. The noise ensuing from such sources is known as “self-noise”. Two latest papers focus on self-noise in maps of the Solar at radio frequencies shaped utilizing the methods of Fourier synthesis imaging. Examples of radio telescopes that exploit this system embody the LOw Frequency ARray (LOFAR), the Jansky Very giant Array (JVLA), the Nançay Radiohelio- graph, and the Expanded Owens Valley Photo voltaic Array (EOVSA). They present that self-noise represents a basic restrict to the dynamic vary with which sturdy supply sources could also be imaged.

Determine 1: Comparability of mannequin sources noticed by EOVSA, the JVLA, and the proposed ngVLA at a nominal frequency of 6 GHz. In every panel the dashed blue line represents $mathcal{I}_D$, the strong blue line is $|mathcal{I}_D+S/sqrt{2n_b}|$, the dashed pink line represents the noise ground, and the inexperienced symbols hint $sigma_n$. High row: the map and map rms noticed for a degree supply with $S = 1$; Second row: the identical for a degree supply with a flux density $S_{rm pt} = 0.2$ and a complete flux $S_{rm pt} +S_{rm bg} = 1$; Third row: The identical for a Gaussian supply with $theta_G = 30″$ and a complete flux $S = 1$. In all instances $N=0$. Be aware the variations in scale for the ordinate.

Paper I develops an intuitive concept of self-noise utilizing the limiting instances of sturdy level sources or sturdy prolonged sources as noticed by a single dish, a two-element interferometer, and the final case of an $n$-element array of arbitrary antenna measurement. Employees typically characterize system noise by way of system temperature $T_{rm sys}$ or the supply equal flux density $N=T_{rm sys}/Okay$ the place $Okay=A_e/2k_B$; $A_e$ is the efficient space of the antenna and $k_B$ is Boltzmann’s fixed. It’s handy to match the supply flux density $S$ with $N$, the place $S$ is said to the antenna temperature $T_{ant}$ by means of $S=T_{rm ant}/Okay$. When $S<>N$, nonetheless, the supply dominates the system noise and manifests itself in doubtlessly advanced methods. Paper I distinguishes between two arrays which are known as a “correlation array” and a “complete energy array”. The previous is the standard strategy to Fourier synthesis imaging within the sense that auto-correlations (complete energy) measurements are discarded. The noise variance solely consists of correlations between visibility measurements. Within the latter, complete energy measurements are retained and, when computing the noise variance, correlations between complete energy measurements between antennas are retained, as are correlations between complete energy measurements and visibilities.

Within the former case, the noise variance has been derived for the final case of $n$ antennas and sources of arbitrary power by Kulkarni (1989) for snapshot integrations (i.e., for a time wherein modifications to the array geometry and the supply are negligible). As $n$ turns into giant the rms noise is given roughly by

$sigma_I(theta_x,theta_y)approx frac{1}{M} Bigl[ mathcal{I}_D(theta_x,theta_y)+frac{S+N}{sqrt{2n_b}} Bigr].$

the place $n_b=n(n-1)/2$ is the variety of antenna baselines within the array and $M=sqrt{Deltanutau}$; $Deltanu$ is the observing bandwidth and $tau$ is the combination time. Be aware that distribution of supply flux is mirrored in $sigma_I$! The noise is due to this fact nonuniform throughout the map. It is usually vital to notice {that a} uniform noise ground is all the time current: $(S+N}/{sqrt{2n_b}approx S/nM$. Lastly, notice that the noise is impartial of antenna space $A_e$. The on-source noise is given by the total expression and the off-source noise is given by the second time period, assuming the sidelobe response of the supply has been roughly eliminated by means of deconvolution, a situation that can’t essentially be met for small-$n$ arrays.

Within the case of a complete energy array, the noise is as a substitute given by the precise expression:

$sigma_I (theta_x,theta_y)=frac{1}{M} Bigl[mathcal{I}^circ_D(theta_x,theta_y)+frac{N} {n}Bigr].$

the place $[mathcal{I}^circ_D]$ is the map shaped from visibility information and complete energy. We see that on this case, the noise ground is simply $sigma_I=N/nM$. The self-noise on places inside the map which are freed from emission may be totally eliminated by means of deconvolution and the formal dynamic vary may be very excessive.

In observe, most giant, trendy Fourier synthesis radio telescopes are correlation arrays designed to deal with a broad program of astrophysics for which the supply doesn’t dominate the system noise ($S<>N$ that such measurements could also be of curiosity.

Paper II considers the implications of self-noise for various photo voltaic science “use instances”. These embody observations of the quiet (non-flaring) Solar, lively areas, small transients, radio bursts, and flares. Since all extant radio arrays are correlation arrays, the primary expression above is related. Expressing the noise by way of brightness temperature sensitivity $sigma_T$ we recast the equation by way of brightness temperature $T_b$, $T_{rm ant}$ and $T_{rm sys}$ and discover that

$sigma_T(theta_x,theta_y)approx frac{1}{M}$ $Bigl[T_b(theta_x,theta_y)+frac{T_{rm ant}+T_{rm sys}}{sqrt{2n_b}} frac{lambda^2}{A_e}frac{1}{Omega_{rm bm}}Bigr]nonumber$ $approxfrac{1}{M}$ $Bigl[T_b(theta_x,theta_y)+frac{T_{rm ant}+T_{rm sys}}{(nA_e/d^2)} Bigr]$

the place $Omega_{rm bm}approx (lambda/d)^2$ is the angular decision of the array,  $lambda^2/A_e$ is the sector of view of the instrument, and $d$ is dimension of the array (e.g., its diameter for a array with a round footprint). One can consider $nA_e/d^2$ as an array filling issue.

There are a selection of subtleties that come into play when contemplating numerous use instances. For instance, photo voltaic radio bursts and flares require snapshot imaging and the on-source dynamic vary is all the time $lesssim{M}$. Within the case of quiet Solar imaging, the noise is well-approximated by a uniform noise ground. On this case it might be attainable to take advantage of Earth rotation aperture synthesis and/or multi-frequency synthesis.

Conclusions

Self-noise represents a basic restrict to the sensitivity of Fourier synthesis arrays when the supply flux density $S$ is way bigger than the system noise $N$. We discover that it’s all the time related to photo voltaic observations though the main points depend upon the science use case in query.

Particulars could also be present in Paper I, which outlines theoretical concerns, and in Paper II, which discusses quite a lot of photo voltaic use instances. The corresponding arXiv reprints could also be discovered right here and right here.

References

Bastian, T. S., Chen, B., Mondal, S., & Saint-Hilaire, P., 2025a, SoPh, 300, concern 7, id. 91, doi: 10.1007/s11207-025-02499-9

Bastian, T. S., Chen, B., Mondal, S., & Saint-Hilaire, P., 2025b, SoPh, 300, concern 7, id. 90, doi: 10.1007/s11207-025-02498-w

Kulkarni, S., 1989, AJ, 98, 1112, doi: 10.1086/115202