The Faint Images of the Radio Sky at Twenty-cm (FIRST) is presently the most sensitive large-area (\(\gg 1 square degree\))survey at radio wavelengths \cite{Becker_1995}. It is a radio snapshot survey performed at the NRAO Very Large Array (VLA) facility. FIRST covers approximately \({10 000 square degree}\) with a resolution of approximately 5 arcseconds. Coverage is shown in Figure 6 and Figure 7. FIRST produces 3-minute snapshots covering a hexagonal grid of the sky, using \(2 \times 7\) 3-MHz frequency channels centered at 1365 and 1435 MHz The survey catalogue contains around one million sources, and it is estimated that nearly \(15\%\) of these sources have optical counterparts. The FIRST survey area has been selected to correspond with that of the SDSS (Sky Survey). FIRST provides a database that is uniform in angular resolution and flux density sensitivity and it offers the opportunity to produce the largest unbiased survey for statistical analysis. FIRST’s design enables the search for radio variability of sources on timescales of minutes to years \cite{Thyagarajan_2011}.
The radio band is approximately five decades in wavelength - tens of meters to millimeters. This is too wide to be covered effectively by a single telescope & / receiver. The specific intensity and angular sizes of radio sources span an even wider range than the radio band a combination of single telescopes & /receivers and interferometers who simultaneously achieve a high angular resolution, large field-of-view while keeping in practical design limitations. The basic interferometer is a pair of radio telescopes whose voltage output are correlated (multiplied and averaged). The larger the collecting area of an ideal radio telescope - for a given system temperature, the more it can detect faint radio sources. The sensitivity of the telescope area is given by:
\(\sigma = \frac{2k_{B} T_{sys}}{A_{e} \times ( {(\Deltaν_{RF} \times \tau)}^{\frac{1}{2}}) }\)
Where \(T_{sys}\) is the temperature of the interferometer system, \(\Deltaν_{RF}\) is the receiver radio-frequency bandwidth, \(\tau\) is the total integration.
The collecting area of circular parabolic radio telescopes is reduced to an effective area because the receiver is on the reflector axis, and together with its supporting legs, the receiver partially blocks the path of radiation falling onto the reflector. The angular resolution of a diffraction-limited telescope is given by \(\theta \approx \frac{\lambda}{D}\) radians (where D is the diameter of the radio telescope dish and \(\lambda\) is the wavelength of light). Large diameters are required to obtain sub-arc second resolution at radio wavelengths. For example, for 1 arcsecond resolution at 16 Hz need 50 km diameter.
FIRST’s high angular resolution and faint flux density threshold (the rms is 0.15 mJy) come at a price. Some of the flux from extended sources is resolved out. This leads to a systematic underestimation of extended source flux density and a survey threshold that is a function of source size
Moreover, the higher angular resolution achieved by a more extended antenna configuration comes at a price of lower brightness temperature sensitivity. Brightness temperature (\(T_{b}\)) is a measure of the source brightness (or specific intensity - referring to frequency) irrespective of the radiation mechanism.
specific intensity: \(I_{v} = \frac{dE}{dAd \Omega dt dv}\) W.\(m^{-2}\).\(sr^{-1}\).\(Hz^{-1}\)
\(T_{b}\) can also be thought of as the temperature of a black-body which radiates at the same specific intensity as an object at some given frequency.
\(I_{v} = B_{v}(T_{b})\)
Where \(B_{v}(T)\) is the Planck distribution brightness. The associated sensitivity is then proportional to the ratio of the system sensitivity and the solid angle subtended by the receiver’s diffraction pattern.
Given that the sensitivity limit of FIRST and our knowledge of radio source populations, we know this survey is dominated by the FR-I and FR-II sources described earlier. That is, radio jets that results from collimated electrons spiraling around magnetic field lines at relativistic speeds following acceleration by a centered SMBH.