# High-Resolution Radio Observations of Five Optically Selected Type 2 [PERSON]
## 5 Discussion
### Revised Radio Spectral Indices  
Based on the newly-obtained flux density data, we reexamined the radio continuum spectral properties of the target LLAGN sources. Figure 2 shows their radio spectra between 1.4 and 8.4 GHz. For recalculating the spectral indices, we used the FIRST 1.4-GHz [31] and the VLASS 2.7-GHz flux densities (Table 2), both based on VLA measurements. The resulting \(\alpha_{1.4}^{2.7}\) values are given in Table 2 and Figure 2. We excluded from the spectral fit the 8.4-GHz VLA values reported by [PERSON] [11] since those appear in most cases an order of magnitude higher than expected from the trend based on lower-frequency data. We did not include the VLBI flux density values either, because the EVN provides about three orders of magnitude higher resolution than the VLA, thus probing radio emission on a much smaller spatial scale, detecting mas-scale compact emission only. Moreover, four out of five sources are undetected at 5 GHz with the EVN, leading to flux density upper limit estimates only. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multicolumn{3}{c}{**Right Ascension**} & \multicolumn{3}{c}{**Declination**} & \multirow{2}{*}{\(\mathbf{\Delta_{radio-opt}}\)} \\  & **h** & **min** & **s** & \(\circ\) & \(\prime\) & \(\prime\prime\) & **mas** \\ \hline SDSS J0741\(+\)3020 & 07 & 41 & 30.518 & \(+\)30 & 20 & 05.245 & 98 \\ SDSS J0956\(+\)5735 & 09 & 56 & 29.046 & \(+\)57 & 35 & 08.751 & 186 \\ SDSS J1014\(+\)0244 & 10 & 14 & 03.513 & \(+\)02 & 44 & 16.265 & 310 \\ SDSS J1447\(+\)0211 & 14 & 47 & 11.283 & \(+\)02 & 11 & 36.389 & 203 \\ \hline \end{tabular}
\end{table} 
Table 3: Tentative VLBI positions of the sources marginally detected with the EVN at 1.7 GHz, and the radio-optical positional offsets. Figure 2: The continuum radio spectra of the sources between 1.4 and 5 GHz with flux density values and their associated uncertainties taken from Table 2 (black dots). For sources undetected with the EVN, flux density values at 5 GHz are shown as upper limits indicated by arrows. For SDSS J1026\(-\)0042 detected with the EVN, among the other 1.7 GHz VLBI flux densities, the values should in fact be considered as lower limits since any extended emission is resolved out on the long baselines. The green lines represent power-law spectra calculated from two VLA data points, FIRST at 1.4 GHz and VLASS at 2.7-GHz. The corresponding \(\alpha_{1.4}^{2.7}\) spectral index values are displayed in the top left corner of the panels. For comparison, the 8.4-GHz VLA flux densities taken from Lal & Ho [11] are also indicated with red symbols. In all cases, these are much higher than expected from the extrapolation of 1.4- and 2.7-GHz VLA values, indicating an issue with the values derived in [11]. Considering our \(\alpha_{1,4}^{2,7}\) spectral index values derived from VLA data (Table 2), the only source that has a flat radio spectrum is SDSS J1026\(-\)0042 (\(\alpha_{1,4}^{2,7}=-0.20\)). All others can be classified as steep-spectrum sources with spectral index below \(\approx-0.5\). Notably, this finding is perfectly consistent with the fact that the only flat-spectrum source, SDSS J1026\(-\)0042, shows a compact VLBI component, while the steep-spectrum ones are all almost completely resolved out with the EVN. However, the \(\alpha_{1,4}^{8,4}\) spectral indices (Table 1) determined by Lal & Ho [11] are markedly different, with opposite sign, all indicating inverted spectra (\(\alpha_{1,4}^{8,4}\) > 0.38). Higher flux densities at 8.4 GHz, as seen in Figure 2, could in principle be caused by extreme variability, because the measurements at different frequencies were not made simultaneously. However, it is remarkable that all five sources show highly elevated flux densities at 8.4 GHz, rendering the variability explanation very unlikely, even though selection at higher frequencies such as 8.4 GHz would be biased to flat-spectrum, more variable sources.