Korean VLBI Network Calibrator Survey (KVNCS). 1. Source Catalog of KVN Single-dish Flux Density Measurement in the K and Q Bands

We selected 2503 sources based on lower frequency VLBI flux density from VCS. Flux densities of 2045 of 2503 sources were simultaneously measured by single-dish observations in the K and Q bands using the KVN Yonsei and Ulsan radio telescopes from 2009 December to 2011 March. The observational information is summarized in Table 1. The cross-scan mode (cs-mode), a one-dimensional on-the-fly method, was used to obtain an accurate flux density measurement. A single cs-mode scan consists of two scans in azimuth (Az) and two in elevation (El). Each scan includes both forward and backward scans. We selected the parameters for the cs-mode considering the telescope beam size, timescales of the sky power variation, and the hardware and software limitations of the KVN system. The applied scan speed, the data sampling interval, and the scan length are mainly 65'' s⁻¹, 0.1 ms, and 13', respectively, which yield a 4 s (K band) and 2 s (Q band) full-beam cross time. We can remove sky power variation with timescales longer than the full-beam cross time by fitting off-source data. Assuming a Gaussian beam pattern, the on-source integration time of a cross scan are 8 and 4 s in the K and Q bands, respectively. The total on-source time for each source is considered based on the estimated source flux density and is calculated by multiplying by the number of scans. The main-beam sizes of the KVN telescopes are around 126'' and 63'' in the K and Q bands, respectively (see footnote 4). The mean beam sizes in the K and Q bands are quite consistent with the known sizes. However, the estimated beam sizes and pointing offsets have large errors for faint sources and under bad weather conditions or rapid sky variation (e.g., Fante 1975). We used them to eliminate low-quality data with 30% differences in beam size from the known ones and with the pointing offsets larger than 25'' arbitrarily. The standard deviations in the beam size and pointing offset data are 7% (K) and 20% (Q) and 4'' (K) and 4'' (Q) in Az and 10% (K) and 19% (Q) and 64 (K) and 60 (Q) in El, respectively. The observing frequencies were 21.7 GHz for the K band and 42.4 GHz for the Q band with a 512 MHz bandwidth. A measured root mean square (rms) error is an order of magnitude higher than the estimated thermal error. This is usual in practice. Hot/cold load calibration was performed in order to determine the antenna temperature scale from KVNCS1.0.1 to KVNCS1.2.1. For hot/cold load calibration, we used two microwave absorbers, one at room temperature of ∼292 K and the other immersed in liquid nitrogen of 80K, as hot and cold loads, respectively. For KVNCS1.2.2 we used the chopper-wheel method, which uses the sky as a cold load together with a microwave absorber at room temperature (Kutner & Ulich 1981; Mangum 2000). The results from these two calibration methods were consistent with each other to within ∼2% uncertainty. The system temperature and zenith optical depth of each observation are presented in Table 1. The sky opacity was corrected using the sky-dipping method based on observations every hour. The source 3C 286 was observed as a flux calibrator every 1.5 h to convert the measured antenna temperature into the flux. The flux densities of 3C 286 are 2.64 and 1.51 Jy in the K and Q bands, respectively. These were measured with a brightness model of Mars at the KVN Yonsei observatory (B.W. Sohn et al. 2017, in preparation).

We developed an analysis program for the KVN single-dish flux density measurements, and the following procedures were applied: (a) Extraction of bad scans due to the weather conditions or instrumental spuriousness, (b) linear baseline fitting to estimate the rms noise level and to eliminate sky level, (c) Gaussian fitting to measure the antenna temperature and to correct pointing offsets deviating from the Gaussian fitted center position using Equations (1) and (2) (Fuhrmann 2004).

$$\begin{eqnarray}&&{({T}_{a,\mathrm{Az}}^{* })}^{\prime }={T}_{a,\mathrm{Az}}^{* }\cdot \exp \left[4\mathrm{ln}2\displaystyle \frac{{x}_{\mathrm{El}}^{2}}{{\theta }_{\mathrm{El}}^{2}}\right]\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{({T}_{a,\mathrm{El}}^{* })}^{\prime }={T}_{a,\mathrm{El}}^{* }\cdot \exp \left[4\mathrm{ln}2\displaystyle \frac{{x}_{\mathrm{Az}}^{2}}{{\theta }_{\mathrm{Az}}^{2}}\right]\end{eqnarray} \tag{ 2 }$$

${T}_{a,\mathrm{Az}}^{* }$ and ${T}_{a,\mathrm{El}}^{* }$ are the measured antenna temperature corrected for atmospheric attenuation along the Az and El axes in the cs-mode, respectively. Furthermore, x_Az and x_El are pointing offsets, and θ_Az and θ_El are the half-power beam width in arcseconds. After the pointing correction, ${({T}_{a,\mathrm{Az}}^{* })}^{\prime }$ and ${({T}_{a,\mathrm{El}}^{* })}^{\prime }$ were averaged. (d) The error propagation of the antenna temperature was calculated using Equation (3).

$$\begin{eqnarray}&&{\sigma }_{{({T}_{a}^{* })}^{\prime }}={({T}_{a}^{* })}^{\prime }\sqrt{\left[\displaystyle \frac{{\sigma }_{{\rm{\Delta }}G}^{2}}{{\rm{\Delta }}{G}^{2}}+\displaystyle \frac{{\sigma }_{{T}_{a}^{* }}^{2}}{{({T}_{a}^{* })}^{2}}\right]}\end{eqnarray} \tag{ 3 }$$

${({T}_{a}^{* })}^{\prime }$ is the corrected and averaged ${T}_{a}^{* }$ for the pointing offset and in Az and El. ${\sigma }_{{T}_{a}^{* }}$ represents the uncertainty of ${T}_{a}^{* }$. ΔG is the temporal variation of the antenna gain, and its uncertainty is written as ${\sigma }_{{\rm{\Delta }}G}$. The gain curves of the KVN radio telescopes are very flat for elevations of 20°–80° in the K and Q bands. The gain variation along this elevations were 2.5% (K) and 2.0% (Q) at KYS and 1.5% (K) and 4.5% (Q) at KUS (see footnote 4). The elevation dependence of the gain variation was therefore ignored. ΔG was obtained by using the ratio of the mean ${({T}_{a}^{* })}^{\prime }$ to ${({T}_{a}^{* })}^{\prime }$ of 3C 286. However, the error was dominated by the thermal random noise. The flux density conversion factors were determined from the ratio of the flux densities to ${({T}_{a}^{* })}^{\prime }$ of 3C 286 in the K and Q bands (see Table 1), which were obtained using the NRAO Mars emission model (Butler et al. 2001). To check the results, we compared these conversion factors with those obtained for planets (Lee et al. 2011), which have ∼10% uncertainty, and found that they are consistent within 10% and 8% in the K and Q bands, respectively. Finally, the conversion factors obtained for 3C 286 were applied to estimate the source flux densities.

Of the 2043 sources, the flux densities of 1533 (75%) and 533 (27%) sources with 3σ noise levels of 66 (K band) and 108 (Q band) mJy were measured successfully. Their median flux densities were 397 and 588 mJy and the lowest flux densities were ∼70 and ∼120 mJy in the K and Q bands, respectively. Of these, the flux densities of 513 sources were simultaneously measured in the K and Q bands. The distribution of the measured flux densities are shown in Figure 2 and the measured flux densities are listed in Table 2.

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The luminosity distribution of 1138 sources as a function of redshift (z) are plotted in Figure 3. Archival redshifts were taken from NASA/IPAC Extragalactic Database (NED) and the Sloan Digital Sky Survey (SDSS) DR13. Only 23 sources were given as the photometric redshifts, and their mean uncertainties are about 0.618. These luminosities are calculated with H₀ = 73 km s⁻¹ Mpc⁻¹ and ${{\rm{\Omega }}}_{m}$ = 0.27 at 21.7 GHz,⁵ according to the arbitrarily spectral indices (α = −1.0 and 0.0, $S\sim {\nu }^{\alpha }$, where S is the flux and ν is the observed frequency). We denote spectra as steep ($\alpha \lt -0.5$ ), flat (−0.5 ≤ α ≤ 0.5), and inverted (α > 0.5) in this study. This figure reflects that our data are those of flux-limited samples, and they show the distribution of high-power radio sources, which ranges from 10²⁴ to 10²⁹ W Hz⁻¹ at 21.7 GHz (the observing frequency). According to the number distribution with respect to z in the bottom right panel in Figure 3, the peak is located at the z ∼ 1. The peak of bright quasars is known to be around z ∼ 1 (White et al. 2000). In addition, these distributions in four-z bins are shown in Figure 4. Gray filled and black hatched bars indicate each distribution according to α = −1.0 and 0.0, respectively. The distributions according to α are similar in the low-z region (z < 0.5), whereas they differ in the high-z region (z ≥ 0.5).

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We compared the VCS flux densities in the S and X bands with those of the KVNCS in the K and Q bands because a large difference, if any, between the observed flux densities in the K and Q bands and the extrapolated flux densities in the S and X bands would signify a VLBI missing flux problem, high source variability, or source evolution (e.g., opacity changes). Their correlations with the weighted linear fit lines are shown in Figure 5. The linear correlation coefficients are 0.77 (S–K), 0.87 (X–K), 0.81 (S–Q), and 0.85 (X–Q). The linear fit lines are obtained using the data with a K-band flux density greater than 397 mJy (median flux) and lower than 1Jy (arbitrarily) and a Q-band flux density greater than 587 mJy (median flux), because the data contain faint sources that were not detected at high frequency (e.g., the K or Q bands) but were detected at low frequency (e.g., the S or X bands). This causes a selection effect for non-detected sources (the red and black arrows), which are faint sources with a flux density lower than 3σ. Thus, sources with a flux lower than the median flux density were excepted from fitting. In addition, the bright sources (>1 Jy) in the K band excluded for fitting because they can always be detected, although they are highly variable. The slopes of the weighted linear fit lines are 1.04 ± 0.024 and 0.79 ± 0.005 for the S–K and S–Q bands, respectively, whereas they are 0.63 ± 0.024 (X–K) and 0.59 ± 0.005 (X–Q). The differences between the slopes in the S and X bands imply that there are missing flux densities in the X band. The flux densities measured from the VCS were calculated from the CLEAN components from VLBI observations, and the flux densities for some sources were obtained within 7 (S band) and 25 (X band) Mλ in projected uv-distance (Petrov et al. 2006; Kovalev et al. 2007). Therefore, there is missing flux density in the X bands, depending on the structure of each source.

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We also compared the flux densities of 232 (K band) and 76 (Q band) common sources from the KVNCS and VLBI imaging survey for the International CRF at 24 and 43 GHz (Charlot et al. 2010). Figure 6 shows their flux–flux relationships in the K and Q bands. On the basis of the structure index (SI) from Charlot et al. 2010, 195 (84%) and 63 (83%) sources were identified as SI < 3 (compact sources), and the remaining 37 (16%) and 13 (17%) sources showed SI ≥ 3 (sources with marginally compact or extended structure) in the K and Q bands, respectively. To obtain the weighted linear fit results, the data were selected in the same way as those in Figure 5. The linear fit at SI < 3 was performed for source flux densities greater than 397 mJy and lower than 1 Jy. However, some compact sources show great differences of flux density between VLBI and single-dish observations. For instance, a source with ∼4 Jy in VLBI and ∼1 Jy in single-dish flux densities has been known as a variable, J0238+1636, which had strong flux variations of around 5 Jy from 2007 to 2010.⁶ In addition, a source with ∼0.3 Jy (VLBI) and ∼3 Jy (single dish) is J1849+6705. This has also been known as a variable and shows year-scale variations (see footnote 8). Therefore, these variables were not considered for the fit in K band. At SI ≥ 3, on the other hand, the linear fit results were calculated with all sources because the number of sources was small to fit. The slope for the compact sources is 1.07 ± 0.065, while that of extended sources is 0.66 ± 0.006 in K band. We infer that most of the radiation from the compact sources (SI < 3) comes from the compact core region, whereas the extended sources (SI ≥ 3) have missing flux. In the Q band, because there are few common sources, the weighted linear fit was applied to all 76 sources. We expect that most of the radiation (∼80%) comes from the compact component, although about 20% of the flux density in the Q band is missing.

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Table 3 shows the statistics of α for 1533 sources in K band and 553 sources in the Q band, and 513 sources simultaneously detected in the K and Q bands. As expected, many of our sources have flat spectra in both the S and X and the K and Q bands. The distributions of the spectral indices of the S and X (α_SX), X and K (α_XK), X and Q (α_XQ), and the Kand Q (α_KQ) bands are shown in Figure 7. The top panel shows the distributions of α_SX and α_XK for 1533 sources and α_XQ for 553 sources. The distribution of α_XK becomes broader than that of α_SX, but ∼88% of the α_SX values and ∼70% of the α_XK values belong to the flat-spectrum ranges. In addition, the distribution of α_XQ is similar, and we expect that these are relatively bright sources. In the bottom panel, the distribution of α_XK is broader than the other distributions and shifts toward the inverted spectrum region because these sources are corrupted by flux density variability. There is an observational epoch gap between the VCS and KVNCS. However, α_XQ shows a distribution similar to that of α_SX. These sources are sufficiently bright. In addition, that of α_KQ is steeper (∼14%) than those of α_SX (∼6%), α_XK (∼6%), and α_XQ (∼3%). We infer that the sources become relatively optically thin in the K and Q bands. Nevertheless, 76% of the sources show flat spectra in the K and Q bands.

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Figure 8 clearly shows that our sample is fairly evenly distributed on the sky (this figure is the same as Figure 1 in Lee et al. 2012). Assuming a spatial coherence scale of 5°, which is the separation angle between a target and the calibrators, 99% of the sky is covered by these sources above −325 in decl. (Figure 9). The sky coverage is improved by more than 20% compared to that of the existing calibrators shown in Figure 1. In the same way, if the spatial coherence scales are assumed as 22 and 3°, the sky coverages are improved by about 28% and 38%, respectively. 22 means a maximum separation of VERA dual-beam⁸ , which is able to observe a target and a calibrator simultaneously, and 3° is a typical coherence scale in K band. Hence it is expected that we have the possibility of improving the sky coverage of the K-band calibrators with a uniform distribution, compared to the existing one (Figure 1).

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