Draftversion January18,2017 PreprinttypesetusingLATEXstyleAASTeX6v.1.0 KOREAN VLBI NETWORK CALIBRATOR SURVEY (KVNCS): 1. SOURCE CATALOG OF KVN SINGLE DISH FLUX DENSITY MEASUREMENT IN THE K AND Q BANDS Jeong Ae Lee1,2, Bong Won Sohn1,2,4, Taehyun Jung1,2, Do-Young Byun1,2 and Jee Won Lee1,3 7 1KoreaAstronomyandSpacescienceInstitute, 776,Daedeokdae-ro, Yuseong-gu, Daejeon,RepublicofKorea,34055 1 2KoreaUniversityofScienceandTechnology, 217,Gajeong-ro,Yuseong-gu,Daejeon,RepublicofKorea,34113 0 3KyungheeUniversity,1732, Deogyeong-daero, Giheung-gu,Yongin-si,Gyeonggi-do, RepublicofKorea,02447 2 4Correspondingauthor,[email protected] n a ABSTRACT J We present the catalog of the KVN Calibrator Survey (KVNCS). This first part of the KVNCS is a 7 1 single dish radio survey conducted at 22 (K band) and 43 GHz (Q band) simultaneously using the Korean VLBI Network (KVN) from 2009 to 2011. A total 2045 sources selected from the VLBA ] A CalibratorSurvey(VCS)with anextrapolatedflux density limit of100mJyatK band. The KVNCS contains 1533 sources in the K band with a flux density limit of 70 mJy and 553 sources in the Q G band with a flux density limit of 120 mJy; it covers the whole sky down to −32.◦5 in declination. . h Five hundred thirteen sources were detected in the K and Q bands, simultaneously; ∼76% of them p are flat-spectrum sources (−0.5 ≤ α ≤ 0.5). From the flux–flux relationship, we anticipated that the - o most of the radiation of many of the sources comes from the compact components. Therefore, the r sources listed in the KVNCS are strong candidates for high frequency VLBI calibrators. t s Keywords: catalogs – quasars: general – radio continuum: galaxies – surveys a [ 1 1. INTRODUCTION v 8 A large proportion of compact radio sources have flat or inverted spectra (e.g., Kellermann & Pauliny-Toth 1981; 7 Zensus 1997; Gurvits et al. 1999; Chen & Wright 2009; de Zotti et al. 2010; Massardi et al. 2011; Mantovani et al. 5 2011). This implies that these sources are optically thick at the observed radio frequencies. Very long baseline 4 interferometry (VLBI) calibratorsare also compact sources. The majorityof sources in the Very Long Baseline Array 0 . (VLBA) Calibrator Survey (VCS) have flat spectra at 2.3 (S band) and 8.4 (X band) GHz (Beasley et al. 2002; 1 Fomalont et al. 2003; Petrov et al. 2005, 2006; Kovalev et al. 2007; Petrov et al. 2008). However, VLBI calibrators at 0 7 higherfrequency(>20GHz)areseverelyrarecomparedtothoseatlowerfrequency. Forexample,858VLBIcalibrators 1 in the K band (∼20 GHz) are known (Petrov et al. 2007; Lanyi et al. 2010; Petrov et al. 2011, 2012; Petrov 2012), v: while ∼3800 sources are listed in the VCS in the S and X bands. High−frequency VLBI observations are useful to i understand the physicalprocesses in the vicinity of supermassive black holes of active galactic nuclei (AGN), because X a study of optically thin region from the synchrotron radiation of compact radio sources is possible. In addition, r a radio sources become more compact in structure so that astrometric errors in the celestial reference frame (CRF) would be minimized (e.g. Fey & Charlot 1997; Ma et al. 1998; Fey et al. 2004; Lanyi et al. 2010; Charlot et al. 2010). Togetherwith the successful operationof the Gaia spacecraftduring the first two yearsof sky survey,high−frequency VLBI sources matching with Gaia samples will be important to compare the radio and optical reference frames (e.g. Bourda et al. 2010, 2011; Jacobs et al. 2014). There is an extensive blind survey of the southern sky that identified 5808 sources at 20 GHz (AT20G) in order to support subtraction of foreground objects for the measurement of the Cosmic Microwave Background (Murphy et al. 2010). Inthenorthernsky,Righini et al.(2012)conductedtheK-bandNorthernWideSurveyandidentified73sources atdeclination>72.◦3(∼880degree2). Recently,Jacobs et al.(2014)constructedanewcompactradiosurveyatX/Ka (8.4/32 GHz) bands in order to improve the accuracy of celestial reference frame and detected 631 sources. However, the sky coverage of known K band calibrators is about 49% of the whole sky by assuming the circles of 5◦ radius as shown in Figure 1, while the VCS sources in the S and X bands cover the full sky above −40◦ in declination with [email protected] 2 this radius (Petrov et al. 2008). The critical separation angle, 5◦ was determined, referring to Dodson et al. (2014). They showed a feasibility of source frequency phase referencing (SFPR) in KVN, considering of 5◦.9 separation angle between a target and a calibrator in Korean VLBI Network (KVN). We therefore performed 21.7 (K band) and 42.4 (Q band) GHz single dish survey observations in order to provide a wider sky coverage of possible VLBI target and calibrator sources at those frequencies (or even higher frequencies), particularly for the KVN. The KVN is composed of three 21-m telescopes in Seoul, Ulsan and Jeju, Korea. Its notable characteristic is the multifrequency receiver system, which makes it possible to observe the radio sources at four different frequencies [22 (K),43(Q),86(W),and129(Dbands)GHz]simultaneously(e.g.,Han et al.2008;Lee et al.2011,2014). Inparticular, this system is very efficient for high frequency VLBI observations when the frequency phase transfer (FPT) method is applied to compensate for the atmospheric coherence loss; this method uses lower frequency phase solutions (e.g., in the K band) to compensate for higher frequency ones (e.g., in the Q/W/D bands), because of the non-dispersive nature of the atmosphere with regard to radio systems (e.g. Jung et al. 2011; Rioja et al. 2014, 2015). As a result, noticeable improvements of coherence time and signal-to-noiseratio (SNR) athigh frequency VLBI observationshave been demonstrated (e.g. Jung et al. 2012, 2014). ForthepracticaluseoftheFPTforhigherfrequencies(Q/W/D-band)VLBIobservationswiththeKVN,increasing available sources in the K and Q bands is very important in the northern sky because the detection of target or calibrator sources at the lower frequencies (e.g. in the K or Q bands) as a reference for the atmospheric calibration is essential. The increase of the detection at high frequencies by the FPT will be able to extend our understanding of radio sources from centimeter to millimeter wavelengthsin VLBI; for example, a statisticalstudy of a spectral energy distribution (SED) of AGNs based on the simultaneously measured flux densities at a range from 20 to 130 GHz, and high frequency astrometric applications (e.g. Rioja et al. 2015). We therefore performed the KVN Calibrator Survey(KVNCS),whichaimstomeasurethesingledishfluxdensitiesof∼2500selectedsourcesintheKandQbands simultaneously in order to utilize as VLBI calibrators of KVN. Inthenextsection,weexplaintheselectioncriteriaforthe∼2500sources. Theobservationsanddatareductionsare described in section 3. In section 4, the observational results and their analysis are presented. Finally, we summarize our findings and future prospects in section 5. The full catalog of the KVNCS is also provided in the appendix. 2. SOURCE SELECTION Atotalof2503sourceswithanextrapolatedtotalfluxdensity(hereafter,SS−X)greaterthan100mJyintheKband K were selected from VCS1 to VCS5 (Beasley et al. 2002; Fomalont et al. 2003; Petrov et al. 2005, 2006; Kovalev et al. 2007). As the most widely used catalog of VLBI calibrators,the VCS contains ∼3800 radio sources that show mostly a compactstructure and flat spectra sources with greaterthan −40◦ in declination. SS−X was calculated, assuming a K power-law spectrum from the total flux densities in the S and X bands (Sohn et al. 2009). The flux density limit of 100 mJy was a selection criterion, which gives >8σ at a baseline sensitivity of the KVN at K band1. A declination limit of −32.◦5 was determined so that all sources are observed at more than 20 ◦ above the horizon at transit. For the first observation as a pilot observation, 595 relatively bright sources that have SS−X higher than 500 mJy in the K K band were selected, and 493 sources (∼83%) were successfully detected with the first single dish observations from KVNCS1.0.1to KVNCS1.1.3in the K andQ bands. Then,we performeda singledish observationtoward1450of the remaining 1908 sources, the flux density of which ranges between 100 mJy and 1 Jy. In order to avoid concentrated on the specific regions, the 1450 sources were selected by considering the sky coverage of the detected source density, which was calculated by the Delaunay triangulation method2, whenever each observation was complete. We assumed that the calibratorsare located on the vertex of the triangle in the triangulationmethod. The target is located in the center ofthe circumcircle ofthis triangle,andthe radius ofthis circle become the maximumseparationangle between the target and the calibrators. 3. OBSERVATION AND DATA REDUCTION 3.1. Observation We selected 2503 sources based on lower frequency VLBI flux density from VCS. A flux densities of 2045 of 2503 sources were measured by single dish observations in the K and Q bands simultaneously using the KVN Yonsei and Ulsan radio telescopes from December 2009 to March 2011. The observational information is summarized in Table 1 KVNstatusreport: http://kvn.kasi.re.kr/status report/ 2 ThismethodwasdevelopedbyBorisDelaunayin1934andiswellknowninmathematicsandcomputational geometry. Thetriangles in Delaunay triangulation method minimizes the summation of the interior angles of the triangles. In addition, these triangles do not includeanypointsexcept thevertices withintheircircumcircle(fromWikipedia). 3 1. The cross-scanmode (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, time scales of the sky power variation, and a hardware and software limitations of the KVN system. The applied scan speed, the data sampling interval and the scan length are mainly 65′′/sec, 0.1 ms, and 13′, respectively, which yield 4 (K band) and 2 (Q band) seconds full−beam cross time. We can remove sky power variation of which time scaleislongerthanthe full−beamcrosstime byfitting off−sourcedata. AssumingaGaussianbeampattern,the on-sourceintegrationtime ofa crossscanare8 and4 secondsin the K andQbands, respectively. The totalon-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 3. The mean beam sizes in the K and Q bands are quite consistent with the known ones. However, the estimated beam sizes and pointing offsets have large errors for faint sources and under the 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 sizeandpointingoffsetdataare7%(K)and20%(Q)and4′′ (K)and4′′ (Q)inAzand10%(K)and19%(Q)and6.4 ′′ (K)and6.0′′ (Q)inEl,respectively. The observingfrequencies were21.7GHz for the Kbandand42.4GHz for the Q band with 512 MHz bandwidth. A measured root-mean-square (RMS) error is an order of magnitude higher than estimated thermal one. 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 in room temperature of ∼292K and the other immersed in liquid nitrogen of 80K, as hot and cold loads, respectively. From KVNCS1.2.2, we used chopper−wheel method which uses a sky as a cold load together with a microwave absorber in room temperature (Kutner & Ulich 1981; Mangum 2000). The results from these two calibration methods were consistent each other within ∼2% uncertainty. The system temperature and zenith optical depthofeachobservationarepresentedinTable1. Theskyopacitywascorrectedusingthesky-dippingmethodbased on observations every hour. 3C 286 was observed as a flux calibrator every 1.5 h to convert the measured antenna temperatureintothe flux. Thefluxdensitiesof3C286are2.64and1.51Jyinthe KandQbands,respectively. These were measured with a brightness model of Mars at the KVN Yonsei observatory (Sohn, in prep.). 3.2. Data reduction We developedananalysis programfor the KVN single dish flux density measurementsand the followingprocedures were applied: (a) Extraction of bad scans due to the weather conditions or instrumental spuriousness, (b) linear baselinefittingto estimatetheRMSnoiselevelandtoeliminateskylevel,(c)Gaussianfitting tomeasurethe antenna temperature andto correctpointing offsets deviating fromthe Gaussianfitted center positionusing equations(1) and (2) (Fuhrmann 2004). x2 (T∗ )′ =T∗ ·exp[4ln2 El] (1) a,Az a,Az θ2 El x2 (T∗ )′ =T∗ ·exp[4ln2 Az] (2) a,El a,El θ2 Az T∗ and T∗ are the measured antenna temperature corrected for atmospheric attenuation along the Az and El a,Az a,El axes in the cs-mode,respectively. Further, x and x are pointing offsets, andθ and θ arethe half-powerbeam Az El Az El width in arcseconds. After the pointing correction, (T∗ )′ and (T∗ )′ were averaged. (d) The error propagation of a,Az a,El the antenna temperature was calculated using equation (3). σ2 σ2 σ =(T∗)′ [ ∆G + Ta∗ ] (3) (Ta∗)′ a s ∆G2 (T∗)2 a (T∗)′ is the correctedand averagedT∗ for the pointing offset and in Az and El. σ representsthe uncertainty of T∗. a a Ta∗ a ∆G is the temporalvariationof the antenna gain, and its uncertainty is written as σ . The gaincurves of the KVN ∆G radiotelescopesareveryflatforelevationsof20to80◦ inthe KandQbands. The gainvariationalongthis elevations were 2.5% (K) and 2.0% (Q) at KYS and 1.5% (K) and 4.5% (Q) at KUS 3. Thus, the elevation dependence of the gain variation was ignored. ∆G was obtained by using the ratio of the mean (T∗)′ to (T∗)′ of 3C 286. However, the a a 3 KVNstatusreport: http://kvn.kasi.re.kr/status report/ 4 errorwasdominatedbythethermalrandomnoise. Theflux densityconversionfactorsweredeterminedfromthe ratio ofthefluxdensitiesto(T∗)′ of3C286intheKandQbands(seeTable1),whichwereobtainedusingtheNRAOMars a 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. 4. RESULTS AND DISCUSSION 4.1. Flux density measurement Among2043sources,the fluxdensitiesof1533(75%)and533(27%)sourceswith3σ noiselevelsof66(Kband)and 108 (Q band) mJy were successfully measured. Their median flux densities were 397 and 588mJy and the lowestflux densities were ∼70 and ∼120 mJy in the K and Q bands, respectively. Among them, the flux densities of 513 sources were measured in the K and Q bands simultaneously. The distribution of the measured flux densities are shown in Figure 2 and the measured flux densities are listed in Table 2. Theluminositydistributionof1138sourcesasafunctionoftheredshift(z)areplottedinFigure3. Archivalredshifts were taken from NASA/IPAC Extragalactic Database (NED) and the Sloan Digital Sky Survey (SDSS) DR13. Only 23sourcesweregivenasthe photometricredshifts andtheir meanuncertaintyareabout0.618. Theseluminosities are calculatedwithH = 73kms−1 Mpc−1 andΩ =0.27at21.7GHz 4,accordingtothe arbitrarilyspectralindices (α 0 m =−1.0and0.0,S ∼να,whereS istheflux,andν istheobservedfrequency). Wedenotespectraassteep(α<−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. That 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-filledand black-hatchedbars 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). 4.2. Comparison with the VLBI flux densities in the S, X, K, and Q bands We comparedtheVCSfluxdensities inthe SandXbandswiththoseofthe KVNCSinthe KandQbands,because large difference, if ever, between the observed flux densities in the K and Q bands and the extrapolated flux densities inthe SandXbandswouldmeanVLBImissingflux problem,highsourcevariabilityorsourceevolution(e.g.,opacity changes). Theircorrelationswiththe weightedlinearfitlinesareshowninFigure5. Thelinearcorrelationcoefficients 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 having a K-band flux density greater than 397 mJy (median flux) and less 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 lowfrequency (e.g., the S orX bands). This causes a selectioneffect for non-detected sources (the red and black arrows), which are faint sources with a flux density less than 3σ. Thus, the sources less than the median flux density were excepted for fitting. In addition, the bright sources (> 1Jy) 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 fromVLBI 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. We alsocomparedthe flux densities of232 (K band) and76 (Q band)commonsourcesfrom the KVNCSand VLBI imagingsurveyfortheInternationalCelestialReferenceFrameat24and43GHz(Charlot et al.2010). Figure6shows theirflux–fluxrelationshipsintheKandQbands. Onthebasisofthe structureindex (SI)fromCharlot et al.(2010), 195(84%)and63(83%)sourceswereidentifiedasSI<3(compactsources),andtheremaining37(16%)and13(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 4 http://ned.ipac.caltech.edu/ 5 at SI < 3 was performed for source flux densities greater than 397 mJy and less than 1 Jy. However, some compact sources show the big differences of flux density between VLBI and single dish. For instance, a source which has ∼4 Jy of VLBI and ∼1 Jy of single dish flux densities has been known as a variable, J0238+1636 which had big flux variationsofaround5Jyfrom2007to20105. Inaddition,asourcewhichhas∼0.3Jy(VLBI)and∼3Jy(singledish) is J1849+6705. Also this has been knownas a variable which shows year-scalevariations5. Therefore,these variables were not considered to fit in the 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 the 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. 4.3. Spectral index distributions Table 3 shows the statistics of α for 1533 sources in the K band and 553 sources in the Q band, and 513 sources detected in the K and Q bands simultaneously. 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 ), X and K (α ), X and Q SX XK (α ), and K and Q (α ) bands are shownin Figure 7. The top panelshows the distributions of α andα for XQ KQ SX XK 1533 sources and α for 553 sources. The distribution of α become broader than that of α , but ∼88% of the XQ XK SX α values and ∼70% of the α values belong to the flat spectrum ranges. In addition, the distribution of α is SX XK XQ similar,andweexpectthatthesearerelativelybrightsources. Inthebottompanel,thedistributionofα isbroader XK 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 shows a XQ distribution similar to that of α . These sources are sufficiently bright. In addition, that of α is steeper (∼14%) SX KQ than those of α (∼6%), α (∼6%), and α (∼3%). We infer that the sources become relatively optically thin SX XK XQ in the K and Q bands. Nevertheless, 76% of the sources show flat spectra in the K and Q bands. 4.4. Sky coverage 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 −32.◦5 in declination (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 spatialcoherencescalesareassumedas2.2and3◦,theskycoveragesareimprovedabout28and38%,respectively. 2.2◦ means amaximumseparationofVERA dual-beam6 whichis able to observeatargetanda calibratorsimultaneously and3◦ isatypicalcoherencescaleintheKband. Hence,itisexpectedthattherewillhavethepossibilityofimproving the sky coverageof the K band calibrators with a uniform distribution, comparing to the existing one (Figure 1). 5. SUMMARY We conducted an extensive single dish survey (the KVNCS) of 2043 extragalactic radio sources in the K and Q bands using the KVN and successfully detected 1533 (75%) of the sources in the K band and 553 (27%) in the Q band. Inaddition,thefluxdensities of513sourcesweremeasuredintheKandQbands,simultaneously. This catalog is an important database for high frequency VLBI observations with the KVN and other available radio telescopes worldwide. In addition, these sources become VLBI calibrator candidates. The sky density distribution of the 1533 sourcescoveredabout99%oftheskyobservablebytheKVN.About76%ofthe513sourcesstillshowedflatspectrain the K and Q bands. On the basis of the flux–flux relationship between the single dish survey and VLBI observations, we inferred that most of the radiation of many of the sources comes from the compact components. To confirm the feasibility of using these sourcesas reliable VLBI phase calibrators,however,VLBI fringe and imaging surveysshould be performed. These VLBI follow-ups areongoingwith the KVN andKaVA(KVN andVERA Array)in the K band. In addition, a simultaneous multiwavelength Active Galactic Nuclei survey is in progress. The authors appreciate the support of DRC programof Korea ResearchCouncil of Fundamental Science and Tech- 5 F-GAMMAproject: http://www3.mpifr-bonn.mpg.de/div/vlbi/fgamma/fgamma.html 6 http://veraserver.mtk.nao.ac.jp/system/dualbeam-e.html 6 nology (FY 2013). We are grateful to all staff members at the KVN who helped to operate the array and to correlate the data. The KVN is a facility operated by KASI (Korea Astronomy and Space Science Institute). KVN operations are supported by KREONET (Korea Research Environment Open NETwork) which is managed and operated by KISTI (Korea Institute of Science and Technology Information). The authors are grateful for the valuable comments of the anonymous referee. REFERENCES Beasley,A.J.,Gordon,D.,Peck,A.B.,etal.2002, ApJS,141, Lanyi,G.E.,Boboltz,D.A.,Charlot,P.,etal.2010,AJ,139, 13 1695 Bourda,G.,Charlot,P.,Porcas,R.W.,&Garrington,S.T. 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This map is drawn using a Mollwide equal-area projection ◦ ◦ (abscissa: right ascension [ ], ordinate: declination [ ]). 8 Figure 2. Flux density distributions of measured sources (≤ 5 Jy) in the K (top) and Q (bottom) bands. Red arrows indicate the median flux densities, 397 and 587 mJy in the K and Q bands, respectively, whereas the mean flux densities are 707 and 1,103 mJy, respectively. 9 Figure 3. Luminosity distributionof 1137 sources asafunction ofredshift (z). Thez valueswere takenfrom theNASA/IPAC Extragalactic Database (NED) and the Sloan Digital Sky Survey (SDSS) DR13. These luminosities are calculated with H0 = 73kms−1 Mpc−1 andΩm =0.27 at21.7 GHz,whichistheobservedfrequency,accordingtothespectralindex,α(−1.0: gray filledcircles, 0: black circles). Theredlinesindicatestheluminositydistribution atα=0asthecriteria forfluxdensities. Top right: Thenumberof sourcesaccording totheirluminosities atα=−1and0. Bottom right: Thenumberofsources according to z. 10 Figure 4. Luminosity distributions in four-redshift (z) bins. Gray filled and black hatched bars stand for the distributions for α = −1.0 and 0.0, respectively.