On the selection effect of radio quasars in the Sloan Digital Sky Survey
aa r X i v : . [ a s t r o - ph . C O ] A p r Published in AJ
On the selection effect of radio quasars in the Sloan Digital Sky Survey
Yu Lu , , Tinggui Wang , , Hongyan Zhou , , Jian Wu [email protected] ABSTRACT
We identified a large sample of radio quasars, including those with complex radiomorphology, from the Sloan Digital Sky Survey (SDSS) and the Faint Images of Ra-dio Sky at Twenty-cm (FIRST). Using this sample, we inspect previous radio quasarsamples for selection effects resulting from complex radio morphologies and adoptingpositional coincidence between radio and optical sources alone. We find that 13 .
0% and8 .
1% radio quasars do not show a radio core within 1 . ′′ ′′ of their optical position,and thus are missed in such samples. Radio flux is under-estimated by a factor of morethan 2 for an additional 8 .
7% radio quasars. These missing radio extended quasarsare more radio loud with a typical radio-to-optical flux ratio namely radio loudness RL & P & W Hz − . They account for more than one thirdof all quasars with RL >
1. Introduction
In past decades, we have witnessed a rapid growth in the number of radio selected ActiveGalactic Nuclei (AGNs) resulting from large and deep radio surveys such as the Faint Images ofRadio Sky at Twenty centimeters (FIRST, Becker, White & Helfand 1995) and the NRAO VLASky Survey (NVSS, Condon et al. 1998) coupled with optical spectroscopy follow-ups or dedicatedspectroscopic surveys such as the Two degree Field (2dF, Maddox et al. 1998; Boyle et al. 2001) Center for Astrophysics, University of Science and Technology of China, Hefei, Anhui, 230026, P.R.China Joint Institute of Galaxies and Cosmology, SHAO and USTC, Hefei, Anhui, 230026, China Department of Astronomy & Astrophysics, the Pennsylvania State University, . ′′ ′′ , Ivezic etal. (2002) estimated that less than 10% SDSS-FIRST associations have complex radio morphology,and core-lobe and double-lobe sources together represent about only 5% in the radio quasars andgalaxy sample. Using a novel technique, de Vries et al. (2006) constructed a Fanaroff-Riley type2 (FR-II) quasar sample, and found that 27% FR-II quasars do not show cores at the FIRST fluxlimit. These authors also compared the emission line properties and optical colors of these FR IIquasars with radio quiet quasars. It should be noted that these missing quasars are not random,but are all extended sources and tend to be more radio loud (Falcke et al 1996; Ivezic et al. 2002;Best et al 2005). As a result, the statistical properties of the sample, such as radio loudness andradio luminosity distribution, will be affected by this selection effect.In this paper we study in detail of selection effects in the SDSS radio quasar samples. Weidentified from SDSS and FIRST a large sample of radio quasars, including those with complexradio morphology. Besides using positional coincidence as a primary selection criterion, we manuallyexamined the FIRST images for all of the candidates with extended radio morphology. Throughthis less efficient process, we obtained a sample of 3641 spectroscopically confirmed quasars with 3 –secure radio identification. A detail comparison of this sample with other radio quasars sample isgiven. Various selection effects are quantified. Throughout this paper, we will adopt a concordantcosmology with H = 70 km s − Mpc − , Ω m = 0 .
3, and Ω Λ = 0 .
2. The Radio Quasar Sample2.1. Optical data
Our starting point is the SDSS quasar catalog constructed by Schneider et al (2005). Thecatalog consists of quasars that contain at least one broad emission line (
F W HM & − ),or are unambiguously broad absorption line quasars. These quasars selected from SDSS photometriccatalog either by their colors or for their positional coincidence with radio sources in the FIRSTcatalog (within 2 " of a FIRST source) or ROSAT X-ray sources (within 10-20 " of a ROSAT source),were spectroscopically confirmed to meet above criteria and their absolute optical magnitudes at i -band M i ≤ − .
0. The sample also includes some supplementary quasars that meet the abovecriteria, but were selected initially as galaxy targets (Eisenstein et al. 2001; Strauss et al. 2002).Note that the magnitude limits for various candidates are different, i < . z ( z < .
0) quasars, i < . z quasars, i < . i < . ,
420 quasars inthe redshift range 0 . ≤ z ≤ . − . ≤ M i ≤ − .
0, and i -bandoptical magnitude range 15 . ≤ i ≤ . Radio counterparts to SDSS quasars are found using the FIRST survey. The survey coversabout 10,000 deg and is 95% complete to 2 mJy, 80% complete to 1mJy (Becker et al 1995). Thesource surface density in this survey is ∼
90 deg − . At the 1 mJy source detection threshold, theresolution is better than 5 ′′ . Individual sources down to 1 mJy threshold have 90% confidence errorcircles with radii of ≤ ′′ .The FIRST catalog was produced by fitting a two-dimensional Gaussian to each source togenerate major axes, minor axes, peak and integrated flux densities from the co-added images. The 4 –major axes have been deconvolved to remove blurring by the elliptical Guassian fitting. For brightsources, the size was determined down to ∼ / . ′′
4. The FIRST survey alsoprovides clean radio images.
Most radio quasars are compact sources in the FIRST images and as such, they can be identifiedthrough cross-correlation of the FIRST catalog with the SDSS quasar catalog by adopting a smallmatching radius in the position offset.The matching radius is a trade-off between the completeness and random association, i.e., thehigher completeness necessarily implies higher random contamination. Knapp et al. (2002) showedthat the random association increases with matching radius at . ′′
5. Magliocchetti & Maddox(2002) found that 2 ′′ matching radius could include ∼
97% of the true matches above 1 mJy level.Gregg & Becker (1996) estimated that more than 95% FBQS-I quasars with magnitude E . . ′′ ∼ ′′ − . ′′ ′′ offset to ∼
20% at 1 . ′′
2, and is constant farther out. Ivezic et al. (2002)estimated that 1 ′′ matching radius produces 72% completeness and 1 .
5% random contamination,and 1 . ′′ ′′ matching radius will cover almost all counterpart but with9% random contamination.Following Richards et al. (2002), we used a matching radius of 2 ′′ for compact FIRST sourcesand obtained 2782 matches with a false rate of ∼ . ′′ matching radius. We added these quasars to our sample after visualconfirmation of the true association. The two point angular correlation function (Cress et al. 1995) can be used to define anappropriate scale for searching for radio matches with complex radio morphologies. The correlationfunction in 0 . − ◦ can be well fitted by a power law A × θ γ , where the angle θ in units of degree, A ∼ × − and γ ∼ − .
1. At the θ ∼ . ◦ (6 ′ ), it drops to a value of only 0.038 which meansthat double and multi-component FIRST sources are shown to have a little clustering amplitude The fraction of chance coincidence is estimated as ρπr N s /N m , where ρ is the surface density of FIRST sources, r the matching radius, N s the number of quasars in the catalog of SDSS DR3, and N m the number of matches. ′ angle at z=0.05 is ∼
353 kpc,approximately to the scale of most radio jet and lobe ( ∼
100 kpc, Readhead et al. 1988; Jackson1999, krolik 1999 ). All quasars in the SDSS DR3 have redshift above 0.05. So we use the 6 ′ × ′ FIRST map surrounding the quasar to determine possible complex structure.The extended radio quasars are extracted in two steps. First, the candidates of radio quasarsare selected with one of the following two simple criteria: (1) two radio sources locate nearlysymmetrically around the quasar position, i.e., the angle between optical-radio connections lies150 ◦ . θ . ◦ , and the ratio of their distances to the quasar is 1 / . d /d .
3; (2) morethan two radio sources scatter around the SDSS quasars. The first criterion allows us to detectradio sources with symmetric lobes, either of FR-II or FR-I type (Fanaroff & Riley 1974), which issimilar to that used by de Vries et al. (2006). The FR-I sources are core-dominated sources with abright nucleus and two extended lobes with the surface brightness decreasing towards the edges. Incontrast, the FR-II sources are generally lobe-dominated sources, and always show brighter lobes,usually with a hot spot, and with or without a weak core (see Fig. 1). However, when viewed at anextreme angle, the FR-II sources may be dominated by the brighter core (Barthel 1989; Hoekstra etal. 1997; Hardcastle et al.1998). By the first criterion, sources with distorted asymmetric lobes maybe missed. The second criterion is designed for more complex radio morphologies, such as sourceswith distorted asymmetric lobes and a compact core or for cases in which extended lobes are resolvedinto complex structure in the FIRST image. (see Fig. 1) With these criteria, we selected 3115 radioquasar candidates. Among them, 1035 sources are selected by the first criterion, and 2080 by thesecond one. A 6 ′ × ′ cutout of FIRST image centered at the quasar candidate was extractedfor each SDSS source, and visually checked. We use the radio morphologies in the 3CR radiosources as the reference for the true matches. We found about 70% of these radio componentsin 6 ′ × ′ cutouts are likely not related to the SDSS quasars, i.e., they are isolated componentsor radio components related to other SDSS sources, or they have no convincing evidence for theirconnection to the quasar. They will be excluded either from the radio flux estimation or from thesample.In the end, 859 extended sources are selected (with unambiguous radio lobes, jets) from initial3115 candidates. Among them, about half (409) show FR-II morphologies, and 564 have radio corecomponents (within 2 " circle of optical quasar position) in the FIRST catalog. In comparison, deVries et al. found 422 FR-II quasars using Abazajian et al. (2005) DR3 quasar sample (44984sources), of which 359 are in common. The members of radio counterparts in the de Vries samplethat are not included in our sample are 63. Most these “lost” objects (41 out of 63) are not includedin the SDSS DR3 quasar catalog of Schneider et al. (2005). The other 18 were excluded by usdue to their ”FIRST-only” or ”ROSAT-only” target-flag. The remaining 4 were excluded by us for http://archive.stsci.edu/vlafirst/getting started.html http : . m i ∼ .
78, the median redshift is ∼ .
36 (seeFig.3). The distributions of optical selected and optical+radio selected sub-sample are significantdifference. As noticed by Richards et al. (2006), radio-selected and optically-selected quasars showdifferent redshift distribution in the sense that the optical selected quasars show deeper deficit at z ∼ .
7, while the optical+radio quasars distribute smoother at z >
2. This is due to the selectioneffect of the optically-selected SDSS quasars based on optical colors. We can also see that radioquasars peak at a slightly lower redshift and are more abundant between redshifts of 2.2 and 3.0.This may be due to the comparatively shallower survey depth of FIRST, so that we can find moreradio counterparts of optical-selected quasars at lower redshift.Note that the redshift distribution of extended sources peaks at lower redshift than the compactquasars, i.e., the fraction of extended sources decreases with redshift. The median radio flux is 5.49mJy for compact quasars and 48.31 mJy for extended quasars.
3. On the selection effect of radio quasar sample3.1. The incompleteness of extended sources caused by the surface brightness limit
FIRST is not sensitive to low surface brightness emission due to its small beam size. As suchdiffuse emission, if present, will be missed in the FIRST survey. It should be noted that the surfacebrightness are lowered due to cosmological expansion ( I ∝ (1 + z ) − − α r ), as such lobes may fallbelow the detection limit (0.75 mJy per beam) of the FIRST survey at large redshift (see below).In the worst case, if the source is dominated by a diffuse component, they may escape the detection 7 –at all in the FIRST survey. We use cross correlation between SDSS and NVSS to constrain this.The 1.4GHz NRAO VLA Sky Survey (NVSS; Condon etal 1998 ) provided a catalog contain2 × sources stronger than 2 . S . GHz =3 mJy and 99 percent complete at S . GHz = 3 . ′′ (FWHM),NVSS is much more sensitive to lower surface brightness components than FIRST. Therefore, itcan be used to check the fraction of quasars with only diffuse emission. For typical redshift ofquasars in this sample, the radio emission should be unresolved by NVSS.In the following we will consider radio sources with NVSS flux density larger than 3 mJy.The matching radius used in the cross-correlation of DR3 quasars and NVSS sources is trade-off between random contamination and completeness. First, we estimate that the fractions ofchance coincidence corresponding to 15 ′′ , 20 ′′ , 25 ′′ matching radius are ∼ . ∼ . ∼ . ∼ . ′′ offset of the quasars. The fraction decreases to 87 .
65% with a 15 ′′ matching radius, and increaseto 95 .
6% with 25 ′′ matching radius. We take 20 ′′ as the matching radius for the NVSS-SDSS match.With 20 ′′ matching radius, we extracted 3029 NVSS radio counterparts to SDSS DR3 quasarsin the overlapping area of FIRST, SDSS DR3 and NVSS, with the NVSS flux density limit of 3 mJy.In this DR3-NVSS sample, 227 sources are not present in our DR3-FIRST radio quasar sample.208 of these ”lost” sources locate at a distance larger than the NVSS major axis from the quasar.We found the NVSS-SDSS offset distribution of these ”lost” sources are significantly different fromthe ”found” ones (see the bottom panel of Fig. 4), indicating most of them are due to chancecoincidence. This number is close to the expected rate of chance coincidences ( ∼ . ∼ / (775 + 19) ∼ . k = log( f NV SS /f F IRST ) at FIRST flux > < f F IRST is the sum of all radio sources within the NVSS beam size. The k is peaked at zero with a tailtoward < k > ∼ .
04 above 3 mJy, which suggests that most of the NVSS flux had been detected bythe FIRST. But below 3 mJy limit, < k > increased to 0.24. This indicates that some diffuse radioflux such as weak lobes of extended sources can be underestimated by the FIRST as flux densitydecreases. As a result, some extended sources with low surface brightness may be mis-identifiedas compact sources. This may explain why most of the extended sources have flux greater than 3mJy (see the right panel of Fig.4). 8 –
In this section, we will address the selection effects introduced by the positional coincidencealone using our radio quasar sample. This includes the lost fraction of lobe-only objects and theunderestimate of the extended flux. In the following, we will divide the radio quasars into extendedand compact sources according to whether one or more extra-core components are present or not.The core component is defined as the single component within the 2 ′′ radius of the optical quasar.The distribution of position offsets of the closest radio component to the SDSS quasar is shownin the left panel of Fig.5 for our radio quasar sample. We find that 13.0% of quasars will be lostwith a matching radius in the position offset of 1 . ′′
2, 10.4% at 1 . ′′ .
1% at 2 ′′ . With thesenumbers, we conclude that the fraction of radio quasars missed due to lack of detectable radiocores is low.Using the positional coincidence will underestimate the radio flux density if there is one ormore off-core components even if a radio core is present. This will be important particularly inlobe-dominated quasars. To quantify this bias, we calculate q as the flux ratio of the core componentto the total radio flux (the summation over all radio counterparts that are associated with the radioquasar). The distribution of q for 564 quasars with core-lobe structure and 295 objects without cores( ∼
35% of all extended sources) are shown in Fig.5. It is interesting to note that the distribution of q keep nearly constant between 0 < q < .
0, i.e., the number of strong-lobe sources ( q < .
5) andweak-lobe sources ( q > .
5) are similar. We found that the radio fluxes are either underestimatedby a factor more than two or complete missed in about 16.8% of all radio quasars. The sources withtwo or more components are significantly more numerous than estimated by Ivezic et al. (2002).Note that with our definitions whether a quasar is compact or extended depends also on theredshift of the quasar. Fig.3 shows that the fraction of extended sources peaks at redshift ∼ . & .
0. Note that this is not due to the increase of the angulardistance because it is peaked around 1.5 for the cosmological model adopt here, and most extendedsources at redshift less than 0.5 have sizes that should be resolved at redshift around 2-4 ( Fig.6).This can be due to either an evolution in the radio structure of quasars or the decrease of brightnesscaused by cosmology expansion ( I ∝ (1 + z ) − − α r ) (Fig.6).We show the optical color distributions in Fig. 7. In order to eliminate the dependence onredshift, we divide our sample into 20 redshift bins. For each bin, we subtract from g − i themedian value of ( g − i ) median in that bin. Surprisingly, the color distribution of extended radioquasars (with and without core) does not appear redder, but slightly bluer than the compact radioquasars. Kolmogorov-Smirnoff test deems the significant difference between the color distributionof extended and compact sources at the confidence level & & f int /f peak ) > .
1, with f int > . z ∼
2, we calculate the k -corrected UV flux at 2500 ˚ A at therest frame of quasars by interpolating or extrapolating the SDSS five apparent magnitudes usinga Spline function. Extrapolation is required for only a small number of quasars at low redshift( z < . k -corrected radio flux at 20 cm andthe UV flux at 2500 ˚ A . An average of radio spectral index α r = − . k -corrected radio power at 20 cm as P radio = 4 πD L f int / (1 + z ) α r ,where the radio spectral index α r is assume to be − . z is shown inright panel of Fig.8. Evidently, extended radio quasars are much more powerful in the radio thancompact radio quasars despite their similar optical luminosity.The difference in the radio power between the extended and compact sources decreases withincreasing redshift, a factor of more than 10 at redshifts less than 0.5 to a factor ≃ z , and an increase in the detecting limit of intrinsicbrightness for the extended lobes at high redshift, i.e., only very bright lobes are detected, andthus only very powerful FR II sources. At redshift less than 0.5, the radio power of compact radioquasars is close to the border of FR-I/FR-II division.It was proposed that strong radio emission from extended quasars may be enhanced by inter-action of powerful radio jets with the interstellar medium (Bridle et al. 1995; Wills & Brotherton1995). As such the difference in the radio power of core-dominated and extended quasars is due totheir different environment, rather than their different central engine. To check this point, we com-pare the core radio power for those quasars with detected cores, and found that extended quasarshave more powerful cores. Therefore, our result does not support this interpretation.The radio and optical flux limits introduce another selection effect on the radio loudnessdistribution of quasars. At a given optical magnitude limit, only quasars with their radio loudnessabove certain limit can be detected in the FIRST survey due its flux limit, i.e., the sample iscomplete above certain radio loudness. Using a similar strip in the log( RL ) − i plane as Ivezic et al.(2004), we estimate the conditional radio loudness distribution under different photometric limit.As shown in Fig.10, the distribution of log( RL ) for compact sources peak at ∼ < i < RL ) ∼ RL ) & . RL ) . .
3. Furthermore, the compact sources distribution peaks atlower radio loudness when i decreased.By plotting the radio loudness under different redshift, we find that the peak of the compactradio quasars moves to small RL as redshift decreases, while the distribution of the extendedradio quasars remains the same (peaked at ∼
3) for all redshift (see Fig.11) This radio loudnessdistribution of the extended (also more radio loud) radio quasars is consistent with Cirasuolo et al.(2003b), who modeled the radio loudness distribution with double-Gaussian function by fitting theFIRST selected 2dF quasars, and found that the intrinsic radio loudness of radio quasars peaks atlog( RL ) = 2 . ± . RL ) = − . ± .
4. Conclusion and Discussion
We have constructed a relatively unbiased large radio quasar sample using the SDSS quasarcatalog (Schneider et al. 2005), and the FIRST catalog and images. Apart from positional coinci-dence of radio sources within 2 ′′ of quasars, we also identify the radio counterpart of quasars withcomplex radio morphologies such as lobe -dominated quasars by visual inspection of their radioimages. We find that using the positional coincidence alone will miss ∼
8% radio counterpart thatdo not show radio core at FIRST flux limit of 1 mJy, and under-estimates the radio flux by a factorof more than two in another ∼
9% objects. By comparing the radio flux from FIRST survey withthat from NVSS, we found that lobes in weak radio sources tend to be missed in this sample. Sothese numbers are only lower limits.Quasars with extended radio emission show both larger radio powers and radio loudness,and appear somewhat bluer than radio compact quasars despite their indistinguishable opticalluminosity. As such, the radio extended quasars account for nearly one third of radio loud quasarsat log( RL ) > .
2. Naturally, including the extended emission and weak core radio sources increasesthe fraction of the radio loud objects and the significance of radio loud peak in the distribution ofHough & Readhead radio loudness.Our results in the first glance are not consistent with the simple unification scheme in whichradio compact quasars are extended ones viewed along radio jet, for which the relativistic beamingenhances the core radio emission and as such the total radio power (Wills & Browne 1986; Hough& Readhead 1988; Barthel 1989; Falcke et al. 2004) when the projection effect would make theapparent size smaller. Within such a scheme, the unresolved core is enhanced because of thebeaming effect. That the lobe-dominated quasars are more luminous in radio seems to contradictthis model. However, there are at least two selection effects that make the average radio power inthe core-dominated sources smaller. 11 –First, as we showed in the last section that the peak brightness of radio lobe component iscorrelated with radio power, and the FIRST will not be able to detect the lobe component in lessradio power sources, especially at high redshift (see also Fig.2). Second, if most of core-dominatedquasars are intrinsically radio weaker (Wang et al. 2006) and if the radio luminosity function ofthem is steep, their average apparent luminosity can be lower even if the radio power had beenboosted.The relative number density of the extended and compact sources also suggests that majorityof compact sources are either of beamed, intrinsically much weak radio quasars or intrinsicallycompact radio sources, such as CSS (Compact Steep Spectrum Objects) or GPS (GigaHertz PeakedSources). With typical Lorentz factor of 10-15 for jets in FR-II radio quasars, the boosted emissioncan be viewed in only relatively small fraction of solid angle between the line of sight and the jet, θ < ◦ , whereas at other angles the core is weakened due to Doppler effect. If the power of theun-beamed radio cores is near 0.005 of that of the lobes, as determined for 3CR sources (Urry &Padovani 1995), and if the intrinsic radio loudness distribution following Cirasuolo et al. (2003b) ,and with the luminosity distribution as DR3 quasar sample, we can estimate that ∼
62% beamedintrinsic radio quiet sources could be detected by FIRST. Since GPS and CSS are all powerfulradio sources, it is likely most of these compact quasars are beamed radio intermediate quasars asproposed by Falcke et al. (1996)Our results suggest that lobe-dominated sources are not particularly reddened, in agreementwith the finding by de Vries et al. (2005). This is valid even for quasars without detectable radiocore at flux down to the FIRST limit. The line of sight does not intercept the dusty torus in thoselobe-dominated quasars. However, Backer et al. (1997) found that most lobe-dominated quasarsin the Molonglo quasars are reddened by A V ≃ −
4, and CSSs are most reddened. It should bepointed out that quasars reddened by this amount cannot be found in the ‘color’ selected sample,in particularly at high redshift due to strong attenuation in ultraviolet. The slightly bluer colorfor lobe-dominated quasars in this sample could be due to inclusion of CSS-like objects in thecore-dominant objects or due to a selection effect by which reddened ”extended” radio quasars arelost. If Baker (1997) is correct, we might miss a large number of heavily reddened lobe-dominatedquasars. Although most such quasars are likely below the magnitude limit of spectroscopic quasarsample, in principle the FIRST selected sample is able to detect some of such reddened quasars,particularly in the low redshift if a weak core is present. We look at the spectroscopic sources thatselected as FIRST sources only, and find that the FIRST-only selected spectroscopic sources areindeed much redder. But the fraction of quasars with extended lobes in FIRST-only sources is verylow( ∼ . REFERENCES
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15 –Fig. 1.— Top two panels: FIRST images of typical FRII-type radio quasars. Bottom two panels:the FIRST images of the multi-component radio quasars. 16 –Fig. 2.— Left panel: The distance of the furthest radio lobe to the quasar versus the total radiopower for extended radio quasars. There is no apparent correlation. Right panel: The intrinsicpeak brightness of resolved lobes versus the total radio power (defined as P tot ) for extended radioquasars.Fig. 3.— Left panel: The redshift distribution of optical selected radio quasars in our sample (greenline) and of all optical selected DR3 quasars in Schneider et al. (2005) (red line). The dot-dashedline shown the ratio of optical+radio quasar to all optical selected quasars. Right panel: Theredshift distribution of extended radio quasars (green line) and compact quasars (red line). Andthe dot-dashed line shown the fraction of extended quasars to all radio quasars. Obviously theratio drops as redshift increases up to z=2.5. 17 –Fig. 4.— Top left panel: The distribution of log( f NV SS /f F IRST ) . The green line represents thesources with FIRST flux above the 3 mJy limit, and the red line with FIRST flux below the 3 mJylimit. The FIRST flux is the sum of all radio sources within NVSS beam size. Top right panel:The flux distribution of extended sources (green line) and compact sources (red line). The verticaldot-dash line marks the 3 mJy flux. Bottom panel: The NVSS-SDSS offset distribution of the”selected” matches and ”rejected” matches in 20 " matching radius. 18 –Fig. 5.— Left panel: The accumulated fraction of sources with nearest FIRST counterpart withincertain matching radius. The solid line represents the lobe-dominant sources and the dashed oneall the radio quasars. Right panel: The distribution of flux ratio q . q defined as the flux ratio of”core” component (the radio counterpart within 2 " ) to the total radio flux (summation over allradio counterparts that associate to the radio quasar).Fig. 6.— Left panel: The intrinsic brightness of the lobes versus redshift. The solid line representsthe surface brightness at the detection limit as 0.75 mJy/beam. Right panel: The physical sizeof extended sources at different redshift. The size is the physical distance of the furthest radiocomponent associated with the quasar. The solid line marks the minimum distance that can beresolved in the FIRST survey at the corresponding redshift (on scales down to ∼ / . ′′ g − i color distribution for quasars with redshift 0 < z < σ scatter around the average.Fig. 9.— The radio luminosity (left panel) and the radio loudness ( f . GHz /f A in rest frame,right panel) distributions. The green line represents for extended radio quasars, and the red linefor compact radio quasars, and the black line for all radio quasars. 21 –Fig. 10.— The left panel: The conditional radio loudness distribution for compact sources and forall cores (component within 2 arcesec offset from quasar. the orange line and red line representcompact sources and cores with 15 < m <
19, the blue and purple line represent compactsources and cores with 19 < m <
21. The right panel: conditional distribution of extendedsources with 15 < m <
19 (dashed line) and 19 < m <
21 (solid line).Fig. 11.— The radio loudness distribution of the compact (left panel) and extended (right panel)sources below certain redshifts, the descending lines for z < , z < , z < . , and z < ..