Continuum Radiation from Active Galactic Nuclei: A Statistical Study. 

(NASA-CE-179925) CONTINUUM RAEIEATXON FROH M87-13368 ACTIVE: GALACTIC NUCLEI: A SIBIISZICAL STUDY 

{Eeunsylvania State Uciv.) 81 p CSCL 03B 

Unclas 

63/90 44659 

192 \\ 

Takashi Isobel and Eric D. Feigelson , 

Kulinder P. Singh , 

AND 

Ajit Kembhavi . 

334 

4 

Rece ived ; accepted 

1. Department of Astronomy, The Pennsylvania State University. 

2. NSF Presidential Young Investigator. 

3. Danish Space Research Institute. 

4. Tata Institute of Fundamental Research. 
t 

ABSTRACT 

The main purpose of this study is to gain insight into physics of the 

continuum spectrum of active galactic nuclei (AGNs) using a large data set and 

rigorous statistical methods. 

which include radio selected quasars, optically selected quasars, X-ray 

selected AGNs, BL Lac objects and optically unidentified compact radio 

sources. Each object has measurements of its radio, optical, X-ray core 

continuum luminosity, though many of them are upper limits. 

sources have extended components, we carefully select out the core component 

from the total radio luminosity. With 'survival analysis' statistical 

methods, which can treat upper limits correctly, these data can yield better 

statistical results than those previously obtained. 

We have constructed a database for 469 objects 

Since many radio 

A variety of statistical tests are preformed, such as the comparison of 

the luminosity functions in different subsmples, and linear regressions of 

luminosities in different bands. Interpretation of the results leads to the 

following tentative conclusions: (1) The main emission mechanism of optically 

selected quasars and X-ray selected AGNs is thermal, while that of BL Lac 

objects is synchrotron; (2) radio selected quasars may have two different 

emission mechanisms in the X-ray band; (3) BL Lac objects appear to be special 

cases of the radio selected quasars; (4) some compact radio sources show the 

possibility of SSC in the optical band; and (5) the spectral index between the 

optical and the X-ray bands depends on the optical luminosity. 

-2- 
I. INTRODUCTION 

One of the most important problems in the studies of active galactic 

nuclei (AGNs) is understanding the mechanisms of underlying continuum 

emission. Although there are already very many observations of AGNs across 

the whole range of spectrum, and the knowledge of properties of AGNs has been 

improving considerably, we still do not understand the fundamental emission 

mechanisms. 

combinations of several mechanisms, including both thermal and non-thermal 

processes. 

radiation. For some objects like BL Lac objects, the synchrotron spectrum 

clearly extends to optical region and perhaps to the X-ray band. On the other 

hand, most of optically selected quasars do not show radio emission and have 

unpolarized continua. 

bumps that are not well understood. 

combinations of unpolarized synchrotron, bremsstrahlung from an accretion 

disk, dust emission, stellar photospheric emission, or Compton scattering by 

thermal or non-thermal electrons; In the X-ray band, synchrotron self-Compton 

(SSC) is one of the more popular models, though multi-temperature 

bremsstruhlung is also probable. 

The continuum emission spectrum distributions probably arise from 

The radio emission is thought to be incoherent synchrotron 

The infrared to ultraviolet regions often have spectral 

The emission mechanisms may be 

Since the Einstein Observatory has provided high quality X-ray 

observations, statistical studies of AGN continua are flourishing (Ku, 

Helfand, and Lucy 1980; Zamorani et al. 1981; Owen, Helfand, and Spngler 1981; 

Owen and Puschell 1982; Kriss and Canizares 1982; Reichert et. al. 1982; 

Zamorani 1982; Avni and Tananbaum 1982; Blumenthai, Keel, and Miller 1982; 

Kembhavi and Fabian 1982; Schwartz and Ku 1983; Ledden and O'Dell 1983; 

Tananbaum, Wandle, and Zamorani 1983; Katgert, Thuan, and Windhorst 1983; 
Marshall et al. 1983; Bregman 1984; Maccacaro et al. 1984; Henriksen, 

Marshall, and Mushotzky 1984; Cruz-Gonzales and Huchra 198rC; Miller 1984; 

Marshall et al. 1984; Ledden and O'Dell 1985; Kriss and Canizares 1985; Stocke 

et al. 1985; Franceschini, Gioia, and Maccacaro 1986). Considerable attention 

has been focused on the evaluation and interpretation of the average opticalto-X-ray spectral index, <a >, for various samples of AGNs. These finding 

are briefly summarized in Table 1. The <a > values have been used, for 

example, to infer that radio-selected quasars are several times more X-ray 

luminous than optically selected quasars (Ku, Helfand, and Lucy 1980, Zamorani 

et al. 19811, that the broad band spectral index evolves with redshift in 

radio-quiet quasars (Ku, Helfand, and Lucy 1980, Zamorani et al. 198l), and 

that high polarization quasars and BL Lac objects have similar continuum 

shapes (Ledden and O'Dell 1985). 

ox 

ox 

In addition to the comparison of broad and spectral indices, statistical 

correlations between radio, optical, and X-ray emissions in AGNs have also 

been studied by the previous workers. Ku, Helfand, and Lucy (1980) show a 

general correlation between radio and X-ray emissions in quasars, which was 

confirmed and refined in our examination of radio-loud quasars (Kembhavi, 

Feigelson, and Singh 1986; hereafter Paper 11). The close correlation between 

optical and X-ray luminosities in Seyferts and quasars has been established by 

a number of workers (e.g. Reichert et al. 1982, Blumenthal, Keel, and Miller 

1982, Kriss and Canizares 1983, Kriss and Canizares 1985). Zamorani (1984) 

and Ami and Tananbaum (1986) have examined the relations between the spectral 

index a and optical luminosity and redshift, and Zamorani (1984) has raised 

the possiblllty that the quasars X-ray'lminosities are slmultaneously 

correlated with their radio and optical luminosities. 

ox 

-4- 
. Some researchers have expressed a reluctance to examine directly the 

correlations between luminosities at different spectral bands for fear of 

encountering spurious correlations, as all luminosities for a given object are 

scaled by the same (distance)* factor. 

distance-dependent effect occurs if all objects are considered, including 

those not detected (Feigelson and Berg 1983 and Paper 11). 

this study has been undertaken is that powerful and well-established 

statistical techniques are now available that fully account for the presence 

of upper limits in luminosity-luminosity diagrams (Feigelson and Nelson 1985, 

Isobe, Feigelson, and Nelson 1986). 

We have shown, however, that no such 

A major reason 

The present study represents an improvement upon previous studies in 

three respects. First, following Paper 11, we take particular care to 

consider CORE radio emission rather than TOTAL radio emission from each AGNs. 

The total radio flux frequently includes jets and lobes, which does not 

reflect the current state of activity in the nucleus. While this distinction 

is small for some classes of AGNs (e.g. radio selected BL Lac objects), it is 

a considerable correction for others (e.g. 3C and 4C quasars). Note that our 

earlier VU observations (Feigelson, Isobe, and Kembhavi 1984; hereafter Paper 

I) were specifically designed to acquire radio core fluxes for this study. 

Radio observations from certain optically selected quasars not presented in 

Paper I, are now presented in 0 11. Second, we analyze a much larger number 

of objects than earlier studies by virtue of having collected most or all of 

the extant literature. The database (0 111) includes all AGNs (except for 

certain classes, such as Seyfert galaxies and radio galaxies, where the data 

suffer significant anbigilities) for vhlch radio core, optical and X-ray 

observations have been reported. All upper limits are included. Third, we 

use the wide variety of statistical methods provided by 'survival analysis', 

-5- 
the field of applied statistics developed over several decades to solve 

problems involving upper limits in medical and industrial situations. These 

methods are reviewed in 8 IV; the reader is encouraged to examine Feigelson 

and Nelson (1985) and Isobe, Feigelson, and Nelson (1986) for more details. 

Applying these statistical methods to the database in § 111, we calculate the 

correlations and linear regressions between X-ray, optical, and radio 

luminosities. We also investigate several specific issues: (1) The dependence 

of optical to X-ray spectral index on the optical luminosity and the redshift; 

(2) a proposed two-component model for X-ray emission of the radio selected 

quasars; (3) a comparison of the BL Lac objects with the radio selected 

quasars; and (4) a comparison of the optically selected quasars with the X-ray 

selected AGNs. The results from these investigation and their interpretations 

are presented in § V. 0 VI summarizes the whole study. 

-6- 
11. RADIO OBSERVATIONS 

Although most of the data are drawn from the published literatures, we 

have made two sets of observations with the NEUO Very Large Array (VU) to 

improve the quality of radio data on certain AGNs with measured X-ray 

1 

luminosities. 

The National Radio Astronomy Observatory is operated by Associated 

Universities, Inc., under contract with the National Science Foundation. 

On 23-24 October 1982, thirty-six optically selected quasars with X-ray 

properties measured by Ku, Helfand, and Lucy (1980), or Zamorani et al. (1981) 

were observed at the VU. These radio quiet quasars were observed at the same 

time as the radio loud quasars discussed in Paper I. The array was in the 

standard B configuration and 26 antennas were operating. 

given in Table 2a. Twenty-eight quasars were not detected with 5 x rms upper 

limits around 1 mJy, and 8 quasars were detected with flux densities between 

0.8 and 40.5 mJy. Of these, four were not (to our knowledge) previously known 

The results are 

radio sources, including the comparatively bright quasars GQ Com and V396 Her. 

In the second set of VLA observations, we observed the X-ray selected 

AGNs from the serendipitous Einstien IPC sample of Kriss and Canizares (1982). 

The observations were performed along with the survey of discussed by Gioia 

et al. (1984) on 28-30 November 1981 with the VLA in the C configuration. The 

results are given in Table 2b. Data for one object in the sample, 0514-003, 

were not good. Snapshots of -12 minutes duration gave 5 x rms upper limits 

around 0.7 mJy for 21 of the sources. Three are detected, one of which 

(1401+085, 2-0.43, S -18.8 dy) is quite radio luminous. 5 

-7- 
. 

I I I. DATABAS E 

This study is base on the radio, optical and X-ray luminosities of a 

variety of AGNs given in Tables 3, 4, and 5. In Table 3, we show data on the 

radio selected, optically selected, and X-ray selected samples of emission 

line AGNs. Data on BL Lacertae type objects are shown in Tables 4a and 4b. 

Table 5 includes optically faint or undetected AGNs for which redshifts 

measurements are not available. 

The database I however, excludes certain classes of AGNs for which 

unambiguous radio cores, optical magnitudes or X-ray data are not available. 

Few Seyfert galaxies have optical core magnitudes reported separately from the 

host galaxy brightness, and their radio structures are frequently complex so 

that the core is not readily discriminated from ejecta (e.g. Ulvestad and 

Wilson 1983). 

the diffuse X-ray of the surrounding intercluster medium (Feigelson and Berg 

1983), and again optical core magnitudes are usually not available. The PG 

sample of bright optically selected quasars (Schmitt and Green 1986, Tananbaum 

et al. 1986), the Braccesi and other fields of faint optically selected 

quasars (Braccesi et al. 1970, Marshall et al. 1984) have X-ray observations, 

but sensitive radio measurements have yet to be published. 

samples have therefore been omitted from our study. 

Radio galaxy nucleus X-ray emission may be often confused by 

All of these 

Data in Tables 3 and 4 are organized as follows: Column 1 lists the 

source by its Right Ascension and Declination. 

name from the various radio and optical surveys. Column 3 gives the redshift 

values taken from the X-ray literature, if available, or from other sources 

described in the Notes to Tables 3 and 4. In column 4, we give the radio core 

luminosities for the sources. The luminosities are cnmpi-i.ted wir?g the 

Column 2 gives the catalog 

-8- 
following formula: 

I- 4~ dR 2 f (l+z) (a-1) , 

where a is the spectral index within the appropriate spectral band (f-v-a), 

and f is 

distance 

where we 

the observed flux density, z is the redshift and dR is the luminosity 

given by 

cz (1+- l+Z) 

2' d =- 

I Ho 

assume a Hubble constant HO= 50 Mpc/km/sec and qo==O. For the radio 

core emission, we assume the spectral index within the radio band, a -0. 

Since many radio selected quasars have extended components, we use the 

following procedure to find the core luminosity density at 5 GHz: 

i) If a map that 

available, the core flux density is used. If the map is not at 5 GHz, the 

core spectral index is assumed to be 0.0, 

ii) If the source is fully resolved and the core is not detected, we use an 

upper limit given in the literature. 

density of the weakest component is used as an upper limit. 

iii) If an interferometric map is not available, but the source is seen by 

single dishes and the spectral index between 1.4 GHz and 5 GHz is less than 

0.3, the entire flux density given for the object is assumed to be the core 

flux density. 

iv) If single dish data are available, and the spectral index is steeper than 

0.3, the 5 GHz flux density given for the object is treated as an upper limit, 

even if it is detected. This is because of the probable existence of extended 

components. Although a distribution of the upper limits set by this procedure 

may not be same as that of the upper limits due to the flux Ilmited 

observation, we assume that all upper limits belong to a same population. As 

discussed in Paper 11, even such careful efforts to isolate radio core fluxes 

r 

clearly resolves the core from any jets or lobes is 

If an upper limit is not given, the flux 

-9- 
;- 

can 1eave.a residual - 50% extra flux from VLBI scale jets. 

The majority of optically selected quasars and X-ray selected AGNs are 

not detected in the radio band. Those that are detected are generally faint 

and unresolved, and their flux is assumed to arise from a core with Q -0.0. 

Cases where the radio measurement, either detection or upper limit, was made 

r 

at 2.7 GHz or 1.4 GHz rather than 5 GHz are marked by a * or + in Table 3. 

The optical luminosities are given in column 5. For optical emission, 

the spectral index within the optical band, a -1.0, is assumed. Visual 

magnitudes are mainly taken from Hewitt and Burbidge (1980). 

magnitudes are converted to the optical luminosity density at 2500 A according 

to Zamorani et al. (1981), 

0 

The visual 

log(RO)-37.878 + 2*10g[~(l<)] - 0.4V +- 0.072 

corr sin(b)' 

where V 

corr 

1968), and the last term is a correction for galactic absorption, where b is 

the galactic latitude. If only a blue magnitude is available, the equation is 

modified as 

is the visual magnitude corrected for MgII line emission (Schmidt 

log(~0)-38.011 + 2*log[z(l$)] - 0.48 + 0.072 

corr sin(b)' 

where Bcorr is the corrected blue magnitude from Schmidt. If a redshift is 

not available, an optical flux density at 2500 A at the observer's frame is 

computed to find a and a 

ro ox ' 

0.072 

log(fo)L19. 756 - Os4' + sin(b) 

For some compact radio objects, since only red magnitudes are available, we 

need to change the constant in the last equation to -19.521 (Johnson 1966). 

Column 6 lists the X-ray luminosities computed for the 0.5-4.5 keV energy 

range in the emitting frame and assuming the spectral index within the X-ray 

band Q -0.5. The X-ray data are obtained mostly from the observations with 

the Einstein Observatory, although some data from observations with the HER.0-1 

X 

- 10 - 
satellite are also included. If the X-ray luminosity in the above energy band 

already exists, then it is adopted directly, else it is calculated from the 

observed flux in the 0.5-4.5 keV energy band according to the fomulae given 

after Table 5. Column 7 lists the radio spectral index of the core wherever 

the measurement exists. 

The values for the spectral index (a ) computed between the radio (5 ro 

GHz) and the optical 

column 8. 

(2500 A) bands in the emitting frame are listed in 

These values are calculated using the following expression: 

a -(logRr - logRo)/5.38. ro 

If the redshifts are not available, we use the flux densities instead of the 

luminosities. The spectral index (aox) between 2500 A and 2 keV emission is 

given by 

a -(logRo - log1 - 17.98)/2.61. ox X 

The values for a are listed in column 9. Column 10, 11, and 12 list the 

references for the radio, optical, and X-ray data respectively. 

ox 

Although not shown as separate tables, a few other subsamples are used. 

For some statistical problems, we use spatially resolved radio selected 

quasars, unresolved radio selected quasars with flat (a <0.3), and steep 

(a >0.3) spectra. 

r 

These samples are discussed in detail in Paper 11. 

r 

Comparison of our data calculated luminosities, a and a values to 

ro ox 

previous collection of continuum emission in AGNs, such as Ku, Helfand, and 

Lucy (1980), Zamorani et al. (1981), and Ledden and O’Dell (1985), shows 

relatively good agreement. One relatively large discrepancy is the radio 

luminosity, since we use the core instead of the total luminosities. The 

difference in the radio luminosities often reachs an order of magnitude 

difference. Because of this, the spectral index between the radio and optical 

- 11 - 
often show large differences from other studies. This may be due to their 

high degree of variability. 

There are several possible sources of error in the database. First, data 

are collected from variety of references and may be differently treated in 

each reference. Second, and related to the first point, uncertainty arises 

when a source is variable and observations are not done simultaneously. 

Third, some error is caused by the extrapolation of published data with fixed 

spectral indices to compute luminosity densities at consistent wavelength in 

the emitting frame. For example, this may be an important error source for 

the optical luminosity density, since we do not consider the effect of 3000 A 

bump and other effects in W region. 

sources in VLA maps as cores, VLBI observations often show that the cores can 

be resolved to further small scale. 

density may be systematically overestimated. Some small errors also arise 

from assuming a specific cosmology. 

affect correlations, the cosmological constant q does. 

Fourth, although we use point radio 

Therefore, the core radio luminosity 

Although the Hubble constant Ifo does not 

0 

Based on comparisons of luminosities with previous studies and our 

estimation of the size of these possible sources of error, we find typical lo 

uncertainties of f0.2 in log(R ), log(Ro), and log(Rx). Although these error 

sources may seem large, uncertainties of less than 0.5 in log form are not 

very significant, since the ranges of 

r 

6 and R are frequently 10 . RrI lo, X 

- 12 - 
TV i STATISTICAL METHODS 

Since the data set contains many upper limits, survival analysis must be 

used to treat the data correctly. 

lifetime data, is developed over several decades to deal with problems arises 

in clinical epidemiology, actuarial science and industrial reliability, where 

'censored data' (i.e. upper or lower limits) frequently arise. The methods 

are typically extensions of parametric (e.g. least square regression) or nonparametric (e.g. Kolmogorov-Smirnov or Mann-Whitney tests) statistical tools 

used for uncensored data, and frequently involve maximum-likelihood concepts. 

Most of the procedures we use in this study are described by Feigelson and 

Nelson (1985) and Isobe, Feigelson, and Nelson (1986). The former study 

treats problems involving one variable: the Kaplan-Meier estimator is the 

maximum-likelihood estimator of the luminosity and gives a mean luminosity and 

a standard deviation for a sample; the Gehan and logrank tests measure whether 

two subsamples are drawn from a same parent population. The latter study 

treats correlation and regression between two variables: Cox regression and 

the generalized Kendall's r test (the BHK method) which measure the degree of 

independence; the EK algorithm and Buckley-James methods perform linear 

regression on the data, 

Survival analysis or the analysis of 

One new method is used in this study. Previously, we could not fit a line 

on a data set which contains upper (or lower) limits in both independent and 

dependent variables, except by Schmitt's (1985) method which does not provide 

analytic estimates of the uncertainties for the regression parameters. Using 

the BHK method described by Isobe, Feigelson, and Nelson (1986), we have 

developed a method to find a slope coefficient and uncertainty. 

database in two variables (X, Y,) with possible non-detections in both 

Consider a 

-c, 

- 13 - 
variables. For a range of slope coefficients b, calculate residuals r.=Y -bXi. 

The value of b that minimizes the generalized Kendali's T rank correlation 

coefficient between the r and X is the most probable value. 

ii 

The la 

uncertainties can be obtained by finding the slope coefficients which give 31% 

of the maximum probability. 

Kaplan-Meier estimator. First, get the residuals r with the best slope 

coefficient b. The best estimate of the intercept coefficient is the KaplanTo find the intercept coefficient, we use the 

Meier mean of the residuals. This combination of survival analysis methods on 

doubly censored data may permit parameter estimation for non-linear models as 

well. We use it in 0 IV to test a two-component model of quasar X-ray 

emission. 

censored data sets by statisticians (Sen 1968, Efron 1984, Lancaster and Quade 

1985), there is no statistical study for censored data sets yet. From our 

Although similar procedures have been already suggested for nonexperience, however, the resulting regression coefficients are quite 

satisfactory when compared to those obtained by other methods. 

Using these survival analysis techniques, we analyze our database. Cox 

regression and the BHK method are used to compute the correlation 

probabilities between the radio, optical, and X-ray luminosities, and the EM 

algorithm and Buckley-James method (and the new linear regression method, if 

needed) are used to calculate the linear regression coefficients (0 Va). The 

mean values of the spectral indices are calculated by Kaplan-Meier estimator 

(8 Vb). Multi-dimensional linear regression among the optical luminosity, the 

redshift, and the spectral index between the optical and the X-ray bands is 

discussed in 0 Vc. The new regression method is applied to analyze the twocomponent model for the X-ray emissior. of the radio selected quasars (§ Vc). 

For the comparison of the BL Lac objects and the radio selected quasars, and 

the comparison of the optically selected and the X-ray selected AGNs, the two 

- 14 - 
sample tests (Gehan and logrank tests) are used (5 Ve,f). 

- 15 - 
V. STATISTICAL ANALYSIS AND INTERPRETATION 

We now proceed to investigate a number of statistical relations between 

the Rr, lo, and R 

Most of the relationships are illustrated in Figures 1 to 3, which plot the 

values listed for the various samples in Tables 3 to 5. 

X 

luminosity densities against each other, and Figure 4, which plots the 

interband spectral indices a vs. a . The plots are displayed so that the 

various subsamples can be easily distinguished. 

ox ro 

All data lie in the range of 29 < log(Rr) < 37, 28 < log(R ) < 33, 42 < 

The radio quasars tend 

0 

log(Rx) < 48, -0.3 < aro < 1.2, and 0.8 < aOX < 1.9. 

to occupy higher and relatively wider range (six decades for radio, four 

decades for optical and X-ray). 

radio quasars. 

magnitude weaker than the radio quasars. 

range as the optically selected quasars do. The X-ray selected BL Lac objects 

are few in number and occupy only two decades in any luminosity; hence we will 

not be surprised if significant statistical results are not obtained. 

BL Lac objects occupy similar range as the 

The optically selected quasars are usually one order of 

The X-ray selected AGNs occupy same 

a) Correlations and Linear Regressions between AGN Luminosities 

Using Cox regression and the BHK method, we establish the significance 

level of correlations between radio and X-ray luminosities, optical and X-ray 

luminosities, optical and radio luminosities, and a and a for all 

subsamples described in 0 111. Quantitative results are shown in Table 6a. 

The first column lists the name of the samples and the second column lists the 

ro ox 

correlations tested. The third column shows the total number of the objects 

- 16 - 
numbers of data points which are censored in the independent variable only, 

the dependent variable only, and both the variables, respectively. The fifth 

and sixth columns show the correlation probabilities by Cox regression and the 

BHK method; This is the probabilities that the two variables are not 

correlated with each other. The last column identifies the corresponding 

figure. Except for some spectral index correlations, all subsamples show high 

significant level between all spectral bands. For example, even the optically 

selected quasars show a highly significant correlation (P<O.Ol%) for the radio 

and X-ray luminosity relation: 

Although we find very high significant levels for nearly all 

correlations, it is difficult to tell which correlations are intrinsic and 

which correlations are secondary. For a completely detected data set, we can 

use a partial linear correlation method and a partial rank correlation, but 

these methods cannot treat a censored data set. Using the generalized 

Kendall’s 7 correlation coefficient, we may be allowed to use a normal partial 

rank correlation formula, but since a partial rank correlation is distribution 

free, we cannot get significant levels. We show the partial correlation 

coefficients results 

qualitative examintion. 

shown in Table 7, but they can be used only for 

For the radio selected quasars, the optical / X-ray relation is most 

significant (r-0.45, where r is the partial correlation coefficient in Table 

7) and the radio / X-ray relation is also important (r-0.42), but the optical 

/ radio relation may not be significant (r-0.13). For the optically selected 

quasars and the X-ray selected AGNs, the optical / X-ray relation is most 

important and two other relations may not be significant. For the radio 

selected BL Lac objects, the radio / X-ray relation is most significant and 

the optical / X-ray relation is moderately significant, but the optical / 
radio relation is weaker. For the X-ray selected BL Lac objects, the optical 

/ X-ray relation is most important, and the optical / radio relation is 

moderately important, though because of small size of the data, this finding 

may not be accurate. We thus find that the Ro / Rx relations are typically of 

greatest importance, with the I / R and R / I relations important only in 

certain subsamples. 

rx r 0 

The linear regressions are done mainly by the EM algorithm which assumes 

the luminosities are distributed in a Gaussian distribution about the best fit 

line, and the Bukley-James method, which makes no assumptions regarding the 

distribution of residuals. Since the relation between log(l ) and log(R ) 

contains upper limits in both variables in the same subsamples, the new method 

described in 0 IV is used to compute coefficients. Quantitative results are 

shown in Table 6b. 

second column lists the independent and the dependent variables. The third 

column shows the total number of the objects and the forth column lists the 

number of censored data. The fifth and sixth columns show the linear 

regression results by the EM algorithm and Buckley-James method respectively. 

The first row in the each set shows the intercept coefficient, the second row 

shows the slope coefficient, and the last row shows the standard deviation. 

If only one set of the result appears, the regression was done by the new 

method described in the 0 IV, or by a normal least square method, if there are 

no censored data, For example, the radio selected quasars have the linear 

regression form, log(Rx)=29.0+(0.48~0.06)log(~ ). This best fit line is shown 

in Figure la. 

r X 

The first column lists the name of the samples and the 

r 

The linear regressions can be summarized as follows. The radio/X-ray 

correlation is about R aRo*5 for quasars of all types but.is significantly 

steeper (R,aR!*8) for BL Lac objects. 

xr 

The optical/X-ray correlation behaves -I L 

- 18 - 
similarly (RxaR:" for quasars compared to R all'' for BL Lacs), though the 

xo 

X-ray selected AGN subsample does not fit the pattern. 

correlation is RraRi*o for the radio and the optical quasars as well as the BL 

Lac objects, but, as stated above, may be an indirect consequence of the l 

and Ro/lx correlations. The correlation is present in X-ray selected AGNs and 

the X-ray selected BL Lac objects, but they have very different forms from the 

others. 

The radio/optical 

JlX 

A plausible theoretical interpretation of these results might be as 

follow. First, the results of partial correlation analysis (strong 

correlation between R 

optically selected quasars and the X-ray selected AGNs, the thermal emission 

(e.g. bremsstrahlung, Comptonization) is the dominant mechanism. The thermal 

emission scale according to I a& (0*7'0'1). 

(1983) and Schlosman, Shaham, and Shaviv (1984) for the thermal emission from 

accretion disks. 

correlation between R and I non-thermal emission is most important. The 

non-thermal emission may have the form of R aRr *'O'l). Third, for the radio 

selected quasars, the X-ray emission depends on both the radio and optical 

emissions. 

emission mechanisms (see 8 Vd for the further disccusion). 

and Rx but not between R 

0 r 

and Rx) suggest that for the 

This form is predicted by Tucker 

xo 

Second, for the BL Lac objects, because of the strong 

r X' 

X 

The result indicates that there are possibly two different X-ray 

b) Mean Values of the Spectral Indices 

The relation between the interband spectral indices are shown in Figures 

4a to 4e with quantitative results given in Table 8. All mean values and 

standard deviations were calculated using the Kaplan-Meier estimator (0 IV). 

As expected from simple selection effects, <a > is relatively large in the 

ro 

- 19 - 
radio selected quasars and BL Lac objects, and <aox> is relatively large in 

the optically selected quasars. 

sources show <a > - 0.5 and <a > > 1.0. On the other hand, the compact 

radio sources show <a This means that one power law with 

a-1.0 can express the entire emission between the radio and X-ray bands for 

this subsample. Close examination of Table 5 also tells that some objects may 

have <a > > <a >. Since this relation cannot be readily produced by thermal 

or the synchrotron processes, this may be direct evidence for the SSC model 

operating in the optical to X-ray bands. 

All subsamples except the compact radio 

ro ox 

> - <aox> - 1.0. 

ro 

ro ox 

In Table 1, we summarized published values a and a from recent 

ox ro 

literature. A comparison with our results shows that although they are not 

exactly the same as our values, they agree reasonably well. For the BL Lac 

objects, our results are very similar to Ledden and O'Dell's (1985) results 

because of the similar database. We note, however, substantial differences 

among different studies of optically selected quasars, ranging from <a 

2 0.10 (Marshall et al. 1983) to <aox>11.65 f 0.03 (this study). 

Marshall et al. treat lower luminosity objects, this may cause the difference 

as we can see in an other study (Zamorani et al. (1981) find for radio quiet 

quasars that a 

log(Ro)>31.4). 

different optical magnitudes (i.e. not those of Hewitt and Burbidge 1980), 

frequences at each band (Owen, Helfand, and Spangler 1981, Cruz-Gonzales and 

Huchra 1984), selection criteria (Zamorani et al. 1981), correction factors 

for absorption and MgII line (Margon, Domes, and Chanan 1985), and different 

spectral indices assumed for extrapolations. 

h1.37 

ox 

Since 

=1.37+0.05/-0.08 for log(Ro)<31.4 but aox -1.62+0.08/-0.11 for 

Other possible causes for discrepances are the use of 

ox 

- 20 - 
c) Luminosity Ratio Dependence on Optical Luminosity and Redshift 

The dependence of a on optical luminosity and/or redshift for the 

ox 

optically selected quasars is often discussed (Reichert et al. 1982, Ami and 

Tananbaum 1982, Zamorani 1982, Maccacaro and Gioia 1983, Zamorani 1984, Kriss 

and Canizares 1985, Avni and Tananbaum 1986). Avni and Tananbaum (1982) were 

the first to obtain a relation among them using survival analysis (the 

"detection-and-bounds1' linear regression method, see Avni and Tananbaum 1986). 

Their relation is expressed as 

a ox =(-0.0+0.3)(~-0.5)+(0.12~0.06)[1og(Ro)-30.5]+1.50, 

where 7 = z/(l+z). They mention that explicit dependence of a on the 

optical luminosity is predominant, but the joint dependence of a on both 

variables is possible. 

and Tananbaum 1986). 

ox 

ox 

This result is confirmed in a more recent paper (Ami 

Zamorani (1982) shows a similar relation for a combined sample of 

optically selected quasars and Seyfert galaxies. 

the redshift, Zamorani (1984) finds 

Ignoring the dependence on 

. a -0.129 10g(L0)-2.427. 

In another subsample, Tanambaum, Wandle, and Zamorani (1983) find a similar 

ox 

relation for radio selected quasars (the 3CR sample), 

10~(~~)~27.63+(0.47+0.15)[10~(~~)-31.20]~(0.14~0.12)[10~(~ )-34.781 

- (0.45kO. 78) [ log( l+z)-O. 261 . 

r 

Because of the weak dependence on the radio luminosity and the redshift, they 

rewrite this relation as 

a =0.20 iog(jO)-4.98. ox 

We look for analogous relations in our data sets; the results are shown 

in Tables 9a and 9b. In Table 9a, we show the relations between a and T and 

ox 

- 21 - 
.. 

between a and log (lo). Assumed regression forms are a -a+b7 and 

a -a+blog(l 1. We find the log(R ) - a slope to be 0.11 f0.02 for radio 

selected and optically selected quasars. 

show high significance levels for both the redshifts and the optical 

luminosity regressions. These relations, however, might be artificial, since 

for the optically selected quasars, the optical luminosity is biased due to 

optical magnitude limited survey. 

selected quasars agrees with the results by Ku, Helfand, and Lucy (1980) and 

Zamorani et al. (1981) (see Table 1). 

ox ox 

ox 0 0 ox 

Only the optically selected quasars 

The direction of evolution of the optically 

We also compute the three dimensional regressions for a 7, and 

ox 

log(R ), using the regression form of Ami and Tananbaum (1982). The results 

are shown in Table 9b. The second column shows Cox probabilities. The first 

value is a joint probability that no correlation exists between a 

redshift and log(Ro), the second value is the probability for the redshift 

alone, and the third is for optical luminosity density alone. The second and 

third values are determined assuming the ratio of the slope coefficient and 

the error is distributed as a Gaussian. 

results. All subsamples, except the X-ray selected BL Lac objects (P-23%), 

show highly significant joint probabilities (P I 0.01%). 

selected quasar sample does not show significant correlations for the 

individual variables (P(z.)-53% and P(10)=42%), even though this subsample is 

the only one which shows high significance levels for correlation between a 

and 7, and a and log(l ). Although this result does not confirm Avni and 

Tananbaum's result which shows that a 

ox 0 

we find similar relations (high joint and individual probabilities) in other 

subsamples. 

0 

and both 

ox 

The third column shows the regression 

Only the optically 

ox 

ox 0 

is positively correlated with log(1 ), 

- 22 - 
The interpretation for the radio selected quasars, X-ray selected AGNs, 

0 

and BL Lac objects is that objects at higher redshifts have higher Rx/R 

ratios, and those with higher optical luminosities have lower R R ratios. 

For example, a typical radio selected quasar at 2-2 will have a R R ratio 

twice that of a similar quasar at 2-0. 

selected quasar with log(R )-32 will have a R 

JO 

x/O 

At a given redshift, a typical radio 

R ratio half that of a similar 

0 x/O 

quasar with log(R )-33. The slope coefficients in Table 9b can be used to 

give analogous results for other subsamples. 

0 

We also examine the dependence of a on an X-ray luminosity and a 

ox 

redshift. 

in Rx as well as a 

and the BL Lac objects. Although the X-ray selected AGNs show a high 

significance level for both the variables, the BL Lac objects do not. 

The results are in Table 9c. Because of the presence of censoring 

we can obtain results only for the X-ray selected AGNs 

ox ’ 

Comparing these three results, we find some inconsistencies. The radio 

quasars, X-ray AGNs, and BL Lac objects show weak positive correlations 

between a and 7 in Table 9a, but strong negative correlations in Table 9b. 

Table 9c shows another problem. In the relations among a 7, and log(Rx), 

the direction of the dependence on 7 is opposite to that of 7 in the relations 

among a on 7, the 

direction should be the same. These inconsistencies suggest that either a 

does not truly depend on 7, or that the evolution is different for the various 

wavebands and subsamples. 

ox 

ox 

7, and log(lo). If there is a real dependence of a 

ox ’ ox 

ox 

d) Two Component Model for X-ray Emission of the Radio Selected Quasars 

Although an important emission mechanism of the radio selected quasars is 

thought to be the synchrotron radiation, the slope of the log(R ) - log(Rx) is r 

- 23 - 
0.77f0.08 much shallower (Ix -1 o'48'o'06) r than that of BL Lac objects (1 xr -1 >, 

whose emission mechanism is almost certainly the synchrotron. 

examination of the plot (Fig. la) shows that the distribution of data points 

A close 

does not follow a straight line. This has been be interpreted as evidence for 

two different types of the radio selected quasars (Owen, Helfand, and 

Spangler 1981, Owen and Puschell 1982, and Zamorani 1984). 

Zamorani (1984) has suggested that there are two different X-ray emission 

mechanisms; for example, a synchrotron component and a thermal component. For 

the relation between R and R (see Fig. la), the emission mechanism of the 

steeper component at high luminosities would be mainly non-thermal, and that 

of the flatter component at lower luminosities would be thermal or a 

combination of the non-thermal and thermal emission. 

r X 

Since if the X-ray 

emission is a thermal origin, the X-ray luminosity is expected to be 

independent from the radio luminosity. This explanation is supported by the 

partial correlation coefficients studied in the 0 Va, since the partial rank 

coefficients between the radio luminosity and the X-ray luminosity and that 

between the optical luminosity and the X-ray luminosity are equally strong. 

The X-ray emission related to the radio luminosity may be a synchrotron or SSC 

radiation because of the similarities to the BL Lac objects, and the emission 

related to the optical luminosity may be a thermal radiation because of the 

similarities to the optically selected quasars. 

dimensional regression model with a form of 

Zamorani adopts a three 

0 br R a1 +Ir, 

b 

xo 

He finds that for the flat spectrum radio selected quasars, bo-0.75 and 

b -0.95, and for the steep spectral radio selected quasars, bo-0.63 and 

b -0.75. Since the survival analysis cannot treat non-linear problems, we 

adopt Zamorani's b-values. Then, using our data set and the application of 

r 

r 

- 24 - 
the BHK method, we find his equations can be rewritten as 

)+21.8, 

log( Rx)-log ( l:*63+3x10-7P0 r * 75)+26. 0, 

-lORO. 95 

r 

respectively. The model seems to fit well; however, we found that the 

computation of b-values heavily depends on a few points and hence the value is 

unstable. 

To judge whether this two component model is needed to fit the data, we 

compare these models to the other simple models. One is a straight line 

(10g(R~)==29.0+0.481og(1~)) and another consists of two straight lines 

(10g(1~)-19.0+0.771og(1~) for log(Rr)>33.77 and log(Rx)-45.0 for 

log(Rr)<33.77). 

components have the same slope coefficient as the BL Lac objects and the flat 

components have a zero slope coefficient. The other coefficients are then 

found using the BHK method. 

The last model is made by assuming that the steeper 

2 Since we do not have either a x -test or an other 

goodness-of-fit test to compare models for censored data, we need to use a 

non-standard method. The Kaplan-Meier estimation of distribution of residuals 

found by subtracting these models from the data is examined. The 25th and 

75th percentiles of the residuals express the dispersion of the data about the 

model. One problem is that these dispersions cannot be translated to 

probabilities, and hence the results are only qualitative. 

We find dispersions of 0.65, 0.63, 0.51, and 0.44 about the straight line 

model, the two straight line model, the flat radio spectra model, and the 

steep radio spectra model respectively. Zamorani's (1984) models are thus 

better than these other models of the X-ray emission for radio selected 

quasars . 

Additional support for these composite models is presented in Paper I1 
unresolved radio quasars. The subsample of the resolved quasars (with 

arcsecond resolution) has a shallower slope (1 

subsample of the unresolved quasars (1 -1 

with a <0.3; see Fig. 3 in Paper 11). These results are confirmed in our 

enlarged data set using survival analysis. 

=1°*35'0'04) compared to the 

xr 

71t0 * O7 for the unresolved quasars xr 

r 

If the X-ray emission mechanism of the resolved radio selected quasars is 

dominantly thermal, and that of the unresolved radio selected quasars is nonthermal, then we can expect a flat slope for the resolved, and a steep slope 

for the unresolved radio selected quasars. 

e) BL Lac Objects 

In our data sets, the radio selected BL Lac objects have a distinct 

position. 

statistical results are free from the selection effect due to the flux limited 

observations. Also because of their nonthermal nature (supported by short 

variabilities, high polarizations, and our partial correlation results), they 

can be used as a standard to which other subsamples are compared. 

Since all the objects are detected in all three frequencies, 

Since the BL Lac objects have no upper limits, the partial linear 

correlation probabilities in Table 7 can be computed to find which relations 

are significant. The partial linear correlation probabilities are 

P(rx,o)<O.Ol%, P(ox,r)-2%, and P(ro,x)=20%, where, for instance, P(ro,x) is 

the correlation probability between the radio and the optical luminosity for a 

fixed X-ray luminosity. 

most significant, and the optical/X-ray relation is moderately significant, 

but the optical/radio relation is not significant. 

The results show that the radio/X-ray relation is 

- 26 - 
*' .' 

Some researchers have pointed out the similarities between the BL Lac 

objects and the radio selected quasars. Using two sample tests, we compare 

these subsamples. First, we use all data in both the samples. The results 

are shown in Table loa. 

selected quasars are higher than those of the BL Lac objects, which is 

probably a consequence of the fact that the radio selected quasars have a much 

wider distribution in the redshift than the BL Lac objects. If the redshift 

range for both the subsamples is restricted to 0.8 and 1.7, better agreements 

in the mean luminosities are found (Table lob). There are, however, some 

problems. There are only eight BL Lac objects in this restricted sample, and 

they do not show any internal radio, optical, or X-ray correlations. The 

radio selected quasars, in contrast, give the slope coefficients 0.34+0.10/- 

0.08 for log(lr)-log(Rx) and 0.45 f 0.11 for log(Ro)-log(Rx), though no 

significant relation exists between log(R ) and log(1 ). These results can be 

interpreted in two ways. 

differences in the continuum spectra of radio selected quasars and BL Lac 

objects, and another is that the data are too fragmentary to give firm 

conclusions. More BL Lac objects are needed. 

The optical and the X-ray luminosities of the radio 

0 r 

One interpretation is that there are no significant 

The unresolved radio selected quasars are also compared with the BL Lac 

objects. The samples with restricted redshift range show strong similarities. 

Therefore the BL Lac objects may be special cases of the radio selected 

quasars. 

The distinctive difference between the radio selected and the X-ray 

selected BL Lac objects are often noted (Ledden and O'Dell 1985, Stocke et al. 

1985). For example, the mean spectral indices are: <a >- 0.62 2 0.02, 

<a h1.46 It 0.03 for the radio selected BL Lac objects, and <a +0.37 f 

ox ro 

0.02, <a--->l.11 f 0.04 for the X-ray selected BL Lac objects. 

ro 

Ledden and UA 

- 27 - 
O'Dell (1985) suggest that the main emission mechanisms of the X-ray BL Lac 

objects is the synchrotron radiation, and the radio selected BL Lac objects 

have extra mechanisms, such as beaming. 

luminosities of the radio selected and the X-ray selected BL Lac objects, we 

find that the radio selected BL Lac objects are 100 times more luminous than 

the X-ray selected BL Lac objects in the radio band, 7 times more luminous in 

the optical band, and nearly same in the X-ray band. 

beaming model. 

If we compare the averaged 

This may support the 

But an alternative possible explanation is a selection effect. In the 

diagram of Q =box relation, we see that the radio selected and the X-ray 

selected BL Lac objects mark the lower and upper bounds of the radio selected 

quasars. 

cases of sources with the same emission mechanism as in the radio selected 

The difference between these two groups may be due to two extreme 

quasars. 

quasars and the optically selected quasars and the X-ray selected AGNs which 

can be attributed largely to the selection methods used in their discovery. 

If so, we may find "optically selected" BL Lac objects somewhere between these 

two groups. 

and it is located among the X-ray selected BL Lac objects. 

for high polarized objects (e.g. Borra and Corriveau 1984) have been generally 

unsuccessful. 

A similar offset in the <aro> is seen between the radio selected 

Only one BL Lac object was possibly found optically (ZWI 186), 

Optical surveys 

f) Comparison of the Optically Selected Quasars and the X-ray Selected AGNs 

It is often mentioned that the optically selected quasars and the X-ray 

selected AGNs have similar natures, and the latter are treated as a lower 

luminosity sequence of the former (e.g. Maccacaro et al. 1984, Kriss and 

- 28 - 
Canizares 1985). 

between the optical and the X-ray luminosities but do not show the other 

relations (see 0 Va). This initially suggests that the X-ray and optical 

emission mechanisms of these subsamples are similar. In the plot of log(R ) 

and log(Rx), however, the slope coefficient of the X-ray selected AGNs are 

significantly steeper (0.87 k 0.05) than that of the optically selected 

In our data sets, both subsamples show a strong correlation 

0 

quasars (0.70 f 0.06). 

to be shallower (<aox> -1.65 k 0.03) than those of the optically selected 

Also the aox indices of the X-ray selected AGNs tend 

quasars (<a >-1.35 f 0102). The average radio and optical luminosities of 

ox 

the optical selected quasars are about 20 times brighter than those of the Xray selected AGNs, but the average X-ray luminosity is nearly the same. 

the emission mechanism of these two subsamples were the same, the difference 

of the brightness of each band should be approximately same. One explanation 

of this difference is suggested by Kriss and Canizares (1985). 

the high redshift objects are much ”redder”, since the optical band shifts to 

shorter wavelength which Is strongly affected by reddening, while the X-ray 

band is not affected much. 

quasars which have, on the average, a higher redshift to the X-ray selected 

AGNs which have, on the average, a lower redshift, then the optically selected 

quasars show more absorption. 

If 

They show that 

Hence, if we compare the optically selected 

(g) Groping towards the Physics of AGN Continua 

Having investigated the relations between the continua of various types 

of AGNs, we should like to know the relevance of the various models of 

physical processes of continuum emission to the results of our statistical 

“-“l.,cbc TI.,.-- --- c..- --.,.-+*ll.. *--- 2:c.C ---- -L uIu. &&&=LE: aAc ~~~LL~c~~~cLLLJ cwu uALIeLe:IiL liiecliaI-iisiiis : a chermai 
radiation from an accretion disk, and a non-thermal radiation from the 

vicinity of the central engine or jets. If the thermal emission from the 

accretion disk is the main mechanism (Tucker 1983, Schlosman, Shaham, and 

Shaviv 1984), X-ray and optical luminosities may show a correlation but the 

radio luminosity is likely to be independent. According to Tucker (1983), the 

emission from an optically thick accretion disk can generate the relation 

RxccRz with a~0.5 to 0.8. Most of our results are consistent: with this 

prediction (a-0.7, except for BL Lac objects where CY - 0.9), though the 

thermal model does not explain the radio/X-ray correlation seen in most 

samples. If the entire continuum is due to synchrotron emission, the X-ray, 

optical, and radio luminosities should be well correlated each other with 

a ia . All subsamples agree with these conditions. If the synchrotron 

self-Compton (SSC) mechanism is important, a strong correlation between the 

ox ro 

radio and X-ray is expected with a possible correlation with the optical 

luminosity through the synchrotron emission. If beaming due to a relativistic 

jet exists, it would lead to correlation between all beamed (presumebly 

nonthermal) components. Other mechanisms, such as Compton scattering of 

blackbody or cyclotron radiation could also be responsible for the power low 

spectrum in the optical to X-ray bands. 

These various models clearly do not make predictions which can be 

uniquely distingushed by the Rr/Ro/lx database studied here. 

not sufficiently developed to predict how radio, optical and X-ray 

luminosities should scale. Nontheless, we can attempt to reach some crude 

conclusions. The fact that Rr is correlated with both R and R in virtually 

all subsampies of AGNs (Table 5aj is evidexe against a thermal model for the 

continuum spectrum unless, for example, there is some indepedent scaling 

between the size of the thermal accretion disk and the strength of the nonMost models are 

0 X 

- 30 - 
thermal jets. 

with a simple or beamed synchrotron model, though models must account for fact 

that the scaling between bands is not quite linear (Table 5b). There are no 

indications that Rr and 1 are correlated with 1 

an SSC model, but this cannot be conclusive evidence against SSC as the 

optical band could be dominated by non-thermal continuum (e.g. K8nigl 1981). 

The correlation between all three bands is fully consistent 

decoupled, as might occur in 

X 0 

Although it is risky to pursue more elaborate models when adjudication 

between the simplest ones is difficult, we find the two component AGN 

continuum model discussed in 8 Vd is attractive. Here all AGNs have the 

thermal emission from the accretion disk and the non-thermal emission from the 

jets. The differences between subsamples may be due to the differences 

between accretion modes (Blandford 1984). If a radiation torus around a black 

hole is radiating at just over the Eddington limit, the emission is dominated 

by the thermal radiation, since there are insufficient relativistic electrons 

to power a synchrotron continuum. The radio loud quasars accrete at higher 

rate so that they produce the jets populated by relativistic electrons, but 

the synchrotron emission (and possibly SSC) need not dominate and hence we see 

both the thermal disk and non-thermal jet radiations. 

be an extreme case with intrinsically luminouse jets and a faint optically 

thin accretion disk, or they may possess ordinary jets that happen to be 

pointed to us so that the synchrotron emission is extremely enhanced and 

dominates the total luminosity. 

The BL Lac objects may 

There are a few complications in any of these interpretations. One 

concern is possible evolution effects. 

bands are intrinsically related, then correlations should appear even if the 

subsamples are divided into narrow redshift bins within which no evolution 

could occur. 

If the continuum emission in various 

We find most of the RJRyly correlations are present in - - a. 

- 31 - 
specified bins, but appear weaker than the correlations seen in the entire 

subsamples. For example, the correlation probabilities between the radio and 

the X-ray luminosities of the radio selected quasars are 

0.5, 0.01% for 0.5 I z < 1.0, 0.03% for 1.0 I z < 1.5, 93% for 1.5 5 z < 2.0, 

17% for 2.0 I z C 2.5, and 0.6% for 2.5 5 z. The low correlation 

probabilities in these subsamples are partly due to the reduced size of the 

data sets in each bin, and partly by the narrow range of luminosities in each 

redshift bin. 

gives some confidence, however, that the correlations are not entierly due to 

cosmological luminosity evolution. 

5% for 0.0 5 z < 

The existence of the correlations within narrow redshift ranges 

Another problem is inappropriately defined samples. We subdivided our 

samples by selection criteria such "X-ray selected" or "optically selected" 

objects. 

samples. 

"radio loud" quasars. 

statistical results, comparison between the "radio selected" (which are chosen 

from their initial discovery in radio surveys) and the "radio loud" subsamples 

(which are chosen from the entire sample with the condition a >0.3) shows 

ro 

that there is no significant difference. 

This method may introduce some mixing of intrinsically different 

For example, the optically selected quasars clearly contain a few 

Although this mixing might lead to some misleading 

We thus find that, although a large number of data were collected, it 

proves difficult to specify a physical model. This is partly because most 

theoretical studies do not show tracks in a ,Jar, or R / R, / lx plots. 

Since these kinds of plots are now widely produced observationally, we 

encourage theorists to make such predictions. It is also desirable to have 

deeper surveys in all bands so that we can examine samples with wide 

luminosity ranges within specific redshift ranges. 

the evolution effect on the emission mechanisms. 

r 

These surveys may clarify 

- 32 - 
VI. SUMMARY 

Using a large database, we investigated statistical properties of AGNs 

continuum levels in the radio, optical, and X-ray bands. For the radio 

luminosity of AGNs, we used the core luminosity to discount effects from radio 

lobes and jets. The statistical methods called survival analysis were used to 

show the statistical relations despite the upper limits in flux limited data 

sets. Our main results are as follows: 

1. For the optically selected quasars and the X-ray selected AGNs, R is 

correlated with R does not correlate with R . X' r X 

suggests that the main emission mechanism of these subsamples is thermal 

emission. 

this suggests that the main emission mechanism of the BL Lac objects is nonthermal. The radio selected quasars show high significance levels for both 

R R and R R relations. Hence they may have both the mechanisms, which is 

further supported by model fitting suggesting that the radio selected quasars 

have two different X-ray emission mechanisms. 

2. The BL Lac objects have similar emission mechanisms as the radio selected 

quasars, at least in the limited redshift range overlapping both samples. The 

radio selected BL Lac objects are perhaps special cases of the unresolved 

radio selected quasars. The difference between the radio selected and the Xray selected BL Lac objects may be due either to beaming effects or selection 

effects. 

3. Some compact radio sources with faint optical counterparts show that 

<a > 2 <a >. This suggests the possibiiity that SSC emission may be present 

in the optical to X-ray bands. 

4. The spectral index between the optical and X-ray luminosities depends on 

0 

but not with Rr. Also R This 

For the BL Lac objects, Ir/Rx relation is most significant, and 

I/X JX 

ro ox 

- 33 - 
the optical luminosity. 

ray luminosity. 

The optical luminosity increases faster than the X- 

- 34 - 
Acknowledgements 

We would like to thank D. J. Helfand and H. KGhr for providing 

unpublished data. One of us (K. P. S.) would like to thank Prof. G. P. 

Garmire for the hospitality at the Pennsylvania State University while working 

on this study. This work was supported in part by NASA grant NAG 8-555 and by 

a NSF Presidential Young Investigator Award (AST 83-51447). 

- 35 - 
Table Captions 

Notes to Table 2a: 

1. First detected by Condon and Dressel (1978). We find a faint radio 

lobe (3 dy) 6" at P.A. 104 ' from the quasar. 

2. A 6xRMS detection within 1" of the optical position. 

3. A 5.5xRMS detection within 1" of the optical position. Mrk 205 was 

also detected by Sulentic (1986) at a level of 1.48 2 0.25 mJy 

at 5 GHz. 

4. First detected by Sramek and Weedman (1980). Our improved position is 

12h58m59.4s, 34'16'38". 

5. A 7xRMS detection within 1" of the optical position. 

6. First detected by Sramek and Weedman (1980). Our improved position is 

16h04m53.4s, 29'03'21". 

Definitions for Table 3: 

Optical 

If a radio AGN has an optical "empty field", D20.0 is used as the optical 

upper limit. 

X-ray 

If only the X-ray flux (or flux density or count number) is available, the 

luminosity is computed according to the descriptions below for the given 

reference: 

* L1 X-ray list gives X-ray data in the flux density at 1 keV. The conversion 

to the flux (0.5-4.5 keV) is 

- 36 - 
S (0.5-4.5) [ erg/sec/cm 2 ]=O. 068 fx( IkeV) nJy X 

* 01 X-ray list gives the X-ray data in the flux (0.15-3.5 keV). The 

conversion is 

S (0.5-4.5)=0.95 Sx(0.15-3.5) 

X 

* B3 X-ray list gives the X-ray (0.5-3.0 keV flux). The conversion is 

S (0.5-4.5)=1.38 Sx(0.5-3.0). X 

* G2 X-ray list gives the X-ray (0.3-3.5 keV flux). The conversion is 

Sx(0.5-4.5)-1.07 Sx(0.3-3.5). 

* W2 X-ray list gives the X-ray K count rate. The conversion is 

2 

sX=2. 88x~~-13~2 erg/sec/cm 2 . 

* The X-ray flux is computed from Einstein IPC photon counts (cts/sec) by 

1.01~~(cts/sec)-3. o~Io-~~ erg/sec/cm 2 

assuming N(H)-3xlO 20 cm -2 and S -(freq) -0.5 

* The X-ray flux density at 2KeV is computed by 

2 

Sx( 2KeV)=1. 47x10-18f erg/sec/cm 

x El o.5-E20.5 

where El and E2 are the band limits in KeV and f is in erg/sec/cm 2 . X 

Notes to Table 8: 

1. Data have too many upper limits and the result is obtained from 

a limited range. 

- 37 - 
Table 1 : Spectral Indices from Recent Literatures 

Study Spectral Indices Descriptions 

Tananbaum et al. a -1.27fO.07 Mixed QSOs ox 

(1979) 

Ku et al. (1980) a -1.46k0.02 Total sample ox 

a -1.38fO.03 Radio selected QSOs 

a -1.52+_0.03 Optically selected QSOs 

a -1.41fO.03 X-ray selected AGNs 

a -1.36kO.04 Radio QSOs with low redshift (~~1.0) 

a -1.40f0.03 Radio QSOs with high redshift(z>l.O) 

a -1.36fO.04 Opt. QSOs with low redshift (z<l.O) 

a -1.65f0.04 Opt. QSOs with high redshift (z>l.O) 

a -1.25f0.05 ow 

a -1.31f0.05 EL Lacs 

ox 

ox 

ox 

ox 

ox 

ox 

ox 

ox 

ox 

Zamorani et al. a -1.27f0.03 Radio loud 

ox 

a -1.46+0.05/-0.07 Radio quiet 

a -1.35+0.05/-0.08 Radio quiet with low redshift (~~1.0) 

a 

a 

a 

ox (1981) 

ox 

-1.62+0.08/-0.16 Radio quiet with high redshift (~1.0) 

=1.37+0.05/-0.08 Radio quiet with log(Ro)<31.4 

=1.62+0.08/-0.11 Radio quiet with log(1 )>31.4 

ox 

ox 

ox 0 

Owen et al. (1981) a -1.02f0.05 nun selected AGNs 

a -1.21f0.19 mm selected AGNs 

mx 

ox 

Stocke et al.(1983) aox=1.3?0.2 

Marshall et al. 

X-ray selected AGNs 

a =1.37k0.10 Optically selected quasars ox 

(1983) 

- 38 - 
Cruz-Gonzales and a -0.59k0.10 

Huchra (1984) a -0.94kO.09 

Margon and Chanan aox=1.26+0.03 

ri 

rx 

(1985) 

Ledden and O'Dell a -0.63kO.12 

a -0.89kO.06 

a -1.40k0.17 

a -0.74f0.10 

a -0.92k0.06 

a -1.30+0.13 

a -0.67kO.12 

a -1.36kO.17 

ro 

rx (1985) 

ox 

ro 

rx 

ox 

ro 

ox 

BL Lac : radio -infrared 

BL Lac : radio - X-ray 

X-ray selected quasars 

BL Lacs 

BL Lacs 

BL Lacs 

HPQs 

HPQs 

HPQs 

Blazars 

Blazars 

- 39 - 
Table 2a : VLA Observations of Optically Selected Quasars 

Object Name S6(mJy) Note Object Name S6(mJy) Note 

0137-010 NAB 

0143-015 MC5 366 

0143-010 MC5 368 

0146+017 MC5 141 

0207 - 378 

0241+011a nrNGC1073 

0241+011b nrNGC1073 

0241+011c nrNGC1073 

0242-410 

0849+154 LB 8796 

0854+194 Ll3 8948 

0855+188 LJ3 8991 

0856+186 LB 9010 

0856+189 LB 9029 

1045+128a nrNGC3384 

1045+128b nrNGC3384 

1045+128c nrNGC3384 

1045+128d nrNGC3384 

<0.8 

<0.8 

<0.8 

4.2 

<1.3 

c2.0 

<2.0 

40.5 

<1.4 

<0.9 

1.8 

<0.9 

<1.0 

<0.8 

4.0 

<0.9 

<0.9 

<1.0 

1 

1045+128e 

1045+12 8 f 

1045+128g 

1045+128h 

1202+28 1 

1219+7 5 5 

1246-057 

1258+286 

1258+342 

1300- 243 

1334+286 

1346 -036 

1604+2 90 

1606+288 

1606+289 

1720+246 

1803+676 

2225-055 

nrNGC3 384 

nrNGC3 3 84 

nrNGC3384 

nrNGC3 384 

GQ Com 

Mrk 205 

W 61972 

KP 33 

RS 23 

KP 63 

KP 64 

KP 67 

V396 Her 

PHL 5200 

4.1 

<0.9 

<0.9 

4.0 

1.1 

0.9 

<0.9 

<0.9 

25.1 

1.3 

<0.8 

4.0 

4.0 

<0.9 

<0.9 

31.0 

<0.8 

<0.8 

2 

3 

4 

5 

6 
Table 2b : VLA Observations of X-ray Selected AGNs. 

Object Name s6 (&y) Object Name '6 (mJy) 

0057+311 

0112+325 

022 5+3 12 

0 244+19 2 

03 5 7+104 

0745+554 

0 7 54+3 9 2 

09 0 6+42 5 

1008+345 

1011+0 3 2 

10 3 1+5 8 2 

1139+104 

1E 

1E 

1E 

1E 

1E . 

1E 

1E 

1E 

1E 

1E 

1E 

1E 

<0.7 

<0.8 

<0.6 

~0.6 

<0.7 

~0.7 

3.6 

<0.8 

<0.8 

<0.7 

<0.6 

4.1 

1205+46 5 

12 2 8+164 

13 04+3 4 1 

135 2+1820 

1352+1828 

1357-022 

1401+09 5 

15 29+050 

15 30+15 1 

1602+241 

1747+6 8 3 

2251-175 

1E <0.7 

1E <0.8 

1E <0.7 

1E <0.7 

1E 4.0 

1E <0.7 

1E 18.8 

1E 3.8 

1E <0.9 

1E <1.2 

1E <0.6 

1E <0.7 

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Table 6a Correlations 

Sample 

Total Censored Significnat level 

Variables no. objects of correlations Plot 

objects no. 

X Y x y both Cox (%) BHK (%) 

Radio Selected 

Quasars 

Optically 

Selected 

Quasars 

X-ray Selected 

AGNs 

Radio Selected 

BL Lac Objects 

~og(Jr)-Iog(Jx) 156 50 7 4 . . . <0.01 la 

log(Jo)-log(Jx) 156 0 11 0 <O.O1 <0.01 2a 

log(Jo)-log(Rr) 156 0 54 0 <O.O1 <0.01 3a 

a ro -a ox 156 50 7 4 <0.01 <0.01 4a 

log(Jr)-lOg(Jx) 103 18 6 68 ... CO.01 lb 

log(Jo)-log(Rx) 103 0 74 0 ~0.01 <0.01 2b 

~og(Jo)-~og(Jx) 103 0 86 0 0.02 0.2 3b 

a -a 103 18 6 68 ... CO.01 4b ro ox 

log(Jr)-log(Rx) 122 103 0 0 . . . CO.01 IC 

log(~o)-log(Rx) 122 0 0 0 co.01 CO.01 2c 

log(Ro)-log(Jr) 122 0 103 0 <0.01 <0.01 3c 

a -a 122 103 0 0 . . . 52 4c ro ox 

- 50 - 
.. 

X-ray Selected log(lr)-log(lx) 10 0 0 0 2 3 Id 

BL Lac Objects log(lo)-log(lx) 10 0 0 0 0.03 0.3 2d 

10g(lo)-lOg(lr) 10 0 0 0 0.7 0.7 3d 

a -a 160004 2 4d 

ro ox 

Compact Radio a -a 19018 ... 0.03 4e ro ox 

Sources 

Flat Spectral log(Rr)-log(lx) 66 0 2 0 <0.01 <o. 01 ... 

Radio Quasars log(lo)-log(lx) 66 0 2 0 <0.01 <o .01 ... 

~og(~o)-log(lr) 66 0 0 0 <0.01 <o .01 ... 

a -a 66 0 2 0 <0.01 <o. 01 ... ro ox 

- 51 - 
Table 6b Linear Regressions 

Sample 

Total Censored Intercept Coeff . 

Variables no. objects Slope Coeff. 

objects Standard Deviation 

X Y x y both EM B-J 

Radio Selected log(lr)-log(Rx) 156 50 7 4 29.0k.. . 

Quasars 0.4820.06 

... 

log( lo) -log( Rx) 156 0 11 0 23.921.6 23.8+ ... 

0.70k0.05 0.7020.05 

0.47 0.45 

log(Ro) -lOg(l,) 156 0 54 0 5.6223.73 6.05+ ... 

0.91k0.12 0.89k0.12. 

1.05 0.96 

156 50 7 4 ... 

-0.75kO.12 

U -Q 

ro ox 

... 

Optically 

Selected 

Quasars 

28.2t ... 

0.51+0.15/-0.11 

... 

log(Ro) -log(Rx) 103 0 74 0 23.1k1.9 23.1+_ ... 

0.70k0.06 0.70k0.07 

0.50 0.48 

- 52 - 
log( lo) -log( Rx) 103 0 86 0 0.32f0.65 -0.68f ... 

0.97f0.21 1.01f0.27 

1.39 1.25 

CY -CY 103 18 4 68 ... ro ox 

-0.60+0.04/-0.05 

... 

X-ray Selected log(lr)-log(Rx) 122 103 0 0 ... 

AGNs 0.46+0.08/-0.06 

... 

log(Ro) -log(Rx) 122 000 18.2f1.4 

0.8720.05 

0.43 

log(Ro) -log(Rr) 122 0 103 0 -34.5f12.1 ... 

2.08f0.40 ... 

2.42 ... 

a -a 122 103 0 0 ... ro ox 

... 

... 

Radio Selected log(R r )-log(R X ) 24 000 18.7f2.6 

BL Lac Objects 0.77f0.08 

0.50 

log(R*) -log(lx) 24 000 17.8f3.3 

0.89f0.11 

0.59 

- 53 - 
log(Ro) -log(Jr) 24 000 3 .2 3k4.13 

1.00k0.14 

0.74 

a -a 49 0 2 0 1.9520.11 1.952 ... ro ox 

-0.93kO.18 -0.93kO.19 

0.18 0.18 

X-ray Selected log(lr)-log(R X ) 10 0 0 0 14.4k0.92 

BL Lac Objects 0.9620.29 

0.34 

log(~o)-log(lx) 10 0 0 0 11.426.9 

1.1320.23 

0.27 

Wlo)-1og(lr) 10 0 0 0 14.7k7.9 

0.5620.27 

0.31 

1.5950.15 

-1.4OkO.41 

0.11 

a -a 

ro ox 

16000 

ro ox 19018 ... Compact Radio a - a 

Sourcs -0.97+0.23/-0.16 

.. 

Flat Spectral log(lr)-log(lx) 66 0 20 22.6k2.7 22.6+ ... 

Radio Quasars 0.67k0.06 0.67k0.08 

0.43 0.42 

log(Ro)-log(Rx) 66 0 . 2 0 24.2k2.0 24.0k ... 

0.69k0.06 0.70k0.06 

0.42 0.39 

- 54 - 
log(Ro)-log(R r j 66 0 

a -a ro ox 

00 11.522.7 

0.74kO. 01 

0.58 

66 0 20 1.91kO.11 1.98+ ... 

-0.92kO.17 -0.91+0.15 

0.16 0.15 

- 55 - 
.. .' 

Table 7 : Partial Rank Correlation Coefficient 

Radio QSOs 

Optical QSOs 

X-ray QSOs 

Radio BL Lacs 

X-ray BL Lacs 

0.31 

0.05 

0.07 

0.56 

0.09 

0.45 

0.16 

0.64 

0.45 

0.60 

0.13 

0.08 

0.07 

0.34 

0.48 

- 56 - 
Table 8: Kaplan-Meier Mean and Standard Deviation 

and a Of Or0 ox 

<a > <a > 

ro ox 

Data 

Radio QSOs 0.6420. 01 1.43+0.02/-0.03 

1.65kO. 03 

X-ray AGNs 0.48+0.05/-0.06 1.3920.02 

Radio BL Lacs 0.62kO. 02 1.4620.03 

X-ray BL Lacs 0.3720.02 1.11+0.04 

Compact Radio Sources 0.9320.03 1.12k0.03 

1 Optical QSOs (0.49k0.02) 

Flat Spectrum Radio 0.63k0.02 1.39+0.03/-0.04 

- 57 - 
Table 9a 

Sample 

censored no. 

total no. 

: Correlations between a 

ox 

7-a 

ox 

Cox prob. Intercept 

Slope 

Stand. Dev. 

and 7 or log(lo) 

log(lo) - ox 

Cox prob. Intercept 

Slope 

(%I Stand. Dev. 

Radio QSOs 9.1 1.2720.05 <o . 01 -2.2120.62 

(11/156) 0.21f0.10 0.11f0.02 

0.20 0.19 

Optical QSOs <0.01 

(73/102) 

X-ray AGNs 37 

(0/123) 

Radio 

BL Lacs 

X-ray 

BL Lacs 

(0/10) 

34 

9.7 

1.35f0.07 <o .01 -1.9420.72 

0.54f0.13 0.llfO. 02 

0.21 0.19 

1.38k0.03 

-0.13fO.09 

0.17 

1.47f0.08 

- 0.2520.22 

0.22 

1.07f0.05 

-0.3920.32 

0.10 

0.13 -0.1OkO.54 

0.05k0.02 

0.16 

29 

85 

0.0521.25 

0.04k0.04 

0.22 

0.0022.72 

0.0320. 09 

0.11 

- 58 - 
.. i . 

Table 9b : Correlations among CY Redshift, and Optical Luminosity ox' 

Data Cox's prob.(%) EM 

censored no. joint Intercept 

z only Slope for z 

total no. Ro only Slope for Ro 

Standard Deviation 

Radio QSOs P(tot)<O.Ol 1.16fO. 03 

11/156 P(z)<O.Ol -0.73fO.15 

P(Ro)<O.Ol 0.25f0.03 

0.17 

Optical QSOs P( tot)-O.Ol 

73/102 P(~)-53 

P(Ro)-42 

X-ray AGNs 

0/123 

P(tot)<O .01 

P ( 2) <o .01 

P(Ro)<O.Ol 

Radio BL Lacs P(t0t)-0.01 

0/24 P(2)-0.02 

P(Ro)=O.O1 

1.56k0.06 

0.21f0.28 

0.07f0.06 

0.20 

1.20f0.02 

-1.29fO.13 

0.27f0.03 

0.13 

1. lOfO. 06 

-1.39f0.26 

0.2620.05 

0.15 

- 59 - 
.- .I( . 

X-ray BL Lacs 

0/10 

P (tot) -23 

P(2)-11 

P (9-77 

0.90+0,12 

-0.4820.32 

0.08f0.90 

0.15 

- 60 - 
Table.9c : Correlation among a Redshift, and X-ray Luminosity ox' 

Data Cox's prob. (%) EM 

censored no. Joint Intercept 

z only Slope for z 

total no. lx only Slope for R 

X 

Standard Deviation 

X-ray AGNs P(tot)<O.Ol 4.53k0.58 

0/123 P(z)<O. 01 0.87k0.20 

P(RX)CO.O1 -0.21kO.04 

0.15 

BL Lacs 

0/24 

P( tot)-51 

P(~)=76 

P(R )-47 X 

X-ray BL Lac P ( tot) -21 

0/10 P(~)=23 

P(R )-45 X 

3.52k1.50 

0.4720.53 

-0.14kO.10 

0.21 

1.9821.07 

-0.2220.34 

-0.07kO.07 

0.10 

- 61 - 
.' 

: 

Table 10a : Comparison of Radio Quasars and BL Lac Objects 

censored no. 

Property Mean and Standard Deviation 

total no. 

~~ 

Radio luminosity QSO : <log(Rr)> = 33.8820.128 (46/156) 

BL Lac: <log(Rr)> - 33.8120.280 (0/24) 

Gehan test : P = 79% 

Logrank test: P - 91% 

Optical luminosity QSO : <log(Ro)> - 31.2620.06 (0/156) 

BL Lac: <log(Ro)> - 30.5420.23 

Gehan test : P = 0.8% 

Logrank test: P = 0.01% 

(0/24) 

X-ray luminosity QSO : <log(Rx)> - 45.6320.06 (11/156) 

BL Lac: <log(Lx)> = 44.8920.24 

Gehan test : P = 0.6% 

Logrank test: P = 0.01% 

(0/24) 

a 

ro 

a 

ox 

QSO : <aro> = 0.64?0.01 (46/156) 

BL Lac: <a > = 0.6220.02 (2/50) ro 

Gehan test : P = 20% 

Logrank test: P = 14% 

QSO : <a > = 1.43+0.02/-0.03 (11/156) ox 

BL Lac: <aox> (2/50) = 1.4620.03 

- 62 - 
Gehan test : P = 29% 

Logrank test: P = 25% 

- 63 - 
Table 10b : Comparison of Radio Quasars and BL Lac Objects (0.8<z<1.7) 

censored no, 

Property Mean and Standard Deviation 

total no. 

Redshift QSO : <z> = 1.1120.03 (0/57) 

BL Lac: <z> - 1.08?0.10 

Gehan test : P - 42% 

Logrank test: P = 81% 

Radio luminosity QSO : <log(Lr)> = 34.40k0.12 (16/57) 

BL Lac: <log(R )> = 35.0420.12 

r 

Gehan test : P - 3% 

Logrank test: P - 0.6% 

(0/8) 

Optical luminosity QSO : <log(Ro)> - 31.34k0.06 (0/57) 

BL Lac: <log(Ro)> = 31.3820.18 

Gehan test : P = 82% 

Logrank test: P - 92% 

(0/8) 

X-ray luminosity QSO : <log(lx)> - 45.78k0.05 (3/57) 

BL Lac: <log(Rx)> - 45.92k0.17 

Gehan test : P - 59% 

Logrank test: P - 44% 

(0/8) 

a 

ro QSO : <a ro > - 0.6020.02 (16/57) 

BL Lac: <aro> - 0.69kO.03 (0/8) 

- 64 - 
Gehan test : P = 8% 

Logrank test: P - 3% 

a 

ox QSO : <a > * 1.37kO.02 (3/57) ox 

BL Lac: <a > - 1.39+0.08/-0.10 (0/8) 

Gehan test : P - 73% 

Logrank test: P - 60% 

ox 

- 65 - 
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- 71 - 
Figure Captions 

Plot of the 0.5-4.5 keV X-ray luminosity against the 5 GHz radio 

luminosity density of the radio selected quasars. The detected 

points are represented by circles and the upper limits are 

represented by bars in this figure and all following figures. 

The solid line in this and following two figures is the 

regression line log(R )-a+blog(lr) obtained by the application 

of the BHK method. 

Figure l(a) 

X 

l(b) Plot of the 0.5-4.5 keV X-ray luminosity against the 5 GHz radio 

luminosity density of the optically selected quasars. 

l(c) Plot of the 0.5-4.5 keV X-ray luminosity against the 5 GHz radio 

luminosity density of the X-ray selected AGNs. 

l(d) Plot of the 0.5-4.5 keV X-ray luminosity against the 5 GHz radio 

luminosity density of the BL Lac objects. The radio selected BL 

Lac objects are represented by circles and the X-ay selected BL 

Lac objects are represented by boxes. The solid line is the 

regression for the radio selected BL Lac objects and the dashed 

line is the regression line for the X-ray selected BL Lacs. 

Both regression lines are assumed to have a form 

log(R )-a+blog(R ) and computed by a least square method. 

X r 

Figure 2(a) Plot of the 0.5-4.5 keV X-ray luminosity against 2500 A optical 

luminosity density of the radio selected quasars. The solid line 

in this and the following two figures is the regression line 

- 72 - 
log(R )-a+blog(R ) by the EM algorithm with normal distribution. 

X r 

2(b) Plot of the 0.5-4.5 keV X-ray luminosity against 2500 

luminosity density of the optically selected quasars. 

optical 

2(c) Plot of the 0.5-4.5 keV X-ray luminosity against 2500 A optical 

luminosity density of the X-ray selected AGNs. 

2(d) Plot of the 0.5-4.5 keV X-ray luminosity against 2500 A optical 

luminosity density of the BL Lac objects. The radio selected BL 

Lac objects are represented by circles and the X-ay selected BL 

Lac objects are represented by boxes. The solid line is the 

regression line for the radio selected BL Lac objects and the 

dashed line is the regression line for the X-ray selected BL 

Lacs. 

Figure 3(a) Plot of the 5 GHz radio luminosity density against 2500 A 

optical luminosity density of the radio selected quasars. The 

solid line here and in the following figures is the regression 

line log(Rr)=a+blog(Ro) by the EM algorithm with the normal 

distribution. 

3(b) Plot of the 5 GHz radio luminosity density against 2500 A 

optical luminosity density of the optically selected quasars. 

The uncertainty of the intercept coefficient is relatively large 

(0.32 f 0.65). 

- 73 - 
h 

3(c) Plot of the 5 GHz radio luminosity density against 2500 A 

optical luminosity density of the X-ray selected AGNs. 

uncertainty of the intercept coefficient is relatively large (- 

34.5 * 12.0). 

The 

3(d) Plot of the 5 GHz radio luminosity density against 2500 A 

optical luminosity density of the BL Lac objects. The radio 

selected BL Lac objects are represented by circles and the X-ay 

selected BL Lac objects are represented by boxes. The solid line 

is the regression line for the radio selected BL Lac objects and 

the dashed line is the regression line for the X-ray selected BL 

Lacs. 

Figure 4(a) Plot of the aox against the a 

The solid line is the regression line a =a+ba 

application the BHK method. 

following four figures represent lower limits. 

of the radio selected quasars. ro 

by the 

ox ro 

The bars in this figure and 

4(b) Plot of the aOX against the a 

quasars. Because of the large uncertainty for the intercept here 

and below, we do not fit a regression line. 

of the optically selected 

ro 

4(c) Plot of the aox against the a of the X-ray AGNs. 

ro 

4(d) Plot of the aOX against the a 

selected BL Lac objects are represented by circles and the X-ay 

selected BL Lac objects are represented by boxes. The solid line 

of the BL Lac objects. The radio 

10 

- 14 - 
is the regression line for the radio selected BL Lac objects and 

the dashed line is the regression line for the X-ray selected BL 

Lac objects. 

4(e) Plot of the aox against the a 

The arrow in this figure represents an upper limit. 

of the compact radio sources 

ro 

- 75 - 

___ 
Authors' Addresses 

Eric D. Feigelson and Takashi Isobe 

Department of Astronomy, The Pennsylvania State University, University 

Park, PA 16802. 

Kulinder P. Singh and Ajit Rembhavi 

Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, 

India. 

- 76 - 
Fig. 1 
Fig. 2 

I I I I I I I I I I I I I I I I I I I I 
Fig. 3 
Fig. 4 
Fig. 4 

x 

0 

1.8 

1.6 \ 3 

k \ 

1.4 fL \ \ 

i 

1.21 

c \- Lot 

0.8 1 

c aj 

-0.1 0.1 0.3 0.5 0.7 09 1.1