MULTIBAND COMPARATIVE STUDY OF OPTICAL MICROVARIABILITY IN RADIO-LOUD VERSUS RADIO-QUIET QUASARS

3C 281. This RLQ is known to reside in a very rich galaxy cluster (Yee & Green 1987). A variation of 0.15 mag in one year has been reported in the infrared (Enya et al. 2002a, 2002b). We observed this object for Paper I in 1997 May, but microvariability was not detected. We observed this quasar with EOCA on 2000 March 1 and March 4, detecting OM events on both nights.

2000 March 1. The object was observed during 2.7 hr three times. A visual analysis of the light curves shows a decrease in brightness of almost 4 hundredths of a magnitude (Figure 1(a)). An ANOVA confirms a microvariation in B and V, detectable at a 0.1% significance level, but not in R. The significance level of the detection remains the same with respect to all of the reference stars. In V, the amplitude is ΔV = 0.031 ± 0.007 mag, in 2.7 hrs, while between the second and third groups ΔV = 0.024 ± 0.007 mag, in ∼1 hr. In B, the amplitudes are ΔB = 0.05 ± 0.01 mag between the first and the third observations and ΔB = 0.03 ± 0.01 mag between the second and the third.

2000 March 4. 3C 281 was observed during 3.75 hr on three occasions. A visual revision of the light curves establishes the occurrence of a possible variation in the three bands (Figure 1(b)). However, an ANOVA only detected a variation in V and a marginal one in R (with a significance level of 5%). The variation amplitude is ΔV = 0.027 ± 0.006 mag between the first group and the third.

PKS 1510−089. This RLQ has shown intense activity on long- and intermediate-term variability (Liller & Liller 1975; Tornikoski et al. 1994; Villata et al. 1997), as well as correlated optical/radio variability (Tornikoski et al. 1994). OM also has been reported (Villata et al. 1997; Xie et al. 2001; Dai et al. 2001; Xie et al. 2004). In particular, Dai et al. (2001) reported a variation of 2 mag in 41 minutes in the R band at the end of 2000 May. However, Romero et al. (1999, 2002) did not detect any activity when they observed it between 1998 and 1999. Our observations show that PKS 1510−089 was in a stage of activity during the first semester of 2000. We monitored this object during 4.3 hr on five different occasions during the night of 2000 March 20 (two months before the observations of Dai et al. 2001). Light curves (Figure 1(c)) indicate the presence of an OM event detected in V and R. While a progressive increase in brightness is detected in V, a variation is observed between the first and the second data sets in R, which remains at the same level of brightness for the rest of the session. An ANOVA agrees with the visual revision of Figure 1(c). This variation is confirmed with a 0.1% level of significance. Comparison between the stars indicates that they do not vary. In V, the microvariation seems to evolve during the 4.3 h of observation, with a total amplitude of 0.104 ± 0.014 mag (with respect to the first data set changes are ΔV = 0.03 ± 0.02 mag in 1 hr, ΔV = 0.07 ± 0.01 mag in 2.2 hr, and ΔV = 0.09 ± 0.01 mag in 3.25 hr). In R, the amplitude between the first data set and the average of the subsequent is ΔR = 0.108 ± 0.008 mag. From the light curves, it is clear that color changes occurred during this OM (see Figure 1(c)).

PKS 0003+15. Historically, this quasar has shown intense activity on long-term and intermediate-term variability (Barbieri et al. 1979; Pica et al. 1988; Schramm et al. 1994; Guibin et al. 1995, 1998; Garcia et al. 1999). OM has also been detected. In October of 1994, Jang & Miller (1995) observed a variation in R with an amplitude of 0.11 mag in 2 hr, while Eggers et al. (2000) reported changes of 0.005 mag hr⁻¹ in R. Garcia et al. (1999) also reported microvariability for this quasar. PKS 0003+15 was reported in Paper I with no evidence of microvariability. We have monitored this quasar during 3.13 hr on four occasions on 2001 October 11. Figure 1(d) shows that while brightness remained constant in B and R, a decrement in V was detected. ANOVA confirms this visual revision. The brightness for this object showed a decrease of ΔV = 0.025 ± 0.005 mag during the monitoring time.

MC3 1750+175. The only variability event previously reported for this quasar corresponds to radio wavelengths (Fanti et al. 1981; Mantovani 1982). On 1999 August 20, we observed this object three times during 3.13 hr. The light curves show a microvariability event visible only in the V band (Figure 1(e)). An ANOVA confirms this variation to be real; the amplitude of this variation is ΔV = 0.04 ± 0.008 mag between the first data set and the third.

CSO 21. Observations for CSO 21 were reported in Paper I, but without a positive detection of microvariability. For the present study, the object was observed on three occasions on 2001 December, during 2.5 hr. A gradual brightness increase is appreciated in the three bands (Figure 1(f)). However, an ANOVA indicates a variation in V only, a barely marginal variation in R (with a significance level of 10%), and no variation in B (if the observed tendency in the B light curve is a variation, it is hidden by the internal data dispersion). The amplitude of the variation is ΔV = 0.025 ±  0.005 mag in 2.5 hr. The variation amplitude of the R band is ΔR = 0.016 ± 0.004 mag between the first data set and the third.

1628.5+3808. In Paper I we reported the cases or microvariability for this object for the first time. They are two events in 1997 February and May: in February, there was a variation with an amplitude of 0.082 mag throughout 2.4 hr; in May, throughout six monitoring hours, the OM consisted of pulsations with amplitudes from 0.04 to 0.057 mag. We observed this quasar on two occasions on 2001 June 13. The light curves show an appreciable brightness decrease in the three bands (Figure 1(g)). An ANOVA indicates that this variation is detectable in the B and R, but in V the variation is only marginal (the significance level is 3%). The data dispersion in the comparison stars does not show evidence for statistical differences. The OM amplitudes are ΔB = 0.061 ± 0.011 mag and ΔR = 0.018 ± 0.004 mag, in the 2.39 hr of monitoring. The V marginal detection would have an amplitude of 0.03 ± 0.01 mag.

US 3472. In Paper I we reported an OM event for this quasar with an increase of 0.02 mag in 50 minutes. During 2 hr, a series of oscillations followed this brightness increase, with amplitudes between 0.040 and 0.055 mag. Long-term optical and infrared variability has also been reported (Enya et al. 2002b). We observed this object during 2.5 hr on three occasions on 2001 December 20. The light curves show a brightness decrease in V and R (Figure 1(h)). An ANOVA confirms the variation. In V, the microvariation seems to have kept a constant rate with a total amplitude of ΔV = 0.020 ±  0.003 mag in 2.35 hr. Between the first and the third data set in the R band, the brightness varied by 0.014 ± 0.002 mag.

Mrk 830. Long- and short-term variability and microvaribility have been reported for this quasar. We observed this object on four different occasions, OM events being detected on 1999 August 17 and 18, and on 2001 June 14. The object possessed a very similar brightness on the three occasions, V ∼ 17.6. This brightness is similar to that reported by Stepanian et al. (2001) (V = 17.29 ±  0.03), and Chavushyan et al. (1995) (V = 17.62). Unfortunately, the fields of the two telescopes used are different, and thus it was more convenient to use a different set of comparison stars for the 1999 August and 2001 June observations.

1999 August 17. The object was observed three times during 2.13 hr. A visual revision of the light curves indicates the possible detection of a microvariability event in V (Figure 1(i)). Due to instrumental problems, in the first sequence of the R band, we missed the object for several images. Thus we can present only the complete curve for the comparison stars. An ANOVA shows that this variation would be marginal, with a significance level of 3%. The increment in brightness, if real, has a constant rate with a total amplitude of ΔV = 0.03 ± 0.01 mag in 2.31 hr.

1999 August 18. The monitoring data set consisted of three observation groups taken during 2 hr. Again, a revision of the light curves shows a possible variation in V (Figure 1(j)). An ANOVA detects this feature as a marginal variation, with a significance level of 3%. As on the previous night, the tendency is a variation at a constant rate, but this time with a total amplitude of ΔV = 0.05 ± 0.03 mag.

2001 June 14. On this night the quasar was observed twice. A visual revision of the light curves indicates a possible variation in the three bands (Figure 1(k)). The brightness increase is a few hundredths of magnitude between the two groups of observations. An ANOVA confirms the reliability of this variation. While in V and R the significance level is 0.1%, in B the value is ∼ 5%. The amplitudes are ΔV = 0.039 ± 0.007 mag and ΔR = 0.030 ± 0.007 mag, occurring during 1.18 hr. If a variation exists in B, the amplitude would be of ΔB ∼ 0.04 mag.

The χ² test for homogeneity is used to compare two or more qualitative properties of several samples when the number of elements in each sample is fixed. In our case, we will split the observations of the two samples of RQQs and CRLQs into those that show variability and those that do not.

For each sample of RQ and CRL objects the microvariability events were counted regardless of the band of detection. As in Paper I, we note that although each observation will be considered independently; some of them may belong to the same object. In doing this, some unwanted effects can be introduced because the observations of the same object may not be completely independent. This may be the case, for example, if one object is intrinsically much more variable than another.

The total number of paired observations for each sample is 63 (although the number differs for each band, i.e., the occasions on which one could observe the two members of the same pair were 61 for B, 63 for V, and 61 for R). In nine of these monitoring microvariability was detected for at least one member of each pair, with a significance level of 0.1%. Five out of these nine were detected in RQQs and four in RLQs. This number rises to 11 when we take into account the two marginal detections of Mrk 830.

Table 2 shows the χ² contingencies for these data. Column 1 displays the number of OM events with a significance level of up to 0.1%. The number of observations in which there is no evidence of variability appears in Column 2, the total number of observations appears in Column 3, and the expected frequencies of microvariations under the null hypothesis, i.e., if both types of objects possess the same microvariability properties, are shown in Columns 4 and 5. These last columns are calculated multiplying the partial totals of each line and each column and then dividing by the total number of observations. The homogeneity test shows that the probability of observing the numbers in Table 2 can be obtained 27% of the times when extracting two samples in an aleatory way from the same population. The probability to obtain the observed OM frequencies is large enough and thus the null hypothesis cannot be rejected. In other words, it is reliable to assume similarity between the two samples.

Although the test for homogeneity did not show differences for the occurrences of OM between RQQs and CRLQs, a test on the quantitative values of the variance for both samples of objects might show whether the OM is larger in one type than in the other. The color changes during variations make it interesting to consider observations of each band separately.

In Paper I we showed that it is better to estimate the difference between RQQs and CRLQs, breaking the variance into two components, than to consider a single observed variance. The intrinsic variance for a source, V_r, can be written as V_r = V_o − e²/5, where V_o refers to the observed variance and e² are the squared errors of the data weighted by the number of observations in each group (five). The last refers to the inherent error of the observation and reduction data processes, and it is calculated empirically from the variance for each of the five observation groups.

Student's t test can be used to find differences between the means when these have a normal distribution. This is approximately the case for the intrinsic variances difference. For these data, we have computed the matched pair test, in which the mean of the distribution of these differences should not be significantly different from zero if both samples are extracted from the same population. The test indicates that there are no significant differences among the samples: it gives a probability that the observed differences occur by chance of 18.7% for B, 19.1% for V, and 87% for R. When an independent pair test is carried out, the mean difference values are similar, within the errors, and so are the uncertainties of such differences.

This test was repeated considering average values of the intrinsic variances for each pair of objects. The qualitative result remains the same; however, quantitative results do change: in V the probability that the observed differences happen by chance increases to 28%, in B it changes to 23%, and in R it diminishes to 53%. The averages in this case are distributed so that the fits are quite good, because although we have lost degrees of freedom, the data of the variations themselves are masked when they are averaged with other data. It is necessary to note that the probability obtained for the data of the V band is consistent with the value obtained in Paper I, where the same filter was used. These results imply that the incidence of OM is independent from luminosity and redshift.

The tests neatly point out an extremely small and nonsignificant difference in the microvariability displayed by the two samples, yielding no evidence that they come from different populations. Figures 2(a)–(c) show the histograms for the intrinsic variance differences of the observations paired for each filter. Except in the case of R, for which data can be fitted using a single Gaussian profile with a standard deviation of 2.3 × 10⁻³ and an average value of ∼0, the others cannot be accurately fitted by a single Gaussian. Taking into account the results presented in Paper I, we separated the data into observations with (dashed line) and without (dotted line) detected variations. Then, good fits were obtained. As in Paper I, we found that some variations could occur and not be detected. An OM event could occur in the three bands even if it is detected in only one.

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In the B band, the data group where OM was not detected is centered at ∼0, and it has a standard deviation of 4 × 10⁻³, i.e., indistinguishable from zero (Figure 2(a)), while the group with variability has a standard deviation of 4 × 10⁻³ and is centered at 1 × 10⁻³. These results indicate that the samples are not statistically distinguishable. In V there is a similar behavior (Figure 2(b)). The nonvariable component was fitted with a Gaussian that has a standard deviation of 1.2 × 10⁻³ and is centered at 4 × 10⁻⁴, while the variable component is centered at ∼0 and has a standard deviation of 4 × 10⁻³. The data with OM detection were fitted by a Gaussian centered at 4 × 10⁻⁴ with standard deviation 3 × 10⁻³, while the non-detection data were best fitted with a Gaussian centered on 0 with standard deviation 2.3 × 10⁻³ (Figure 2(c)). These results can change when we consider that some quasars were observed on more occasions than others.

All the statistics discussed here indicate that there are no significant differences in the OM properties between CRLQ and RQQ. While this is at odds with some other studies, it is consistent with the results reported in Paper I, by Stalin et al. (2004), and by Gupta & Joshi (2005).

We can characterize the probability with which an OM event is detected as a function of the duration of monitoring. The DC is a very useful tool for comparing the behavior of different types of AGNs, and for planning future observations. The DC is defined as the ratio of the number of observations with a positive detection of OM to the total number of observations, weighted by the period of time during which the objects have been observed (see Romero et al. 1999). Of course, OM depends also on intrinsic causes that determine its occurrence. The last, however, are unpredictable and unquantifiable. OM is believed to be a transient phenomenon. Independent of its origin, neither thermal nor nonthermal instabilities are expected to be permanent. We have calculated the DC using Expression (2) from Romero et al. (1999), but considering the joined observations for RQQs and CRLQs, because we detect no difference between both samples. When the DC is calculated without taking into account the band, a value of 8.45% is obtained. If marginal detections are considered, the value does not change too much: 10%. Separating data by band, we obtain DC_B = 2.3%; DC_V = 6.8%, and DC_R = 5.8%.

The DC_V is three times lower than the one reported in Paper I, where the same filter was used. The discrepancy could be due to the use of three filters in the present study. When we analyze the light curves from Paper I, we can see that one third of the events correspond to variations with constant increase or decrease. The rest correspond to changes with oscillating behavior. If this proportion is a general behavior, and since we have now a lower temporal covering, we expect to detect only the constant changes, i.e., a third of all the possible detections with one filter.

For the blazar class, Sagar et al. (2004) reported DC = 72%, and Gupta & Joshi (2005) reported DC = 60%, for microvariability, while Carini (1990) reported a DC of ∼80% for timescales from hours to days. For the quasars, Stalin et al. (2004) calculated DC_RQQ = 17% and DC_RLQ = 15%. Their observations were carried out in the R band. Using the data from Table 4 of Paper I, and the expression of Romero et al. (1999), a DC of 18% is obtained for the joint RQQ and CRLQ samples.

Other groups have found differences in the DCs of these objects. Romero et al. (1999) calculated a DC of 68% and 6.9% for RL and RQ objects, respectively (their observations were carried out with a V filter). Taking the data of Jang & Miller (1997), the DC_RQQ = 7.6% (their observations were carried out with an R filter), while DC_RLQ = 60.6%. With the data from Gopal-Krishna et al. (2000), DC_RQQ = 6.1% (not taking into account their detections that at least are very probable, while when including those probable detections DC_RQQ = 29.4%). These results show a clear difference between RLQs and RQQs, which represents a behavior very different to that found in the present study.

At this point we want to stress the relevance of good sample selection. However, all these groups included BL Lac objects among the RLQ samples, and it is very possible that this can alter the value of the DC for the RL sample. The DCs for the RQQs, on the other hand, are very similar (∼6%–7%) to that found by us (for the complete sample). To illustrate this point, we point out that Romero et al. (1999) use a sample of RL objects that includes several BL Lac objects. Fifty-three percent of their observations and 67% of their microvariability detections correspond to blazar type objects. On the other hand, the RQQ sample of Jang & Miller (1997) is constituted mainly by non-OM objects, since it is composed of 90% low-brightness quasars. The average magnitudes for RQs are similar to the average magnitudes for RLs (averages differ in only 2%), but the average redshifts are much smaller for RQs (average redshifts differ in 62%; for RQQ, z average is 0.5 while z average for RLQ is 1.3). Although in Paper I we have not found evidence of dependence of OM on brightness and/or redshift, it would be necessary to investigate further such possible biases. The nonhomogeneous samples problem could also be present in the work of Gopal-Krishna et al. (2000). These authors report observations of RQQs, without a control sample, comparing with their previous results on radio loud objects.

It is also worth noticing that, when the above authors make a subselection of objects with the selection criteria described here and in Paper I (except for the use of lobe dominated radio quasars instead of CRLQs), they obtain similar comparative results to those reported in Paper I (see also Stalin et al. 2004).

Finally, in Paper I we developed an alternative method for calculating the DC. This method considers all the quasars present the same DC in H hours of monitoring. We grouped the data in parcels according to monitoring duration, with intervals of 1 hr. Parcels larger than 6 hr have been excluded from the sampling since there were very few for a good statistic. Using the current data in Equations (1)–(3) from Paper I, we find that the mean value for the probability of detecting an OM event in 1 hr of monitoring, P₁, has a value of 8.9 ± 2%, which is marginally different from the value found in Paper I (P₁ = 5 ±  2%; however, also take into account the fact commented above that in this study the detection of oscillating variability may be dumped by the larger lags in the monitoring). Table 3 is similar to Table 4 in Paper I. Columns show, respectively, the values of the number of monitoring hours, H, the number of monitors in H hours, N_H, the number of OM events detected in H hours, E_H, the probability of detecting an OM event in H monitoring hours, P_H, and the probability of detection in 1 monitoring hour, P₁.

To illustrate the reliability in the use of an ANOVA, additionally we have applied a χ² test to the data. The average, B_i, has been taken from each group of five observations, and the error, s_i, is obtained from the dispersion of these five observations. Table 4 shows the differential photometric data for each group of observations (t₁, t₂, and t₃ of US 3472). Taking the whole data set mean, 〈B〉, we can obtain the statistical

$$\begin{equation} \chi ^2 = \sum {(B_i - \langle B\rangle)^2 \over s_i^2}. \end{equation} \tag{ 1 }$$

As an example, we consider the case of US 3472 for the V band. Please note that we are carrying a large number of decimal places during the calculations. For this quasar we have obtained the following values from differential photometry, comparing with a stars field

$$\begin{equation} B_1= 0.5602 \pm 0.00206, \end{equation} \tag{ 2 }$$

$$\begin{equation} B_2= 0.5718 \pm 0.00116, \end{equation} \tag{ 3 }$$

$$\begin{equation} B_3= 0.5808 \pm 0.0022. \end{equation} \tag{ 4 }$$

From these values, the median is 〈B〉 = 0.57093. Thus, we have χ² = 27.13095 + 0.5625 + 20.12746 = 47.82091. As the tabulated value for χ², with 2 degrees of freedom, for a level of meaning to the 0.1% has a critical value of 13.8150, we have detected variations at this level.

For the case of the stars field, the raw differential photometric data is shown in Table 5, and the means are

$$\begin{equation} B_1= -0.9446 \pm 0.00558, \end{equation} \tag{ 5 }$$

$$\begin{equation} B_2= -0.9422 \pm 0.00256, \end{equation} \tag{ 6 }$$

$$\begin{equation} B_3= -0.9466 \pm 0.00216, \end{equation} \tag{ 7 }$$

whose median is 〈B〉 = −0.94447. With this, we have χ² = 0.000542773 + 0.78627 + 0.97242 = 1.75923.

For comparison, using an ANOVA the sum of the differences of the averages of the data shown in Table 4 is 0.00107, while the square difference of the internal dispersion is 0.0002084. As the degrees of freedom are k − 1 = 2 and N − k = 12, we have F = 30.80614203. With a level of significance of 0.001, a value of 12.97 is obtained. With such a result, we have a positive detection of OM.

With the same procedure for the field stars (Table 5), we find that the sum of the square difference of the averages is 0.0000485335, while the difference of the internal dispersion is 0.0008472. Thus, we have that F = 0.34721671.

This example illustrates that microvariability detections with ANOVA are at least as reliable as those that can be obtained using χ². In our example, we could estimate errors for each observation in the χ² test from the same quasar data set, because the observations were performed using an ANOVA design. This is not usually the case with error estimates in χ² based designs. In χ² tests, errors are usually calculated either from different data sets (one or more comparison stars; e.g., Romero et al. 1999) or from IRAF theoretical errors multiplied by a correction factor (e.g., Stalin et al. 2005). Besides, this estimated error is often considered as a constant along the data set, missing the internal variability of the data due to short timescale factors (tiny clouds, seeing changes, etc.). By contrast, ANOVA uses internally consistent errors calculated from the same data set.