Spectral variability of FIRST bright QSOs with SDSS observations

With the FIRST survey and the Automated Plate Measuring Facility (APM) catalog of the Palomar Observatory Sky Survey I (POSS-I) plates, White et al. (2000) presented their FIRST Bright Quasar Survey (FBQS) catalog with 636 QSOs distributed over 2682 $deg^{2}$. There are four criteria to select FBQS candidates: radio-optical positional coincidence (1”.2); E$\leq$ 17.8; optical morphology (stellar-like); POSS color bluer than O-E=2. They do not find a bimodal distribution in radio to optical flux ratio, and the numbers of RQ/RL QSOs are comparable. Spectra for the FBQS were obtained at different observatories: the 3 m Shane telescope at Lick Observatory, the 2.1 m telescope at Kitt Peak National Observatory, the 3.5 m telescope at Apache Point Observatory,the $6\times 1.8m$ Multiple Mirror Telescope (MMT), and the 10 m Keck II telescope. These FIRST spectra can be downloaded from the CDS ¹¹1http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/ApJS/126/133.

The SDSS DR7 (York et al. 2000) contains imaging of almost 11663 $deg^{2}$ and follow-up spectra for roughly $93\times 10^{4}$ galaxies and $12\times 10^{4}$ quasars. All observations were made at the Apache Point Observatory in New Mexico, using a dedicated 2.5m telescope. The SDSS spectra were obtained through 3” fibers. With these 636 FBQS, we cross-correlate them with the total SpecPhotoALL table ²²2http://cas.sdss.org/CasJobs/MyDB.aspx in the SDSS DR7. Applying the FBQS criterion of stellar-like morphology, we find 544 objects in SDSS DR7 spectral database with separations less than 1”, which is about 86% of 636 FBQSs. There are 312 RL QSOs and 232 RQ QSOs. Except for several objects, most of the FBQS objects have only one spectrum in the SDSS DR7 spectral database. For the SDSS spectra, the observational wavelength coverage is from  3800 to 9200Å. For spectra from White et al. (2000), the observational wavelength coverage can be found in their Table 1, which typically stops at a little shorter wavelength than the SDSS spectrum in the red part and starts a little longer than the SDSS spectrum in the blue part.

In order to isolate the spectrally variable QSOs from the total QSOs, we calculate the integrated relative flux change ($\Delta f/f$). For the two-epoch spectra of a QSO, we calculate the mean flux ($f$) and the difference flux ($\Delta f$) at every wavelength (SDSS flux minus FIRST flux). This integrated relative flux change measures the total relative flux change between the two epochs over a large optical wavelength range, rather than the variation at just one wavelength or in one filter. With the stars to calibrate the QSO flux variability, Wilhite et al. (2005) found that the criterion for selecting spectrally variable QSOs is that the absolute value of the integrated $\Delta f/f$ is larger than 0.2-0.1 when the high-S/N epoch S/N is below 50. Here, we examine two-epoch spectra and find this criterion of 0.2 is appropriate to select the spectrally variable QSOs. In the left panel of Figure 1, we give the integrated relative flux change, $\Delta f/f$, versus the integrated S/N from SDSS and the redshift. The total numbers of two-epoch measurements are 242 and 319 for RQ QSOs and RL QSOs. Considering the S/N in the ratio spectrum, we select QSOs with ratio spectral S/N greater than 5.0. There are 221 RQ QSOs and 269 RL QSOs ratio spectra meeting the criterion. For the subsample of variable QSOs, the two-epoch numbers are 142 (58%) for variable RQ QSOs, and 204 (64%) for variable RL QSOs. We define the convention that the SDSS spectrum is in the brighter phase and the relevant FIRST spectrum is in the fainter phase if $\Delta f/f$ is positive.

For our variable QSO sample, the rest-frame time-lag is from $\sim 1$ to $\sim 10$ years (right panel in Fig. 1), while the rest-frame time-lag is less than 1 year for Whihite et al. (their Fig. 7, 2005), less than 2 years for Vanden Berk et al. (2004). We calculate structure functions at three continuum wavelengths of 5100Å, 3000Å, and 1350Å. However, the data are so dispersed that we can’t give the slopes measurement of the structure functions. The right panel of Figure 1 is the integrated relative flux change versus the rest-frame time-lag. For the distribution of $\Delta f/f$, K-S statistic $d$ is 0.081 with a signification level of 81%. Assuming that the RL and RQ QSOs were drawn from the same population, the probability that we would have observed a K-S statistics as at least as large as 0.081 is 81%. There is no obvious difference of $\Delta f/f$ for variable RL QSOs and RQ QSOs.

Figure 3 is the spectral slope distributions for SDSS QSOs (left panel) and the slope variation distribution (right panel). The mean of the slope distribution of SDSS QSOs is $-1.41$ with a standard deviation of 0.59. It is $-1.39\pm 0.56$, $-1.41\pm 0.51$, respectively for RQ QSOs and RL QSOs from SDSS. In checking the spectra with the reddest slopes, it is found that these are mainly QSOs with obvious host galaxy contribution. For the slope variation distribution in the subsample of variable QSOs, the mean slope variation (the slope of brighter phase minus the slope of the fainter phase) is $-0.003$ with a standard deviation of 0.42. It is $-0.03\pm 0.42$, $0.02\pm 0.42$, respectively for variable RQ QSOs and RL QSOs.

In Figure 4, we give the slope variation versus the integrated relative flux change $\Delta f/f$ for selected variable QSOs. About half QSOs get redder during their brighter phases. Selecting for $\Delta f/f$ larger than 1.0, this is still the case. For the distribution of $\Delta\alpha$, K-S statistic $d$ is 0.066 with a signification level of 90%. Assuming that the RL and RQ QSOs were drawn from the same population, the probability that we would have observed a K-S statistics as at least as large as 0.066 is 90%.

For the UV/optical spectrum, clean determinations of continuum fluxes are mainly at three wavelengths from 5100Å, 3000Å, and 1350Å, which are used in the mass calculation (et al., Shen et al. 2011). These three wavelengths of 5100Å, 3000Å, and 1350Å are selected to discuss the relationship between the slope variation and the continuum flux ratio. The continuum flux ratio is the flux at the brighter epoch divided by the flux at the fainter epoch at the specified rest wavelength. In order to exclude the limits of observed spectral range, we consider the slope variation at a wavelength of 5100Å for variable QSOs with $z<0.7$, at a wavelength of 3000Å for variable QSOs with $0.7<z<1.9$, and at a wavelength of 1350Å for variable QSOs with $z>1.9$.

In Figure 5, we give the relation between the slope variation and the continuum flux ratio at 5100Å for low redshift selected variable QSOs ($z<0.7$) (top left, top right panel); at 3000 Å ($0.7<z<1.9$, bottom left panel); at 1350 Å ($z>1.9$, bottom right panel). For the top right panel, it is done for the [O iii] flux correction in FIRST spectra. We did not find strong correlations between the slope variation and the continuum flux ratio, the Spearman coefficients are -0.03, -0.07, -0.10, -0.25, and the probabilities of null hypothesis are 0.75, 0.55, 0.24, 0.14, respectively (Figure 5, from left to right and from top to bottom).

It is also clear that the slope variation of half the points is positive when the flux ratio is larger than zero in all different subsamples, i.e., about half of the objects become redder during their brighter phases. The red points are for RL QSOs and the black points are for RQ QSOs. In low redshift QSOs, the host would contribute in the observed object spectrum and make it complex (e.g., Shen et al. 2011). For the low luminosity QSO sub-sample ($L_{\lambda}(5100\AA )$ ¡ $10^{45}$ erg s^-1 ), it is still the case. The top right panel in Figure 5 is the same relation but with the recalibration for FIRST spectra from White et al. (2000) from the [O iii] 5007 flux (see section 4.4).

In order to clarify the average slope variability of RL and RQ QSOs, we calculate their composite ratio spectra. There are two methods to derive the composite spectrum, one is the median spectrum, which can preserve the relative fluxes of the emission lines; the other is the geometric mean spectrum, which can preserve the global continuum shape. In order to investigate the slope variation, we use the geometric mean spectrum, $<f_{\lambda}>_{gm}=(\prod^{n}_{i=1}f_{\lambda,i})^{1/n}$, where $f_{\lambda,i}$ is the flux of spectrum number i at wavelength $\lambda$, and n is the total number of spectra contributing to the bin (e.g., Vanden Berk et al. 2001). In the left panel of Figure 6, the geometric composite spectra of our SDSS QSOs and FBQS QSOs are very consistent. Vanden Berk et al. (2001) suggested the best fitting windows in the composite spectrum are 1350-1365Å and 4200-4230Å. Using a power law function to fit the composite spectrum in the windows of 1450-1470Å and 4200-4320Å, we find that their slopes are $-1.41\pm 0.03$ for SDSS spectra and $-1.47\pm 0.03$ for FIRST spectra, which is a little larger than -1.56 by Vanden Berk et al. (2001) for a large sample of 2204 QSOs from SDSS.

Here we also use that approach to calculate the geometric composite spectrum for the flux ratio spectrum. The flux ratio is the ratio of the brighter phase spectrum to the fainter phase spectrum. All spectra of variable QSOs are scaled to the continuum flux at 3060Å. In the right panel of Figure 6, we show the geometric mean composite spectra for the flux ratio spectra for variable RL and RQ QSOs. The black curve is for all QSOs, the red curve is for RL QSOs, and the green one is for RQ QSOs. For clarity, the magnitudes are multiplied by 2 and 3 for RL and RQ QSOs. The geometric mean flux-ratio spectrum for RL QSOs is almost the same as that for RQ QSOs. All the geometric mean composite spectra are very flat. This is consistent with our results in Figures 3, 4, and 5, where about half of the objects have spectra becoming redder during their brighter phases.

For the slope variability for individual QSOs, we found that all the nearby PG QSOs in the sample of Kaspi et al. (2000; for the reverberation mapping technique) appear bluer during their brighter phases over multiple-epochs (Pu et al. 2006). However, when just considering two-epoch, it is not the case (see Fig. 1 in Pu et al. 2006). Using just two-epoch to investigate the slope variability for an entire ensemble of quasars, Wilhite et al. (2005) suggested that the QSOs continua are bluer when brighter. Here we directly calculate the slope variation for every object and find that almost half the objects appear redder continua when brighter. This paper uses the analysis framework developed in Pu et al.(2006) on a much bigger sample of QSOs. The advantages of the current sample are that it has a roughly equal fraction of RL and RQ objects, and that it contains a substantial sub-sample of objects that vary strongly in the optical/UV.

The uncertainty of the slope variation is mainly due to the selection of ”continuum windows” in the power-law fitting. Its mean error is less than 0.1. For the continuum flux ratio, the uncertainty is mainly due to the different calibration of SDSS spectra and spectra from White et al. (2000). For SDSS spectra, with the calibration from non-variable stars, it is suggested that the flux correction between High-S/N to low-S/N is about 1.03-1.01 between 4000Å and 9000Å (Wilhite et al. 2005). In logarithm space, it is 0.004-0.01, or 0.01-0.025 mag. For the spectra from White et al. (2000), we use the flux of [O iii] 5007Å to estimate their flux uncertainties.

Considering that [O iii] 5007Å emission is coming from narrow line region (NLRs), spatially extended low-density regions, we assume that the [O iii] fluxes do not vary significantly over several year timescales and then normalize each FIRST spectrum to have the same [O iii] flux as the SDSS spectrum. Due to the blending of H$\beta$ with [O iii] , we use the following steps to calculate the [O iii] flux (see Hu et al. 2008 for details). The first step is subtraction of the power-law, Balmer continuum, and pseudo-continuum Fe ii emission. The second is the multi-Gaussian fit to the [O iii] 4959, 5007 Å doublet lines and Hermite-Gaussian for H$\beta$ . We excluded objects when the absorption in  6900Å and  7600Å is in the fitting region of [O iii] 5007Å and H$\beta$ . The measured flux ratio for [O iii] 5007Å is shown in Figure 7. The mean value of the [O iii] flux ratio in logarithm space is $-0.04$ with a standard deviation of 0.23. It suggests that the SDSS flux calibration is consistent with that for FBQS but with a moderate dispersion.

In the top right panels in Figure 5, we show the slope variation versus the bright-to-faint flux ratio after considering the [O iii] 5007Å correction for the spectra from White et al. (2000). It maintains the result that almost half of the QSOs are not bluer during their bright phases. Of course, that correction can’t be used for higher redshift QSOs without observations of [O iii] 5007Å. In Figure 5, considering the continuum flux ratio larger than 0.23 from the [O iii] recalibration, a little more QSOs with z ¡ 0.7 tend to be bluer during brighter phases, and there is still half QSOs showing redder during brighter phases for QSOs with $z>0.7$.

It is suggested that arithmetic and geometric mean composites have different properties (Vanden Berk et al. 2001). Because QSO spectra can be described by power laws, by the definition of geometric mean, the geometric mean can preserve the average power-law slope. The arithmetic mean can retain the relative strength of the non-power-law features, such as emission lines.

For the subsample of variable QSOs, the composite difference spectrum is calculated from the geometric/arithmetic mean for QSO spectra with flux scaled to 3060Å. For the difference spectra (brighter phase minus fainter phase), the geometric mean composite difference spectrum is almost the same as the geometric mean composite spectrum. However, with the arithmetic mean, they are different, with the slope of the arithmetic mean composite difference spectrum of $-1.75\pm 0.04$ and the slope of arithmetic composite spectrum of $-1.42\pm 0.03$. The slope of -1.75 for the difference spectrum is larger than -2.0 by Wilhite et al. (2005).

In Figure 8, the blue curve is the arithmetic mean composite spectrum from the SDSS spectra scaled to a value of 1 at 3060Å. The ratio of the arithmetic mean composite difference spectrum to the arithmetic mean composite spectrum is shown as a black curve. Larger values of this ratio indicate a more variable portion of the spectrum. We can find smaller values in emission lines of C iv ,Mg ii ,H$\beta$ , etc on the ratio spectrum, showing that the emission lines are considerably less variable than the continuum. It is consistent with the intrinsic Baldwin effect for emission lines (Kinney et al. 90). For rest wavelengths greater than 2500 Å, the ratio is flat (near 1), showing that the composite difference spectrum has the same continuum slope as the composite spectrum. However, the values blueward of 2500 Å in the ratio spectrum become larger than 1. Vanden Berk et al. (2004) showed that the variability dependence appears to flatten around 3000 Å (see their Figure 13), which is consistent with the flatness in this dataset around 3000 Å.

The ratio spectrum from 2500 Å to 3600 Å is flat (near 1), showing that the composite difference spectra have the same continuum slope as the composite spectrum. Blueward of 2500 Å, the composite difference spectrum (brighter phase minus fainter phase) has more variance than the average QSO spectrum. Redward of 3600 Å, the variance becomes slightly greater than 1 and increases slowly toward longer wavelengths.

Since the ratio spectrum is flat excluding the region blueward of 2500 Å, the steep slope of the composite difference spectrum is due to the higher value blueward of 2500 Å, which also shows a difference in the composite spectra constructed from both the arithmetic and geometric means. The variability for the region blueward of 2500 Å is different from that for the region between 2500 Åand 3600 Å, and different from the region redward of 3600 Å.

Our interpretation of this result is that the lack of variability from 2500 Å to 3600 Å arises because this spectral region is dominated by Balmer continuum and Fe II emission. As pointed out above, the arithmetic mean is sensitive to spectral features. The Fe II region is composed of the many members of the stronger UV multiplets, and they may completely dominate the continuum emission (e.g., Wampler 1986). Since the emission lines in general are shown to vary less than the continuum in the composite difference spectrum, this region crowded with line emission and Balmer continuum (the 3000 Å bump) is likely to have a similarly lower variability.

The variability for the region blueward of 2500 Å and redward of 3600 Å is due to the accretion disk. During the brighter phase, the accretion disk becomes hotter and its emission peak would move to shorter wavelengths (big blue bump), which would lead to larger variance in the blue spectrum. For the region redward of 3600 Å  the more slowly varying outer regions of the disk would dilute the variability from the increased flux from the hotter regions, To the extent that the increase in variability to the red is significant, the density of slowly varying emission lines (particularly the higher Balmer series and optical UV multiplets) is decreasing in that direction.

The more variance blueward of 2500 Å does not mean that the spectrum becomes bluer when the spectrum becomes brighter. Due to accretion power energy mechanics, it is believed that the UV-optical continuum can be described by a power-law function. However, for the different spectrum, it is not the case (see cyan curves in Figure 2). Sometimes, respect to the ratio spectrum, the slope would be oppositive if we use a power-law function to fit the different spectrum.

In Figure 8, we also give the ratio spectra for variable RL QSOs (red curve), and variable RQ QSOs (green curve). Blueward of 2500 Å, they are almost the same. And we notice that number of RQ QSOs are not as many as RL QSOs in our variable sample. There is a small bump redward of 4000 Å for variable RL QSOs, however, that is not the case for variable RQ QSOs.

There is no obvious difference in the distribution of the slope variations for subsamples of RQ and RL QSOs (Figure 4). The color change with increases in brightness is not different between RL and RQ QSOs. It implies that the presence of a radio jet does not affect the slope variability on 10-year timescales. The variability must be from disk instabilities or some other variation,such as reprocessing of X-rays and reflection of optical light by the dust (Breedt et al. 2010).