THE FIRST FERMI MULTIFREQUENCY CAMPAIGN ON BL LACERTAE: CHARACTERIZING THE LOW-ACTIVITY STATE OF THE EPONYMOUS BLAZAR

The LAT, on board the Fermi Gamma-ray Space Telescope (Atwood et al. 2009), is a pair-conversion γ-ray telescope, sensitive to photon energies from about 20 MeV up to >300 GeV. It consists of a tracker (composed of two sections, front and back, with different angular resolutions), a calorimeter, and an anti-coincidence system to reject the charged-particle background. The LAT has a large peak effective area (∼8000 cm² for 1 GeV photons in the event class considered here), viewing ≈2.4 sr of the sky with angular resolution (68% containment radius) better than ≈1° at E = 1 GeV. The large field of view, improved effective area and sensitivity, and the survey nominal mode make Fermi-LAT an optimal all-sky hunter for high-energy flares and an unprecedented monitor of γ-ray sources. The data set used in this paper was collected during the first 18 months of Fermi science observations, from 2008 August 4 to 2010 February 4 (about 550 days, 78 weeks from MJD 54682.7 to 55232.9, as shown in the weekly light curve in Figure 2, upper panel). This interval includes the period chosen for the first Fermi MW campaign on BL Lac (2008 August 19–October 7, MJD 54697.8–54746, i.e., about 48 days, indicated by the line in Figure 2, upper panel). Fermi-LAT data analysis was performed with the standard Fermi-LAT ScienceTools software package⁶⁵ using version v9r15p5. Only events belonging to the "Diffuse" class in the energy range 0.1–100 GeV were used in the analysis. Instrument response functions used were version P6_V3_DIFFUSE. In order to provide protection against significant background contamination by Earth-limb γ rays, all events with zenith angles >105° were excluded.

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The 18 month light curve was built using 1 week time bins (Figures 2 and 4). For each time bin, the integrated flux (E > 100 MeV) values were computed using the maximum-likelihood algorithm implemented in the science tool gtlike. For each time bin, we analyzed a region of interest (RoI) of 12° in radius, centered on the position of the source. All point sources listed in the 1FGL (one year) LAT catalog (Abdo et al. 2010b) within 19° from BL Lac and having test statistic⁶⁶ TS >50 and fluxes above 10⁻⁸ photons cm⁻² s⁻¹ were included in the RoI model using a power-law spectrum (dN/dE ∝ E^−Γ, where Γ is the photon index). The isotropic background (the sum of the residual instrumental background and extragalactic diffuse γ-ray background) was included in the RoI model using the standard model file isotropic_iem_v02.txt,⁶⁷ and the Galactic diffuse emission was included in the modeling using the file and the standard file gll_iem_v02.fit. In the final light curve computation, the photon index value was frozen to the value resulting from the likelihood analysis on the entire period. For each time bin, if the TS value for the source was $\rm TS<4$ or the number of model predicted photons N_pred < 10, the values of the fluxes were replaced by the 2σ upper limits. All errors reported in the figures or quoted in the text are 1σ statistical errors. The estimated relative systematic uncertainty on the flux, according to Abdo et al. (2010b) and reflecting the relative systematic uncertainty on the effective area, is set to 10% at 100 MeV, 5% at 500 MeV, and 20% at 10 GeV.

The γ-ray spectral analysis of BL Lac was performed both for the entire 18 month period and for the 48 days of the campaign. These spectra are shown in Figure 3. The flux value for each energy bin and for the two periods is reported in Table 1. The most energetic photon observed within the 95% point-spread function (PSF) containment radius of the source for the 18 month period had an energy of 70 GeV, while for the campaign period the highest energy photon had 10 GeV. The energy-spectrum binning was built requiring $\rm TS > 50$ and/or model-predicted source photons >8, except for the last bin, which had an upper limit rather than a detection. The 18 month spectrum results in an integrated average flux of (19.85 ± 0.40) × 10⁻⁸ photons cm⁻² s⁻¹, in the 0.1–100 GeV range, with $\rm TS=2375$ and photon index Γ = 2.38 ± 0.01, while the value for the 48 day interval of the multifrequency campaign (11.5 ± 2.7) × 10⁻⁸ photons cm⁻² s⁻¹, and the photon index slightly flatter (Γ = 2.27 ± 0.10), with a $\rm TS = 111$.

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In order to quantify the departure of the 18 month spectrum from a power-law shape, we use a spectral curvature index $\mathcal {C}$ as in Abdo et al. (2010b),

$$\begin{equation} \mathcal {C} = \sum _{i} \frac{\big(F_{i} - F_{i}^{\rm PL}\big)^{2}}{\sigma ^{2} + \big(f_{i}^{{\rm rel}} F_{i}\big)^{2}}, \end{equation} \tag{ 1 }$$

where i is the index for a particular energy bin, F_i is the observed flux, F^PL_i is the flux in the ith bin predicted by the global power-law fit, σ is the error in F_i, and f^rel_i is the relative systematic uncertainty in that bin (reported in Table 1). The power-law fit has two parameters: the normalization and photon index. The curvature parameter is expected to follow a χ² distribution with 9 − 2 = 7 degrees of freedom (dof) if the power-law hypothesis is true. With 99% confidence, the spectral shape is significantly different from a power law when $\mathcal {C} > 18.48$. For the accumulated 18 month data on BL Lac, we found $\mathcal {C} = 20.88$ (0.1 GeV < E < 100 GeV), which implies a curved spectrum. The same procedure, when applied to the spectrum of the 48 day multifrequency campaign, resulted in $\mathcal {C} = 2.83$ (0.1 GeV < E < 100 GeV), implying there is no significant evidence for deviation from a simple power law in this spectrum (Figures 3 and 10). This does not necessarily mean that there is no curvature during this 48 day period, because it could be due to the lower emission state and accumulated statistics.

To further explore the curvature, the 18 month spectrum was fit with a log-parabola function in the 0.1–300 GeV energy band. This was performed in two runs: first a fit with E_break left free, then another with E_break frozen at the value found in the first run (300 MeV) to improve the calculation of the other parameter values. The result of the latter fit gives

$$\begin{eqnarray*} d\!N/d\!E &= & (2.02 \pm 0.07) \times 10^{-10} \\ && \times (E/ 300\ \rm MeV)^{- \left((2.23 \pm 0.05) + (0.07\pm 0.02) \log (E/300\ {\rm MeV}) \right)},\nonumber \end{eqnarray*}$$

with TS = 2384.1. The higher TS value shows that the 18 month LAT spectrum does not follow a simple power-law function, and the log-parabola model can describe this spectrum.

The weekly light curve in the 0.1–100 GeV band for the 18 month period is presented in Figure 2 (upper panel). In order to quantify the variability, the variability index as defined in Abdo et al. (2010b) was computed from

$$\begin{eqnarray} &&V = \sum _{i} w_{i}(F_{i} - F_{wt})^{2}, \end{eqnarray} \tag{ 2 }$$

where

$$\begin{eqnarray} &&w_{i} = \frac{1}{\sigma ^{2}+(f^{{\rm rel}} F_{i})^{2}}, \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} &&F_{\rm wt} = \frac{\sum w_{i}F_{i}}{\sum w_{i}}, \end{eqnarray} \tag{ 4 }$$

and the index i runs over all data points except the upper limits (61 bins). Here, F_i and σ_i are flux values and the relative statistical errors, respectively, and f_rel is equal to 3% of the flux for each interval, as suggested by Abdo et al. (2010b). For the 18 months, F_wt was found to be 17.48 × 10⁻⁸ photons cm⁻² s⁻¹ and V = 193 with 60 dof, which is consistent with variability (the probability the source is non-variable is less than 10⁻¹⁵). The same values computed just for the first 9 weeks, containing the period of the MW campaign, give F_wt = 10.67 × 10⁻⁸ photons cm⁻² s⁻¹ and V = 0.6 with 8 dof, which is consistent with a non-variability hypothesis at >99% confidence. Each of the LAT flux data points in the upper panel of Figure 4 has $\rm TS>10$.

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This interval with no observed γ-ray variability characterizes the intensive coordinated campaign period. After the campaign, starting from about halfway through 2008 November until 2010 February 4, BL Lac showed variable weekly γ-ray flux with V = 162 with 51 dof, F_wt = 19.15 × 10⁻⁸ photons cm⁻² s⁻¹. In particular, a one-week γ-ray flare occurred in the week MJD 54928.5–54935.5 (2009 April 7–14), with a flux value of 72 × 10⁻⁸ photons cm⁻² s⁻¹. This is about four times greater than the mean flux value (F_wt) computed above. Moreover, this is the highest weekly flux yet detected from BL Lac, although another likely flare was detected in the week around MJD 55221 (2010 January 25; Sokolovsky et al. 2010). After the 2009 April flare the source also showed slightly higher activity and flux.

The 78 points of the 18 month light curve were also used to compute the global normalized excess variance, as defined in Vaughan et al. (2003) and Abdo et al. (2010c): $\sigma ^{2}_{\rm NXS} = (S^{2} - \bar{\sigma ^{2}_{{\rm err}}})/\bar{x}^{2}$, where S² is the variance of the light curve and σ²_err = σ²_i + σ²_sys, the sum in quadrature of the statistical uncertainty of the flux in the time bin and the systematic error estimate (0.03〈F_i〉). This quantity measured an intrinsic variability amplitude of 0.23 ± 0.03, in good agreement with the value found in Abdo et al. (2010c) reporting the weekly light curve of BL Lac (flux E>300 MeV) during the first 11 months. This confirms again that BL Lac was variable after the first couple of months of Fermi science operations.

The RXTE/PCA space observatory performed sub-daily monitoring of BL Lac for 20 days, during the same epoch as LAT and Swift, for a total of 80 pointings between 2008 August 20 and September 9. Only PCU2 was active for a total exposure of 157.3 ks. The PCA STANDARD2 data were reduced and analyzed with the routines in HEASOFT V6.8 using the filtering criteria recommended by the RXTE Guest Observer Facility. Only the top-layer events were processed, and a check was performed in the 40–100 keV range to assure that the model background reproduced the observed one. The average net count rate in the 3–18 keV band is 0.55 ± 0.01 counts s⁻¹ pcu⁻¹. The RXTE spectra were extracted and fitted separately for each pointing, and summed to obtain the average spectrum. Each spectrum is well fit by a single power-law model with Galactic absorption. The Galactic N_H was fixed at two values: that measured by Elvis et al. (1989), based on dedicated 21 cm observations (2.015 × 10²¹ cm⁻²); and the sum of this value with that inferred from millimeter observations (Lucas & Liszt 1993), which includes the contribution from molecular hydrogen along the line of sight (N_H ≃ 3.6 × 10²¹ cm⁻²). In the RXTE band, however, this difference yields negligible effects, with a difference in spectral indices ΔΓ_X ∼ 0.02.

The RXTE data showed modest flux variations, with a rate which remained constant at ∼0.6 counts  s⁻¹ up to MJD 54708, and slowly decreasing to ∼0.4 counts  s⁻¹ toward MJD 54718. Spectral variations were modest as well, ranging from 1.95 ± 0.09 to 2.28 ± 0.07. The total average spectrum is well fit with a single power-law model, with Γ_X = 2.18 ± 0.06, and an unabsorbed flux in the 2–10 keV band of F_2–10 = (7.2 ± 0.3) × 10⁻¹² erg cm⁻² s⁻¹ and χ²_r = 0.81 (15 dof). This spectrum can also be fit by a concave log parabola or broken power-law model, with the slope hardening above 8–9 keV from ∼2.2 to ∼1.9 (χ²_r ≃ 0.7); however, the low statistics do not allow one to determine if the improvement is significant, and the single, rather flat (Γ_X ≃ 2, therefore νF_ν ∝ ν⁰) power law gives a good fit.

In the context of the overall SED, the low X-ray flux and the Γ_X ≃ 2 spectrum (flat X-ray SED) are evidence that the RXTE band might correspond to the passage between the two humps of the blazars' SED, as typical for ISPs. In the following, we show that the Swift–XRT results provide us with further evidence for this conclusion.

The Swift gamma-ray burst satellite (Gehrels et al. 2004) performed daily monitoring simultaneous with RXTE and LAT observations for 20 days (from 2008 August 20, 15:19 UT, to 2008 September 9, 02:37 UT; MJD 54698.64–54718.11), plus three more separate observations after September 18. Data reduction and analysis were performed running a processing script customized for the XRT and UVOT data (D. Donato et al. 2011, in preparation). The script reprocesses the Swift data, stored in the HEASARC archive using the standard HEASoft software (version 6.8) and the latest calibration database (20091130 for XRT and 20100129 for UVOT). The reduction of XRT data consists of running xrtpipeline, selecting only the events with 0–12 grades in photon counting mode (PC). The UVOT image mode data are processed following the steps reported in the UVOT Software Guide 2.2.

The XRT data analysis is performed using the script xrtgrblc, available in the HEASoft software package. In brief, the script selects the best source and background extraction regions based on the source intensity (a circle and an annulus, respectively). In the case of BL Lac, the source extraction region typically has a 55'' radius and the background region has a 110''–210'' inner–outer radius. Field sources are excluded by applying circular masks whose radius depends on the field source intensity. Using these regions, source and background count rates, spectra, and event lists are extracted. The net source count rate must be corrected for irregularities in the exposure map and the PSF. The total correction factor is obtained using the HEASoft tool xrtlccorr.

The script that handles the UVOT analysis is uvotgrblc (available within HEASoft). It determines the presence of field sources and excludes them from the background region with circular regions whose sizes depend on their intensity. The optimal background region is chosen after comparing three annular regions centered on the main source in the summed images. The region with the lowest background is selected. The inner and outer radii are 27'' and 35'', respectively, for all the filters except V, for which the two radii are 35'' and 42''. The source extraction region is also intensity dependent: the script selects the aperture size between 3'' and 5'' based on the observed source count rate and the presence of close field sources. BL Lac is a relatively bright object and an extraction region of 5'' is preferred. The field of view in the V and B filters is full of field sources and in particular there is a bright star east of the blazar. To avoid contamination from such a source, the extraction region is reduced to 3''. The script estimates the best source position using the task UVOT centroid and the photometry using the task UVOT source. The obtained values are already corrected for aperture effects, while we used the dust maps of Schlegel et al. (1998) and the Milky Way extinction curve of Pei (1992) to compensate the Galactic extinction. XRT and UVOT light curves and SEDs are shown in Figures 4–6.

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As with the harder energy band with RXTE, BL Lac does not show any major sign of variability in the Swift-XRT data. The same Galactic (N_H ≃ 3.6 × 10²¹ cm⁻²) fixed value was used also for the XRT analysis. The 2–10 keV flux derived from Swift observations lies between 6 and 8 × 10⁻¹² erg cm⁻² s⁻¹with a hint of a lower intensity at the end of the campaign when the flux was below 5 × 10⁻¹² erg cm⁻² s⁻¹. We found that in the day-by-day spectral analysis, the photon index does not change significantly either. Using a single power-law model with fixed Galactic absorption, Leiden–Argentine–Bonn (LAB; Kalberla et al. 2005) weighted average equal to 1.73 × 10²¹ cm⁻²), the slope varies between 1.75 and 2.06. Since the typical error on this parameter is of the order of 0.1, the variability is within 2σ.

The absence of spectral changes allows us to extract an accumulated spectrum. As a first step, a comparison of the XRT and RXTE spectra accumulated over the same period and using the same lower energy threshold of 3 keV results in very good agreement with the power-law photon index Γ_X found by RXTE. The best fit in the 3–8 keV range is obtained with a power law whose slope is 2.19^+0.13_−0.11. The 2–10 keV integrated flux is 6.37^+0.12_−0.11 × 10⁻¹² erg cm⁻² s⁻¹. The X-ray photon index is consistent within 1σ with the results obtained using RXTE data.

Using the entire XRT energy band from 0.3 to 10 keV (Figure 6) and profiting from the increased statistics (the spectrum is binned with 100 counts bin⁻¹), the spectral fit is more constrained and underlies two emission components: the best fit (χ²_r = 0.82 with 146 dof) is obtained with a broken power law with the energy break located at 1.71^+0.15_−0.14 keV and fixed absorption at the Galactic value. The soft and hard photon indices are 2.57^+0.06_−0.05 and 2.09±0.05, respectively, and therefore the break in this XRT spectrum is significant compared to the power law. The 0.3–10 keV integrated flux is 9.67^+0.14_−0.10 × 10⁻¹² erg cm⁻² s⁻¹.

The UVOT optical–UV light curves showed some variability during the campaign period (Figure 4), but this is not well correlated with the X-ray or γ-ray emission (which is not variable). The daily simultaneous near-IR, optical, and UV-SEDs, reconstructed thanks to UVOT, and OAGH observations (reported in Figure 5), showed no significant spectral variability and a trend consistent with a single power law except for the two higher frequency UV bands. This may be in agreement with the hypothesis of UV excess due to thermal emission from an accretion disk (Raiteri et al. 2009, 2010).

As part of an ongoing blazar monitoring program, the 37 GHz observations were made with the 13.7 m diameter Metsähovi radio telescope, which is a radome-enclosed paraboloid antenna situated in Finland. The measurements were made with a 1 GHz band dual beam receiver centered at 36.8 GHz. The high electron mobility pseudomorphic transistor front end operates at room temperature. The observations are ON–ON, alternating the source and the sky in each feed horn. A typical integration time to obtain one flux density data point is 1200–1400 s. The detection limit of the telescope at 37 GHz is on the order of 0.2 Jy under optimal conditions. Data points with a signal-to-noise ratio <4 are handled as non-detections. The flux density scale is set by observations of DR 21. Sources 3C 84 and 3C 274 are used as secondary calibrators. A detailed description of the data reduction and analysis is given in Teräsranta et al. (1998). The error estimate in the flux density includes the contribution from the measurement rms and the uncertainty of the absolute calibration.

BL Lac was also observed with the Very Long Baseline Array (VLBA) at seven frequencies (4.6, 5.0, 8.1, 8.4, 15.4, 23.8, and 43.2 GHz) in the framework of a survey of parsec-scale radio spectra of 20 γ-ray bright blazars (Sokolovsky et al. 2011). The multifrequency VLBA observation was carried out on 2008 September 2. The data reduction was conducted in the standard manner using the AIPS package (Greisen 1990). The final amplitude calibration accuracy is estimated to be ∼5% at 4.6–15.4 GHz range and ∼10% at 23.8 and 43.2 GHz. The Difmap software (Shepherd et al. 1994) was used for imaging and modeling of the visibility data.

The VLBA images (Figures 7 and 8) reveal a wide, rather smooth, curved jet extending ∼50 mas (at 5 GHz) southeast from the bright compact core. A few distinct, bright emission features aligned along the south–southwest direction can be seen in the inner jet at higher frequencies. We have modeled the observed brightness distribution with a small number of model components having two-dimensional Gaussian profiles. The core region (i.e., the bright feature at the north end of the jet) is elongated in the 43 GHz image and can be modeled by two Gaussian components separated by 0.25 mas (0.32 pc projected distance). At distances of 1.5 mas and 3.4 mas from the core, there are two other distinct emission features in the jet. A table listing the parameters of the distinct features ("components") can be found in Sokolovsky et al. (2011).

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The inner 0.25 mas part of the jet (i.e., the "core") may contain two (or more) distinct emission features or it may be a continuous emission region. The angular resolution even at 43 GHz is not sufficient to distinguish between these possibilities. However, it is evident that the radio spectrum is changing along this region and it cannot be described by a single, uniform, self-absorbed, synchrotron emitting component. A turnover caused by the synchrotron self-absorption is detected in the averaged core spectrum at a frequency of ∼12 GHz (an average over the whole area with the negative spectral index at Figure 8). Due to the inhomogeneity, the innermost component at millimeter wavelengths most likely has an even higher turnover frequency, ≳40 GHz. Using the method described in Sokolovsky et al. (2011), the magnetic field, B, of the core, in the frame of the relativistic jet, can be constrained, given the Doppler factor, $\mathcal {D} = (\Gamma [ 1 - \beta \cos \theta ])^{-1}$, where Γ = (1 − β²)^−1/2 and θ here are the bulk Lorentz factor and jet angle to the line of sight, respectively. Assuming a Doppler factor $\mathcal {D} = 7.3$ (Hovatta et al. 2009), an upper limit can be placed on the magnetic field strength in the core: B < 3 G. We note that this upper limit corresponds to a typical value across an extended and inhomogeneous region contributing the bulk of the radio emission in 4.6–43 GHz range. The magnetic field strength can exceed the above limit locally or in a more compact regions hidden from sight in the observed frequency range by synchrotron opacity.

During the campaign, several multiband near-infrared and optical observations of BL Lac were also performed from the ground by the 2.1 m telescope of the OAGH observatory, Sonora, Mexico, and the 1.3 m McGraw-Hill Telescope of the MDM Observatory, Arizona, USA. In addition, a long-term monitoring in optical R and V bands during the first 18 months of Fermi observations (Figure 2) was performed by the observing monitoring programs at the Tuorla Observatory (1 m Tuorla and 0.35 m KVA telescopes), Turku, Finland, and at the Steward Observatory (2.3 m Bok and 1.5 m Kuiper telescopes), USA, respectively.

Optical (UBVRI) data were taken with the 1.3 m McGraw-Hill Telescope (MDM observatory). Exposure times ranged from 40 s (R band) to 120 s (U band). The raw data were bias and flat-field corrected using IRAF. Instrumental magnitudes of BL Lac and comparison stars B, C, H, and K of Smith et al. (1985) were extracted using DAOPHOT and subsequently converted to physical magnitudes through differential photometry.

INAOE (Instituto Nacional de Astrofísica, Óptica y Electrónica) operates the Observatorio Astrofísico Guillermo Haro (OAGH) located in the Mexican state of Sonora. The 2.1 m telescope of the OAGH has a current allocation of over 50 nights per semester dedicated to the study of γ-ray sources, through optical photometry and spectroscopy and infrared photometry. The Cananea Near Infrared Camera (CANICA) is equipped with a Rockwell 1024 × 1024 pixel Hawaii infrared detector working at 75 K and standard J, H, and K_s bands. The plate scale in CANICA is 0.32 arcsec per pixel. Observations are usually carried out in series of 10 dithered frames in each filter. Data are co-added after bias and flat-field corrections. CANICA observations of BL Lac presented in this work were made on seven epochs between MJD 54715 and 54747. The data are shown in Figures 4 and 5, and do not show signs of variability.

The photometric and polarimetry monitoring program at the Tuorla Observatory, a division of the Department of Physics and Astronomy at the University of Turku, Finland, is performed through the 1.03 m telescope at Tuorla Observatory, and the 35 cm telescope at the KVA observatory on La Palma, Canary Islands, Spain. Most of the monitored sources are BL Lac objects listed in Costamante & Ghisellini (2002), as potential TeV γ-ray sources.⁶⁸ All photometric measures are taken using the R filter (other details in Takalo et al. 2008).

The optical spectropolarimetry and spectrophotometry of blazars at the University of Arizona is performed on a regular basis since the launch of Fermi using the Steward Observatory 2.3 m Bok telescope on Kitt Peak, Arizona, and 1.54 m Kuiper telescope on Mt. Bigelow, Arizona, USA. Depending on weather conditions, BL Lac is observed nightly during each of the monthly monitoring campaigns, which typically last a week. All of the measurements have been made with the SPOL spectropolarimeter (Schmidt et al. 1992). The Steward Observatory blazar monitoring program associated with the Fermi mission is described by Schmidt et al. (2009) and the data are publicly available.⁶⁹ Details concerning the reduction and calibration of both the polarimetry and photometry can also be found in Schmidt et al. (2009) and references therein. The data products include high signal-to-noise flux and linear polarization spectra spanning λ = 4000–7550 Å and differential V-band photometry.

The optical R- and V-band light curve in the bottom panel of Figure 2 shows more rapid variability due to the increased sampling with respect to the weekly averaged LAT light curve. Overlapping time intervals of the 18 month light curves in γ-rays and in the R band were used to calculate the discrete cross-correlation function (DCCF), following Edelson & Krolik (1988). In Figure 9, the DCCF is plotted with error bars estimated by a Monte Carlo method, taking measurement errors and data sampling into account (Peterson et al. 1998). The correlation strength and lag were computed by fitting a Gaussian profile to the DCCF between lag −20 to +20 days. The result was a correlation intensity of 0.17 ± 0.09 (corrected for the effect of measurement noise) and a lag of −5 ± 5 days, where negative lag means γ-rays lagging the R band. The choice of lag range for the fit, from −15, +15 to −30, +30, as well as bin size, 3 or 4 days, only had a small effect on the estimated time lag of the peak and on the correlation strength, with the latter ranging from 0.14 to 0.17. The rather weak long-term correlation between gamma rays and optical tends to disfavor a one-zone synchrotron plus SSC model, since in this model, one would expect electrons with approximately the same energies to make both the optical and γ-ray emission, and might favor an ERC or multizone synchrotron/SSC model (e.g., Aharonian et al. 2009; Böttcher et al. 2009). The optical–UV variability observed during the 48 days of the MW campaign is neither correlated with the weaker X-ray variability seen by Swift-XRT and RXTE  nor with the non-variable γ-ray emission observed in the same period by the LAT (Figure 4). The lack of correlation might support the scenario where both synchrotron and IC photons contribute to the X-ray emission. Variability produced by the highest energy electrons would be smeared out by the IC component, and the mix of photons from the low- and high-energy component would dilute the correlation with the synchrotron, or synchrotron plus thermal, optical–UV emission. This would explain why variability in the optical/UV is greater than in X-rays. Moreover, if the synchrotron and IC emission components come from physically distinct regions, they would also weaken the correlation. No evidence for a contribution by accretion disk radiation during this low-activity state of the campaign was found, although this might contribute to the lack of clear correlation between the X-ray and optical–UV emission. The recent discovery of a luminous Hα emission line in the optical spectra of BL Lac (Vermeulen et al. 1995; Corbett et al. 1996, 2000; Capetti et al. 2010), likely a product of the BLR photoionized by the disk radiation, can suggest a more relevant role played by the disk during major outburst with a high γ-ray Compton dominance (as seen in the EGRET 1997 outburst).

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The averaged SED from the MW campaign (2008 August 20–September 9) is reported in Figure 10. For the first time, the multifrequency emission for the eponymous blazar source BL Lac is mapped from radio to GeV γ-rays during a low-activity state. The relevant archival observations of BL Lac are also reported in this figure for comparison in addition to our data. The difference in γ-ray integrated flux with respect to the outburst state of 1997 measured by EGRET is about 15 times lower.

The XRT spectral results are in agreement with the RXTE results in the common energy range 2–10 keV and with the usual SED properties of ISP blazars. In fact, the confirmation of a flat X-ray SED ($\nu F_{\nu } \simeq \rm const$) of moderate flux level with both instruments in such range makes us more confident that the X-rays are from a transition region between the synchrotron and inverse Compton energy components. In addition, as reported in Section 3.1, the whole 0.3–10 keV range spectrum accumulated during the campaign by Swift-XRT showed a broken power-law best fit, i.e., a steeper soft X-ray spectral slope which should be the tail of the synchrotron emission and a flatter slope above 3 keV, which should be the first part of the IC energy component.

The LAT γ-ray spectrum accumulated in 18 months is reported as well for comparison (open/orange circles representing non-simultaneous data in Figure 10).

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A single-zone SSC description, usually successful for TeV blazars, has also been used to model the SED of this eponymous BL Lac in the past (Ravasio et al. 2002, 2003) and is thus the first step in the attempt to reproduce its broadband emission. This model (Finke et al. 2008) is applied to the SED of BL Lac (blue/dark thick line on the top panel of Figure 10). The energetic blob is modeled with Doppler factor ${\mathcal D}=\Gamma =26$, comoving radius R = 5.3 × 10¹⁵ cm (which is consistent with a 2 hr variability time observed in the source on previous occasions) and tangled magnetic field of intensity B = 0.33 G. The electron distribution has the form of a broken power law, so that $N_e(\gamma) \propto \gamma ^{-p_1}$ for γ_min = 600 < γ < γ_break = 1.4 × 10³, and $N(\gamma) \propto \gamma ^{-p_2}$ for γ_break < γ < γ_max = 10⁶ where γ = E/(mc²) is the electron Lorentz factor. The best-fit electron indices were found to be p₁ = 2.0 and p₂ = 3.8, which is consistent with electrons in the fast cooling regime. It is interesting to note that γ_min is well constrained, for a given a blob size, by the X-ray observations, and thus it is impossible for this model to reproduce the radio points. This means that, if this model is correct, the emitting region must be closer to the black hole than the radio photosphere. In this model, the Poynting flux power and the kinetic power in relativistic electrons are L^(B)_jet = 1.5 × 10⁴³ erg s⁻¹ and L^(e)_jet = 2.2 × 10⁴⁴ erg s⁻¹, respectively, implying an equipartition fraction _B ≡ U'_B/U'_e = L^(B)_jet/L^(e)_jet = 0.068. This is well below the equipartition value, which may be argued as a reason to disfavor this model. In this case, the Doppler factor is considerably higher than the radio-variability Doppler factor reported in Hovatta et al. (2009), although they evaluated that from the estimated timescale of each radio flare component and the known brightness temperature, and therefore referred to a much larger region beyond the radio photosphere than this model suggests.

Since the one-zone SSC model has difficulty reproducing the variability of this source and giving reasonable energetics (_B substantially below 1), as further step we attempt a fit with a two-zone SSC model (blue/dark thick line in the central panel of Figure 10), using two emitting blobs via SSC emission: a compact and faster emission region and a larger, slower and diluted region accounting also for the radio-band emission. The energetic blob responsible for most of the emitted power and originating in a limited part of the jet is modeled with ${\mathcal D}_1=10$, R₁ = 9.0 × 10¹⁵ cm, and B₁ = 0.45 G. The radio-band and hard X-ray emission is reproduced using a much larger emitting region characterized by parameter values ${\mathcal D}_2=6.5$, R₂ = 1.6 × 10¹⁷ cm, and B₂ = 0.02 G. Doppler factors of the two zones are found to be closer to the average value (${\mathcal D}=7.3$) found in previous years by Hovatta et al. (2009) than the one-zone SSC model presented above. The kinetic partial differential equation of this model describes the evolution of the particle energy distribution N(γ, t) after the injection of shock-accelerated electrons, with a rate equal to a power law with an exponential cutoff: $Q(\gamma) \propto \gamma ^{-p}e^{-\gamma /\gamma _{{\rm max}}}$ (cm^-3s⁻¹), where γ = E/(mc²), between γ_min and γ_max. More details on the numerical model can be found in Ciprini (2008, 2010). For the compact region: (1) we obtain γ⁽¹⁾_min = 3.0 × 10³ and γ⁽¹⁾_max = 7.0 × 10⁵ with soft injection index p⁽¹⁾ = 3.5, and L^(B)_jet(1) = 6.1 × 10⁴² erg s⁻¹, L^(e)_jet(1) = 2.2 × 10⁴² erg s⁻¹, implying an equipartition fraction ⁽¹⁾_B = 2.8. Considering the larger diluted region: (2) we obtain γ⁽²⁾_min = 600 and γ⁽²⁾_max = 3.0 × 10⁴ with injection index p⁽²⁾ = 2.4, and L^(B)_jet(2) = 1.6 × 10⁴² erg s⁻¹, L^(e)_jet(2) = 7.9 × 10⁴³ erg s⁻¹, implying an equipartition fraction ⁽²⁾_B = 0.020. In this case for the two regions, the total _B = 2.16, a value slightly closer to energy equipartition than the one-zone model. The hypothesis of two synchrotron components present at different distances from the nucleus of BL Lac and accounting for the optical and the X-ray spectra, respectively, was suggested in the past in Ravasio et al. (2003). In our case, X-rays could be considered produced from both the emitting regions (central panel of Figure 10), and this can explain the lack of evident correlation between UVOT and XRT/RXTE light curves. On the other hand, the fact that the variations in γ-rays are not seen, or not resolved by the LAT, contrary to the optical–UV variable flux, tell us that the two-zone pure SSC model does not explain the multifrequency light curve of Figure 4 observed in BL Lac during the campaign, although the energetics is closer to (and above) equipartition with respect to the previous single-zone model.

SSC emission with the relevant addition of ERC emission was used to explain the large Compton dominance of BL Lac during the 1997 γ-ray outburst recorded by EGRET (Bloom et al. 1997; Madejski et al. 1999; Böttcher & Bloom 2000; Ravasio et al. 2002; Böttcher & Reimer 2004). An accretion disk emitting component and emission lines were also observed several times in this blazar (Vermeulen et al. 1995; Corbett et al. 1996, 2000; Capetti et al. 2010). The SSC plus ERC hybrid model, where X-ray emission is produced via the SSC mechanism and the GeV γ-ray emission is produced by ERC, was used by Madejski et al. (1999) for this source. This motivates us to see if it is able to reproduce also the 2008 low state of BL Lac. A model fit to this SED is shown as the blue/dark thick line of the bottom panel of Figure 10. For this model fit, an equilibrium version of the time-dependent jet model reported in Böttcher & Chiang (2002) was used. A power-law distribution of electrons, Q(γ) = Q₀γ^−p, with lower and upper cutoff γ_min = 1.1 × 10³ and γ_max = 2.0 × 10⁵, respectively, and injection index p = 2.85, is injected into a compact region of radius R = 3 × 10¹⁵ cm, moving relativistically along the jet, oriented at an angle θ_obs = 38 with respect to the line of sight, with bulk Doppler factor ${\mathcal D}=15,$ and tangled magnetic field intensity B = 2.5 G. The instantaneous electron injection is self-consistently balanced with particle escape on a timescale t_esc = η_escR/c, where η_esc = 60 is a free parameter, and radiative cooling through synchrotron, SSC, and ERC emission. For the ERC emission, both the direct accretion disk radiation field and accretion disk emission reprocessed in the BLR are taken into account, although for our fit, the BLR-reprocessed radiation strongly dominates the radiation which is directly from the disk. We assume an accretion disk luminosity of L_disk = 6 × 10⁴⁴ erg s⁻¹ and an emitting region distance from the black hole of r₀ = 0.1 pc. The BLR is represented as a spherical shell of reprocessing material with radial Thomson depth τ_BLR = 0.01, located at a distance r_BLR = 0.21 pc from the central black hole. Although the model fits the radio data well, the assumed distance from the black hole within the BLR implies that the blazar region is well within the radio-band photosphere. The numerical model self-consistently evaluates the energy content in the resulting equilibrium electron distribution and compares this value to the magnetic-field energy density. This model gives L^(B)_jet = 4.75 × 10⁴³ erg s⁻¹ and L^(e)_jet = 3.2 × 10⁴³, and ratio _B = 1.48. This is closer to equipartition than the one- and two-zone pure SSC models described above. Considering the equipartition ratio, _B, the differences between the two-zone SSC and the ERC scenario do not appear particularly significant because of the uncertainties in the estimate of this parameter, but the uncorrelated variability can still be explained more easily in the ERC scenario.

The parameters used for the three SED models that are shown in Figure 10 are in agreement with the limit on the magnetic field obtained from the VLBA observations, while the Doppler factors used in the two-zone SSC are in better agreement with the value extracted from radio-band structure historical observations. The magnetic field and Doppler factor could be different for the γ-ray emitting region than for the radio core region described in Section 3.2, since the γ-ray emission region could be from a smaller region than the radio core, closer to the black hole. A ERC+SSC model can produce more complex SEDs and less correlated variability patterns, partly because of variability in the ERC field. The emission region could move through an inhomogeneous radiation field, when it leaves the BLR. Synchrotron and SSC depend on the magnetic field, while the ERC component does not. Therefore, magnetic-field fluctuations may also produce uncorrelated variability patterns between optical X-rays (SSC) on the one hand and γ-rays (ERC) on the other.