Article The Microvariable Activity of BL Lacertae

Alberto C. Sadun 1,* , Masoud Asadi-Zeydabadi 1,*, Lauren Hindman 2 and J. Ward Moody 3

1 Department of Physics, University of Colorado Denver, Campus Box 157, P.O. Box 173364, Denver, CO 80217, USA 2 Department of Physics, University of Arizona, 1118 E. Fourth Street, P.O. Box 210081, Tucson, AZ 85721, USA; [email protected] 3 Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA; [email protected] * Correspondence: [email protected] (A.C.S.); [email protected] (M.A.-Z.)

 Received: 10 December 2019; Accepted: 5 February 2020; Published: 7 February 2020 

Abstract: We report on seven nights of optical observation taken over a two-week period, and the resultant analysis of the intermediate-frequency peaked BL Lac object (IBL), BL Lac itself, at z = 0.069. The microvariable behavior can be confirmed over the course of minutes for each night. A model was used in our analysis, to infer changes to the line of sight angles for the motion of the different relativistic components. This model has very few free parameters. The light curves we generated show both high and moderate frequency cadence to the variable behavior of BL Lac itself, in addition to the well documented long-term variability.

Keywords: galaxies: active; BL Lacertae objects: individual: BL Lacertae; galaxies: jets

1. Introduction BL Lacertae at z = 0.069 [1] is a high energy [2] that is detectable at all wavelengths, from radio waves to high energy γ-rays. are highly variable BL Lac objects, i.e., AGN with relativistic beaming properties. Indeed, the high frequency component of the spectrum is often attributable to Compton scattering—Doppler boosting from relativistic electrons of lower energy spectral components. This object is also a microvariable source as well. Such a source exhibits rapid, low amplitude variation, and is sometimes called intra-day variability. Our source produces very high cadence variations in the optical range, a phenomenon which has been studied by many, but is not represented by a single accepted model. What has been addressed is that relativistic jets are an important contribution to such variability [3,4]. From this, we believe that there are several relativistic components aligned closely to the line of sight for this object. Indeed, the challenge is to find and describe the relativistic components from an optical light curve—something we wish to accomplish here. We use a geometrical beaming model as an alternative to intrinsically occurring variations in intensity by other means.

2. Observations Observational data were collected over seven nights of BL Lac. All images were taken with the Johnson–Cousins R filter, and with the Remote Observatory for Variable Object Research (ROVOR) robotic telescope of Brigham Young University [5]. This automated telescope is a 0.4 m f/9 optical telescope is in central Utah, and was constructed for rapid observations. The telescope uses an Apogee Ap47p camera with a 1024 1024 13 µm pixel Marconi 47-10 CCD detector. All images were binned × 2 2 before data reduction. The data logs are shown in Table1 below, indicating the date of observation, ×

Galaxies 2020, 8, 11; doi:10.3390/galaxies8010011 www.mdpi.com/journal/galaxies Galaxies 2020, 8, 11 2 of 7 number of data points, time duration, secular drift, and number of identifiable flares of BL Lac for Galaxies 2020, 8, x FOR PEER REVIEW 2 of 7 each night. observation, number of data points, time duration, secular drift, and number of identifiable flares of Table 1. Record of seven nights of microvariability observations of BL Lac. BL Lac for each night. Date Number of Points Approximate Duration (hours) Secular Drift (mag) Number of Flares Oct 12, 2017Table 1581. Record of seven nights 5.56of microvariability observations+0.11 of BL Lac. 7 Oct 14, 2017 209Number of Approximate 7.82 Secular Drift+0.04 Number of 34 Date Oct 23, 2017 210Points Duration 7.40 (hours) (mag) 0.02Flares 4 − Oct 24, 2017Oct 12, 2017 269 158 9.48 5.56 +0.11 0.03 7 7 − Oct 25, 2017Oct 14, 2017 223 209 7.84 7.82 +0.04+ 0.08 34 9 Oct 23, 2017 210 7.40 −0.02 4 Oct 26, 2017 262 9.24 +0.20 12 Oct 24, 2017 269 9.48 −0.03 7 Oct 27, 2017 260 8.53 0.11 12 Oct 25, 2017 223 7.84 +0.08− 9 Oct 26, 2017 262 9.24 +0.20 12 In FigureOct1 27, below, 2017 we see 260 all seven nights 8.53 displayed in magnitude−0.11 form. One12 can see from inspectionIn Figure that 1 each below, night we is see very all di sevenfferent nights from displayed each other, in and magnitude that some form. display One a can considerable see from amountinspection of that secular each drift, night that is is,very the different difference from in magnitudeeach other, betweenand that thesome beginning display anda considerable the end of theamount night. of secular drift, that is, the difference in magnitude between the beginning and the end of the night.

Figure 1. Light curves (smoothed) of BL Lac over seven nights in October 2017.

All images were reduced using Mira Pro 7.0 commercial image processing software [[6].6]. Aperture Aperture photometry waswas performed performed using using an aperturean aperture of 10 arcsecof 10 diameter.arcsec diameter. The finding The chart finding and comparisonchart and starcomparison magnitudes magnitudes were taken from were Smith, taken etfrom al. [Smith,7]. All et data al. are[7]. availableAll data are upon available request. upon request. With aperture photometry, onon aa givengiven frame,frame, afterafter background subtraction, the aperture fluxflux of the variablevariable isis compared compared to to the the flux flux of of each each comparison comparison star. star. In this In this way, way, changes changes in transparency in transparency (local conditions(local conditions as well as as well changes as changes in air mass)in air shouldmass) should not aff ectnot the affect values. the values. There areThere secondary are secondary effects, however,effects, however, so to take so those to take into account,those into the account, fluxes of severalthe fluxes comparison of several comparison are also compared stars are to eachalso other.compared We plotto each in Figureother. 2We both plot the in variabilityFigure 2 both of thethe source,variability as well of the as source, the variability as well as of the two variability selected comparisonof two selected stars comparison to each other. stars to each other.

Galaxies 2020, 8, 11 3 of 7 Galaxies 2020, 8, x FOR PEER REVIEW 3 of 7

V-B Smooth (a) -1.38 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 -1.4

-1.42

-1.44

-1.46 -(V-B) -1.48

-1.5

-1.52

-1.54 Time (hours)

B-C Smooth (b) 1.9 1.88 1.86 1.84 1.82 -(B-C) 1.8 1.78 1.76 1.74 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Time (hours)

Figure 2. a b Figure 2. LightLight curves curves of of BL BL Lac Lac for for the the entire entire night night of of Oct Oct 27, 27, ( (a)) BL BL Lac Lac variability, variability, and and ( (b)) variability variability of the comparison stars. of the comparison stars. Previous work by Clements and Carini [8] shows similar activity of BL Lac. In particular, they Previous work by Clements and Carini [8] shows similar activity of BL Lac. In particular, they show nightly variations ranging from 0.1 to 0.6 magnitude, which is similar to the activity shown show nightly variations ranging from 0.1 to 0.6 magnitude, which is similar to the activity shown above in Figure1. above in Figure 1. 3. Analysis 3. Analysis We converted values to flux values to help us with our later calculations. Then,We we converted applied standard apparent smoothing magnitude and values curve to fitting flux algorithms.values to help We us evaluated with our the later light calculations. curve, and scrutinizedThen, we applied it for micro-outbursts. standard smoothing The flux,and apartcurve from fitting major algorithms. variability, We has evaluated a standard the deviation,light curve,σ, afterand scrutinized smoothing, ofit 0.5%.for micro-outbursts. Any flux more than The 1.0% flux, greater apart thanfrom the major median variability, value for localhas a quiescence standard σ wasdeviation, deemed , toafter be smoothing, a micro-outburst. of 0.5%. Figure Any 2flux shows more a than sample 1.0% of greater smoothed than data the (weighted median value boxcar for smoothing)local quiescence in apparent was deemed magnitude to be for a BLmicro-outb Lac. urst. Figure 2 shows a sample of smoothed data (weightedLong-term boxcar variability smoothing) of BL in Lacapparent is well magnitude documented for [ 9BL] and Lac. can vary by two orders of magnitude in brightnessLong-term (five variability magnitudes) of BL at Lac shorter is well wavelengths. documented Additionally, [9] and can vary shorter-term by two orders variability of magnitude over the coursein brightness of days (five and weeksmagnitudes) is shown at inshorter Figure wavelengths.1 above. The generallyAdditionally, accepted shorter-term model of suchvariability variability over the course of days and weeks is shown in Figure 1 above. The generally accepted model of such

Galaxies 2020, 8, 11 4 of 7

Galaxies 2020, 8, x FOR PEER REVIEW 4 of 7 regards the Doppler boosting from a plasma jet pointed almost directly towards the observer. What variabilitywe wish to addressregards inthe this Doppler paper asboosting well, is thefrom very a plasma high cadence jet pointed variability almost as also directly shown towards in Figure the1, observer.one night What of which we iswish shown to address in considerably in this paper more as detail well, in is Figurethe very2 above. high cadence variability as also shownWe in use Figure a strictly 1, one geometrical night of which model is shown to analyze in considerably the data. The more advantage detail in of Figure our model 2 above. is that we onlyWe need use to a consider strictly ageometrical minimum numbermodel to of analyze free parameters. the data. GeometricThe advantage models of our similar model to the is that one we onlypresent need have to consider been considered a minimum in the number past. Forof free instance, parameters. a shifting Geometric jet is considered models similar in the to long-term the one weactivity present of CTAhave 102 been [10 considered]. In our case, in the however, past. For due inst toance, the microvariablea shifting jet is natureconsidered of our in source,the long-term we are activityconsidering of CTA several 102 relativistic[10]. In our components, case, however, but due with to di theffering microvariable angles to thenature line of our sight. source, Since we we are consideringdealing with several the prototype relativistic BL Laccomponents, object which but necessarily with differing involves angles Doppler to the boosting,line of sight. in this Since model we arewe assumedealing thewith slowly the prototype varying portion BL Lac of object each light which curve necessarily is composed involves mainly Doppler of boosted boosting, emission in fromthis modeltrue quiescence, we assume which the weslowly determine varying from portion the historical of each lightlight curve,curve asis havingcomposed an apparent mainly of magnitude boosted emissionin R of 15.99 from [9 ].true Thus, quiescence, the emission which is alreadywe determine boosted from before the we historical even analyze light curve, the microvariability. as having an apparent magnitude in R of 15.99 [9]. Thus, the emission is already boosted before we even analyze The microflares then represent a small and temporary change in angle to the line of sight from the the microvariability. The microflares then represent a small and temporary change in angle to the line original angle, but this time of independent optical components (plasmons). of sight from the original angle, but this time of independent optical components (plasmons). We follow along the lines of the detailed calculations of jet dynamics that have been previously We follow along the lines of the detailed calculations of jet dynamics that have been previously applied to Mrk 501 [11], but now as applied to the high cadence, microvariability part of the model for applied to Mrk 501 [11], but now as applied to the high cadence, microvariability part of the model BL Lac. The geometry of this model is depicted in Figure3 as shown below. for BL Lac. The geometry of this model is depicted in Figure 3 as shown below.

Figure 3. Figure 3. GeometricGeometric modelmodel showing showing the the source source emitting emitti independentng independent optical optical components components which which result in relativistic beaming. The Lorentz factor γ is taken to be 10 [12], and the angle to the line of sight is result in relativistic beaming. The Lorentz factor γ is taken to be 10 [12], and the angle to the line of designated θ, as shown. sight is designated θ, as shown. From this model, we can then calculate those angles of the microflares from the following equations: From this model, we can then calculate those angles of the microflares from the following equations: 2 M = L/L0 = δ (1) 2 M = L/L0 = δ (1) where 1 1 where δ = γ− (1 βcosθ)− , (2) − and δ = γ−1(1 − βcosθ)−1, (2) 2 1/2 β = (1 γ− ) . (3) and − M represents the luminosity magnification as seen from the laboratory frame, δ is the Doppler −2 1/2 factor, and β is the Lorentz factor, respectively.β = (1 − γ ) . (3) M represents the luminosity magnification as seen from the laboratory frame, δ is the Doppler 4. Results factor, and β is the Lorentz factor, respectively. The statistical results of analyzing all the very high-quality October 2017 data of BL Lac 4.microvariability Results are shown in Figures4 and5 below. We take our magnification M from a baseline as taken from our own observations. Indeed, we are not dealing with the angle to the line of sight The statistical results of analyzing all the very high-quality October 2017 data of BL Lac to the blazar itself, which would be a magnification taken from quiescence (R = 15.99) [9], but rather microvariability are shown in Figures 4 and 5 below. We take our magnification M from a baseline of plasmon ejection from an established but slowly varying line of sight, which we hypothesize is as taken from our own observations. Indeed, we are not dealing with the angle to the line of sight to responsible for the microvariability, implying rather small angles. Figure4 shows the distribution the blazar itself, which would be a magnification taken from quiescence (R = 15.99) [9], but rather of of the luminosity magnification, M, of the ensemble of microbursts presented, here in histogram plasmon ejection from an established but slowly varying line of sight, which we hypothesize is responsible for the microvariability, implying rather small angles. Figure 4 shows the distribution of

GalaxiesGalaxies 20202020,, 88,, xx FORFOR PEERPEER REVIEWREVIEW 55 ofof 77 Galaxies 2020, 8, 11 5 of 7 thethe luminosityluminosity magnification,magnification, MM,, ofof thethe ensembleensemble ofof microburstsmicrobursts prpresented,esented, herehere inin histogramhistogram form.form. form.OneOne noticesnotices One notices aa roughlyroughly a roughly GaussianGaussian Gaussian distribution,distribution, distribution, asas may asmay may bebe be expected,expected, expected, withwith with aa a singlesingle single outlier outlier asasas aaa comparativelycomparativelycomparatively very veryvery bright brightbright microburst. microburst.microburst.

FigureFigureFigure 4. 4.4.Histogram HistogramHistogram of ofof the thethe luminosity luminosityluminosity magnification magnificationmagnification of ofof the thethe microvariable microvariablemicrovariable outbursts outburstsoutbursts of ofof BL BLBL Lac. Lac.Lac.

We also show in Figure5 below the distribution of the angle deviation of the optical components WeWe alsoalso showshow inin FigureFigure 55 belowbelow thethe distributiondistribution ofof thethe angleangle deviationdeviation ofof thethe opticaloptical componentscomponents responsible for heightened microvariable activity. Here notice that we have a distribution that is responsibleresponsible forfor heightenedheightened microvariablemicrovariable activity.activity. HeHerere noticenotice thatthat wewe havehave aa distributiondistribution thatthat isis skewed to the larger angles. (This includes, of course, that outlier that was presented in Figure4.) The skewedskewed toto thethe largerlarger angles.angles. (This(This includes,includes, ofof coursecourse,, thatthat outlieroutlier thatthat waswas presentedpresented inin FigureFigure 4.)4.) TheThe angle of deviation ranges from essentially zero to around 0.16 degrees. Even a small change in angle, angleangle ofof deviationdeviation rangesranges fromfrom essentiallyessentially zerozero toto aroundaround 0.160.16 degrees.degrees. EvenEven aa smallsmall changechange inin angle,angle, which we are now calling θ, can be responsible for a measurable microburst. whichwhich wewe areare nownow callingcalling∆ ΔθΔθ,, cancan bebe responsibleresponsible forfor aa measurablemeasurable microburst.microburst.

Figure 5. Histogram of the angle deviations of the microvariable outbursts of BL Lac. FigureFigure 5.5. HistogramHistogram ofof thethe angleangle deviationsdeviations ofof ththee microvariablemicrovariable outburstsoutbursts ofof BLBL Lac.Lac. Let us compare our results using the aforementioned jet model on BL Lac, to the results of using LetLet usus comparecompare ourour resultsresults usingusing thethe aforementionedaforementioned jetjet modelmodel onon BLBL Lac,Lac, toto thethe resultsresults ofof usingusing the same model as applied to a very different object, Mrk 501 [11]. The objects are quite different thethe samesame modelmodel asas appliedapplied toto aa veryvery differentdifferent object,object, MrkMrk 501501 [11].[11]. ThThee objectsobjects areare quitequite differentdifferent (one(one (one is a BL Lac object while the other is an optical ); they also have very different light curves. isis aa BLBL LacLac objectobject whilewhile thethe otherother isis anan opticaloptical galaxy);galaxy); theythey alsoalso havehave veryvery differentdifferent lightlight curves.curves. TheThe The cadence of BL Lac itself is of much higher frequency and much lower amplitude than as seen for cadencecadence ofof BLBL LacLac itselfitself isis ofof muchmuch higherhigher frequencyfrequency andand muchmuch lowerlower amplitudeamplitude thanthan asas seenseen forfor MrkMrk Mrk 501. Nevertheless, the histograms for the distribution of luminosity magnification M seem rather 501.501. Nevertheless,Nevertheless, thethe histogramshistograms forfor thethe distributiondistribution ofof luminosityluminosity magnificationmagnification MM seemseem ratherrather similar. This would validate, at least to some degree, the hypothesis that the cause of the underlying similar.similar. ThisThis wouldwould validate,validate, atat leastleast toto somesome degrdegree,ee, thethe hypothesishypothesis thatthat thethe causecause ofof thethe underlyingunderlying variability for each object is the same, namely Doppler boosting of jets and beams directed close to the variabilityvariability forfor eacheach objectobject isis thethe same,same, namelynamely DopplDopplerer boostingboosting ofof jetsjets andand beamsbeams directeddirected closeclose toto line of sight. thethe lineline ofof sight.sight.

Galaxies 2020, 8, 11 6 of 7

5. Conclusions BL Lacertae is a blazar that has been extensively studied, and has displayed considerable variability at many time scales. Indeed, this object has become the prototype for an entire class of AGN, so understanding its behavior is very important. Multiband microvariability observations have been made by others [8,13]. Indeed, it has been observed in particular by Bhatta and Webb [13] that when brighter, BL Lac becomes bluer, and furthermore that emission is highly correlated across the various optical bands. Our observations were made in only one filter, R, but from previous work [13], we may assume that our documented outbursts were also well represented at other wavelengths. Here we add to the general understanding of this object by presenting very high-quality data sets (small relative error in brightness, long strings of data, and excellent temporal resolution), and analyzing these sets in terms of a simple jet model of multiple components. We find that with very few assumptions, a plausible model can be made for its optical light curve, particularly for its microvariability. This is not to say that other alternatives are not possible, but simply that this one is a reasonable one to consider. Indeed, other models such as magnetic reconnection [14] may be an important component for longer term variability. In comparison with Mrk 501, when using the same jet model, we obtain very similar results in terms of distribution of luminosity enhancement, despite the vast differences in the extent and kind of variability. Since BL Lac is well studied and is the prototype for an entire subclass of objects, it is important that we try to understand its behavior. We hope that by further research of BL Lacertae itself, we can shed light on this very important subgroup of AGN.

Author Contributions: Conceptualization, A.C.S. and M.A.-Z.; methodology, A.C.S. and M.A.-Z.; software, M.A.-Z.; formal analysis, A.C.S. and M.A.-Z.; data curation, J.W.M. and L.H.; writing—original draft preparation, A.C.S.; writing—review and editing, A.C.S., M.A.-Z., J.W.M. and L.H.; visualization, M.A.-Z.; supervision, A.C.S. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: We gratefully acknowledge the contributions of the ROVOR robotic telescope team in helping to acquire the microvariability data. Conflicts of Interest: Alberto C. Sadun is on the Editorial Board of galaxies.

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