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Short timescale variability in the broadband emission of the blazars Mkn421 and Mkn501
Astroparticle Physics 14 (2000) 131±140
www.elsevier.nl/locate/astropart
Short timescale variability in the broadband emission of the blazars Mkn421 and Mkn501 B. McKernan a,*, M.J. Carson a, T. Yaqoob b, D.J. Fegan a b
a Department of Physics, University College Dublin, Dublin 4, Ireland Laboratory for High Energy Astrophysics, Code 660.2 Goddard Space Flight Center, Greenbelt, MD 20771, USA
Received 26 August 1999; accepted 26 November 1999
Abstract We analyse ASCA satellite X-ray data and Whipple Observatory TeV c-ray data from the Blazars Mkn421 and Mkn501 for short timescale variability using the excess pair fraction method. We discuss the method and the data as well as EPF sensitivity to these data. We ®nd that in these data sets, we can rule out an amplitude of variability greater than 10% on timescales less than 10 min from both sources and at both wavelengths at a con®dence level of >99.7%. We discuss brie¯y the implications of low amplitudes of variability on short timescales for the beamed jet of relativistic particles probably producing these radiations and, we derive limits from the data on the local percentage change in both the lepton density and the magnetic ®eld strength in these Blazar jets. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The active galaxies Mkn421 and Mkn501 are the nearest of the blazar class of active galactic nuclei (AGN) which are characterised by their variable polarised synchrotron emission and are associated with radio jets emerging from giant elliptical galaxies. Both Mkn421 and Mkn501 are sources of broadband radiation, from radio waves to TeV c-rays. The highest energy (TeV) radiation from these sources has been detected only recently by the Atmospheric Cerenkov Telescope (ACT) of the Whipple collaboration [13,14] and others [4,12] (see also Ref. [11] and references therein). Broadband radiation from these AGN is thought to originate in relativistic collimated out¯ows of
*
Corresponding author. E-mail address: [email protected] (B. McKernan).
plasma (also known as jets), which may be warped and are aligned close to the line of sight. The jet emission from both Blazars may therefore be strongly beamed [1] and so could swamp most of the emission from other parts of the AGN central engine, such as an accretion disk around a putative supermassive black hole. The broadband emission from both Blazars is variable, with both Mkn421 and Mkn501 occasionally exhibiting spectacular ¯aring episodes in both X-rays and c-rays on relatively short timescales [14,9]. A number of major questions concerning Blazar radiation processes have yet to be answered. Which particle dominates the production of crays, the proton or the electron? How are these particles accelerated and how are the c-rays produced? Several competing models of the radiation processes exist and a study of short timescale variability can help in distinguishing between them. Indeed, the core regions of AGN cannot be
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resolved with existing interferometers and so variability studies in general are important in understanding the physics of these central regions. For example, rapid variability in Blazar emission requires a rapid cooling process for the particles producing the radiation. In terms of Blazar radiation models, this is easier to achieve with electrons than with protons, especially when model parameters are derived from ®ts to Blazar spectral energy distributions. Short timescales of variability are also useful in distinguishing between dierent models within the electron or proton family of models, since limits on the magnetic ®eld strength in the jet may be derived and this can help in constraining dierent models. An exciting new application of very short timescale variability in the high-energy radiation from Blazars lies in constraining models of quantum gravity. A study of short timescale variability in Mrk421 has provided the strongest constraints yet on D-brane models of a quantum gravity spacetime foam [2]. In this article, we search for variability in noncontemporaneous data sets of X-rays and c-rays from Mkn421 and Mkn501, over timescales which are less than the fastest observed doubling times of ¯ares in c-rays. Evidence for rapid variability on these timescales allows the calculation of physical parameters associated with the jet and might favour electron models over most proton models as well as providing better limits for models of quantum gravity. Variability studies have been carried out at dierent wavelengths on the blazar class of AGN [7] and on these two AGN in particular [15]. These studies have all used the v2 test against a constant hypothesis, which searches for variability over the entire lightcurve, relative to some mean level. The ®ndings of these studies, after looking at a range of timescales, were: (i) TeV variability down to 15 min for Mkn421 and 2 h for Mkn501, based on the doubling time of the shortest observed ¯ares from these sources and (ii) X-ray variability on timescales down to a few hours for both sources (see in particular Refs. [18,19] and references therein). Our variability analysis is dierent from previous studies because it utilises the excess pair fraction (EPF) method [16], which picks out variability
on a spectrum of timescales. We have previously presented a brief discussion of the application of EPF to TeV c-ray data from Mkn501 in Ref. [5]. Here, we present a discussion of the EPF method and its application to X-ray and TeV c-ray data from both Mkn421 and Mkn501. The EPF method is a simple means of analysing gapped time series, and measures explicit bin-to-bin variability. Spurious variability due to gaps in data is automatically eliminated using EPF, which constrains our analysis to small timescales of the order of fractions of continuous data sets. However, it also allows an analysis of a continuum of small timescales, something that to our knowledge, has not been done before with these Blazars. We can do this for a range of bin widths to build an EPF spectrum. We emphasise that EPF is dierent from the standard v2 test for variability, in that v2 does not measure bin-to-bin variability as EPF does, rather it measures variability on a timescale corresponding to the length of the lightcurve. 2. The broadband data 2.1. The c-ray data The TeV data were recorded by the Whipple Observatory Imaging Atmospheric Cerenkov Telescope (IACT) [6]. The IACT indirectly observes very high-energy c-rays from high-energy sources, such as AGN jets and supernova remnants. The c-rays are detected via the camera image of the Cerenkov pulse associated with the air shower that they produce in the upper atmosphere. However, by far, the majority of the Cerenkov showers in the upper atmosphere are due to the impact of high-energy cosmic rays (hadrons or leptons), therefore, the parent c-ray data, as observed by the IACT have a very small signal-tonoise ratio. The procedure of extracting c-ray events from data dominated by hadronic air showers requires the parameterisation of shower image properties [8]. These Hillas parameters may be classi®ed into `shape' parameters (such as length or width) or `orientation' parameters such as a, which de®nes the angle made by the image length axis with the
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centre of the ®eld of view of the camera. Selection of events (cuts), based on image parameters, provides an ecient way of removing most noise whilst preserving most of the signal. Where elimination of noise is most important, cuts may remove around 40% of signal along with nearly all noise leaving a cut data set with a typical signal-tonoise ratio of around 3:2. However, if signal retention is important then, almost 100% of the signal may be retained by employing (for example) trigger cuts which eliminate spurious events that can account for up to 1=3 of the parent data. The parent data are typically recorded in approximately 28 min intervals in one of the three modes: ON, OFF or tracking. The ON/OFF mode consists of tracking the source for 28 min and then observing the same region of sky through which the source has passed for the same duration in order to provide comparison background data for the ON source observation. Subtracting OFF data from ON data gives the excess of events from the source. Tracking mode involves continuously tracking the source across the sky over several 28 min observations. This mode is useful when the source may be particularly active. Poor weather can cause large changes in the parent data rate due to light scattering from clouds passing through the line-of-sight of the telescope, for example. Elevation changes between and during data collecting runs may also signi®cantly change the parent data rate, particularly at low elevations. Good weather conditions are logged at the time the run is taken and correspond to low variability (62r) in the raw parent count rate. The Mkn421 data analysed were taken from the period April 1996±May 1996, during which time the most signi®cant ¯aring event ever seen at this energy was observed [10]. The Mkn501 data were taken from the period April 1997±May 1997, during which time this AGN was at its most active since its detection at this energy in 1995. The presence of strong ¯aring within these data is important for our purposes as the count rate from the AGN increases typically from 61 to P10 c minÿ1 during a strong ¯aring state. A count rate as low as 61c minÿ1 would make it very dicult to pick out statistically signi®cant variability on timescales 65 min using any method;
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however, large ¯ares allow us to probe such timescales for variability. The continuous stream of TeV data are recorded by the ACT using GPS, UTC and livetime clocks. The livetime clock is most susceptible to errors, such as dropped frames (random missing sequences of events), so we use the more reliable UTC clock (which is derived from the GPS clock). The GPS clock has nanosecond resolution, so we can de®ne good time intervals (GTI) for the TeV data by ¯agging the ®rst and last events in a parent data set as the start and end times of a data set. 2.2. The X-ray data The ASCA satellite [20] observed Mkn421 and Mkn501, obtaining moderate energy resolution spectra in the 0.5±10 keV band, with a timeresolution of better than 2 s for two of the four instruments onboard (4 s for the other two). Mkn421 was observed on 18 occasions between 10 May 1993 and 3 June 1997, with a total exposure time of 240 103 s. The 1996 data do not overlap with the TeV data reported in this article. Mkn501 was observed on four occasions between 21 March 1996 and 2 April 1996, with a total exposure time of 49 103 s. Additional ASCA observations of both sources exist but only those made on the dates mentioned above were in the public archive at the time of writing. An excellent account of the Mkn421 ACSA observations and results can be found in Ref. [19] and the ASCA results for Mkn501 can be found in Ref. [18]. 3. Excess pair fraction method The EPF method is a simple method of analysing gapped time series for timescales on which the source is varying [16]. The method allows the measurement of bin-to-bin variability within a time series, and comparison with a theoretical Poisson source, for a whole spectrum of bin widths. The time series is binned at a bin width T and the number of counts in each bin is found. We then count the total number of bin pairs with nonzero counts in each and compute the fraction of those bins which satisfy the condition
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jCi ÿ Ci1 j P
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p p Ci Ci1 ;
1
where Ci is the number of counts in the ith bin. The resulting fraction is termed EPF(T). We do not consider pairs of bins where one or both have zero counts since these automatically ful®ll the condition for variability in Eq. (1) but which represent an absence of data rather than counts which can be treated statistically. The statistical signi®cance of any intrinsic variability within a gapped time series is computed by comparing the calculated EPF(T ) with the EPF(T ) obtained from a simulated, constant Poisson source with the same mean-count rate. In deriving the comparison Poisson source EPF curve, the counts in each of 106 bin pairs used are taken from a Poisson distribution, and a normalised mean count rate of 1 sÿ1 is used. We ®nd that the EPF curve for a Poisson source tends to a theoretical value of 0:159 in the limit of large statistics (analytically as well as for simulations). A direct comparison of this reference curve with the data simply requires dividing this Poisson curve by the mean-count rate of the data. As the number of bins into which the data set is divided tends to one, EPF tends to one, and as the number of counts per bin tends to zero, EPF tends to zero in both the reference curve and actual data. We can also generate EPF for simulated sources with some intrinsic percentage variability, by de®ning the mean number of counts in each simulated bin to be some factor 1 f m times the mean-count rate (usually normalised to 1 sÿ1 ), where f 0:0; 1:0 represents the percentage variability and m is a uniform random deviate between ÿ1 and 1 [16]. The statistical signi®cance of the variability at a particular bin width T, corresponding to EPF(T ), is given by the multiple of its 1r errorbar from EPF(T ) for a constant Poisson source. This is true at least for a well-de®ned signal with little or no noise contamination, such as the X-ray data. In practice, a relatively large proportion of the TeV data that passes parameter cuts is noise; therefore, unless that noise is (approximately) Poissonian, our task is complicated. If the background noise that passes cuts were non-Poissonian and we wished to attach statistical signi®cances to any
variability in the signal, we would have to replace the reference EPF curve described above with an EPF curve that mimics the behaviour of the background. We ®nd, however, that the TeV background does indeed appear to be consistent with a Poisson source (Fig. 1), by constructing a small timescale EPF spectrum for seven OFF runs, which should contain a negligible amount of crays. The statistics become poor beyond around 500±600 s, re¯ecting only two to three bins per data set. EPF at or around this point tends to rise rapidly to 1. This does not mean that the source is varying at these bin widths, rather simply it re¯ects the ever decreasing number of bins being analysed. This is also evident from the much larger error bars associated with the EPF points at these bin widths. Thus EPF points above 500±600 s will be disregarded due to poor binning statistics. Spurious variability due to partially ®lled bins at the start or the end of a data set, is eliminated by rejecting these bins. In the case of TeV data, events are usually binned in approximately 28 min sets and every event in the parent data set is registered by the UTC clock with an accuracy of the order of 5 ms. We equate the start and end times for each parent data interval with the ®rst and last trigger
Fig. 1. The EPF spectrum for c-ray background. The solid line is the EPF curve for a constant source with the same mean count rate as the data. As the bin width tends to zero, the EPF spectrum for a constant also tends to zero. As the bin width approaches half the length of the run, EPF saturates. The open circles are EPF(T ) and errorbars are 1r.
B. McKernan et al. / Astroparticle Physics 14 (2000) 131±140
events in that set and ¯ag these times. Any bins which include the ¯agged times are rejected. This means that the maximum theoretical bin size which we can test for variability is approximately 14 min (840 s). In practice, this limit is closer to 10 min (600 s), which gives two bins per data set. Evidently an upper limit to a bin size of this magnitude implies that changes in elevation between data sets are not relevant to our analysis. However, changes in elevation within a data set may cause some variation in signal, although this should not appear signi®cantly in the context of our analysis, since EPF measures explicit bin-tobin variability, so only signi®cant elevation eects will manifest themselves in the resulting EPF(T ) curve. A similar approach is used to eliminate spurious variability due to binning when applying EPF to X-ray data (see Ref. [16] for details). We indicated above that the EPF method is dierent from the standard v2 test for variability, in that EPF explicitly tests bin-to-bin variability, implying that a simple comparison between results of both methods is not possible. A simple example illustrates this point very well. Consider a lightcurve containing 100 2-min bins, 98 of which are consistent with a constant, but two of which (roughly at each end of the lightcurve say) are very deviant. An application of the EPF test to the data will indicate that the 2 min variability is small because only two out of the 100 bins show variability. On the other hand, an application of the v2 test to the lightcurve will indicate that the variability is large. However, if the lightcurve were chopped, v2 will now indicate that there is no variability, whereas EPF will give the same result as before. This is because v2!! is not measuring 2 min variability, rather it is measuring variability on a timescale corresponding to the length of the lightcurve. 3.1. An example of excess pair fraction applied to TeV data The EPF technique has been demonstrated on ASCA X-ray data [16], where it was shown that the variability of the Seyfert I AGN MCG-6-30-15 did not cease down to approximately 20 s. Here, we apply the EPF method to IACT data, in a
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search for signi®cant short timescale variability. Within the context of EPF, variability at a particular timescale T means that the lightcurve derived from the time series changes according to Eq. (1) at bin width T . To test this, we analysed an uncut data set containing injected strong contamination from a periodic source with a period of 2.5 s. The contamination was strongest at the start of the data set and grew less as the telescope tracked away from the source. Fig. 2(a) shows the EPF curve for the uncut data from this source. We expect to see minima in EPF(T ) at T equal to the period of the beacon, since EPF will pick out variability when the time series is binned on a time scale comparable with the source variability. This is because variability, as de®ned in Eq. (1) is a minimum because there are approximately equal number of counts in each bin (the light curve looks ¯at). This is indeed the case as the EPF reaches a maximum at 1.25 s with a signi®cance of 16r, at a binwidth corresponding to half of the period of the beacon signal. The ®rst minimum occurs at 2.5 s which must be the period of the beacon. The ®rst harmonic of the signal occurs at 3.75 s at 5r, after which the statistics become too poor to clearly pick out any more of the signal's harmonics. We estimate the signal (periodic source)-to-noise ratio (S=N ) in this test run to be 61=5, by comparing the ratio of the rate at the start of the run when the periodic source is strongest, to the rate at the end of the run, where the periodic source is no longer detected. It is perhaps not surprising that the variability is picked out for such a strong signal, but it is an instructive demonstration of the method nonetheless. In order to test the limits of the technique in analysing periodic sources, arti®cial noise was added to the signal, thereby reducing S=N and the resulting EPF calculated for each simulation. Poisson noise with multiples of the mean-count rate and number of events of the parent data was added to the data set. Fig. 2(b)±(f) shows the dilution of the periodic signal by the addition of successively larger sets of Poisson-distributed (non-periodic) arti®cial events to the run. We know that the magnitude of the periodic signal in the run is 1/5 the magnitude of the background
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Fig. 2. The EPF spectrum for a periodic source with varying levels of added noise (see the text for details).
B. McKernan et al. / Astroparticle Physics 14 (2000) 131±140
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in that run, so as we add increasing amounts of arti®cial Poisson background, we can estimate the new value of S=N . We ®nd that variability can be picked out with an S=N of 1=20 at the 4:5r level, where signi®cance is measured in terms of the distance from the EPF point to the Poisson background curve as a multiple of the 1r error-bar of the EPF point. At this level of added noise, it is not obvious that the embedded signal is periodic since periodicity appears to vanish at an S=N of 1=10, but EPF tells us that the signal is still varying at a statistically signi®cant level on small timescales.
4. Results of excess pair fraction applied to X-ray data The ASCA Mkn421 and Mkn501 data were reanalysed and reduced in the same manner as described in Ref. [17]. We made EPF spectra for each source following the methods described in Ref. [16], averaged over all the available data sets. The results for both sources are shown in Figs. 3 and 4. The solid, dotted and dashed curves show theoretical EPF for a source with 0%, 5%, and 10% random amplitude of variability, respectively. The curves were generated as described in detail in Ref. [16]. If an EPF point is y multiples of its 1r error bar lower than a theoretical EPF curve with x%
Fig. 4. The EPF spectrum for ASCA X-ray data on Mkn501.
random amplitude of variability, then we say that this rules out variability at the x% level in the source with a con®dence level of y standard deviations. It can be seen that in Mkn421, we can rule out variability at the 5% level with a con®dence level greater than 3r from 500 s down to timescales of 11 s. (Note: The kink at 32 s is due to only two of the four ASCA instruments being used below this timescale because the two Solid State Spectrometers have less timing resolution than the two Gas Imaging Proportional Counters). For Mkn501, for which much less data are available, we can rule out variability at the 10% level with a con®dence level greater than 3r from 400 s down to timescales of 32 s.
5. Results of excess pair fraction applied to c-ray data
Fig. 3. The EPF spectrum for ASCA X-ray data on Mkn421.
The TeV data for Mkn421 were taken from the period April 1996±May 1996, during which time the most signi®cant ¯aring event ever seen at this energy was observed. The Mkn501 data were taken from the period April 1997±May 1997, during which time this AGN was at its most active since its discovery at this energy in 1995. The presence of strong ¯aring within these data is important for statistical purposes as the count rate from the AGN increases from typically 61c to
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B. McKernan et al. / Astroparticle Physics 14 (2000) 131±140
Fig. 5. The EPF spectrum for Whipple c-ray data on Mkn421.
10c minÿ1 during a strong ¯aring state. Fig. 5 shows EPF for Mkn421 at TeV energies. Approximately 1760 min of data are used in this analysis. None of the data points are greater than 3r from that of a theoretical constant source with the same mean count rate. Because of the 28 min data binning only timescales less than 14 min can be considered using this technique. The c-ray rate (3c minÿ1 ) prevents us probing timescales much lower than 200 s. Fig. 6 shows EPF for Mkn501 with approximately 1900 min of data. Again, none of the data points are greater than 3r from that of
Fig. 6. The EPF spectrum for Whipple c-ray data on Mkn501.
a constant source with the same mean count rate indicating a lack of signi®cant variability in these data from Mkn501 below 10 min. Here the rate is 9 minÿ1 and so the lower timescale below which the statistics become too poor is 100 s. By comparing the EPF spectrum with the simulated 10% variability amplitude, we can rule out variability amplitudes of >10% in TeV c-rays in both sources on timescales below 10 min at a con®dence level > 3r. These results are consistent with the results of previous short timescale studies, which employed the v2 test [14,9] and which found no signi®cant variability, although we emphasise again that EPF explicitly measures bin-to-bin variability, unlike v2 , and so there is no direct comparison between the two methods.
6. Discussion and conclusions Our results for the data under discussion show that there appears to be no statistically signi®cant variability in either of the two AGN, in either X-ray or TeV c-rays below timescales of 600 s. Certainly, we can rule out amplitudes of variability in these data at the 10% level on these timescales, in both these sources, with a con®dence level of >99.7%. In fact, we can rule out X-ray variability in the Mkn421 data at the 5% amplitude level also at the >99.7% con®dence level. We see no statistically signi®cant variability on very short timescales that might suggest electron dominated radiation processes in the jets or allow for improvement of the observational limits in Ref. [2] on theories of quantum gravity. Nevertheless, if we assume that the source is not varying on timescales shorter than 10 min then we can estimate the minimum causal size of the emission region, attempt to constrain the location of the emission region and produce model-dependent limits on the magnetic ®eld strength and electron population within the jet. The Doppler beaming factor is given by D 1=Cb 1 ÿ b cos h, where Cb is the Lorentz boost, b v0 =c (where v0 is the velocity of the emitting region) and h is the angle between the velocity vector of the emitter and the line of sight of the observer. Causal ar-
B. McKernan et al. / Astroparticle Physics 14 (2000) 131±140
guments require that the size of the emission region Rem is constrained to satisfy Rem P c dt
D ; 1 z
2
where dt is the observed variability timescale (>10 min here) and z is the redshift of the source. For Mkn421, z 0:031 and D P 18 (estimated from the Mkn421 ¯are of 7 May 1996 [9]) so the minimum causal size of the emission region Rem is 3:1 1014 cm. If the emission region is located in the putative jet then, given a narrow, collimated jet opening angle of say 5°, the emission region is at least 3:7 1015 cm from the base of the jet, or assuming a black hole mass of 108 M , the emission region is at least 120 gravitational radii (rg ) from the black hole, which is consistent with expectations that this emission cannot originate too near (6100rg or so) the black hole due to the very dense ambient radiation ®eld. Similarly, assuming that the minimum timescale over which variation occurs in the jet is 600 s, we can estimate the lower limit on the magnetic ®eld strength (B) as [18] B P 4 106 = dtD3 P 1:14 G. The fact that we can rule out variability at the 10% level on these timescales, in both of these sources with >99.7 con®dence in both X-rays and TeV c-rays, indicates that the density of the electron population qe E, which is believed to produce the X-rays via synchrotron emission in all broadband models of Blazar emission, does not vary by more than 10% in a region Rem across. This is because the intensity of the X-ray synchrotron radiation I m in the frequency range m to m dm results from electrons in the energy range E to E dE and is given by [3] dE N E dE I m dm ÿ dt 2 2 4 E B N E dE; 3 rT c 3 me c2 2l0 where N E dE qe E is the number of the electrons per unit volume (R3em ) per energy range E to E dE, rT is the Thomson cross-section, B is the magnetic ®eld strength and l0 is the magnetic permeability of the vacuum.
139
Thus, dI m d 2 dm AB xqe E; x dx dx dB dq B2 e A 2qe B dx dx I m dm 6 0:1 dx
4
(60:05 I m dm=dx for Mkn421), where dx 6 Rem and 2 4 E 1 A rT c : 5 3 me c2 2l0 Thus, the rate of change of the intensity of synchrotron emission in a volume of diameter Rem is proportional to both the change of magnetic ®eld strength and the change in lepton density in that volume. Hence, dB AB2 qe 2 dqe ; 6 6 0:1 B A 2qe B dx dx dx dB dqe 2 B q 6 0:1; e
7
where the left-hand side represents the sum of the percentage changes in B and qe , in a volume dx 6 Rem in diameter. Thus, if there is a large local percentage change of B within the jets of Mkn421 and Mkn501 on a scale 6Rem , then it must be matched by an opposite percentage change in qe so that the sum of the changes obeys Eq. (7). It seems more likely that both B and qe have very small scale variability amplitudes and so the maximum fractional change in qe by assuming dB=B 0 is dqe =qe 0:1. Similarly, the maximum fractional change in B by assuming dqe =qe 0 is dB=B 0:05 (or dB P 0:06 G). Hence, assuming small local changes in B and qe , the change in the number of leptons injected into a unit volume (R3em ) of the jet, in a time 10D= 1 z min, either from the environment of the accretion disk via magnetic ®eld lines or from material at the base of the jet, is <10%. From the results of our EPF analysis of short timescale variability in the broadband emission of these two Blazars, we can begin to constrain some of the physical parameters
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that are believed to govern radiation processes in the jet, indicating the importance of continued short timescale studies of these objects. In particular, we derive limits from the data for the ®rst time on the local percentage change in both the lepton density and the magnetic ®eld strength in these Blazar jets. Acknowledgements We would like to thank the Whipple collaboration for the use of their data. We also thank the HEASARC at NASA/GSFC for use of the ASCA public data archive. This work was supported in part by a grant from Enterprise Ireland. References [1] J.H. Beall, W. Bednarek, Astrophys. J. 188 (1999) 510. [2] S. Biller, et al., Phys. Rev. Lett. 83 (1999) 2108.
[3] M.S. Longair, High Energy Astrophysics, vol. 2, Cambridge University Press, London, 1996, p. 252. [4] S. Bradbury, et al., Astronom. Astrophys. 320 (1997) L5. [5] M.J. Carson, B. McKernan, T. Yaqoob, D.J. Fegan, Astropart. Phys. 11 (1999) 153. [6] M.F. Cawley, T.C. Weekes, Exper. Astronom. 1 (1990) 173. [7] A. Comastri, F. Giovanni, G. Gabriele, M. Silvano, Astrophys. J. 480 (1997) 534. [8] M. Hillas, Proc.19th ICRC (La Jolla) 3 (1985) 445. [9] J. McEnery, Ph.D. Thesis, National University of Ireland, 1997. [10] J. Gaidos, et al., Nature 383 (1996) 319. [11] M. Catanese, T. Weekes, Proc. Pac. Conf. Astro., in press. [12] R. Ong, Phys. Rep. 305 (1998) 93. [13] M. Punch, et al., Nature 358 (1992) 477. [14] J. Quinn, et al., Astrophys. J. Lett. 458 (1996) L83. [15] J. Quinn, et al., Astrophys. J. 518 (1999) 693. [16] T. Yaqoob, B. McKernan, A. Ptak, K. Nandra, P.J. Serlemitsos, Astrophys. J. Lett. 490 (1997) L25. [17] T. Yaqoob, I.M. George, T.J. Turner, K. Nandra, A. Ptak, P.J. Serlemitsos, Astrophys. J. Lett. 505 (1998) L87. [18] J. Kataoka, et al., ApJ 514 (1999) 138. [19] T. Takahashi, G. Madejski, H. Kubo, Astropart. Phys. 11 (1999) 177. [20] Y. Tanaka, H. Inoue, S.S. Holt, PASJ 46 (1994) L37.
www.elsevier.nl/locate/astropart
Short timescale variability in the broadband emission of the blazars Mkn421 and Mkn501 B. McKernan a,*, M.J. Carson a, T. Yaqoob b, D.J. Fegan a b
a Department of Physics, University College Dublin, Dublin 4, Ireland Laboratory for High Energy Astrophysics, Code 660.2 Goddard Space Flight Center, Greenbelt, MD 20771, USA
Received 26 August 1999; accepted 26 November 1999
Abstract We analyse ASCA satellite X-ray data and Whipple Observatory TeV c-ray data from the Blazars Mkn421 and Mkn501 for short timescale variability using the excess pair fraction method. We discuss the method and the data as well as EPF sensitivity to these data. We ®nd that in these data sets, we can rule out an amplitude of variability greater than 10% on timescales less than 10 min from both sources and at both wavelengths at a con®dence level of >99.7%. We discuss brie¯y the implications of low amplitudes of variability on short timescales for the beamed jet of relativistic particles probably producing these radiations and, we derive limits from the data on the local percentage change in both the lepton density and the magnetic ®eld strength in these Blazar jets. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The active galaxies Mkn421 and Mkn501 are the nearest of the blazar class of active galactic nuclei (AGN) which are characterised by their variable polarised synchrotron emission and are associated with radio jets emerging from giant elliptical galaxies. Both Mkn421 and Mkn501 are sources of broadband radiation, from radio waves to TeV c-rays. The highest energy (TeV) radiation from these sources has been detected only recently by the Atmospheric Cerenkov Telescope (ACT) of the Whipple collaboration [13,14] and others [4,12] (see also Ref. [11] and references therein). Broadband radiation from these AGN is thought to originate in relativistic collimated out¯ows of
*
Corresponding author. E-mail address: [email protected] (B. McKernan).
plasma (also known as jets), which may be warped and are aligned close to the line of sight. The jet emission from both Blazars may therefore be strongly beamed [1] and so could swamp most of the emission from other parts of the AGN central engine, such as an accretion disk around a putative supermassive black hole. The broadband emission from both Blazars is variable, with both Mkn421 and Mkn501 occasionally exhibiting spectacular ¯aring episodes in both X-rays and c-rays on relatively short timescales [14,9]. A number of major questions concerning Blazar radiation processes have yet to be answered. Which particle dominates the production of crays, the proton or the electron? How are these particles accelerated and how are the c-rays produced? Several competing models of the radiation processes exist and a study of short timescale variability can help in distinguishing between them. Indeed, the core regions of AGN cannot be
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resolved with existing interferometers and so variability studies in general are important in understanding the physics of these central regions. For example, rapid variability in Blazar emission requires a rapid cooling process for the particles producing the radiation. In terms of Blazar radiation models, this is easier to achieve with electrons than with protons, especially when model parameters are derived from ®ts to Blazar spectral energy distributions. Short timescales of variability are also useful in distinguishing between dierent models within the electron or proton family of models, since limits on the magnetic ®eld strength in the jet may be derived and this can help in constraining dierent models. An exciting new application of very short timescale variability in the high-energy radiation from Blazars lies in constraining models of quantum gravity. A study of short timescale variability in Mrk421 has provided the strongest constraints yet on D-brane models of a quantum gravity spacetime foam [2]. In this article, we search for variability in noncontemporaneous data sets of X-rays and c-rays from Mkn421 and Mkn501, over timescales which are less than the fastest observed doubling times of ¯ares in c-rays. Evidence for rapid variability on these timescales allows the calculation of physical parameters associated with the jet and might favour electron models over most proton models as well as providing better limits for models of quantum gravity. Variability studies have been carried out at dierent wavelengths on the blazar class of AGN [7] and on these two AGN in particular [15]. These studies have all used the v2 test against a constant hypothesis, which searches for variability over the entire lightcurve, relative to some mean level. The ®ndings of these studies, after looking at a range of timescales, were: (i) TeV variability down to 15 min for Mkn421 and 2 h for Mkn501, based on the doubling time of the shortest observed ¯ares from these sources and (ii) X-ray variability on timescales down to a few hours for both sources (see in particular Refs. [18,19] and references therein). Our variability analysis is dierent from previous studies because it utilises the excess pair fraction (EPF) method [16], which picks out variability
on a spectrum of timescales. We have previously presented a brief discussion of the application of EPF to TeV c-ray data from Mkn501 in Ref. [5]. Here, we present a discussion of the EPF method and its application to X-ray and TeV c-ray data from both Mkn421 and Mkn501. The EPF method is a simple means of analysing gapped time series, and measures explicit bin-to-bin variability. Spurious variability due to gaps in data is automatically eliminated using EPF, which constrains our analysis to small timescales of the order of fractions of continuous data sets. However, it also allows an analysis of a continuum of small timescales, something that to our knowledge, has not been done before with these Blazars. We can do this for a range of bin widths to build an EPF spectrum. We emphasise that EPF is dierent from the standard v2 test for variability, in that v2 does not measure bin-to-bin variability as EPF does, rather it measures variability on a timescale corresponding to the length of the lightcurve. 2. The broadband data 2.1. The c-ray data The TeV data were recorded by the Whipple Observatory Imaging Atmospheric Cerenkov Telescope (IACT) [6]. The IACT indirectly observes very high-energy c-rays from high-energy sources, such as AGN jets and supernova remnants. The c-rays are detected via the camera image of the Cerenkov pulse associated with the air shower that they produce in the upper atmosphere. However, by far, the majority of the Cerenkov showers in the upper atmosphere are due to the impact of high-energy cosmic rays (hadrons or leptons), therefore, the parent c-ray data, as observed by the IACT have a very small signal-tonoise ratio. The procedure of extracting c-ray events from data dominated by hadronic air showers requires the parameterisation of shower image properties [8]. These Hillas parameters may be classi®ed into `shape' parameters (such as length or width) or `orientation' parameters such as a, which de®nes the angle made by the image length axis with the
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centre of the ®eld of view of the camera. Selection of events (cuts), based on image parameters, provides an ecient way of removing most noise whilst preserving most of the signal. Where elimination of noise is most important, cuts may remove around 40% of signal along with nearly all noise leaving a cut data set with a typical signal-tonoise ratio of around 3:2. However, if signal retention is important then, almost 100% of the signal may be retained by employing (for example) trigger cuts which eliminate spurious events that can account for up to 1=3 of the parent data. The parent data are typically recorded in approximately 28 min intervals in one of the three modes: ON, OFF or tracking. The ON/OFF mode consists of tracking the source for 28 min and then observing the same region of sky through which the source has passed for the same duration in order to provide comparison background data for the ON source observation. Subtracting OFF data from ON data gives the excess of events from the source. Tracking mode involves continuously tracking the source across the sky over several 28 min observations. This mode is useful when the source may be particularly active. Poor weather can cause large changes in the parent data rate due to light scattering from clouds passing through the line-of-sight of the telescope, for example. Elevation changes between and during data collecting runs may also signi®cantly change the parent data rate, particularly at low elevations. Good weather conditions are logged at the time the run is taken and correspond to low variability (62r) in the raw parent count rate. The Mkn421 data analysed were taken from the period April 1996±May 1996, during which time the most signi®cant ¯aring event ever seen at this energy was observed [10]. The Mkn501 data were taken from the period April 1997±May 1997, during which time this AGN was at its most active since its detection at this energy in 1995. The presence of strong ¯aring within these data is important for our purposes as the count rate from the AGN increases typically from 61 to P10 c minÿ1 during a strong ¯aring state. A count rate as low as 61c minÿ1 would make it very dicult to pick out statistically signi®cant variability on timescales 65 min using any method;
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however, large ¯ares allow us to probe such timescales for variability. The continuous stream of TeV data are recorded by the ACT using GPS, UTC and livetime clocks. The livetime clock is most susceptible to errors, such as dropped frames (random missing sequences of events), so we use the more reliable UTC clock (which is derived from the GPS clock). The GPS clock has nanosecond resolution, so we can de®ne good time intervals (GTI) for the TeV data by ¯agging the ®rst and last events in a parent data set as the start and end times of a data set. 2.2. The X-ray data The ASCA satellite [20] observed Mkn421 and Mkn501, obtaining moderate energy resolution spectra in the 0.5±10 keV band, with a timeresolution of better than 2 s for two of the four instruments onboard (4 s for the other two). Mkn421 was observed on 18 occasions between 10 May 1993 and 3 June 1997, with a total exposure time of 240 103 s. The 1996 data do not overlap with the TeV data reported in this article. Mkn501 was observed on four occasions between 21 March 1996 and 2 April 1996, with a total exposure time of 49 103 s. Additional ASCA observations of both sources exist but only those made on the dates mentioned above were in the public archive at the time of writing. An excellent account of the Mkn421 ACSA observations and results can be found in Ref. [19] and the ASCA results for Mkn501 can be found in Ref. [18]. 3. Excess pair fraction method The EPF method is a simple method of analysing gapped time series for timescales on which the source is varying [16]. The method allows the measurement of bin-to-bin variability within a time series, and comparison with a theoretical Poisson source, for a whole spectrum of bin widths. The time series is binned at a bin width T and the number of counts in each bin is found. We then count the total number of bin pairs with nonzero counts in each and compute the fraction of those bins which satisfy the condition
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jCi ÿ Ci1 j P
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p p Ci Ci1 ;
1
where Ci is the number of counts in the ith bin. The resulting fraction is termed EPF(T). We do not consider pairs of bins where one or both have zero counts since these automatically ful®ll the condition for variability in Eq. (1) but which represent an absence of data rather than counts which can be treated statistically. The statistical signi®cance of any intrinsic variability within a gapped time series is computed by comparing the calculated EPF(T ) with the EPF(T ) obtained from a simulated, constant Poisson source with the same mean-count rate. In deriving the comparison Poisson source EPF curve, the counts in each of 106 bin pairs used are taken from a Poisson distribution, and a normalised mean count rate of 1 sÿ1 is used. We ®nd that the EPF curve for a Poisson source tends to a theoretical value of 0:159 in the limit of large statistics (analytically as well as for simulations). A direct comparison of this reference curve with the data simply requires dividing this Poisson curve by the mean-count rate of the data. As the number of bins into which the data set is divided tends to one, EPF tends to one, and as the number of counts per bin tends to zero, EPF tends to zero in both the reference curve and actual data. We can also generate EPF for simulated sources with some intrinsic percentage variability, by de®ning the mean number of counts in each simulated bin to be some factor 1 f m times the mean-count rate (usually normalised to 1 sÿ1 ), where f 0:0; 1:0 represents the percentage variability and m is a uniform random deviate between ÿ1 and 1 [16]. The statistical signi®cance of the variability at a particular bin width T, corresponding to EPF(T ), is given by the multiple of its 1r errorbar from EPF(T ) for a constant Poisson source. This is true at least for a well-de®ned signal with little or no noise contamination, such as the X-ray data. In practice, a relatively large proportion of the TeV data that passes parameter cuts is noise; therefore, unless that noise is (approximately) Poissonian, our task is complicated. If the background noise that passes cuts were non-Poissonian and we wished to attach statistical signi®cances to any
variability in the signal, we would have to replace the reference EPF curve described above with an EPF curve that mimics the behaviour of the background. We ®nd, however, that the TeV background does indeed appear to be consistent with a Poisson source (Fig. 1), by constructing a small timescale EPF spectrum for seven OFF runs, which should contain a negligible amount of crays. The statistics become poor beyond around 500±600 s, re¯ecting only two to three bins per data set. EPF at or around this point tends to rise rapidly to 1. This does not mean that the source is varying at these bin widths, rather simply it re¯ects the ever decreasing number of bins being analysed. This is also evident from the much larger error bars associated with the EPF points at these bin widths. Thus EPF points above 500±600 s will be disregarded due to poor binning statistics. Spurious variability due to partially ®lled bins at the start or the end of a data set, is eliminated by rejecting these bins. In the case of TeV data, events are usually binned in approximately 28 min sets and every event in the parent data set is registered by the UTC clock with an accuracy of the order of 5 ms. We equate the start and end times for each parent data interval with the ®rst and last trigger
Fig. 1. The EPF spectrum for c-ray background. The solid line is the EPF curve for a constant source with the same mean count rate as the data. As the bin width tends to zero, the EPF spectrum for a constant also tends to zero. As the bin width approaches half the length of the run, EPF saturates. The open circles are EPF(T ) and errorbars are 1r.
B. McKernan et al. / Astroparticle Physics 14 (2000) 131±140
events in that set and ¯ag these times. Any bins which include the ¯agged times are rejected. This means that the maximum theoretical bin size which we can test for variability is approximately 14 min (840 s). In practice, this limit is closer to 10 min (600 s), which gives two bins per data set. Evidently an upper limit to a bin size of this magnitude implies that changes in elevation between data sets are not relevant to our analysis. However, changes in elevation within a data set may cause some variation in signal, although this should not appear signi®cantly in the context of our analysis, since EPF measures explicit bin-tobin variability, so only signi®cant elevation eects will manifest themselves in the resulting EPF(T ) curve. A similar approach is used to eliminate spurious variability due to binning when applying EPF to X-ray data (see Ref. [16] for details). We indicated above that the EPF method is dierent from the standard v2 test for variability, in that EPF explicitly tests bin-to-bin variability, implying that a simple comparison between results of both methods is not possible. A simple example illustrates this point very well. Consider a lightcurve containing 100 2-min bins, 98 of which are consistent with a constant, but two of which (roughly at each end of the lightcurve say) are very deviant. An application of the EPF test to the data will indicate that the 2 min variability is small because only two out of the 100 bins show variability. On the other hand, an application of the v2 test to the lightcurve will indicate that the variability is large. However, if the lightcurve were chopped, v2 will now indicate that there is no variability, whereas EPF will give the same result as before. This is because v2!! is not measuring 2 min variability, rather it is measuring variability on a timescale corresponding to the length of the lightcurve. 3.1. An example of excess pair fraction applied to TeV data The EPF technique has been demonstrated on ASCA X-ray data [16], where it was shown that the variability of the Seyfert I AGN MCG-6-30-15 did not cease down to approximately 20 s. Here, we apply the EPF method to IACT data, in a
135
search for signi®cant short timescale variability. Within the context of EPF, variability at a particular timescale T means that the lightcurve derived from the time series changes according to Eq. (1) at bin width T . To test this, we analysed an uncut data set containing injected strong contamination from a periodic source with a period of 2.5 s. The contamination was strongest at the start of the data set and grew less as the telescope tracked away from the source. Fig. 2(a) shows the EPF curve for the uncut data from this source. We expect to see minima in EPF(T ) at T equal to the period of the beacon, since EPF will pick out variability when the time series is binned on a time scale comparable with the source variability. This is because variability, as de®ned in Eq. (1) is a minimum because there are approximately equal number of counts in each bin (the light curve looks ¯at). This is indeed the case as the EPF reaches a maximum at 1.25 s with a signi®cance of 16r, at a binwidth corresponding to half of the period of the beacon signal. The ®rst minimum occurs at 2.5 s which must be the period of the beacon. The ®rst harmonic of the signal occurs at 3.75 s at 5r, after which the statistics become too poor to clearly pick out any more of the signal's harmonics. We estimate the signal (periodic source)-to-noise ratio (S=N ) in this test run to be 61=5, by comparing the ratio of the rate at the start of the run when the periodic source is strongest, to the rate at the end of the run, where the periodic source is no longer detected. It is perhaps not surprising that the variability is picked out for such a strong signal, but it is an instructive demonstration of the method nonetheless. In order to test the limits of the technique in analysing periodic sources, arti®cial noise was added to the signal, thereby reducing S=N and the resulting EPF calculated for each simulation. Poisson noise with multiples of the mean-count rate and number of events of the parent data was added to the data set. Fig. 2(b)±(f) shows the dilution of the periodic signal by the addition of successively larger sets of Poisson-distributed (non-periodic) arti®cial events to the run. We know that the magnitude of the periodic signal in the run is 1/5 the magnitude of the background
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Fig. 2. The EPF spectrum for a periodic source with varying levels of added noise (see the text for details).
B. McKernan et al. / Astroparticle Physics 14 (2000) 131±140
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in that run, so as we add increasing amounts of arti®cial Poisson background, we can estimate the new value of S=N . We ®nd that variability can be picked out with an S=N of 1=20 at the 4:5r level, where signi®cance is measured in terms of the distance from the EPF point to the Poisson background curve as a multiple of the 1r error-bar of the EPF point. At this level of added noise, it is not obvious that the embedded signal is periodic since periodicity appears to vanish at an S=N of 1=10, but EPF tells us that the signal is still varying at a statistically signi®cant level on small timescales.
4. Results of excess pair fraction applied to X-ray data The ASCA Mkn421 and Mkn501 data were reanalysed and reduced in the same manner as described in Ref. [17]. We made EPF spectra for each source following the methods described in Ref. [16], averaged over all the available data sets. The results for both sources are shown in Figs. 3 and 4. The solid, dotted and dashed curves show theoretical EPF for a source with 0%, 5%, and 10% random amplitude of variability, respectively. The curves were generated as described in detail in Ref. [16]. If an EPF point is y multiples of its 1r error bar lower than a theoretical EPF curve with x%
Fig. 4. The EPF spectrum for ASCA X-ray data on Mkn501.
random amplitude of variability, then we say that this rules out variability at the x% level in the source with a con®dence level of y standard deviations. It can be seen that in Mkn421, we can rule out variability at the 5% level with a con®dence level greater than 3r from 500 s down to timescales of 11 s. (Note: The kink at 32 s is due to only two of the four ASCA instruments being used below this timescale because the two Solid State Spectrometers have less timing resolution than the two Gas Imaging Proportional Counters). For Mkn501, for which much less data are available, we can rule out variability at the 10% level with a con®dence level greater than 3r from 400 s down to timescales of 32 s.
5. Results of excess pair fraction applied to c-ray data
Fig. 3. The EPF spectrum for ASCA X-ray data on Mkn421.
The TeV data for Mkn421 were taken from the period April 1996±May 1996, during which time the most signi®cant ¯aring event ever seen at this energy was observed. The Mkn501 data were taken from the period April 1997±May 1997, during which time this AGN was at its most active since its discovery at this energy in 1995. The presence of strong ¯aring within these data is important for statistical purposes as the count rate from the AGN increases from typically 61c to
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Fig. 5. The EPF spectrum for Whipple c-ray data on Mkn421.
10c minÿ1 during a strong ¯aring state. Fig. 5 shows EPF for Mkn421 at TeV energies. Approximately 1760 min of data are used in this analysis. None of the data points are greater than 3r from that of a theoretical constant source with the same mean count rate. Because of the 28 min data binning only timescales less than 14 min can be considered using this technique. The c-ray rate (3c minÿ1 ) prevents us probing timescales much lower than 200 s. Fig. 6 shows EPF for Mkn501 with approximately 1900 min of data. Again, none of the data points are greater than 3r from that of
Fig. 6. The EPF spectrum for Whipple c-ray data on Mkn501.
a constant source with the same mean count rate indicating a lack of signi®cant variability in these data from Mkn501 below 10 min. Here the rate is 9 minÿ1 and so the lower timescale below which the statistics become too poor is 100 s. By comparing the EPF spectrum with the simulated 10% variability amplitude, we can rule out variability amplitudes of >10% in TeV c-rays in both sources on timescales below 10 min at a con®dence level > 3r. These results are consistent with the results of previous short timescale studies, which employed the v2 test [14,9] and which found no signi®cant variability, although we emphasise again that EPF explicitly measures bin-to-bin variability, unlike v2 , and so there is no direct comparison between the two methods.
6. Discussion and conclusions Our results for the data under discussion show that there appears to be no statistically signi®cant variability in either of the two AGN, in either X-ray or TeV c-rays below timescales of 600 s. Certainly, we can rule out amplitudes of variability in these data at the 10% level on these timescales, in both these sources, with a con®dence level of >99.7%. In fact, we can rule out X-ray variability in the Mkn421 data at the 5% amplitude level also at the >99.7% con®dence level. We see no statistically signi®cant variability on very short timescales that might suggest electron dominated radiation processes in the jets or allow for improvement of the observational limits in Ref. [2] on theories of quantum gravity. Nevertheless, if we assume that the source is not varying on timescales shorter than 10 min then we can estimate the minimum causal size of the emission region, attempt to constrain the location of the emission region and produce model-dependent limits on the magnetic ®eld strength and electron population within the jet. The Doppler beaming factor is given by D 1=Cb 1 ÿ b cos h, where Cb is the Lorentz boost, b v0 =c (where v0 is the velocity of the emitting region) and h is the angle between the velocity vector of the emitter and the line of sight of the observer. Causal ar-
B. McKernan et al. / Astroparticle Physics 14 (2000) 131±140
guments require that the size of the emission region Rem is constrained to satisfy Rem P c dt
D ; 1 z
2
where dt is the observed variability timescale (>10 min here) and z is the redshift of the source. For Mkn421, z 0:031 and D P 18 (estimated from the Mkn421 ¯are of 7 May 1996 [9]) so the minimum causal size of the emission region Rem is 3:1 1014 cm. If the emission region is located in the putative jet then, given a narrow, collimated jet opening angle of say 5°, the emission region is at least 3:7 1015 cm from the base of the jet, or assuming a black hole mass of 108 M , the emission region is at least 120 gravitational radii (rg ) from the black hole, which is consistent with expectations that this emission cannot originate too near (6100rg or so) the black hole due to the very dense ambient radiation ®eld. Similarly, assuming that the minimum timescale over which variation occurs in the jet is 600 s, we can estimate the lower limit on the magnetic ®eld strength (B) as [18] B P 4 106 = dtD3 P 1:14 G. The fact that we can rule out variability at the 10% level on these timescales, in both of these sources with >99.7 con®dence in both X-rays and TeV c-rays, indicates that the density of the electron population qe E, which is believed to produce the X-rays via synchrotron emission in all broadband models of Blazar emission, does not vary by more than 10% in a region Rem across. This is because the intensity of the X-ray synchrotron radiation I m in the frequency range m to m dm results from electrons in the energy range E to E dE and is given by [3] dE N E dE I m dm ÿ dt 2 2 4 E B N E dE; 3 rT c 3 me c2 2l0 where N E dE qe E is the number of the electrons per unit volume (R3em ) per energy range E to E dE, rT is the Thomson cross-section, B is the magnetic ®eld strength and l0 is the magnetic permeability of the vacuum.
139
Thus, dI m d 2 dm AB xqe E; x dx dx dB dq B2 e A 2qe B dx dx I m dm 6 0:1 dx
4
(60:05 I m dm=dx for Mkn421), where dx 6 Rem and 2 4 E 1 A rT c : 5 3 me c2 2l0 Thus, the rate of change of the intensity of synchrotron emission in a volume of diameter Rem is proportional to both the change of magnetic ®eld strength and the change in lepton density in that volume. Hence, dB AB2 qe 2 dqe ; 6 6 0:1 B A 2qe B dx dx dx dB dqe 2 B q 6 0:1; e
7
where the left-hand side represents the sum of the percentage changes in B and qe , in a volume dx 6 Rem in diameter. Thus, if there is a large local percentage change of B within the jets of Mkn421 and Mkn501 on a scale 6Rem , then it must be matched by an opposite percentage change in qe so that the sum of the changes obeys Eq. (7). It seems more likely that both B and qe have very small scale variability amplitudes and so the maximum fractional change in qe by assuming dB=B 0 is dqe =qe 0:1. Similarly, the maximum fractional change in B by assuming dqe =qe 0 is dB=B 0:05 (or dB P 0:06 G). Hence, assuming small local changes in B and qe , the change in the number of leptons injected into a unit volume (R3em ) of the jet, in a time 10D= 1 z min, either from the environment of the accretion disk via magnetic ®eld lines or from material at the base of the jet, is <10%. From the results of our EPF analysis of short timescale variability in the broadband emission of these two Blazars, we can begin to constrain some of the physical parameters
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that are believed to govern radiation processes in the jet, indicating the importance of continued short timescale studies of these objects. In particular, we derive limits from the data for the ®rst time on the local percentage change in both the lepton density and the magnetic ®eld strength in these Blazar jets. Acknowledgements We would like to thank the Whipple collaboration for the use of their data. We also thank the HEASARC at NASA/GSFC for use of the ASCA public data archive. This work was supported in part by a grant from Enterprise Ireland. References [1] J.H. Beall, W. Bednarek, Astrophys. J. 188 (1999) 510. [2] S. Biller, et al., Phys. Rev. Lett. 83 (1999) 2108.
[3] M.S. Longair, High Energy Astrophysics, vol. 2, Cambridge University Press, London, 1996, p. 252. [4] S. Bradbury, et al., Astronom. Astrophys. 320 (1997) L5. [5] M.J. Carson, B. McKernan, T. Yaqoob, D.J. Fegan, Astropart. Phys. 11 (1999) 153. [6] M.F. Cawley, T.C. Weekes, Exper. Astronom. 1 (1990) 173. [7] A. Comastri, F. Giovanni, G. Gabriele, M. Silvano, Astrophys. J. 480 (1997) 534. [8] M. Hillas, Proc.19th ICRC (La Jolla) 3 (1985) 445. [9] J. McEnery, Ph.D. Thesis, National University of Ireland, 1997. [10] J. Gaidos, et al., Nature 383 (1996) 319. [11] M. Catanese, T. Weekes, Proc. Pac. Conf. Astro., in press. [12] R. Ong, Phys. Rep. 305 (1998) 93. [13] M. Punch, et al., Nature 358 (1992) 477. [14] J. Quinn, et al., Astrophys. J. Lett. 458 (1996) L83. [15] J. Quinn, et al., Astrophys. J. 518 (1999) 693. [16] T. Yaqoob, B. McKernan, A. Ptak, K. Nandra, P.J. Serlemitsos, Astrophys. J. Lett. 490 (1997) L25. [17] T. Yaqoob, I.M. George, T.J. Turner, K. Nandra, A. Ptak, P.J. Serlemitsos, Astrophys. J. Lett. 505 (1998) L87. [18] J. Kataoka, et al., ApJ 514 (1999) 138. [19] T. Takahashi, G. Madejski, H. Kubo, Astropart. Phys. 11 (1999) 177. [20] Y. Tanaka, H. Inoue, S.S. Holt, PASJ 46 (1994) L37.