AN EXPERIMENT TO LOCATE THE SITE OF TeV FLARING IN M87

Our data processing of M87 5 ks observations (we have accumulated over 60 of these during the years 2002–2009; Harris et al. 2009; Acciari et al. 2010) has purposefully remained essentially unchanged except for the changes made to the CALDB. In brief, we check for high background levels, remove pixel randomization (the intentional degradation of image quality by adding a random number to the pixel location of each event; this process was a part of the pipeline processing until quite recently), register the X-ray event file by changing the values of appropriate keywords in the fits header so as to align the X-ray nucleus with the radio nucleus, and then construct flux maps regridded to one-tenth of the native ACIS pixel size (i.e., pixels size changes from 0492 to 00492). This last step is done for the soft band (0.2–0.75 keV), the medium band (0.75–2 keV), and the hard band (2–6 keV). Because of severe pileup¹⁹ for the knot HST-1 during its high-intensity flaring in 2005, we forsook cgs units (the flux maps) and instead made our primary intensity measurement in terms of keV s⁻¹. This photometry was performed using the event 1 file²⁰ with no grade filtering and integrated from 0.2 keV up to whatever energy was required to recover essentially all the events associated with a given feature. In the rest of this paper, it is important to distinguish between counts s^–1 (used primarily in dealing with evaluation of pileup) and keV s⁻¹, which is the sum of each event multiplied by its energy. Since most photons are of order 1 keV, the magnitudes of these two observational parameters are quite similar. Further details of our processing methods can be found in Papers I, III, and V of our series (Harris et al. 2003, 2006, 2009, respectively).

For the current effort we have altered our procedures in a few particulars. First, we changed the "bad pixel" routine to the "hot pix" recently released in CIAO. More importantly, however, we used acis_process_events to apply the EDSER algorithm²¹ in place of the removal of pixel randomization. In various tests, we found that data processed with EDSER produce a more narrow point-spread function and consequently a higher peak intensity. While not a drastic improvement, it is sufficiently good so as to be a valuable asset in separating the nucleus from HST-1 (separated by 086). An example (our first observation, "eda1") is shown in Figure 1, which will also serve to illustrate the apertures for photometry.

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Before attempting to evaluate the characteristics of the nuclear data that exceed 1 keV s⁻¹, it behooves us to consider the effects of pileup in the ACIS CCDs.

Although we have had to deal with severe pileup for the high intensity of the knot HST-1 in 2005, we generally considered levels of ⩽1 keV s⁻¹ as weak enough so that pileup could be ignored. However, in the present case, we realize that even if a minority of incoming photons arrived during a frame time with another photon, the resulting events would masquerade as single photons of higher energy, distorting the spectral distribution. Therefore, to understand the effects of mild pileup, we examined three parameters indicative of pileup and use the count rate of the event 1 file as our independent variable.

The first is the ratio of the measured intensities (keV s⁻¹) in the event 2 file to that in the event 1 file. We time filtered the event 1 file but did not filter for standard grades since we wanted to recover those events which suffered grade migration,²² a common symptom of pileup. For knot A which is slightly resolved and not expected to suffer pileup, the intensity is about 0.2 counts s⁻¹ (0.08 counts per frame since we always use 0.4 s frame time). Values for the ratio keV s⁻¹(evt2/evt1) range between 0.95 and 0.98 for the 10 observations of Table 1. For knot D which has an intensity roughly half that of knot A, the observed ratios go from 0.96 to 0.99.

For the nine observations of 2010, HST-1 had an intensity between 0.25 and 0.28 counts s⁻¹ and the observed ratio ranged from 0.89 to 0.95. In 2008 February the intensity was 0.82 counts s⁻¹ and the ratio was 0.79. For the nucleus, the two intensities greater than 1 keV s⁻¹ had ratios of 0.78 and 0.85 whereas the lower intensity observations ranged from 0.91 to 0.93 for the ratio.

The loss of detected energy passing from event 1 to event 2 is reflected in the loss of detected events caused by grade migration. In Figure 2 we show this effect.

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Another indicator of pileup is the average energy of all detected events. Although 〈E〉 is ambiguous since it will increase if the intrinsic source spectrum hardens, if coupled with detectable grade migration, it is a necessary consequence of pileup. Not only will the energy of piled events be much larger than the average of unpiled events, but the average energy will be augmented because there are fewer events than there should be owing to the doubling up of piling. This predicted effect is present in our data: the mean energies for the nucleus for the eight observations of intensity <1 keV s⁻¹ range between 1.38 and 1.53 keV while for Zhed it is 1.78 and for eda1 it is 1.57. Similarly, 〈E〉(Zhed) for HST-1 is 1.47 keV compared to the 2010 values which range between 1.15 and 1.28.

We have also used PIMMS²³ to estimate pileup. Specifying the input as Chandra counts s⁻¹ with frame time 0.4 s, a power law with photon index = 2, and absorption by a column density of N_h = 4 × 10²⁰ cm⁻²; we constructed a "look-up" table of input (photons per second arriving at the detector) and output counts s⁻¹, which is the count rate of the unpiled photons. We calculated the total event rate from the expression:

$${\rm observed(evt1\ {\rm counts\,s^{-1}})} = \frac{{\rm PIMMS}({\rm output}) {\rm counts\,s^{-1}}}{1-{\rm Fp}},$$

where Fp is the fractional pileup reported by PIMMS and is defined as the number of piled events divided by the total number of events. We use the observed event rate from the event 1 file which has been time filtered but not grade filtered because PIMMS does not accommodate corrections for grade migration. In this way we can estimate the inferred counting rate from each component in the absence of pileup. Relevant numbers are given in Tables 2 (nucleus) and 3 (HST-1), and it is clear that even with a frame time of 0.4 s, pileup will significantly affect most source parameters except for the intensity in keV s⁻¹, which was specifically designed to circumvent first-order pileup problems.

X-ray intensities were measured using the rectangular apertures defined previously. The keV s⁻¹ values are given in Tables 2 and 3, and plotted in Figure 3. We do not include tabular data for knots D and A since they are not viable candidates for the site of flaring TeV emission and pileup is negligible for both: knot D has a much smaller counting rate than the nucleus and HST-1, whereas knot A is resolved. The data for these two knots are included in Figure 3 as "control features"; any intrinsic variability in these two knots is at a much lower level than for the nucleus and HST-1.

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For the case of HST-1, we became convinced that the huge flare of 2005 could be described by a broadband synchrotron emission from the radio to the X-rays in an equipartition field of ≈1 mG (Papers I, III, and V). With the presence of electrons with Lorentz factors, γ ≈ 10⁷, we showed that such a source would be expected to produce IC emission in the TeV range from ambient photons (Paper IV). Moreover, although it is probable that expansion losses were operative, there were time intervals which manifest the signature of energy-dependent radiative losses and the decay times were consistent with a 1 mG field (Paper V).

When we consider the emission from the unresolved (by Chandra) nuclear component, we cannot devise a complete scenario because there are so many unknowns: primarily the source size and the broadband nature of the emission. It may be the case that the operative field strength is significantly larger than that of HST-1, the emitting volume may be much smaller, and the beaming factor could be quite different (either larger or smaller than the estimate of δ ≈ 5 for HST-1; Perlman et al. 2011). In Abramowski et al. (2011) it is clearly shown that the evidence at hand provides mixed results when attempting to show broadband emission associated with TeV flaring. While one can argue that the X-ray flux observed from the nucleus is always a bit larger than normal at the time of TeV flaring, the 43 GHz "activity" from the milliarcsecond core appeared on one occasion but was absent on another.

One might, in fact, propose that the major acceleration mechanism could be reconnection rather than shock acceleration, and therefore, there could well be quite a different distribution of relativistic electrons from the broken power law from low values of γ up to 10⁷ or 10⁸ suggested to explain the broadband emission from HST-1. If such were to be the case, there is no a priori reason to expect that a particular band will show anomalous emission directly associated with the TeV flaring. With this caveat in mind, we will now argue that there is, in fact, circumstantial evidence for X-ray emission from the nucleus of M87, which is associated with TeV flaring.

For the nucleus, the spectral differences we have measured between the first and remaining observations are in the same direction as would be expected from the change in pileup fraction.

The drop in the nuclear intensity between our first two observations (separated by 1.68 days) permits us to measure the fractional change per day, "fpd" (see Paper V where fpy—"fractional change per year" was introduced) and compare its value to the historical behavior during 8 years of monitoring. Typically, the largest values found previously for the nucleus were fpy ≈50, corresponding to an fpd value of fpy/365 ≈0.137 (both positive and negative fpys of this magnitude were observed). The fpd (or fpy) formulae are as follows:

$$fpd=(I_2-I_1)/(I_i\Delta t)$$

$$\sigma (fpd) = \frac{1}{\Delta (t)}\times \frac{I_j}{I_i}\times \sqrt{\left(\frac{\sigma _1}{I_1}\right)^2 + \left(\frac{\sigma _2}{I_2}\right)^2},$$

where I₁ and I₂ are successive intensities, Δt = (t₂ − t₁), and i = 1, j = 2 when the source is getting brighter and i = 2, j = 1 when the intensity is dropping. The time it would take to change the intensity by a factor of two for an observed value of fpd is 1/fpd.

The calculated values of fpd (between eda1 and eda2) for various intensity measurements are −0.454 ± 0.027 for keV s⁻¹, −0.150 ± 0.041 for the soft flux, −0.266 ± 0.030 for the medium flux, and −0.643 ± 0.071 for the hard flux. While it would be useful to know if the hard flux was dropping faster than the soft flux, the apparent effect could be caused, in whole or in part, by the reduction of the pileup fraction between eda1 and eda2.

To estimate the spectral distribution of the incident photons (i.e., what we would have observed in the absence of pileup), we adopted the rather extreme assumption that all the piled events ended up in the hard band, and assumed that of the arriving photons which eventually piled, 1/3 came from the soft band and 2/3 came from the medium band. This is "extreme" because some of the piled events will actually end up in the medium band and because some fraction of the piled events will actually consist of three photons rather than just two. Taking the observed count rates from the event 1 file (i.e., no grade filtering) we were then able to estimate the incident count rates for each band for both eda1 and eda2. It is then a simple matter to calculate fpd values but the uncertainties will be dominated by errors in assuming the particulars of the pileup. Therefore, we have calculated the uncertainties for the observed fpd, but not for the assumed incident count rates: the results are presented in Table 4.

The "exercise" of assuming how the piled events are distributed among the energy bands is just to get some rough idea to differentiate between pileup effects and intrinsic attributes. Fpd is a good measure of the rate of decay of intensity and we take the decrease of fpd(incident) moving from soft to hard as evidence for the presence of energy-dependent radiative losses. The fact that the spectral index for eda2 is the largest among all our observations even though the intensity is second only to eda1 is further evidence that pileup is not the dominant factor for the fpd dependency on energy.

Generally speaking, the most plausible mechanisms for a drop of intensity for a non-thermal source is either expansion (which has no first-order effect on the spectral shape of the electron energy distribution) or the radiative cooling with the energy loss rate increasing with increasing energies of the radiating particles (for example, as ∝E² in the case of the synchrotron and IC emission).²⁴ Although the dimming of radio emission from parsec scale knots is often ascribed to expansion, when dealing with high-energy emissions which must come from electrons with much greater energies than those producing radio emission, energy-dependent radiative losses are much more likely to contribute to the dimming, with or without expansion.

From the general magnitude of fpd values we may also infer that the light-travel time across the X-ray emitting region is limited to a few days, thus being consistent with estimates of the size of the TeV flaring regions deduced by the timescale of TeV variability (Aharonian et al. 2006; Abramowski et al. 2011).

Although our experiment did not succeed in isolating similar features in the X-ray and TeV light curves, we find evidence that supports the notion that there was concomitant flaring in the X-rays, and we witnessed the last phase of that flaring.