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Astron. Astrophys. 342, 69-86 (1999)

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6. Correlation of the TeV emission with the X-ray emission

A correlation of X-ray and TeV fluxes would give clues regarding the emission mechanism. The All Sky Monitor on board the Rossi X-Ray Timing Explorer has been regularly observing bright X-ray sources in the energy range from 2 - 12 keV since January 5th, 1996. It observed mainly X-ray binaries and a list of initially 10, and since May 1997 a list of 74 bright active galactic nuclei. Each object is monitored roughly 5 times a day, each time for 90 seconds. The detection threshold per 90 second observation is 30 mCrab. The ASM data is publicly available over the Internet.

The ASM monitors Mkn 501 since January 5th, 1996. In Fig. 20 the time histories of the ASM flux and the hardness ratio counts (5-12.1 keV) / counts (1.3-3.0 keV), both computed with bins of 1 week duration, are compared to the light curve of the HEGRA IACT-system. We derived the ASM count rates [FORMULA] from the "definitive" ASM products satisfying the requirement of a dwell duration larger than 30 s and a flux fit with a reduced [FORMULA]-value smaller than 1.25. We excluded days with poor sampling (less than 25% of the data), by using only the diurnal rates values which have an error smaller than 0.375 counts/sec. The binned light curves, hardness ratios, and correlation coefficients ("slow" method with error propagation) have been obtained using the "ftools 4.0" package.

[FIGURE] Fig. 20. The ASM count rates [FORMULA] (2-12 keV), the ASM hardness ratios counts (5-12.1 keV) / counts (1.3-3.0 keV), and the daily HEGRA differential fluxes at 2 TeV against time, for the time period from January 1997 until February 1998.

The count rate increases from 0.4/sec in February, 1996, slowly to 1 counts/sec in January, 1997, and then dramatically to 2 counts/sec in June/July 1997. After reaching its maximum of 3.1[FORMULA]0.4 on June 24th, 1997, the count rates returned to around 1 counts/sec until April 1998. During the major flaring phase in 1997, the X-ray spectrum hardens, i.e. the hardness ratio increases from 0.8 in January 1997 to 1.5 in July 1997 and decreases again to 1 until April 1998.

A correlation between the X-ray activity and the TeV-activity can be recognized in the sense that the X-ray activity peaked in June/July when the amplitudes of the TeV flares reached their maximum.

In Fig. 21 the correlation between the daily differential flux at 2 TeV, [FORMULA], and the count rate [FORMULA] is shown. Hereby, for each daily [FORMULA]-value, the ASM rate has been averaged over all 90 second measurements within the 24 h time interval centered close to 0:00 UT. One sees indications of a correlation between the emission in the two energy bands. A fit to the data gives the correlation:

[EQUATION]

[FIGURE] Fig. 21. The correlation of the one-day ASM count rates [FORMULA] (2-12 keV) with the daily HEGRA differential fluxes at 2 TeV. Superimposed is a straight line fit to the data.

A possible time shift [FORMULA] between the TeV- and X-ray variability has been searched for by computing the discrete correlation function, DCF, (Edelson & Krolik 1988)

[EQUATION]

as function of [FORMULA]. The index i runs over all nights with TeV-measurements, the [FORMULA] are the daily TeV flux amplitudes, and the [FORMULA] are the ASM count rates averaged over 24 h, centered close to 0:00 UT. In Fig. 22 the results are presented. The DCF shows a positive peak reaching from [FORMULA] (TeV variability follows X-ray variability after 1 day) to [FORMULA] (TeV variability precedes X-ray variability by one day).

[FIGURE] Fig. 22. The correlation coefficient of the daily HEGRA differential fluxes at 2 TeV and the one-day ASM count rates [FORMULA] (2-12 keV) as a function of the time shift [FORMULA] between the considered TeV and X-ray fluxes. Positive [FORMULA]-values correspond to the TeV variability preceding the X-ray variability.

The data indicates a correlation of the TeV- and X-Ray emission with a time lag of one day or less. For [FORMULA], 50 pairs of TeV and X-ray data enter the calculation and give a DCF of 0.37[FORMULA]0.03. Even completely uncorrelated time series are expected to produce non-zero values of the DCF (Edelson & Krolik 1988). The probability distribution of the DCF depends on the number of pairs used for its calculation and on the temporal autocorrelation characteristics of the TeV emission and the X-ray emission. Assuming 50 statistically independent flux measurements in two energy bands which follow Gaussian distributions around their mean values, the chance probability for DCF-values exceeding 0.37[FORMULA]0.03 is 0.43%. Reducing the number of statistically independent flux pairs from 50 to 15, increases this chance probability to 8%. The true chance probability of the correlation indicated in Figs. 21 and 22 will lie between these two extremes. Note, that the same correlation is found in the CT1 data and in the CT2 data (see Part II).

We interpret the structure of the DCF which can be recognized in Fig. 22 as to arise from the periodic gaps in the HEGRA observation time, paired with the spiky structure of the Mkn 501 light curve in both energy bands.

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© European Southern Observatory (ESO) 1999

Online publication: December 22, 1998
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