3. Analysis and result
The standard method of image analysis was applied for these data which is based on the well-known parameterization of the elongated shape of the erenkov light images using "width ,""length ,""concentration " (shape), "distance " (location), and the image orientation angle "alpha " (Hillas 1985, Weekes et al. 1989, Reynolds et al. 1993). However, the emitting region of TeV gamma-rays in this target may be extended, as in the case of SN1006. For extended sources, use of the same criteria as for a point source in the shower image analysis is not necessarily optimal. We made a careful Monte Carlo simulation for extended sources of various extents and found the distribution of the shower image parameter of width , length , and concentration for gamma-ray events is essentially the same within a statistical fluctuation as in the case of a point source. However, the simulation suggests that we should allow a wider range dependent on the extent of the source for the parameter of distance and alpha to avoid overcutting gamma-ray events. In this analysis, gamma-ray-like events were selected with the criteria of 0.o01 width 0.o11, 0.o1 length 0.o45, 0.3 concentration 1.0 and 0.o5 distance 1.o2.
Fig. 1a shows the resultant alpha distribution when we analyzed the distribution centered at the tracking point (right ascension , declination (J2000)), which is the brightest point in the remnant in hard X-rays (Koyama et al. 1997). The solid line and the dashed line indicate the on-source and off-source data respectively. Here we have normalized the off-source data to the on-source data to take into account the difference in observation time and the variation of trigger rates due to the difference in zenith angle between on- and off-source data and due to subtle changes in weather conditions. The value of the normalization factor is estimated to be 1.03 from the difference in total obsevation time for on- and off-source measurements. On the other hand, the actual value of the normalization factor is estimated to be from the ratio of /, where and indicate the total number of gamma-ray-like events with alpha between 40o and 90o for on- and off-source data respectively. We selected the region with alpha 40o to avoid any "contamination" by gamma-rays from the source, in the knowledge that the source may be extended. The small discrepancy in the two estimates of the value might come from a slight change in the mirror reflectivity during the observation due to dew. Here we adopt the value 0.99 for in the following analysis by taking the small discrepancy into the systematic errors due to the uncertainty in the mirror reflectivity as shown below. Fig. 1b shows the alpha distribution of the excess events for the on-source over the off-source distribution shown in Fig. 1a. A rather broad but significant peak can be seen at low alpha , extending to . The alpha distributions expected for a point source and several disk-like extended sources of uniform surface brightness with various radii centered at our FOV were calculated using the Monte Carlo method. These distributions are shown in the same figure. The alpha distribution of the observed excess events appears to favour a source radius of , which suggests the emitting region of TeV gamma-rays is extended around the NW rim of RX J1713.7-3946. The statistical significance of the excess is calculated by () / , where and are the numbers of gamma-ray-like events with alpha less than in the on- and off-source data respectively. The significance at the peak of the X-ray maximum was when we chose a value of alpha considering the result of the Monte Carlo simulation shown in Fig. 1b.
In order to verify this extended nature, we examined the effects of the cut in shape parameters on the alpha distribution by varying each cut parameter over wide ranges. We also produced alpha distributions for different energy ranges and data sub-sets. Similar broad peaks in the alpha distribution persisted through these examinations. Also we examined more recent data from PSR1706-44 from July and August 1998 and obtained a narrow peak at alpha , as expected for a point source. This confirms that the extended nature of the TeV gamma-ray emitting region does not come from some malfunction of our telescope system and/or systematic errors in our data analysis. A similar, but not as broad, alpha peak was seen for SN1006 (Tanimori et al. 1998b).
In order to see the extent of the emitting region, we made a significance map of the excess events around the NW rim of RX J1713.7-3946. Significances for alpha were calculated at all grid points in steps in the FOV. Fig. 2 shows the resultant significance map of the excess events around the NW rim of RX J1713.7-3946 plotted as a function of right ascension and declination, in which the contours of the hard X-ray flux (Tomida 1999) are overlaid as solid lines. The solid circle indicates the size of the point spread function (PSF) of our telescope which is estimated to have a standard deviation of for alpha based upon Monte Carlo simulations for a point source with a Gaussian function. The area which shows the highest significance in our TeV gamma-ray observation coincides almost exactly with the brightest area in hard X-rays. The region which shows the emission of TeV gamma-rays with high significance ( level) extends wider than our PSF and appears to coincide with the ridge of the NW rim that is bright in hard X-rays. It extends over a region with a radius of . This region persisted in similar maps calculated for several values of alpha narrower than .
The integral flux of TeV gamma-rays was calculated, assuming emission from a point source, to be (5.3 0.9 [statistical] 1.6 [systematic]) 10-12 photons cm-2 s-1 ( 1.8 0.9 TeV). The flux value and the statistical error were estimated from the excess number of , where the value of for alpha is chosen by the argument mentioned before. The causes of the systematic errors are categorized by uncertainties in (a) assumed differential spectral index, (b) the loss of gamma-ray events due to the parameter cuts, (c) the estimate of core distance of showers by the Monte Carlo method, (d) the trigger condition, (e) the conversion factor of the ADC counts to the number of photo-electrons, and (f) the reflectivity of the reflector. These errors from (a) to (f) are estimated as 15%, 22%, 3%, 12%, 10%, and 8% for the integral flux and 24%, 2%, 8%, 20%, 29%, and 17% for the threshold energy, respectively. The total systematic errors shown above are obtained by adding those errors quadratically.
To summarise, all our observed data support the hypothesis that the emitting region of the NW rim is extended. In general, the value of the effective detection area of the telescope system for extended sources would be reduced by some factor from that for a point source, because the gamma-ray detection efficiency decreases with the distance of emitting points from the center of the FOV when we observe with a single dish. We calculated the efficiency as a function of the distance by the Monte Carlo method by analyzing the data with the same criteria as applied to the actual data. We estimated the value of the correction factor to the effective area to be for our target by integrating the efficiency over the distance for an extended disk-like source of uniform surface brightness with a radius of . The factor of 1.2 is less significant than the systematic errors estimated above.
© European Southern Observatory (ESO) 2000
Online publication: January 31, 2000