Flux Estimation of the Hard X-ray Sources with IBIS

We have estimated the fluxes of the hard X-ray point sources basically with the IBIS lightcurves. And, we define the estimation with the IBIS lightcurves as ”the IBIS method”. Lightcurves of the hard X-ray sources detected by IBIS are shown in Fig-ure 6.28 and FigFig-ure 6.29. We have utilized these lightcurves to estimate the fluxes of the sources in the FOV of the HXD-PIN. We show the term, when the Suzaku observa-tion took place, as blue lines in the figure. We can see clear time variaobserva-tion during the observation with Suzaku. Figure 6.30 shows an example of a blow-up of lightcurves of

”1A 1742-294”. Three sets of monitoring were performed during 32 days when Suzaku observed, which is the monitor every 4 days roughly. In the cases of almost all the other terms and sources, the same is true or they are more frequent. Errors of the lightcurves are constant roughly and ∼ 1 counts/sec which is equivalent to 4 mCrab.

Figure 6.28: Lightcurves of the hard X-ray sources with IBIS (20 - 60 keV).

Figure 6.29: The same as Figure 6.28

Figure 6.30: Enlarged lightcurve of 1A 1742-294.

Figure 6.31: Lightcurves of 1A 1742-294 fitted with a linear function. MJD of the blue circle means estimated flux during the observation of ”501008010”

We estimated the fluxesby fitting the lightcurves with a linear function. An example of the fitting is shown in Figure 6.31. In the figure, Modified Joulian Day (MJD) of the blue dots is the day of Suzaku observation whose sequence number is ”501008010”. In fitting the lightcurves, we have selected the fitting plots to take in at least 3 plots both before and after the target MJD. We have set the fitting range ±1 day at first, and have expanded the range by 1 day if the number of the plots are fewer than 3. The fitting errors are ∼ 0.3 counts/sec which is equivalent to 1 mCrab.

In order to verify if a linear function is adequate to the lightcurve fitting, we have calculated structure functions (SFs) from the individual lightcurves. Typical time scaleof time variability of individual sources can be estimated from the break point of the SFs.

If the time scales are smaller than frequencies of the monitoring which are several days, the fitting with the linear functions are not adequate. We use the formalism described in Simonetti, Cordes, & Heeschen (1985). One modifications is that since photon statistics dominate the error in X-ray data, we use a continuous weighting factor proportional to its significance of each data point instead of taking only either 0 or 1 as in Simonetti, Cordes, & Heeschen (1985). The definition of the 1st order SF for a light curve described as f(i) is then,

SF(τ) = 1 N(τ)

∑

i

w(i)w(i+τ)[f(i+τ)−f(i)]², (6.4) where

N(τ) =∑

i

w(i)w(i+τ), (6.5)

w(i)∝ f(i)

σf(i). (6.6)

Here, w(i) is the weighting factor, andσf(i) is the 1 σ uncertainty of the data pointf(i) in the lightcurve. The summations are made over all pairs.

Figure 6.34 shows a schematic drawing of the ’typical’ SF for measured time series. In the figure, constant offset means white noise which is made from measurement noise and real fluctuations not depending on frequencies, which are not able to be resolved. The slope of τ^β means red noise which is random walk, and the slope increases until typical time scale of the fluctuations.

Figure 6.32 and Figure 6.33 show the structure functions extracted from the lightcurves of Figure 6.28 and Figure 6.29. We have confirmed that, in all the case of the sources but ”IGR J17497-2821”, the typical time scales are above 10 days, or the SFs’ have no typical time scale and then are shown as white noises in whole frequencies. Therefore, the monitoring frequencies of IBIS are enough to follow up the fluctuations of the sources and the fitting with a linear function is adequate for these light curves. In the case of ”IGR

Figure 6.32: Structure functions extracted from the light curves of Figure 6.28.

Figure 6.33: Structure functions extracted from the light curves of Figure 6.28.

White noise

Typical time scale ^log τ

log SF(τ)

τ

Figure 6.34: Schematic drawing of the ’typical’ structure function for mea-sured time series.

J17497-2821”, the SF have mostly formed by one flare at the MJD of ∼54000 as shown in Figure 6.29. This effects only the observation of ”500005010”. The IBIS lightcurve of ”IGR J17497-2821” can not follow up the real flux of the source in the observational term of ”500005010”.

We have evaluated other uncertainties of the flux estimations by following methods.

First we have excluded a real data point in the lightcurves, and we have performed the fitting the same as described above using the data points around the excluded data point.

Second, we have compared the estimated count rate from the fitting with that of the real data point. In the fitting, however, we have also excluded the data points within 1 day from the MJD of the target data point. Differences between the count rate from the fitting and of the real data point are distributed with root mean squares of∼1 counts/sec, which are comparable to statical errors of the actual data points. These are also comparable to the white noises in the SFs’ which is ∼√

SF(τ)/2. These uncertainties mean unknown fluctuations within the interval of the IBIS lightcurves. We have adopted the uncertainty as a systematic error and named as the short fluctuation uncertainties. That is, finally, the errors are shown as error = (fitting error)±(short fluctuation uncertainty). The short fluctuation uncertainty is dominant in this error, and therefore the error is estimated to be ∼ 1 count/sec, 4 mCrab.

In order to subtract the contaminations of the hard X-ray sources from the HXD-PIN fluxes using the IBIS fluxes, it is necessary to obtain a factor between counting rates of HXD-PIN and IBIS. We have obtained the factor using the HXD-PIN spectrum and the IBIS flux of the Crab. The analyzing process of the HXD-PIN spectrum is the same as that of the Galactic center observations as described in section 6.2. We have performed a spectral fitting for the Crab spectra adopting a power-law model in the

energy range of IBIS (20–60 keV), and obtained a photon index of 2.12± 0.01 and a flux of 1.39(±0.01)×10⁻⁸ erg/cm²/sec at 90% confidence. While, the IBIS counting rate of the Crab is 240 counts/sec in 20–60 keV (Kuulkers et al. 2007). Therefore, we have defined the flux of IBIS of 240 counts/sec as 1.39×10⁻⁸ erg/cm²/sec when the photon index of the source is 2.12 in this thesis. A utilized energy response of IBIS is released by the INTEGRAL Science Data Centre, whose version is ”6.5”.

In order to obtain the HXD-PIN spectra subtracted the contaminations of the sources, we need to assume shapes of the source spectra because we are not able to know the spectra with only the IBIS. Since dependencies of effective area on energy of between HXD-PIN and IBIS are different with each other, it is necessary even to obtain just the HXD-PIN fluxes subtracted the contaminations in IBIS’s energy range of 20–60 keV.

Basically, we assume the spectra as simple power-law models from previous works for the individual sources as listed in Table 6.8.

Table 6.8: Summary of the assumed photon indices of power-law model for hard X-ray sources.

Source name photon index referecese AX J1749.2-2725 1.0 [1],[2],[3]^a AX J1749.1-2733 1.0 [3],[4]^a

IGR J17497-2821 1.8 [5]^a

IGR J17475-2822 1.8 [6]^a

1E 1743.1-2843 3.2 [7]^a

1A 1743-288 2.4 [8]^a

IGR J17456-2901 3.0 [9]^a

GRS 1741.9-2853 1.6 [10]^a

KS 1741-293 2.3 [11]^a

1A 1742-294 1.6 [12],[13]^a SLX 1744-299/300 1.6 [12],[13]^a

1E 1740.7-2942 1.5 [14]^a

a[1]; Torii et al. (1998). [2]; Santangelo et al. (2006) . [3]; Sakano et al. (2002). [4]; Bird et al. (2002) [5]; ?. [6]; Revnivtsev et al. (2004). [7]; Del Santo et al. (2006). [8]; Natalucci et al. (2000). [9];

Belanger et al. (2006). [10]; Cocchi et al. (1999). [11]; De Cesare et al. (2007). [12]; Lutovniv et al.

(2001). [13]; Tanaka et al. (1997). [14]; Del Santo et al. (2005)