Multiwavelength Spectral Study

The spectrum newly obtained with Suzaku is compared with the data of TeV gamma-rays and radio band, for comprehensive understanding of the particle acceleration and radiation processes in RX J1713.7−3946. We have obtained high-quality and wide-band X-ray spectrum with Suzaku, and it clearly shows the cutoff structure around 10 keV.

This should strongly constrain the physical parameters by itself and also by combining with other wavelengths.

Figure 7.1 shows the X-ray, TeV gamma-ray, and radio data plotted in an energy flux diagram. The X-ray data are those obtained in §5.5 for the entire remnant. The interstellar absorption is corrected using the value of N_H= 0.77×10²² cm⁻², which was obtained when we fitted the XIS spectrum with an absorbed power-law model. The TeV gamma-ray points are the latestH.E.S.Sdata taken from Aharonian et al. (2006b), which are also for the whole SNR. This data set is generated by combining the results from their observations in 2003, 2004, and 2005. The EGRET upper limit is taken from Aharonian et al. (2006a). They calculated the limit by modeling and subtracting the known EGRET source 3EG 1714−3857 (Hartman et al. 1999), assuming that 3EG 1714−3857 is not associated with RX J1713.7−3946. The two data points in the radio band are ATCA results from Lazendic et al. (2004). The exact values reported by Lazendic et al. (2004) are plotted although the radio flux is only detected from the NW rim region.

In what follows, we investigate two different models to describe the multiwavelength spectrum: so-called leptonic and hadronic models. The multiwavelength spectrum of RX J1713.7−3946 constructed by our Suzaku measurements and the recent H.E.S.S.

observations is most detailed ever for shell-type supernova remnants. This allows us to constrain the radiation and acceleration models at an unprecedented level. In fact, as

which is consistent with estimated values by Koyama et al. (1997), Fukui et al. (2003), and Moriguchi et al. (2005).

Synchrotron+IC model

Figure 7.1: Broadband spectral energy distribution (SED) of the entire SNR RX J1713.7−3946 with synchrotron+IC models. The models have an electron injection spectrum with number index of 1.7 (red lines) and 2.1 (black), and an exponential cutoff at 40 TeV (red) and 60 TeV (black). The magnetic field strength is 10µG for both cases. Steady electron injection during 1000 years is assumed.

Firstly, we investigate a synchrotron+IC model in which a population of relativistic electrons with TeV energies emits synchrotron radiation in the X-rays and Compton-upscatters the CMB photons into TeV gamma-rays. The characteristic energy of inverse Compton photons, ǫ_IC, and of synchrotron photons, ǫ_sync, produced by an electron are related by

ǫIC≃2( ǫsync

0.1 keV )(

B 10 µG

)⁻1

TeV, (7.1)

in the Thomson regime (see Aharonian et al. 1997 for the derivation). This indicates that TeV electrons producing 0.1 keV X-rays via synchrotron (with B = 10µG) emit 2 TeV gamma-rays via inverse-Compton, simultaneously. The ratio of the synchrotron and inverse Compton fluxes at these energies can be determined solely by the magnetic

field strength (also see Aharonian et al. 1997) as

fIC(ǫIC)

f_sync(ǫ_sync) ≃0.1 ( B

10 µG )⁻2

. (7.2)

This relation is also valid for the Thomson regime. The strength of the magnetic field can be determined from the ratio of the X-ray flux and the gamma-ray flux, because the TeV energy flux is nearly constant at around 2 TeV. We found that the ratio of the Suzaku flux and the H.E.S.S. flux requires the magnetic field of≃10µG. A slight change in the magnetic strength causes a large change of fsync(ǫsync)/fIC(ǫIC) since it is proportional to the square of the magnetic field as shown in equation (7.2). When we change the magnetic field in the range of ±1 µG, the X-ray/gamma-ray ratio varies ±20%, which is comparable to the systematic errors in the absolute flux of the H.E.S.S. spectrum (Aharonian et al. 2006b) and that of the HXD spectrum. Therefore, the magnetic field should be in the range of 9 µG ≤B ≤11 µG if the magnetic field strength is spatially uniform.

The Klein-Nishina effect becomes important at energies&10 TeV, so we need numeri-cal numeri-calculations to model the shape of the TeV spectrum. Calculations are performed with constant electron injection overt0 = 1000 years into the emission volume having uniform magnetic field strength B = 10µG. We neglect any spatial dependencies such as escape from the volume. The energy distribution of electrons is of the formCE^−pexp[−(E/E0)].

The solid curves in Figure 7.1 show the resultant models that well describe the observed X-ray spectrum, for two different electron indexes: p = 1.7 (red) and p = 2.1 (black).

The maximum electron energy is set by fitting the broadband X-ray spectrum. We ob-tain E0 = 40 TeV for p = 1.7 and E0 = 60 TeV for p = 2.1. In Table 7.1, we list the parameters obtained for these two cases.

The hard electron index of p = 1.7 is unlikely because the predicted TeV spectrum (IC radiation) significantly deviates from the H.E.S.S. spectrum below 1 TeV (see the red curve in Fig. 7.1). To reproduce the TeV spectrum at a comfortable level, a steeper electron spectrum is necessary (p >2). On the other hand, in order not to overproduce the radio emission, the index steeper thanp= 2.1 is not allowed. Therefore, the electron index is constrained tightly as p ≃ 2.1. Thanks to the wide-band and high statistic Suzaku data, as well as the H.E.S.S. data, the parameters describing the population of electrons are strongly constrained. The maximum electron energy, E₀, is obtained as 60 TeV. If we change the energy in the range of 60± 10 TeV, the flux of X-ray and TeV gamma-ray varies ∼ ±20%, which is the same level of uncertainties in the absolute

Table 7.1: Parameters for IC modeling

Parameters Case 1 Case 2

Magnetic field,B [µG] 10 10

Electron index, p 2.1 1.7

Maximum electron energy, E0 [TeV] 60 40 Total energy of electrons,W_e [erg] 6.7×10⁴⁷ 1.0×10⁴⁷ (>100 MeV)

Comments OK disagree below 1 TeV

Figure 7.2: Broadband SED of RX J1713.7−3946 with synchrotron+π⁰-decay models. Both electron and proton number indices are p = 2. Results for different magnetic field strength are shown: B = 30µG (black) and 100µG (red). For the larger field of 100µG, the radio emission is overproduced. The inverse-Compton components are much lower thanπ⁰-decay gamma-rays. The exponential cutoffs of electrons are at 50 TeV (red) and 30 TeV (black), while the exponential cutoff of protons is at 150 TeV.

Figure 7.3: Broadband SED of RX J1713.7−3946 with synchrotron+π⁰-decay models. Both electron and proton number indices are p = 1.8. Results for different magnetic field strength are shown: B = 100µG (black) and 30µG (red). The exponential cutoffs of electrons are at 20 TeV (black) and 40 TeV (red), while the exponential cutoff of protons is at 150 TeV.

Table 7.2: Parameters forπ⁰-decay modeling

Parameters Case 1 Case 2 Case 3 Case 4

Magnetic field,B [µG] 30 100 30 100

Electron/proton index,p 2.0 2.0 1.8 1.8

Maximum electron energy,Ee0[TeV] 50 30 40 20

Maximum proton energy,Ep0 [TeV] 150 150 150 150

Total energy of electrons,We[erg] 7.2×10⁴⁶ 4.9×10⁴⁶ 3.4×10⁴⁶ 1.8×10⁴⁶ (>100 MeV)

Total energy of protons,nWp 2.0×10⁵⁰ 2.0×10⁵⁰ 2.0×10⁵⁰ 2.0×10⁵⁰ [erg cm⁻³]

Comments OK radio overproduced disagree below 1 TeV same as Case 3

Synchrotron+π⁰-decay model

We here explore the possibility that the TeV gamma-rays are produced by π⁰-decays resulting from proton-proton interactions. The radio-to-X-ray spectrum is modeled as synchrotron radiation by relativistic electrons in the same way as the IC model. Now we consider that the accompanying IC radiation does not have significant contributions to TeV gamma-rays, so the magnetic field strength should be larger than 10µG. Unlike the case of the synchrotron-IC scenario, the two spectral components (i.e., synchrotron and π⁰-decay gamma-rays) do not have an intimate connection. Below we assume a common number indexpfor electron and proton injection spectra, only by which the two components are related.

The spectral shape of π⁰-decay gamma-rays depends only on the energy distribution of high-energy protons. To reproduce the H.E.S.S. spectrum, we obtain p = 2 and Ep0 = 150 TeV as shown in Fig. 7.2. (In figure 7.3, we present the case of harder index p = 1.8, in which the π⁰ gamma-ray spectrum deviates from the observed TeV spectrum below 1 TeV.) The product of total energy of protons and gas density amounts tonWp = 2.0×10⁵⁰ erg cm⁻³, where n is the gas density in units of cm⁻³.

The SuzakuX-ray spectrum is modeled as synchrotron radiation for different electron indexes (p = 2.0 and 1.8) and different magnetic fields (B = 30µG and 100µG). The resultant spectra are shown in Figs. 7.2 and 7.3. The derived parameters are summarized in Table 7.2. A combination of p = 2 and 100µG can be ruled out by the radio flux.

Also, as we stated above, p= 1.8 seems too hard to explain the H.E.S.S. spectrum. We found a reasonable range of parameters becomes 10µG < B < 100µG , 1.8 < p ≤ 2.0, and 20 TeV< Ee0 ≤50 TeV. It is interesting to note that the maximum electron energy is much smaller than the proton maximum energy of 150 TeV. This indicates that the maximum energy attainable by electron acceleration is limited by synchrotron cooling.

17h12m 17h14m

17h16m -39d30m

-40d00m 1

2

3 4

5 6 7 8

° Radius = 0.6

17h12m 17h14m

17h16m -39d30m

-40d00m

1

2

3 4

5 6 8 7

° Radius = 0.6

Figure 7.4: Eight wedge-shaped regions for comparison of radial profiles drawn on theSuzaku image (left) and on the H.E.S.S. image (right).

7.1.2 Comparison of the X-ray Morphology with TeV