Fluorescent Iron K-line Emission and its Emission Region

If emission mechanisms for the iron K_α emission line is fluorescence, we expect that their EWs are roughly proportional to iron column density, N_Fe, and solid angle of the reprocessing matter viewed from the X-ray source, Ω. The EWs are also related to the ratio of the number of photons above the absorption edge to the intensity of the continuum at the line energy. This ratio is represented by the HR η, defined in § 5.1.2, or a spectral slope of the continuum around the line energy. To study the relation between the iron K_α emission line flux and the column density of the intervening gas as well as the spectral slope of the continuum, in Figure 6.1 the iron line flux in unit of EW was plotted against the equivalent hydrogen column density N_H (panel (a)) and HR η (panel (b)). The N_H, derived from the low energy cutoff, is statistically well determined from the observed spectra and is thought to be proportional to N_Fe.

The panel (a) of Figure 6.1 shows positive correlation between the EW and the equivalent hydrogen column density (hence N_Fe) above N_H ∼ 5×10²² cm⁻², though several sources locate at the lower left corner of this diagram away from the others. On the other hands, any correlation between HR and EW is not obvious at first glance. However, if we focus on only BeXB pulsars (in color of yellow), their EW show possible positive correlation with HR.

10¹⁹ 10²⁰ 10²¹ 10²² 10²³ 10²⁴

N

(cm

)

10¹ 10² 10³

eq.W (eV)

OAO1657-415 GX301-2 4U1909+07 4U1907+097 4U1907+097

4U1538-522 VelaX-1

CenX-3 HerX-1

4U1822-37

GX1+4

(a)

Be stars

Supergiants(wind fed) Supergiants(disk fed) LMXB

SyXB

0.4 0.5 0.6 0.7 0.8

HR

η

F

/F

OAO1657-415 GX301-2 4U1909+07

4U1907+097 4U1907+097

4U1538-522 VelaX-1CenX-3 HerX-1 4U1822-37 GX1+4

NH= 10²⁴cm⁻²

NH= 10²³cm⁻²

NH= 10²²cm⁻²

(b)

Be stars

Supergiants(wind fed) Supergiants(disk fed) LMXB

SyXB

Figure 6.1: Panel (a) shows correlation between the EW of iron Kα line and the equivalent hydrogen column density (N_H). Panel (b) is same as the panel (a), but plotted as a function of the HR η. The calculated model is indicated with dashed lines, respectively.

We discuss the relation, shown in Figure 6.1, of the EW of the iron Kα line against the hydrogen column density and the HRη, as followings. It is assumed that the observed X-ray spectrum consists of an X-ray continuum, f(E), and an iron emission line with a flux of L, those are modified ones from the original emission, I(E), due to a photoelectric absorption by a surrounding matter with a column density, N. Then, the expected X-ray spectral continuum, f(E) and the line flux L, are represented by

f(E) = I(E)·exp (−σ(E)N) (6.1)

L=ε_Fe Ω

4π ·exp (−σ(E_line)N)·

∫ _∞

Eedge

I(E^′) (1−exp (−σ_Fe(E)(E^′)N_Fe))dE^′ (6.2)

where E_line and E_edge are energies of the K_α emission line and absorption K-edge of iron, respectively, and σ(E) is the total photoelectric absorption cross section assuming the ISM abundance (Wilms et al. 2000),σ_Fe(E) is the photoelectric absorption cross section of neutral iron (Henke et al. 1993), N and N_Fe are representative column densities of the total matter and iron, respectively, ε_Fe (=0.34) is iron fluorescence yields for K-shell (Kaastra & Mewe 1993), and Ω is the solid angle of the X-ray source with respect to the reprocessing matter.

When an isotropically radiating X-ray source is spherically covered by neutral matters, that is Ω = 4π, according to Makishima (1986), the expected EW of the fluorescent lines is expressed as;

EW =L/f(E_line). (6.3)

Given the incident continuum spectrum by I(E) = AE^−Γ (Γ;photon index, A; normaliza-tion), calculated EW from Equation 6.3 is plotted with dashed line in panel (a) of Figure 6.1, as a function of N_H with Γ=1.1, which is utilized to calculate it by Inoue (1985). Dashed lines in panel (b) of Figure 6.1 show the EWs as function of HRηassuming NH =10²², 10²³, and 10²⁴ cm⁻².

The prediction by the assumption with isotropic and uniform distribution is considered to correspond to the sources located on the dashed line in the panel (a) of Figure 6.1. This is consistent with the correlation in GX 301-2 obtained fromTenma and ASCAobservations (Makino et al. 1985; Endo et al. 2002) and in GX 1+4 obtained from Ginga and ASCA observations (Kotani et al. 1999). From these results, we confirmed that the fluorescent is a plausible emission mechanism for observed iron lines, which were described by many authors (Ohashi et al. 1984; Makino et al. 1985; Koyama 1985; Inoue 1985; Makishima 1986).

However, we see that the some sources (e.g., Her X-1, Cen X-3, Vela X-1, 4U 1907+097, 4U 1822-37, and 4U 1538-522) indicate that their EWs remain several tens of electron volts, even when the line of sight N_H is very small. Several authors (Ohashi et al. 1984; Koyama 1985; Inoue 1985; Makishima 1986) have interpreted this as a situation that some thick matter with N_H ∼ 10²³ cm⁻² must be present out of the line of sight. Koyama (1985) suggested another possibility that the X-ray intensity out of our line of sight is larger than that in our line of sight.

6.2.1.1 Homogeneous Matter

In this section, the distribution of the matter being the fluorescent region is discussed specifically. As a first step, we examine the reprocessing site based on the following simple assumption. We assume the matter in the fluorescent region is distributed homogeneously around the X-ray source. Furthermore we assume that the distance from the X-ray sourcer is comparable to the size of the matterδ (say the radius of the matter). A schematic picture is shown in Figure 6.2. By these assumptions, N_Fe =N_HZ_Fe ∼nδZ_Fe ∼nrZ_Fe, is obtained.

Then the ionization parameter can be rewritten as ξ = ^L_rN^XZFe

Fe . If the ionization state of the gas is determined, the distance of the fluorescent region from the X-ray source can be estimated by using the obtained values of the X-ray luminosity and the iron absorption column density. In particular, for 4U 1907+097, 4U 1538-522, GX 301-2 and GX 1+4, which exhibited iron line flux modulations with pulse phase, their energies of iron K_α line were found to be almost 6.4 keV and iron K-edge features in their broadband spectra were able to be represented by the absorption by neutral atoms. These results indicate the iron is in a state of neutral or lowly ionized. In addition, during the Suzaku observation of GX 1+4, the ionization state of iron atoms was determined to be Fe_II–III by Yoshida et al. (2017). We therefore assume that the ionization state of iron atoms in these sources are at most Fe_II–III. This corresponds to a value of the ionization parameterξ of less than 3.98 (logξ <0.6) and 22.4 (logξ < 1.35) in the case of optically thin and thick plasma, respectively (Kallman &

McCray 1982; their model 1 and 4). Since the optically thick case gives a laxer restriction on the ionization parameterξthan the optically thin case, in the following discussion, unless otherwise specified, all restriction on the ionization parameter are given as ξ <22.4. Using the value of this ionization parameter, the obtained iron column absorption densities and estimated X-ray luminosities, which are listed in Table 5.2, the distance of the fluorescent region to be more than 1–3×10¹²cm for 4U 1907+097, 4U 1538-522, GX 301-2 and GX 1+4.

The flux modulations of the fluorescent lines with the NS rotation were significantly detected from the several pulsars. Therefore, the flux modulation of the fluorescent lines emitted from such a large region should be explained, if we adopt the assumed situation.

In the next section, we therefore point out the importance of the following two effects in the discussion of the observed time variation of the line flux. If the fluorescent lines are emitted from such a large region, then the observed time variation should be smeared with the light-crossing time of the region, which is roughly 100 s for the size of 3×10¹² cm. On the other hand, we should take into account an apparent flux modulation of the fluorescent lines by an effect of the finite light speed, as described in the next section.

r

Figure 6.2: A schematic picture of the assumed situation of homogenously distributed matter.