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In this section we are going to discuss the physics and phenomenology of what astronomers call an X-ray reflection nebula (XRN); this is the analog of the typical reflection nebulae seen in the optical domain, where a cloud of dust and gas scatters and partially absorbs and re-emits the incident light coming from a nearby star. In the case of an XRN, the source of photons is an X-ray source (AGN, X-ray binary, etc.) and the nebula must have a minimum density in order to be able to absorb and scatter X-rays and make this measurable for astronomers. The spectral and timing features arising from the illumination of a dense MC by a powerful X-ray source have been studied by Sunyaev & Churazov (1998), whose study was performed after the discovery of fluorescent X-ray emission at 6.4 keV from neutral Fe arising from massive MCs in the GC region (Koyama et al., 1996). The goal of this investigation is to derive the features of the Fe-Kα line (flux, equivalent width, shape, morphology, time behaviour) and the reflected continuum in the context of X-ray illumination, in order to be able to differentiate between different mechanisms of excitation which can produce Fe fluorescence as observed in cosmic sources. This treatment of the problem is more focused on the phenomenology of the XRN, and it will be of great utility in the development of this work.

X-ray observations allow us to measure the 6.4 keV line flux from a cloud of neutral material; starting from this measurement, it is possible to infer the luminosity (and/or luminosity history if some variability in the fluorescent signal is detected) of the original putative source of photons. In formula (Sunyaev & Churazov, 1998):

F6.4 = Ω 4πD2nF e r YF e Z _∞ 7.1 I(E)σph(E)dE photons s−1 cm−2, (2.10)

where Ω is the solid angle between the ionising source and the cloud, D is the distance between the cloud and the observer, nF er is the Fe column density inside the cloud (in

units of cm−2), and I(E) the source photon spectrum intensity (photons s−1 keV−1). As we discussed earlier in this Chapter, the σph is a steep function of the photon energy;

accordingly, the photons which can more efficiently contribute to the Fe ionisation are the ones with energies in the range ∼7-9 keV. As a result, it is convenient to write the expression for the 6.4-keV line flux as a function of the photon spectrum intensity at 8 keV. This is (Sunyaev & Churazov, 1998)

F6.4 =φ Ω 4πD2 δF e 3.3×10−5τTI(8keV) photons s −1 _cm−2_{, (2.11)}

where φ∼1 is a factor which accounts for the shape of the source spectrum, δF e is the

Fe abundance with respect to H, andτT is the optical depth for Thomson scattering of the

cloud. If we convert the intensity of the photon flux at 8 keV into the luminosity of the X-ray source in a 8 keV wide energy band, we can write that I8=L8/8·8·1.6×10−9=107·L8.

2.2 Photoionisation: theory and phenomenology 51

Substituting this expression in the last formula, we can derive the luminosity that the putative X-ray source must have in order to produce the observed flux. This is (Sunyaev & Churazov, 1998) L8 = 6×1038 F6.4 10−4 0.1 τT δF e 3.3×10−5 ₋1 d 100 pc 2 erg s−1, (2.12) where d is the distance between the source and the cloud. As we will se in the Chapters 4 and 5, this formula is a very powerful tool to study the 3D distribution of the MCs radiating in the Fe fluorescent line; indeed, assuming an X-ray luminosity for the source and measuring the 6.4-keV line flux, it is possible to infer the solid angle Ω, and therefore the distance along the line of sight of a certain cloud.

Of course, if the source is located inside the cloud, more photons will interact with it and the corresponding X-ray luminosity needed in order to produce the same Fe-Kα flux significantly decreases; using the same notation as before, the X-ray luminosity of a source embedded in the 6.4-keV emitting MC can be written as (Sunyaev & Churazov, 1998)

L8 = 6×1035 F6.4 10−4 0.1 τT δF e 3.3×10−5 ₋1 erg s−1, (2.13) a value which is significantly lower than the one required in the external source scenario. When a cloud is illuminated by an external source, the geometry of the X-ray illumina- tion has been illustrated by Sunyaev & Churazov (1998) and shown in Fig.2.5. The surface of a parabola at a certain time t represents the set of points for which the sum of the distance to the source and the distance to the observer is the same. Therefore, an observer located far away from both the source and the cloud will see fluorescent emission (and the relative reflected continuum) from the regions of the cloud(s) currently (we do not consider the propagation time from the source to the observer) illuminated by the X-ray photons . In the right panel of Fig.2.5 we show the surface brightness distribution of an MC which is illuminated by steady radiation which suddenly turns off, as a function of the relative position of the cloud and the source. The surface brightness was calculated integrating over the sight line the product of the cloud density and the radiation field density (Sunyaev & Churazov, 1998).

The simulations were run for a radius of the cloud of 22.5 pc (comparable to what observed for the Sgr B2 complex at the GC). The position of the cloud with respect to the primary source is indicated by the pairs of numbers at the bottom of the plot. The first number represents the cloud relative shift (in pc) to the left with respect to the source; for example, 0 means that the source and the MC are along the same line of sight of the observer, while -100 means that the cloud is located 100 pc left to the source. The second number represents the location of the cloud along the line of sight; negative (positive) numbers are for a cloud position behind (in front) the plane of the source. Therefore, the first two columns represent a situation where the source is located inside the cloud. On the vertical axis, instead, the temporal evolution of the surface brightness is shown for increasing time (in years). The first noticeable thing is the difference in the surface

Figure 2.5: Left: geometry of the illumination of an MC by a distant source. The points of the parabola, whose equation is also written in the plot, has the same delay time with respect to the primary radiation going directly from the source to the observer, and not scattered by the cloud into the line of sight. The structure of this parabola and its duration in time (∆t) determine the topology and the temporal variability of the 6.4-keV line flux and the associated reflected continuum at high energy. Right: distribution of the surface brightness of an MC with a radius of 22.5 pc for different locations of the cloud-source; here the source of radiation is a steady flare which suffer a sudden fading at the time t=0 (see text) (from Sunyaev & Churazov, 1998).

brightness distribution for a source located inside the MCs, compared to a source located outside; when the source is inside the cloud, the surface brightness distribution shows a rather sharp profile, with characteristic peaks which simply reflect the fact that the radiation field is more intense in the immediate vicinity of the source. On the opposite case, when the source is located outside the MC, the surface brightness profile is rather smooth and at first order reflects the Thomson depth of the cloud; moreover, the side of the cloud closer to the source is brighter (Sunyaev & Churazov, 1998).

We want now to discuss the surface brightness profile of an MC which is illuminated by a very short flare (compared to the size of the cloud), in the case of an optically thick and thin cloud (respectively, left and right panel of Fig.2.6). For the optically thin case the distribution of the surface brightness resembles the density of the cloud at the position of the parabolic surface; on the other hand, the optically thick case eliminates these peaks because of the enhanced photoabsorption, i.e. photons produced in the inner cloud do not easily escape the absorbing matter (Sunyaev & Churazov, 1998). This difference between the optically thin and thick case can be seen in the three cases highlighted by red circles in the plots in Fig.2.6; while we see peaks in the emission in the optically thin case (right panel), we do not see them in the optically thick case (left panel).

2.2 Photoionisation: theory and phenomenology 53

Figure 2.6: Left: distribution of the surface brightness of an MC with a radius of 22.5 pc for different illumination geometries; here the source of radiation is a short (compared to the size of the cloud) flare and the cloud has been modelled do be opticaly thick. Right: same as in the left panel but for an optically thin case (from Sunyaev & Churazov, 1998).

powerful X-ray source, the spectral parameter that has a primary importance in the study of the possible nature of the primary source is the equivalent width of the Fe-Kα line. This parameter is defined as the number of photons in the line divided by the number of photons at 6.4 keV in the continuum emission; a high value (&1 keV) of the EW of the 6.4-keV line is always attributed to the illumination of the cloud by an X-ray source. However, the situation in most of the MCs is not so clear and easy to allow us to safely and definitely conclude that an EW larger than 1 keV must be attributed to photoionisation; as we will see in the next sections, bombardment by low energy CR can also produce an large Fe- Kα EW, especially when the Fe abundance in the clouds is high or when protons are the particles responsible for the inner shell ionisation. Therefore, all the spectral parameters of the 6.4-keV line must be taken into account for a safe conclusion about the excitation mechanism. For the case of a source located inside the cloud the EW of the Fe line is ∼1 keV×τT, where τT is the optical depth for Thomson scattering of the medium surrounding

the source. On the other hand, if the source is located outside the cloud, the EW of the 6.4-keV line is expected to be ∼1 keV (for solar abundance of Fe) regardless the value of τT; this happens because both the Fe-Kα line flux and the continuum at 6.4 keV are

proportional to the intensity of the illuminating radiation and the density of the cloud (Sunyaev & Churazov, 1998). As a conclusion, we see that an optically thin cloud located away from the illuminating source will have a large EW of the 6.4-keV line, whereas the same line will have a lower EW if the source is located inside the cloud.

To conclude our discussion about the phenomenology of an X-ray reflection nebula we want here to discuss the other spectral parameter, together with the EW of the Fe fluorescent line, which can help in discerning between different ionisation processes. In

the XRN scenario, the intense 6.4-keV line is expected to be accompanied by a significant absorption at the Fe-K edge energy of 7.1 keV. In the case of a source located inside the cloud, the optical depth at the Fe-K edge can be directly associated with the flux of the Fe-Kαline through the fluorescence yield (∼34%). However, for the case of an illumination from the side, the situation is much more complex. For example, for low optical depth of the cloud (and therefore very small absorption at 7.1 keV), the EW of the 6.4-keV line can still be higher than 1keV (see Sunyaev & Churazov, 1998). The relation between the depth of the observed edge and the thickness of the cloud also depends on the geometry of the problem. For example, if the source is located inside the cloud, then there is exponential attenuation of the flux at the Fe-K edge. If the source is outside the cloud and we observe the illuminated side of the cloud, then the attenuation is not exponential any more (e.g., for an hypothetical cloud with very large depth the flux near the edge does not go to zero). In the case of negligibly small optical depth the scattered continuum has a shape identical to the incident continuum + fluorescent line (with large equivalent width). In other words, the relation of the flux missing due to the absorption edge and the flux in the 6.4 keV line is not a universal constant, but may vary depending on (i) mutual position of the cloud, illuminating source and observer and (ii) the optical depth of the cloud. For what concerns our work, the clouds that will be studied are neither optically thin nor thick, but somehow in the middle, and moreover there is no clue on the possible position within the CMZ, i.e. the distance along the line of sight. All these elements will contribute to make the discussion of the measurements of the absorption edge more complicated than in the ideal cases discussed above.

To add: some plots for the quantitative analysis. These will also be part of the 3rd paper, so will be added at the end (after response by Prof. Bob Warwick).