Ray Spectra

This section deals with the general characteristics of the X-ray spectra of black-hole XBs, and discusses the differences from those of neutron-star LMXBs of which neutron stars are weakly magnetized.

As shown later, there are at least three distinctly different states with respect to the spectral properties. These are a high-luminosity soft state (HS state), a low-luminosity hard state (LH state), and the quiescent state. These are believed to be related to intrinsic changes of the disk structure depending on the mass accretion rate M (hence Lx). There appears to be a certain Lx value that divides the HS state and the LH state, which is around Lx — 1037 erg s"1(or M — 1017 g s"1). However, it may vary somewhat from source to source and from time to time. For previous reviews, see e.g., [39,76,78,79].

16.4.3.1 X-Ray Spectrum at High Luminosities

In the HS state, black-hole XBs typically show a common characteristic spectral shape, consisting of a soft thermal component and a hard nonthermal tail, as shown in Fig. 16.2. Of the 20 secure black-hole XBs known so far (Table 16.1), 17 show such an X-ray spectral shape. (For three exceptions, see later.) In this state, the time variability of the soft component is generally small and slow. The hard component varies much more than the soft component.

101

r^ Cyg X-1

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Energy (keV)

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Fig. 16.2 X-ray photon spectra of secure black-hole XBs in the HS state obtained with Ginga, except for Cyg X-1, which is from the data of ASCA and RXTE [22]

Energy (keV)

Energy (keV)

Energy (keV)

Fig. 16.2 X-ray photon spectra of secure black-hole XBs in the HS state obtained with Ginga, except for Cyg X-1, which is from the data of ASCA and RXTE [22]

The soft component shows the characteristics of thermal emission. It is interpreted as the emission from an optically-thick geometrically-thin accretion disk (hereafter abbreviated to "thin disk"). The observed soft component is well expressed by the "multicolor blackbody disk" (MCD) model developed by Mitsuda et al. [49], and later elaborated by Makishima et al. [36]. The disk emits blackbody radiation locally and the blackbody temperature increases toward the center, hence the emission is "multicolored." The MCD model is a formulation of such a spectrum based on the standard disk model. The simplest MCD model includes only two free parameters, i.e., R^ and kTin, where Rin represents the innermost disk radius and kTin is the temperature at Rin. The actual formula includes the source distance D and the disk inclination angle i in the form Rin(cosi)1/2/D, which are assumed to be known here. Note that kTin is the "color" temperature, and not the effective temperature.

The observed value of kTn is typically <1.0keV at a soft X-ray luminosity £soft < 1038 erg s"1, and becomes lower as the luminosity decreases. The color temperature is substantially higher than the effective temperature because of the electron scattering effect that dominates at such high temperatures [71].

The hard tail has a power-law form, and extends to well-over 100 keV, sometimes observed up to <1 MeV without a cut-off, as shown for example in Fig. 16.6b. The luminosity of the hard component relative to the soft component varies irregularly by a large factor (see Fig. 16.6a). The photon index r of the power-law, for a photon number spectrum of the form E"r, is <2.5, and remains essentially constant against changes in intensity. This power-law spectrum has been considered to be produced

Fig. 16.3 X-ray photon spectra of neutron-star LMXBs in the HS state (Ginga), each consisting of a soft MCD component (solid curve) and a blackbody component (dashed curve)

as a result of multiple scattering of soft photons with high-energy electrons, gaining energy by the inverse Compton effect: the process called Comptonization [74]. Yet, the origin of the power-law tail is still unsettled, including the questions as to how the electrons are accelerated to — 1 MeV and why r is commonly regulated at -2.5.

Turning to neutron-star LMXBs, they also reside in the HS state when Lx — 1037 erg s_1. However, as shown in Fig. 16.3, their spectra are distinctly different from those of black-hole XBs. The spectrum of neutron-star LMXBs in the HS state actually consists of two separate components: a soft thermal component and another harder thermal component. It is to be emphasized that these two components are real, not artificially introduced for the purpose of reproducing the observed spectrum. Since these two components change in intensity with time independently of each other, they can be identified and their spectra can be determined separately (see [23,49,79]). An additional nonthermal hard tail is occasionally noticed, yet much less pronounced than in the case of the black-hole XBs.

This soft thermal component is also well fit with the MCD model, supporting that this is the emission from the standard thin disk. However, the observed color temperature kTin, typically —1.5keV for Lx — 1038 erg s_1, is significantly higher than that in the black-hole XBs at a similar Lsoft (see below for the implication).

The harder thermal component shows a single blackbody spectrum with a color temperature of —2keV. This component is most probably the emission from the neutron star surface where the kinetic energy of accreting matter is eventually deposited and thermalized. The intensity of this blackbody component varies irregularly without changing the shape, and its average luminosity is comparable to the soft component from the thin disk as expected. The fact that this spectrum is very similar to that of so-called Type I X-ray bursts further supports this interpretation. The Type I X-ray burst is a thermonuclear flash on the neutron star surface producing a blackbody radiation [32]. (More on the Type I X-ray burst in 16.4.3.2.) In fact, the Type I X-ray burst has never been observed from the secure black-hole XBs.

The above summarizes the X-ray spectral properties of the black-hole XBs and neutron-star LMXBs in the HS state. In what follows, the fundamental differences between them are discussed.

The first clear distinction is that none of the black-hole XBs show a "2-keV" blackbody component characteristic of the spectra of the neutron-star LMXBs in the HS state. For the reason mentioned earlier, the absence of this blackbody component and of the Type I X-ray bursts argue for the absence of a solid surface.

Furthermore, the lower kTin values of the disk emission of black-hole XBs are understood in terms of the standard disk model. The radius of the innermost stable orbit is proportional to the mass of the compact object (see later). For a given luminosity, the larger the mass, the lower is the blackbody temperature (kTin « M-1/4). Hence, the X-ray spectrum of the disk around a black hole is expected to appear softer (lower temperature) than that around a neutron star. Moreover, the presence of the additional 2-keV blackbody component for the neutron-star LMXBs makes the thermal component of the black-hole XBs look much softer, hence sometimes called "ultrasoft" [83] (compare Figs. 16.2 and 16.3).

For at least three long-observed black-hole XBs, the observed value of Rm is found to remain essentially constant against large changes in the soft component luminosity Lsoft [76], as shown in Fig. 16.4. This fact strongly supports an interpretation that Rin represents the radius of the innermost stable orbit. For a nonspinning black hole, the radius of the innermost stable orbit is 3Rs, hence proportional to the compact object mass. Therefore, the mass can be estimated from the Rin-value, if the estimated source distance and the inclination angle are available. In fact, the observed values of Rin obtained for a set of black-hole XBs turned out to be larger than those for neutron-star LMXBs by a factor of 3 to 4 [79]. Thus estimated black hole masses are qualitatively consistent with those obtained from the mass functions (except for GRO J1655-40 and GRS 1915+105, as explained below). Similar results of constant Rin against changes in Lsoft have later been found from more black-hole XBs (see [39]).

The above considerations strongly support that such a "soft + hard-tail" spectrum in the HS state is a signature of an accreting black hole. In addition to 17 among the 20 secure black-hole XBs, there are about 20 additional soft X-ray transients that exhibited this characteristic spectral shape. Also, they showed neither regular pulsation nor Type I X-ray burst (see 16.4.3.2). On the basis of these properties, they can be considered to be black hole candidates [39].

Fig. 16.4 Time histories of measured quantities for three black-hole LMXBs [76,79], based on the MCD model. From the top, the soft MCD flux, the color temperature kTm, and Rin(cosi)1/2/D. Note that the inclination angle is denoted 6 here. For LMC X-3, the distance D is taken to be 50kpc, and the luminosity is shown instead of flux

Fig. 16.4 Time histories of measured quantities for three black-hole LMXBs [76,79], based on the MCD model. From the top, the soft MCD flux, the color temperature kTm, and Rin(cosi)1/2/D. Note that the inclination angle is denoted 6 here. For LMC X-3, the distance D is taken to be 50kpc, and the luminosity is shown instead of flux

Among the 20 secure black-hole XBs, GS 2023+338, GRO J0422+32, XTE 1650-500, and XTE J1118+480 are exceptions. These four sources show an approximately single power-law spectrum typical for the LH state (see 16.4.3.2). It is possible that GRO J0422+32, XTE 1650-500, and XTE J1118+480 did not enter into the HS state, since their peak Lx were relatively low; —1037 erg s^1 for

GRO J0422+32 and XTE 1650-500, and —1036 erg s-1 for XTE J1118+480. On the other hand, GS 2023+338 was extremely luminous, —1039 erg s-1, and probably reached the Eddington limit LEdd. The reason why it did not show the soft + hard-tail spectrum is still unknown.

Two secure black-hole XBs GRO J1655-40 and GRS 1915+105, both exhibiting a "soft + hard-tail" spectrum and superluminal jets, show significantly higher kTin than other black-hole XBs (hence smaller Rin). Zhang et al. [86] suggest that the black holes in these systems may be prograde Kerr holes, for which the maximum disk temperature can be substantially higher. The highly relativistic jets from these sources could be related to the high black-hole spin.

Occasionally, black-hole XBs become exceedingly luminous (>0.2LEdd), and the hard power-law component dominates the X-ray spectrum, which looks significantly different from the typical HS state spectrum shown in Fig. 16.2. At the same time, (1) rapid and large variability associated with the intense hard component and (2) quasi-periodic oscillations (QPO) appear. Miyamoto et al. [50] first noted this behavior in GX 339-4, and named it the "very high (VH) state." The photon index r still remains in the typical range for the HS state or somewhat steeper, r — 2.5, without showing a cut off. In this regard, the VH state may be called the "power-law dominated" HS (PLD-HS) state. This state has been observed for many black-hole XBs. Of particular importance is the appearance of high-frequency (— 100Hz) QPO in the PLD-HS state, as addressed in Sect. 16.5. (See [39] for more on the VH state.)

An additional difference from the standard HS properties is noticed in the PLD-HS state. The constancy of Rm (i.e., Lsoft « T^) breaks down. Compared with the normal HS state, shows anomalously high values, and consequently Rin drops down. Such cases have been found from GRO J1655-40 [29, 72], XTE 1550564 [30], and GRS 1915+105 [14]. Kubota et al. [29,30] showed that the normal Lsoft - Tin relation is retained if a Comptonized MCD is included (see Fig. 16.5), and interpreted it to reveal an appearance of a hot corona that Comptonizes a part of the disk photons. This Comptonized component also contributes to the increase of the hard component in the PLD-HS state.

It has been theoretically predicted that the standard (gas pressure-dominated) thin disk is no longer stable when the radiation pressure becomes dominant (e.g., [33,70]). As M increases, the inner disk goes through an unstable regime, and shifts to another stable structure [1,25], which Abramowicz et al. [1] named a "slim disk." This instability predicts a possible limit-cycle variability between the thin disk and the slim disk. A unique behavior of GRS 1915+105 displaying repeated transitions between two flux levels [6] can be interpreted as such a case [84]. The highly-variable PLD-HS state probably corresponds to the intermediate unstable regime [30]. However, the limit-cycle behavior is rarely observed, which suggests that some effects suppress the onset. Energy disspation with the Comptonizing corona may be a possible one [14].

The concept of the slim disk applies when M > LEdd/c2, where LEdd/c2 is called the critical accretion rate. The slim disk model has been elaborated later (e.g., [46,56,57]). The model predicts that Lx may well exceed LEdd for extremely

Tin[keV] Tin[keV]

Fig. 16.5 Ldisk(= ¿soft) - rta relation of XTE 1550-564 [30]. (a) Fits with (MCD + power-law) model. (b) When Comptonized MCD is included in Period 1 and Period 7. The solid and dashed lines are for Ldisk « T^ and Ldisk « T^, respectively

Tin[keV] Tin[keV]

Fig. 16.5 Ldisk(= ¿soft) - rta relation of XTE 1550-564 [30]. (a) Fits with (MCD + power-law) model. (b) When Comptonized MCD is included in Period 1 and Period 7. The solid and dashed lines are for Ldisk « T^ and Ldisk « T^, respectively high M [57]. The radiation efficiency of a slim disk is considered to be reduced because photons are trapped and carried away in the mass flow (advective energy transport). Hence, the Lx -M relation tends to become saturated [56,57]. The spectrum is expected to be dominated by a MCD component, except that Tin is significantly higher than extrapolated from lower luminosity levels. Actually, such a feature has been observed in some black-hole XBs, e.g., GRS 1915+105 [14] and XTE 1550-564 [30] (see Fig. 16.5).

16.4.3.2 X-Ray Spectrum at Lower Luminosities

The X-ray spectrum at low luminosities is distinctly different from that at high luminosities. Because the spectrum is hard, much harder than in the HS state, it is called the low-luminosity hard (LH) state. Both neutron-star LMXBs and black-hole XBs exhibit a dramatic change, undergoing a transition of state, across Lx — 1037 erg s-1(or M — 1017 g s-1), as mentioned in Sect. 16.4.3. The spectral shape in the LH state is a hard power-law form, as shown in Fig. 16.6a. Another outstanding difference is in the properties of time variability. When sources enter into the LH state, rapid large-amplitude intensity fluctuations (flickering) build up in all time scales down to milliseconds. Such a transition between the two spectral states has been observed in several soft X-ray transients during the decay, and also in Cyg X-1 and LMC X-3. Since this bimodal behavior is observed regardless of whether the compact object is a neutron star or a black hole, it is believed to be a fundamental property of an accretion disk, depending on the accretion rate. Once they go into the LH state, the spectral shape and variability are essentially the same for both

Energy (teV)

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Fig. 16.6 (a) Changes in the spectral shape of the black-hole LMXB GS 1124-684 with luminosity [15]. The upper three are the spectra in the HS state, while the lower two are those after transition to the LH state. (b) Hard X-ray spectra of the black-hole soft X-ray transients [24]. Note that the lower five are those in the HS state, whereas the upper three are those in the LH state. The spectra are scaled by arbitrary factors (in brackets) for clarity ic'

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Fig. 16.6 (a) Changes in the spectral shape of the black-hole LMXB GS 1124-684 with luminosity [15]. The upper three are the spectra in the HS state, while the lower two are those after transition to the LH state. (b) Hard X-ray spectra of the black-hole soft X-ray transients [24]. Note that the lower five are those in the HS state, whereas the upper three are those in the LH state. The spectra are scaled by arbitrary factors (in brackets) for clarity black-hole XBs and neutron-star LMXBs. Hence, these systems are no longer distinguishable [78].

The power-law spectrum in the hard state is clearly different from the hard tail of black-hole XBs in the HS state. It is substantially harder with the observed photon indices r in the range 1.7-1.9. In addition, unlike the hard tails of black holes in the HS state, the power-law spectrum shows a clear fall-off above several tens kilo-electronvolt (high-energy cut-off), as seen in a few examples in Fig. 16.6b (upper three). The power-law spectrum with a cut-off observed in the LH state can be reproduced by Comptonization of soft photons with thermal electrons of kT < 100 keV, a process called thermal Comptonization (see [74]).

The transition between the HS state and the LH state has been considered as due to a change in the disk structure. There is evidence that a tenuous hot plasma, the so-called "disk corona," builds up above the disk when a source goes into the LH state. For instance, when 4U 1608-522 (a neutron-star LMXB) was about to go into the LH state, the spectra of X-ray bursts (blackbody emission from the neutron star surface) began to show a hard tail [51], implying that a part of the burst photons were injected into the corona and Comptonized. Also, the disappearance of the 2keV blackbody component of the neutron-star LMXBs in the LH state suggests that the neutron star surface is obscured by the disk corona. Whether the thin disk in the LH state still extends to the innermost stable orbit (embedded in the corona) or it recedes to a larger radius is an unsettled issue. The physical mechanism for the transition of state and other unique properties of the LH state are yet to be understood.

As mentioned erlier, the Type I X-ray burst is a thermonuclear flash of the matter accumulated on the surface of neutron stars (see [32] for a review), hence a unique signature of neutron-star LMXBs. Except for very luminous ones, such as Sco X-1 and LMC X-2, Type I X-ray bursts are frequently observed from neutron-star LMXBs. According to the LMXBs catalogue by Liu et al. [34], Type I X-ray bursts were detected from 63 out of total 150 LMXBs. Excluding the 17 secure black-hole LMXBs, it gives a high probability of <50%. The rest of LMXBs includes <20 transients that are selected as black hole candidates on the basis of a "soft + hard-tail" spectrum. Significantly, no Type I X-ray burst has been detected from them, despite a long watch before going into quiescence. Together with the absence of the 2-keV blackbody component in the HS state, this fact strongly supports that they are also black-hole LMXBs. (See also 4.3.3).

Another important characteristics of the LH state is the associated radio emission. While the sources are in the HS state, they are usually radio-quiet. When they go into the LH state, quasi-steady radio emission, sometimes resolved into jets, shows up.

Incidentally, the properties of XBs in the LH state are strikingly similar to those of many active galactic nuclei, i.e., similar power-law index, and high time-variability. These similarities suggest that despite huge differences in the system scale and power, the basic process of accretion is essentially the same in both systems. On this basis, many properties of active galactic nuclei are interpreted in the light of what is known about LMXBs. Most of active galactic nuclei are considered to be accreting supermassive black holes in the LH state.

16.4.3.3 X-Ray Spectrum in Quiescent State

Soft X-ray transients spend most of their life-times in a quiescent state. Since the X-ray luminosity in quiescence is below 1033 erg s~\ observations of them require high sensitivity. Most of the observations so far have been made with ROSAT, ASCA and more recently with Chandra and XMM-Newton.

The observed results of the quiescent state show distinct differences between black-hole XBs and neutron-star XBs. Neutron-star XBs are systematically more luminous than black-hole XBs [40]. Moreover, there is an essential difference in the X-ray spectra in quiescence. Some examples are shown in Fig. 16.7. The available spectra of black-hole XBs show a hard power-law spectrum with a photon index r < 2 [3,28,54]. In contrast, neutron-star XBs commonly show a low-temperature blackbody-like component with kT < 0.1 keV in addition to a hard tail [3,66-68]. This low-temperature component qualitatively accounts for higher luminosities of neutron-star XBs. It is most probably the thermal emission from the surface of a cooling neutron star. In fact, Rutledge et al. [66-68] showed that, if a proper atmosphere model is adopted, the estimated radius for the observed thermal component is of the order of 10 km, consistent with the canonical value for a neutron star. Here again, the lack of a thermal component in the spectra of black-hole XBs in quiescence provides further evidence for the absence of a visible surface.

Cen X-4

GS 2023+338

Cen X-4

GS 2023+338

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Fig. 16.7 X-ray spectra of two soft X-ray transients in quiescence: the neutron-star XB Cen X-4 and the black-hole XB GS 2023+338 [3]

Energy (keV)

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Fig. 16.7 X-ray spectra of two soft X-ray transients in quiescence: the neutron-star XB Cen X-4 and the black-hole XB GS 2023+338 [3]

The accretion flow in the quiescent state seems quite different from those in the HS and LH states. There are optical observations that prove continued mass transfer from the companion even during quiescence at a rate M — 1015 g s-1(see [78]). On the other hand, the observed quiescent X-ray luminosities are 103°~32 erg s^1, which indicates an extremely low efficiency of radiation of < 0.01%.

Narayan, McClintock, and Yi [53] proposed a disk model consisting of two distinct zones: at large radii the disk is thin and cool in which a part of the transferred matter is stored, whereas the inner region is filled with a hot (kTe — 100 keV) tenuous quasi-spherical plasma flow in which most of the energy released is carried away (advected) and only a tiny fraction is radiated. This advection-dominated accretion flow (ADAF) model also explains the observed power-law spectrum in quiescence. Variant models of low radiation-efficiency accretion flow were proposed later (see [39] for references).

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