# An additional soft X-ray component in the dim low/hard state of black hole
binaries

C. Y. Chiang1, Chris Done1, M. Still2,4, and O. Godet3
1Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK
2Mullard Space Science Laboratory, Dorking, Surrey, UK
3X-ray and Observational Astronomy Group, Department of Physics and Astronomy,
University of Leicester, LE1 7RH, UK
4NASA Ames Research Center, Moffett Field, CA 93045, USA
E-mail<EMAIL_ADDRESS>
(Submitted to MNRAS)

###### Abstract

We test the truncated disc models using multiwavelength (optical/UV/X-ray)
data from the 2005 hard state outburst of the black hole SWIFT J1753.5-0127.
This system is both fairly bright and has fairly low interstellar absorption,
so gives one of the best datasets to study the weak, cool disc emission in
this state. We fit these data using models of an X-ray illuminated disc to
constrain the inner disc radius throughout the outburst. Close to the peak,
the observed soft X-ray component is consistent with being produced by the
inner disc, with its intrinsic emission enhanced in temperature and luminosity
by reprocessing of hard X-ray illumination in an overlap region between the
disc and corona. This disc emission provides the seed photons for Compton
scattering to produce the hard X-ray spectrum, and these hard X-rays also
illuminate the outer disc, producing the optical emission by reprocessing.

However, the situation is very different as the outburst declines. The optical
is probably cyclo-synchrotron radiation, self-generated by the flow, rather
than tracing the outer disc. Similarly, limits from reprocessing make it
unlikely that the soft X-rays are directly tracing the inner disc radius.
Instead they appear to be from a new component. This is seen more clearly in a
similarly dim low/hard state spectrum from XTE J1118+480, where the 10$\times$
lower interstellar absorption allows a correspondingly better view of the
UV/EUV emission. The very small emitting area implied by the relatively high
temperature soft X-ray component is completely inconsistent with the much
larger, cooler, UV component which is well fit by a truncated disc. We
speculate on the origin of this component, but its existence as a clearly
separate spectral component from the truncated disc in XTE J1118+480 shows
that it does not simply trace the inner disc radius, so cannot constrain the
truncated disc models.

###### keywords:

X-rays: binaries – accretion, accretion discs

††pagerange: An additional soft X-ray component in the dim low/hard state of
black hole binaries–References††pubyear: 2009

##  1 Introduction

The accretion disc in black hole binary systems (BHB) is unstable at the point
where Hydrogen goes from being predominantly neutral to ionised. This gives
rise to dramatic, transient outbursts in which the reservoir of material built
up in the outer disc during quiescence can accrete down onto the black hole.
The peak luminosity of the outburst is set by the mass in the quiescent disc
and the time taken for this to accrete. Both these depend on the size of the
disc taking part in the outburst, which is set by the binary separation. Hence
there is a link between orbital period and peak luminosity, with short period
systems showing smaller peak outburst luminosities (King & Ritter 1998;
Shahbaz et al. 1998; Lasota 2001; Done, Gierliński & Kubota 2007 hereafter
DGK07).

The peak luminosity determines the number of spectral states which are seen
during the outburst. Systems with peak luminosity below $\sim 0.1L_{Edd}$
remain in the low/hard state (LHS), where the energy output peaks at $\sim$
100 keV. Brighter systems instead show a distinct transition to a much softer
thermal dominated state (TDS, also termed a high/soft state) which peaks at
$\sim$ 1 keV, while the brightest systems can also show a very high state
(VHS, alternatively steep power law state). These dramatic changes in the
spectrum are correlated with equally dramatic changes in the rapid variability
properties (see e.g. McClintock & Remillard 2006) and the jet (Fender, Belloni
& Gallo, 2004), implying distinct changes in the nature and geometry of the
accretion flow. These can be plausibly explained if there is a hot, optically
thin, geometrically thick solution to the accretion flow equations at low
luminosities (Shapiro, Lightman & Eardley 1976; Narayan & Yi 1995).This can be
put together with a cool, optically thick, geometrically thin disc (Shakura &
Syunyaev, 1973) in the truncated disc/hot flow model where the disc
progressively replaces more of the inner hot flow as the mass accretion rate
increases. The distinct hard/soft spectral transition then marks the point at
which the cool disc extends down to the last stable orbit, replacing all the
hot flow (Esin, McClintock & Narayan 1997; DGK07).

Such models make a clear prediction that the inner radius of the cool disc
should recede as the LHS drops in luminosity. This can in principle be tested
using the colour temperature and luminosity of the cool disc component to
estimate its radius (e.g. Poutanen, Krolik & Ryde 1997; Shrader & Titarchuk
1999). However, such observations are complicated by the fact that the disc is
at low temperature at low luminosities, $\sim 0.3$ keV for a $10M_{\odot}$
black hole at $0.02L_{Edd}$, even if the disc extends down to $6R_{g}$ (where
$R_{g}=GM/c^{2}$). Such low energy X-rays cannot be seen with the 3 keV
bandpass limit of _RXTE_ , the satellite which has accumulated the most BHB
data to date (Done & Gierliński 2003; Dunn et al. 2009). CCD observations can
extend the bandpass down to lower energies, but these are still not
straightforward to interpret as the disc is not the dominant spectral
component in this state. Instead, the hard X-ray emission dominates the
spectrum, so irradiation can change the disc temperature (Gierliński, Done &
Page 2008, hereafter GDP08), while the disc luminosity can be underestimated
due to photons which are Compton upscattered into the hard X-ray spectrum
(Makishima et al., 2008). This component is still not easy to study even with
CCD detectors since low energy X-rays are absorbed by interstellar gas. Most
BHB are in the galactic plane so have gas columns of $N_{H}\geq 10^{22}$ cm-2
which effectively block emission below 1 keV.

However, there are a few black holes which have intrinsically much lower
columns which have been observed with CCD detectors, namely XTE J1118+480:
$N_{H}\sim 1.1\times 10^{20}$ cm-2, XTE J1817-330: $1.1\times 10^{21}$ cm-2
and SWIFT1753.5-0127: $2-3\times 10^{21}$ cm-2 (Cabanac et al., 2009). XTE
J1118+480 has only snapshot spectra available (Hynes et al. 2000; Esin et al.
2001; Frontera et al. 2001; 2003), but both SWIFT1753.5-0127 and XTE J1817-330
were well sampled throughout their outbursts by the _Swift_ satellite.
However, XTE J1817-330 is a long period system, so spends most of its time in
the disc dominated state, with only two, rather faint, LHS spectra at the end
of its outburst. Thus the short period LHS outburst of SWIFT1753.5-0127 is the
best candidate to study the disc evolution in the LHS. Here we analyse these
data with sophisticated models to describe the behaviour of the X-ray
irradiated disc (GDP08; Gierliński, Done & Page 2009, hereafter GDP09) to
constrain its inner radius as the outburst declines.

##  2 Data reduction

###  2.1 _Swift_

Figure 1: The top panel shows the evolution of the observed flux in the _Swift_ XRT band, while the lower panel shows the simultaneous UVOT data (in UVW1, UVW2 and B filters, where available). Figure 2: The ratio of the X-ray data (red:XRT, black:PCA, green:HEXTE) to an absorbed power law model fit to the 2-4 and 7-10 keV ’continuum dominated’ bands for spectra taken from the peak (10) through to the end of the decline (30) as marked by arrows on Fig 1. At the peak is clear that the continuum spectrum strongly declines above 70 keV, indicating that the electron temperature of the thermal Comptonisation is low enough to be seen. There is also a strong additional soft component at low energies, most probably from the accretion disc, together with a small features around the iron line and edge, indicating reflection of the continuum from the accretion disc. As the outburst declines, the electron temperature increases, so the high energy break can no longer be seen, and the soft X-ray emission drops dramatically in strength.  Table 1: The table details the datasets we use from _Swift_ and _RXTE_. We refer to the combined spectrum by the last two numbers of its _Swift_ obsID. The remaining columns give the QPO frequency from fitting the _RXTE_ power spectrum, followed by the results for fitting the 0.5-200 keV X-ray data with a wabs*(diskbb+thCompml) model. We fix the absorption to $0.2\times 10^{22}$ cm-2, and assume reflection is from neutral, solar abundance material inclined at $60^{\circ}$. We tie the seed photons for Comptonisation to the disc temperature in these fits, but then also show the difference in $chi^{2}$ for removing the disc and fixing the seed photon energy for the Compton scattering to 0.1 eV  Number | _Swift_ | _RXTE_ | QPO (Hz) | $kT_{disc}(keV)$ | $N_{dbb}$ | $\Gamma$ | $\Omega/2\pi$ | $N_{pl}$ | $\chi^{2}/\nu$ | $\bigtriangleup\chi^{2}$
---|---|---|---|---|---|---|---|---|---|---
00 | 00143778000 | 91094-01-01-00 | $0.64\pm 0.01$ | $0.22\pm 0.01$ | 47557 | $1.80\pm 0.02$ | $0.34^{+0.10}_{-0.13}$ | 0.58 | 712/713 | 699
03 | 00030090003 | 91094-01-01-04 | $0.83\pm 0.01$ | $0.25^{+0.00}_{-0.01}$ | 63806 | $1.86^{+0.00}_{-0.02}$ | $0.35^{+0.05}_{-0.08}$ | 1.06 | 544/548 | 1024
04 | 00030090004 | 91423-01-01-04 | $0.91\pm 0.01$ | $0.24^{+0.00}_{-0.01}$ | 66358 | $1.86\pm 0.01$ | $0.27\pm 0.06$ | 1.06 | 870/757 | 1503
07 | 00030090007 | 91094-01-02-01 | $0.75^{+0.01}_{-0.02}$ | $0.24^{+0.01}_{-0.00}$ | 69967 | $1.83^{+0.02}_{-0.01}$ | $0.36^{+0.04}_{-0.08}$ | 1.16 | 702/679 | 1112
06 | 00030090006 | 91094-01-02-01 | “ | $0.24^{+0.00}_{-0.01}$ | 83839 | $1.82^{+0.02}_{-0.01}$ | $0.32^{+0.08}_{-0.07}$ | 1.26 | 868/762 | 1674
10 | 00030090010 | 91094-01-02-00 | $0.72^{+0.00}_{-0.01}$ | $0.25^{+0.00}_{-0.01}$ | 70377 | $1.82^{+0.01}_{-0.02}$ | $0.33^{+0.03}_{-0.04}$ | 1.17 | 752/726 | 2192
08 | 00030090008 | 91094-01-02-00 | “ | $0.28\pm 0.02$ | 36514 | $1.81\pm 0.01$ | $0.28^{+0.05}_{-0.04}$ | 0.86 | 275/273 | 232
09 | 00030090009 | 91094-01-02-00 | “ | $0.24^{+0.01}_{-0.00}$ | 73119 | $1.81^{+0.01}_{-0.01}$ | $0.28\pm 0.05$ | 1.17 | 873/784 | 2955
11 | 00030090011 | 91094-01-02-02 | $0.70\pm 0.01$ | $0.25\pm 0.02$ | 59219 | $1.81\pm 0.01$ | $0.29\pm 0.06$ | 1.02 | 333/320 | 250
12 | 00030090012 | 91094-01-02-02 | “ | $0.23^{+0.01}_{-0.00}$ | 79673 | $1.81\pm 0.01$ | $0.29^{+0.05}_{-0.06}$ | 1.09 | 860/746 | 1898
13 | 00030090013 | 91094-01-02-02 | “ | $0.23^{+0.01}_{-0.00}$ | 75104 | $1.81\pm 0.01$ | $0.30\pm 0.06$ | 1.08 | 622/633 | 1134
15 | 00030090015 | 91094-01-02-03 | $0.63\pm 0.01$ | $0.23^{+0.00}_{-0.01}$ | 69620 | $1.79\pm 0.01$ | $0.31^{+0.07}_{-0.06}$ | 0.99 | 818/743 | 1231
16 | 00030090016 | 91094-01-02-03 | “ | $0.25\pm 0.01$ | 49618 | $1.79\pm 0.01$ | $0.31^{+0.06}_{-0.07}$ | 0.94 | 717/655 | 1030
18 | 00030090018 | 91423-01-03-06 | $0.47\pm 0.01$ | $0.23^{+0.01}_{-0.02}$ | 42447 | $1.73\pm 0.01$ | $0.24\pm 0.06$ | 0.64 | 396/435 | 347
19 | 00030090019 | 91423-01-04-02 | $0.45^{+0.00}_{-0.01}$ | $0.22\pm 0.01$ | 39291 | $1.72\pm 0.01$ | $0.28^{+0.07}_{-0.06}$ | 0.57 | 626/646 | 732
20 | 00030090020 | 91423-01-06-00 | $0.29\pm 0.01$ | $0.23^{+0.01}_{-0.02}$ | 17415 | $1.67^{+0.02}_{-0.01}$ | $0.20^{+0.07}_{-0.09}$ | 0.36 | 433/460 | 178
21 | 00030090021 | 91423-01-08-02 | - | $0.22\pm 0.02$ | 9122 | $1.65\pm 0.03$ | $0.19^{+0.16}_{-0.17}$ | 0.21 | 514/518 | 50
23 | 00030090023 | 91423-01-10-00 | - | $0.17\pm 0.02$ | 14876 | $1.65^{+0.01}_{-0.02}$ | $0.16^{+0.05}_{-0.09}$ | 0.18 | 635/659 | 32
24 | 00030090024 | 91423-01-11-00 | - | $0.16^{+0.02}_{-0.03}$ | 16135 | $1.67^{+0.01}_{-0.02}$ | $0.24^{+0.11}_{-0.13}$ | 0.16 | 602/631 | 19
26 | 00030090026 | 91423-01-13-00 | - | $0.17^{+0.05}_{-0.10}$ | 4629 | $1.63^{+0.02}_{-0.04}$ | $0.13^{+0.14}_{-0.13}$ | 0.11 | 559/562 | 4
30 | 00030090030 | 91423-01-16-01 | - | $0.04^{+0.05}_{-0.03}$ | 934 | $1.64^{+0.01}_{-0.02}$ | $0.09^{+0.14}_{-0.09}$ | 0.11 | 559/592 | 3
31 | 00030090031 | 91423-01-17-00 | - | $0.13^{+0.04}_{-0.12}$ | 13157 | $1.63^{+0.02}_{-0.03}$ | $0.14^{+0.16}_{-0.14}$ | 0.10 | 576/508 | 3

We use publicly available _Swift_ data from SWIFT J1753.5-0127 taken during
the period from July 2005 to July 2007. We extracted both X-ray telescope
(XRT) and UVOT data. All of our XRT data was in Windowed Timing mode, and we
extracted source counts using a circle with radius of 20 pixels. Background
was taken from an off source region using a circle of the same size. However,
the source was very bright during the peak of the outburst, and some of the
datasets were piled up as the count rate was above 100 counts $s^{-1}$. We
determined the size of the central piled up region by excluding progressively
larger radii regions until the spectra stopped softening at high energies.
This gave an exclusion region of 3 pixels for brightest observations, and 2
pixels for more moderately piled up data. The data was grouped to 20 counts
$s^{-1}$, and fit between 0.5-10 keV.

The evolution of the observed (i.e. not corrected for interstellar absorption)
flux in the X-ray (upper) and UV (lower) bands is plotted in Fig. 1. We derive
the flux by integrating the absorbed model fit over 0.5-10 keV for the X-rays.
For UV data, we find energy band for each filter and define the effective
bandpass to be between the energies determined by FWHM ($5.6\times 10^{-3}$ to
$7.45\times 10^{-3}$ keV for UVW2 filter, $4.2\times 10^{-3}$ to $5.45\times
10^{-3}$ keV for UVW1 filter, and $2.55\times 10^{-3}$ to $3.2\times 10^{-3}$
keV for B filter).

The observations fall into 3 clearly distinct time segments. The first covers
the outburst rise and decline, after which the flux remains fairly constant.
Hence in this paper we concentrate on this first data group, in order to track
the evolution of the disc during the flux decline.

###  2.2 _RXTE_

The _RXTE_ satellite also followed the 2005 outburst. We use the standard
extraction techniques with the bright source background to derive PCA spectra
from all layers of detector 2, adding 1 percent systematic error and use these
data from 3-16 keV. We also extract Standard 1 power spectra over the full
2-60 keV bandpass for intervals of 256 s, and fit these with multiple
Lorentzian components in order to determine the QPO frequency. These are given
in Table 1.

We extract HEXTE data from cluster 0 and use these over the energy range
25-200 keV. We select the subset of _Swift_ and _RXTE_ data which are taken
within one day of each other. This gives a total of 27 observations which have
quasi-simultaneous coverage of the optical/UV/X-ray/hard X-ray spectrum. Table
1 details these composite spectra.

##  3 Disc plus Comptonisation plus reflection

###  3.1 X-ray data

Figure 3: The plot shows the results of the disc temperature, inner radius and
reflection evolution obtained from the diskbb+thCompml model. The value of
inner radius were derived from the diskbb normalisation assuming an
inclination of $60^{\circ}$ and distance of 5.4kpc. As these are poorly known,
the absolute value of the radius is not well constrained. However, trends
should be robust, and clearly the derived inner radius remains constant or
mildly decreases during the outburst. This is in sharp contrast to the
expected increase from truncated disc models. Reflection (third penal) and the
QPO frequency (lower panel, see also Table 1), on the other hand, decreases
when leaving the peak, as expected if the disc is receding.

We first concentrate on the X-ray data alone, and show the different
components present in the spectrum. We fit a power law to the ’continuum
dominated’ bands at 2–4 keV and 7–10 keV, and then show a ratio of the data to
this model over the entire bandpass (assuming absorption fixed at the galactic
column of $N_{H}=0.2\times 10^{22}$ cm-2). Fig. 2 shows this at different
points along the outburst (marked by arrows in Fig. 1), from the peak to the
end of the decline. Close to the peak, the continuum clearly has a rollover at
high energies, so is most likely due to thermal Comptonisation. There is also
clearly an additional soft X-ray component, which decreases in strength as the
outburst declines. However, there are also more subtle features seen in the
high signal-to-noise PCA data, with a small excess around the iron line,
followed by a slight dip and subsequent rise to 20 keV. This is characteristic
of reflection

Thus we use a model including a disc to produce the soft X-ray component,
thermal Comptonisation of these disc seed photons to produce the hard
continuum, and reflection of the hard continuum from the surface of the disc.
We use the thcomp model to describe the Comptonisation, developed and tested
by Zdziarski, Poutanen & Johnson (2000), extended to include its reflected
continuum and self-consistent line emission by Życki, Done & Smith (1999). We
assume that the reflecting material is neutral, with solar abundances and
inclined at $60^{\circ}$. We fix the galactic absorption column at
$N_{H}=0.2\times 10^{22}$ cm-2 corresponding to an $E(B-V)=0.34$ (Cadolle Bel
et al., 2007). The results for each spectrum are detailed in Table 1. We
assess the significance of the detected disc emission by removing the disc
from the model, and fixing the seed photon temperature instead at 0.1 eV. This
results in a loss of 2 degrees of freedom, so the disc is only significant at
greater than 99 per cent confidence for $\Delta\chi^{2}>4.61$. Thus all the
spectra apart from the final 3 (26, 30 and 31) strongly require the presence
of an additional soft component. We similarly assess the significance of
reflection (driven mostly by the presence of the iron line) and find that it
is required in all the datasets apart from the final 3.

Fig. 3 shows the derived disc temperature and radius (see Table 1). The disc
radius _decreases_ as the outburst progresses (see also Cabanac et al. 2009),
in apparent conflict with the truncated disc model where the inner disc should
progressively recede during the LHS decline. Yet the amount of reflection
decreases, as expected if the disc is receding. Additionally, the low
frequency QPO seen in the variability power spectrum drops dramatically, again
as expected if the truncation radius sets the QPO frequency and is increasing
(DKG07). Thus while the behaviour of the reflected emission and QPO fit the
truncated disc models, the behaviour of the soft X-ray component does not.

###  3.2 Optical data

We show these X-ray model fits extrapolated down to the optical/UV data and
corrected for the effects of interstellar absorption. Fig. 4a shows this for
the outburst peak (10). This clearly shows that extrapolating the hard X-ray
power law spectrum down in energy overpredicts the optical/UV data. This
implies that the hard X-ray spectrum must break at UV/soft X-ray energies,
supporting our modeling of it as due to Comptonisation of seed photons from
the accretion disc. However, extrapolating the soft X-ray disc emission
underpredicts this emission, making it clear that intrinsic gravitational
energy release in the disc is insufficient to produce the observed optical/UV
data.

In general, the optical can include additional contributions from reprocessed
emission from hard X-ray illumination of the outer disc, as well as
contributions from the jet and the companion star(e.g. Russell et al. 2006).
However, SWIFT J1753.5-0127 is a short period, low mass X-ray binary, so the
companion star must faint. Instead we try to quantify the jet contribution
from observed radio flux of $\sim 2.1$ Jy at 1.7 GHz (Fender et al. 2005. We
show the extrapolation of this up through our optical/UV/X-ray bandpass
assuming a flat spectrum (black line on Fig. 4a). This is a factor $\sim 3$
below the observed optical flux, but this is the maximum possible jet
contribution as its spectrum should break where it becomes optically thin. It
seems most likely that this break is at IR frequencies (Markoff et al. 2001;
Gallo et al. 2007) so the jet is also probably negligible in the optical/UV
for these data. Thus X-ray reprocessing from hard X-ray illumination of the
outer disc seems the most likely origin for the optical/UV flux (van Paradijs,
1996).

Figure 4: The unabsorbed data and X-ray model fit (diskbb + thCompml) at the
outburst peak (top panel, spectrum 10), midway down the decline (middle panel,
spectrum 20) and in the outburst tail (lower panel, spectrum 30). The magenta
and blue components are disc emission and Comptonisation in corona,
respectively. Figure 5: The red squares show the evolution of UV excess i.e.
the observed UVW1 flux divided by the UVW1 flux predicted by the model fit to
the soft X-ray disc. This always underpredicts the observed UVW1 emission, by
an amount that increases as the source fades. The soft X-ray disc component is
not significant in the final 3 points but the trend is already clear even
without these data. The blue triangles show the ’UV deficit’ i.e. the ratio of
model to observed flux in the UVW1 filter predicted from extrapolating the
thCompml continuum down into the optical assuming the seed photons are at 0.1
eV rather than from the disc. Close to the peak of the outburst this UV
deficit is large, showing that the X-rays over-predict the UV flux.
Conversely, towards the end of the outburst, the UV data lie very close to the
extrapolation of the hard X-ray flux.

There are additional radio observations from midway down the outburst decline
(Cadolle Bel et al., 2007). Fig. 4b shows this radio emission, extrapolated as
above, onto spectrum 20, the dataset closest in time to the radio
observations. Again, the optical/UV points are not fit by either the hard
X-ray power law extrapolated down (though this time the mismatch is not so
large), or by the radio emission extrapolated up, or by the disc inferred from
the soft X-ray component, as also shown in Cadolle Bel et al. (2007).

Fig. 4c shows a spectrum from the end of the outburst (30), where there are no
radio observations. The disc emission fit to the soft X-ray component is now
very weak and cool, and its extrapolation down to the optical lies
dramatically below the observed optical/UV emission. However, the optical/UV
emission does lie remarkably close to the extrapolated hard X-ray flux in
these low-luminosity data.

We quantify this by calculating the factor by which the disc component
underpredicts the observed flux in the UVW1 filter (’UV excess’: GDP09) in
each spectrum. We also calculate a ’UV deficit’, which is the factor by which
the Comptonisation model overpredicts the flux in the UVW1 filter if its seed
photons put at 0.1 eV rather than fixed to the disc temperature. Such low
energy seed photons may be produced by cyclo-synchrotron emission by the same
thermal electrons which produce the Compton scattered emission interacting
with the tangled magnetic field in the hot flow itself (Narayan & Yi 1995; Di
Matteo, Celotti & Fabian 1997; Wardziński & Zdziarski 2000). Fig. 5 shows how
these evolutions during the outburst. This confirms the results seen in the
three individual spectra discussed above. The ’UV excess’ (red triangles)
increases strongly with time, as the soft X-ray disc component makes less and
less contribution to the UV flux. The disc is not significantly detected in
the final three spectra, but the trend in UV excess is already clearly
apparent. Conversely, the UV deficit (blue squares) decreases, and is roughly
consistent with the observed UV flux from spectrum 21 onwards.

##  4 Irradiated Disc Model

We first look at the possibility that irradiation of the disc is responsible
for all the issues highlighted in the previous section. Irradiation of the
inner disc changes its derived temperature and radius compared to that derived
from fitting purely gravitational energy release models of the disc (GDP08).
Similarly, irradiation of the outer disc can also increase the optical/UV
emission from that expected from an unilluminated disc (van Paradijs
1996;GDP09)

We use a slightly modified version of the diskir model of GDP08 so that the
disc temperature and normalisation are set by the physical variables of the
mass, distance, mass accretion rate and inner and outer radii. This has the
advantage that the outer radius is set in terms of physical units, rather than
relative to the (possibly changing) inner radius as in diskir. We parameterise
the inner and outer radii in terms of $R_{g}=GM/c^{2}$, and leave the inner
disc radius, $R_{d}$ as a free parameter in the fits. We fix the mass and
distance at the best (though poorly constrained) estimates of $12~{}M_{\odot}$
and 5.4 kpc, respectively (Zurita et al., 2008).

This model uses the diskbb parameterisation of disc temperature with radius
i.e. $T\propto r^{-3/4}$ (Mitsuda et al., 1984), so does not include a stress-
free inner boundary condition or colour temperature correction. If the disc is
truncated then the lack of stress-free inner boundary condition is probably
more appropriate, but the colour temperature correction, $f_{col}$, is still
an issue. The derived value of the inner radius is then underestimated by a
factor $f^{2}_{col}\sim 2.9$ for $f_{col}\sim 1.7$ (Kubota, Makishima &
Ebisawa, 2001). However, the main aim of our spectral fitting is to track
changes in the value of the inner disc radius, as its absolute value depends
on the poorly known system parameters. The key aspect of the truncated disc
model which we are testing is the prediction that the truncation radius
increases as the spectrum hardens during the decline. Thus we are focussing on
the relative values of the inner disc radius during the decline.

The outer radius should remain constant, as should the absorption (but see
Cabanac et al. 2009) so we constrain these by simultaneously fitting three
datasets from various points in the outburst with the modified diskir model,
together with X-ray absorption parameterised by wabs and UV reddening by
redden. Assuming standard gas to dust ratios allows us to tie
$E(B-V)=1.5\times N_{H}/10^{22}$ (GDP08). This gives a best fit at
$N_{H}=2.1\times 10^{21}cm^{-2}$ and $R_{out}=10^{5.25}R_{g}$, which are fixed
to these values in all fits hereafter.

###  4.1 Evolution of the irradiated disc model parameters

We fit this model to all the _Swift-RXTE_ datasets. Guided by previous
low/hard state data (Poutanen, Krolik & Ryde 1997; GDP08), we fix the radius
of the irradiated portion of the inner disc at $1.1\times R_{d}$. Fig. 6 shows
the evolution of the source parameters in this model. The top panel gives the
bolometric flux, which varies by an order of magnitude. This is dominated by
the hard X-ray component, whose spectral photon index (second panel) decreases
from 1.8 to 1.6 during the first section of the decline, and then stabilizes
at this value hereafter. The source did not make a transition to the high/soft
or even intermediate state, but remained in the hard state throughout the
outburst.

Figure 6: Evolution of an irradiated disc model fit to the optical/UV/X-ray
spectrum. The top panel shows the bolometric flux, taken from the unabsorbed
model integrated between 0.001-100 keV. This drops by a factor of 10 during
the outburst, close to that seen from the X-ray emission alone in Fig. 1. The
second panel shows the hard X-ray spectral index, which hardens from $1.8$ to
$1.6$. The third panel shows the mass accretion rate $\dot{m}_{d}$ required to
power the intrinsic (gravitational) emission from the disc luminosity,
$L_{d}=GM\dot{m}_{d}/2R_{d}$. This drops by nearly two orders of magnitude, so
the ratio of this to hard X-ray luminosity in the corona $L_{c}/L_{d}$
increases by a factor 10 (fourth panel). The intrinsic disc luminosity is
enhanced by irradiation of the inner disc by the hard X-ray corona. The
fraction of irradiation required drops during the decline (fifth panel) as
does the amount of (neutral) reflected emission (sixth panel). The seventh
panel shows the fraction of the bolometric flux which is required to
thermalise in the outer disc in order to make the observed optical/UV flux.
This strongly increases during the decline (see also Fig. 4). The final panel
shows the inferred inner radius of the disc. This remains remarkably constant
in this model at around $10~{}R_{g}$ (see also Fig. 2), corresponding to $\sim
30~{}R_{g}$ after a colour temperature correction. This lack of change in the
inner disc radius is in conflict with the truncated disc model predictions
that the change in spectral hardness (see second panel) is driven by changes
in the solid angle subtended by the disc to the hard X-ray source. If instead
there is a separate soft X-ray component (see Fig. 8) as required in the
similarly dim low/hard state spectra from XTE J1118+480 then these data do not
constrain the disc radius.

Figure 7: The same 3 spectra (10, 20 and 30) as in Fig. 3, fit with the
irradiated disc model and corrected (data and model) for absorption. The
magenta dashed line is the intrinsic disc emission, the red line includes
irradiation of the outer disc, and the cyan line shows the additional flux
from irradiation of the inner disc. The Comptonised emission and its reflected
spectrum are shown in blue. While the inner disc irradiation, $f{in}$, drops,
the increase in $L_{c}/L_{d}$ means that the total disc spectrum is more
distorted by irradiation at lower fluxes.  Figure 8: Irradiated disc model
mass accretion rate through the disc, $\dot{m}_{d}$ versus that through the
corona, $\dot{m}_{c}$, derived from $(L_{c}/L_{d})(R_{d}/R_{c})\dot{m}_{d}$,
with $R_{c}=3.5~{}R_{g}$ fixed by requiring $\dot{m}_{c}\approx\dot{m}_{d}$
(shown by the red dashed line) for the brightest spectra. The red points show
the 3 faintest spectra where there is no significant additional soft X-ray
component. Even without these spectra the trend is clear that $\dot{m}_{c}$
gets progressively larger than $\dot{m}_{d}$ as the source declines. This is
opposite to the expected trend from a radiatively inefficient flow. are away
from the line.

The disc spectrum forms a component which connects the soft X-ray rise to the
optical emission in this model. Part of this is powered by gravitational
energy release, and the inferred mass accretion rate through the disc
decreases by more than 2 orders of magnitude during the decline (third panel).
Thus the ratio of the hard X-ray flux to this inferred intrinsic disc flux
increases by an order of magnitude (fourth panel).

The intrinsic gravitational energy of the disc is augmented by thermalisation
of the irradiating flux on the inner disc. The fraction of the hard X-ray
spectrum which illuminates the inner disc and is thermalised basically
decreases during the decline (fifth panel), as expected if the inner edge of
the disc is receding. Similarly, the amount of hard X-ray reflection also
declines (sixth panel). Conversely, the fraction of hard X-rays which
thermalise in the outer disc increases by almost an order of magnitude
(seventh panel). The final panel shows the disc inner radius. This is plainly
consistent with a more or less constant value, at $\sim 10~{}R_{g}$,
(corresponding to $\sim 30~{}R_{g}$ after a colour temperature correction)
although the error bars become large at later stages of the decline. Fig. 7a-c
show the corresponding fits to the data of Figs. 4a-c for this model.

###  4.2 Inferred mass accretion rate

We can use these derived parameters to explore how the mass accretion rate
through the disc compares to that required to power the hard X-rays. We
calculate the mass accretion rate of the corona by:

$L_{c}=\frac{\eta_{corona}}{\eta_{disc}}\frac{GM\dot{m}_{c}}{2R_{c}},$

where $\eta_{corona}/\eta_{disc}$ is the relative efficiency of converting
mass to radiation in a coronal flow which extends down to $R_{c}$ versus that
in a disc extending down to the same radius. However, the disc itself only
extends down to a radius $R_{d}$ so its luminosity from gravitational energy
release alone is $L_{d}=\frac{1}{2}GM\dot{m}_{d}/R_{d}$. Thus

$\frac{L_{c}}{L_{d}}=\frac{\eta_{corona}}{\eta_{disc}}\frac{\dot{m}_{c}}{\dot{m}_{d}}\frac{R_{d}}{R_{c}}.$

The spectral fitting parameters give $L_{c}/L_{d}$, $\dot{m}_{d}$ and $R_{d}$.
Close to the peak of the outburst, even a radiatively inefficient flow should
have $\eta_{corona}/\eta_{disc}\sim 1$. Here we also expect
$\dot{m}_{c}\sim\dot{m}_{d}$, which requires $R_{c}$ to be around 3 times
smaller than $R_{d}$ at this point. We can then calculate $\dot{m}_{c}$
assuming $\eta_{corona}/\eta_{disc}$ and $R_{c}$ remain constant. This is
plotted against $\dot{m}_{d}$ in Fig. 8. The red line is
$\dot{m}_{c}=\dot{m}_{d}$, showing clearly that these models favour a larger
mass accretion rate through the corona than through the disc on the decline.
This conclusion is strengthened if the flow is increasingly radiatively
inefficient at lower mass accretion rates, as the observed X-ray flux would
then require an even larger coronal mass accretion rate to power the same
amount of hard X-ray emission.

This conclusion is driven by the observational requirement for a soft X-ray
component in the late state decline data. This is weak, but significantly
present in all but the last three datasets (assuming that the absorption
column remains constant: Cabanac et al. 2009). It combines a low luminosity
with a fairly high (soft X-ray) temperature, which leads to the derived small
radius and low mass accretion rate. This low mass accretion rate is then much
smaller than that required to power the observed hard X-ray emission.

We illustrate this by re-coding the irradiated disc model to force
$\dot{m}_{c}=\dot{m}_{d}$ for $\eta_{corona}/\eta_{disc}=1$. This forces the
disc to have a higher mass accretion rate, so it must truncate at a larger
radius so as not to overproduce the observed soft X-ray component. Irradiation
of the inner disc should then be negligible, so we fix $f_{in}=0$ for physical
consistency, and we focus first on the X-ray data alone so we also fix
$f_{out}=0$.

We fit this to spectrum 24 (the lowest luminosity data for which the disc is
significantly detected in the soft X-ray flux), and first focus on the X-ray
data alone. The mass accretion rate through the disc is much higher ($1.2\pm
0.1\times 10^{17}$ g/s compared to $1.0\times 10^{16}$ in the diskir fits) and
the disc inner radius increases to $30~{}R_{g}$ from $\sim 5~{}R_{g}$ (i.e.
$90~{}R_{g}$ and $15~{}R_{g}$ after a colour temperature correction). This
disc contributes to the spectrum only at the softest energies of the _Swift_
XRT, and its sharp rise is rather different to the more gradual curvature seen
in the soft X-ray emission. Thus this gives a significantly worse fit
($\chi^{2}_{\nu}=626/632$ versus $600/630$, where the two extra free
parameters are $L_{c}/L_{d}$ and $f_{in}$). We can only recover the same
quality of fit with $\dot{m}_{d}=\dot{m}_{c}$ by including an additional soft
component. This allows the disc to recede back even further, to $\sim
50~{}R_{g}$ (i.e. $\sim 150~{}R_{g}$), so that the truncated disc makes no
contribution to the soft X-ray flux. Fig. 9 shows this fit including now the
optical/UV data with $f_{out}=2\times 10^{-3}$ (similar to that derived from
the original fits, see Fig. 6).

Irradiation can make such a hot, weak component if the irradiated disc area is
small. We fixed the radius of the reprocessing region at $1.1\times R_{d}$ for
the fits in Fig. 6, but as the disc recedes then the changing geometry means
that this should also drop. We allow this to be a free parameter with
$\dot{m}_{c}=\dot{m}_{d}$ and can recover as good a fit as before
($\chi^{2}=601/632$) with $\sim 1$ per cent of the bolometric flux being
reprocessed in a region with $R_{irr}=1.002R_{d}$. However, illumination of
such a tiny area of the disc surface seems unreasonable from illumination by a
central source.

Figure 9: Spectrum 24 fit by a model where $\dot{m}_{d}=\dot{m}_{c}$ and a
separate component (cyan, modelled with diskbb) to fit the soft X-ray
emission. The observed strong X-ray flux requires a large mass accretion rate
through the disc, so this has to truncate at $\sim 50~{}R_{g}$, forming the UV
peak, so as not to overproduce the soft X-ray emission.

##  5 Origin of Soft X-ray Component

###  5.1 Outburst Peak

The soft X-ray component seen at the peak of the hard state during the
outburst of SWIFT J1753.5-0127 is clearly from the disc. While the system
parameters are rather poorly known, the radii derived close to the peak are
$\sim 15~{}R_{g}$, corresponding to $\sim 45~{}R_{g}$ after a colour
temperature correction. This is consistent with the disc being recessed back
from the last stable orbit, as required for the truncated disc/hot inner flow
interpretation of the hard state. There are two independent lines of support
for this number. The first comes from the fact that the hard X-ray spectrum is
softer close to the peak, clearly consistent with the disc providing an
increasing source of seed photons to Compton cool the hot X-ray plasma. Since
most of the gravitational potential energy to power this corona is
concentrated within $20R_{g}$ then it seems most likely that the disc extends
down to similarly small radii. This means that there can also be irradiation
of the inner disc by the hard X-ray emission, leading to reflection and
thermalisation of the incident flux. We see evidence for both these processes
in the spectrum, with the extra flux from irradiation increasing the inferred
disc radius from the value of $\sim 11~{}R_{g}$ inferred from the simple
(unirradiated) disc fits to the X-ray spectrum, to $15~{}R_{g}$ (i,e, from
$30$ to $45R_{g}$ after colour temperature correction). The second is from low
frequency QPO which is at its maximum of $\sim 0.8$ Hz in these data. This
implies an outer radius of $\sim 20-30~{}R_{g}$ assuming that the QPO is
produced by Lense-Thirring (vertical) precession of the hot flow around a
$10~{}M_{\odot}$ black hole (Ingram, Done & Fragile, 2009).

The mass accretion rate required to power the disc emission is comparable with
that required to power the coronal hard X-ray emission assuming that the
corona extends down to a radius which is $\sim 5$ times smaller than that of
the disc i.e. $3.5R_{g}$ for the parameters assumed here, i.e. $\sim
9~{}R_{g}$ with a colour temperature correction. We stress again that these
system parameters are poorly known, thought this appears quite reasonable.
Much smaller radii could be potentially feasible for a hot inner flow,
irrespective of the spin of the black hole, as numerical simulations of the
MRI turbulence show that the large scale height magnetic fields can extract
energy from the infalling material beyond the last stable orbit (e.g. Krolik,
Hawley & Hirose 2005).

###  5.2 Late Stage Decline

The outburst peak spectra then form a template for comparison with the later
stages of the decline, where the bolometric flux is lower by a factor 10. The
truncated disc/hot inner flow model makes a clear prediction that these should
have a larger inner disc radius, decreasing the importance of illumination on
the inner edge of the disc, and decreasing the amount of associated
reflection. Thus illumination of the surface of the disc is not expected to be
important in distorting the derived inner disc radii in these spectra.
Similarly, as there is little (or no) overlap in radii between the hot inner
flow and disc, so the disc emission cannot be strongly suppressed by
Comptonisation as can be the case close to the transition (Kubota & Done 2004;
Makishima et al. 2008). Thus any disc component seen in these spectra should
give a fairly unbiased view of the inner radius of the flow. Yet associating
the observed soft X-ray component with this disc gives derived radii which are
as small, if not smaller than, the radii seen at the outburst peak, in clear
conflict with the truncated disc models (see Figs 4 and 6).

However, these radii are themselves in more subtle conflict with the
observations. The small disc has very small luminosity compared to the coronal
emission. This requires that the coronal mass accretion rate must be large
compared to that through the disc if the corona is powered by matter accreting
through it. Thus the corona cannot be predominantly fed by material
evaporating from the inner edge of the disc, but instead requires a completely
separate coronal flow which incorporates most of the incoming mass accretion
from the companion star. Yet it seems quite unlikely that the incoming cool
Roche lobe overflow stream would be able to form such a coronal flow at large
radii.

Instead it seems more feasible that the corona is not powered by its own mass
accretion supply, as in the truncated disc models, but is instead powered by
mass accreted through the disc, but whose energy is released in the corona
(e.g. Svensson & Zdziarski 1994). However, this model itself runs into
difficulties since the simplest idea would be for magnetic buoyancy to
transport the energy vertically. The energy is then released in a corona above
the disc, so the corona is co-spatial with it and illuminates it. This gives
rise to a reprocessed luminosity $L_{rep}=\frac{1}{2}(1-a)L_{c}$ (where $a$ is
the albedo, and the factor $\frac{1}{2}$ assumes the corona emits
isotropically) adds to the intrinsic disc luminosity (Haardt & Marashi, 1993).
For hard spectra, such as those observed here, the reflection albedo $a<0.3$,
hence the disc flux should be at least $L_{c}/3$. Yet we observe a disc flux
of $\leq L_{c}/20$ towards the end of the outburst. Thus the only way to
circumvent the reprocessing limits whilst having all the mass accrete via the
disc is if the energy is advected radially as well as vertically. Then it can
be released in a more centrally concentrated region, on size scales smaller
than the (small!) disc inner radius. The alternative of having the hard X-rays
be strongly beamed away from the disc, is ruled out by the very similar dim
low/hard state spectra seen in XTE J1118+480 (Frontera et al. 2001; 2003;
Reis, Miller & Fabian 2009), which has high inclination ($\geq 70^{\circ}$) so
that we must see a similar hard X-ray flux to that of the disc.

A potentially less arbitrary solution than using magnetic fields to transport
the energy in a dissipationless fashion is if the observed soft X-ray
component in the late stages of the decline is not from the disc. The spectra
clearly show that the observed soft X-ray emission cannot produce the
optical/UV emission without a large change in the reprocessed fraction in the
outer disc from that seen during the outburst peak. Yet the outburst remained
in the low/hard state, so there is no expected change in source geometry, so
the fraction of the total flux which illuminates the outer disc should not
change dramatically. Similarly, there is no large change in spectral shape
which might produce such a large difference in thermalisation fraction. Yet
the observed soft X-ray component is a factor 10 further below the UV emission
than at the outburst peak (Fig. 5). This could be used to argue that the real
disc is truncated, as in Fig. 7, so is larger and cooler, so that the same
amount of reprocessing can produce the optical/UV.

However, it is clear that the optical/UV emission does change character during
the decline. The rapid variability of the optical flux changes dramatically
during the decline, switching to an anti-correlation of the optical and X-ray
emission (Hynes et al., 2009). Clearly this shows that the optical is no
longer made predominantly by reprocessing of the hard X-ray flux, so it gives
only an upper limit to the irradiated disc flux.

Thus the optical emission does not trace the outer disc, so cannot constrain
our inner disc models. Instead, we use the similarly dim low/hard state
spectra from XTE J1118+480 to argue for a non-disc origin for the soft X-ray
component. This object has an absorption column which is an order of magnitude
lower than that to SWIFT J1753.5-0127. This gives a correspondingly more
sensitive view of the UV and soft X-ray emission, where it is clear that there
is a large, cool disc seen in the UV and EUV bandpass (Esin et al. 2001;
McClintock et al. 2001) which is completely inconsistent in luminosity and
temperature with the much weaker, higher temperature ’disc’ emission seen in
soft X-rays (Frontera et al. 2001; 2003; Reis, Miller & Fabian 2009). There
are plainly two components in this source, one which is consistent with a
truncated disc, making no impact on the soft X-ray emission, and another
component which produces weak soft X-ray flux. This is very similar to the
spectrum of 24 as shown in Fig. 9.

Thus for the late stage decline, our modeling with an irradiated disc is not
supported by the data. The cross-correlation of the rapid variability clearly
shows that the optical/UV cannot be made by reprocessing in the outer disc,
while XTE J1118+480 clearly shows that the soft X-rays form a separate
component to the observed UV/EUV emission from the (truncated!) disc. What
then produces the observed soft X-ray component, and what produces the
observed optical/UV emission ?

Figure 10: Two potential geometries for a soft X-ray component (highlighted in
green) from a small area, with short timescale variability dominated by
reprocessing of the hard X-rays, and additional variability at longer
timescales. With irradiation of a residual inner disc, the small area implies
a small radial extent. Conversely, with irradiation of the inner rim of a
large radius truncated disc, a small area implies a small vertical extent.
Additional long timescale variability can be generated at the disc outer or
inner edge, respectively, by clumping or turbulence.

##  6 Origin of the soft X-ray component during the decline

SWIFT J1753.5-0127 was observed by _XMM-Newton_ in March 2006 i.e. after the
end of the first intensive SWIFT campaign covering the outburst decline. These
data are analysed by Wilkinson & Uttley (2009), and have much better signal-
to-noise than those of the late decline _SWIFT_ spectra, but are very similar
in shape and intensity. The higher statistics in these data mean that the soft
component is unambiguously detected, at very high significance. The same
spectra model as used in Table 1 (diskbb+thcomp with absorption fixed at
$0.2\times 10^{22}$ cm-2)gives $kT_{disc}=0.25\pm 0.01$ keV and norm of
$1080\pm 100$.

The timing analysis of Wilkinson & Uttley (2009) showed that this soft X-ray
component variability strongly correlates with the hard X-ray variability on
short timescales i.e. is driven by reprocessing. However, on longer
timescales, there is additional variability in the soft X-ray flux, implying
that there are intrinsic fluctuations in the disc emission as well. The result
that much of the short term variability correlates with the hard X-rays rules
out a completely separate soft X-ray component such as the jet, while the
additional soft X-ray variability shows that the component is truly separate
as opposed to being produced from continuum curvature of the X-ray emission or
reflection (suggested by Hiemstra et al. 2009 as a potential origin for the
soft X-rays). These variability constraints mean that there are only two
potential origins for the soft X-ray component which arises from a small area
with relatively high temperature. Firstly, this could be emission from the
surface of a residual inner disc, forming a small ring from the last stable
orbit to some (small) outer radius. Secondly, this could be the inner face of
a truncated disc. We sketch these two possibilities in Fig. 10, and outline
them below.

###  6.1 Irradiation of a residual inner disc

Evaporation of the disc by thermal conduction is a plausible mechanism to form
a truncated disc/ hot inner flow geometry (e.g. Liu et al. 1999).
Counterintuitively, this is not most efficient at the smallest radii, as these
also have the highest coronal densities, so have the highest condensation
rates. Evaporation first erodes a gap in the disc, leaving a residual inner
disc. This gap expands radially, eventually giving a fully truncated disc if
the mass accretion rate is low enough(Mayer & Pringle, 2007). However, close
to the transition, the residual disc can remain. This geometry allows the
outer disc to carry all the mass accretion rate. This disc evaporates into a
corona, truncating it at some large radius into a coronal flow which carries
all the mass accretion rate. However, as the flow accretes to smaller radii,
the increasing density gives an increasing condensation rate and some small
fraction of the material can condense out of the hot flow. This forms a cool
ring at the innermost radii, with a mass accretion rate which is only a small
fraction of the total mass accretion rate, with the rest of the material
accreting via the coronal flow(Liu & Meyer-Hofmeister, 2001).

Reprocessing is still an issue, but if the ring is small, extending over a
very narrow range of radii, then it does not subtend a large solid angle to
the coronal X-ray emission, so could potentially produce the large observed
ratio of coronal to (inner) disc luminosity. Some reprocessing is required in
order to produce the short term variability, but there could also be intrinsic
variability in the extent of this residual disc.

###  6.2 Irradiation of the inner face of a truncated disc

The temperature of the irradiated region is required to be substantially
hotter than that of the disc itself, requiring a very small reprocessing area.
This seems very unlikely for a central source illuminating the top/bottom
surface of thin disc. However, the disc has some (small) half thickness,
$H_{d}$, so its inner rim forms a distinct, small area $\approx 4\pi
R_{d}H_{d}$ and subtends a solid angle $\approx H_{d}/R_{d}\times 4\pi$ to the
central source. The small reprocessing area found in section 4.2 above
corresponds to $H_{d}/R_{d}\sim 0.004$, predicting
$f_{in}=(1-a)H_{d}/R_{d}\approx 0.002$, where $a$ is the the reflection
albedo. This is a factor 5 smaller than $f_{in}$ derived from the data, but
potentially feasible given the large uncertainties both on the parameters and
on the modeling.

The irradiation origin then gives directly the rapid variability, while
turbulence caused by clumping instabilities on this edge could give the
required longer term additional variability.

##  7 Origin of Optical/UV emission during the decline

As noted by Motch et al. (1985) in GX339-4, the X-ray emission in the dim
low/hard state can extrapolate back quite accurately to fit the optical
spectrum (see also Corbel & Fender 2002; Nowak 2005). One way to produce this
is via a single synchrotron component from the innermost post-shock region of
the jet. This is self absorbed in the IR, strongly suppressing the emission at
lower frequencies. As the jet stretches out , each part of it produces a
synchrotron component which peaks at a lower frequency than those closer to
the center. All of these make the flat spectrum seen in the radio (e.g.
Markoff & Nowak 2005; Maitra et al. 2009). However, the non-thermal
synchrotron makes the optical and X-ray emission from a single scattering in a
single region, so it is hard to see how this can make the weak anti-
correlation between the optical and X-ray flux with lead of a few hundred
milliseconds which seems typical of this state (Motch et al. 1985; Kanbach et
al. 2001; Gandhi et al. 2008; Durant et al. 2008).

Conversely, the cross-correlation signal can be explained if the optical
emission is from the jet, while the X-ray emission is from the corona (Malzac,
Merloni & Fabian, 2004). However, the close match of the optical and X-ray
spectra is then very unexpected if these are really from different components.

Instead, if the spectrum is formed from thermal Comptonisation from self-
produced cyclo-synchrotron photons in the hot flow then there can be complex
time variability properties imprinted via propagating fluctuations through an
inhomogeneous flow (Kotov, Churazov & Gilfanov 2001; Arévalo & Uttley 2006).
Whether these can indeed explain the anti-correlation between optical and
X-ray by such spectral pivoting (Körding & Falcke, 2004) remains to be seen.

##  8 Conclusions

The combined _Swift_ and _RXTE_ observations from the black hole transient
SWIFT J1753.5-0127 give one of the best datasets to probe the evolution of the
inner edge of the accretion disc in the low/hard state. These instruments
cover the optical/UV and soft/hard X-ray bandpasses, giving a detailed picture
of the spectral evolution during the low/hard state outburst.

We fit these with a sophisticated irradiated disc model and find that this
gives a self-consistent picture around the outburst peak. Weak irradiation
increases the inferred radius of the inner disc by a factor $\sim 1.5$.
Photons from the disc are the seeds for Compton upscattering to produce the
hard X-ray emission, and this hard X-ray emission weakly illuminates the outer
disc to produce the observed optical/UV by reprocessing, as confirmed by the
optical/X-ray cross-correlation (Hynes et al., 2009).

However, we find clear evidence that the model breaks down as the source flux
declines. The optical spectra require increasingly unlikely levels of
reprocessing to explain the observed emission. A change in origin of the
optical emission is confirmed by the dramatic change in optical/X-ray cross-
correlation signal (Hynes et al., 2009). While the cross-correlation can be
explained in models where the optical is produced by the jet and the X-rays in
a corona (Malzac, Merloni & Fabian, 2004), this does not explain the excellent
match between the optical and X-ray spectra. Instead it seems more likely that
there is a single component connecting the optical and X-ray spectra. The
complex cross-correlation then remains an issue especially for a single
synchrotron component from the jet, but it may potentially be explained by
thermal Comptonisation of IR cyclo-synchrotron emission in an inhomogeneous
hot flow.

More fundamentally for the focus of this paper, the soft X-ray emission during
the decline may not be thermal emission from the disc either. If it is, its
radius does not change markedly from that seen at the outburst peak, in clear
conflict with the predictions of the truncated disc model. But it also implies
that the mass accreting through the disc is much less than the mass accretion
rate required to power the corona. Yet it seems most likely that the mass does
accrete through the outer disc, in which case the observed weak soft X-ray
disc emission is a problem. Either the mass accretes through the disc but most
of the energy is transported vertically and radially (to get around the
reprocessing limits) by magnetic fields to power a small, central hard X-ray
corona, or the soft X-rays are from an additional component, with the
truncated disc peaking in the UV.

The lower absorption to XTE J1118+480 allows us to distinguish between these
possibilities. Here, we can see a cool component peaking in the UV which is
clearly distinct from the soft X-ray emission. The UV component fits well to a
cool disc, truncated at large radii, so the soft X-ray component cannot be the
same material. This may still be associated with the inner disc, perhaps from
irradiation of its inner rim, or via a residual inner disc in the
discontinuous disc geometry predicted by evaporation models (e.g. Liu & Meyer-
Hofmeister 2001). However, it is also possible that the soft X-rays are
instead produced in a completely different way, such as ionised reflection
from grazing incidence angle illumination of the outer disc. Whatever their
origin, it is clear from XTE J1118+480 that the weak soft X-ray component seen
in the dim low/hard state does not trace the inner edge of the disc, so cannot
be used to constrain the truncated disc models.

## Acknowledgements

CYC and CD would like to thank Kim Page for help in extracting the _Swift_ XRT
data.

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