A&A 419, 291-299 (2004)
DOI: 10.1051/0004-6361:20034424
K. Beuermann1 - Th. E. Harrison2,
- B. E. McArthur3 - G. F. Benedict3 - B. T. Gänsicke4
1 - Universitäts-Sternwarte Göttingen, Geismarlandstr. 11,
37083 Göttingen, Germany
2 -
New Mexico State University, Box 30001/MSC 4500, Las Cruces 88003, Mexico
3 -
McDonald Observatory, University of Texas, Austin, 78712 Texas, USA
4 -
Department of Physics and Astronomy, University of Southampton,
Highfield, Southampton SO17 1BJ, UK
Received 1 October 2003 / Accepted 10 February 2004
Abstract
Using the Hubble space Telescope Fine Guidance Sensor,
we have measured the trigonometric parallax of the bright cataclysmic
variable 1223 Sgr. The absolute parallax is
mas, making V1223 Sgr the most distant CV with a
well-determined trigonometric parallax. This distance, a Lutz-Kelker
correction, and the previously measured extinction yield an absolute
visual high-state magnitude
.
We outline a
model, which is consistent with the observed spin-down of the white
dwarf and provides for much of the UV/optical emission by
reverberation of X-rays. From previous X-ray and UV/optical
data, we derive an accretion luminosity
erg s-1, a white dwarf mass
,
and an accretion rate
g s-1,
Key words: astrometry - stars: individual: V1223 Sgr - stars: novae, cataclysmic variables
V1223 Sgr (4U1849-31) is one of the brightest confirmed intermediate polars, both optically and in X-rays. The only previous distance estimate of 600 pc was based on the observed EB-V=0.15and a mean reddening of 0.25 mag kpc-1 (Bonnet-Bidaud et al. 1982). Since V1223 Sgr is not included in ground-based parallax programs, we have obtained a high-precision parallax using the Hubble Space Telescope Fine Guidance Sensor (FGS). This observation increases the number of CV parallaxes measured with the HST FGS to eight (Harrison et al. 1999, 2000, 2003; McArthur et al. 1999, 2001; Beuermann et al. 2003).
V1223 Sgr shows modulations at the orbital period
= 3.366 h, the
spin period of the white dwarf
= 745.5 s (Osborne et al. 1985), and the beat period
= 794.38 s (Steiner et al. 1981). The
UV/optical spectral energy distribution was interpreted by
Bonnet-Bidaud et al. (1982) and Mouchet (1983) in terms of an
accretion disk which reaches close to the white dwarf and should cause
it to be spun up. Unexpectedly, however, the white dwarf was found to
spin down (Jablonski & Steiner 1987; van Amerongen et al. 1987)
suggesting that the disk stays much further away from the white
dwarf. Our accurate distance allows us to determine the luminosity of V1223 Sgr, estimate its accretion rate, and to show that a standard
intermediate-polar model is consistent with the available
observations.
Table 1: Photometric and spectroscopic data for the V1223 Sgr reference frame.
Table 2: Astrometric data and derived spectroscopic parallaxes for the V1223 Sgr reference frame.
The process for deriving a parallax for a cataclysmic variable from HST FGS observations has been described in papers by McArthur et al. (2001, 1999) and Harrison et al. (1999). The process used here is nearly identical to those efforts, as well as our recent program on EX Hya (Beuermann et al. 2003). An FGS program consists of a series of observations of the target of interest, and a set of four or more reference stars located close to that target. Typically, three epochs of observations, each comprised of two or more individual HST pointings (orbits), are used to solve for the variables in the series of equations that define a parallax solution. For V1223 Sgr, we obtained observations on four different epochs (2000 September, 2001 March, 2001 September, and 2002 September) during which nine orbits of HST time were used. The extra epoch of observation was essential in deriving the high precision in the smallest parallax we have yet measured using the FGS. Extensive calibration data, as well as estimates of the distances and proper motions of the reference stars, are required to obtain a robust parallax solution.
We have used a combination of spectroscopy and photometry to estimate
spectroscopic parallaxes for the reference stars.
The optical BVRI photometry of the five reference stars was
obtained on 2001 March 13 using the CTIO 0.9 m telescope and the
Cassegrain Focus CCD imager. These data
were calibrated to the standard system using observations of Landolt
standards. The final photometric data set is listed in
Table 1. Included is the Two Micron All-Sky Survey (2MASS) JHK photometry of the reference stars, transformed to the homogenized
system of Bessell & Brett (1988) using the transformation equations
from Carpenter (2001). Typical error bars on the photometry are
0.02 mag for the V-band measurements, and
0.03 mag for the
optical colors. The 2MASS photometry for the five reference stars has
error bars of
0.02 mag.
Optical spectroscopy of the reference stars, and a number of MK spectral type templates, was obtained on 2001 March 9 and 10 using the
CTIO 1.5 m telescope with the Cassegrain
Spectrograph
with the 831 l/mm "G-47'' grating and a two arcsecond
slit, giving a spectral resolution of 0.56 Å/pix. We estimated
spectral types of the reference stars from a comparison of the spectra
with those of the MK-templates and present the results in the last
column of Table 1.
The visual extinctions of the reference stars (Col. 9 of Table 1)
were estimated from a comparison of their spectral types and the
photometric data, using the standard relations from Reike &
Lebofsky (1985). Finally, spectroscopic parallaxes were derived
using the spectral types and visual extinctions. The results are
listed in the last column of Table 2. To determine these values,
we used the Hipparcos calibration of the absolute magnitude for
main sequence stars by Houk et al. (1997), and that for giant stars
tabulated by Drilling & Landolt (2000). The distinction between main
sequence stars and giants is facilitated by (i) the dichotomy of the
MV-distribution in the Hertzsprung-Russell diagram for stars of
spectral type G and later and (ii) the ability of the Bayesian-like
astrometric software to identify an object with a true parallax
substantially different from the one used as the starting value in the
iterative approach. Details of the procedure are given in our
previous papers cited above. For the astrometric solution discussed
below, we assumed error bars of
20% on our spectroscopic
parallaxes.
The reference stars span a wide range in spectral type, and have
significant extinctions. Four of the five reference stars turn out to
be late-type giants, providing the exceptionally quiet reference
frame, which is an essential for the high quality of the parallax
derived for V1223 Sgr. Three of them (#2, #3, and #4) have
extinctions similar to that of V1223 Sgr which has
(Bonnet-Bidaud et al. 1982). It is somewhat disquieting
that AV does not correlate better with
.
A similar
situation, however, was also found in the fields of RR Lyr (Benedict et al. 2002a) and
Cep (Benedict et al. 2002b).
The data reduction process for deriving a parallax of the target from
FGS observations was identical to previous efforts, except for the
fact that the astrometer has changed from FGS3 to FGS1R, successfully
calibrated by Benedict et al. (2001). With the positions measured by FGS1R, we determine the scale, rotation, and offset plate constants
for each observation set relative to an arbitrarily adopted constraint
plate. The solved equations are
x' | = | x + lc(B-V) | (1) |
y' | = | y + lc(B-V) | (2) |
![]() |
= | ![]() |
(3) |
![]() |
= | ![]() |
(4) |
As in all our previous astrometric analyses, we employed GaussFit
(Jefferys et al. 1987) to minimize .
Since we had five high-quality reference star observations at each
epoch, we were able to use the eight-parameter model, instead of the
six-parameter model used in our previous parallax measurements,
which had A = E and B = -D. The additional parameters yielded a
significantly improved
compared with the simpler model. The
input proper motions for V1223 Sgr and the reference stars were taken
from the USNO CCD Astrograph Catalog, the "UCAC2'' (Zacharias et al.
2004)
, and are listed in Cols. 3 and 6 of Table 2. The
Bayesian-like reduction software models the proper motions and the
spectroscopically determined parallaxes of the reference stars as
observations with errors to produce an absolute (not relative)
parallax for V1223 Sgr. It yields the final proper motions listed in
Cols. 4 and 7 of Table 2. The internal consistency of the solution
obtained for the V1223 Sgr field is very good. Figure 1 shows
the histograms of the residuals for all 220 individual x and y positional measurements of the target and the reference
stars. Gaussian fits give standard deviations of 0.88 and 0.90 mas,
respectively, which is better than usually obtained for parallax
measurements with the HST FGS. Columns 8 to 11 of Table 2 list
the "catalog'' positions
and
and their standard
deviations
and
which result from the
fit of Eqs. (3) and (4) to the time series of the individual
observations. The frequency-weighted mean values of these standard
deviations are
mas and
mas. Reference star #3 has standard deviations
in both coordinates as low as the other stars, confirming that its
input parallax is not grossly in error. Hence, we must presently
accept that it is a giant at a distance of
2.5 kpc, although
its implied tangential velocity is large.
The final absolute parallax of V1223 Sgr is
mas. The fine precision of this result is directly attributed to the
very stable reference frame afforded by the distant giants. The
limiting factor in the error budget turns out to be the remaining
uncertainty in the proper motions of the reference frame.
![]() |
Figure 1: Histograms of the x and y residuals obtained from modeling V1223 Sgr and its reference frame. |
Open with DEXTER |
The measured distance to V1223 Sgr is
pc. As pointed out by Lutz & Kelker (1973),
parallaxes suffer from a systematic error in addition to the
observational one in the sense that the most probable true parallax
is smaller than the observed absolute parallax because the number of
objects per
-interval increases as
with n=4 for
a constant space density. More detailed analyses of the problem
including the magnitude and space density distributions of the parent
population have been considered, e.g., by Hanson (1979), by Smith
(1987), and by Oudmaijer et al. (1998). Here, we have simply assumed
that the parent population has an absolute magnitude at the brighter
end of the range
0 < MV < 10, giving an index of n=3.0for the space density (Hanson 1979). The Lutz-Kelker correction is
usually quoted as a correction in visual magnitude and, for this
choice of parameters, is
.
The most
probable distance modulus of V1223 Sgr including the Lutz-Kelker
correction is
m-M=8.61+0.21-0.19 and the most probable
distance including this correction is
d=527+54-43 pc. This is
the largest distance of a CV so far measured with the HST FGS.
In its normal high state, V1223 Sgr has a long-term mean magnitude of B = 13.1 (Garnavich & Szkody 1988), around which it varies by 0.5 mag. Of this, the orbital and spin modulation accounts for about
0.3 mag. There are also long-term trends and a time span
between 1937 and 1951 when it experienced drops to much fainter states
(Garnavich & Szkody 1988). With
in the high state
(Table 2), V and B are practically the same. From the depth of the 2200 Å feature, Bonnet-Bidaud et al. (1982) derived
EB-V=0.15 with an error of about 0.01, which yields a visual absorption
.
This value of the absorption, the mean
visual magnitude of V=13.1, and our new distance modulus give an
absolute mean visual magnitude in the normal high state of
.
This value has still to be corrected for inclination
effects.
Penning (1985) and Watts et al. (1985) assumed that the mass of the
secondary in V1223 Sgr is that of a Roche-lobe filling main sequence
star,
M2 = 0.40 .
In many CVs, however, the secondaries seem
to be expanded over their main sequence radii and have smaller masses
than the main-sequence assumption suggests (e.g. Beuermann et al. 1998). We adopt
M2 = 0.40
as the nominal secondary mass
and comment on the effect a mass as low as 0.25
will have on
the the results. For a spectral class M 4, a secondary in this mass
range has a K-band magnitude of
K=15.1-15.4 and contributes 8-11% of the observed K-band flux (Table 1).
According to et al. (1985), the radial velocity amplitude
of the orbital motion of the white dwarf as derived from the wings of
the Balmer emission lines is
km s-1. Penning
(1985), using a superior time resolution, found that the Balmer and He II
radial velocities were modulated, in addition, at
the spin period (see his Figs. 9 and 3 and note that the spin
modulation is clearly present in his Fig. 3). Penning's K1agrees closely with that of Watts et al., which we adopt here. As
noted already by these authors, the implied inclination is small. For
M1 = 0.93
(see below), we obtain
with M2=0.40
and
with
M2=0.25
.
Our derivation of the white dwarf mass M1 and the
accretion rate
rests on the results of the X-ray spectral
analysis of Beardmore et al. (2000). These authors fitted a
multi-temperature shock model to the ASCA and Ginga X-ray
spectra of V1223 Sgr, which included a treatment of the X-albedo and
of internal absorption within the source. From this fit, they deduced
a shock temperature of
=
43+13-12 keV and the emitted
spectrum
as a function of photon energy E (called "incident''
spectrum by them). Integration of
over all photon energies
above the Lyman edge gives the total flux
erg cm-2 s-1 (Table 3, line 1), which we call "X-ray
flux'' because only 3% of it is emitted below 0.1 keV.
refers to
= 43 keV and scales, to a first approximation,
as
.
The X-ray luminosity
then scales as
,
too. The
emitted spectrum
is based on the observed ASCA spectrum
for photon energies E>0.4 keV, but for still lower energies it
merely represents an extrapolation of the multi-temperature thermal
model spectrum. We demonstrate in the next section, however, that a
substantial additional XUV source does not exist in V1223 Sgr.
The observed X-ray luminosity based on the Beardmore et al. (2000)
emitted spectrum and our Lutz-Kelker corrected distance from
Sect. 2.4, is
erg s-1, where the error accounts for the
uncertainties in the normalization of the observed X-ray flux, in
,
and in d. We assume that
represents the luminosity of
one accreting pole and that the second pole is hidden behind the white
dwarf. Such a geometry is generally expected if the shock height his small compared with the white dwarf radius R1, as it is in the
model of Beardmore et al., and still holds for a finite shock
height if the inclination is small and the magnetic axis is more or
less aligned with the rotational axis. We account for the second pole
by writing
and use
,
below.
Table 3: Integrated observed and inferred fluxes for individual wavelength ranges (see text).
In magnetic CVs of the polar subtype, a large fraction of the accretion energy is released as soft X-rays and dominates the total X-ray flux, which is used to estimate their accretion rates (Beuermann & Burwitz 1995). Does a soft X-ray component exist also in the intermediate polar V1223 Sgr?
The XUV luminosity can be estimated by the Zanstra method using
the observed line flux F4686 of He II
photons
with
eV in erg cm-2 s-1. The number flux of ionizing photons needed to
produce this line is:
![]() |
(5) |
Steiner et al. (1981) quote an energy flux of the
line
in V1223 Sgr of
erg cm-2 s-1 and other papers suggest
values within a factor of two in both directions (Bonnet-Bidaud
et al. 1982; Penning 1985; Watts et al. 1985). We adopt the Steiner et al. value which becomes
erg cm-2 s-1 after
correction for reddening. Because of the large internal absorption at
soft X-ray energies, we use
.
This
choice of parameters yields
photons cm-2 s-1, with an
uncertainty of about a factor of two from the error in F4686 and the uncertainties in
and
.
For comparison, the Beardmore et al. X-ray spectrum
provides 0.11 photons cm-2 s-1 with
energies above 54 eV, of which 50% are below 0.3 keV. As argued
above, this number probably refers only to the pole facing the
observer. The number from both poles would then be 0.22 photons cm-2 s-1,
in agreement with the number needed to produce the observed
flux. We conclude that there is no evidence for an
additional component of XUV photons. The conservative limit to the
energy flux of a potential XUV source given in line 2 of Table 3
refers to a source which provides the same number of ionizing photons
as the X-ray source.
For further discussion of V1223 Sgr, we adopt a simple
intermediate polar model in which an accretion disk is broken up by
the magnetic field of the primary at an inner radius
.
At
,
matter couples onto the field and falls along the field
lines towards both magnetic poles of the white dwarf. We assume that
there is no viscous energy release inside
and that all
gravitationally released energy is radiated in the flow behind the
strong shock which forms near the white dwarf surface. This is the
usual assumption, which allows to treat the guided motion as a free
fall. It neglects the fact that the ionized matter in the funnel has
to get rid of the particle momenta perpendicular to the field and does
so by radiative losses. Nevertheless, photoabsorption of X-rays in the
guided stream and reemission of the absorbed energy is in line with
the model and may cause the funnel to be an intense source of
UV/optical radiation.
Outside
,
we assume a circularly symmetric steady state disk in
which the individual annuli radiate at local effective temperatures
(r) as given by Shakura & Sunyaev (1973). In addition, we
include an inner ring at
,
which mimics the boundary layer and
emits the energy released when the matter is braked from the Kepler
velocity to the angular velocity of the white dwarf. Following
Bonnet-Bidaud et al. (1982) and Mouchet (1983), we use blackbody
spectra, which has the advantage of simplicity, but the disadvantage
of systematically distorting the spectrum, especially at short
wavelengths.
For the outer disk, we allow for the possibility of heating by
radiation from the central source or from the elevated magnetically
guided flow by letting
(r) not drop below a temperature
.
This is obviously a very rough approach, which we justify by
its simplicity.
The location of the inner edge of the disk is restricted by two requirements. As a first condition,
should not exceed the
circularization radius
of matter with the specific
angular momentum it carries over from the inner Lagrangian point. No
disk can form for
>
.
For
M1 = 0.93-1.18
and
M2=0.25-0.40
,
falls in the range of
to
cm. The second condition results
from the observation that the white dwarf in V1223 Sgr is being spun
down, which indicates that it should rotate close to equilibrium. The
equilibrium inner radius of the disk
is located inside the
corotation radius
=
cm, with
s the spin period of the white dwarf in V1223 Sgr (Osborne
et al. 1985). The theory of Ghosh & Lamb (1979) with later
corrections by Wang (1987) predicts
0.98
.
This
does not account, however, for the synchronization torque between
primary and secondary star. Warner (1996) estimates this torque from
considerations of the magnetism of the secondary star. For
conciseness, we refer to his Eqs. (22)-(24), and note that
the magnitude of the effect depends not only on the uncertain magnetic
moment of the secondary star, but also on the ratio between inner edge
and spherical Alfvén radius, usually taken to be
,
and on the poorly known screening of the
magnetic moment of the primary by the accretion disk. In our preferred
model B (see below), the disk in V1223 Sgr has a rather large
central hole and may be quite flimsy. We assume, therefore, that
screening is rather weak (
in Warner's
terminology). For the parameters of V1223 Sgr, we then obtain
=
cm, which is smaller than
for the entire range of possible values of M1 and M2.
This theory also allows to estimate the magnetic moment of the primary
and its surface field strength. We use
with
cm, where
is the
magnetic moment,
is the surface field strength of the
white dwarf in the orbital plane, and the dipolar magnetic axis is
assumed to be aligned with the rotational axis. In the aligned case,
the polar field strength is
,
while for an inclined
magnetic rotator, the factor between
and
is
smaller than two.
The free fall of matter from
to R1 releases an accretion
luminosity
in a shock with temperature
![]() |
= | ![]() |
(6) |
![]() |
= | ![]() |
(7) |
![]() |
(8) |
Equation (7) can be solved for M1 with
=
43+13-12 keV
(Beardmore et al. 2000), an adopted value for
and a mass radius
relation of white dwarfs R1(M1). We use the relation
cm,
which we found from fitting the radii of CO white dwarf models by Wood
(1995) with a thick hydrogen envelope, an effective temperature of
K, and masses between 0.80 and 1.20
.
We use two
values of
,
which correspond to the two models considered below,
cm and
cm (see
Sects. 3.6.1 and 3.6.2). The white dwarf masses for these two cases
are M1 =
and M1 =
,
respectively. A white dwarf mass lower than
0.8
can be
excluded, as noted already by Beardmore et al. (2000).
We derive the accretion rate
needed to generate the
emitted X-ray spectrum
by eliminating GM1(1/R1-1/
)
from Eq. (6) with help of Eq. (7) and replacing
from
Eq. (8). With
and
from Sect. 3.3.1, we then obtain
g s-1, where
the error depends primarily on the remaining uncertainty in d and
the value of
.
Note that
is independent of the white
dwarf mass. The X-ray luminosity is
erg s-1.
In what follows, we interprete the observed UV/optical spectral
energy distribution in terms of two simple models and list their
parameters in Table 4. Model A is that of a luminous accretion disk,
which has its inner edge close to the white dwarf (Bonnet-Bidaud et al. 1982; Mouchet 1983). Model B has the inner edge at
cm and requires a different origin for most of the
UV emission.
We use a distance of 527 pc and a radial velocity amplitude of the
white dwarf K1=56 km s-1 (Sect. 3.2). We quote the results in
Table 4 for the nominal secondary mass M2=0.40
and comment
on the effect of choosing a lower value of M2.
![]() |
Figure 2:
Overall energy distribution of V1223 Sgr for
![]() |
Open with DEXTER |
Figure 2 shows the mean orbital and rotational spectral energy
distribution of V1223 Sgr in its normal bright mode. It is based on
the IUE spectrophotometry and optical photometry of Bonnet-Bidaud et al. (1982) and Mouchet (1983) (solid circles) and is supplemented by
the (non-simultaneous) 2MASS infrared photometry from Table 1 (open
circles). The integrated flux for the wavelength range
Å is given in Table 3, line 5, and an estimate of the flux
between the Lyman edge and 1250 Å in line 4.
The model of a luminous accretion disk (Bonnet-Bidaud et al. 1982; Mouchet 1983) can account for the observed
UV/optical/infrared emission. The model requires a high white dwarf
mass, an outer disk radius of 90% of the Roche radius, an inner
radius close to the white dwarf, and an accretion rate
g s-1, which exceeds
from above. The best fit
to the spectral flux distribution is shown in Fig. 2 (upper data set
and curve) and the parameters are listed in Table 4. The spacing
between
and R1 is tailored to yield
= 43 keV.
The derived accretion rate
represents an
overestimate because the blackbody disk and its boundary layer at
emit 2/3 of the total flux in the Lyman continuum, while typical CV disks have the Lyman jump strongly in absorption. The blackbody
disk is a coarse approximation and we quote
in Table 4 in
brackets to indicate this uncertainty.
If the secondary mass is reduced from 0.40 to 0.25
,
the
blackbody accretion rate increases to
g s-1,
partly because the now larger inclination of
implies a
smaller projected area of the disk.
The real problem of the disk model is the location of the inner edge
of the disk far inside the corotation radius, which is incompatible
with the observed spin down of the white dwarf (van Amerongen et al. 1987; Jablonski & Steiner 1987). The theory presented above
suggests that
should be about an order of magnitude larger than
assumed in this model. Whatever the remaining uncertainties in the
theory, the inner edge of the disk can not be close to the white
dwarf.
Table 4:
Parameters of disk models A and B. For both models, we
assume M2=0.40 ,
K1=56 km s-1, and d = 527 pc (see text).
The alternative model B assumes a disk, which is truncated at
cm. Since the
truncated disk is intrinsically faint, we assume that heating by
irradiation raises its flux to the observed level, which requires
= 11 000 K. The truncated disk is represented in Fig. 2 by an 11 000 K blackbody (short dashed curve). In Table 4, Sect. 4,
lines 1 and 2, we list its UV/optical flux. The contribution from the
secondary star is minute in comparison (dotted curve for a 3100 K
blackbody adjusted to K=15.1). Heating the disk to 11 000 K requires
that it is moderately inflated. For a point source at the white
dwarf, a solid angle of
sr or a half opening
angle
is needed. If the disk is irradiated by the
funnel emission,
could be smaller. In this model, much of
the observed UV radiation must be due to the reverberation of X-rays.
That the observed ultraviolet radiation is not entirely of disk
origin was indicated already by Mouchet's (1983) observation that the
UV flux varied by 23% over 1.5 h while the V magnitude stayed
constant. Furthermore, Bonnet-Bidaud et al. (1982, see also Welsh &
Martell 1996) showed that the pulsed component has a steeper spectrum
than the mean light. When corrected for extinction, it is almost as
steep as a Rayleigh-Jeans spectrum,
.
The wavelength dependence of this component is
depicted by the open triangles in Fig. 2, adjusted to 30% of the
total mean flux in the B-band. This percentage is at the upper
end of the observed range of amplitudes (Steiner et al. 1981;
Bonnet-Bidaud et al. 1982; King & Williams 1983; Warner & Cropper
1984) and is a reasonable choice if the observed variations in
amplitude represent variations in the visibility of the modulation
rather than true variations of the pulsed flux. For illustrative
purposes, we have adjusted a 40 000 K blackbody to fit these
fluxes (Fig. 2, long dashed curve) and the sum of the two components
to fit the total observed flux. The "reprocessed'' flux is listed in
Table 4, Sect. 4, lines 3 and 4. We do not contend that the
794 s pulsed component extends into the UV as indicated by the 40 000 K blackbody, but suggest that there may exist more than
one component of reprocessed light. Combined they may account for
much of the UV flux. In view of Penning's (1985) discovery of
radial velocity variations at the spin period of the white dwarf, we
suspect that a spin-modulated component may still be
hidden in the UV. The heated pole cap of the white dwarf is a viable
contender. The fact that such a component has not been found at
optical wavelengths may be due to a small amplitude of modulation
and/or a contrived geometry (Hellier 2003). The sum of
truncated disk and "reprocessed'' component is seen to fit the data as
well as the model of a luminous disk. The present model B has the
advantage of being internally consistent with the spin down of the
white dwarf and with the X-ray derived accretion rate
.
Its
parameters depend only weakly on the choice of M2.
Is the generation of much of the UV flux by reverberation of X-rays
energetically feasible?
In order to test this hypothesis, we convert the components of
the observed flux F in Table 4, Sect. 4, to luminosities
L = g d2F using appropriate (i.e. non-blackbody) geometry
factors g. For the "disk'' flux we assume a grey limb darkening law,
,
which yields
for
.
For the "reprocessed'' component, g is similar to that of the disk if the heated polar cap is the main
source, while an estimated
applies to the toroidal
geometry of the magnetically guided flow inside
.
We use an average
.
The resulting luminosities are listed in Table 4,
Sect. 5. After corrections for the contributions by the
un-illuminated disk and the secondary star, we obtain an upper limit
to the reprocessed luminosity
erg s-1 = 0.80
.
The
uncertainty in this number is fairly large because of possible errors
in the geometry factors and the remaining uncertainty in the X-ray
luminosity. Long-term variability of V1223 Sgr could affect the
result, but is probably of minor importance because the AAVSO records
(Mattei 2003) show V1223 Sgr at V=13.1 at the time of the ASCA
X-ray observations, in agreement with its long-term mean magnitude.
The load on the X-ray source is reduced if part of the optical
emission is of cyclotron origin, represented by the quantity
introduced in Sect. 3.4, which depends on the field strength and the
pre-shock mass flow density
(in g cm-2 s-1). From
and an
estimate of the area of the ring-shaped accretion region on the white
dwarf we expect
g cm-2 s-1. For
MG,
we then estimate
using the
radiation-hydrodynamic calculations of Woelk & Beuermann (1996, their
Fig. 9, bottom panel, lower curve). For
,
/
drops to a comfortable 0.69, which can easily be accounted
for by X-ray heating of the pole cap of the white dwarf and
reprocessing in the funnel, in the accretion disk, and the irradiated
face of the secondary star (see Beardmore et al. 2000 for an analysis
of the energy-dependent X-ray albedo from the white dwarf). For
,
the accretion rate and the total accretion
luminosity increase over the values quoted in Sect. 3.5 and in Table 4
to
g s-1 and
erg s-1, where the
errors are from Sect. 3.5 and the numerical factor in the last
relation accounts for the energy released outside
.
Since the field
estimate given below suggests that some cyclotron emission should be
present, we accept the latter values as our best estimates.
The different sizes of the central holes in the accretion disks imply
different surface field strengths
of the white dwarfs in
models A and B. A rough estimate of
may be obtained by
equating
with
(see above). For model B
with
cm,
G cm3, and for
cm
(Table 4),
MG. Depending on the obliquity of the
dipole, the polar field strength is in the range of
MG.
The small inner hole of the disk with
cm in
model A implies a much smaller surface field strength of about 0.5 MG. Our favored model B places V1223 Sgr at the lower range of
field strengths observed in polars. Since low-field polars are
characterized by weak soft X-ray emission, the lack of a strong soft
X-ray source in V1223 Sgr is not surprising.
We have presented an accurate parallax of V1223 Sgr which allows us to
derive the luminosities in the different wavelength bands. Based on
this result, we have tested the hypothesis that much of the UV/optical
emission is produced by the reverberation of X-rays and not by the
release of gravitational energy in a luminous disk. Our
analysis is based on the assumption that we see only the X-rays from
one pole. This assumption and the high X-ray temperature reported by
Beardmore et al. (2000) lead to a total X-ray luminosity
,
which is much higher than previously thought
and can power a large fraction of the observed UV/optical radiation by
the reprocessing of X-rays. Interestingly, this is possible without
the presence of a substantial source of XUV radiation. Likely
reprocessing sites are the pole cap of the white dwarf, the
magnetically guided accretion flow, the disk, and the irradiated face
of the secondary star. While the latter two sites may be responsible
for the observed flux modulated at the sideband frequency (Steiner et al. 1981), reprocessing in the former locations may produce a so far
undiscovered component, which is photometrically modulated at the spin
period of the white dwarf. The accretion rate derived from the X-ray
luminosity and X-ray temperature is
g s-1, which includes a small correction for the
contribution by cyclotron emission. This result is independent of the
white dwarf mass.
The observed UV/optical/IR spectral energy distribution can equally well be fitted by a truncated disk plus reprocessed component (model B) and by a luminous disk (model A). The observed spin-down of the white dwarf (Jablonski & Steiner 1987; van Amerongen et al. 1987), however, requires that the the inner edge of the disk is not too far inside the corotation radius, a condition which is met only by the truncated-disk model B.
Strong internal absorption and the reprocessing of a major fraction of the emitted X-rays is a general feature observed also in other intermediate polars, some of which are even more strongly internally absorbed than V1223 Sgr (e.g. Norton & Watson 1989). Simultaneous X-ray/UV studies could shed light on the physical processes acting in these systems. It is surprising that no such study is yet available.
Acknowledgements
One of (K.B.) thanks Andrew Beardmore for providing his model fits to the X-ray spectrum of V1223 Sgr and Coel Hellier for a stimulating discussion on the physics of intermediate polars. We thank the referee John Thorstensen for pointing out errors in Table 2 and for very helpful comments which led to an improved presentation. This research was supported in Germany by DLR/BMFT grant 50 OR 99 03 1. In the UK, BTG was supported by a PPARC Advanced Fellowship. In the Unites States, partial support for TEH, BEM, and GFB for proposal #9230 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. This research has made use of the NASA/ IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This publication also makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research.