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Astronomy & Astrophysics manuscript no.
(will be inserted by hand later)
Time-resolved spectral analysis of the pulsating helium star
V652 Her. ?
C.S. Jeery 1 , V.M. Woolf 1 , and D.L. Pollacco 2
1 Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland.
2 School of Physical Sciences, Queen's University Belfast, Belfast BT7 9NN, Northern Ireland
Received . . . , 2001; accepted . . .
Abstract. A series of 59 moderate-resolution high signal-to-noise spectra of the pulsating helium star V652 Her
covering 1.06 pulsation cycles was obtained with the William Herschel Telescope. These have been supplemented
by archival ultraviolet and visual spectrophotometry and used to make a time-dependent study of the properties
of V652 Her throughout the pulsation cycle. This study includes the following features: the most precise radial
velocity curve for V652 Her measured so far, new software for the automatic measurement of eective temperature,
surface gravity and projected rotation velocities from moderate-resolution spectra, self-consistent high-precision
measurements of eective temperature and surface gravity around the pulsation cycle, a demonstration of excessive
line-broadening at minimum radius and evidence for a pulsation-driven shock front, a new method for the direct
measurement of the radius of a pulsating star using radial velocity and surface gravity measurements alone, new
software for the automatic measurement of chemical abundances and microturbulent velocity, updated chemical
abundances for V652 Her compared with previous work (Paper IV), a reanalysis of the total ux variations
(cf. Paper II) in good agreement with previous work, and revised measurements of the stellar mass and radius
which are similar to recent results for another pulsating helium star, BX Cir. Masses measured without reference
to the ultraviolet uxes turn out to be unphysically low ( 0:18 M ). The best estimate for the dimensions
of V652 Her averaged over the pulsation cycle is given by: h Te i = 22 930  10 K and h log gi = 3:46  0:05
(ionization equilibrium), h Te i = 20 950  70 K (total ux method), hRi = 2:31  0:02 R , hLi = 919  14 L ,
M = 0:59  0:18 M and d = 1:70  0:02kpc. Two signicant problems were encountered. The line-blanketed
hydrogen-decient model atmospheres used yield eective temperatures from the optical spectrum (ionization
equilibrium) and visual and UV photometry (bolometric ux) that are inconsistent. Secondly, the IUE spectra
are poorly distributed in phase and have low signal-to-noise. These problems may introduce systematic errors of
up to 0:1 M .
Key words. stars: fundamental parameters { stars: abundances { stars: helium { stars: individual (V652 Her) {
stars: pulsation { techniques: spectroscopic
1. Introduction
The early-type helium star V652 Her pulsates with
a period of 0.108 days (Landolt 1975), a visual am-
plitude of 0.1 mag. and a radial velocity amplitude
of  70 km s 1 (Hill et al. 1981 = Paper I). These
properties have made it amenable to detailed analyses,
notably the direct measurement of its average radius
(R = 1:98 R , Lynas Gray et al. 1984 = Paper II),
leading to precise estimates of its mass (M = 0:7 M )
and luminosity (Paper II, Jeery et al. 1999 = Paper IV).
Added to these data is the observation that the pulsa-
Send oprint requests to: C.S. Jeery, e-mail:
csj@star.arm.ac.uk
? Based on observations obtained with the William Herschel
Telescope, the United Kingdom Infrared Telescope, and on
INES data from the IUE satellite.
tion period is decreasing at a rate commensurate with
a secular contraction (Kilkenny & Lynas-Gray 1982,
Kilkenny & Lynas-Gray 1984, Kilkenny 1988,
Kilkenny et al. 1996). Such statistics have enabled
the evolutionary status and pulsational properties of the
star to be investigated using theoretical models. Both
pose serious challenges to stellar structure theory.
In the case of pulsations, the instability of V652 Her
could only be understood correctly when the contribu-
tion of iron-group opacities at around 10 5 K was correctly
taken into account (Saio 1993). Models with R = 2 R
and M = 0:7 M now reproduce the pulsational proper-
ties of V652 Her (Fadeyev & Lynas-Gray 1996) very well.
The evolutionary status of V652 Her also poses a
conundrum. Neither of the principal candidates for the
progeny of carbon-rich extreme helium stars is satisfac-
tory because the surface of V652 Her consists entirely of

2 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
a CNO-processed material. A substantial yield of surface
carbon is anticipated from both the merger of a CO with
a He white dwarf (Webbink 1984, Iben & Tutukov 1985)
and from a late helium shell- ash in a CO white dwarf
(Iben et al. 1983, Iben & McDonald 1995). Models de-
rived from both scenarios also predict evolutionary tracks
that are overluminous compared with V652 Her. However,
in contrast to the merger of a CO and He white dwarf, re-
cent models for the merger of two helium white dwarfs
(Saio & Jeery 2000) have successfully reproduced nearly
all of the observed properties of V652 Her.
Consequently, V652 Her provides a very important test
for stellar evolution and pulsation theory. Being compara-
tively bright, may also allow sensitive tests of the physics
of stellar pulsation and evolution and of radiative transfer
in pulsating star atmospheres. The observations presented
in this paper were obtained in order to signicantly rene
results obtained previously. They have also precipitated
the development of powerful new tools for the analysis of
stellar spectra.
2. Observations
2.1. High resolution optical spectroscopy
Observations were made with the William Herschel
Telescope of the Isaac Newton Group on La Palma dur-
ing 3 hours of service time on the night of 1998 July 16.
Spectra were obtained using a 1200 line/mm grating and
the EEV10 CCD on the blue arm of ISIS and a slit-width
of 0:7 00 yielding a nominal (2 pixel) resolution R=10 000.
Repeated integrations of 100 seconds yielded 59 spectra of
the target, with a typical signal-to-noise (1 ) ratio of 100
in each spectrum. Integrations were interrupted every 40
minutes to obtain comparison spectra of a copper-argon
lamp. The journal of observations is re ected by the he-
liocentric Julian times given in Table 1. These times have
been converted to pulsation phase using the most recent
quartic ephemeris (Kilkenny et al. 1996).
The stellar spectra were bias subtracted, atelded,
sky subtracted, optimally extracted to one dimension us-
ing figaro data reduction software. The comparison lamp
frames were interpolated linearly in time to provide a
wavelength calibration frame corresponding to each stel-
lar observation. Both stellar spectra and the interpolated
comparison lamp spectra were calibrated and linearized in
order to provide an independent check of the subsequent
velocity measurements.
Each individual stellar spectrum was normalized with
respect to the local continuum. This local continuum was
dened, for each spectrum, by tting an 11th order poly-
nomial to data dened by 23 spectral windows judged to
be, as far as possible, free of signicant absorption lines.
A further correction to the continuum was applied during
the spectral tting procedure discussed in Sect. A.
Table 1. Observational data for V652 Her, including WHT
Run number, heliocentric Julian time of observation (HJD),
pulsation phase () according to the quartic ephemeris of
Kilkenny et al. (1996), heliocentric radial velocity (v), astrocen-
tric radial velocity ( _
r) assuming p from Eq. 4, radial displace-
ment (ôr), surface accleration (r), eective temperature ( Te ),
eective surface gravity (log ge ), and true gravity at stellar
surface ( log g). Around   0:15, the sum ge  r becomes
negative for reasons discussed in Sect. 6, hence log g = NaN.
2.2. IUE and visual spectrophotometry
Although the high-resolution spectroscopy is suôcient to
make a completely self-consistent and independent mea-
surement of the mass of V652 Her, important additional
information is available from optical and ultraviolet spec-
trophotometry.
Johnson V-band photometry
(Kilkenny & Lynas-Gray 1982) were used in two ways.
In the rst instance they were combined with eective
temperatures measured spectroscopically to provide mea-
surements of angular diameter at much higher phase reso-
lution. In the second they were combined with Stromgren
photometry (also from Kilkenny & Lynas-Gray 1982)
and with ultraviolet data to provide phase-resolved
spectrophotometry eectively covering the wavelength
interval 1150 to 5500  A.
Several spectra of V652 Her were obtained with
IUE (cf. Paper II). All available spectra were down-
loaded from the IUE Newly-Extracted Spectra (INES,
Rodriguez-Pascual et al. 1999) archive web server in
February 2000. The IUE data do not sample V652 Her's
pulsation cycle evenly. We analyzed the data where we
could nd SWP (1150  A <  < 1980  A) and LWR (1850  A
<  < 3350  A) spectra measured at similar phases. The
phase bins chosen and the IUE spectra used are listed in
Table 3 in Sect. 4. The phases listed for each spectrum
were calculated using the ephemeris of Kilkenny et al.
(1996). When preparing the spectra we used the SWP
data in the region where SWP and LWR spectra overlap
in wavelength.
2.3. Infrared spectroscopy
A low dispersion J-band spectrum of V652 Her was ob-
tained using a cooled grating spectrometer (CGS4) on
the United Kingdom Infrared Telescope (UKIRT) on 2000
June 07. With a 2-pixel spectral resolution of  900, the
entire interval from 0.98 to 1.23 m. As far as we know,
this is the rst infrared spectrum of a B-type extreme he-
lium star to be published. Tha data are presented and
discussed brie y in section 5.
3. Radial Velocities
Radial velocities (v i ) were measured by cross-correlating
individual spectra with respect to a template spectrum.

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 3
Table 1. Variable properties from 1998 spectroscopy of V652 Her: see opposite page for legend
Run HJD {  v _
r ôr  r Te log ge log g
2451010 km s 1  km s 1 10 5 km km s 2 kK  (cgs)  (cgs)
486 0.4376 0.107 34.94 1.11 -38.74 -1.191 0.125 25.23 0.09 3.61 0.01 {NaN
487 0.4394 0.123 21.17 0.76 -19.61 -1.235 0.163 25.10 0.10 3.72 0.01 {NaN
488 0.4412 0.140 -0.86 0.81 11.20 -1.242 0.171 25.19 0.10 3.76 0.01 {NaN
489 0.4430 0.157 -16.55 1.29 33.03 -1.208 0.101 25.18 0.10 3.75 0.01 {NaN
490 0.4448 0.173 -23.27 1.07 42.34 -1.149 0.040 24.88 0.09 3.59 0.01 {NaN
491 0.4466 0.190 -25.52 0.94 45.45 -1.082 0.014 25.17 0.09 3.57 0.01 3.36
492 0.4483 0.207 -26.38 0.97 46.64 -1.011 0.002 24.74 0.09 3.46 0.01 3.44
493 0.4501 0.223 -25.86 0.74 45.92 -0.940 -0.005 24.69 0.09 3.42 0.01 3.49
494 0.4519 0.240 -25.30 0.78 45.15 -0.870 -0.004 24.10 0.09 3.33 0.01 3.42
495 0.4537 0.256 -24.87 0.68 44.56 -0.801 -0.009 23.81 0.09 3.38 0.01 3.52
497 0.4569 0.286 -22.43 0.83 41.18 -0.682 -0.011 23.68 0.09 3.39 0.01 3.56
498 0.4587 0.303 -21.29 0.39 39.61 -0.620 -0.012 22.92 0.09 3.31 0.01 3.51
499 0.4604 0.319 -19.87 0.64 37.63 -0.561 -0.014 22.81 0.09 3.36 0.01 3.57
500 0.4622 0.336 -18.10 0.61 35.18 -0.505 -0.017 23.03 0.09 3.27 0.01 3.55
501 0.4640 0.352 -16.14 0.58 32.46 -0.453 -0.014 22.53 0.09 3.25 0.01 3.50
502 0.4658 0.369 -15.02 0.60 30.90 -0.404 -0.010 22.44 0.09 3.31 0.01 3.49
503 0.4675 0.386 -13.87 0.64 29.32 -0.358 -0.009 22.20 0.08 3.37 0.01 3.50
504 0.4693 0.402 -13.10 0.62 28.25 -0.314 -0.010 22.12 0.08 3.23 0.01 3.43
505 0.4711 0.419 -11.69 0.70 26.28 -0.272 -0.009 22.31 0.09 3.26 0.01 3.44
506 0.4729 0.435 -11.12 0.75 25.50 -0.232 -0.012 21.96 0.08 3.26 0.01 3.48
507 0.4748 0.454 -8.83 0.42 22.30 -0.192 -0.015 21.75 0.08 3.21 0.01 3.49
509 0.4780 0.483 -6.37 0.45 18.87 -0.135 -0.014 21.81 0.08 3.26 0.01 3.51
510 0.4798 0.500 -4.58 0.74 16.39 -0.108 -0.015 21.51 0.08 3.20 0.01 3.49
511 0.4816 0.516 -3.01 0.74 14.20 -0.085 -0.013 21.64 0.08 3.22 0.01 3.48
512 0.4833 0.533 -1.63 0.69 12.27 -0.065 -0.011 21.76 0.08 3.23 0.01 3.46
513 0.4851 0.549 -0.50 0.68 10.68 -0.047 -0.008 21.58 0.08 3.23 0.01 3.40
514 0.4869 0.566 0.13 0.68 9.81 -0.031 -0.010 21.29 0.08 3.20 0.01 3.42
515 0.4887 0.582 1.76 0.71 7.52 -0.018 -0.014 21.38 0.08 3.20 0.01 3.48
516 0.4904 0.599 3.31 0.52 5.36 -0.008 -0.017 21.28 0.08 3.22 0.01 3.53
517 0.4922 0.616 5.57 0.46 2.19 -0.002 -0.015 21.41 0.08 3.15 0.01 3.47
518 0.4940 0.632 6.65 0.68 0.68 0.000 -0.016 21.27 0.08 3.22 0.01 3.52
519 0.4958 0.649 9.18 0.48 -2.87 -0.002 -0.010 21.32 0.08 3.21 0.01 3.42
523 0.5016 0.703 11.49 0.70 -6.09 -0.024 -0.008 21.36 0.08 3.22 0.01 3.39
524 0.5034 0.720 12.83 0.69 -7.97 -0.035 -0.007 21.62 0.08 3.26 0.01 3.39
525 0.5052 0.736 12.99 0.67 -8.20 -0.048 -0.015 21.31 0.08 3.24 0.01 3.51
526 0.5070 0.753 16.10 0.68 -12.55 -0.064 -0.021 21.26 0.08 3.18 0.01 3.56
527 0.5087 0.770 17.58 0.73 -14.61 -0.084 -0.014 21.30 0.08 3.19 0.01 3.46
528 0.5105 0.786 19.07 0.48 -16.70 -0.108 -0.020 21.43 0.08 3.17 0.01 3.54
529 0.5123 0.803 21.89 0.44 -20.61 -0.137 -0.023 21.86 0.08 3.16 0.01 3.58
530 0.5141 0.819 24.24 0.74 -23.89 -0.171 -0.019 21.61 0.08 3.21 0.01 3.55
531 0.5159 0.836 26.05 0.72 -26.41 -0.210 -0.012 21.81 0.08 3.23 0.01 3.46
532 0.5176 0.852 26.92 0.67 -27.62 -0.251 -0.004 21.90 0.08 3.19 0.01 3.29
533 0.5194 0.869 26.94 0.64 -27.64 -0.294 -0.010 22.16 0.08 3.28 0.01 3.47
535 0.5235 0.907 30.69 0.67 -32.85 -0.400 -0.013 22.92 0.09 3.29 0.01 3.51
536 0.5253 0.923 31.59 0.65 -34.10 -0.451 -0.010 22.74 0.09 3.35 0.01 3.52
537 0.5270 0.940 32.97 0.67 -36.01 -0.505 -0.018 23.80 0.09 3.36 0.01 3.61
538 0.5288 0.957 35.49 0.85 -39.50 -0.564 -0.014 24.00 0.09 3.36 0.01 3.57
539 0.5306 0.973 36.04 0.86 -40.26 -0.625 -0.006 24.53 0.09 3.41 0.01 3.50
540 0.5324 0.990 36.80 0.81 -41.32 -0.687 -0.012 24.60 0.09 3.39 0.01 3.56
541 0.5341 1.006 38.65 0.72 -43.88 -0.753 -0.018 24.75 0.09 3.38 0.01 3.62
542 0.5359 1.023 40.73 0.62 -46.75 -0.822 -0.008 25.49 0.08 3.49 0.01 3.60
543 0.5377 1.039 40.52 0.65 -46.46 -0.894 -0.001 25.60 0.08 3.56 0.01 3.57
544 0.5395 1.056 40.92 0.56 -47.01 -0.966 -0.015 25.74 0.08 3.50 0.01 3.67
545 0.5413 1.072 43.79 0.50 -50.97 -1.041 0.013 25.40 0.09 3.57 0.01 3.37
547 0.5444 1.102 36.77 0.64 -41.27 -1.167 0.054 25.99 0.09 3.62 0.01 {NaN
548 0.5462 1.118 27.11 1.04 -27.88 -1.220 0.140 25.24 0.10 3.72 0.01 {NaN
549 0.5480 1.135 5.90 0.35 1.73 -1.240 0.183 25.47 0.10 3.83 0.01 {NaN
550 0.5497 1.151 -13.21 1.32 28.40 -1.217 0.123 25.74 0.10 3.90 0.01 {NaN
551 0.5515 1.168 -21.16 0.97 39.43 -1.165 0.072 25.10 0.09 3.64 0.01 {NaN

4 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
Fig. 1. The radial velocity curve of V652 Her (top). Vertical
lines represent the errors from table 1. Also shown are the ab-
sorption line widths as represented by the ccf width (FWHM,
middle) and the residual shifts of the interpolated comparison
arcs (bottom).
The procedure included the subtraction of the continuum
and the conversion of the wavelength scale to logarithmic
units, before calculation of the cross-correlation function
(ccf). Several strong lines, namely He i 4388,4471,4921  A,
H and H , were excluded. The ccf was then converted to
velocity units and the position and width of its peak were
measured by tting a Gaussian to those data within the
peak having values between 0.3 and 1.0.
The exercise was repeated using the interpolated com-
parison lamp spectra. Small systematic shifts were ob-
served within each continuous run, with larger shifts oc-
curring between runs (Fig. 1). In principle, these shifts
could have been applied to the velocity data. However
they are substantially smaller than the formal errors in
the stellar velocities, and their origin is not entirely clear.
Fig. 2. The run of Te , log ge and v sin i as a function of
phase as derived from the high-resolution spectra. The individ-
ual data for Te and log ge are given in table 1. The values
of v sin i represent the formal solution from the free-parameter
t; the excess broadening around minimum radius (  0:15)
is dicussed in the text. Vertical bars represent the formal mea-
surement errors. The data are also shown folded by 1 cycles
(dots) to show the phase overlap.
The template adopted for the stellar ccf's was the
spectrum for run 518, corresponding to  = 0:633 and
very close to maximum radius (Paper II). Here, the pho-
tosphere is stationary and line distortions introduced by
the center-to-limb dierence in the projected radial ve-
locity are minimal. The radial velocity of the template
v T was measured initially by cross-correlation with a syn-
thetic spectrum computed for the (stationary) model at-
mosphere described in Paper IV, and subsequently with
the best-t synthetic spectrum described in Sect. 4. The
individual and template velocities were combined and cor-
rected to the heliocentric frame, v i = v i +vT v  , where
v is the correction for the earth motion. The results are

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 5
Fig. 3. The run of Te versus log ge (with error bars) and
log g(). The model grid used by sfit is represented by dots.
The loci of previous results for V652 Her are shown as II
(Paper II: an ellipse indicating the total range of Te and the
error in log g), and IV (Paper IV: an error ellipse showing the
location of the phase-averaged spectrum).
shown in Table 1 and in Fig. 1. The errors shown are the
formal errors in v i given by the least squares Gaussian t
to the ccf peaks. The error in v T is 0:92 km s 1 .
The mean or systemic radial velocity (v ? ) is deter-
mined by the condition that the integral of the velocity
relative to the center of mass over a complete pulsation
cycle must vanish:
Z 1
0
(v 0 v ? ) dt
d d = 0: (1)
From the current data we nd v ? = 7:14  0:92 km s 1 .
This result is independent of the velocity projection fac-
tor (Sect. 6) and the error is dominated by the measure-
ment of vT . It is tempting to compare this result with that
of (Jeery & Hill 1986 = Paper III), where systemic ve-
locities of 1.25 km s 1 and 3.51 km s 1 were deduced from
data obtained from 1979{1982 and in 1984 respectively.
However it may be premature to suggest that these dif-
ferences represent any more than major improvements in
detector and measurement technology; the earliest data
were calibrated against an F-star velocity standard and
the 1984 data were calibrated by tting parabolae to se-
lected lines in a template spectrum which had been inte-
grated over several pulsation cycles.
A cursory examination of the spectra as a function
of phase quickly demonstrated large changes in both the
strengths and widths of several lines, particularly around
phases corresponding to minimum radius. The variations
in line width are re ected in the widths of the ccfs
measured above (Fig. 1). Several line-broadening mech-
anisms are in operation and are discussed discussed below
(Sect. A.5).
4. Temperatures, Gravities and Abundances
The analysis of such a series of spectra entails tting
a large quantity of data with theoretical models that
have many free parameters including eective tempera-
ture ( T e ), surface gravity ( log g), microturbulent and
rotational velocity ( v t , v sin i) and elemental abundances
(n). This tting has been achieved through the develop-
ment of a suite of modelling and tting programs, in-
cluding sterne, spectrum, lte lines, ffit, sfit and
sfit synth. These are described more fully in appendix
A.
4.1. The model grid
Using sterne and spectrum, grids of model atmo-
spheres, spectral energy distributions and high-resolution
synthetic spectra were calculated for use with the tting
programs. After iteration, the nal composition adopted
as input for the grid of model atmospheres and synthetic
spectra comprised nH = 0:01; n He = 0:99, nC = 0:00004
and nN = 0:0025. All other elements were assumed to have
solar-like relative abundances. The grid covered the ranges
T e = 17 000(1 000)30 000 K and log g = 2:75(0:25)4:25
(cgs).
4.2. T e , log g e , v sin i
Procedure sfit was applied to the 1998 spectroscopy. The
central 2  A of each of the strongest He i lines was excluded
from the  2 minimization because current helium-rich
model atmospheres consistently fail to match the cores
of these lines. This is true for both variable and non-
variable stars (cf. Heber 1983). Note that for a pulsating
star, this procedure measures the eective surface grav-
ity ( g e ), representing the sum of the true surface gravity
g = GM=r 2 and any other forces  r acting on the stellar
photosphere,
g e = g +  r: (2)
The nal results for T e and log g e are shown in table 1
and in Fig. 2. The results for v sin i are also shown in
Fig. 2. The behaviour of g e and g as a function of T e
through the pulsation cycle are compared with previous
measurements for the average values of these quantities in
Fig. 3.
The robustness of these measurements was checked by
removing a small number of lines, including He ii 4686  A,
from the t. The change in T e was less than 100K.
It is expected that v sin i should be approximately
constant for a given star, although conservation of an-
gular momentum may provoke a small increase in angu-
lar velocity as a pulsating star approaches minimum ra-
dius. It might seem logical, therefore, to adopt a constant
value of v sin i for all spectra and treat any variation in
other broadening mechanisms separately. However, the ad-
ditional broadening proles are not known a priori, while
solving for \ v sin i" explicitly makes an intrinsic and nec-

6 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
Fig. 4. A sequence of line proles demonstrates line broadening around minimum radius. The pulsation phase for each spectrum
is shown on the left hand side. A single spectrum obtained around maximum radius ( = 0:633) is shown for comparsion. Line
proles are shown for Si iii, He i, He ii and other ions. The bar in the left hand panel representing 20% of continuum indicates
the vertical scale. The wavelength scale is the same in all panels; tickmarks are separated by 2.5  A. Wavelengths have not
been transformed, so the rapid acceleration around minmum radius is visible as a change from a red to a blue shift. Note the
behaviour in the line core of He i 4713  A, where the line core around phases 0.125 and 0.131 becomes signicantly broader.
This behaviour is exactly mimicked by He i 4437  A (not shown).
essary allowance for variations or errors in other parame-
ters which aect the apparent linewidths.
Thus, around maximum radius (0:3    0:9) v sin i
remains steady at  9  2 km s 1 , dependent upon the
adopted v t = 9 km s 1 . However, v sin i around minimum
radius was considerably higher than this. On inspection,
the spectral lines at phases 0:10 <   <  0:20 are system-
atically broader than at other phases (Fig.4). This does
not appear to be due to projection broadening, the latter
is a continuous function of expansion/contraction veloc-
ity and not acceleration. The observed eect far exceeds
that of acceleration broadening, which was never greater
than 10 km s 1 for a 100s exposure. Having considered ev-
ery other possible source of line broadening in the current
model, it is conjectured that dynamical processes at these
phases violate the equilibrium assumption. There is ev-
idence, for example, of doubling in some lines as might
indicate the passage of a shock wave. This will be dis-
cussed further in Sect. 7. The failure of the models to
correctly measure v sin i is re ected by the negative val-
ues for g indicated in table 1. Around minimum radius,
log g e is presumably underestimated in comparison with

r as a consequence of the breakdown of one or more equi-
librium conditions assumed in the model atmosphere.

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 7
Fig. 5. Sections of the average normalized spectrum of the pulsating helium star V652 Her near maximum radius are shown
(histogram) together with the synthetic spectrum (smooth curve) calculated using Te = 22 000 K; log ge = 3:25(cgs); v t =
9 km s 1 ; v sin i = 7 km s 1 and abundances given in Table 2. Selected strong lines have been labelled.
Table 2. Atmospheric abundances of V652 Her, two similar gravity helium stars and the Sun. Abundances are given as log n,
normalised to log n = 12:15.
Star H He C N O Ne Mg Al Si P S A Fe Ref.
log n
V652 Her 9.61 11.54 7.29 8.69 7.58 7.95 7.80 6.12 7.47 6.42: 7.05 6.64 7.04
(1999) 9.38 11.54 7.14: 8.93 7.54 8.38: 7.76 6.49 7.49 5.35 7.44 6.73 7.40 1
 0.07 0.27: 0.06 0.08 0.40: 0.36 0.19 0.21 0.22 0.11 0.19 0.15
BX Cir 8.1 11.5 9.02 8.4 8.0 7.2 6.0 6.8 5.0 6.6 6.6 2
HD144941 10.3 11.5 6.80 6.5 7.0 6.1 4.8 6.0 5.7 3
Sun 12.0 11.0 8.55 7.97 8.87 8.08 7.58 6.47 7.55 5.45 7.23 6.56 7.50 4
Notes. : value uncertain.
References. 1: Paper IV 2: Drilling et al. 1998, 3: Harrison & Jeery 1997, Jeery & Harrison 1997, 4: Grevesse et al. 1996.

8 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
4.3. v t and abundances
In orded to measure the chemical composition in the atmo-
sphere of V652 Her, sfit synth was applied to ve spec-
tra close to maximum radius (run numbers 510, 512, 514,
516 and 518, table 1) and also an average spectrum formed
from run numbers 510 { 519. The wavelength scales of all
spectra had been transformed into the laboratory refer-
ence frame prior to analysis. Near maximum radius, T e
and log g vary suôciently slowly that forming such an av-
erage spectrum introduces negligible systematic errors. It
does give a factor of three improvement in signal-to-noise
ratio.
The value for microturbulent velocity, v t , was obtained
by allowing it to vary at the same time as either the oxy-
gen or the nitrogen abundance. Working with the aver-
age spectrum, values of 8.7 and 10.3 km s 1 were ob-
tained from the nitrogen and oxygen lines respectively.
Previously, v t = 5 km s 1 was obtained from O ii lines
alone (Paper IV), but this was from an average spectrum
obtained around the pulsation cycle, including phases
around minimum radius. The higher values are more con-
sistent with measurements of v t in other helium star at-
mospheres. There is virtually no dierence between abun-
dances derived with either 8.7 or 10.3 km s 1 and we adopt
9 km s 1 in the current analysis.
The abundances given by sfit synth are shown
in table 2, where they are compared with the re-
sults obtained previously for V652 Her (Paper IV) and
for related hydrogen-decient stars (Drilling et al. 1998,
Harrison & Jeery 1997, Jeery & Harrison 1997). There
are reductions of up to a factor of two in the abundances
of most species, primarily as a result of using a higher
value for the microturbulence.
While all changes are within 3 of the previous values,
the previous error estimates for some individual species
appear to have been optimistic, possibly as a consequence
of adopting formal values, but probably because they do
not include the systematic eect of v t . The formal errors
in the abundances given by sfit synth are unrepresen-
tatively small, typically 0.04 dex, although they do repre-
sent the spectrum-to-spectrum variation very well. They
do not take into account errors in the atomic data, and
systematic errors due to the adopted model atmospheres,
v t , T e , etc.
An example of the quality of the t between theoreti-
cal and observed spectrum is shown in Fig. 5. The astro-
physical signicance of the peculiar surface composition
of V652 Her, which consists almost entirely of helium pro-
duced by the CNO-process, has already been discussed at
length (Paper IV).
The measurement for phosphorus is unreliable.
While our synthesis comprises some 17 phosphorus
lines in the observed wavelength range, only two
lines ( P ii 4499.2 and 4589.9  A) are clearly resolved.
Contributions from very weak lines and lines in blends
is likely to be responsible for skewing the abundance mea-
sured by sfit synth. Given either the adopted abundance
Fig. 6. IUE and visual spectrophotometry of V652 Her near
maximum radius ( = 0:59, bold histogram), with a series of
model ux distributions, Te = 18; 20; 22kK (dotted lines).
The observed uxes have been binned by 20  A and dereddened
by the amounts shown. The models have been normalized to
the observed V magnitude. The best t solution had Te =
20:1kK; EB V = 0:06.
or one tenth of this value, both lines are too strong in the
model compared with the observation (Fig. 5). The older
value, based on stronger lines, should be preferred for the
present. An alternative measurement of the phosphorous
abundance could be obtained by removing weaker lines
from the linelist input to sfit synth. We remain suô-
ciently uncertain of the correctness of our models that this
seems premature when a better result should be obtained
from lines further in the blue.
4.4. T e ; ; EB V
The grid of sterne line-blanketed model atmospheres de-
scribed above was used with the tting program ffit to
measure eective temperatures T e , angular diameters ,
and interstellar extinction EB V , for each of the combined
IUE spectra and from the Stromgren photometry.
We found that the log g used in the model atmo-
spheres makes a negligible dierence in the temperature

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 9
Table 3. IUE spectra and optical photometry used and temperatures and angular radii found in phase bins for V652 Her,
assuming EB V = 0:06.
phase SWP SWP LWR LWR u v b V Te   
(bin spectrum phase spectrum phase (kK) (10 11 rad)
0.11 09451 0.1274 15921 0.1029 10.421 10.502 10.494 10.558 22.15 0.25 2.93 0.014
0.31 09444 0.3263 04883 0.3011 10.450 10.514 10.502 10.561 21.24 0.23 3.02 0.014
0.38 05633 0.3724 15922 0.3877 10.457 10.507 10.493 10.551 20.81 0.21 3.08 0.014
09448 0.3970
0.50 09453 0.5305 15926 0.4770 10.471 10.508 10.493 10.551 20.40 0.20 3.13 0.015
0.59 09449 0.6180 15919 0.5730 10.487 10.516 10.501 10.559 20.08 0.19 3.16 0.016
0.74 09445 0.7373 15927 0.7531 10.490 10.520 10.505 10.563 20.04 0.19 3.16 0.015
0.80 09454 0.7914 15920 0.8187 10.485 10.518 10.503 10.561 20.41 0.20 3.11 0.015
0.95 05799 0.9467 15924 0.9526 10.400 10.450 10.460 10.520 21.42 0.22 3.07 0.014
09446 0.9500
and angular radius found by ffit, so in the end only the
log g = 3:25 models, appropriate to most of the pulsation
cycle, were used.
In the analysis of the IUE data we used the spectral re-
gions 1229  A   3200  A. These wavelength cutos were
chosen to remove regions where interstellar Ly (short
wave) and noise (long wave) caused trouble in the tting
procedure.
We initally ran ffit with EB V as a free parameter
and with dierent combinations of data: a) IUE uxes
only, b) IUE uxes + V magnitude, c) Stromgren pho-
tometry + V magnitude, d) IUE uxes + Stromgren pho-
tometry + V magnitude. Due to a coincidence between
strong metal-blocking in the stellar spectrum and the in-
terstellar absorption band at 2175  A, ts (a) and (b) were
unable to establish the exinction reliably, EB V = 0 gave
the best ts. With the addition of Stromgren photometry
and considering data obtained between phases 0.3 and 0.9
(i.e. away from minimum radius), ts (c) and (d) gave
EB V = 0:061  0:001 and EB V = 0:059  0:001 respec-
tively. We here adopt EB V = 0:06.
This is slightly dierent to EB V = 0:07 found in pre-
vious work (e.g. Paper II). The likely source of the dif-
ference is that our analysis includes line blanketing. In
these analyses it can be diôcult to distinguish between
line blanketing in the star and interstellar extinction. Both
eects tend to depress the observed ux around 2175  A.
Using line blanketing in the models means less extinction
is needed to match the synthetic spectra to the observa-
tions. Fits to the observed ux distribution near maximum
radius are shown in Fig. 6.
The temperatures and angular radii found with the
specied input data are shown in table 3 and Fig. 13. We
nd the mean temperature through the pulsation cycle
to be 20.0 kK. This value is lower by 3.0 kK than that
obtained from the ionization equilibrium in the optical
spectroscopy.
A likely reason for the discrepancy is the treatment
of line opacity ( l ) in the model atmospheres. The line
lists used to construct the distribution functions were far
from complete (see appendix A.1) and tailored for extreme
helium stars. Thus the hydrogen Lyman line opacity will
have been underestimated by a factor  10 and the carbon
line opacity considerably overestimated. A comparison of
the low-dispersion uxes from the models (sterne) with
synthetic high-resolution optical spectra (spectrum) in-
dicates that  l could be too low by a factor of as much as
two. Increasing the total  l would increase back-warming
in the atmosphere, raising the temperature of the con-
tinuum forming layers relative to that of the line-forming
layers.
As a simple experiment, a model atmosphere with
T e = 22:0 kK and log g = 3:50 was computed with
 l multiplied by two at all wavelengths. The theoreti-
cal ultraviolet spectral energy distribution and the high-
resolution otical spectrum predicted by this model were
compared with the standard models using ffit and sfit.
The experimental energy distribution was measured to
have T e = 20:5 kK and the high-resolution spectrum
gave T e = 21:8 kK, log g = 3:39. Consequently, increas-
ing  l in the model grid would have had the opposite eect
on the measurements for V652 Her, increasing both T e
and log g, and reducing the discrepancy between the two
measurements of T e . It is clear that a more appropriate
treatment of the line opacity is urgently required.
4.5. Lyman  and EB V
An independent measurement of the extinction can be
obtained from the interstellar contribution to the hydro-
gen Ly line prole. Two high-resolution observations of
V652 Her were obtained with the SWP camera on IUE in
1983 (image numbers SWP19841 and SWP 19966). The
reduced and calibrated images have been recovered from
the INES data archive and an average spectrum has been
constructed. The region around Ly is shown in Fig. 7.
The predicted stellar contribution to Ly is compara-
tively weak (dashed line in Fig. 7), and is obscured by geo-
coronal Ly emission and the interstellar Ly absorption
prole. The latter can be obtained as a function of the hy-
drogen column N(H) (Groenewegen & Lamers 1989) and
hence of the extinction EB V (Bohlin et al. 1978). The
upper-left panel in Fig. 7 shows the contributions of in-
terstellar Ly alone, and suggests that values of EB V

10 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
Fig. 7. IUE high-resolution spectrum of V652 Her around hydrogen Ly convolved with a 0.2  A Gaussian (heavy line, all panels).
Geocoronal emission has been removed. The predicted stellar contribution to Ly (dashed line) convolved with interstellar
absorption computed for EB V=0.05, 0.10 and 0.15 is shown in the upper-left panel (thin lines). A synthetic spectrum for the
whole region, convolved with interstellar absorption computed for EB V=0.07 only is shown in the lower panel, also convolved
with a 0.2  A Gaussian (thin line). The upper-right panel shows the central 20  A of the Ly prole compared with similar models
for EB V=0.05, 0.07 and 0.10. The lowermost model corresponds to the largest value of EB V .
between 0.10 and 0.15 might be appropriate. However, it
is necessary to consider the metal-line spectrum as well in
order to establish the true Ly prole - as is suggested by
the apparently high continuum placement.
The continuum level has been estimated by con-
structing an experimental synthetic spectrum for V652
Her around Ly. We assumed a typical model atmo-
sphere corresponding roughly to maximum radius and
measured abundances from the optical analysis, except
for that of silicon which was reduced by 1 dex in or-
der to approximately match the prole of Si iii 1206.5  A.
Abundances of additional elements were assumed to be so-
lar. A linelist comprising some 10 000 lines between 1170
and 1260  A (Kurucz & Petryemann (1975), Kurucz 1988,
Hubeny et al. 1994) was compiled, but not critically eval-
uated. Therefore this spectrum is only statistically repre-
sentative of line absorption in the region and only useful
for estimating the continuum level and interstellar Ly
prole.
After convolution with an interstellar Ly prole for
EB V =0.07, the theoretical spectrum is found to be satis-
factorily similar to the observed spectrum (Fig. 7: bottom
panel). Allowing for some uncertainty in the metal abun-
dances and errors in the construction and choice of model
atmosphere, an error of 0:02 in EB V might be enter-
tained, but ts with EB V= 0.05 or 0.10 are demonstrably
poorer than that adopted (Fig. 7: upper-right).
5. Infrared spectroscopy
Being the rst infrared spectrum of an early-type helium
star, the UKIRT spectrum (Fig. 8) is signicant. Several
He i and two hydrogen Paschen lines are easily identi-
ed (Moore 1945). The hydrogen lines are considerably
stronger than the He i lines, despite the latter being ap-
proximately 100 times more abundant. Most remarkably,
the normally strong He i 10830  A line is undetectable.
A diôculty with analysing such data is that strong in-

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 11
Fig. 8. CGS4 J-band spectrum of V652 Her showing He i (la-
belled by transition) and hydrogen Paschen lines (P ; ô).
Fig. 9. LTE model spectrum for V652 Her matching the
UKIRT J-band spectrum in Fig. 8. The model parameters
are shown (top). He i 10830  A, diuse He i lines and hydro-
gen Paschen lines (P ; ô) are also marked. The model uxes
have been normalized to unity at 1m and smoothed with a
FWHM=0.6nm Gaussian to emulate the instrumental resolu-
tion of the UKIRT spectrum.
frared lines of hot stars are considered to be aected by
departures from LTE. Nevertheless, an LTE model may
demonstrate where attention should be focused.
spectrum has been substantially extended by
including Stark broadening data (electron damping
widths) for infrared lines calculated from the im-
pact approximation (Dimitrijevic & Sahal-Brechot 1989,
Dimitrijevic & Sahal-Brechot 1990). These are tabulated
as a function of electron density and temperature.
Calculations were made using both constant values (T =
20 000 K, log n e = 15) and interpolated values. A small dif-
ference in the line proles was found for the diuse lines,
leading us to adopt the interpolated values.
The theoretical spectrum computed from a T e =
22 000, log g = 3:5 model atmosphere with nH = 0:011
(Table 2) is shown in Fig. 9. The predicted hydrogen
lines are substantially weaker than observed { as expected
Fig. 10. The change in total radius (ôr top), the expansion
velocity ( _
r, center) and the surface acceleration (r, bottom)
of V652 Her as a function of pulsation phase. The vertical
bars represent the propagated measurement errors. The dots
represent the same data folded over 1 cycle.
but contrary to observation. The diuse He i lines are
the strongest lines, again as expected and broadly in
agreement with observation. He i 10830  A is predicted
to be stronger than the neighbouring 3 3 P 6 3 S line,
which can be detected in the UKIRT spectrum. Why it
is not detected will require high-resolution observations
of He i 10830  A around the pulsation cycle and a con-
sideration of how departures from LTE aect this line in
particular.
6. The radius of V652 Her
6.1. Radial velocity transformation
Direct methods for measuring the radii of pulsating stars
require a transformation from the measured (v) to the

12 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
Fig. 11. The change in relative radius (
p
g0=g 1 = ôr=r0)
as given by the surface gravity method is plotted against the
total change in radius (ôr, lower panel). The total stellar radius
corresponding to the reference phase (r0) is given by the inverse
slope of the best t line. Lines with gradients corresponding to
1 and 2 Rare also shown (dashed). The corresponding true
surface gravity g obtained from Eq. 2 is shown in the upper
panel. Measurements close to minimum radius and marked `'
were omitted from the regression.
actual radial velocity ( _
r) of the stellar surface, and hence
to the integrated displacement (ôr). The integration over
the stellar disk of a spherical expansion projected into the
line of sight has been examined at length during the last
century (e.g. Shapley & Nicholson 1919, Parsons 1972),
but in general only for the case of Cepheids. The behaviour
of the projection factor p has only recently been examined
for hydrogen-decient early-type pulsators by Monta~nes
Rodriguez & Jeery (2001a). They nd that for radial
velocities of V652 Her measured using the same cross-
correlation procedure as here (Sect. 3), _
r is given by:
_
r = p(v v) = pôv (3)
if
p = 1:402 0:028 ; (4)
where = j _
rj=w 1=2 is the expansion velocity scaled by the
width (in velocity units) at half depth of the line (wave-
length ) w 1=2 =
 1=2 c=. The variation with velocity
was not unexpected; for example Parsons (1972) showed
that for isolated lines in Cepheids, p depends on linewidth
(
 1=2 = 0 ) and shift (ôv),
p = 1:37 0:039 0
c
 1=2
jôvj
 1:37 0:042 :
(5)
It is important to note that an increase in p results in a
proportional increase in the radius measured directly from
combined radial velocity and angular diameter variations.
Applying Eqs. 3 and 4 to the data for v in Table 1
yields _
r. The acceleration  r and radius change ôr, dened
as

r i = _
r i+1 _
r i 1
t i+1 t i 1
(6)
and
ôr i =
Z t i
t 0
_
rdt (7)
are then derived; t i are the times of observation. The true
surface gravity can then be derived from the apparent sur-
face gravity using Eq. 2. The derived quantities _
r;  r; ôr and
g are given in Table 1.
6.2. Radius from surface gravity measurements
Classical methods such as Baade's method and the Baade-
Wesselink method for measuring the radii of radially pul-
sating stars depend on photometry to provide the angular
radius variation as a function of phase. A substantial vol-
ume of visual and ultraviolet photometric data for V652
Her is already available and has been used to good eect
(Paper II). We have reanalyzed this data (Sect. 6.4), in
order to ensure that our own methods are fully consistent
with these earlier results. Further progress can no doubt
be achieved with the addition of infrared photometry to
further constrain the total ux measurement.
However, to supplement Baade's approach, we here
propose and apply a novel method for measuring the an-
gular radius variation in a radially pulsating star. The ad-
vantage of this method for us is that it is completely inde-
pendent of any previous measurement or analysis and de-
pends only upon observational material already presented
in this paper. The disadvantage is that the result may not
be so precise.
The key to this method is the precise measurement of
surface gravity as a function of phase. The graph of dis-
placement ôr = r r 0 against
p
g 0 =g 1  (r r 0 )=r 0 ,
where the subscript 0 refers to a reference phase such as
maximum radius, should then be a straight line with gra-
dient r 0 .
The surface gravity method has been applied to the
data of Table 1. Data points with 0:05 <  < 0:30 (around
minimum radius) have been excluded because the gravity
measurement appears to become unreliable as the equilib-
rium assumption breaks down.
As reference phase, we have adopted  0 = 0:6260:027
representing the mean phase of runs 512{525. Values for
r 0 ; g 0 and  0 are thus also dened at this phase, so that

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 13
Table 4. Dimensions of V652 Her using three dierent methods employing surface gravity (g), visual magnitude (V ) and
ultraviolet spectrophotometry (IUE). The results are presented in two groups, the rst referring to the stellar dimension at
maximum radius 0 , the second to the cycle-averaged dimensions. Previous results (Paper II) are shown for comparison.
g  V  IUE  Paper II 
0 0.626 0.005 0.626 0.005 0.59 y0.856
Te0 /kK 21.42 0.16 21.42 0.16 20.08 0.19 23.20 1.40
0=10 11 rad 3.10 0.02 3.16 0.02 2.97 0.10
log g 0 /cm s 2 3.46 0.05 3.46 0.05 3.46 0.06
R0= R 1.06 0.18 1.32 0.003 2.37 0.16
L0= L 211 50 331 5 821 80
M=M 0.11 0.03 0.18 0.02 0.59 0.09
d/parsec 963 6 1693 115
EB V 0.06 0.01 0.07
< Te >/kK 22.93 0.01 22.93 0.01 20.95 0.07 23.45 1.32
<  > =10 11 rad 2.97 0.00 3.07 0.01
< log g >/cm s 2 3.50 0.06 3.48 0.12 3.48 0.12 3.7 0.2
< R > = R 0.99 0.02 1.26 0.00 2.31 0.02 1.98 0.21
< L > = L 244 8.4 393 1 919 14 1070 340
< M > = M 0.11 0.02 0.17 0.05 0.59 0.18 0.7 +0:4
0:3
< d >/parsec 957 1 1695 16 1500 100
y reference phase (RP).
log g 0 = 3:46 0:05. The regression shown in Fig. 11 gives
r 0 = 1:06  0:18 R .
Even with the quality of the present data, this method
measures the radius to no better than 20 per cent and
possibly worse. It is susceptible to errors in measuring
the He i line proles, to systematic errors in the model
atmopsheres and in the atomic data for He i. We cannot
therefore rely on this measurement alone.
6.3. Radius from spectroscopic temperature and visual
magnitudes
Since we have measured the eective temperature spec-
troscopically, an alternative approach is to measure the
angular radius using the visual light curve of Kilkenny
& Lynas-Gray (1982, Fig. 12). This is achieved by nor-
malising the V-band ux from a model atmosphere with
eective temperature T e () to the observed visual mag-
nitude V (). The resulting angular radius () (Fig. 12)
can then be used, as before to dene the radius  0 at ref-
erence phase  0 . The stellar radius is obtained from
(  0 )
 0
 (r r 0 )
r 0
= ôr
r 0
(8)
where ,  0 and ôr are known. The regression shown in
Fig. 12 gives r 0 = 1:325  0:003R , in reasonable agree-
ment with the result obtained from the log g measure-
ment. This method assumes that the V magnitude and
spectroscopic T e may be combined to derive the angu-
lar diameter. If the model atmospheres are correct, this
should be true.
6.4. Radius from ultraviolet and optical
spectrophotometry
The angular radii found with ffit were used with the
changes in radius found from radial velocity measure-
ments (Sect. 3) to plot ô= 0 versus ôr (Fig. 13). If all
data are used (eight points), the regression gives r 0 =
2:37  0:16R , where the uncertainty is derived from the
standard error in the least squares t to the slope. The
result is practically identical to an earlier analysis of the
same data (Paper II), given that the current r 0 and the
previous < R > are dened slightly dierently.
If EB V = 0:07 is chosen, as in previous analyses, in-
stead of 0.06, then the estimated mean temperature in-
creases but the derived radius is almost unaected. Tests
run with several extinction values between 0.03 and 0.15
did not change the estimated stellar radius by more than
0:02R . The variations were uncorrelated with the extinc-
tion used.
There is a clear dierence between the measurements
of r 0 obtained from optical data alone and that derived
here. A partial contribution to the discrepancy may be
seen in Fig. 13 where one IUE datum lies close to mini-
mum radius while the remainder lie within 0:3 cycles of
maximum radius. Hence the ôr volume is not well sam-
pled compared with the optical spectroscopy. If the stellar
photosphere at   0:1 is out of LTE, this single datum
would seriously alias the result. However, omitting it only
reduces the value of r 0 to 2:2  0:4R .
6.5. Mass, luminosity and distance
Having measured g 0 ;  0 ; r 0 and T e0 , the values of other
stellar dimensions including mass M , luminosity L and
distance d follow from standard identities. Since these re-

14 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
Fig. 12. Derivation of radius from visual photometry
(Kilkenny & Lynas-Gray 1982, top panel). The angular radius
 is estimated by tting model ux distributions correspond-
ing to the spectroscopic Te to the visual photometry (centre).
The radius may be deduced from the gradient of ô=0 with ôr
(bottom panel).
fer in general to the stellar dimensions at the reference
phase (maximum radius, subscript 0), they may be ad-
justed by integration around the pulsation cycle to give
average values for < T e >; < log g >; < r > and < L >.
The values of M and d obtained from reference phase
and cycle-average values are, as expected, the same to
within measurement errors. All of these values are given
in Table 4.
V652 Her was observed by Hipparcos (Schrijver 1997)
but the measured parallax (p = 0:90  1:77 mas) is un-
helpful although quite consistent with the distances given
in Table 4.
It is appropriate to comment on the dierence in r
derived from optical spectroscopy and visual photom-
Fig. 13. Derivation of radius from ultraviolet and visual spec-
trophotometry. The eective temperature Te (top) and angu-
lar radius  (center) obtained by tting model ux distributions
to combined IUE spectrograms and appropriate data from the
visual light curve (Kilkenny & Lynas-Gray 1982) are shown in
table 3. The values of  obtained from the visual photome-
try and spectroscopic temperatures (Fig. 12) are overplotted
(dots). The stellar radius may be deduced from the gradient of
ô=0 with ôr (bottom).
etry and that derived after including ultraviolet spec-
trophotometry. In the rst case, optical spectroscopy xes
T e and the V-band photometry xes the angular radius ;
the total ux from the star is not considered. In the sec-
ond case, the ultraviolet uxes establish T e , Since the
measurement of r depends on ô=, scaling errors should
not be important providing d=d T e is constant. However,
this quantity is  30% larger for the ultraviolet uxes
than for the optical spectroscopy which results in r be-
ing larger by a similar amount. The dierence in d=d T e
must be a consequence of systematic errors in the model

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 15
v 1
r 1
.
r .
2
00001111
0000
0000
0000
1111
1111
1111
0000
0000
0000
1111
1111
1111
00001111
00001111
u
H
v 2
surface
interior
f=0.17
f=0.12
Fig. 14. Schematic of the compression wave (dashed line) pass-
ing through the line-forming region (shaded area) in the stel-
lar rest frame (left) and in the compression-wave rest frame
(right).
atmospheres; inadequate line opacities have already been
discussed (Sect. 4.4), departures from equilibrium will be
discussed below.
7. Hydrostatic equilibrium
It has been shown that the surface acceleration of V652
Her at minimum radius is large ( 0:17 km s 2 ) and that
the absorption lines are broader than indicated by the
hydrostatic approximation. The question of whether the
latter is a valid approximation for spectral analysis has
already been introduced. With the results derived above,
it is possible to examine the question in more detail. In
particular, it is necessary to understand how the acceler-
ation of the atmosphere aects the local state variables
such as pressure p, density  and temperature T .
Consider a plane-parallel atmosphere divided horizon-
tally into two regions. The upper moves downwards with
velocity _
r 1 , the lower moves upwards (velocity _ r 2 ). The
downward ow is thus accelerated at a compression front
where it meets the upward ow. The position of the front
moves upwards (velocity u) as material ows through it
(Fig. 14). To a rst approximation, _
r 1  _
r( = 0:1) and
_ r 2  _
r( = 0:2). The compression wave velocity can be
obtained from the time ôt taken for the line-forming re-
gion to accelerate from _
r 1 to _
r 2 and the pressure scale
height H . Taking the line formation region to be at op-
tical depth   0:1 the local temperature T  20 000 K.
With log g  3:5 and the mean atomic mass   2 for
singly-ionized helium,
H = p
g = kT
gmH  2:6 10 3 km (9)
(p; ; k and mH represent pressure, density, Boltzmann's
constant and the mass of the hydrogen atom, respec-
tively). Considering that 90% of the acceleration lasts just
0.05 cycle (Fig. 10), ôt  500s. Hence
u  H=ôt  5 km s 1 (10)
Assuming the ratio of specic heats = 5=3 for conve-
nience, the local sound speed is given by
c 1 =

p

 1=2
=

kT
mH
 1=2
 12 km s 1 : (11)
Paper III obtained similar values and argued essentially
that no shock would occur because the speed of the com-
pression front was less than the sound speed. The authors
failed to appreciate that the crucial parameter is the gas
velocity relative to the compression front. Transforming
to the frame of the compression front (see Fig. 14),
v 1 = u + (_r 1 _ r 2 ); v 2 = u: (12)
The Mach number of the gas owing into the front is then
M 1 = v 1
c 1
= 104
12  8: (13)
Thus the uid ow into the front is supersonic and the
development of a shock is inevitable. Properties of the
atmosphere behind the shock can be deduced from the
Rankine-Hugoniot conditions (cf. Shore 1992, p.106f.) and
give the Mach number, gas temperature, pressure, and
density in terms of gas properties in front of the shock.
Thus, with = 5=3,
M 2
2 = ( 1)M 2
1 + 2
2 M 2
1 ( 1))
)M 2 =

M 2
1 + 3
5M 2
1 1
 1=2
 0:46
T 2
T 1
= (2 M 2
1 ( 1))(( 1)M 2
1 + 2)
(( + 1)M 1 ) 2
= (5M 2
1 1)(M 2
1 + 3)
16M 2
1
 21
p 2
p 1
= 2 M 2
1 ( 1)
+ 1 = 1
4 (5M 2
1 1)  80
 2
 1
= ( + 1)M 2
1
( 1)M 2
1 + 2 = 4M 2
1
M 2
1 + 3 = v 1
v 2
= 3:8:
(14)
This last result lies close to the strong shock limit  2 = 1 
4. The shock locally heats the uid to  400 000 K.
Adiabatic expansion will reduce this relatively quickly, but
it is not expected that hydrostatic and thermal equilib-
rium will be achieved immediately after passage of the
shock front.
From this thumbnail calculation it may be seen that
the dynamical consequences of the pulsations in V652 Her
will be profound for at least part of the pulsation cycle,
and maybe throughout. In deeper layers, where the sound
speed is higher, the compression and heating factors will
be weaker, but the radiative cooling times will also be
longer. Model atmospheres which consider radiation hy-
drodynamics will need to be constructed.
An interesting consequence of this calculation is that
temperatures  4 10 5 K in the shock front may produce
an X-ray ash once every pulsation cycle. Further calcu-
lations will demonstrate whether this could be detected
with current X-ray telescopes. Recombination lines might
also be expected to appear for a short interval each cycle;
none have been observed to date.
A more disturbing consequence is that, while it is evi-
dent that current methods of spectroscopic analysis break

16 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
down around minimum radius, the validity of the hydro-
static approximation used in the spectroscopic analysis
during the remainder of the pulsation cycle must come un-
der scrutiny. The dynamical timescale may be estimated
from free-fall through a pressure scale height,
t dyn =
s
2H
g  300s; (15)
while the thermal relaxation time may be estimated from
the sound-speed
t th = H
c 1
 200s: (16)
Both are short compared with the pulsation period (
9000 s) so that, according to these estimates, approximate
hydrostatic equilibrium should be re-established shortly
after the shock front has passed through the atmosphere.
Further diagnostics of the shock passage are expected
to be visible in the infrared, where He i and Paschen
lines are formed at higher levels in the atmosphere. High-
resolution observations with 8m class telescopes are now
capable of resolving the line proles with suôcient tem-
poral resolution to allow such a study to be made.
7.1. Non-equilibrium phenomena in V652 Her and
other pulsating stars
The occurrence of non-equilibrium phenomena should, in
fact, be expected from both observational and theoret-
ical consideration of pulsations in other stellar classes.
The doubling of metallic lines was rst seen in W Vir
(Sanford 1952) and explained by the passage of an up-
ward propagating shock front (Schwarzschild 1952) split-
ting the line forming region into two components mov-
ing in opposite directions. In terms of stellar dimensions
and pulsational characteristics, the variables most simi-
lar to V652 Her are possibly the RR Lyraes and the 
Cepheids. H-absorption line doubling during rising light in
RR Lyr is well known (Sanford 1949, Preston et al. 1965);
metallic line doubling in RR Lyr has also been estab-
lished (Preston et al. 1965, Chadid & Gillet 1996a). Very
detailed observations of these lines have enabled a va-
riety of phenomena within the pulsating atmosphere,
including turbulence and shocks, to be studied (e.g.
Chadid & Gillet 1996b, Fokin et al. 1999).
A feature of the observations of line doubling in RR
Lyr was that a resolving power of 42 000, signal-to-noise
ratio > 50 and a time resolution close to 1% of the 13.6h
pulsation period were required (Chadid & Gillet 1996a).
Moreover the intrinsic line widths, due to heavier ions and
lower T e , are much smaller than in V652 Her, making
line doubling naturally easier to detect. Therefore the evi-
dence for line broadening, at least, in our much lower res-
olution observations of V652 Her points to the existence
of non-equilibrium phenomena worthy of further study.
Other non-equilibrium phenomena include dierences
in amplitude or phase lags beween the radial velocity
curves measured from metal lines and neutral or ionized
helium lines. Such phase lags are well known in  Cepheids
(the Van Hoof eect: van Hoof & Struve 1953) and in RR
Lyr (Mathias et al. 1995). These have been looked for in
the current dataset but so far without success.
There is marginal evidence for small cycle { to { cycle
changes in the radial velocity (Paper III) and light curve
(Kilkenny et al. 1996) of V652 Her. The long-term cover-
age of either has so far been insuôcient to detect anything
like the Blazhko eect (Blazhko 1907), but a corollary may
be drawn with irregularities in the single-line radial veloc-
ity curve for RR Lyr (Chadid 2000). Two explanations
were proposed for the latter, one being a connection with
the Blazhko eect and the second being a dynamical in-
teraction between the highest and lowest layers of the at-
mosphere mediated by strong outward shock waves.
Clearly, it is too early to draw direct comparisons be-
tween the pulsations in V652 Her and other stellar classes.
However the prospects for exploring the physics of stellar
pulsations in a dierent area of parameter space are good.
8. The Mass of V652 Her
8.1. Comparison with previous analyses
The new measurements of r 0 and M for V652 Her are
clearly smaller than those given before (Paper II). Reasons
include an improved projection factor which has increased
all of the derived radii by  10%. All mass estimates are
reduced because the eective surface gravity has been re-
duced by  0:35 dex relative to Paper II. The new phase-
dependent measurements of log g are far more reliable
than previous results except at phases close to minimum
radius and automatically give a substantial reduction in
mass, irrespective of radius.
8.2. Which is the correct mass?
Table 4 lists four alternative sets of mass, radius and ef-
fective temperature for V652 Her. A major conclusion of
the present work is that the current model atmospheres
are not able to provide consistent T e from optical spec-
troscopy and total ux methods, so that it is probably
premature to draw a nal conclusion. It would be inap-
propriate to use the radii and masses measured from op-
tical spectroscopy and V-band photometry alone because
the corresponding models do not have suôcient ux com-
pared with the ultraviolet observations. Moreover, these
masses (0:18  0:05 M ) appear to be unphysically low.
The mass measured by the total ux method (0:59 
0:18 M ) and that reported in Paper II (0:7 +0:4
0:3 M ) are
within the error estimates of each other, which is reas-
suring. Paper IV rened the latter to 0:69 +0:15
0:12 M by re-
ducing the measurement error on log g, but this has little
bearing on the current question.
For the present, it seems reasonable to regard the mea-
surements of Paper II and those presented here from the
total ux method as likely extremes. A mass of 0:59 M

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 17
with a random error of 0:18M and a systematic error of
0:1M would represent the current observational data
and model atmospheres.
The mass for V652 Her (0:59 M ) should be com-
pared with that deduced for the pulsating helium star
BX Cir (=LSS 3184, Woolf & Jeery 2000) with M =
0:42  0:12 M . The pulsation periods for BX Cir and
V652 Her are almost identical. The average radii of both
stars were measured using almost identical methods, giv-
ing 2:31  0:01 R for V652 Her and 2:31  0:10 R for
BX Cir. The original mass measurement for BX Cir had
seemed small compared with that expected from previous
work on V652 Her. Now the close correspondence of their
radii and their pulsation periods encourages us to sup-
pose that the mass measurements are still dominated by
systematic eects. By virtue of the period mean-density
relation for radially pulsating stars, the masses of BX Cir
and V652 Her must be very similar.
Regarding the evolutionary origin of V652 Her, this
value or range of possible values for the mass, together
with the corresponding radii and eective temperau-
res and the measured chemical composition are quite
appropriate for the merged binary white dwarf model
(Saio & Jeery 2000). While a hydrodynamical model
with 0:7 M (Fadeyev & Lynas-Gray 1996) matches the
pulsation properties very well, we are currently studying
(Monta~nes Rodriguez & Jeery 2001b) a more extended
family of such models with dierent masses and radii.
These have very similar pulsation properties including pe-
riod, and light and velocity curve amplitude and shape.
One cause for concern is that the total ux method de-
pends on relatively few IUE measurements which are both
noisy and poorly distributed in phase. Omitting just one of
these can have a major eect on the nal mass. More fre-
quent and less noisy ultraviolet measurements are crucial
to a more accurate measurement. Similarly, improvements
in the model atmospheres are prerequisite to signicant
further progress.
Acknowledgements
This research was supported through grants in aid from
the Departments of Education and of Culture, Arts and
Leisure in Northern Ireland, and through a UK Particle
Physics and Astronomy Research Council (PPARC) grant
/PPA/G/S/1998/00019 to the Armagh Observatory. Dr
Dave Kilkenny (SAAO) kindly provided the data from the
visual light curve for V652 Her. Dr Tom Kerr (UKIRT)
kindly reduced the infrared spectrum. Discussions with
Prof Philip Dufton concerning the implementation of He i
line broadening data were much appreciated. As referee,
Prof Ulrich Heber made many valuable suggestions which
have been incorporated. Much of the analysis software
was developed from programs provided orginally through
CCP7, a PPARC project for the 'Analysis of Astronomical
Spectra'.
Appendix A: Computer Programs for Analysing
Stellar Spectra
The availability of spectra covering a large wavelength
range with good spectral and temporal resolution makes
an attempt to measure the instantaneous eective tem-
perature ( T e ) and surface gravity ( log g) throughout
the pulsation cycle attractive. In contrast, the previous
spectral analysis (Paper IV) only considered an \average
spectrum" integrated over the pulsation cycle, with a res-
olution and S/N poorer than that of each individual spec-
trum considered here.
Under ideal circumstances, such an analysis should
take the dynamical nature of the atmosphere into account.
The primary argument in favour of using the hydrostatic
approximation is that it should be shown to be inadequate
before investing the eort required to construct dynamical
model atmospheres. The assumptions of hydrostatic and
thermal equilibrium will be re-examined later (Sect. 7).
With these considerations, the following tools were
adopted or developed to analyse the high-quality spectra
of V652 Her.
A.1. sterne
We have used model atmospheres calculated using the
code sterne (Jeery & Heber 1992). The code assumes
hydrostatic, radiative and local thermodynamic equi-
librium and plane-parallel geometry. Continuous opaci-
ties are nearly the same as those adopted by Kurucz
(1979), with the addition of carbon and nitrogen from
Peach (1970), while line opacities are accounted for us-
ing an opacity distribution function computed for a
hydrogen-decient mixture by (Moller 1990) from the
Kurucz & Petryemann (1975) list of 265000 lines, in the
same manner as adopted in Kurucz's stellar atmosphere
program ATLAS6 (cf. Kurucz 1979). Radiative transfer
is solved using the Feautrier scheme (Feautrier 1964) and
temperature correction is achieved using the Unsold-Lucy
procedure (Lucy 1964). The plane-parallel approximation
is justied since the pressure scale height in the atmo-
sphere of V652 Her is small (< 0:2%) compared to the
stellar radius, even for the lowest gravity models consid-
ered.
The emergent ux distributions, sampled at 342 wave-
lengths between 229  A and 20m, were used to measure
eective temperatures and angular diameter from ultravi-
olet and visual photometry. The model structures describe
temperature, pressure and electron density as a function
of optical depth on a grid of fty depth points, and were
used as input for the spectral synthesis calculations de-
scribed below (Sect. 4.3).
A.2. ffit
The method adopted here to measure eective tempera-
ture, angular diameter and insterstellar extinction was to

18 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
STERNE
High resolution
spectrograms
UV + visual
spectrophotometry
Model flux grid
High resolution
model grid
v_t, composition
FFIT v_t
Atomic data
Teff, log g, v sin i
Teff, , Eb-v
q
SPECTRUM
LTE_LINES
SFIT
composition
Model structure grid
SFIT_SYNTH
Fig. A.1. Block diagram illustrating the procedures (boxes), inputs (ellipses) and outputs (oval boxes) used in the analysis of
high-resolution optical spectra and broad-band spectrophotometry of V652 Her.
t the reddened theoretical ux distribution
  ( EB V ; T e ; ) =  2 f  ( T e )A  ( EB V ) (A.1)
to the observed ux distribution F  using the method of
 2 minimization. The ux distributions are rst resampled
to the resolution of the theoretical ux distributions, this
being lower. The specic extinction A  is taken from the
average Galactic extinction law due to Seaton (1979). In
computing
 2 =  
(F    ) 2
 2

; (A.2)
 2

are the variances of the binned uxes. The errors as-
sociated with the best t parameters x i are given by the
diagonal elements ( 1 ) ii of the inverse of the covariance
matrix , whose elements are given by
 ij =  

@ 
@x i
@ 
@x j
= 2


: (A.3)
The minimum in the multi-dimensional  2 sur-
face was located using the downhill simplex method
(Nelder & Mead 1965), implemented using a variant of
the algorithm amoeba (Press et al. 1989). The method
was proven to give identical results to an independently
developed brute-force algorithm (cf. Jeery et al. 2000).
The principal dierence between our version of amoeba
and that published by Press et al. is that ours passes
both the free parameters and the observed spectrum to
the function to be minimized. In this case, the function is
 2 (cf. chisq, Press et al. 1989).
In applying ffit, care was taken to ensure that the
normalization of theoretical and observed uxes was car-
ried out at optical wavelengths, otherwise small errors
in EB V and T e would have led to major errors in .
Although EB V may be found as an independent param-
eter in each t, the nal results were constrained to have a
single \average" value of EB V for repeated observations
of V652 Her.
ffit was tested by application to a spectrum of
Vega used for calibration of the Hubble Space Telescope
(Colina et al. 1996). The calibration spectrum was re-
stricted to match the IUE wavelength interval, and sup-
plemented with UBVRI photometry, assuming U =
B = V = R = I = 0:0. The photometry was
converted to ux units with the calibration constants
C  = 20:94; 20:51; 21:12; 21:89; 22:70, respec-

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 19
tively. Using a grid of ATLAS9 model atmospheres
(Kurucz 1991) with log g = 4:0 and [Fe=H] = 0:5, ffit
yielded T e = 9617  24 K;  = 7:67  0:02:10 9 radians
and EB V = 0:000  0:004 (formal errors). Both T e
and  dier by less than 1% from the result reported by
Castelli & Kurucz (1994).
A.3. spectrum
The formal solution code spectrum was written origi-
nally by Prof P.L.Dufton and extended by Drs D.J.Lennon
and E.S.Conlon at Queen's University Belfast. It was
adapted for use with H-decient mixtures and consider-
ably extended by one of us (CSJ). From a given model
atmosphere and a line list including gf-values, radiative
and collisional broadening constants and excitation ener-
gies, spectrum can now compute synthetic spectra over
large wavelength intervals and for many absorption lines.
The usual output product is the normalized spectrum
s  ( T e ; log g; v t ; n i ; i = 1; : : :) = f 
f c
(A.4)
computed as a function of T e , log g, microturbulent ve-
locity v t , and chemical composition given as the relative
abundance by number n i of species i. In addition, the to-
tal emergent ux f  , the continuum ux f c and specic
intensities I  may also be obtained explicitly.
Metal line proles are computed as Voigt functions,
including thermal and Doppler broadening due to mi-
croturbulence, and radiative and collisional broadening.
Hydrogen lines are computed using broadening tables
from Lemke (1997) and based on broadening theory by
Vidal, Cooper & Smith (1973). Neutral helium line pro-
les for He i 4471, 4026, 4922 and 4388  A are computed
from broadening tables by Barnard et al. (1969, 1974,
1975). Proles for He i 4144 and 4009  A are computed
from broadening theory by Gieske & Griem (1969) and
by Dimitrijevic & Sahal-Brechot 1984 (1984), whilst the
remainder are computed as Voigt proles. Line proles
for ionized helium are computed from broadening tables
by Schoning & Butler (1989).
The model atmopheres grid described above was used
to generate grids of synthetic spectra comprising some
1100 absorption lines on the interval 4250 { 4950  A.
A.4. lte lines
Atomic data for metal lines comes from a large variety of
sources; much of the data has been tested extensively in
analyses of B stars. A description of the atomic database
lte lines, which includes a utility for selecting appro-
priate ions to include in the linelist, has been provided
by Jeery (1991) and is also available on the WWW
at http://www.arm.ac.uk/csj/linelists.html.Data
for some lines have been obtained from linelists provided
on CD-ROM (Kurucz 1993) and from the Vienna Atomic
Line Database (Piskunov et al. 1995). Where both exper-
imental or theoretical broadening constants are unavail-
able, classical values are used.
A.5. sfit
Our goal was to estimate the various parameters of the
stellar atmosphere (eective temperature, surface gravity,
chemical composition, etc.) by nding the combination
that produces a theoretical spectrum which most closely
resembles the observed spectrum.
In addition to the natural broadening of spectral lines
in the stellar atmosphere by processes described above, ad-
ditional broadening processes must be considered. These
processes are applied to the synthetic spectra before com-
parison with the observed spectrum and include:
{ Instrumental broadening I(
): each spectrum is con-
volved with a Gaussian having a FWHM
 equal to
the instrumental resolution measured from the com-
parison lamp emission lines and being 0.46  A.
{ Rotation broadening V ( v sin i; ): each spectrum is
convolved with the rotation broadening function
(Unsold 1955, Dufton 1972), assuming a limb dark-
ening factor  = 1:5. The projected rotation velocity
v sin i is a free parameter of the model.
{ Acceleration broadening A(ôv): the change in radial ve-
locity ôv during each 100s exposure of V652 Her is
typically 1 km s 1 and around minimum radius rises to
 10 km s 1 . An experiment was performed in which
each spectrum was convolved with a boxcar of full
width equal to the acceleration. In practise, more con-
sistent solutions were found without this broadening
being applied.
{ Projection broadening P (v v): the projection of
the spherical expansion onto the line of sight con-
volved with the specic intensity of the emer-
gent ux distorts and broadens the line prole
as a function of phase, as discussed elsewhere
(Monta~nes Rodriguez & Jeery 2001a). The asymme-
tries predicted for V652 Her, when convolved with
other eects were found to be negligible. We have been
unable to detect any asymmetry in the line prole as
a continuous function of pulsation phase.
For a given observation, an optimum t in T e , log g
and v sin i was obtained by minimizing  2 , the weighted
square residual between the normalized observed spec-
trum S  = F  =F c and the theoretical spectrum
s 0

=s  ( T e ; log
g)
I(
)
V ( v sin i; )

A(ôv)
P (v v):
(A.5)
The model spectrum for arbitrary T e , log g was ob-
tained using a two dimensional polynomial interpola-
tion in the discrete model grid. For accuracy, the algo-
rithm polin2 (Press et al. 1989) was adopted. The  2 -
minimization was carried out using the new-variant algo-
rithm amoeba described above. The method was proven
to be robust by repeated applications using dierent
model grid spacings and starting values.

20 C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her
In the construction of  2 , each wavelength point was
given a weight w  = 1=  , dened as the standard de-
viation about the mean ux in line-free regions, where
   0:01. Since the cores of strong He i lines still con-
sistently fail to provide agreement between theory and
observation, they were partially excluded from the t by
assigning a lower weight to the corresponding wavelength
points (  = 0:1).
In any such tting procedure, the normalization of
the observed spectrum can be of crucial importance (cf.
Paper IV). The initial normalization was carried out by
tting a high-order polynomial to apparent sections of
\continuum". The presence of even a few weak lines
can mean that this procedure sets the \continuum" too
low. We adopted a single improvement iteration (cf.
Jeery et al. 1998). Having found a best-t s 0

, the ratio
S  =s 0

was trimmed to exclude values more than 5% from
continuum and convolved with a low-pass Gaussian lter
of FWHM 18  A. This provided a renormalization function
for each spectrum which departed not more than 1% from
unity, with a standard deviation of <  0:5%. The renormal-
ization had no eect on individual line proles.
An extension of the above code allows for the varia-
tion of one other parameter, the helium abundance n He
for example, was not used in the current investigation but
is noted for completeness. The grid of model atmospheres
and synthetic spectra may be extended to three dimen-
sions T e , log g and the fractional helium abundance
n He . Interpolation is carried out rst in n He to obtain
a subgrid in which the two-dimensional interpolation for
T e and log g can be carried out as above.
A.6. sfit synth
If T e , log g and v sin i are known, the composition of
a star may be obtained by adjusting the abundances of
the dierent atomic species which contribute to the ab-
sorption spectrum, together with the microturbulent ve-
locity ( v t ), so that the theoretical spectrum matches the
observed spectrum. This can be achieved by minimizing
the same weighted  2 residual between observed and the-
oretical spectrum as used by sfit tgv. However, in the
present case, the number of free parameters, namely the
abundances of H, C, N, O, Al, Si, P, S, Ne, Mg, and Fe
and v t , was so large that precomputing multidimensional
grids of theoretical spectra would have been prohibitive.
The solution adopted was to compute synthetic spectra
in real time as demanded by the  2 minimization proce-
dure, amoeba. The same line-broadening (rotation, in-
strumental, acceleration, projection) could be introduced
as before.
In principle, this code sfit synth could solve simul-
taneously for as many parameters as are required. It was
found to be more practical to restrict each run of the code
to between two and four parameters. A single model atmo-
phere is assumed as input, so that T e , log g and v sin i
remain xed for a given solution. Then the code would
attempt to solve for v t and one chemical abundance to-
gether, or for two or three chemical abundances simultane-
ously, whilst other chemical abundances were kept xed.
A.7. Operation of the Programs
Given the physical assumptions outlined above and either
a high-resolution optical spectrum or low-resolution spec-
trophotometry covering ultraviolet and visual wavelengths
(at least), these programs allow us to drive various phys-
ical quantities in an objective manner. The outputs are
either T e , log g, v sin i, v t and chemical composition
from a high-resolution spectrum, or T e ,  and EB V
from spectrophotometry. A block diagram illustrating the
procedures, inputs and outputs, is shown in Fig. A.1. Note
that it is essential to ensure that the composition used as
input to the model atmospheres is consistent with that
derived as output from the spectral analysis. The latter
critically aects the background opacities and hence the
temperature stratication in the former, especially where
hydrogen is absent from the stellar atmosphere. Therefore
a few iterations may be necessary before a nal solution
is achieved.
References
Barnard A.J., Cooper J., Shamey L.J., 1969. A&A 1, 28
Barnard A.J., Cooper J., Smith E.W., 1974. JQSRT 14, 1025
Barnard A.J., Cooper J., Smith E.W., 1975. JQSRT 15, 429
Blazhko S., 1907. Astr. Nachr. 175, 325
Bohlin R.C., Savage B.D., Drake J.F., 1978. ApJ 224, 132
Castelli F., Kurucz R.L., 1994. A&A 281, 817
Chadid M., 2000. A&A 359, 991
Chadid M., Gillet D., 1996a. A&A 308, 481
Chadid M., Gillet D., 1996b. A&A 315, 475
Colina L., Bohlin R., Castelli F. 1996, HST instrument science
report CAL/SCS-008
Dimitrijevic M.S., Sahal-Brechot S., 1984. JQSRT 31, 301
Dimitrijevic M.S., Sahal-Brechot S., 1989. Bull. Obs. astr.
Belgrade, 141, 57
Dimitrijevic M.S., Sahal-Brechot S., 1990. A&AS 82, 519
Drilling J.S., Jeery C.S., Heber U., 1998. A&A 329, 1019
Dufton P.L., 1972. A&A, 16, 301
Fadeyev Yu.A., Lynas-Gray A.E., 1996. MNRAS 280, 427
Feautrier P., 1964. C.R.Acad.Sci.Paris 258, 3189
Fokin A.B., Gillet D., Chadid M., 1999. A&A 344, 930
Gieske H.A., Griem H.R., 1969. ApJ 157, 963
Grevesse N., Noels A., Sauval A.J., 1996. Cosmic abundances,
eds. Holt S.S., Sonneborn G., ASP Conf Ser. 99, 117
Groenewegen M.A.T., Lamers H.J.G.L.M., 1989. A&A Supp.
79, 359
Harrison P.M., Jeery C.S., 1997. A&A 323, 177
Heber U., 1983. A&A 118, 39
Hill P.W., Kilkenny D., Schonberner D., Walker H.J., 1981.
MNRAS 197, 81 (Paper I)
Hubeny I., Lanz T., Jeery C.S., 1994. CCP7 Newsletter No.
20, p.30
Iben I.,Jr., Kaler J.B., Truran J.W., Renzini A., 1983. ApJ
264, 605
Iben I., Jr., MacDonald J., 1995, White Dwarfs, Lecture Notes
in Physics, Vol. 443, p.48, eds. D. Koester & K. Werner.
Springer-Verlag, Berlin Heidelberg New York

C.S. Jeery et al.: Time-resolved spectroscopy of V652 Her 21
Iben I.,Jr., Tutukov A., 1985. ApJS, 58, 661
Jeery C.S., 1991. Newsletter on `Analysis of Astronomical
Spectra' No. 16, p.17
Jeery C.S., Hamill P.J., Harrison P.M., Jeers S.V., 1998.
A&A 340, 476
Jeery C.S., Harrison P.M., 1997. A&A 323, 393
Jeery C.S., Heber U., 1992. A&A 260, 133
Jeery C.S., Hill P.W., 1986. MNRAS 221, 975 (Paper III)
Jeery C.S., Hill P.W., Heber U., 1999. A&A 346, 491 (Paper
IV)
Jeery C.S., Starling R.L.C., Hill P.W., Pollacco D., 2000.
MNRAS in press
Kilkenny D., 1988. MNRAS 232, 377
Kilkenny D., Lynas-Gray A.E., 1982. MNRAS 198, 873
Kilkenny D., Lynas-Gray A.E., 1984. MNRAS 208, 673
Kilkenny D., Lynas-Gray A.E., Roberts G., 1996. MNRAS 283,
1349
Kurucz R.L., 1979. ApJS 40, 1
Kurucz R.L., 1988. in IAU Trans., ed. M.McNally, Vol. 20B
(Kluwer, Dordrecht), 168
Kurucz R.L., Petryemann E., 1975. A Table of Semiempirical
gf Values, SAO Special Report No. 362, Cambridge,
Massachussets 02138
Kurucz R.L., 1993. SAO KURUCZ CD-ROM No. 18
Kurucz R.L., 1991. in 'Stellar Atmospheres: Beyond Classical
Models', p.441, eds. L.Crivellari, I.Hubeny, D.G.Hummer,
NATO ASI Series Vol. C341, Kluwer, Dordrecht
Landolt A.U., 1975. ApJ 196, 787
Lynas-Gray A.E., Schonberner D., Hill P.W., Heber U., 1984.
MNRAS 209, 387 (Paper II)
Lemke M., 1997. A&AS 122, 285
Lucy L., 1964. SAO Special Report No. 167, p.93
Mathias P., Gillet D., Fokin A.B., Chadid M., 1995. A&A 298,
843
Moore C.E. 1945. Contr. Princeton Univ. Obs. No. 20,
Princeton, New Jersey
Moller R. U., 1990. Diplom. Thesis, Universitat Kiel
Monta~nes Rodriguez P., Jeery C.S., 2001a. A&A (submitted)
Monta~nes Rodriguez P., Jeery C.S., 2001b. A&A (in prepa-
ration)
Nelder J.A., Mead R., 1965. Computer Journal 7, 308
Parsons S.B., 1972. ApJ 174, 57
Piskunov N.E., Kupka F., Ryabchikova T.A., Weiss W.W.,
Jeery C.S. 1995. A&AS 112, 525
Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T.,
1989. Numerical Recipes: The Art of Scientic Computing.
Cambridge University Press
Preston G.W., Smak J., Paczynski B., 1965. ApJS 12, 99
Rodriguez-Pascual P.M., Gonzalez-Riestra R., Schartel N.,
Wamsteker W., 1999. A&AS, 139, 183
Saio H., 1993. MNRAS 260, 465
Saio H., Jeery C.S., 2000. MNRAS 313, 671
Sanford R.F., 1949. ApJ 109, 208
Sanford R.F., 1952. ApJ 116, 331
Schoning T., Butler K., 1989. A&AS 78, 51
Schrijver H., 1997, The Hipparcos and Tycho Catalogue, vol.
8, European Space Agency
Schwarzschild M., 1952. Transaction of the IAU VIII, 8111
Seaton M.J., 1979. MNRAS 187, 73P
Shapley H., Nicholson S.B., 1919. Proc. Nat. Acad. Sci., 5, 417.
Shore S.N., 1992. An Introduction to Astrophysical
Hydrodynamics, Academic Press.
Unsold A., 1955. Physik der Sternatmospharen, 2nd ed. Berlin:
Springer-Verlag
van Hoof A., Struve O., 1953. PASP 65, 158
Vidal C.R., Cooper J., Smith E.W., 1973. ApJS 25, 37
Webbink R.F., 1984. ApJ 277, 355
Woolf V.M., Jeery C.S., A&A 358, 1001