arXiv:astro-ph/0410230v1 8 Oct 2004
European Workshop on White Dwarfs
ASP Conference Series, Vol. 999, 2005
D. Koester, S. Moehler
The mass of the sdB primary of the binary HS 2333+3927
U. Heber, H. Drechsel, C. Karl
Dr. Remeis-Sternwarte, Astronomisches Institut der Universit¨at
Erlangen-N¨urnberg, Sternwartstraße 7, D-96049 Bamberg, Germany
R. Østensen, S. Folkes
Isaac Newton Group of Telescopes, E -37800 Santa Cruz de La Palma,
Canary Islands, Spain
Department of Physics & Astronomy, University of Le i cester, University
Road, Leicester LE1 7RH, UK
Departamento de Astronomia, Universidad de Chile, Camino El
Observatorio 1515, Las Condes, Chile
Sternwarte der Universit¨at, Auf dem H¨ugel 71, D53121 Bonn, Germany
Institute of Theoretical Astrophysics University of Oslo, p.box 1029,
N-0315 Blindern-Oslo, Norway
B. Voss, D. Koester
Institut f¨ur Theoretische Physik und Astrophysik, Universit¨at Kiel,
24098 Kiel, Germany
Abstract. Short period sdB binaries with cool companions are crucial to un-
derstand pre-CV evolution, because they will evolve into cata c lysmic variables,
when the sdB will have left the extended horizontal branch. Recently we dis-
covered the sixth such system, HS 2333+3927, consisting of an sdB star and an
M dwarf (period: 0.172 d) with a very strong reﬂection eﬀect, but no eclipses.
The reﬂection is stronger than in any of the other similar systems which renders
a quantitative spectral analysis very diﬃcult because the Balmer line proﬁles
may be disturbe d by the reﬂected light. A spectroscopic analysis results in T
= 36 500 K, log g = 5.70, and log(n
) = −2.15. Mass-radius relations were
derived from the results of the analysis of light and radial-velocity curves. Com-
parison with the mass-radius relation derived from the sur face gravity of the
sdB s tar favours a rather low mass of 0.38 M
for the primary. The mass of the
companion is 0.29 M
. HS 2333+3927 is the only known sdB+dM system with
a period above the CV period gap.
2 Heber et al.
SdB binaries are important to clarify the evolutionary origin of sdB stars because
the analysis of light an d radial velocity curves can constrain their dimensions
and masses. However, only ﬁve suitable systems are known up to now.
There is general consensus that the sdB stars can be identiﬁed with models
for Extreme Horizontal Branch (EHB) stars (Heber 1986). Like all HB stars
they are core helium burning objects. However, their internal structure diﬀers
from typical HB stars, because their hydrogen envelope is very thin (<1% by
mass) and therefore in ert. As a consequence EHB stars evolve directly to the
white dwarf cooling sequence, thus avoiding a second r ed giant phase. How they
evolve to the EHB conﬁguration is controversial. The problem is how the mass
loss mechanism of the progenitor manages to remove all but a tiny fraction of
the hydrogen envelop e at precisely the same time as the He core has attained
the mass (∼0.5 M
) required for the He ﬂash.
Considerable evidence is accumulating that a signiﬁcant fraction of the sdB
stars reside in close binaries (Maxted et al. 2001; Napiwotzki et al., 2004, see also
Karl et al, these proceedings). Therefore mass tr ansfer should h ave p layed an
important role in the evolution of such binary systems. Detailed investigations
of sdB binaries, in particular eclipsing systems, are crucial to determine their
masses. However, only three such eclipsing b inaries, HW Vir, PG 1336-013,
and HS 0705+6700 (see Drechsel et al. 2001) and two non-eclipsing ones are
known up to now, which consist of an sdB star and an M dwarf companion
revealed by reprocessed light from the primary (reﬂection eﬀect). Recently,
Heber et al. (2004) discovered another related sys tem, HS 2333+3927, which is,
however, not eclipsing, but otherwise possesses very similar system parameters
The ﬁrst hint for light variations emerged when HS 2333+3927 was monitored
at the Nordic Optical Telescope on October 19, 1999 in order to search for
pulsations. The light curve of HS 2333+3927 (see Fig. 1) was measured from
CCD photometry in the B, V , and R bands at four telescopes (JKT 1.0m, Calar
Alto 1.23 m, IAC 0.8 m & Hoher List 1.06 m) in 15 nights between July 2 and
November 11, 2002.
The radial velocity curve (see Fig. 2) was measured during an observing
run at the Calar Alto Observatory with the TWIN spectrograph at the 3.5m
telescope. A total of 18 spectra were taken from 11 to 18 August 2002 covering
the wavelength ranges from 3900
A to 5000
A at a resolution of 1.3
A in the
blue part of the spectrum, and from 6000
A to 7000
A at a resolution of 1.2
in the red part.
HS 2333+3927 was also observed at the Calar Alto Observatory with the
CAFOS spectrograph at the 2.2m telescope in order to derive atmospheric pa-
rameters by Balmer line ﬁtting. A total of 13 low resolution spectra were taken
on August 31, 2003 covering the wavelength range from 3300
A to 6000
A at a
spectral resolution of 4.5
A. This allowed to measure the entire Balmer series
(except Hα) up to the Balmer jump .
The mass of the sdB primary of the binary HS 2333+3927 3
Figure 1. BV R light curves of HS 2333+3927 (Heber et al. 2004).
3. Analysis of light and radial velocity curves
The numerical solution of the light curves was performed with the Wilson-
Devinney (1971) based light curve program MORO (Drechsel et al. 1995). The
best ﬁt to the B, V , R light curves is shown in Fig.1. A s tron g reﬂection eﬀect is
visible (∆B = 0.21, ∆V = 0.28, ∆R = 0.33 mag), but no eclipses are apparent.
We determined the period to be P =0.1718023 d.
The spectrum of HS 2333+3927 is single-lined an d the radial velocity curve
is sinusoidal (Fig. 2) indicating that the orbits are circular. The semi-amplitude
= 89.6 km/s and the mass function follows as f (m) = 0.0128 M
The light curve analysis provided us with an estimate of the system’s in-
clination. For any assumed primary mass we can calculate the secondary mass
from the mass function. In addition the orbital rad ius a
of the primary can be
calculated. The s ep aration a of the components can then be calculated from the
mass ratio q. The light curve allows u s to determine the ratio of the radii in units
of the separation. Hence we can determine the radii of both components for any
given sdB mass, i.e we can derive mass-radius relations for both components.
4. Spectroscopic Analysis
The Balmer and helium lines in the blue spectra can b e used to determine the
atmospheric parameters by performing a quantitative spectral analysis. Because
the medium resolution TWIN spectra cover only few of the Balmer lines, we used
the CAFOS spectra which cover the Balmer series to its limit. Since the high
Balmer lines are probably least aﬀected by reprocessed light from the secondary,
much emphasis was put in the ﬁt procedure to reproduce these lines well. Since
4 Heber et al.
-0.4 -0.2 0 0.2 0.4
Figure 2. Radial velocity curve of HS 2333+3927 (Heber et al. 2004).
the spectrum displays helium lines from two stages of ionization, we made also
use of the ionization equilibrium of helium to determine T
The atmospheric parameters determined from spectra taken near lower con-
junction should be least aﬀected by reprocessed light from the secondary and,
therefore, the atmospheric parameters derived from them should be the closest
approximation to the true atmospheric parameters of the sdB star.
Based on the above considerations we derived T
= 36 500 ± 1000 K, log g
= 5.70 ± 0.1 and log(n
) = −2.15 ± 0.15 for the atmospheric parameters
of HS 2333+3927.
5. Masses and Radii
The mass-radius relations derived from the analysis of the light and radial ve-
locity curves can be compared to independently determined relations. For the
sdB star such a relation follows from the gravity (Newton’s law). For the cool
companion a theoretical mass-radius relation for M-dwarfs may be appropriate.
In principle the masses an d radii of the sdB star and the M dwarf, respectively,
could be determined by requesting these mass-radius r elations to be consistent.
Fig. 3a compares the mass-radius relation of the sdB derived from the light
and radial velocity curves to that derived from gravity. The gravity of log g = 5.7
is too low to match the M-R-relation from light and radial velocity curve for
reasonable masses. The intersection of both M-R-relations in Fig. 3a would
give a sdB mass of 0.2 M
, clearly too low for a core helium burning star.
Evolutionary scenarios by Han et al. (2003) suggest that the most likely mass is
, but possible masses range from 0.38 to 0.8 M
. As can be seen from
Fig. 3a the sdB gravity should be log g ≈ 5.86 if the sdB star is of canonical mass.
This is signiﬁcantly higher than derived from a quantitative spectral analysis of
the Balmer lines: log g = 5.7±0.1. However, if we adopt th e lowest mass core
The mass of the sdB primary of the binary HS 2333+3927 5
Figure 3. a) left: Comparison of the sdB mass-radius relation fro m the
analysis of light and radial velocity curves to those derived from diﬀerent
gravities. The spectroscopic lo g g estimate is 5.7±0.1. Dashed lines mark
the most probable (0.47 M
) and the lowest mass (0.38 M
according to the
evolutionary models of Han et al. (2003). Note that the gravity would need
to be as high as 5.8 6 if the star were of canonical mass (0.47 M
b) right: Comparison of the companions mass-radius relation derived from
the analysis of light and radial velocity curves to relations for M-type dwarfs
(short-dashed: observed relation fr om Clemens et al. 1998; dashed: theo-
retical predictions from Baraﬀe & Chabrier, 1996). Filled circle: sdB has
canonical mass (0.47 M
); triangle: sdB has lowest pos sible mass.
helium burning star that can form in the Han et al. scenario, consistency could
be achieved if we adopt the largest gravity allowed by the spectroscopic analysis
(see Fig. 3a).
The mass-radius relation for the companion star is compared to observations
and model predictions f or M-type main sequence stars in Fig. 3b. The empirical
relation for the unseen companion of HS 2333+3927 lies above those for normal
M-stars. However, it is possible that the M-star is over-luminous due to the
strong irradiation of its surface by the nearby hot star and hence has a larger
radius than a normal M dwarf of the same mass.
From the analysis presented above we conclude that a model for a low mass
) core helium burning sdB star and a 0.29 M
M-dwarf ﬁts the
observations best. However, the results have to be taken with a grain of salt.
The spectral analysis of the Balmer lines, is plagued by reﬂected light, as is
evident from the line proﬁle variations observed in Hα, but less obvious in other
6 Heber et al.
Balmer lines. An improved m easurement of the gravity, therefore, is urgently
Another important observational constraint would be a precise measure-
ment of the projected rotational velocity. The rotation of the sdB star in
HS 2333+3927 is very likely tidally locked to the orbital motion. Drechsel et al.
(2001) showed this to b e true for HS 0705+6700. Determining the projected ro-
tation velocity would therefore allow an independent estimate of the inclination
of HS 2333+3927.
The spectral lines of the Lyman series are sensitive gravity indicators and
plenty of metal lines can be used to measure v sin i. These measurements will
allow us to constrain mass and radius much better
6.2. SdB stars and pre-CV Evolution
Short period sdB binaries with main sequence companions, like HS 2333+3927,
are important not only to understand the formation and evolution of sdB stars.
When the sdB star will have left the EHB, it will evolve into a cataclysmic vari-
able. Therefore, these objects are also crucial to understand pre-CV evolution.
Sch en ker (these proceedings) has suggested that cataclysmic variables with short
periods, i.e. below the CV period gap evolve from sdB + dM binaries. While
four other known systems have periods between 1.7 h to 2.8 h, i.e. below the
CV period gap, the period (4.13 h) of HS 2333+3927 is a bit above the CV
period gap. Its orbital separation is so small that the secondary is appreciably
distorted. Th e shrinkage of the binary orbit by gravitational wave radiation
will initiate mass transfer turning the system into a cataclysmic variable. It is
likely that the HS 2333+3927 system will then still have a period larger than the
CV period gap. Hence sdB + d M binaries form an evolutionary channel to the
population of longer period cataclysmic variables as well as to the short-period
Acknowledgments. C.K. gratefully acknowledges ﬁnancial support by the
conference organizers. M.A. is ﬁnancially supported by FONDAP 1501 0003.
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