SDSS J233325.92+152222.1 and the evolution of intermediate polars
Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 4 November 2018 (MN LATEX style file v2.2)
SDSSJ233325.92+152222.1 and the evolution of
intermediate polars
John Southworth1 ⋆, B. T. Gänsicke1, T. R. Marsh1, D. de Martino2,
A. Aungwerojwit1,3
1 Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
2 INAF – Osservatorio di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
3 Department of Physics, Faculty of Science, Naresuan University, Phitsanulok, 60500, Thailand
4 November 2018
ABSTRACT
Intermediate polars (IPs) are cataclysmic variables which contain magnetic white
dwarfs with a rotational period shorter than the binary orbital period. Evolution-
ary theory predicts that IPs with long orbital periods evolve through the 2–3hr pe-
riod gap, but it is very uncertain what the properties of the resulting objects are.
Whilst a relatively large number of long-period IPs are known, very few of these
have short orbital periods. We present phase-resolved spectroscopy and photometry
of SDSS J233325.92+152222.1 and classify it as the IP with the shortest known or-
bital period (83.12 ± 0.09min), which contains a white dwarf with a relatively long
spin period (41.66± 0.13min). We estimate the white dwarf’s magnetic moment to be
µWD ≈ 2× 10
33 Gcm3, which is not only similar to three of the other four confirmed
short-period IPs but also to those of many of the long-period IPs. We suggest that
long-period IPs conserve their magnetic moment as they evolve towards shorter or-
bital periods. Therefore the dominant population of long-period IPs, which have white
dwarf spin periods roughly ten times shorter than their orbital periods, will likely end
up as short-period IPs like SDSS J2333, with spin periods a large fraction of their
orbital periods.
Key words: stars: novae, cataclysmic variables – stars: binaries: close – stars: white
dwarfs – stars: magnetic fields – stars: individual: SDSS J233325.92+152222.1
1 INTRODUCTION
Cataclysmic variables (CVs) are interacting binary stars
containing a white dwarf primary star and a low-mass sec-
ondary star in a tight orbit (Warner 1995). In most of these
systems the secondary star is unevolved and fills its Roche
lobe, losing material to the white dwarf primary via an
accretion disc. About a quarter of CVs contain magnetic
white dwarfs, and these systems are split into two cate-
gories: the AMHer stars (polars) and the intermediate po-
lars (IPs). In polars, the strong magnetic field of the white
dwarf causes its spin period, Pspin, to synchronise to the or-
bital period, Porb. The evolution of these objects is expected
to be strongly affected by interaction between the magnetic
fields of the white dwarf and the late-type secondary star
(Webbink & Wickramasinghe 2002). In IPs it is believed
that the lower magnetic field of the white dwarf means that
⋆ E-mail: j.k.taylor@warwick.ac.uk (JS),
Boris.Gaensicke@warwick.ac.uk (BTG),
T.R.Marsh@warwick.ac.uk (TRM)
its rotation has not become synchronised to the orbital mo-
tion. The evolution of IPs and in particular their relation
to polars is still a debated issue (Hellier 2001; Norton et al.
2004, hereafter NWS04).
While the total number of confirmed IPs has been
boosted substantially over the past few years (e.g.
Woudt & Warner 2003; Araujo-Betancor et al. 2003;
Rodŕıguez-Gil et al. 2004; Woudt et al. 2004; Schlegel
2005; Rodŕıguez-Gil et al. 2005; Gänsicke et al. 2005;
Bonnet-Bidaud et al. 2006; Norton & Tanner 2006;
de Martino et al. 2006), only a handful of these have
short orbital periods (i.e., below the 2–3 hr gap which
is prevalent in the observed population of CVs). Con-
versely, the known population of polars mostly lies below
Porb = 4hr (Webbink & Wickramasinghe 2002). This
has led to suggestions that long-period IPs may evolve
into short-period polars (see Patterson 1994). A detailed
theoretical study by NWS04 found that in general this
should be the case. However, those with a white dwarf
magnetic moment of µWD . 5 × 10
33 Gcm3 and secondary
stars with weak magnetic fields will remain IPs, because the
c© 0000 RAS
http://arxiv.org/abs/0704.0513v1
2 Southworth et al.
magnetic interaction between the stars is not strong enough
to synchronise the the rotation of the white dwarf to the
orbital motion. This picture of the evolution of magnetic
CVs has not yet been confirmed observationally because
very few short-period IPs are known.
We are conducting a research program (Gänsicke 2005)
to measure the orbital periods of objects spectroscopi-
cally identified as CVs (Szkody et al. 2002, 2003, 2004,
2005, 2006) by the Sloan Digital Sky Survey (SDSS).
The main motivation of this work lies in the characterisa-
tion of an homogeneously identified sample of CVs which
can be used to investigate the properties of the intrinsic
CV population. The relatively faint limiting magnitude of
the SDSS spectroscopic observations means that this sur-
vey is much less biased towards intrinsically brighter ob-
jects than previous work. A very high proportion of the
SDSS CVs which we have studied so far are faint short-
period systems (Gänsicke et al. 2006; Southworth et al.
2006, hereafter Paper I; Littlefair et al. 2006). In Paper I
we found that SDSSJ023322.61+005059.5 was a probable
IP with Porb = 96.08 ± 0.09min and Pspin ≈ 60min.
Here we present a detailed analysis of another system,
SDSSJ233325.92+152222.1 (hereafter SDSSJ2333), which
we find to be an IP with Porb = 83.12min and Pspin =
41.66min1.
Szkody et al. (2005) presented the identification spec-
trum of SDSSJ2333 alongside time-resolved photometry and
spectroscopy. They found modulation at 21min in the light
curve and at 82min in the Hα and Hβ emission line ra-
dial velocities, and suggested that this object could be an
IP with an orbital period close to the 80min period mini-
mum for CVs (Knigge 2006). The SDSS spectrum shows the
Balmer and He I emission lines characteristic of CVs as well
emission at He II 4686 Å which is a hallmark of magnetic
systems. Whilst the Balmer and He I lines have the double-
peaked profile indicative of an accretion disc, the He II line
is single-peaked. However, it is difficult to conclude anything
from this because the line may be contaminated by emission
from the C III and N III Bowen blend. X-ray emission from
SDSSJ2333 was not detected by ROSAT.
2 OBSERVATIONS AND DATA REDUCTION
2.1 WHT spectroscopy
Spectroscopic observations were obtained in 2006 September
using the ISIS double-beam spectrograph on the William
Herschel Telescope (WHT) at La Palma (Table 1). For the
red arm we used the R316R grating and Marconi CCD
binned by factors of 2 (spectral) and 4 (spatial), giving a
wavelength range of 6300–9200 Å and a reciprocal disper-
sion of 1.66 Å per binned pixel. For the blue arm we used
the R600B grating and EEV12 CCD with the same bin-
ning factors, giving a wavelength coverage of 3640–5270 Å
at 0.88 Å per binned pixel. From measurements of the full
1 The reduced spectra and photometry presented in this work will
be made available at the CDS (http://cdsweb.u-strasbg.fr/)
and at http://www.astro.keele.ac.uk/∼jkt/
Figure 2. Greyscale plots of the continuum-normalised and
phase-binned trailed spectra around the Hα and Hβ emission
lines. Other Balmer lines give similar result, but trails for the
helium emission lines are too noisy to be useful.
widths at half maximum (FWHMs) of arc-lamp and night-
sky spectral emission lines, we find that this gave resolutions
of 3.5 Å (red arm) and 1.8 Å (blue arm).
Data reduction was undertaken using optimal extrac-
tion (Horne 1986) as implemented in the pamela2 code
(Marsh 1989). The wavelength calibration was interpolated
from copper-neon and copper-argon arc lamp exposures
taken every hour. We removed the telluric lines and flux-
calibrated the target spectra using observations of G191-
B2B, treating each night separately.
A total of 38 spectra were obtained over two nights
and the average spectrum is shown in Fig. 1. They show
strong double-peaked Balmer emission and double-peaked
emission from the other usual suspects, He I, Fe II and
Ca IIK. There is no hint of the Balmer lines of the under-
lying white dwarf or of Ca II emission. However, there is
significant single-peaked emission at He II 4686 Å, which is
characteristic of systems containing magnetic white dwarfs
(e.g., DWCnc, Rodŕıguez-Gil et al. 2004). The trailed spec-
tra (Fig. 2) show that the emission lines have double-peaked
emission with a strong S-wave component. The spectrum of
SDSSJ2333 is reminiscent of those of the short-period IPs
HTCam (Kemp et al. 2002), DWCnc (Rodŕıguez-Gil et al.
2004) and V1025Cen (Buckley et al. 1998). The equivalent
widths of Hα, Hβ and He II 4686 Å are 78 ± 4, 56 ± 3 and
8±1 Å, respectively. The ratio
EW (4686)
EW (Hβ)
= 0.14±0.02 is typ-
ical for short-period IPs (e.g., DWCnc) and not unusual for
short-period non-magnetic CVs (e.g. Thorstensen & Fenton
2003).
2.2 Calar Alto photometry
Unfiltered differential photometry of SDSSJ2333 was ob-
tained on the night of 2006 September 13 using the
2.2m telescope at Calar Alto Observatory equipped with
the CAFOS focal reducer (Table 1). We used the blue-
optimised SITe CCD without binning, giving a plate scale
pamela and molly were written by TRM and can be found at
http://www.warwick.ac.uk/go/trmarsh
c© 0000 RAS, MNRAS 000, 000–000
http://cdsweb.u-strasbg.fr/
http://www.warwick.ac.uk/go/trmarsh
The intermediate polar SDSSJ233325.92+152222.1 3
Figure 1. Flux-calibrated averaged blue-arm (left) and red-arm (right) WHT spectra of SDSS J2333.
Table 1. Log of the observations of SDSS J2333.
Start date Start time End time Telescope and Optical Number of Exposure
(UT) (UT) (UT) instrument element observations time (s)
2006 09 13 19 57 23 58 CA 2.2 CAFOS (unfiltered) 293 40
2006 09 25 00 46 04 46 WHT ISIS R600B R316R 22 600
2006 09 25 23 07 01 39 WHT ISIS R600B R316R 15 600
of 0.53” px−1. The images were reduced and aperture pho-
tometry was performed using the pipeline described by
Gänsicke et al. (2004), which applies bias and flat-field cor-
rections within midas3 and uses the sextractor package
(Bertin & Arnouts 1996) to obtain aperture photometry for
all objects in the field of view. The differential magnitudes
were converted into apparent magnitudes using the SDSS g
and r photometry of the main comparison star.
3 DATA ANALYSIS
3.1 Radial velocity analysis
We measured radial velocities from the Balmer emission
lines by cross-correlation with single and double Gaussian
functions (Schneider & Young 1980). For each line we tried
a range of different widths and separations for the Gaussians
in order to verify the consistency of our results (see Paper I
for further details). We found that the best results for period
determination were obtained using the Hα line and a sin-
gle Gaussian of FWHM 1000 kms−1, as expected given the
prominence of the S-wave emission in the spectra (Fig. 2).
For a double Gaussian the best parameters were FWHM
300 kms−1 and separation 2000 kms−1. The choice of emis-
sion line, measurement technique and Gaussian parameters
does not have a significant effect on the derived period. Ra-
dial velocities derived for the He I 4471 Å line gave similar
results but with much larger noise as the line is weaker.
Periodograms were calculated from the measured Hα
radial velocities using the Scargle (1982) method, analysis
3 http://www.eso.org/projects/esomidas/
of variance (AoV; Schwarzenberg-Czerny 1989) and orthog-
onal polynomials (ORT; Schwarzenberg-Czerny 1996), as
implemented within the tsa4 context in midas. All three
types of periodogram contain a strong signal close to 83min,
accompanied by one-day aliases, and a few small peaks at
much shorter periods (Fig. 3). As the three periodogram
techniques agree well we have restricted further analysis to
the Scargle algorithm, which is the most appropriate for a
simple sinusoidal variation. We obtained the orbital period
by fitting a circular spectroscopic orbit (sine wave) to the
radial velocities (Fig. 3) using the sbop5 program, which we
have previously found to give reliable error estimates for
the optimised parameters (Southworth et al. 2005). Whilst
the radial velocities measured using a single Gaussian have
a larger scatter than those from the double-Gaussian tech-
nique, the velocity variation in the core of the emission lines
is much larger. These radial velocities therefore give the best
results, and we find a period of Porb = 83.12 ± 0.09min.
To investigate the probability that our chosen alias is
the correct one we have both fitted sine curves for each of
the possible alias periods and conducted bootstrapping sim-
ulations (see Paper I). For the sine curves we would expect
the lowest errors and residuals, and the highest amplitude,
for the correct period. The bootstrapping gives results which
can be directly interpreted as a probability distribution, but
there will be some bias away from the correct period because
the process of resampling the observations leads to a loss of
temporal resolution, degrading the resulting periodograms.
Thus bootstrapping will underestimate the probability that
http://www.eso.org/projects/esomidas/doc/user/98NOV/volb/node220.html
5 Spectroscopic Binary Orbit Program, written by P. B. Etzel,
http://mintaka.sdsu.edu/faculty/etzel/
c© 0000 RAS, MNRAS 000, 000–000
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http://www.eso.org/projects/esomidas/doc/user/98NOV/volb/node220.html
4 Southworth et al.
Table 2. Results of the bootstrapping analysis and the best-fitting circular spectroscopic orbits for the Hα line, both radial velocity
measurement techniques and for different possible periods. The orbit adopted as a final result is indicated in bold. The results of the
bootstrapping analysis are given as the percentage of simulations returning a highest peak close to a particular period.
Radial velocity Orbital period Velocity amplitude Systemic velocity σrms Scargle bootstrap
measurement (day) ( km s−1) ( km s−1) ( km s−1) probability (%)
Double Gaussian 0.051038± 0.00011 51.6± 7.8 −2.7± 5.6 34
Double Gaussian 0.054111± 0.00012 56.3± 6.4 −0.8± 4.6 28 11.5
Double Gaussian 0.057622± 0.00013 58.4± 6.0 2.6± 4.3 26 85.6
Double Gaussian 0.061608± 0.00016 57.1± 7.0 6.6± 4.9 30 2.9
Single Gaussian 0.051149± 0.00012 151.8± 17.6 21.3± 12.9 78
Single Gaussian 0.054222± 0.00008 168.2± 11.6 27.5± 8.5 52 17.4
Single Gaussian 0.057724±0.00006 176.3±8.8 38.9±6.4 39 82.6
Single Gaussian 0.061713± 0.00009 175.5± 12.9 52.5± 9.1 55
Figure 3. Scargle periodogram of the Hα radial velocities mea-
sured using a single Gaussian of width 1000 km s−1 (upper panel)
and the phased velocities with the best-fitting circular spectro-
scopic orbit (lower panel). On the periodogram the chosen peak
is indicated with an arrow.
the best period is in fact the correct one. Both the sine curve
fitting and the bootstrapping simulations clearly favour the
83.12min period.
3.2 Light curve analysis
The light curve of SDSSJ2333 shows clear sinusoidal vari-
ation with a large amplitude of about 0.2mag (Fig. 4). An
ORT periodogram of these data has strong power at one half
and one quarter of the orbital period (Fig. 4) but not at the
orbital period itself. A visual inspection of the light curve
suggested that it exhibits a double-humped variation so we
fitted the function
f(x) = a1 sin
2π(x+ φ1)
+ a2 sin
2π(2x+ φ2)
Figure 4. Calar Alto 2.2m photometry of SDSS J2333. The top
panel shows the observed light curve, which displays a clear sinu-
soidal variation. The middle panel contains an ORT periodogram
and the lower panel depicts the phased light curve with a double-
sine fit.
where the optimised parameters are a1 and a2 (the ampli-
tudes of variation), P (the period) and φ1 and φ2 (the phase
zeropoints). This process confirmed the double-humped na-
ture of the variation (Fig. 4) and yielded a period of 41.66±
0.13min.
Szkody et al. (2005) found a periodicity of 21min in
their light curve of this system, which was obtained with a
much smaller telescope (1.0m) than our data. Aside from
the fact that the double-peaked nature of the variation was
not apparent in their data, this periodicity is consistent with
our own measurement and demonstrates that it is stable.
We have found that SDSSJ2333 has Porb = 83.12 ±
0.09min, close to the minimum orbital period for CVs, and
a light curve with a strong double-humped modulation of
amplitude 0.2mag and period 41.66±0.13 min. We interpret
c© 0000 RAS, MNRAS 000, 000–000
The intermediate polar SDSSJ233325.92+152222.1 5
the light variation to be due to accretion heated spots on the
white dwarf primary, which has a largely bipolar magnetic
field. Therefore we classify SDSSJ2333 as an IP with an
orbital period below the period gap and white dwarf which
rotates with twice the frequency of the orbital motion.
4 DISCUSSION
In Table 3 we have collected the observed orbital and
spin periods for the five confirmed IPs with Porb < 2 hr.
These are plotted in Fig. 5. Classification as an IP re-
quires the presence of coherent variation at the white dwarf
spin period over a significant span of time (e.g. Buckley
2000). As the photometric observations for an additional
two objects, RXJ1039.7−0507 (Woudt & Warner 2003) and
SDSSJ023322.61+005059.5 (Paper I), have only a short
baseline their IP nature needs additional confirmation. The
white dwarf magnetic moments, µWD, of the objects in Ta-
ble 3 have been obtained from NWS04 under the assumption
that the systems are in rotational equilibrium, either taken
from their Table 1 or estimated from their Fig. 2.
SDSSJ2333 is joined by the objects DWCancri and
V1025Centauri in having Pspin ≈ 0.5Porb and µWD ∼
2 × 1033 Gcm3. Assuming a canonical white dwarf radius
of 107 m, this gives a field strength of 2MG for the white
dwarf. The properties of EXHya are also similar, whereas
those of the fifth system, HTCam, are quite different.
The majority of IPs with Porb > 3 hr have Pspin ≈
0.1Porb (Barrett et al. 1988; Gänsicke et al. 2005) and
µWD ∼ 2 × 10
33 Gcm3 (NWS04). This magnetic moment
is strikingly similar to those of SDSSJ2333, DWCnc and
V1025Cen. This is an empirical indication that long-period
IPs with Pspin ≈ 0.1Porb conserve µWD as they evolve and
become short-period IPs with Pspin ≈ 0.5Porb. This is consis-
tent with the evolutionary picture of magnetic CVs drawn by
Patterson (1994); Webbink & Wickramasinghe (2002) and
NWS04.
HTCam is a short-period IP with a lower µWD of
2.7 × 1032 Gcm3. In the scenario we have outlined, an ob-
ject such as this will result from the evolution of systems
which currently resemble SDSSJ223843.84+010820.7 (Aqr 1
in Woudt et al. 2004) for which µWD = 2.6×10
32 Gcm3 has
been estimated (NWS04). A similar argument can be ad-
vanced for RXJ1039.7−0507, which has µWD ≈ 10
33 which
is very similar to that of several known IPs (NWS04), for
example 1RXSJ062518.2+733433 (Staude et al. 2003).
King & Wynn (1999) have found that there is a large
continuum of equilibrium spin levels for short-period IPs,
and that an IP with a specific mass ratio, mass transfer rate
and orbital period can have any of a wide range of values of
Pspin/Porb, depending on the value of µWD
The theoretical calculations of NWS04 suggest that
long-period IPs will evolve into polars unless µWD . 5 ×
1033 Gcm3 and the magnetic field of the secondary star is
weak. In this case they may become EXHya-like systems as
the interaction between the magnetic fields is too weak to
synchronise the rotation of the white dwarf to the orbital
motion.
Whilst there are twelve long-period IPs listed in NWS04
with µWD similar to that of SDSSJ2333, there are only four
short-period systems with this property. As short-period
Figure 5. Comparison of the orbital and spin periods of IPs
with short orbital periods. Dotted lines indicate where the spin
period is 0.1, 0.25 and 0.5 times the orbital period. Those sys-
tems which are not confirmed IPs are plotted with open circles.
The error bars are smaller than the points for all systems except
SDSS J023322.61+005059.5.
CVs are predicted to be intrinsically far more common than
long-period ones (de Kool 1992; Kolb 1993; Politano 1996),
this means either that the vast majority of the long-period
IPs become polars or that the known population of short-
period IPs is much less complete than for those with longer
periods. The latter possibility could easily arise as short-
period IPs are in general intrinsically fainter than long-
period IPs (Warner 1995).
5 CONCLUSIONS
SDSSJ2333 was identified as a cataclysmic variable from a
spectrum taken by the SDSS, which shows strong double-
peaked Balmer emission, double-peaked He I emission and
the single-peaked He II emission which is often found in CVs
containing a magnetic white dwarf. We have measured its
orbital period to be 83.12 ± 0.09min from a radial veloc-
ity analysis of the Balmer emission lines. It is therefore an-
other SDSS-identified CV with an orbital period close to the
minimum period for CVs containing unevolved mass donor
stars. Its light curve shows a strong variability with a double-
humped nature and a period of 41.66 ± 0.13min, which is
precisely half that of its orbital period. We interpret this as
arising from hot spots on the surface of the white dwarf pri-
mary component caused by accretion of matter controlled by
a mostly dipolar magnetic field. SDSSJ2333 is therefore the
shortest-period example of a relatively rare class of short-
period intermediate polars. An X-ray detection of its spin
period is highly desirable to further investigate its IP nature.
The fact that its spin period is precisely half of its orbital
period suggests the presence of a physical mechanism which
is maintaining this as an equilibrium state.
Four out of a total of five confirmed short-period IPs,
including SDSSJ2333, have a spin period of approximately
half their orbital period. These systems contain a white
c© 0000 RAS, MNRAS 000, 000–000
6 Southworth et al.
Table 3. Orbital and spin periods of intermediate polar CVs with orbital periods shorter than the 2–3 hr period gap. The estimated
magnetic moments of the systems are from NWS04, either taken from their Table 1 or traced from their Fig. 2.
∗ The IP nature of RXJ1039−0507 and SDSS J023322.61+005059.5 has not been confirmed.
References: (1) Tovmassian et al. (1998); (2) Kemp et al. (2002); (3) de Martino et al. (2005); (4) Rodŕıguez-Gil et al. (2004); (5)
Patterson et al. (2004); (6) Buckley et al. (1998); (7) Hellier et al. (1998); (8) Hellier et al. (2002); (9) Mumford (1967); (10) Vogt et al.
(1980); (11) Hellier & Sproats (1992); (12) Woudt & Warner (2003).
System Orbital period (min) Spin period Pspin Estimated magnetic References
(min) (min) Porb moment (G cm
HT Cam 85.9853± 0.0014 8.58430± 0.00000 0.100 0.3×1033 1, 2, 3
DW Cnc 86.1015± 0.0003 38.58377± 0.00006 0.448 1.5×1033 4, 5
V1025 Cen 84.62 35.73± 0.05 0.422 1.8×1033 6, 7, 8
EX Hya 98.256738± 0.000006 67.02688± 0.00001 0.682 ∼5×1033 9, 10, 11
SDSS J2333 83.12± 0.09 41.66± 0.13 0.501 ∼2×1033 This work
RXJ1039.7−0507 ∗ 94.4597± 0.0001 24.062 ∗ 0.255 0.9×1033 12
SDSS J023322.61+005059.5 ∗ 96.08± 0.09 60± 5 ∗ 0.625 Paper I
dwarf with a magnetic moment of µWD ∼ 2 × 10
33 Gcm3
(corresponding to a field strength of about 2MG). A rela-
tively large number of long-period (Porb & 3 hr) IPs have
spin periods close to a tenth of their orbital periods and
µWD ∼ 2×10
33 Gcm3. From this we suggest that the popu-
lation of long-period IPs with Pspin ∼ 0.1Porb will conserve
µWD during their later evolution and become short-period
IPs with Pspin ∼ 0.5Porb.
ACKNOWLEDGEMENTS
This work is based on observations made with the William
Herschel Telescope, which is operated on the island of La
Palma by the Isaac Newton Group in the Spanish Observa-
torio del Roque de los Muchachos (ORM) of the Instituto
de Astrof́ısica de Canarias (IAC).
JS acknowledges financial support from PPARC in the
form of a postdoctoral research assistant position. BTG ac-
knowledges financial support from PPARC in the form of
an advanced fellowship. TRM was supported by a PPARC
senior fellowship during the course of this work. DDM ac-
knowledges financial support from the Italian Ministry of
University and Research (MIUR). AA thanks the Royal Thai
Government for a studentship. We thank the referee for a
positive report.
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	Introduction
	Observations and data reduction
	WHT spectroscopy
	Calar Alto photometry
	Data analysis
	Radial velocity analysis
	Light curve analysis
	Discussion
	Conclusions
