Spectroscopic Observations of the Intermediate Polar EX Hydrae in
  Quiescence
Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 30 October 2018 (MN LATEX style file v2.2)
Spectroscopic Observations of the Intermediate Polar EX Hydrae in
Quiescence
N. Mhlahlo1,2⋆, D.A.H. Buckley2, V.S. Dhillon3, S.B. Potter2, B. Warner1 and
P.A. Woudt1
1Astronomy Department, University of Cape Town, Rondebosch 7700, Cape Town, South Africa
2South African Astronomical Observatory, Observatory 7935, Cape Town, South Africa
3Physics and Astronomy Department, University of Sheffield, Sheffield, S3 7RH, UK
30 October 2018
ABSTRACT
Results from spectroscopic observations of the Intermediate Polar (IP) EX Hya in quiescence
during 1991 and 2001 are presented. Spin-modulated radial velocities consistent with an outer
disc origin were detected for the first time in an IP. The spin pulsation was modulated with
velocities near ∼ 500− 600 km s−1. These velocities are consistent with those of material
circulating at the outer edge of the accretion disc, suggesting corotation of the accretion cur-
tain with material near the Roche lobe radius. Furthermore, spin Doppler tomograms have
revealed evidence of the accretion curtain emission extending from velocities of ∼ 500 km
s−1 to ∼ 1000 km s−1. These findings have confirmed the theoretical model predictions of
King & Wynn (1999), Belle et al. (2002) and Norton et al. (2004) for EX Hya, which predict
large accretion curtains that extend to a distance close to the Roche lobe radius in this system.
Evidence for overflow stream of material falling onto the magnetosphere was observed,
confirming the result of Belle et al. (2005) that disc overflow in EX Hya is present during
quiescence as well as outburst.
It appears that the Hβ and Hγ spin radial velocities originated from the rotation of the
funnel at the outer disc edge, while those of Hα were produced due to the flow of material
along the field lines far from the white dwarf (narrow component) and close to the white dwarf
(broad-base component), in agreement with the accretion curtain model.
Key words: accretion discs, binary - stars: cataclysmic variables.
1 INTRODUCTION
EX Hya is an Intermediate Polar (IP), a sub-class of magnetic Cat-
aclysmic Variable Stars (mCVs) where a late-type main sequence
star transfers material to the magnetic white dwarf star as the two
stars orbit each other under the influence of their mutual grav-
itation. Unlike in Polars, another subclass of mCVs, where the
white dwarf is in synchronous rotation with the binary rotation
(Pspin = Porb), the white dwarf in an IP is in asynchronous rotation
with the orbital motion of the system. EX Hya, however, is nearer
synchronism than the majority of IPs as it has a spin period (∼67.03
min) which is about 2/3 its orbital period (98.26 min) (Mumford
1967; Hellier et al. 1987), and is one of only six out of thirty nine
confirmed IPs with its orbital period below the 2-3 h CV period gap
(Norton et al. 2004). It has an inclination i = 78◦±1◦.
Recent studies have shown that EX Hya does not conform
to the traditional IP model (King & Wynn 1999; Wynn 2000;
Belle et al. 2002; Norton et al. 2004; Belle et al. 2005). This sys-
⋆ E-mail: nceba@circinus.ast.uct.ac.za
tem has a large Pspin/Porb ratio (∼ 0.68) implying that it can-
not be in the usual spin equilibrium rotation since most IPs
have been shown to attain spin equilibrium near Pspin/Porb ∼
0.1 (King & Wynn 1999; Wynn 2000). This further implies that
the corotation radius is far greater than the circularisation radius
(Rco ≫ Rcir) and that EX Hya cannot possess a Keplerian disc.
Systems with Keplerian discs are expected to have Rco < Rcir and
thus a smaller Pspin/Porb. These factors have prompted theorists to
suggest that the spin equilibrium state in EX Hya is determined
by Rco ∼ b, where b is the distance to the inner Lagrangian point,
L1 (King & Wynn 1999; Wynn 2000; Norton et al. 2004). In this
model the accretion curtains extend to near the L1 point, and EX
Hya resembles an asynchronous Polar where most of the material
accretes via the stream (King & Wynn 1999; Wynn 2000) and via
both the ring of material near the Roche lobe radius of the primary
and the stream (Norton et al. 2004), depending on the orbital and
spin periods of the system, and the magnetic field strength. In the
later publication it was shown that material in EX Hya is fed from
a ring of material at the outer edge of the Roche lobe, and that for
c© 0000 RAS
http://arxiv.org/abs/0704.0017v1
2 N. Mhlahlo, D.A.H. Buckley, V.S. Dhillon, S.B. Potter, B. Warner and P.A. Woudt
Date HJD (start) Time Spectra
24-04-91 2448371.3884097 3.28 90
25-04-91 2448372.3603850 2.93 72
29-04-91 2448376.2402973 7.00 100
24-03-01 2451993.5427099 2.79 42
25-03-01 2451994.3581177 3.77 56
25-03-01 2451994.5147196 3.96 66
26-03-01 2451995.4360089 1.94 48
26-03-01 2451995.5412087 2.92 50
Table 1. Table of spectroscopic observations during quiescence in 1991 and
2001. The column Date denotes the date at the beginning of the observing
night (before midnight), the column Time denotes the number of observing
hours and Spectra the number of spectra obtained.
the Pspin/Porb of EX Hya, this mode of accretion is preferred over
stream-fed accretion.
In this work we present spectroscopic data of EX Hya in qui-
escence obtained from the SAAO in 1991 (just before EX Hya went
into outburst, and a day or two after outburst) and in 2001. Outburst
data of 1991 will be discussed in a later publication.
2 OBSERVATIONS AND DATA REDUCTION
2.1 1991 Observations
EX Hya was observed in April of 1991 by Buckley et al. (1991)
using the SAAO 1.9-m telescope with the Reticon photon counting
system (RPCS) detector on the Cassegrain spectrograph. A grating
with a resolution of 1200 mm−1 was used and a wavelength range
of 4000 - 5080 Å was covered at a spectral resolution of ∆λ ∼1.2
Å and at a time resolution of 100 - 120 s. The spectrograph slit
width was 250 µm (∼1.5 arcsecs). Wavelength calibration expo-
sures were taken using a CuAr arc lamp. Three nights of observa-
tions (24, 25 and 29 April 1991) were covered in quiescence and,
in total, 262 spectra were obtained. The observing log is given in
Table 1 together with the starting times of the observations.
Following wavelength-calibration and sky-subtraction, the
data were flux calibrated using the spectra of the standard star
LTT3864.
2.2 2001 Observations
The 2001 observations were obtained using the SITe CCD detector
(266× 1798 pixels) on the Cassegrain spectrograph of the SAAO
1.9-m telescope. A grating with a resolution of 1200 mm−1 was
used over the wavelength range 4200 - 5100 Å on the nights of
the 25th and 26th April. Another grating with a resolution of 1200
mm−1 was used on the 24th, 25th and 26th April over the range
6300 - 7050 Å. The spectral resolution was ∼1.0 Å and a 1×2
binning scheme was employed (i.e. binning by 2× in the spatial
direction). The exposure times during observations were 60 s. The
observations covered the period 24 April - 26 April 2001 and, in
total, 262 spectra were obtained (Table 1). The extraction and re-
duction of the data were performed the standard way using the
Image Reduction and Analysis Facility (IRAF)1 package and the
1 IRAF is a software package for the reduction and analysis of astronom-
ical data distributed by National Optical Astronomy Observatory (NOAO)
Figure 1. Radial-velocity Fourier amplitude spectra from the 1991 com-
bined data are shown for α = 3000 km s−1 and 900 km s−1 for the Hβ line
(top left panel and second left panel from the top) and for 3000 km s−1 and
1200 km s−1 for the Hγ line (top right panel and second right panel from the
top). Ω denotes the orbital frequency of the system, 2Ω its first harmonic
and ω+Ω the upper orbital side band where ω is the spin frequency. The
data were prewhitened by the orbital frequency and are displayed in the
third panels from the top. Window spectra are plotted below the amplitude
spectra (bottom panels).
spectra were flux calibrated using observations of the standard star
LTT3218.
3 THE RADIAL VELOCITIES
It is widely accepted that in a canonical CV, the high velocity emis-
sion line wings are formed in the inner parts of the accretion disc
orbiting close to the white dwarf and thus should reflect its orbital
motion (Shafter 1983; Shafter & Szkody 1984; Shafter 1985).
In IPs, however, high velocity emission line wings are formed
in the gas streaming towards the white dwarf at high velocities
(Hellier et al. 1987; Ferrario & Wickramasinghe 1993). The ra-
dial velocities were determined by measuring the wings of the Hβ
and Hγ emission lines from the 1991 data (24 and 25/04/91 - the
data obtained on the 29th was not added since EX Hya had not
fully recovered from outburst); and the wings of Hα, Hβ and Hγ
emission lines from the 2001 data using the Gaussian Convolution
which is operated by the Association of Universities for Research in As-
tronomy (AURA)
c© 0000 RAS, MNRAS 000, 000–000
Spectroscopic Study of the IP EX Hydrae in Quiescence 3
Figure 2. Radial velocity amplitude spectra shown for the Hα line from
2001, for α = 3500 km s−1 and 1200 km s−1. The vertical dashed line
shows the expected position of the orbital and spin period peaks. The data
were prewhitened by Ω and are shown in the third panel from the top. A
window spectrum is shown at the bottom.
Scheme (GCS, Schneider & Young 1980; Shafter & Szkody 1984;
Shafter 1985). The GCS method convolves each spectrum with two
identical Gaussian, one in the red wing and one in the blue wing.
The separation between the two Gaussians is 2α. Care was taken
not to include regions far out in the wings where the continuum be-
gins to dominate by choosing reasonable values of the width (σ) of
the Gaussians and α. Twelve standard Gaussian band-passes were
used with α values ranging from 3500 to 100 km s−1 and corre-
sponding width values from 1200 to 100 km s−1.
3.1 Period Searches
The radial velocities were Fourier transformed using the Discrete
Fourier Transform (DFT) algorithm to search for any periods in
the data (Deeming 1975; Kurtz 1985). The Hβ and Hγ amplitude
spectra from 1991 (24 and 25 April) are shown in Figure 1 and the
Hα amplitude spectra from 2001 are shown in Figure 2.
A prominent peak at a frequency corresponding to the 98-
minute orbital frequency, Ω, is observed in all the emission lines.
Second in strength to the orbital frequency is the spin frequency,
ω, of the narrow s-wave component (NSC) (α = 900,1200 km
s−1) (Figures 1 and 2). The third panels from the top in Figures 1
and 2 show the data after prewhitening by Ω. Power at ω is clearly
present.
The spin frequency was not detected at high values of α
(α = 3000,3500 km s−1) where it is most expected (since at these
velocities the material is quite close to the white dwarf and its emis-
sion is expected to be modulated at the white dwarf spin period).
It was also not present in Hβ and Hγ radial velocities of 2001. The
amplitude of ω relative to Ω was found to be ∼81% for Hβ, ∼64%
for Hγ and ∼18% for Hα.
4 ORBITAL VARIATIONS OF THE EMISSION LINES
The data were phase-binned on the orbital ephemeris of Hellier &
Sprouts (1992),
Teclipse = 2437699.94179+0.068233846(4)E, (1)
where E is the number of orbital cycles and T is the time of mid-
eclipse. This ephemeris is defined by the zero point of mid-eclipse,
where minimum intensity is at phase 0.0. This means that for the
radial velocities, maximum blueshift is perpendicular to the line of
centres, at phase 0.75, meaning that spectroscopic phase zero oc-
curs at the blue-to-red crossing of the emission line radial velocity
curve. 40 phase bins were used to produce the radial velocities.
4.1 Orbital Tomograms and Trailed Spectra
The Hα, Hβ and Hγ Doppler tomograms were computed using
the Back Projection Method (BPM) with the application of a fil-
ter, and the Maximum Entropy Method (MEM) (Marsh & Horne
1988; Marsh 1988; Horne 1991; Spruit 1998). The BPM Doppler
maps are shown in Figure 3 and those constructed using MEM are
shown in Figure 4. Error in ephemerides (both orbital and spin) is
sufficiently small to phase all of our data accurately on the orbital
and spin cycles.
A velocity amplitude of the primary, K1 = 74 ± 2 km s
from our radial velocity measurements and that of the secondary,
K2 = 360± 35 km s
−1, taken from Vande Putte et al. (2003) and
Beuermann et al. (2003), were used to fix the positions of the Roche
lobe and the stream trajectories on the tomograms. A secondary
mass, M2 = 0.10±0.01 M⊙ for EX Hya was derived from the up-
to-date secondary mass-period relation of Smith & Dhillon (1998).
The mass of the primary, M1, was then determined from the above
values using K1K2 =
, and was found to be 0.50±0.05 M⊙.
The Hβ, Hγ and HeI λ4471 Doppler tomograms (Figure 3
and 4) show strong emission at the bright spot, some at the Roche
lobe and the stream, and some from the disc. Those of Hα also
show strong bright spot emission but less or no emission from the
stream. Disc emission is diminished in Hα when compared to other
emission lines, especially at higher velocities. This is more obvious
in the BPM tomogram. The bright spot emission falls near the re-
gion (-100, 350) km s−1. Average-subtracted trailed spectra (Fig-
ure 4) show the corresponding NSC. ∼ 1× 10−11ergs cm−2 s−1
(∼60-70%) of the original line fluxes is contained in the average-
subtracted profiles of Hβ and Hγ, and ∼ 1× 10−12ergs cm−2 s−1
(∼80-90%) is contained in Hα and HeI λ4471. This flux is mainly
due to the bright spot and the stream. The trailed spectra have been
repeated over 2 cycles for clarity.
The trailed spectra of 2001 have revealed two interesting fea-
tures. The first one is the asymmetry in the intensity of the s-wave
(Figure 4). In Hα, the red wing of the NSC is brighter at φ98 ∼
0.1−0.3 and seems to reach maximum brightness near φ98 ∼ 0.25,
whereas the blue wing is dimmer in the range φ98 ∼ 0.7−0.9 and
seems to reach minimum brightness near φ98 ∼ 0.75. A similar ef-
fect is seen in the Hβ and the Hγ lines, and to a lesser extent in HeI
λ4471. The second feature is redshifted emission extending from
the NSC to high velocities (∼ 1000 km s−1) at early binary phases
(φ98 ∼ 0.0−0.2).
c© 0000 RAS, MNRAS 000, 000–000
4 N. Mhlahlo, D.A.H. Buckley, V.S. Dhillon, S.B. Potter, B. Warner and P.A. Woudt
Figure 3. The panels show the Hα, Hβ, Hγ and HeI λ4471 orbital Doppler maps from 2001, and Hβ tomograms of 1991, constructed using the Back-Projection
Method with the application of a filter (top panels) and after subtracting the average of the line profile (bottom panels). The positions of the Roche lobe and
stream trajectories are shown (velocity amplitudes of K1 = 74 km s
−1 and K2 = 360 km s
−1 for the primary and secondary stars, respectively, were used). The
two curves with marked intervals represent the gas stream velocity (upper curve) and the Keplerian velocity along the stream (lower curve). The circles on all
tomograms represent 0.1 of the distance from the L1 point to the primary. The three crosses are centres of mass of the secondary, system and primary, from
top-to-bottom. The asterisk represents the velocity of closest approach. All the maps are plotted on the same velocity scale. The lookup table of this figure is
such that the brightest emission features appear with decreasing intensity from yellow/green to light blue in the online edition, or white to grey in the printed
edition.
The reconstructed trailed spectra suggest that this latter fea-
ture is another s-wave, which we shall refer to as the high velocity
component (HVC), crossing the NSC near φ98 ∼ 0.2 − 0.3. The
Doppler tomograms show emission extending from the bright spot
position, passing along the stream path, to the bottom-left quadrant
at high velocities near 1000 km s−1 which is responsible for the
HVC; most of this emission does not fall within the disc and gas
stream velocities on the map, suggesting that there was small or no
overlap of the stream component with the disc.
The 1991 tomograms showed similar results. It is worth noting
that most of the disc emission in 1991 came from the outer disc than
in 2001.
Even though the MEM and BPM pick out the same features,
in the BP tomograms some features are more prominent than in
the MEM tomograms while the reconstruction obtained using the
MEM reproduces the observed data well.
The advantage of BPM over MEM is that it is faster and it
is easier to get a consistent set of maps of different emission lines
(in terms of the apparent noise in the images). For this reason both
methods have been used.
5 SPIN VARIATIONS OF THE EMISSION LINES
5.1 The Spin Radial Velocity Curve
The radial velocities were phase-folded using 30 bins on the
quadratic spin ephemeris of Hellier & Sproats (1992), where spin
maximum was defined as φ67 = 0. Figure 5 shows the variation of
the Hβ, Hγ and Hα narrow components with ω. Maximum blueshift
is seen at φ67 = 0.79 for Hβ and at φ67 = 0.77 for Hγ. Whereas for
Hα, maximum blueshift is seen at φ67 = 0.90. It should be noted
that Hα and Hβ / Hγ have not been observed simultaneously and so
both data sets probably sample the spin phases at different orbital
phases.
Figure 6 shows the Hα narrow component (α = 1200 km s−1)
and the broad-base component (α= 3500 km s−1) overplotted. The
two components are in phase. The radial velocity variation with the
spin period of the Hβ and Hγ broad-base component could not be
detected, possibly due to velocity cancellation We discuss this in
Section 6.
5.2 Spin Tomograms and Trailed Spectra
Spin tomograms of EX Hya were constructed by Hellier (1999)
but revealed little information. Also, Belle et al. (2005) observed
no coherent emission site/s on their tomograms folded on the spin
phase.
The Hβ and the Hγ BPM and MEM spin tomograms from
2001, however, have revealed a coherent emission site between
Vx ∼ 500 km s
−1 and ∼ 1000 km s−1 which is evidence of emis-
sion from the accretion curtains (Figures 7 and 8). But it is a well
known fact that since the spin period is ∼ 23 of the orbital period in
EX Hya, orbital cycle variations do not smear out when folded on
the spin phase but repeat every 3 spin cycles (Hellier et al. 1987).
This is thought to be the origin of most of the structure in the emis-
sion lines at velocities < 1000 km s−1 (Hellier 1999). To address
this problem, phase-invariant subtraction is performed where emis-
sion that does not vary with the spin cycle is subtracted from the
data. This is achieved by measuring minimum flux at each wave-
length and subtracting this value. The results are shown in the sec-
ond panels from the top of Figure 8. It should be mentioned though,
that even subtracting the invariant part of the line profiles does not
guarantee that the influence of the orbital period variations has been
completely removed.
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Spectroscopic Study of the IP EX Hydrae in Quiescence 5
Figure 4. 2001 Hα, Hβ, Hγ and HeI λ4471 trailed spectra (top row of pan-
els) and MEM orbital Doppler maps (second row of panels from the top)
as well as the average-subtracted trailed spectra (third row of panels) are
shown plotted on the same scale except for Hα panels. The HVC and the
NSC are indicated. The fourth row shows the average-subtracted Doppler
maps and the models plotted for q = 0.21, i = 78◦ and M1 = 0.50M⊙ . The
bottom panels are the reconstruction of the average-subtracted data. The
fourth and bottom panels are also plotted on the same scale except for Hα
panels. The lookup table of this figure is such that the brightest emission
features appear with decreasing intensity from black to light grey.
A spin-wave (to differentiate it from the s-wave which is nor-
mally caused by the bright spot) in the Hα trailed spectra (Figure 8)
was detected from the data after the phase-invariant subtraction was
performed. This is the first detection of modulation over the spin
cycle in the optical emission line data of EX Hya. This spin-wave
can be seen in the trailed spectra before (but hard to see) and af-
ter subtraction of the phase-invariant line profile. The narrow peak
component is responsible for this spin-wave which is shown ex-
Ηγα =1200
α = 900
α =1200 αΗ
SPIN PHASE
Figure 5. The Hβ (top panel), Hγ (middle panel) and Hα (bottom panel)
spin radial velocities of the narrow component from the 1991 combined data
(Hβ and Hγ) and 2001 data (Hα). The radial velocities were prewhitened by
the orbital frequency and phase-folded on the spin frequency using 30 bins
and are shown plotted as a function of the spin phase.
Figure 6. The spin radial velocity curves of the Hα narrow (crosses) and
broad (dots) components from 2001 (30 bins) plotted as a function of the
spin phase. The solid line represents a fit to the data.
panded in the second column of panels in Figure 8 (the narrow peak
component was selected by hand over a velocity range of ±500 km
s−1). The spin-wave shows maximum blueshift near phase 1.0 and
maximum redshift near phase 0.5, and has an amplitude of ∼ 500
km s−1. The Hα tomogram shows corresponding emission near the
“3 o’clock” position (blob of emission right at the edge of the map),
around ∼ 500 km s−1. DFTs show lower amplitude (∼ 40 km s−1
for Hα and ∼ 130−140 km s−1 for Hβ and Hγ) probably due to di-
lution by stationary material. Also, the Hα MEM tomogram shows
stronger emission that peaks in a broad structure at lower velocities
(Vx ∼ -200 km s
−1 – ∼ +200 km s−1 – around the “5-6 o’clock”
position). Circular motion gives rise to low or zero radial velocities
when the motion is perpendicular to the line of sight, and the emis-
sion seen around the “5-6 o’clock” position could not be from such
velocities since it shows maximum blueshift at φ67 ∼ 0.2− 0.25.
Similar emission was observed in a Polar and was thought to be
due to material that has just been decelerated after having attached
to the magnetic field lines (Schwarz et al. 2005) (we discuss an
alternative explanation in Section 6). The emission near the edge
c© 0000 RAS, MNRAS 000, 000–000
6 N. Mhlahlo, D.A.H. Buckley, V.S. Dhillon, S.B. Potter, B. Warner and P.A. Woudt
Figure 7. The Hα, Hβ, Hγ and HeI λ4471 trailed spectra from 2001 folded
on the spin period are shown at the top panels and the average-subtracted
spectra are shown at the second panels. Doppler maps constructed from
the phase-invariant subtracted spectra are shown in the bottom panels. The
Doppler maps were constructed using the BPM and are shown on the same
velocity scale with the trailed spectra. The lookup table is as in Figure 3.
of the tomogram (at ∼ 500 km s−1) shows maximum blueshift at
φ67 ∼ 1.0 and therefore cannot be due to motion perpendicular to
the line of sight either.
The Hα trailed spectra also show emission coupled to the spin-
wave near φ67 ∼ 0.1 − 0.6 that extends to high velocities in the
red, a similar situation to that seen the in orbital tomograms due
to the HVC (Section 4.1). The corresponding emission in the Hα
tomograms extending to higher velocities in the red spectral region
is not clear.
Both the Hβ and Hγ phase-invariant subtracted trailed spectra
show three weak-intensity spin-waves. The most clearly visible of
the three is phased with maximum redshift near φ67 ∼ 0.3− 0.4,
with an estimated velocity amplitude of ∼ 900 km s−1 and corre-
sponds to the emission near the “3 o’clock” position in the tomo-
gram (Figure 8). The reconstructed trailed spectra reproduce the
observed data.
The Hβ and Hγ trailed spectra in Figure 7 seem to support
these results. The emission observed near the “3 o’clock position”
in the tomograms has also been seen in other IPs such as AO Psc
and FO Aqr (Hellier 1999) and was interpreted as emanating from
the upper accretion curtain.
The spin-waves are weak in intensity though, and more data
are needed to support these results.
6 DISCUSSION OF THE ORBITAL AND SPIN DATA
The generally accepted model of EX Hya has the material leaving
the secondary star through the L1 point, passing via a stream of
material which orbits about the white dwarf, to form an accretion
Figure 8. Hα, Hβ and Hγ trailed spectra of 2001 folded on the spin period
are shown in the top panels and the phase-invariant subtracted trailed spectra
are shown in the second panels from the top. MEM spin Doppler tomograms
constructed from the phase-invariant subtracted spectra are shown in the
third panels with the reconstructed spectra in the bottom panels. The spin
wave observed in the Hα phase-invariant subtracted trailed spectra, which
was caused by the Hα narrow component, is shown expanded on a smaller
velocity scale. The first column of panels are plotted between -1500 km s−1
and 1500 km s−1 and the last two column are plotted between -2000 km
s−1 and +2000 km s−1. The lookup table is as in Figure 4.
disc. The magnetic field lines of the white dwarf which form accre-
tion curtains above and below the orbital plane channel the material
from the disc, starting from the co-rotation radius (Rco) where the
disc is truncated by the field lines, to the surface of the white dwarf
(Hellier et al. 1987; Rosen et al. 1991).
King & Wynn (1999) challenged this model by arguing that
systems with Pspin/Porb > 0.1 cannot possess Keplerian discs since
this implies Rco ≫Rcir. They showed that the spin equilibrium state
in EX Hya is determined by Rco ∼ b, where b is the distance to the
L1 point. In this model the accretion curtains extend to near the L1
point, and EX Hya resembles an asynchronous polar where most of
the material accretes via the stream (King & Wynn 1999; Wynn
2000).
Belle et al. (2002) revised the model of EX Hya after they
showed that their EUV data support the model of King & Wynn
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Spectroscopic Study of the IP EX Hydrae in Quiescence 7
(1999). Their revised model suggested that the magnetic field in
EX Hya forms a large accretion curtain extending to the outer edge
of the Roche lobe causing:
• part or all of the non-Keplerian disc (hereafter the ring of ma-
terial or the ring) to rotate with the white dwarf,
• an extended bulge (later, Belle et al. (2005) showed that there
was Vertically Extended Material (VEM) obscuring the s-wave
emission during φ98 = 0.57− 0.87, and evidence for overflowing
stream accretion in EX Hya), and
• the ring of material to feel magnetic force at the regions of the
ring close to the poles, causing the ring material at these locations
to be controlled by the magnetic field, forming two chunks along
the accretion ring that rotate with the white dwarf.
Recently, Norton et al. (2004, 2004a) have shown that for sys-
tems with Pspin/Porb ∼ 0.72, when the mass ratio is smaller at
q = 0.2, the material forms a ring near the edge of the primary
Roche lobe, from where accretion curtains funnel down to the white
dwarf surface, in agreement with King & Wynn (1999) and Belle
et al. (2002). The material is fed from the ring (ring-fed accretion)
and channeled along the magnetic field lines (when the angle be-
tween the white dwarf spin axis and magnetic dipole axis is small
i.e < 30◦, which is true for EX Hya).
The discussion by Eisenbart et al. (2002) on the IR-UV flux
distribution in EX Hya implies a disc (isobaric and isothermal) with
an outer radius of 1.6×1010 cm and a thickness of 2×108 cm, and
an assumed central hole of 6×109 cm, but Eisenbart et al. (2002)
suggested that the structure could also be a ring with a larger in-
ner radius, in line with the suggestion of King & Wynn (1999);
Belle et al. (2002) and Norton et al. (2004). They found that the
disc component contains about 1/6 of the total flux which is a bit
more than expected from gravitational energy release at the inner
radius, Rin > 6×10
9 cm.
Our spectroscopic data support both the model of Belle et al.
(2002) and Norton et al. (2004) in which material from a ring, cir-
cling the white dwarf and co-rotating with the magnetic field lines
at the outer edge of the Roche lobe, is accreted by the white dwarf.
The presence of the bright spot revealed by the trailed spectra,
the DFTs of the radial velocities and the Doppler maps (Figures 3
and 4) suggest the presence of a disc or ring of material extending
to near the Roche lobe radius, around the white dwarf. When com-
paring the 1991 and 2001 tomograms for the Hβ they appear to be
in the same state or similar, given the fact that they are ten years
apart. It is reassuring that the fact that the two groups of lines have
not been measured simultaneously is not a significant problem in
the analysis.
More importantly, a spin pulse modulated at velocities con-
sistent with those of the material circulating at the outer edge of
the disc (∼ 500−600 km s−1) (Figures 1 and 2) was detected and
provides evidence for co-rotation of the extended accretion curtains
with the ring material. As discussed in Section 5.2, these low radial
velocities mentioned above were not caused by motion perpendic-
ular to the line of sight near the white dwarf, neither were they
caused by velocity cancellation as will be shown later.
A spin wave was detected in the spin-folded trailed spectra
of Hα (Figure 8) with a velocity semi-amplitude of ∼ 500-600
km s−1. The spin wave shows maximum blue-shift near phase
φ67 ∼ 1.0 (when the upper magnetic pole is pointed away from
the observer) and maximum redshift near phase φ67 ∼ 0.5. The Hα
equivalent widths show maximum flux near φ67 ∼ 1.0. This picture
is consistent with the accretion curtain model of IPs and is possible
if accretion occurs via a disc/ring. The spin tomograms (Figures 7
and 8) show evidence of the accretion curtain emission extending
from ∼ 500 km s−1 to high velocities (∼ 1000 km s−1), suggesting
that material is channeled along the field lines from the outer ring.
The Hα narrow and broad base components show similar phase
variation, suggesting same position of maximum radial velocity as
shown in Figures 6 and 9 (line OA). This indicates that material is
channeled from the ring (at low velocities) to high velocities along
the field lines.
A mass ratio of q ∼ 0.2 was measured from our data, and so
the period ratio Pspin/Porb ∼ 0.68 is consistent with the ring accre-
tion model of Norton et al. (2004).
Decreased prominence of the narrow s-wave component
around φ98 = 0.57−0.87 (Figure 3 and 4) was observed and sug-
gests the presence of VEM at the outer edge of the ring of ma-
terial obscuring the emission at these phases. The presence of the
overflow stream may be infered from this observation (Belle et al.
2005). But direct evidence comes from orbital Doppler tomograms
which show an asymmetry in the emission, where more emission
is observed from the secondary Roche lobe to the lower left quad-
rant than from the opposite side. Average-subtracted orbital tomo-
grams show this emission at higher velocities (∼900-1000 km s−1)
(Figures 3 and 4), and it corresponds to the HVC observed in the
trailed spectra, which is modulated with a velocity semi-amplitude
of ∼ 1000 km s−1. This HVC is reminiscent of that detected by
Rosen et al. (1987) in the trailed spectra of the AM Her system
V834 Cen. Their HVC was blueshifted with a velocity of 900 km
s−1and was said to be produced in the stream close to the white
dwarf. The only difference is that there was no evidence of the
HVC emission when it was expected to be seen redward of another
component (medium-velocity component) in their data, whereas in
EX Hya the evidence of the HVC emission is missing between
φ98 ∼ 0.3− 0.85. The HVC emission is maximally blueshifted at
φ98 ∼ 0.3−0.4. This phasing is consistent with the expected phase
of impact of a stream of material from the secondary with the disc
or of the overflow stream material free-falling onto the magneto-
sphere of the primary (Hellier et al. 1989).
Support for overflow stream is also provided by spin tomo-
grams where emission is observed on the upper accretion curtain
with velocities consistent with stream velocities. This suggests that
this emission site may also have resulted due to impact of overflow
stream with the magnetosphere. The resulting emission is receding
from the observer at maximum redshift near φ67 ∼ 0.4 (Figure 8),
in agreement with the accretion curtain model.
The model of King & Wynn (1999) is not fully supported by
our observations since it predicts direct accretion via a stream. Our
observations, however, fit the models of Norton et al. (2004) and
Belle et al. (2002, 2005). There is evidence for strong Hα emis-
sion of the narrow s-wave component in the spin tomograms, cen-
tred around ∼ 100 km s−1 (Figure 8), that is not accounted for by
these models. This emission shows maximum blueshift at phase
φ67 ∼ 0.2, suggesting that these are rotational velocities (or a com-
bination of streaming and rotational velocities) of the antiphased
motion of a source locked to the white dwarf. One possible expla-
nation is that this emission comes from the opposite pole of the
white dwarf, at a radial distance of 6×109 cm (∼8Rwd). Siegel
(1989) found that the eclipsed optical source in EX Hya is centred
at a radial distance of 1.5×109 cm (∼2Rwd), which is about four
times closer to the white dwarf compared to our result. This could
be the same emission region, but in our observations the emission is
spread out, possibly due to the quality of the data, and this could ac-
count for the difference in the radial distance values quoted above.
But we cannot imagine a geometry where such low rotational ve-
c© 0000 RAS, MNRAS 000, 000–000
8 N. Mhlahlo, D.A.H. Buckley, V.S. Dhillon, S.B. Potter, B. Warner and P.A. Woudt
Observer
ring of material
through upper pole
magnetic axis
phases of maximum blueshift of the 
phase of maximum blueshift
phases of maximum redshift
chunk of material’s
overflowing stream 
of the s−wave
narrow s−wave 
chunk of
material
with field
corotating 
phase of maximum
blueshift of the HVC
Observer
0.75 0.7
outer disc
corotating with field
part of disc 
maximum blueshift
Ηα BBC
phase of
maximum intensity
phase of
magnetic axis
through
upper pole
phase of
minimum intensity
Ηα BBC
maximum redshift
phase of
Figure 10. A model of EX Hya in quiescence. The figures are drawn over the orbital cycle (left) and spin cycle (right) and show the magnetosphere extending
to the outer edge of the ring, and the chunk of material corotating with the field lines. A verticaly extended material (VEM) is irradiated by the white dwarf in
its inner regions (left).
Observer
Figure 9. A depiction of the regions where Hα was formed. Both the nar-
row and broad base components fall along the same radial direction, OA,
resulting in similar phase variation.
locities can dominate over streaming velocities along the field lines
near the white dwarf. We therefore suggest that this is evidence for
material that is diverted out of the orbital plane. Since one of the
assumptions of Doppler tomography is that everything lies on the
plane, it is not possible to locate the exact position of this emission
relative to the white dwarf.
6.1 White dwarf and secondary masses
Hellier et al. (1987) showed that maximum line widths of ±3500
km s−1 constrain the mass of the white dwarf, and a free-fall
velocity of this magnitude could be achieved for white dwarf
masses greater than 0.48 M⊙. We found M1 = 0.50 ± 0.05M⊙ ,
in good agreement with the results obtained from recent stud-
ies by Hoogerwerf et al. (2004); Beuermann et al. (2003) and
Vande Putte et al. (2003).
For the secondary, we derived M2 = 0.10 ± 0.01 M⊙ from
the secondary mass-period relation of Smith & Dhillon (1988), and
this value agrees with that obtained by Vande Putte et al. (2003).
Beuermann et al. (2003) and Hoogerwerf et al. (2004) find lower
values for M2 consistent with 0.09 M⊙. Eisenbart et al. (2002) ar-
gues that for a secondary mass as low as 0.1 M⊙ the secondary
would have to be substantially expanded by ∼10%.
6.2 The revised model of EX Hya
We propose a model where one of the two chunks alluded to by
Belle et al. (2002), which are formed by the magnetic pull along
the accretion ring, co-rotates with the accretion curtains at the outer
edge of the Roche lobe at ∼ 500-600 km s−1, giving rise to the pul-
sation of emission at the spin period which we observe in our data,
while the other is hidden by the accretion curtain below the ring
of material. The resulting emission is maximally blueshifted near
φ67 ∼ 0.8 (Figure 5). In the accretion curtain model, at φ67 ∼ 0.5
in the spin cycle, minimum flux (due to higher opacity) is observed
when the upper accretion pole of the white dwarf is pointed to-
wards the observer (Hellier et al. 1987), and so the phasing men-
tioned above is compatible with the motion of a rotating accretion
funnel. This is illustrated in Figure 10, where the position of the
observer at pulse maximum is indicated, and the axis of the mag-
netic pole is shown. The disruption of the disc by the magnetic
field at the outer disc is illustrated and part of the disc co-rotating
with the magnetosphere is shown. At a corotation radius, Rc ∼
b = a(0.500 − 0.227log M2M1 ) (∼ 3× 10
10 cm), the material is ro-
tating at a velocity of v2 = GMb ∼ 500 km s
−1, in good agreement
with the observations. Also, a rotation velocity of ∼ 600 km s−1
was measured from the spectra and the radial distance from the star
to the ring of material was found to be ∼ 3× 1010 cm, which is
similar to b, for a white dwarf mass of 0.5 M⊙ (Keplerian motion
about the white dwarf had to be assumed in these calculations).
At this radius, the accretion curtain is also rotating at a velocity of
2πRco/Pspin ∼ 500 km s−1.
∼ 6× 10−12 ergs cm−2 s−1 (64% - integrated over one spin
cycle) of the original line fluxes that is contained in the average-
c© 0000 RAS, MNRAS 000, 000–000
Spectroscopic Study of the IP EX Hydrae in Quiescence 9
subtracted profile of Hα shows radial velocity variations with the
spin period. Assuming that Hβ and Hγ also show a similar flux
variation (Hβ and Hγ spin tomograms also show a low-velocity s-
wave but this result is not secured due to poor quality of data),
the total line fluxes showing radial velocity variations with the
spin period can be estimated to be ∼ 2× 10−11 ergs cm−2 s−1
for the three emission lines. This is ∼2/10 of the total disc flux
(Eisenbart et al. 2002), suggesting that only part of the ring coro-
tates with the white dwarf while the rest of the material may be in-
volved in a near Keplerian motion (this is a rough comparison since
the flux is integrated over one spin cycle for Hα, Hβ and Hγ in our
data whereas Eisenbart et al. (2002) derived their total flux values
from one spectrum over the wavelength range λ = 912−24000 Å).
While some of the ring material co-rotates with the accre-
tion curtains (i.e. remains in the disc rather than being immedi-
ately channeled along the field lines), some is channeled along the
field lines at ∼ 500 km s−1 towards the white dwarf. There is also
some material that overflows the ring and attaches onto the mag-
netic field lines. The overflow stream hits the magnetosphere, prob-
ably causing a second bright spot on the slowly rotating magneto-
sphere (Figure 10). The overflow stream is irradiated by the white
dwarf in its inner regions close to the white dwarf (the regions fac-
ing the white dwarf). This results in the HVC emission being ob-
scured at φ98 ∼ 0.4− 0.9, which are phases where the stream is
viewed from behind-opposite the side facing the white dwarf, hid-
ing the irradiated inner regions. HVC emission from the stream is
blueshifted when that from the narrow s-wave component shows
maximum redshift. Near φ98 ∼ 0.25 the two s-waves intersect, ex-
plaining the asymmetry in the brightness of the s-wave seen near
φ98 ∼ 0.25 (Figure 4). The overflow stream curls nearly behind the
white dwarf and it is truncated by the field when the upper magnetic
pole is facing the stream.
Ferrario & Wickramasinghe (1993) and Ferrario, Wickramas-
inghe & King (1993) showed that in IPs the accretion curtain below
the orbital plane can contribute in the radial velocities of a system
if it can be seen either through the central hole of the truncated
disc, or from below the disc, or both. This effect will result in ve-
locity cancellation due to nearly equal quantities of material that
are blueshifted and redshifted on the accretion curtains (Ferrario,
Wickramasinghe & King 1993).
In EX Hya where the inclination is high (78◦) and the disrup-
tion radius is large (∼ 40 RW D, for a white dwarf mass of 0.5 M⊙)
as proposed in Figure 10, it is clear that we see spin-varying emis-
sion from two opposite magnetic poles, producing a fairly symmet-
ric structure in the spin-folded line profiles (Hellier et al. 1987;
Rosen et al. 1991). If emission from these opposite poles is can-
celling out then the sum will have a much lower velocity. This could
explain the near zero and low amplitude of the radial velocity vari-
ation at the spin period of the Hβ and Hγ, and Hα (6 40 km s−1)
broad-base component, respectively (see also Hellier et al. (1987)
and Ferrario, Wickramasinghe & King (1993)).
One could take this argument further by suggesting that the
spin modulation we observe in our data at velocities near ∼ 500
km s−1 (Figures 1 and 2) is just the slight asymmetries between
the two poles. The resulting velocity could just be a measure of
the degree to which the poles cancel their velocities near ±3500
km s−1(Coel Hellier; private communication). This, however, can-
not be the case for Hβ and Hγ since these two emission lines show
motion that is consistent with that of a rotating object, suggesting
that the line profiles are not dominated by the infall velocities at
the two opposite accretion poles. If they were produced close to
the white dwarf then maximum rotational velocity near ±3500 km
s−1 would be 2πR/Pspin ∼ 30 km s−1, which is much smaller than
∼ 500 km s−1. However, rotional velocities close to the ring are
∼ 500 km s−1. For Hα, however, we observe maximum blueshift
at φ67 ∼ 1.0, and so velocity due to cancellation anywhere between
0 and ±3500 km s−1are expected, depending on how much the
two poles cancel. If both accretion curtains are still visible and
symmetric at large radii (which is possible as suggested by Fer-
rario, Wickramasinghe & King (1993) and our model), velocity
cancellation will still result in smaller amplitudes than those of
∼ 500 km s−1observed in our data. This would then count against
the argument above. Furthermore, Hα orbital Doppler tomograms
show strong emission at the bright spot. If our model is correct, the
field lines should also attract this Hα dominated material, which is
chanelled along the field lines, as already shown above. The veloc-
ity of this material due to streaming motion near the outer ring is
less than that of the Hα broad-base component close to the white
dwarf, as expected. A strong constraint on our model is that the
disruption radius of EX Hya has been shown to be at 5-9×109 cm
(Hellier et al. 1987; Beuermann et al. 2003) which implies a white
dwarf magnetic moment of µ ∼ 7× 1031 G cm3. For our model
this would imply that the accretion curtains do not extend to near
the Roche lobe radius. The theoretical analysis of King & Wynn
(1999) and Wynn (2000), however, has shown that equilibrium ro-
tation is possible if the magnetic moment in EX Hya falls within the
range of 1033 6 µ6 1034 G cm3. These are comparable to weakest
field AM Hers below the period gap, and that EX Hya could pos-
sess such magnetic moments is supported to a certain extent by the
average-subtracted trailed spectra of EX Hya that are reminiscent
of emission lines seen in some Polars, e.g. V834 Cen (as discussed
above), EF Eri (Crampton et al. 1981; Cowley et al. 1982), QS Tel
(Romero-Colmenero et al. 2003) and VV Pup (Diaz 1994). Fur-
thermore, Cumming (2002) raised the possibility that the magnetic
fields in IPs are buried by the material due to high accretion rates
and so are not really as low as they appear. The ring structure in EX
Hya could imply higher accretion rates in EX Hya than previously
thought since the capacity of the ring of material to store matter
may be low when compared to that of a classical disc, resulting in
the accretion of more material than in a classical disc case.
7 SUMMARY
Optical observations of EX Hya and the analysis have suggested
that large accretion curtains extending to a distance close to the
L1 point exist in this system. The DFTs and spin tomograms have
for the first time provided evidence for corotation of the field lines
with the ring material near the Roche lobe. Also, tomography and
the phasing of the spin waves have suggested that feeding by the
accretion curtains of the material from the ring (ring-fed accretion)
takes place. These findings support the models of Belle et al. (2002)
and Norton et al. (2004) for EX Hya and the simulations done by
Norton et al. (2004a) which have shown that for systems with the
parameters of EX Hya, the accreting material forms a ring at the
outer edge of the primary Roche lobe, from where accretion cur-
tains funnel down to the white dwarf surface.
Evidence for stream overflow accretion has been observed.
The HVC caused by the overflow stream disappeared at φ98 ∼
0.4−0.9 due to obscuration by the stream. Obscuration of the NSC
at φ98 ∼ 0.57−0.87 suggested the presence of the VEM which was
irradiated by the white dwarf in its inner regions.
The Hα broad-base component shows a radial velocity varia-
tion with the spin period whereas that of Hβ and Hγ could not be
c© 0000 RAS, MNRAS 000, 000–000
10 N. Mhlahlo, D.A.H. Buckley, V.S. Dhillon, S.B. Potter, B. Warner and P.A. Woudt
detected. The low-amplitude velocity variations modulated at the
spin period for Hα and for Hβ and Hγ is explained in terms of ve-
locity cancellation effects.
We have provided an explanation for the asymmetry in the
intensity of the narrow s-wave component seen in EX Hya trailed
spectra in the optical. The narrow s-wave component and the HVC
cross at φ98 ∼ 0.25, resulting in the asymmetry in brightness that
we observe at these phases.
The spin-folded trailed spectra are not of good quality and
more data are needed to confirm these results.
ACKNOWLEDGMENTS
NM would like to acknowledge financial support from the Sains-
bury/Linsbury Fellowship Trust and the University of Cape Town.
We would like to thank Kunegunda Belle, Coel Hellier and Andrew
Norton for invaluable discussions and for their constructive com-
ments. We acknowledge use of D. O’Donoghue’s and Tom Marsh’s
programs Eagle and Molly, respectively.
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c© 0000 RAS, MNRAS 000, 000–000
http://arxiv.org/abs/astro-ph/9806141
	Introduction
	Observations And Data Reduction
	1991 Observations
	2001 Observations
	The Radial Velocities
	Period Searches
	Orbital Variations of the Emission Lines
	Orbital Tomograms and Trailed Spectra
	Spin Variations of the Emission lines
	The Spin Radial Velocity Curve
	Spin Tomograms and Trailed Spectra
	Discussion of the Orbital and Spin Data
	White dwarf and secondary masses
	The revised model of EX Hya
	Summary
	References
