Solving the kilo-second QPO problem of the intermediate polar GK Persei

Abstract

We detect the likely optical counterpart to previously reported X-ray QPOs in spectrophotometry of the intermediate polar GK Persei during the 1996 dwarf nova outburst. The characteristic timescales range between 4000--6000 s. Although the QPOs are an order of magnitude longer than those detected in the other dwarf novae we show that a new QPO model is not required to explain the long timescale observed. We demonstrate that the observations are consistent with oscillations being the result of normal-timescale QPOs beating with the spin period of the white dwarf. We determine the spectral class of the companion to be consistent with its quiescent classification and find no significant evidence for irradiation over its inner face. We detect the white dwarf spin period in line fluxes, V/R ratios and Doppler-broadened emission profiles. Comment: 14 pages, 11 figures. Accepted for publication in MNRAS

Full text

Page 1

arXiv:astro-ph/9901302v1 21 Jan 1999
Mon. Not. R. Astron. Soc. 000, 1–14 (0000)Printed 1 February 2008(MN LaTEX style file v1.4)
Solving the kilo-second QPO problem of the intermediate
polar GK Persei
L. Morales-Rueda1, M.D. Still2and P. Roche1
1Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QJ (lmorales@star.cpes.susx.ac.uk, pdr@star.cpes.susx.ac.uk)
2Physics and Astronomy, University of St. Andrews , North Haugh, St. Andrews, Fife KY16 9SS (mds1@st-and.ac.uk)
Accepted 1999 January 20. Received 1998 December 16; in original form 1998 July 29.
ABSTRACT
We detect the likely optical counterpart to previously reported X-ray QPOs in
spectrophotometry of the intermediate polar GK Per during the 1996 dwarf nova out-
burst. The characteristic timescales range between 4000–6000s. Although the QPOs
are an order of magnitude longer than those detected in the other dwarf novae we
show that a new QPO model is not required to explain the long timescale observed.
We demonstrate that the observations are consistent with oscillations being the re-
sult of normal-timescale QPOs beating with the spin period of the white dwarf. We
determine the spectral class of the companion to be consistent with its quiescent clas-
sification and find no significant evidence for irradiation over its inner face. We detect
the white dwarf spin period in line fluxes, V/R ratios and Doppler-broadened emission
profiles.
Key words:
accretion, accretion discs – binaries: close – line profiles – stars: cataclysmic variables
– stars: individual: GK Per – X-rays: stars.
1 INTRODUCTION
GK Per (Nova Per 1901; Campbell 1903), belongs to a sub-
group of cataclysmic variables (CVs) called Intermediate
Polars (IPs). In these systems an asynchronously-rotating,
magnetic white dwarf accretes material from a less-massive,
late-type companion filling its Roche lobe. Gas leaving the
companion star attempts to form an accretion disc around
the primary star but its magnetic field either prevents the
formation of the disc or truncates it near the white dwarf.
GK Per was identified with the X-ray source A0327+43
by King, Ricketts & Warwick (1979) and confirmed as an IP
by the detection of a 351s X-ray spin pulse by Watson, King
& Osborne (1985; hereafter WKO) and Norton, Watson &
King (1988). The same period was subsequently found in
optical photometry by Patterson (1991). GK Per has the
longest orbital period from the sample of known CVs, Porb
= 2d, (Crampton, Cowley & Fisher 1986; hereafter CCF).
The wide binary separation combined with a relatively weak
magnetic field (∼ 1 MG) means that a truncated accretion
disc must be present if current theories of disc formation
are correct (Hameury, King & Lasota 1986). The presence
of a disc has yet to be confirmed by direct observation, al-
though the system does undergo dwarf nova outbursts every
2–3years where its optical brightness increases from 13th to
10th magnitude (Sabbadin & Bianchini 1983). The most-
likely mechanism for dwarf nova outbursts is a thermal in-
stability within an accretion disc (Osaki 1974). GK Per out-
bursts have been modelled as such by Cannizzo & Kenyon
(1986) and Kim, Wheeler & Mineshige (1992).
This paper is a continuation of paper i (Morales-Rueda,
Still & Roche 1996), in which we presented spectrophoto-
metric observations of GK Per taken on the rise to its 1996
outburst (Mattei et al. 1996). We reported the detection
of quasi-periodic oscillations (QPOs) within the Doppler-
broadened emission lines of H i and He ii. This provides
an opportunity to map the velocity structure of the oscilla-
tions. QPOs are defined as low-coherence brightness oscil-
lations thought to be associated with material within the
inner accretion flows of CVs. Theoretical models developed
to explain QPOs consider the presence of dense blobs of ma-
terial orbiting in the inner regions of the accretion disc (Bath
1973), or non-radial pulsations over the surface of the white
dwarf (Papaloizou & Pringle 1978), or radially-oscillating
acoustic waves in the inner disc (Okuda et al. 1992; Godon
1995). In these models, the QPO timescales match observa-
tions of dwarf novae and are of the order of a few hundred
seconds. However the QPO periods detected in GK Per are
an order of magnitude longer than this. Previous to this
paper they have only been detected in X-ray data taken
during outbursts; WKO discovered them in 1.5–8.5 keV EX-
OSAT data at the peak of the 1983 outburst, while Ishida
c ? 0000 RAS

Page 2

2L. Morales-Rueda, M.D. Still, P. Roche
Figure
1996
(http://www.kusastro.kyoto-u.ac.jp/vsnet/). The arrows indi-
cate the times of our spectrophotometric observations.
1. The visual light curve of GK Per during the
outburstobtainedfrom theVariableStarNetwork
et al. (1996) report a second detection at 0.7–10 keV with
ASCA during the rise to the 1996 outburst discussed in this
paper.
To explain the long timescales WKO suggested the
QPO mechanism is caused by beating between the 351s
white dwarf spin period and inhomogeneous gas orbiting at
the inner edge of the accretion disc. Hellier & Livio (1994;
hereafter HL) noted that the X-ray hardness ratio varies
over the QPO cycle as expected from photoelectric absorp-
tion by cool gas and that a period of a few thousand sec-
onds is consistent with the orbital frequency of gas if it is
deposited onto the disc by a gas stream which has partially
avoided impacting the outer disc rim and follows a ballistic
trajectory. They propose that the QPO mechanism is X-
ray absorption by vertically-extended blobs of gas orbiting
at this preferred inner impact radius. In paper i we deter-
mined that the characteristic velocity structure of the optical
counterpart to the QPOs observed by Ishida et al. (1996) is
consistent with blobs in the inner disc. In the current paper
we present further analysis which indicates that the optical
QPO is also driven by absorption, but favours strongly a
beat model over the disc-overflow interpretation.
2OBSERVATIONS
Between 1996 February 26 and 28, 6–8 days before the
ASCA pointings of Ishida et al. (1996), we obtained spec-
trophotometry of GK Per using the Intermediate Dispersion
Spectrograph mounted on the 2.5m Isaac Newton Telescope
(INT) on La Palma. Table 1 gives a journal of observations.
In Fig. 1 we show a visual light curve obtained by the Vari-
able Star Network during the 1996 outburst, with arrows
indicating the days on which we made observations. The
quick readout mode was used in conjunction with a Tek-
tronix CCD windowed to 1024×150 pixels to reduce dead
Table 1. Journal of observations. E is the cycle number plus
binary phase with respect to the ephemeris given by Crampton,
Cowley & Fisher (1986). Phases have been adjusted by π/2 so
that phase 0 corresponds to superior conjunction of the white
dwarf.
DateStart End Start
(E− 2000)
EndNo. of
spectra(1996 Feb)(UT)
26
27
28
20.06
20.04
20.06
0.12
0.07
0.04
617.119
617.620
618.121
617.204
617.704
618.204
109
116
117
time and obtain good sampling of the spin cycle. The expo-
sure times and resolution of the data were already described
in paper i.
After debiasing and flat-fielding the frames by tungsten
lamp exposures, spectral extraction proceeded according to
the optimal algorithm of Horne (1986). The data were wave-
length calibrated using a CuAr arc lamp and corrected for
instrumental response and extinction using the flux stan-
dard HZ15 (Stone 1977). The spectrograph slit orientation
of PA 249.1◦allowed a 15th magnitude nearby star approx-
imately 0.5arcsec ENE of GK Per to be employed as cali-
bration for light losses on the slit.
We also have available to us spectroscopy of various K-
type stars from 1995 October 11 to 13 obtained from the
INT and from 1995 October 30 to November 2 with the
2.1m telescope in the McDonald Observatory in Texas. The
INT instrumental setup was identical to the one used for
the 1996 observations described above. For the McDonald
data, the low-to-moderate resolution spectrometer ES2 was
employed in conjunction with the TI1 CCD and a grating
ruled at 1200 linesmm−1covering the wavelength region
λ4196˚ A–λ4894˚ A giving a resolution of 200 km s−1at Hβ.
The spectra were flat-fielded, optimally extracted and
wavelength calibrated also in the standard manner. Flux
calibrations were applied using observations of the standards
HD19445 (Oke & Gunn 1983) and Feige 110 (Stone 1977) for
the October and November data respectively. Table 2 gives
a list of the K-type templates observed over both runs.
3RESULTS
3.1Average spectra
Fig. 2 presents the average of all the data collected on 1996
Feb 28. It is characterised by a flat continuum, broad Balmer
and Hei lines in emission, high excitation lines of Heii, Niii
and Ciii and numerous faint, narrow absorption features of
Fe i, Cai, Tiii and Srii that had been identified as signa-
tures of the K-type secondary star by Kraft (1964), Gal-
lagher & Oinas (1974), CCF and Reinsch (1994).
We employed K star spectral templates to determine
which luminosity class best matched the secondary star in
this system during outburst and search for signatures of in-
creased X-ray irradiation. Using CCF’s fit to the orbital ra-
dial velocity of the secondary star we shifted out the orbital
motion of the absorption lines with a quadratic rebinning
algorithm. We binned in velocity the spectra of GK Per and
the K-type templates to ensure that they all had identical
wavelength ranges and dispersions. We employed the op-
timal subtraction algorithm of Marsh, Robinson & Wood
c ? 0000 RAS, MNRAS 000, 1–14

Page 3

The kilo-second QPOs of GK Per3
Figure 2. The top spectrum is an average of all GK Per spectra obtained during the third night of observations. The bottom spectrum
corresponds to the K1IV template HD197964 multiplied by 3×10−4. The middle spectrum is the residual resulting from the subtraction
of the template from the averaged GK Per spectrum and probably resembles the spectrum of the accretion flow.
(1994) to determine the K star spectral type – we multiply
the template by a monochromatic constant which represents
the contribution to the spectrum from non-stellar sources of
light and subtract the resulting spectrum from the GK Per
data. The residual was smoothed using a high-pass band fil-
ter (FWHM of gaussian = 13˚ A), and a χ2test performed
between the original and smoothed residual. This is an it-
erative procedure to determine the optimum value of the
monochromatic constant which continues until χ2is min-
imised. Table 2 lists the templates, their spectral classes,
and the reduced χ2obtained after applying optimal sub-
traction. The best fit template is the K1iv star HD197964
which provided a reduced χ2of 2.5. The secondary star con-
tributes 13 per cent of the total light in this spectral region
on the third night of observations. This compares to 33 per
cent found by CCF and Gallagher & Oinas (1974) during
quiescence indicating that the accretion flow has increased
in brightness.
The best-fit luminosity classes are consistent with the
quiescent classifications of K2ivp by Kraft (1964), K2ivp–
K2v by Gallagher & Oinas (1974), K0iii by CCF, and K3v
by Reinsch (1994). We find the spectral type to be con-
stant across our two phase samples - one during which a
large area of the white dwarf-facing surface is visible and the
other when it is mostly limb-occulted. Consequently there
Table 2. A list of template K star used to determine the best-fit
spectral type for the secondary star.
NameSpectral
type
χ2
NameSpectral
type
χ2
October 1995November 1995
HR190
HR8688
HR8415
HR8632
HR8974
HR8881
HR222
HR8832
K1iii
K1iii
K2iii
K3iii
K1iv
K1v
K2v
K3v
4.3
6.6
6.5
6.2
5.9
6.2
3.0
3.2
13 Lac
1 Peg
69 Aql
39 Cyg
33 Vul
3ηCep
HD197964
K0iii
K1iii
K2iii
K3iii
K3.5iii
K0iv
K1iv
4.0
5.7
3.9
4.0
3.8
5.9
2.5
is no observational evidence for an increase in irradiating
flux from the accretion regions over the inner face of the
companion star, although we are limited by a small range of
spectral templates and poor orbital sampling.
In order to measure integrated emission line fluxes
from each of the three nights, we fitted a third order
polynomial through wavelength bands relatively free of
line features (λλ4147-4212˚ A, λλ4278-4306˚ A, λλ4560-4608˚ A,
λλ4770-4838˚ A and subtracted the fit from the data. Fluxes
were measured by summing under each line profile and these
c ? 0000 RAS, MNRAS 000, 1–14

Page 4

4 L. Morales-Rueda, M.D. Still, P. Roche
Table 3. Emission line fluxes in units of 10−13erg cm−2s−1from the spectra of GK Per on 1996 Feb 26-28. The minimum and maximum
fluxes throughout the night as well as the average nightly flux are provided. The error on the average flux is the standard deviation.
Negative fluxes correspond to line absorption.
LineFlux
range
Average
flux
Flux
range
Average
flux
Flux
range
Average
flux
26/2/9627/2/96 28/2/96
Hγ
Hβ
Hei λ4387.9˚ A
Hei λ4437.6˚ A
Hei λ4471.7˚ A
Hei λ4713.2˚ A
Hei λ4921.9˚ A
Heii λ4541.7˚ A
Heii λ4685.8˚ A
Bowen blend
1.24 – 2.97
1.43 – 3.63
-0.70 – 0.31
-0.83 – 036
-0.47 – 0.72
-0.70 – 0.52
-0.06 – 0.93
-0.46 – 0.25
4.01 – 7.36
0.04 – 1.05
2.05 ± 0.34
2.32 ± 0.40
-0.04 ± 0.15
-0.29 ± 0.18
0.13 ± 0.18
0.02 ± 0.14
0.38 ± 0.15
-0.06 ± 0.14
5.23 ± 0.77
0.50 ± 0.17
1.57 – 3.31
1.73 – 3.27
-0.18 – 0.29
-0.60 – -0.15
-0.36 – 0.41
-0.18 – 0.27
0.18 – 0.58
-0.30 – 0.30
3.24 – 7.72
0.39 – 1.08
2.27 ± 0.30
2.45 ± 0.35
0.03 ± 0.08
-0.34 ± 0.09
0.12 ± 0.14
0.05 ± 0.08
0.39 ± 0.09
0.02 ± 0.10
5.44 ± 0.78
0.65 ± 0..13
2.09 – 4.03
2.17 – 4.57
-0.14 – 0.35
-0.68 – -0.23
-0.28 – 0.68
-0.22 – 0.31
0.26 – 1.03
-0.21 – 0.26
6.04 – 12.19
0.71 – 1.89
3.06 ± 0.37
3.41 ± 0.46
0.11 ± 0.09
-0.44 ± 0.09
0.25 ± 0.18
0.02 ± 0.10
0.68 ± 0.13
0.02 ± 0.11
8.27 ± 0.94
1.06 ± 0.17
Table 4. Power indices α obtained from fitting with a power
law function to the integrated flux of each emission line and the
continuum over the three nights of observations.
LinePower indexLinePower index
Hγ
Heiλ4388˚ A
Heiλ4472˚ A
Heiiλ4686˚ A
Continuum
2.3 ± 0.1
1.1 ± 0.4
2.1 ± 0.7
3.5 ± 0.1
2.41 ± 0.01
Hβ
Heiλ4438˚ A
Heiλ4922˚ A
Bowen blend
2.7 ± 0.1
2.5 ± 0.8
3.5 ± 0.5
2.3 ± 0.2
are provided in Table 3. The intensity of the continuum, the
lines and the relative intensity of Heiiλ4686˚ A with respect
to the Balmer lines, increases from the first night to the last
as the system approaches the outburst maximum. We fit
the emission lines during the three nights with a power law
function of time F ∼ tα, and provide the index α for each
line in Table 4.
Power-law fits of the form fν = ναon each consecutive
night provide α = −1.61 ± 0.03, −1.43 ± 0.03 and −1.39
± 0.11. Continuum slope changes slightly within statistical
uncertainties during the observing run, the spectra becom-
ing bluer with time consistent with a rise in temperature
through the accretion flow. These indices are inconsistent
with an accretion disc emitting as a discrete set of black-
bodies (Pringle 1981).
A comparison of the Feb 28 averaged spectrum with the
spectra presented by Reinsch (1994) reveals that the Balmer
line fluxes are ∼1.7 times larger than during quiescence
and the Heiiλ4686˚ A feature and the Ciii/Niiiλλ4640–50˚ A
Bowen blend are ∼5.3 times brighter. Hei λ4471.7˚ A and
Hei λ4921.9˚ A are 1.4 and 2.3 times brighter during this
outburst stage, respectively. In quiescence the Balmer lines
are the brightest emission lines, whereas the strongest line
in the current data is Heiiλ4686˚ A. Szkody, Mattei & Mateo
(1985) and CCF present spectra of GK Per taken during the
1983 outburst maximum and 20 days after outburst respec-
tively in which this behaviour is also clear.
3.2 Radial velocities
In paper i we provided an analysis of the emission line ve-
locities. To complete the radial velocity analysis we now
consider the absorption lines. In Sec. 3.1 we determined
that our best secondary star template has a spectral type
of K1iv. By masking out the emission lines in individual
GK Per data and subtracting fits to the continua from all
spectra, we were able to cross-correlate the absorption spec-
trum of GK Per with our template (Tonry & Davis 1979).
We corrected the resulting radial velocities by the systemic
velocity of the template star (-6.5kms−1; Evans 1979) and
fitted them with a circular function:
V = γ + K sin2π [φ − φ0] (1)
Orbital phases were adopted relative to the corrected CCF
ephemeris, where φ0 corresponds to superior conjunction of
the white dwarf. γ represents the systemic velocity of the
binary, K is the radial velocity semiamplitude of the com-
panion star and φ is the orbital phase.
We combined the radial velocities measured by previ-
ous authors (Kraft 1964; CCF; Reinsch 1994) with our own
values and plot them together in Fig. 3. We assume that
the errors on all individual measurements previous to this
study are equal to the mean error of 20 kms−1. The solid
curve is the fit to all data, providing γ = 30 ± 1kms−1,
K = 119±2kms−1and φ0 = 0.998 ±0.003. The dot-dashed
curve is a fit to all the data excluding the current set where
γ = 22±2kms−1, K = 128±2kms−1and φ0 = 0.009±0.003,
providing reasonable agreement although the fits are not
consistent within the given errors. Martin (1988) showed
that an elliptical fit can account approximately for irradi-
ation processes over the inner face of the secondary star.
Elliptical fits to the quiescent data have already been pro-
duced by CCF and Reinsch (1994). We do not have suitable
phase sampling to produce a significant elliptical fit with
the current data. Therefore although we find no evidence
for secondary star irradiation in the absorption line radial
velocities during outburst, our phase coverage prevents us
from ruling it out.
3.3Emission line profiles
The continuum-subtracted data are presented as time-series
of selected line profiles over each night of observation in
Fig. 4. At times theses lines display double-peaked profiles.
This is often considered a signature of accretion disc emis-
c ? 0000 RAS, MNRAS 000, 1–14

Page 5

The kilo-second QPOs of GK Per5
Figure 3. Radial velocities obtained from the current data by cross-correlating absorption features from the companion star against a
K1iv template, combined with similar measurements during quiescence from Kraft (1964), CCF, and Reinsch (1994). We provide two
circular fits to the data.
sion (Smak 1981), however the velocity structure across the
accretion flow is so complex in IPs that this cannot be con-
sidered a conclusive detection of the accretion disc. The pro-
files are asymmetric where the peak apparently shifts from
the blue to the red and back again in the Balmer lines over
the observations. This behaviour is reminiscent of emission
from a localised region in the system such as the bright spot
where the accretion stream strikes the outer rim of the disc,
or an irradiated region on the secondary star, but we note
that the orbital phasing of the observed Hβ feature is in-
consistent with both interpretations. Moreover, the orbital
phases at which we see these variations are not those at
which the hot spot and the irradiated face of the secondary
are best observed, i.e. phases 0.8 and 0.5 respectively. The
profile variations of the Hei and Heiiλ4686˚ A lines are dif-
ferent to those of Hβ either because they originate from
different locations or are more sensitive to intervening ab-
sorption regions.
The most interesting variation occurs in the blue wings
of all these profiles. First we note that the profiles are asym-
metric about their rest velocities, regardless of orbital phase,
where each line has a red bias. This shift is much larger than
the systemic velocity of the binary, measured from secondary
star photospheric lines. Secondly we note that this asymme-
try is periodic, at least in Hβ and Heiiλ4686˚ A, and this
period corresponds to the kilo-second QPOs we reported in
paper i. The QPOs manifest in blue-shifted material and ap-
pear to be the result of absorption either of the line source
or the underlying continuum. We have presented trails of
Hβ and Heiiλ4686˚ A against QPO phase after subtracting
the nightly average from each spectrum in paper i.
After the orbital period, the third likely signal present
in these trails is the 351s spin period of the white dwarf. We
attempted to remove the orbital variations in the line pro-
file by shifting out the motion of the white dwarf according
to the ephemeris and radial velocity fit of CCF. The QPO
contribution was accounted for approximately by combining
the resulting spectra into 40 bins phased over the QPO cycle
and subtracting the spectrum in the bin nearest in time from
each individual spectrum. Fig. 5 shows the resulting trails
c ? 0000 RAS, MNRAS 000, 1–14