# Confirmation of a Second Propeller: A High-Inclination Twin of AE Aquarii

Peter Garnavich  University of Notre Dame, Notre Dame, IN 46556, USA  Colin
Littlefield  University of Notre Dame, Notre Dame, IN 46556, USA  Department
of Astronomy, University of Washington, Seattle, WA 98195, USA  R. M. Wagner
Department of Astronomy, Ohio State University, Columbus, OH 43210, USA  Jan
van Roestel  Departments of Astronomy and Physics, California Institute of
Technology, Pasadena CA 91125, USA  Amruta D. Jaodand  Departments of
Astronomy and Physics, California Institute of Technology, Pasadena CA 91125,
USA  Paula Szkody  Department of Astronomy, University of Washington, Seattle,
WA 98195, USA  John R. Thorstensen  Department of Physics and Astronomy,
Dartmouth College, Hanover, NH 03755 USA

###### Abstract

For decades, AE Aquarii (AE Aqr) has been the only cataclysmic variable star
known to contain a magnetic propeller: a persistent outflow whose expulsion
from the binary is powered by the spin-down of the rapidly rotating,
magnetized white dwarf. In 2020, LAMOST J024048.51+195226.9 (J0240) was
identified as a candidate eclipsing AE Aqr object, and we present three epochs
of time-series spectroscopy that strongly support this hypothesis. We show
that during the photometric flares noted by Thorstensen (2020), the Balmer and
He I emission lines reach velocities of $\sim$3000 km s-1, well in excess of
what is observed in normal cataclysmic variables. This is, however, consistent
with the high-velocity emission seen in flares from AE Aqr. Additionally, we
confirm beyond doubt that J0240 is a deeply eclipsing system. The flaring
continuum, He I and much of the Balmer emission likely originate close to the
WD because they disappear during the eclipse that is centered on inferior
conjunction of the secondary star. The fraction of the Balmer emission
remaining visible during eclipse is likely produced in the extended outflow.
Most enticingly of all, this outflow produces a narrow P Cygni absorption
component for nearly half of the orbit, and we demonstrate that this scenario
closely matches the outflow kinematics predicted by Wynn et al. (1997). While
an important piece of evidence for the magnetic-propeller hypothesis—a rapid
WD spin period—remains elusive, our spectra provide compelling support for the
existence of a propeller-driven outflow viewed nearly edge-on, enabling a new
means of rigorously testing theories of the propeller phenomenon.

Cataclysmic variable stars: Intermediate Polars; White dwarf stars; Magnetic
stars; Eclipsing binary stars; AE Aquarii

##  1 Introduction

Intermediate polars (IPs, aka DQ Herculis stars) are a type of cataclysmic
variable star (CV) consisting of a cool, non-degenerate companion transferring
mass to a magnetized white dwarf (WD) whose spin period is significantly
shorter than the binary orbit (Patterson, 1994). IPs generally accrete from a
truncated accretion disk whose inner rim extends to the edge of the WD’s
magnetosphere. Once the magnetic pressure exceeds the disk’s ram pressure, the
gas begins to travel along the WD’s magnetic fields lines. The magnetically
confined part of the flow is often called an “accretion curtain,” and as the
WD rotates, the changing aspect of the curtain causes a photometric modulation
at the WD’s spin period (Patterson, 1994). However, in some IPs, the WD’s
magnetic field is large enough to prevent the formation of an accretion disk,
and in these diskless systems, the ballistic accretion stream from the
companion star directly impacts the WD’s magnetosphere (e.g., V2400 Oph:
Buckley et al., 1995).

If the magnetized WD is spinning sufficiently fast, donated gas may be ejected
from the system via a “magnetic propeller” mode (Wynn et al., 1997), in which
the rapidly rotating magnetosphere of the WD acts as a centrifugal barrier
that inhibits accretion onto the WD. The magnetic propeller mechanism is
believed to operate over a wide range of accreting systems, including neutron
stars and young stellar objects (Campana et al., 2018), but in WD systems, the
propeller mode appears extremely rare.

Until now, the only confirmed IP in a propeller mode has been AE Aqr
(Eracleous & Horne, 1996; Wynn et al., 1997), which displays unique
photometric and spectroscopic properties, including a WD spin period of 33 s
(Patterson, 1979). Meintjes et al. (2015) review the major observational and
theoretical studies of AE Aqr. Several additional IPs with WD rotation periods
near 30 s have recently been identified (e.g. Lopes de Oliveira et al., 2020;
Ashley et al., 2020), but their magnetic fields are apparently insufficient to
power an AE Aqr-like propeller. AE Aqr and these other IPs may require a
recent episode of thermal time-scale mass transfer to spin-up their WDs to
these extreme rates (Schenker et al., 2002).

Recently, Thorstensen (2020) pointed to the flaring light curves and spectral
properties of LAMOST J024048.51+195226.9 (J0240 hereafter) as being similar to
those of AE Aqr and suggested that it might be only the second IP in the
propeller mode. Littlefield & Garnavich (2020) analyzed its long-term light
curve from sky surveys and concluded that the secondary star eclipses the
location of the flaring activity, implying a high orbital inclination. The
system’s relatively long orbital period of 7.33 h (Drake et al., 2014;
Thorstensen, 2020) has been refined by Littlefield & Garnavich (2020) to a
precise value of 0.3056849(5) d. Here, we present fast-cadence, time-resolved
spectroscopy and photometry to compare J0240 with the observational properties
of original propeller AE Aqr.

Figure 1:  Light curves around the time of inferior conjunction. During periods of active flaring the outline of the eclipse is clearly seen. The red lines are a model eclipse of a constant source located at the position of a WD as described in the text. left: Five nights of MDM $B$-band photometry. The three runs where flaring was active is plotted in the top panel, while two quiescent eclipses are shown in the lower panel. right: The blue flux density and Hα emission line flux from the September $LBT$ spectra are displayed with an eclipse model. A small rise in the continuum flux accompanied by a larger brightening in the emission line flux begins precisely at inferior conjunction.  Figure 2: The MDM and Palomar light curves, with their two-dimensional power spectra. The smooth red curves were subtracted from the observed data (black points) prior to computation of the power spectra. There is no convincing evidence of a stable period in any of these light curves. Figure 3: left: Trailed spectra of J0240 around Hα and He I 6675 Å. A full binary orbit is shown and the sequence is repeated. Several absorption lines from the secondary are visible in the continuum. The full orbit is constructed by combining the September and October runs resulting in discontinuities in the emission profiles at phases 0.50 and 0.84. right: The $R$-band light curve synthesized from the individual spectra. The star was brighter and flaring more active during the October run.  Table 1: Photometric Observations  Date | Start Time | Length | CadenceaaCadence is the average time between consecutive exposures. | Filter | Telescope
---|---|---|---|---|---
(UT) | (UT) | (hours) | (s) |  |
2020-11-11 | 04:01 | 6.87 | 16.5 | $B$ | MDM
2020-11-13 | 07:09 | 0.93 | 3.0 |  $g^{\prime}$,$i^{\prime}$ | P200
2020-11-14 | 03:40 | 1.60 | 3.0 |  $g^{\prime}$,$i^{\prime}$ | P200
2021-01-07 | 03:51 | 1.96 | 20.4 | $B$ | MDM
2021-01-08 | 01:50 | 2.00 | 20.4 | $B$ | MDM
2021-01-10 | 05:03 | 2.15 | 20.4 | $B$ | MDM
2021-01-11 | 03:15 | 2.02 | 20.4 | $B$ | MDM

##  2 Data

###  2.1 Spectroscopy

We observed J0240 with the Large Binocular Telescope (LBT111The LBT is an
international collaboration among institutions in the United States, Italy and
Germany. LBT Corporation partners are: The University of Arizona on behalf of
the Arizona Board of Regents; Istituto Nazionale di Astrofisica, Italy; LBT
Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, The
Leibniz Institute for Astrophysics Potsdam, and Heidelberg University; The
Ohio State University, representing OSU, University of Notre Dame, University
of Minnesota and University of Virginia.) and twin Multi-Object Dual
Spectrographs (MODS; Pogge et al., 2012) on 2020 September 12, October 13, and
November 20 (UT). The spectrographs were set up in dual grating mode providing
wavelength coverage from 320 nm to 1.01 $\mu$m, with a dichroic splitting the
light into the red and blue optimized arms at 565 nm. A 0.8 arcsec slit was
employed on all the nights giving a spectral resolution of R=1350 near Hα. The
typical seeing during the observations was between 0.8 and 1.0 arcsec. The sky
was clear and seeing was steady around 1.0 arcsec for the September and
October runs. In November, there were some clouds and the seeing varied
between 1.2 and 1.5 arcsec.

The four MODS spectrographs (SX/MODS1, DX/MODS2 plus the red and blue arms for
both) were run independently and each have slightly different readout and
overhead costs. So, despite all the spectrographs being set to take 180s
integrations, the start times for a long series of exposures soon become
unsynchronized. This results in an improved temporal resolution when data from
the two telescopes are combined. On the September night, 135 red exposures
were obtained covering 4.7 hours while on the October, 72 red-side exposures
were taken covering 2.5 hours. The average cadence was 2 minutes for the red
spectra. Serendipitiously, the September run covered orbital phases 0.87-1.51,
while the October data spanned orbital phases 0.52-0.87, so the two runs
combined covered an entire 0.306 day binary orbit. The November run generated
75 red-side spectra that covered orbital phases 0.61-0.98, significantly
overlapping with phases observed in October.

The two-dimensional CCD images were processed and one-dimensional spectra
extracted using a 1.0 arcsec aperture. The spectra were wavelength calibrated
using neon, argon, and mercury emission lamps. To correct for flexture over
the time series, the wavelength scale was adjusted slightly to shift the
airglow emission lines to their rest wavelengths. The J0240 spectra were flux
calibrated using the spectrophotometric standard star BD+28∘4211\. Synthetic
$B$, $V$, and $R$ magnitudes were estimated by averaging the flux densities
over the Johnson-Cousins bandpasses.

###  2.2 Photometry

We obtained time-resolved photometry with the MDM 2.4m Hiltner telescope and
OSMOS camera on five nights in late 2020 and early 2021. A log of the
observations is given in Table 1. The first run covered nearly an entire
binary orbit with an average time between exposures (the cadence) of 16.5 s.
The observations in 2021 January were timed to cover two hours centered around
inferior conjunction with a slightly longer cadence of 20.4 s. The data were
obtained through a Johnson $B$ filter and calibrated assuming that a
comparison star 91′′E and 25′′N of J0240 has an apparent brightness of
$B=16.00\pm 0.06$ mag222From the APASS catalog (Henden et al., 2015).

Very high cadence photometry was also obtained with the Palomar 200-inch
telescope (P200) and CHIMERA fast photometer (Harding et al., 2016) on 2020
November 13 and 14 (UT). Because the frame-transfer camera had no dead time
between images, the cadence matched the 3 s exposure time. Images were
obtained simultaneously through Sloan $g^{\prime}$ and $i^{\prime}$ filters.
The length of the first time series was nearly an hour and the next night
covered 1.6 hours. The images were bias subtracted and divided by twilight
flat fields using the standard CHIMERA pipeline333https://github.com/caltech-
chimera/PyChimera. We used a variable aperture applied to the target and
reference star of 1.5 times the seeing width to generate a differential light
curve of the target.

##  3 Analysis

###  3.1 Photometry

####  3.1.1 Eclipses of the flaring region

We obtained $B$-band photometry of five eclipses predicted by the Littlefield
& Garnavich (2020) ephemeris and the light curves are shown in Figure 1. As a
guide to interpret the eclipses, we have generated a model eclipse light curve
for a WD and a Roche lobe-filling secondary that assumes a mass ratio of
$q=0.5$ (Eggleton, 1983). Eclipses in polars tend to have very sharp ingress
and egress due to the small size of the WD. The eclipses in J0240 during
flaring shown in Figure 1 have a gradual ingress lasting 5 to 10 minutes. To
soften the transition, the model uses a Gaussian distribution for the light
source assumed to be located at the position of the WD. We adjusted the
Gaussian parameters and found that a width of 0.15$a$ (FWHM), or 15% of the
stellar separation approximated the ingress length. Finally we adjusted the
orbital inclination to $i=81^{\circ}$ so that the model approximately matches
the length of the eclipse. Certainly, other combinations of parameters could
also approximate the observed eclipse profile, but the goal for this model is
simply to use it as a consistent reference to compare the various photometric
and spectroscopic observations.

The appearance of the eclipses in Figure 1 depends profoundly on whether there
is flaring activity near the time of eclipse. Three of the eclipses occurred
during periods of flaring, and the outline of the eclipse is well-defined,
confirming the identification of eclipses by Littlefield & Garnavich (2020).
Conversely, the eclipse is not evident in the two runs during which there was
little or no flaring. Nevertheless, the brightness of the system at inferior
conjunction was extremely consistent in all five light curves, with the
average measured at $B=19.01\pm 0.02$ mag. Even during strong flares, the
brightness at mid-eclipse is within a mmag of the mid-eclipse brightness in
the runs without significant flaring, which suggests that the region producing
the continuum flares is totally blocked by the secondary.

Some of the $B$-band light curves show a slight rise at the 0.1 mag level
immediately after inferior conjunction. Further, the eclipse egress during
flaring is more shallow than the ingress. Both of these characteristics imply
that the intensity distribution of the continuum flaring region may be
asymmetric, yet sufficiently compact to be nearly totally obscured by the
secondary star.

The photometry obtained by Thorstensen (2020) near inferior conjunction hints
at some variability in the eclipse width when compared with the very
consistent eclipse profile seen in our data. Any comparisons are complicated
by the rapid brightness changes in the flares and differences in the central
wavelengths between the two sets of observations.

Figure 4: The evolution of the Hα emission profile during a September flare.
The average spectrum just before the initiation of the flare was subtracted
from each subsequent spectrum. The evolution is divided into three panels to
show the changes clearly. The top panel displays the rapid rise of the flare
and the development of the high-velocity wings. Red and blue-shifted emission
is seen out to 3000 km s-1 during the rise, but the redshifted emission fades
as the blue side continues to strengthen. Over the next 8 minutes (center
panel), the Hα profile remains fairly constant except for the loss of the
highest velocity wings. A narrow absorption is seen over the flare. Its
blueshift increases from $300$ km s-1 to 400 km s-1 over 25 minutes. The lower
panel shows the emission narrowing while the flux remains well above the pre-
flare level.

####  3.1.2 Non-detection of a spin signal

To search for the spin period of the WD, we obtained high-cadence photometry
of J0240, with the goal of detecting the spin modulation. Thorstensen (2020)
found no evidence of a spin period in his 23.3 s cadence photometry. For each
night’s time series, we computed the Lomb-Scargle power spectrum up to the
Nyquist frequency of the sampling, but we also did not detect any significant
candidate spin periods in the power spectra. Because the Palomar photometry
was obtained on consecutive nights, we combined them into one dataset and
performed the Lomb-Scargle analysis, but as before, there was no sign of
coherent variability.

To estimate a limit on the amplitude of any spin signal, we removed the low-
frequency variations in the P200 data and randomized the magnitude
measurements before calculating a power spectrum. We repeated this process 500
times, recording the maximum power between frequencies 0.7$<f<9.5$ cycles/min
in each randomized light curve. Injecting a sinusoid signal with a 4 mmag
amplitude resulted in a peak at the 3$\sigma$ level in the combined $g$-band
P200 data. We conclude that any spin modulation with a period between 6.3 s
and 85 s must have an amplitude below 4 mmag during our observation.

Because AE Aqr flares can display relatively high-amplitude quasi-periodic
oscillations (QPOs) close to the spin period (Patterson, 1979), we also
created two-dimensional power spectra of each light curve in order to search
for intermittent periodic variations during the flares (Figure 2). However, we
do not see any evidence of a QPO.

###  3.2 Spectroscopy

####  3.2.1 Flares

While collecting the data, it was obvious that the star was varying rapidly in
brightness, color, emission line flux, and line width. The synthetic $R$-band
magnitude variations shows the flaring pointed out by Thorstensen (2020), and
it is consistent with that seen in AE Aqr.

The Hα emission profile over a full binary orbit is shown in Figure 3,
although the orbit was constructed from two runs separated by a month. Over
the September run, the system slowly brightens from inferior conjunction
(orbital phase $\phi=0.0$ based on the Littlefield & Garnavich 2020
ephemeris). Some flares are seen bracketing inferior conjunction as well as a
major flare at $\phi=0.40$. The width of the Hα emission line narrows as the
flare fades. The continuum reaches a deep minimum around superior conjunction
($\phi=0.5$) that is likely due to a lack of flaring combined with the
ellipsoidal shape of the secondary. The September $LBT$ sequence transitions
to the October run at $\phi=0.51$. A narrow P Cygni-like (P Cyg) absorption
feature is seen through the October spectral series. Flaring in J0240 was more
active in October than in September, displaying many overlapping events and a
bright continuum.

In AE Aqr, the highest emission velocities during flares reach $\pm 2000$ km
s-1(Welsh et al., 1998). In comparison, emission at the peak of the flares for
J0240 extends to $\pm 3000$ km s-1. These high velocities last only a few
spectra, or approximately 10 min. In isolated flares (see Figure 3), the
continuum flux fades more quickly than the emission line flux, a behavior also
seen in AE Aqr (Welsh et al., 1998).

Balmer emission is visible throughout the orbit, even during periods of
relatively low activity. During quiescent periods between flares, Hα is seen
with a substantial velocity width of 1200 km s-1 HWZF. Around inferior
conjunction the Hα emission width reaches its minimum value of 980 km s-1
HWZF. From this behavior we infer that some level of flaring activity is
visible at all times, except when the flaring region is obscured by the
secondary star at inferior conjunction.

Figure 5: Example spectra of J0240 obtained during the inferior conjunction
(eclipse; red), before a flare (orange), and at the peak of a flare (blue).
The flare spectra are shown with the eclipse spectrum subtracted. The eclipse
spectrum is dominated by the early M-type secondary, narrow Balmer and Ca II
emission (note the eclipse spectrum flux has been divided by 10).

During the September sequence, a fairly isolated flare occurred that allows us
to examine its evolution. We subtracted the Hα profile obtained immediately
before the onset of the flare that began at orbital phase 0.40 and the results
are displayed in Figure 4. As noted above, the high-velocity wings are seen
early in the flare and fade quickly, on the time-scale of the continuum
decline. The emission profile is always asymmetric with the red side twice the
flux of the blue. This asymmetry suggests that the blue-shifted emission is
self-absorbed in an expanding wind. Some asymmetry in the line shape is seen
in AE Aqr (Welsh et al., 1998), but the high inclination of J0240 may increase
this effect.

Once the flare reaches its peak emission flux the line shape remains fairly
constant except for the loss of the high-velocity wings. An unresolved
absorption feature is seen throughout the flare. Its blue-shifted velocity
increases from 300 to 400 km s-1 over the 25 min. This absorption may
correspond to the P-Cyg features seen during the second half of the orbit as
its velocity is consistent with an extrapolation from the later orbital
phases.

In Figure 5, we show representative spectra of J0240 in three different
intervals: at the maximum of a flare, before the flare, and during eclipse.
Before a flare, Balmer, Paschen, He I, and Ca II emission lines are visible.
During the flares, the emission lines broaden and intensify. The strengths of
He I lines are enhanced, weak He II $\lambda 4686$Å emission briefly appears
as well as the Si II $\lambda 6340$Å doublet. The continuum becomes bluer
during the flares with an increasing continuum across the Balmer jump into the
ultraviolet (UV).

####  3.2.2 Eclipse spectra

Our $LBT$ spectra obtained during an eclipse offer additional insight into the
eclipse photometry. The eclipse spectra indicate that the Hα emission line
flux does not match the profile of the continuum eclipse (Figure 1). The line
flux rises rapidly beginning at inferior conjunction, suggesting that the
emission lines may be slightly offset from the location of continuum flares,
or extend further from the flare location than the continuum emission. As seen
in both AE Aqr and J0240 flares, the emission lines fade more slowly than the
continuum flux, implying that the gas producing the emission lines may flow
out of the location of the continuum flare.

The eclipse spectrum is dominated by the secondary star (Figure 5), and the
continuum is very red as expected for the early M-type companion (Thorstensen,
2020). Weak Balmer and Ca II emission lines remain visible through eclipse,
but the He I lines are not detectable. This supports the proposal by
Littlefield & Garnavich (2020) that the main He I-emitting region is blocked
by the donor star.

During the eclipse, the Balmer decrement becomes very steep in comparison to
flare and pre-flare spectra. The Balmer decrement,
$D_{3,4}=F(H_{\alpha})/F(H_{\beta})$, is 5.4$\pm 0.2$ in eclipse,
$D_{3,4}=3.3\pm 0.1$ before a flare, and $D_{3,4}=2.1\pm 0.1$ during the peak
of a flare. Since the eclipse blocks the source of the continuum flaring
activity, it is likely that the Balmer emission visible during an eclipse
comes from gas ejected by the propeller and is moving away from the binary.
While interstellar dust reddening can be a cause of a steep Balmer decrement,
for J0240 the reddening is very small (see Thorstensen, 2020). We propose that
the steep decrement results from a very large Hα optical depth (e.g. Netzer,
1975) caused by viewing the circumbinary gas close to the orbital plane.

####  3.2.3 Color Variations

The photometry synthesized from the spectra and compared with the variations
in the emission line fluxes are shown in Figure 6. Flaring is seen around
inferior conjunction and at orbital phase 0.4, as well as nearly continuous
activity in the October run that covered phases 0.50 to 0.85.

Figure 6: Light curves derived from the September and October spectroscopy. In
all the panels the dotted vertical line indicates the transition between the
two runs and the solid line is the time of inferior conjunction. top: Relative
flux of Hβ versus orbital phase. middle: Synthesized $U$ and $B$ magnitudes
versus orbital phase. bottom: Color index of the synthesized $B$ and $V$
magnitudes versus orbital phase. The color index reaches 0.8 to 0.6 mag during
flares. Around eclipse the color is 1.6 mag, consistent with the M type
secondary star.

The Balmer emission line flux and continuum brightness rise quickly, on time
scales of a few minutes, then fade more slowly. The emission lines clearly
take longer to fade after a flare when compared with the continuum flux. The
$U$-band variations are more similar to the emission line changes than to the
$B$-band fluctuations. For example, the Hβ flux and $U$-band brightness begin
to rise at the time of inferior conjunction (orbital phase 0.0), while the
$B$-band and $B-V$ color are relatively flat around conjunction.

The $B-V$ color index is reddest near inferior conjunction suggesting that the
eclipse is blocking nearly all of the flaring activity. The color index at
eclipse is $B-V=1.6\pm 0.1$ mag, consistent with the color of an early M-type
star (Thorstensen, 2020). During quiescent periods outside of eclipse the
color index is 1.4 mag, while at the peak of flares the color reaches between
0.8 and 0.6 mag. Simultaneous multi-band photometry of AE Aqr shows color
variations between $1.0>B-V>0.5$ mag (Zamanov et al., 2017). The secondary in
AE Aqr is hotter than in J0240, corresponding to an early K-type spectrum
(Echevarría et al., 2008).

Figure 7:  Top: The radial velocity estimates for the secondary star as a
function of orbital phase. The points are measurements from individual MODS2
spectra obtained on three separate nights. The blue line is the best fit
sinusoid assuming a fixed orbital period from Littlefield & Garnavich (2020).
The data show that inferior conjunction occurs 3.0$\pm 0.5$ minutes earlier
than mid-eclipse predicted by the Littlefield & Garnavich (2020) photometric
ephemeris. Bottom: Residuals between the data and the best fit sinusoid. The
large flare seen at orbital phase 0.4 impacted the cross-correlation
velocities and generated a 10 km s-1 amplitude wave in the radial velocity
curve.

####  3.2.4 Orbital Motion of the Secondary

Absorption features from the M-star secondary are clearly seem in all the
$LBT$ spectra. This allows us to measure the orbital motion of the secondary
star with the goal of precisely measuring the time of inferior conjunction
relative to the eclipse ephemeris (Littlefield & Garnavich, 2020). Thorstensen
(2020) classified the secondary star as an M1.5 dwarf, so we cross-correlated
sections of the $LBT$ spectra with a late stellar spectrum synthesized from
the MILES stellar library (Vazdekis et al.,
2010)444http://research.iac.es/proyecto/miles/.

Cross-correlations between the spectra and the template were performed using
the fxcor routine implemented in IRAF. Only the red arm of $MODS2$ was used
for this analysis as it has the highest signal-to-noise ratio in the continuum
of the four spectrographs. To avoid emission lines and reduce telluric
contamination, only the wavelength ranges 6000-6530 Å and 7800-8400 Å were
used in the cross-correlations. Over the three observing nights, 143 spectra
were measured covering an entire orbital cycle with redundant measurements
between phases 0.6 and 0.9. The typical uncertainty of each measurement was 11
km s-1. A heliocentric correction was applied to each spectrum and the
resulting radial velocity curve for the J0240 secondary star is shown in
Figure 7.

We converted the barycentric Julian day (BJD) at the center of each exposure
to photometric phase using the Littlefield & Garnavich (2020) ephemeris and
fit a sinusoid function to the data using a least-squares algorithm. The half
amplitude of the radial velocity curve is 241$\pm 3$ km s-1, which is
consistent with the Thorstensen (2020) estimate of 250$\pm 8$ km s-1. Inferior
conjunction was found to occur at phase $\phi=-0.0068\pm 0.0011$ relative to
the photometric ephemeris. This is very close to the predicted center of the
eclipse, but 3.0$\pm 0.5$ minutes earlier than the photometric ephemeris time.
The small size of this offset implies that the location of the flares is near
the radius vector (the line passing through both stars and the system center
of mass). Combining our measurement of $T_{0}$ with the Littlefield &
Garnavich (2020) orbital period, we obtain a new ephemeris of

$T_{conj}=2459105.84663(3)+0.3056849(5)\times E,$ (1)

where $T_{conj}$ is the time of inferior conjunction expressed as a
Barycentric Julian Date in Barycentric Dynamical Time (TDB) and $E$ is the
integer cycle count. The precise time of inferior conjunction defines the
orbital phase of the secondary star and this is critical in narrowing the
location of the flaring emission in the binary system.

The radial velocity curve shown in Figure 7 shows a small deformation at
orbital phase 0.40. The amplitude of the wave is about 10 km s-1. This was a
phase covered in the 2020 September run and is coincident with a large flare
seen in the continuum and in the emission lines. While the cross-correlation
segments avoided major emission features, some lines such as the Si II 6340 Å
are seen in emission only during flares. These weaker emission features appear
to have a mild impact on the absorption line cross-correlation velocity
estimates.

Figure 8: The flux-weighted average Hα velocity versus orbital phase (repeated
for two orbits). The November run overlaps with the October data so it is
shown in magenta. The red line is a best-fit sinuosoid with an amplitude of
145 km s-1 and the opposite phase of the secondary star. The zero point used
in plotting the velocities is the systemic radial velocity, found from the
mean velocity of the secondary’s absorption lines.

####  3.2.5 Orbital Motion of the Emission Line Region

A close inspection of the trailed Hα spectrum in Figure 3 suggests a pattern
in the velocity of the emission centroid with orbital phase. The emission
appears most redshifted near $\phi\approx 0.75$ and mildly blueshifted around
$\phi\approx 0.25$, although the high velocity flares and P Cyg absorption
makes this difficult to detect. In disk systems, a “double Gaussian” is often
used to detect the orbital motion of the inner disk by focusing on the high-
velocity wings of emission lines. For AE Aqr and J0240, the high velocity
emission likely comes from shocked gas that would not be a good tracer of
orbital motion, and application of this technique may have resulted in the
conflicting phase estimates of Robinson et al. (1991) and Welsh et al. (1998).
Instead, we measure the flux-weighted mean wavelength of the Hα emission
feature. The results are shown in Figure 8.

The shifting centroid of the Hα emission moves in anti-phase to that of the
secondary star’s motion. The velocity centroid is redshifted over the orbital
phases $0.5<\phi<1.0$ while the secondary is blue-shifted over those phases. A
sinusoidal fit to the centroid velocity suggests an offset of only 0.045 in
orbital phase when compared to the secondary star. The center-of-mass appears
shifted to the red by 40 km s-1, but this shift may result from the asymmetry
of the emission caused by the P Cyg absorption and other optical depth effects
that have a major impact on the blue side of the line.

We propose that the Hα line emitting region is nearly fixed in the binary
frame and orbiting about the system’s center of mass. As the Hα emission has
about the same phasing as expected for the WD, the emission would be
originating within 20∘ of the radius vector connecting the two stars and on
the WD side of the system. Indeed, the velocity amplitude is close to what is
expected for the WD given the orbital period of this system. To illustrate
this point, from the velocity amplitude of the secondary, $V_{2}$, and its
orbital angular velocity ($\Omega^{-1}$=4203.5 sec rad-1), we can estimate the
physical distance of the secondary from the center-of-mass, $r_{2}$, as

$r_{2}\;=V_{2}/(\Omega\;{\rm sin}(i))$ (2)

and for a mass ratio $q$, the WD separation from the center-of-mass is simply
$r_{1}\;=q\;r_{2}$. The parameter of interest is the location of the emitting
region relative to the WD, or,

$r_{Ha}/r_{1}\;=V_{Ha}/(qV_{2})$ (3)

where $r_{Ha}/r_{1}$ is the ratio of the center-of-mass distances of the
emitting region and WD and $V_{Ha}$ is the orbital amplitude of the emission
region. The inclination dependence has cancelled, but it would be small anyway
given that J0240 is eclipsing. The velocities have been estimated as
$V_{2}=241$ km s-1 and $V_{Ha}=145$ km s-1, so $r_{Ha}/r_{1}\;=0.6/q$. If the
velocity amplitude of the Hα emission is a good representation of its orbital
motion, then the emitting region is close to the WD for reasonable mass
ratios. For example, for $q\approx 0.5$, the emitting region is 20% further
from the center-of-mass than the WD. From this analysis, it is unlikely that
ejected blobs colliding at several stellar separations from the center of mass
would produce such a low velocity amplitude and be in phase with the WD orbit.

Figure 9: bottom: Trailed spectra centered on the Hα emission from $LBT$ data
taken 2020 October (left) and 2020 November (right). The narrow blueshifted
absorption feature is seen continuously over the second half of the orbit.
top: Individual spectra from the two data sets. On the left is a spectrum
showing a pair of narrow absorption lines at $-550$ and $-1025$ km s-1.
Displayed on the right is a spectrum obtained near inferior conjunction where
the absorption is well below the continuum of the secondary star. The deep
absorption at this orbital phase suggests that the intervening gas is on the
opposite side of the system from the WD and in circumbinary orbit after
acceleration by the propeller.

####  3.2.6 Blue-shifted Absorption Feature

Thorstensen (2020) noted a strong, blueshifted absorption feature that he
associated with periods of flaring. Our spectra reveal that this absorption is
present—even when J0240 is not flaring—across a wide range of orbital phases
(Figure 9), particularly between orbital phases 0.5$<\phi<$1.0. The
blueshifted absorption feature provides direct evidence of an outflow, and as
Sec. 4.4 will explain in detail using the Wynn et al. (1997) modeling, we
conclude that it occurs in J0240 when the gas expelled by the magnetic
propeller passes in front of the secondary and/or the flaring region. Similar
absorption features have not been observed in AE Aqr, due to its much lower
inclination. Because the absorption directly probes the conditions in the
outflow, it is especially important to characterize it properties.

The most obvious feature of the blueshifted absorption is that it is present
during the second half of the orbit, as is particularly apparent in the
October and November spectra (Figure 9). During that time, the absorption
varies slowly in velocity, and in general, the absorption minima are seen to
become more negative with orbital phase, starting around $-380$ km s-1 at
$\phi\sim 0.5$ and reaching to $-600$ or $-700$ km s-1 approaching inferior
conjunction. In Figure 10, we plot the blueshift of the absorption (when it
was present) against the orbital phase of the observation. During the November
run, the minimum of the absorption is seen at slightly higher velocities than
measured in the October and September data, suggesting that its properties
vary over time.

A few spectra showed multiple blue-shifted absorption components, with the
velocity of the additional components between 1000 to 1200 km s-1. An example
of a double absorption feature is shown in Figure 9 at $\phi=0.86$. The high-
velocity component was detectable for approximately 15 minutes.

The equivalent widths (EW) of the absorption can be as high as 4 Å, but
typically the EW are between 1 and 3 Å over the second half of the orbit. When
the system is not flaring, the absorption falls below the continuum of the
secondary. This is clearly seen in the spectrum taken near inferior
conjunction and shown in Figure 9. Because the flaring region is completely
hidden during the eclipse (see Sec. 3.1.1), the fact that the P Cyg absorption
cuts into the donor’s continuum demonstrates that the absorption must
originate in gas on the opposite side of the secondary from the WD.

The width of the absorption feature is difficult to measure precisely because
of the steep continuum slope on the line wings. The absorption full-width at
half minimum (FWHM) corresponds to 230$\pm 30$ km s-1, which is similar to the
FWHM of the night sky lines, implying that the absorption feature is
unresolved.

Figure 10: The blue-shifted velocity (in km s-1) of the narrow P Cyg feature
as a function of orbital phase depicted on a polar projection. The spectra
obtained in November (blue points) shows a slightly larger velocity over the
same orbital phases when compared with the September (orange) and October
(red) data. The size of each point is proportional to the equivalent width of
the absorption. The P Cyg absorption feature is most clearly seen over the
second half of the orbit.

##  4 Discussion

###  4.1 Location of the Flares

The presence of eclipses in J0240 provides an opportunity to estimate the
location of the flaring activity in the binary system. One of the longstanding
debates with AE Aqr is whether its flares are produced when blobs are shocked
in the WD’s magnetosphere (Eracleous & Horne, 1996) or when they collide in
the propeller’s outflow, well past the WD (Welsh et al., 1998). The major
difference between these two scenarios is that in the latter, the flares are
produced at a large distance from the WD.

We confirm the inference by Littlefield & Garnavich (2020) that there is no
visible flaring in optical broadband photometry during the eclipses.
Furthermore, our spectra verify that mid-eclipse coincides with the
secondary’s inferior conjunction, implying that the flares are constrained to
occur near the line passing through the two stars. This strongly favors the
Eracleous & Horne (1996) model, in which the flares are predicted to be
generated in the WD magnetosphere.

As pointed out in section 3.2.5, the apparent orbital velocity amplitude of
the Hα emission region is similar to that expected for the WD. In addition,
the radial velocity of the line emitting region is anti-phased to that of the
secondary. Combining these observations suggests that the emission line
emitting region is near the WD.

In the Welsh et al. (1998) blob-blob collision model, the expected flaring
location would result in eclipses well before inferior conjunction. The large
extent of the predicted interaction region would generate long partial
eclipses that would be difficult to identify given the flaring variability.
Furthermore, in the Welsh et al. (1998) scenario, the location of the
collision region should vary because blobs follow different trajectories,
depending on their size and density. We would therefore expect eclipses to
vary in phase, rather than producing the sharply defined eclipse seen in
survey photometry (Littlefield & Garnavich, 2020).

That said, the emission line and ultraviolet (UV) light curves generated from
our spectra (see Figure 6), differ from the broad-band photometric eclipses
shown in Figure 1. The UV and line emission start to rise at zero orbital
phase, while the continuum flux is relatively flat on either side of inferior
conjunction. The flat-bottomed continuum eclipses suggest that most of the
continuum-emitting region is blocked by the secondary. The rise of Hα emission
and UV flux during the continuum eclipse implies that the line-emitting region
may be more extended and peeking around the secondary at the moment of
inferior conjunction.

This geometry is consistent with the Eracleous & Horne (1996) model where
blobs traveling ballistically from the secondary are shocked when encountering
the WD magnetosphere. This occurs near the WD and the shocks generate the
continuum flares. The accelerated blobs continue past the WD while expanding
and cooling, resulting in Balmer emission on the leading side of the WD. This
process is likely to be messy judging by the range of observed absorption
velocities, but with the data we have in hand, the continuum flares appear to
be confined to within $0.2a$ of the WD, where $a$ is binary separation.

###  4.2 Flare High Velocity Emission

We interpret the extreme velocity dispersion observed during the flares
(HWZI$\sim 3000$ km s-1) as the expansion velocity of the blobs when they are
shocked, as opposed to the initial velocity of the blobs immediately following
their acceleration by the propeller. We base this inference on the presence of
the extreme, nearly-simultaneous redshifts and blueshifts observed around
inferior conjunction, when the trajectory of the expelled blobs is roughly
perpendicular to our line of sight. If we treat the blobs as simple particles
following trajectories out of the system, their velocity vectors at certain
orbital phases would be perpendicular to our line of sight, so we would
observe high-velocity flares only at certain orbital phases. Conversely, if
the blobs rapidly expand after being shocked, the resulting Doppler shifts
would be observable even if the blobs were moving in the transverse direction.
Eracleous & Horne (1996) argued that shocked blobs could expand at several
thousand km s-1 because they would be opaque to the X-rays produced internally
by the shock-heated plasma.

The blueshifted absorption component provides a second argument against
interpreting the HWZI as the initial velocity of the ejecta. The hyperbolic
excess velocity $v_{term}$ of an object is given by
$v_{term}=\sqrt{v^{2}_{0}-v^{2}_{escape}}$, and we find that if $v_{0}\sim
3000$ km s-1, the outflow will decelerate only slightly. Since the outflow
expands in the radial direction (see Sec. 4.4), the projected velocity of the
outflow’s P Cyg absorption component would therefore be much larger than what
is observed.

###  4.3 The Lack of Coherent Oscillations

In most characteristics, J0240 and AE Aqr are extremely similar. A 33 s
oscillation is seen in AE Aqr associated with the spin period of its WD;
however, our fast photometry does not detect a coherent oscillation from
J0240. For AE Aqr, Patterson (1979) found the spin and its harmonic with
amplitudes ranging between 1 and 10 mmag, but generally the signals were 2 to
3 mmag, just below our limit of detection. Observations by Bruch et al. (1994)
found that the spin oscillations in AE Aqr fell below detectability for a
month, suggesting that we might simply be unlucky in the timing for our
search.

From UV observations, Eracleous et al. (1994) modeled the spin modulations
from AE Aqr as hotspots on its WD. Their best fit placed the spots at mid-
latitudes on the star in order to match the very large amplitude variations
seen in the UV. In J0240, any hotspots may be close to the spin axis,
resulting in a smaller amplitude. It may even be that J0240 is a more
efficient propeller than AE Aqr, and no accretion heating is occurring at the
magnetic poles.

More sensitive searches for the WD spin signature are needed. In AE Aqr, the
amplitude of the spin modulation increases toward shorter wavelengths, so fast
cadence photometry in the UV might be the best way to detect the WD spin
period in J0240.

Figure 11:  Left: Schematic diagram of an outflow that produces line
absorption at high inclination, presented in the binary rest frame. The
magnitude of the velocity vector is represented in color, and the numbers
around the edge of the figure indicate orbital phases. The parameters used to
create this model are discussed in the text. Center: The predicted radial
velocity of an absorption feature resulting from the outflow model displayed
in the left panel. This can be directly compared to the observed absorption
velocities in J0240 displayed in Figure 10. Right: The motion of the outflow
in velocity space. This panel describes emission from the outflow (not
absorption), so the requirement of a backlight from the center panel is
lifted.

###  4.4 Application of Wynn et al. (1997) to J0240

Our results are strongly consistent with the model of AE Aqr from Wynn et al.
(1997), who argued that the accretion flow is clumpy, with discrete,
heterogeneous blobs that each experience a drag force as they encounter the
WD’s magnetosphere. Near their point of closest approach to the WD, the blobs
are accelerated above the binary escape velocity and expelled. As they leave
the system, the blobs trace a spiral pattern in the binary rest frame. We
refer to the blob velocity after ejection as the “terminal” velocity, but this
is just an approximation as the blobs continue to slowly decelerate in the
potential well of the binary.

Although the modeling in Wynn et al. (1997) is tailored to AE Aqr
specifically, nearly all of our observations can be understood within its
framework. For example, in the Wynn et al. (1997) model, there is no accretion
disk, and we see no evidence of one in our observations. Even more
importantly, the persistent P Cyg profile seen during the second half of the
orbit is a natural consequence of the outflow trajectories computed by Wynn et
al. (1997). Their Figure 7 predicts that shortly after its interaction with
the magnetosphere, the propeller’s outflow will begin to spiral outward from
the binary (as seen in the binary rest frame), and we would expect to see line
absorption when this outflow lines up with our view of the secondary and
flaring region. The velocity vectors in their Figure 7 are pointed outward
radially, so the resulting absorption would be blueshifted by several hundred
km s-1, as observed. Unless the orbital inclination is exactly 90∘, the
outflow will eventually be too far from the binary to intersect our line of
sight to the secondary, and the absorption will therefore cease.

At present, J0240 cannot be modeled in the same way as AE Aqr because its spin
period is unknown. Therefore, to provide a quantitative basis for our
interpretation, we shall consider how AE Aqr would appear if it were viewed at
a high orbital inclination. Blobs are expected to expand out of the orbital
plane, and they may become comparable in size to the WD’s Roche lobe after
being expelled (Eracleous & Horne, 1996). In this scenario, ejected blobs
could intercept the line between the observer and a source of light in the
system, such as the secondary or flaring region. For example, at orbital phase
0.75, the propeller’s outflow would be $\sim 4a$ from the secondary in the
modelling by Wynn et al. (1997). If the secondary and one of the expelled
blobs have radii of $0.3a$ and $0.4a$, respectively, the blob could occlude
the secondary if $i\geq\tan^{-1}(4a/(0.3a+0.4a))=80^{\circ}$. A quarter-orbit
later, when the outflow is $\sim 5a$ from the secondary, the inclination
required for an occlusion increases to $i\geq 82^{\circ}$. These simple
geometric considerations suggest that $i$ dictates the range of orbital phases
that the P Cyg absorption component remains visible, because as the outflow
becomes increasingly distant from the secondary, an increasingly high value of
$i$ would be needed to produce an absorption feature.

Additionally, we note that a blob’s path and its terminal velocity, can be
tweaked by adjusting the drag coefficient, $k$, from Wynn et al. (1997).
Increasing this value causes the accretion stream to begin interacting further
from the WD and results in a higher terminal velocity. We illustrate this for
AE Aqr using the parameters from Wynn et al. (1997) in Figure 11, which shows
a single-particle trajectory for AE Aqr for $k=2\times 10^{-5}$ s-1. Of
particular note is the center panel of Figure 11, which shows the predicted
radial velocity of a blob backlit by an emitting source at the binary center
of mass. The center of mass was chosen for this calculation because it is
conveniently situated between the two likely sources of light in the system:
the secondary star and the flaring region near the WD. The predictions of the
absorption velocities from gas close to the interaction region are unreliable
in this approximation, but the absorption velocities from distant blobs do not
strongly depend on the location of the light source.

Figure 11 displays a model for AE Aqr, but its overall similarity to the P Cyg
velocities and orbital phases observed in J0240 (Figure 10) is quite striking.
There are certainly differences in the details between the observed and
modelled absorption features. The terminal velocities in the AE Aqr model are
nearly constant between phases $0.5<\phi<1.0$ at about 400 km s-1. In
contrast, the observed J0240 absorption velocities are seen to increase from
400 km s-1 near $\phi=0.5$, to 600 to 700 km s-1 at inferior conjunction. If
the spin period were known, the $k$ parameter could be adjusted to achieve a
better fit with the observed velocities. Nevertheless, with the parameters of
AE Aqr, we cannot find a value of $k$ that causes the predicted absorption
velocity to increase at later orbital phases; indeed, this gas is far from the
influence of the propeller and conservation of energy suggests that the
expelled blobs would slowly decelerate as they move outward through the
binary’s gravitational potential.

We speculate that the drag coefficient in a real propeller system may
systematically vary on a time scale of minutes, hours, and days. This could
result from variations in the blob properties as they leave the secondary, or
from active flares modifying blobs approaching the WD. We see kinks with
amplitudes of 50 km s-1 in the absorption line velocities (Figure 10) over a
single observing run, as well as differences of $\sim$100 km s-1 between runs,
suggesting that the ejection velocities are varying at both short and long
time scales. Further high-quality J0240 spectroscopy is needed to determine if
the absorption velocities consistently increase with orbital phase as seen in
two of our observing runs.

The ease of detecting the outflow in J0240 offers a stark but refreshing
contrast with AE Aqr, whose outflow is challenging to detect at that system’s
much lower inclination. Many previous studies have attempted to use Doppler
tomography to discern the outflow (e.g. Wynn et al., 1997; Welsh et al., 1998;
Horne, 1999), but the resulting tomograms have tended to show little more than
a featureless blob of emission centered in the $-V_{x},-V_{y}$ quadrant. In
contrast, the P Cyg absorption in J0240 offers a direct and unambiguous means
of studying the outflow. In particular, if a future study can identify the
spin period as well as the orbital inclination $i$ from eclipse modeling, the
exact trajectory of the outflow could be rigorously mapped. Likewise,
theoretically predicted outflow velocities, such as those in Fig. 11, can be
tested against the radial velocity of the P Cyg absorption (see Figure 10)
once the spin period is known.

##  5 Conclusion

Our observations and analysis establish that J0240 is a magnetic CV in a
propeller state and the first eclipsing AE Aqr type star. Our major
conclusions are as follows.

  1. 1.

We confirm that the flaring region undergoes eclipses by the secondary star in
J0240 as noted by Littlefield & Garnavich (2020).

  2. 2.

The optical flares noted by Thorstensen (2020) coincide with transient
emission-line flares whose wings extend to $\pm 3000$ km s-1 in the Balmer and
He I lines. This unique high-velocity flaring is seen in AE Aqr and points to
a strong similarity between the two systems.

  3. 3.

We identify a persistent narrow Balmer absorption feature between orbital
phases 0.5-1.0. Its blue-shifted velocity is seen to increase with orbital
phase. We argue that this P Cyg absorption results from gas ejected by the
propeller into circumbinary orbit.

  4. 4.

The narrow absorption is seen below the level of the continuum from the
secondary around inferior conjunction, showing that the absorbing gas is
consistent with the outflow models of Wynn et al. (1997) and our own
simulations.

  5. 5.

The emission lines are formed primarily in two distinct regions. One of them,
which we identify as the magnetic-propeller region close to the WD, is the
source of the higher-order Balmer, He I, and high-velocity H$\alpha$ and
H$\beta$ emission. The other is an extended outflow that produces mostly low-
velocity H$\alpha$ emission, and its blue edge is defined with the presence of
P Cyg absorption.

  6. 6.

We unsuccessfully searched for a photometric signature of the spinning WD as
is seen in AE Aqr. We placed a 4 mmag upper limit on the $g$-band spin
amplitude for periods between 6.3 s and 85 s. This is consistent with the non-
detection of a spin signal noted by Pretorius et al. (2021).

J0240 appears to be only the second member of the AE Aqr sub-class of IPs. The
proposed WD pulsar, AR Sco (Marsh et al., 2016; Stiller et al., 2018;
Garnavich et al., 2019) may also be related to these AE Aqr-like propellers.
The propellers and AR Sco appear to efficiently extract spin energy from their
WDs, and are unusually strong radio emitters, implying a significant non-
thermal power source derived from an interaction with the rapidly spinning
magnetic WD. (Bookbinder & Lamb, 1987; Stanway et al., 2018; Pretorius et al.,
2021).

Because of its high orbital inclination, J0240 enables observational tests
that are impossible with AE Aqr, which has a much lower orbital inclination.
It is therefore a compelling candidate for theoretical modeling.

We thank R. Pogge and O. Kuhn for their help in obtaining the LBT
observations. This work is partly based on observations obtained at the MDM
Observatory, operated by Dartmouth College, Columbia University, Ohio State
University, Ohio University, and the University of Michigan.

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# Data-and-Knowledge Dual-Driven Automatic Modulation Recognition for Wireless
Communication Networks

Rui Ding§, Hao Zhang§, Fuhui Zhou§, Qihui Wu§, Zhu Han†
§Nanjing University of Aeronautics and Astronautics, China, †University of
Houston, USA
Email: _{ rui_ding<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>and<EMAIL_ADDRESS>This work was supported by National
Key R&D Program of China under Grant 2020YFB1807602, the National Natural
Science Foundation of China under Grant 62071223, Grant 62031012 and Grant
61931011, Young Elite Scientist Sponsorship Program by CAST.

###### Abstract

Automatic modulation classification is of crucial importance in wireless
communication networks. Deep learning based automatic modulation
classification schemes have attracted extensive attention due to the superior
accuracy. However, the data-driven method relies on a large amount of training
samples and the classification accuracy is poor in the low signal-to-noise
radio (SNR). In order to tackle these problems, a novel data-and-knowledge
dual-driven automatic modulation classification scheme based on radio
frequency machine learning is proposed by exploiting the attribute features of
different modulations. The visual model is utilized to extract visual
features. The attribute learning model is used to learn the attribute semantic
representations. The transformation model is proposed to convert the attribute
representation into the visual space. Extensive simulation results demonstrate
that our proposed automatic modulation classification scheme can achieve
better performance than the benchmark schemes in terms of the classification
accuracy, especially in the low SNR. Moreover, the confusion among high-order
modulations is reduced by using our proposed scheme compared with other
traditional schemes.

###### Index Terms:

Automatic modulation classification, data-and-knowledge dual-driven, low
signal-to-noise radio.

##  I Introduction

Artificial intelligence and intelligent communication are indispensable parts
in wireless communication systems. As an indispensable intelligent
communication technology in wireless communication systems, automatic
modulation classification (AMC) has been widely used in various applications.
In military applications, AMC helps to recover the transmitted information and
generate interference signals with matching modulation [1]. In civilian
applications, AMC is able to determine the appropriate demodulation method to
realize the correct recovery of transmitted information [2].

The existing automatic modulation classification (AMC) schemes can be mainly
classified into two categories, namely, model-driven AMC and data-driven AMC.
The model-driven schemes mainly include likelihood-based (LB) schemes [3] and
feature-based (FB) schemes [4]. The LB classifier treats AMC as a hypothesis
testing problem. Different test statistics are constructed firstly. Then, the
likelihood functions are calculated under the modulation hypothesis by using
the constructed test statistics. Lastly, these functions are compared to make
the final decision [3]. The FB schemes aim to extract unique characteristics
of different types of signals and have robust performance with low
implementation complexity [5]. In contrast, data-driven methods, such as
support vector machine (SVM) [6], and logistic regression [5], etc., perform
modulation classification by learning the difference among data distributions.
Moreover, the data-driven deep learning utilize the neural networks to extract
the visual features automatically from the original data, such as I/Q samples.
The related works are classified as follows.

_Model-driven methods_ : The authors in [7] used the maximum-likelihood method
to recognize digital amplitude-phase modulations. It was shown that the
maximum-likelihood classifier is capable of classifying any finite set of
distinctive constellations with the zero error rate when the number of
available symbols goes to infinity. However, the maximum-likelihood method
suffers from high computational complexity. With the FB schemes, the authors
in [8] utilized the high-order statistical features to realize the modulation
classification. It was shown that the FB method can achieve good performance
with low computational complexity.

_Data-driven methods_ : A long short-term memory (LSTM) based AMC algorithm
was proposed in [9]. LSTM learns the dependency relationship between the
current element and the elements before-after through the gating structure.
However, its recurrent structure results in high computational complexity.
Meanwhile, spatial correlation features are ignored in this scheme. The
authors in [10] utilized the CNN-LSTM to efficiently explore the feature
interaction and the spatial-temporal properties of raw complex temporal
signals. However, the increase of the depth of the network can cause the
gradient vanishing and over-fitting problems. A deep residual network (ResNet)
was proposed in [11] by using residual learning with skip connection for image
classifications, which alleviates the over-fitting problem when training deep
networks. Meanwhile, it is able to learn discriminative features for achieving
a better performance. However, the complex architecture of deep network needs
a lot of computing resources and takes a long time to train. This drawback
makes it unrealistic in the practical scenarios since the real-time
performance is of crucial importance in practical applications. In [12], the
authors designed a lightweight model with smaller model sizes. High
computation efficiency was achieved by using model compression. The simulation
results demonstrated that the lightweight model reduces the training time
significantly with negligible loss in classification accuracy.

All the data-driven AMC schemes mentioned in [9]-[12] require a large amount
of training samples, which are difficult to be obtained in practical
communication scenarios. Meanwhile, pure data-driven schemes cannot satisfy
the classification performance requirements under the dynamically changing
communication scenarios. In particular, the classification performance
achieved by using those methods is very poor in low SNRs. Recently, radio
frequency machine learning (RFML) has been proposed [13],[14] and envisioned
to be promising to tackle these problems. It exploits expert knowledge to
achieve superior performance. Motivated by RFML, a novel data and knowledge
dual-driven AMC scheme is proposed in this paper. Our main contributions are
as follows.

  * •

It is the first time that semantic information, e.g., class attributes, is
exploited to decrease the required number of training samples, which is of
crucial importance in the practical complex and dynamic wireless networks.

  * •

An improved residual network is proposed for attribute learning.

  * •

A novel data and knowledge dual-driven framework for AMC is proposed to
construct the classifier to learn the muti-dimensional representations of
different modulations from I/Q signals.

  * •

Simulation results demonstrate that our proposed scheme has a better
classification performance compared with other DL-based AMC schemes,
especially in the low SNR. Moreover, the confusion between 16QAM and 64QAM is
reduced significantly.

The remainder of this paper is organized as follows. The preliminary is
presented in Section II. Section III presents our proposed scheme. Section IV
presents the simulation results. Finally, the paper concludes with Section V.

##  II Preliminaries

###  II-A Problem Statement

The modulation classification can be identified as a $K$-class hypothesis
test, where $K$ denotes the number of modulations. The received signal under
the $k$th modulation hypothesis ${H}_{k}$ is given as

$\displaystyle\
{{H}_{k}}:{{x}_{k}}(n)={{s}_{k}}(n)+{{\omega}_{k}}(n),n=1,2,...,N,$ (1)

where ${s}_{k}(n)$ and ${x}_{k}(n)$ are the transmitted signal and the
received signal, respectively. $N$ is the number of signal symbols.
${{\omega}_{k}}(n)$ is the additive white Gaussian noise with mean being zero
and variance being ${{\sigma}^{2}}$.

The in-phase and quadrature (I/Q) parts of the received signal are both
utilized. These two parts usually obey an identical independent distribution,
which can be input into the neural network without normalization [15]. The I/Q
signal samples can be expressed as a vector by turning the received signal
${x}_{k}(n)$ into the vector $\mathbf{x}_{k}$, given as

$\displaystyle{\mathbf{x}_{k}}$
$\displaystyle={\mathbf{I}_{k}}+{\mathbf{Q}_{k}}$ (2a)
$\displaystyle=\Re({\mathbf{x}_{k}})+j\Im({\mathbf{x}_{k}}),$ (2b)

where $\mathbf{I}_{k}$ and $\mathbf{Q}_{k}$ represent the in-phase part and
the quadrature part of the received signal, respectively, and $j=\sqrt{-1}$.
$\Re(\cdot)$ and $\Im(\cdot)$ represent the operators of the real and
imaginary parts of the signal, respectively. The raw data $\mathbf{x}_{k}$ can
be specifically expressed as the form of matrix, given as

$\displaystyle{\mathbf{x}_{k}}=\left[\begin{matrix}{\Re}\left[x(1),x(2),...,x(N)\right]\\\
{\Im}\left[x(1),x(2),...,x(N)\right]\\\ \end{matrix}\right].$ (3)

###  II-B Traditional AMC Methods

The DL-based schemes such as CNN and RNN are utilized to extract features from
the raw data. Then, a fully connected (FC) layer is utilized to integrate the
information and carry out the conversion of feature dimension. The feature
learning can be expressed as a process that the raw data
$\mathbf{x}_{k}\in{\mathbb{R}^{N\times 2}}$ is mapped into a $L$-dimensional
vector $\mathbf{y}$, given as

$\displaystyle f:{\mathbf{x}_{k}}\in{\mathbb{R}^{N\times
2}}\to\mathbf{y}\in{\mathbb{R}^{L}},$ (4)

where mapping function $f$ represents the feature learning model with the
fully connected layer, and $\mathbf{y}$ represents the feature vector output
from the FC layer.

Figure 1: The deep visual-semantic embedding model.

Finally, the learned feature vectors are classified by another FC layer with
the $softmax$ classifier. The number of neurons in the last layer is equal to
the number of modulation formats. Thus, each output neuron corresponds to a
modulation format. $Softmax$ is used to convert the output into the
probability that the input signal belongs to each candidate modulation format.
The cross-entropy loss function is utilized to measure the gap between the
model output and the true label. It can be given as

$\displaystyle
loss=\frac{1}{N}\sum\limits_{j=1}^{N}{\sum\limits_{k=1}^{K}{{{q}_{j,k}}\log({{p}_{j,k}})}},$
(5)

where $K$ represents the number of classes, $N$ represents the number of
samples. ${p}_{j,k}$ is the output of $softmax$, which represents the
probability when data sample $j$ belongs to class $k$. ${q}_{j,k}$ is a
indicative variable, which is given as

$\displaystyle{{q}_{j,k}}=\left\\{\begin{array}[]{*{35}{l}}1,\text{if }j\text{
belongs to }k\\\ 0,\text{if }j\text{ does not belongs to }k.\\\
\end{array}\right.$ (8)

However, the pure data-driven AMC method requires a large number of samples to
complete the training of deep networks. Moreover, the classification accuracy
of traditional methods is poor in the practical complex and dynamic scenarios,
especially in the low SNRs. Fortunately, the exploitation of expert knowledge
is promising to tackle those problems [16]. However, to our best knowledge,
few investigations have studied it. Therefore, we propose a novel data and
knowledge dual-driven AMC method.

##  III Proposed AMC Scheme

The architecture of our proposed AMC scheme is shown in Fig. 1. On one branch,
the visual model encodes the raw I/Q data into visual vectors. The visual
feature space is used as the embedding space where both the visual content and
the attribute vector of the class that the modulation format belongs to are
embedded. On the other branch, the attribute learning model learns the
attribute vectors corresponding to different modulation formats according to
the deterministic attribute labels that are set artificially. Then, the
transformation model converts the attribute vectors into the visual feature
space. Lastly, a least square embedding loss is utilized to minimize the
discrepancy between the visual feature vectors and the attribute vectors.

###  III-A Visual Model

Fig. 2 illustrates the framework of the visual model. The multi-scale
convolutional network (MSNet) is employed as the visual model. The MSNet
consists of several multiscale (MS) modules, global average-pooling (GAP), FC
layers and the $softmax$ classifier. MS modules are used to capture the multi-
level feature information by using a $3\times 1$ convolution layer with stride
= 2 to reduce the feature dimension at the top layer of the module. Then,
several parallel convolutions with different kernel sizes are utilized to
capture multi-level features. Features from different convolutional layers are
consolidated together by using the concat operation. After the concat
operation, the FC layer of the traditional CNN is replaced by the GAP for
aggregating information from the MS modules to average each feature output
from the four corresponding channels. Compared with the traditional FC layer,
the over-fitting problem is avoided since there is no parameter required to be
optimized in GAP. Moreover, another FC layer with rectified linear units
(ReLU) is utilized to reduce the feature dimensionality. ReLU function can be
expressed as

$\displaystyle\ f(z)=\max(0,z),$ (9)

where $\max(\cdot)$ represents the operator for obtaining the maximum value.

The values of several neurons are set to be zero, which results in the
sparsity of the network and reduces the interdependence among parameters.
Therefore, the occurrence of over-fitting problems can be alleviated.
Moreover, different from $sigmoid$ and $tanh$ activation function, ReLU
function dose not have the saturation zone. Thus, the gradient vanishing
problem can be avoided. The specific architecture of the visual model is shown
in Table I.

###  III-B Attribute Learning Model

The core goal of AMC is to recognize the category of different modulations.
Each modulation has its unique characteristics. Thus, modulation can be
identified based on the high-level description that is phrased in terms of
semantic attributes. Different classes are usually different in the high
dimensional feature space. In this case, it is promising to combine semantic
attributes and visual features to achieve a higher classification accuracy.

An adaptation of residual network was exploited to learn the attribute
representation of different modulations. The residual unit is shown in Fig.
3(a). Two 2D convolution operations with kernel size $3\times 3$ are performed
in the residual unit. Different from ResNet in [15], the batch normalization
layer is used to standardize the data in the intermediate layers to avoid the
gradient disappearance caused by the saturation of the partial derivative of
the intermediate variable. Alongside, ReLU activation is used after the first
convolution and after the skip connection to introduce non-linear operations
as shown in Fig. 3(a). The residual stack, as shown in Fig. 3(b) consists of a
convolution operation with a kernel size of $1\times 1$ followed by two
residual units. The maxpool layer is used to compress features. Moreover, the
GAP is used to average the outputs of different channels. Therefore, the
parameters are reduced greatly compared with FC in ResNet proposed in [15].
The specific architecture of the attribute learning network is shown in Fig.
3(c). The number of residual stack is decreased from 6 to 3 to reduce the
complexity of the model. The kernel size and output dimensions corresponding
to different layers of the attribute learning model are shown in Table II.

Since the learning of each attribute transcends the specific classification
task, the attribute learning model can be pre-learned independently [16]. In
this way, we can perform attribute learning through bigger datasets that are
not limited to AMC datasets.

Figure 2: The architecture of the visual model.

(a)

(b)

(c)

Figure 3: (a) ResUnit. (b) Residual stack. (c) The attribute learning model.

###  III-C The Visual-Attribute Embedding Model

The visual-attribute embedding model has two branches. One branch is the
visual encoding branch adapted from the MSNet in Fig. 1, and the $softmax$
classification layer is removed. The visual encoding branch can output the
visual feature vector. It takes the raw data of the signal samples
$\mathbf{I}_{{i}}$ as the input. Then, the MS module is used to extract multi-
dimensional features. The GAP is used to flatten multi-channel features.
Finally, the FC layer outputs a $D$-dimensional feature vector
$\phi_{1}({\mathbf{I}_{i}})\in{\mathbb{R}^{D\times 1}}$.

TABLE I: The Specific Architecture of the Visual Model Input Layers | Kernel Size | Output
---|---|---
Input | $-$ | $2\times 128$
MS module | $3\times 1,[7\times 1,5\times 1,3\times 1,1\times 1]$ | $128\times 64$
MS module | $3\times 1,[7\times 1,5\times 1,3\times 1,1\times 1]$ | $128\times 32$
GAP | $1\times 1$ | $128\times 4$
FC/ReLU | $512\times 128$ | $128$
FC/Softmax | $128\times 4$ | $4$
TABLE II: The Specific Architecture of the Attribute Learning Model Input Layers | Kernel Size | Output Dimensions
---|---|---
Input | $-$ | $2\times 128$
Conv | $1\times 1$ | $32\times 128$
ResUnit | $3\times 2$ | $32\times 128$
ResUnit | $3\times 2$ | $32\times 128$
Maxpool | $2\times 1$ | $32\times 64$
ResUnit | $3\times 2$ | $32\times 64$
ResUnit | $3\times 2$ | $32\times 64$
Maxpool | $2\times 1$ | $32\times 32$
ResUnit | $3\times 2$ | $32\times 32$
ResUnit | $3\times 2$ | $32\times 32$
Maxpool | $2\times 1$ | $32\times 16$
GAP | $1\times 1$ | $32\times 1$
FC | $32\times 6$ | $6$

The semantic embedding is achieved by the other branch which is a attribute
learning subnet as illustrated in III-B. The subnet outputs a $L$-dimensional
feature vector $\phi_{2}({\mathbf{I}_{i}})\in{\mathbb{R}^{L\times 1}}$.
Moreover, a joint embedding space is learned where both the attribute vectors
and the visual feature vectors can be projected. The authors in [16] has
proved that the visual feature space is the most appropriate embedding space,
which can alleviate the hubness problem [16]. Therefore, a transformation
subnet is designed to convert attribute vectors into vectors in the same
dimensional space as the visual feature vectors. Specifically, it takes the
$L$-dimensional attribute representation vector
$\phi_{2}({\mathbf{I}_{i}})\in{\mathbb{R}^{L\times 1}}$ of the attribute
learning subnet as input, and after going through two FC layers and the ReLU
activation outputs a D-dimensional semantic embedding vector
${{\phi}_{3}}({{\phi}_{2}}({\mathbf{I}_{i}}))\in{\mathbb{R}^{D\times 1}}$. In
order to show the process of the transformation subnet in detail, the output
can be expressed as

$\displaystyle\
{{\phi}_{3}}({{\phi}_{2}}({\mathbf{I}_{i}}))={{f}_{2}}({\mathbf{W}_{2}}{{f}_{1}}({\mathbf{W}_{1}}{{\phi}_{2}}({\mathbf{I}_{i}}))),$
(10)

where $\mathbf{W}_{1}\in{\mathbb{R}^{L\times M}}$ and
$\mathbf{W}_{2}\in{\mathbb{R}^{M\times D}}$ are the weights to be learned in
the first FC layer and the second FC layer. The rectified linear units
$f(\cdot)$ is used as the activation function to introduce non-linearity into
the network.

Each of the FC layer has a ${l}_{2}$ parameter regularization loss. The two
branches are linked together by a least square embedding loss which aims to
minimise the discrepancy between the visual feature vector
$\phi_{1}({\mathbf{I}_{i}})\in{\mathbb{R}^{D\times 1}}$ and its class
representation embedding vector in the visual feature space. The loss function
is given as

$\displaystyle L({\mathbf{W}_{1}},{\mathbf{W}_{2}})=$
$\displaystyle\frac{1}{N}\sum\limits_{i=1}^{N}{{{\left\|{{\phi}_{1}}({\mathbf{I}_{i}})-{{f}_{2}}({\mathbf{W}_{2}}{{f}_{1}}({\mathbf{W}_{1}}{{\phi}_{2}}({\mathbf{I}_{i}})))\right\|}^{2}}}$
(11)
$\displaystyle+\lambda({{\left\|{\mathbf{W}_{1}}\right\|}^{2}}+{{\left\|{\mathbf{W}_{2}}\right\|}^{2}}).$

where $N$ is the number of training samples and $\lambda$ is the hyper-
parameter weighting the strengths of the two parameter regularization losses
against the embedding loss.

As is shown in Fig. 3, different from the traditional pure data-driven
architecture, our proposed scheme constructs a embedding space where both
visual features and attribute features can be projected. The integration of
attribute features can improve the performance of the model in low SNRs.
Meanwhile, the existence of two pre-trained models makes end-to-end training
only be required for the transformation model. Therefore, the training speed
of our proposed scheme can be extremely high. Moreover, due to the
introduction of attribute knowledge, we can reduce the requirements for visual
model data. Lastly, different from abstract visual features, the attribute
features labels are composed of deterministic binary variables which have
clear physical implications.

##  IV Simulation Results

In this section, simulation results are presented to evaluate the performance
of our proposed AMC scheme and compare with the benchmark schemes. The
simulation settings are based on the works in [4]. The performance is measured
on a system equipped by a 3.00-GHz CPU, 16GB RAM, and a single NVIDIA GeForce
GTX 1660SUPER GPU.

Figure 4: Classification performance comparison among MSNet [4], ResNet [15],
CNN [17], VGG [15], LSTM [18] and our proposed scheme.

(a) (b)

Figure 5: Comparison of confusion matrices (a) MSNet [4]. (b) Our proposed
scheme.  Figure 6: Comparison of training loss between MSNet [4], ResNet [15],
CNN [17], VGG [15], LSTM [18] and our proposed scheme.

(a) (b)

Figure 7: Visualization scatter map of extracted features by different
networks (a) MSNet [4]. (b) Our proposed scheme.

For the attribute learning model, we train it by using the stochastic gradient
descent (sgd) optimizer with an initial learning rate of 0.01, and a momentum
of 0.9 for 40 epochs. Different from the training of visual model, the
attribute learning is not a classification problem. Therefore, the mean
squared error function is utilized to measure the gap between the model output
and the true attribute label.

The classification performance is operated on a publicly available dataset,
which is presented on the website 111https://www.deepsig.ai/datasets.. Fig. 4
shows the classification performance comparison of our proposed scheme with
those achieved by several representative DL-based models for AMC including
MSNet [4], ResNet [15], VGG [15] and LSTM [18]. It is evident that the
proposed scheme is superior to other traditional models, and it can provide 2%
gains over ResNet, 5% gains over MSNet, 17% gains over LSTM and VGG at 12dB.
Moreover, our proposed scheme has superior classification performance in low
SNRs. It can reach about 60% accuracy when the SNR is -20dB, and it can
achieve over 70% accuracy when the SNR is over -14dB, while the performance of
ResNet is only about 25% at -20dB and 32% at -14dB.

The comparison of the confusion matrices between MSNet [4] and our proposed
scheme is shown in Fig. 5. It is seen that the proposed scheme has less
confusion compared to other traditional models. Specifically, two modulation
formats perform worse in MSNet, which are 16QAM and 64QAM as shown in Fig.
5(a) and Fig. 5(b), respectively.

Fig. 6 illustrates the training loss of each model for AMC. The proposed
scheme can achieve a lower loss in the training set compared to the other
models and obtains a higher convergence speed than other models. Specifically,
our proposed model can achieve convergence at only about the $9$th epoch. This
is reasonable, since the pre-trained subnets can greatly reduce the end-to-end
training time.

To further demonstrate the effectiveness of the proposed scheme, we visualize
the extracted feature and convert them into a two-dimensional scatter map [19]
shown in Fig. 7. It can be seen that 16QAM and 64QAM are mixed together in
MSNet [4]. In contrast, the features between 16QAM and 64QAM are much more
discriminative in our proposed scheme. This indicates that our proposed scheme
can achieve better classification performance for high-order modulations.

##  V Conclusion

A novel data and knowledge dual-driven AMC scheme based on RFML was proposed
by exploiting attribute features and visual features. The attribute learning
model was utilized to learn different attribute representations. The
transformation model was used to convert attribute features into visual space
to embed with the output of visual model. Simulation results demonstrated that
our proposed scheme is superior to other benchmark schemes in terms of the
classification accuracy especially in the low SNR. Moreover, the confusion
between high-order modulations is reduced compared with other benchmark
schemes.

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