# A Surprising Periodicity Detected During a Super-outburst of V844 Herculis
by TESS

Anousha Greiveldinger Department of Physics and Astronomy, University of Notre
Dame, Notre Dame, IN 46556, USA  Peter Garnavich Department of Physics and
Astronomy, University of Notre Dame, Notre Dame, IN 46556, USA  Colin
Littlefield Department of Physics and Astronomy, University of Notre Dame,
Notre Dame, IN 46556, USA  Bay Area Environmental Research Institute, Moffett
Field, CA 94035 USA  Mark R. Kennedy School of Physics, University College
Cork, Cork, Ireland  Jodrell Bank Centre for Astrophysics, Department of
Physics and Astronomy, The University of Manchester, Manchester M13 9PL,
United Kingom  Jules P. Halpern Department of Astronomy, Columbia University,
New York, NY 10027 USA  John R. Thorstensen Department of Physics and
Astronomy, Dartmouth College, Hanover, NH 03755 USA  Paula Szkody Department
of Astronomy, University of Washington, Seattle, WA 98195, USA  Arto Oksanen
American Association of Variable Star Observers, 49 Bay State Rd, Cambridge,
MA 02138, USA  Rebecca S. Boyle Department of Physics and Astronomy,
University of Notre Dame, Notre Dame, IN 46556, USA

###### Abstract

We identify a previously undetected periodicity at a frequency of 49.08$\pm
0.01$ ${\rm d}^{-1}$ (period of 29.34$\pm 0.01$ minutes) during a super-
outburst of V844 Her observed by TESS. V844 Her is an SU UMa type cataclysmic
variable with an orbital period of 78.69 minutes, near the period minimum. The
frequency of this new signal is constant in contrast to the superhump
oscillations commonly seen in SU UMa outbursts. We searched without success
for oscillations during quiescence using MDM, TESS, and XMM-Newton data. The
lack of a periodic signal in the XMM light curve and the relatively low X-ray
luminosity of V844 Her suggests that it is not a typical IP. We consider the
possibility that the 29 min signal is the result of super-Nyquist sampling of
a Dwarf Nova Oscillation with a period near the 2-minute cadence of the TESS
data. Our analysis of archival AAVSO photometry from a 2006 super-outburst
supports the existence of a 29 min oscillation, although a published study of
an earlier superoutburst did not detect the signal. We compare the X-ray
properties of V844 Her with short orbital period intermediate polars (IP),
V1025 Cen and DW Cnc. We conclude that the new signal is a real photometric
oscillation coming from the V844 Her system and that it is unlikely to be an
aliased high-frequency oscillation. The steady frequency of the new signal
suggests that its origin is related to an asynchronously rotating white dwarf
in V844 Her, although the precise mechanism producing the flux variations
remains unclear.

cataclysmic variables: individual (DW Cnc, V1025 Cen, V844 Her, WZ Sge) -
stars: oscillations - white dwarfs - X-rays:stars

††facilities: AAVSO, TESS, McGraw-Hill (Templeton), XMM

##  1 Introduction

Cataclysmic variables (CV) are binary star systems consisting of an accreting
white dwarf (WD) and a late-type secondary star. In CVs, the secondary star
generally fills its Roche lobe and transfers mass to the WD through a stream.
An intermediate polar (IP) is a subclass of CV in which the primary is midly
magnetic. The accretion process results in a wide range of periodic and quasi-
periodic oscillations on time scales of the orbital period and the WD spin
period. In high mass-ratio systems, for example, a dynamical accretion disk
instability results in “superhump” oscillations seen at frequencies within a
few percent of the system’s orbital period (Whitehurst, 1988; Osaki, 1989).
Accretion onto a rapidly spinning, magnetic WD, as seen in IPs, may result in
the optical and X-ray modulations at the WD spin period or the beat period
between the spin and orbital frequencies (Patterson, 1994).

CVs can also show rapid photometric oscillations with periods ranging from
tens to hundreds of seconds. This variability is called Dwarf Nova
Oscillations (DNO) because they are often detected when an accretion disk has
transitioned to a bright, hot, highly viscous state seen as a dwarf nova
outburst. The complex observational characteristics of DNO were reviewed by
Warner (2004) and Warner & Woudt (2008), and include long-period DNO (lpDNO)
and associated quasi-periodic oscillations (QPO). These oscillations are
thought to result from an interaction between the accretion disk and a
spinning, magnetic WD. DNO and related oscillations seen in CVs appear to have
corresponding phenomena in neutron star and black hole binaries (Warner et
al., 2003).

The 1800 s and 120 s cadences of TESS observations are ill-suited for the
study of DNO phenomena that typically show oscillation frequencies of 10 s to
a few 100 s. However, the extremely precise cadence of TESS leads to Nyquist
aliasing where an oscillation at a frequency greater than the Nyquist
frequency appears as a lower frequency signal. This “Super-Nyquist” technique
has been applied to asteroseismology with Kepler (Murphy, 2015), and it may be
useful in identifying DNO-like oscillations with TESS.

V844 Her has been classified as an SU UMa type dwarf novae (DN) due to
evidence of longer and brighter super-outbursts, as well as normal outbursts.
It has a very short orbital period of 78.69 min (Thorstensen et al., 2002).
Oizumi et al. (2007) noted that normal outbursts from V844 Her are rare and
that the time between super-outbursts is about 300 days.

Figure 1: The Lomb-Scargle periodogram for V844 Her calculated from the sector
24 TESS light curve. The strong superhump signal is seen at 18 ${\rm
d}^{-1}$(80 min), and the its harmonics are detected out to 108 ${\rm
d}^{-1}$(13.3 min). The strong peak at 49 ${\rm d}^{-1}$ (29.34 min) has not
been identified. A weak signal near 98 ${\rm d}^{-1}$ (14.7 min) may be a
harmonic of the unidentified oscillation.

##  2 Data

###  2.1 TESS

V844 Her, TIC 39950064, was observed by TESS in the fast cadence mode (120 s
exposures) during sectors 24 and 25. Observations were recorded in sector 24
from April 16 to May 12, 2020, and V884 Her was visible on Camera 1, CCD 1.
The star was in super-outburst over sector 24. In sector 25, observations were
conducted from May 14 to June 8, 2020, and V884 Her was visible on Camera 1,
CCD 2. V844 Her was noted by Kato (2022) to be in super-outburst during sector
24. Kato (2022) analyzed the behavior of superhumps in the data, but we focus
on the periodicity occuring at 49 ${\rm d}^{-1}$ that was not included in the
analysis. V844 Her was again observed over sectors 51 and 52 covering the
dates April 22 through June 13, 2022. The star was in quiescence over these
dates.

The data were acquired using the Lightkurve python package (Lightkurve
Collaboration et al., 2018) and periodograms were calculated using the Lomb-
Scargle technique (L-S hereafter; Lomb, 1976; Scargle, 1982). The periodogram
of sector 24 is displayed in Figure 1. It clearly shows the superhump (SH)
oscillations at 80.45$\pm 0.45$ min (17.9$\pm 0.1$ ${\rm d}^{-1}$) and their
harmonics. The SH signals are broadened by the classic SU UMa frequency
variations as described by Kato (2022) for this same data set. Any orbital
modulation would appear at 78.69 min (18.30 ${\rm d}^{-1}$), but it is not
easily seen in the TESS data.

A fairly strong signal is obvious at 49.08$\pm 0.01$ ${\rm d}^{-1}$, or 29.34
$\pm 0.01$ minutes, (29 min hereafter), but it appears unrelated to the SH
oscillations or orbital period. An excess of power is seen at 98 ${\rm
d}^{-1}$ (14.7 min) which may be a weak harmonic of this unidentified signal.
The peak at 29 min in the periodogram is narrow and unresolved, suggesting a
nearly constant frequency during sector 24.

The variability of the oscillations is tested using a time-resolved power
spectrum shown in Figure 2. The Lomb-Scargle periodogram is calculated in a
sliding 1-day window. The amplitudes of the SH oscillations and harmonics are
seen to decline along with the fading of the super-outburst. The amplitude of
the 29 min signal fades more slowly than the SH oscillations and remains
detectable to the end of sector 24 and into sector 25.

Figure 2: Top: A portion of the TESS light curve of V844 Her during sector 24.
The super-outburst is seen fading from a maximum at the start of the
observations. The development of classical superhump oscillations (Kato, 2022)
is seen. Bottom: The time-resolved power spectrum is displayed over sector 24.
The amplitude of the superhump oscillations decays with the fading of the
super-outburst. The strength of the 29 min signal fades over the sector, but
more slowly than that of the superhumps. By the end of the sector, the 29 min
oscillation is the strongest signal seen. The new signal and the primary
superhump oscillation are marked on the right side of the figure with their
periods of 29 min and 80 min, respectively.

###  2.2 MDM Photometry

V844 Her was observed with the MDM 1.3 m McGraw-Hill telescope on four
consecutive nights starting on May 28, 2022 (UT). A $GG420$ long-pass filter
was used with the MDM Templeton detector. To minimize overheads, only a
130-arcsec section of the sky was recorded for analysis. The star was observed
for three hours each night with a 20 s exposure time resulting in an average
cadence of 23 s.

V844 Her had an approximate $V$-band magnitude of 17.9 while observed at MDM.
This is consistent with its typical quiescent brightness. The light curves
revealed a flickering with an amplitude of $\pm 0.15$ mag over a timescale of
tens of minutes.

###  2.3 AAVSO

Searching the American Association of Variable Star Observers (AAVSO)
International Database 111https://www.aavso.org/LCGv2/, we identified a long
photometric time-series of V844 Her obtained during a super-outburst. The
unfiltered CCD photometry was taken over three consecutive nights beginning
April 29, 2006. The time-series had a typical cadence of 30 s between
exposures, and a total of 771 measurements were made over the three nights. No
error estimates were included in the data table, but the scatter of the points
near minima of the superhumps implies a photometric precision of approximately
0.02 mag.

Observations began five nights after the start of the super-outburst when V844
Her was at 12.9 mag. The superhump amplitude was initially 0.2 mag. A Lomb-
Scargle periodogram of the photometry is strongly impacted by the sampling
window, but the fundamental superhump signal and its first harmonic are
clearly detectable. Further analysis of this data is discussed in Section 3.

###  2.4 XMM

V844 Her was serendipitously observed by _XMM-Newton_ as part of observation
ID 0784521701, which was intended to target the galaxy cluster Abell 2199. It
was observed on March 22, 2017, at 01:59:14 (UT) for 31.9 ks. Both of the
EPIC-MOS sensors Turner et al. (2001) and the EPIC-pn sensor Strüder et al.
(2001) were operated in Full Frame Mode with a Medium Filter. The two
Reflection Grating Spectrometer (RGS) instruments Rasmussen & XMM/Newton RGS
Team (2000) were operated in Spectroscopy HER + SES mode without a filter. The
Optical Monitor (OM) Cordova et al. (2000) was operated in Image Mode and used
three different filters throughout the observation: U, UVW1, and UVM2.

For comparison with known and suspected IPs, we re-analyzed archival XMM
observations of V1025 Cen, DW Cnc and, WZ Sge.

V1025 Cen, observation ID 0673140501, was executed by _XMM-Newton_ on Jan 1,
2012, at 22:21:43 (UT) for a total of 16.5 ks. The EPIC-MOS sensors (Turner et
al., 2001) were operated in Small Window Mode with a Medium filter and the
EPIC-pn sensor (Strüder et al., 2001) was operated in Large Window Mode with a
Medium filter. The OM (Cordova et al., 2000) was operated in the Image + Fast
mode with the UVM2 filter and both the RGS instruments (Rasmussen & XMM/Newton
RGS Team, 2000) were operated in the Spectroscopy HER + SES mode without a
filter.

DW Cnc was observed by _XMM-Newton_ on April 2, 2012, at 09:06:03 (UT) for a
total of 9.4 ks with observation ID 0673140101. The three EPIC sensors and two
RGS sensors were operated in the same modes as for V1025 Cen. The OM was
operated in Fast mode with the UVM2 filter.

WZ Sge was observed by _XMM-Newton_ on May 16, 2003, at 14:52:07 (UT) for a
total of 9.9 ks with observation ID 0150100101. The EPIC-MOS sensors were
operated in Large Window Mode with a Thin1 filter and the Epic-pn sensor was
operated in Full Frame mode with the same filter. The OM was in Image + Fast
mode with the UVW1 filter and the RGS instruments were both run in the
Spectroscopy HER + SES mode without a filter.

The data were collected from the _XMM-Newton_ Science Archive using RISA
analysis of EPIC exposures. The bin size was set to the default value of 100
seconds and counts were calculated by averaging the number of counts per bin.
The data were reduced and analyzed using _XMM_ -Science Analysis System (SAS
v19.0.0). The observation raw data files (ODFs) were downloaded from the _XMM-
Newton_ Science Archive and the current calibration files (CCF) were retrieved
using the _cifbuild_ command. The redistribution matrix files (RMF) were
generated using the _rmfgen_ and _rmfset_ commands. Then, the spectrum,
background, RMF, and ancillary response files (ARF) files were grouped for
easier handling in _XSPEC_ (Arnaud, 1996).

##  3 Analysis

###  3.1 Optical Variations

The 29 min signal observed in the TESS observations has not been reported
before. An extensive photometric study of V844 Her during a 1997 outburst by
Thorstensen et al. (2002) did not show any excess signal around 29 min (their
Figure 6). We note that the SH harmonic at 26.7 min, near the new periodicity,
was also not seen, but harmonics at 40 and 20 min were well detected. From the
AAVSO archive, the outburst studied by Thorstensen et al. (2002) reached a
maximum visual magnitude of 12.2, with the bright state lasting for 15 days
before fading to quiescence over 1-2 days. The brightness and length are
consistent with it being a superoutburst.

With no ground-based confirmation, we must consider that the TESS signal could
be an artifact or a periodicity from a source near V844 Her.

Its detection in TESS but not in ground data also suggests that it could be an
oscillation with a period shorter than the TESS cadence and appearing as a
super-Nyquist sampled signal at the difference between its true frequency and
the TESS sampling frequency.

Alternatively, TESS is highly sensitive to weak, but long-lasting signals,
suggesting that ground-based observations may have not been sufficient to
detect the signal in the past. Thus, when possible, we searched for variations
at a 29 min period in several other datasets, as well as for signals at the
super-Nyquist frequencies around 2 minutes (720 ${\rm d}^{-1}$).

Figure 3: An analysis of the Target Pixel Files (TPF) showing the location
V844 Her and the location of the oscillations. Top-Left: The average TPF over
the first 9 days of the outburst. Top-Right: The difference between the
brightest 9 days and the average of the final 10 days of sector 24. As the
outburst had faded significantly, the residuals isolate the light distribution
of V844 Her during sector 24. Lower-Left: The strength of the superhump signal
as measured by the S/N ratio of the periodogram peak. As expected, the
strongest signal coincides with the light distribution of V844 Her. Lower-
Right: Shows the strength of the 29 min signal in the TPF images. The position
of highest S/N ratio of the 29 min oscillation matches the location of V844
Her and the superhump signal strength.

####  3.1.1 Localization of the Oscillation Signals

The aperture used to extract the light curve of V844 Her is likely to include
light from one or more nearby stars. The 29 min signal may be originating from
one of these contaminating stars (e.g. Higgins & Bell, 2023). The average
target pixel file (TPF) image while V844 Her was in outburst is shown in the
top-left panel of Figure 3. Several sources are visible in the TPF.

To determine the precise location of the light associated with V844 Her, we
averaged the TPF images from the last ten days of sector 24 when the outburst
had significantly faded. We then subtracted the faint epochs from the outburst
epochs, and this result is shown in the top-right panel of Figure 3. Stars
that have remained constant over the sector are removed, while the positive
residuals show the flux distribution coming exclusively from V844 Her.

The superhump oscillations are undoubtedly coming from V844 Her, and we
localize the oscillations by calculating the L-S periodogram for each TPF
pixel and estimating the signal-to-noise ratio (S/N) of the first superhump
harmonic at 40 min. The noise level is estimated by taking the median value of
the power on each side of the signal peak. The signal is assumed to be the
maximum of the periodogram between $35.5<f<36.3$, where $f$ is the frequency
in ${\rm d}^{-1}$. The strength of the superhump signal in each pixel is shown
in the lower-left panel of Figure 3. As expected, the highest S/N of the
superhump power corresponds to the position of V844 Her.

To determine the location of the 29 min signal, we repeat the calculation done
previously, but with the peak power estimated from the range $48.7<f<49.8$
${\rm d}^{-1}$, and the noise is estimated from the median of frequencies on
each side of the peak. The distribution of the S/N from the 29 min signal is
shown in the lower-right panel of Figure 3. The centroid of the 29 min signal
is consistent with the superhump signal and the position of V844 Her.

####  3.1.2 Behavior of Other Stars on the TESS Detectors

The periodic thruster firing of the Kepler spacecraft during the extended K2
mission induced periodic signals into its stellar photometry (e.g. Clarke et
al., 2021). TESS has been very stable in comparison, but there may be spurious
signals added to the data through electronic noise, and this may depend on the
detector or be time-dependent. To test if the 29 min signal is a detector
artifact, we selected several stars near V844 Her that were recorded on Camera
1/CCD 1 during sector 24 using the 2-minute cadence.

We calculated L-S periodograms for two dozen stars that met the above
criteria. The stars brighter than T${}_{mag}\approx 10$ consistently showed
excess power spread between 131 and 144 min (between 10 and 11 ${\rm
d}^{-1}$). Time-resolved power spectra revealed that this excess was
concentrated over the dates 1964$<BTJD<1968$ and this time range also
corresponds to a general increase in photometric noise. No excess power
detected in nearby stars was seen around periods of 29 min.

Figure 4: The L-S periodogram of the three nights of V844 Her photometry from
the AAVSO database. The faint red line shows the “dirty” periodogram resulting
from daily gaps in the sampling window. The heavy blue line is the clean
spectrum clearly showing the fundamental superhump signal and its harmonics.
The 29 min periodicity is recovered in the cleaned spectrum, and its amplitude
relative to the SH harmonics is similar to what was seen in the TESS sector 24
data.

####  3.1.3 AAVSO

The 29 min signal was not detected by Thorstensen et al. (2002) during a 1997
superoutburst despite their analysis of 10 nights of ground-based photometry.
To further test for the presence of the 29 min signal in ground-based data, we
analyzed three nights of CCD photometry from the AAVSO database taken five
days after the peak of a super-outburst. Despite the high-quality data, the
daily gaps in the sampling window resulted in a highly structured L-S
periodogram shown in Figure 4. The fundamental superhump signal and its first
harmonic are obvious in the “dirty” periodogram. There appears to be a
possible signal near 29 min blended with the second superhump harmonic.

To confirm the suspected detections in the dirty periodogram, we applied a
cleaning algorithm based on the deconvolution of radio images synthesized from
irregularly spaced apertures (Högbom, 1974). Here, the dirty beam is generated
by calculating the periodogram of the temporal sampling window. The dirty beam
is then convolved with the dirty periodogram to identify the frequency of the
strongest signal matching the beam shape. The dirty beam is shifted to the
frequency of the identified signal, scaled to its peak, and then multiplied by
a gain factor before being subtracted from the periodogram. This process is
repeatedly applied to the residual periodogram after recording the amplitude
and frequency of each subtracted beam.

The clean periodogram is constructed by placing a scaled Gaussian at the
frequency corresponding to each subtracted dirty beam. The residuals remaining
after subtraction of all the dirty beams are then added to the synthesized
Gaussian periodogram. Adding the residuals is useful in deciding if more clean
iterations are required. The results of the cleaning are shown in Figure 4.
The assumed gain was 0.4 and the number of subtracted beams was limited to 12.
Because the superhumps vary in frequency with time, the cleaning algorithm
identified multiple peaks for the fundamental and major harmonics of the
superhumps.

A 29 min signal is well-detected after the clean algorithm is applied. Given
that plausible SH harmonics are detected at lower amplitudes, we conclude that
this ground-based data supports the presence of this new periodicity. The
amplitude of the 29 min signal relative to the SH harmonics is similar to that
seen in the TESS periodogram from early in the outburst (see Figure 1). We
note that the 29 min signal was not detected in the extensive photometry
obtained during a superoutburst analyzed by Thorstensen et al. (2002), yet it
was seen in the more modest set of AAVSO data. Given the difficulty in
detecting this signal, future intensive ground-based observations during
outbursts are recommended.

####  3.1.4 Optical Photometry in Quiescence

We searched for evidence of periodicities in the four nights of MDM data
obtained with a 23 s cadence, corresponding to a Nyquist frequency of 1870
${\rm d}^{-1}$(46.2 seconds). The L-S periodogram of the full MDM data is
shown in Figure 5 and the light curves are reproduced as an appendix. No clear
signal associated with the 29 min TESS oscillation is seen in the dirty or
cleaned periodograms. Injecting a sinusoid at the 49 ${\rm d}^{-1}$ frequency
shows that an amplitude of 40 mmag is required to assure detectability. Also,
no evidence of a possible super-Nyquist signal is present at high frequencies.
Again, by injecting signals with various amplitudes into the MDM light curve,
we estimate that a sinusoid with an amplitude of 7 mmag would be detectable
with a 3-$\sigma$ significance for frequencies greater than 500 ${\rm
d}^{-1}$(2.88 min).

The strongest peak in the cleaned periodogram is at 79 min, which is
consistent with the orbital period. There appears to be excess power in the
frequency range 100 to 150 ${\rm d}^{-1}$, corresponding to periodicities
between 10 and 15 minutes. This suggests the presence of QPOs during
quiescence in V844 Her.

Figure 5: Top: The periodogram of four nights of MDM photometry obtained
during quiescence. The dirty specturm is shown in light red and the cleaned
spectrum in dark blue. No excess power is detected at 29 min. A peak at 79 min
likely corresponds to the orbital period of the binary. Bottom: A high-
frequency extension of the periodogram without cleaning does not show evidence
of super-Nyquist frequencies at 671 or 769 ${\rm d}^{-1}$(1.87 to 2.15 min).
Both plots suggest the presence of quasi-periodic oscillations (QPO)
corresponding to periodicities between 10 and 15 minutes.

####  3.1.5 TESS Sector 51

TESS began sector 51 in April, 2022, approximately one month after the end of
a super-outburst from V844 Her. Based on the ASAS-SN photometry (Shappee et
al., 2014; Kochanek et al., 2017), the super-outburst was caught on the rise
March 7, 2022 (HJD=2459646.0) and faded from outburst between March 21 and
March 26, 2022 (HJD=2459660 and 2459665). A periodogram using the entire
sector reveals no significant signal at 29 min . In sector 24, the 29 min
signal had faded below detectability a month after the end of the super-
outburst, so it is not surprising that the 29 min periodicity is not seen in
sector 51.

The second harmonic of the orbital period is detected during quiescence in
sectors 51 and 52 and might be attributable to the secondary’s ellipsoidal
variations.

###  3.2 X-Ray Properties

An asynchronously spinning WD in V844 Her could generate a fixed frequency
oscillation as this is often seen in IPs. To check if V844 Her could be an IP,
it was compared to two known IPs: V1025 Cen and DW Cnc. V1025 Cen has an
orbital period of 84.6 minutes (Buckley et al., 1998) and DW Cnc 222An in-
depth discussion of DW Cnc’s photometric variablity can be found in Ramírez et
al. (2022). has a period of 86.1 minutes (Patterson et al., 2004), both near
the period minimum. Both these IPs are also considered low-luminosity IPs
(Mukai & Pretorius, 2023), making them likely to be most similar to V844 Her.
The X-ray spectra of the three systems were compared using data from _XMM-
Newton_.

Figure 6: The X-ray periodograms of V1025 Cen (top), DW Cnc (middle), and V844
Her (bottom) using 30-second binning. The spectra are normalized to the
strength of the signal in V1025 Cen. A clear peak and subsequent harmonics can
be seen in the power spectra of the known IPs, but the spectrum of V844 Her
shows no distinctive peak at the 29 min period or possible super-Nyquist
frequencies.

####  3.2.1 Comparison of X-Ray Light Curves

The X-ray light curves for V844 Her, V1025 Cen, and DW Cnc were constructed
with 30 s binning of the X-ray count rate. Since the Nyquist frequency is then
1 min, the L-S periodograms were calculated out to that limit, and are
displayed in Figure 6. V1025 Cen shows a strong peak at 40.25 ${\rm d}^{-1}$,
corresponding to the spin period of its WD (Buckley et al., 1998). The
periodogram of DW Cnc shows significant peak at its WD spin frequency of 37.3
${\rm d}^{-1}$(Patterson et al., 2004). In the periodogram of V844 Her, no
significant peaks are seen at 29 min or at the plausible TESS super-Nyquist
frequencies.

Figure 7: The X-ray spectra of the two known IPs and V844 Her without the
bandpass filter applied. The normalized counts $s^{-1}$ $keV^{-1}$ for V844
Her have been multiplied by 8 to scale the spectrum to the same height as the
other two at 1 keV.

####  3.2.2 Comparison of X-Ray Spectra

Models of the two known IPs were created using three mekal components (Mewe et
al., 1985, 1986; Liedahl et al., 1995) and a Gaussian along with a Tuebingen-
Boulder ISM (_tbabs_) absorption model (Wilms et al., 2000). This allowed just
the hydrogen column density to vary. Using XSPEC, the model was created with
the command _model tbabs*(mekal+mekal+mekal+gaussian)_.

Table 1: Xspec model parameters for the four systems obseved by XMM.

stara | $N_{H}$ |  mekal Temperature |  Gaussianb | $\chi^{2}$ |  dof
---|---|---|---|---|---
|  | $kT_{1}$ | $kT_{2}$ | $kT_{3}$ | E | $f_{g}$ |
| ($10^{-22}$) | (keV) | (keV) | (keV) | ($10^{-4}$) | (keV)
V1025 Cen | 0.050(2) | 10.48(49) | 1.51(15) | 0.671(20) | 0.102(24) | 0.069(63) | 183.6 | 152
DW Cnc | 0.014(2) | 10.87(75) | 1.34(10) | 0.623(24) | 0.163(84) | 0.27(16) | 138.2 | 130
V844 Her | 0.023(7) | 16.7(61) | 1.080(63) | - | - | - | 201.3 | 145
WZ Sge | 0.014(5) | 11.0(1.1) | 1.28(60) | - | - | - | 112.9 | 109

aafootnotetext: The model for WZ Sge was based on data from the MOS1 sensor
while all the other models were based on data from the PN sensor. This is
because calibration files for the PN sensor during the observation of WZ Sge
could not be generated.

bbfootnotetext: For the models that include a Gaussian, the peak was frozen at
6.4 to ensure it represented an iron line.

We used a bandpass of 0.3-10 keV, mirroring the range used in Kennedy et al.
(2017). This is due to the energy sensitivity range of the CCD on _XMM-
Newton_. For each model, a Gaussian emission line was frozen at 6.4 keV, with
the $\sigma$ and norm thawed. To create the model for V844 Her, a two-mekal
model with the _tbabs_ absorption model was used. Only two mekal components
were used because the $\chi^{2}$ of the fit did not change significantly with
the addition of a third. For the known IPs, three mekal components were needed
to appropriately fit the soft end of the spectrum below 1.0 keV. A Gaussian
was also not used in the model of V844 Her because the spectrum did not show a
peak around 6.4 keV. WZ Sge was fit in the same way as V844 Her. The model
parameters and normalized $\chi^{2}$ are shown in Table 1.

A comparison of the X-ray spectra is displayed in Figure 7. The three spectra
have been shifted to have the same count rate at 1.0 keV. The shape of the
spectra are very similar, but V844 Her tends to have a slightly softer
spectrum relative to the IPs.

From the models, the flux was calculated using the XSPEC command _flux
errorsims_. The luminosity was then calculated based on GAIA distances and the
values can be seen in Table 2. V844 Her and WZ Sge both have X-ray
luminosities much lower than the two confirmed IPs. The luminosity of non-
magnetic CVs was found to range between $10^{29}$ and $10^{32}$ ergs/s
Pretorius & Knigge (2012), with V844 Her being at the fainter end of that
interval.

Table 2: The distance, flux, and luminosity of the systems.

star | distancea | fluxb | luminosity
---|---|---|---
| (pc) | ($10^{-12}$ ergs/cm2/s) | ($10^{30}$ ergs/s)
V1025 Cen | 196.0 ${}^{3.17}_{3.05}$ | 13.1 ${}^{0.11}_{0.12}$ | 60.2${}^{2.01}_{1.95}$
DW Cnc | 203.1 ${}^{1.62}_{1.72}$ | 9.81 ${}^{0.110}_{0.124}$ | 48.4${}^{0.94}_{1.02}$
V844 Her | 304.9 ${}^{5.38}_{5.31}$ | 1.01 ${}^{0.036}_{0.056}$ | 11.2${}^{0.56}_{0.74}$
WZ Sge | 41.18 ${}^{0.08}_{0.05}$ | 11.4 ${}^{0.107}_{0.151}$ | 2.31${}^{0.02}_{0.03}$

aafootnotetext: Distances from Gaia EDR3 Bailer-Jones et al. (2021).

bbfootnotetext: To calculate flux, the XSPEC command _flux errorsims_ was used
with a range from 0.3 keV - 10 keV.

Figure 8: top: The light curve of V844 Her over sectors 24 and 25. The average
count rate over a 1-day wide moving window has been converted to an
approximate magnitude. The outburst ends on BTJD=1972, but the system
continues to fade exponentially until BTJD$\approx 1988$. middle: The time-
resolved power spectrum focused on the frequency region that includes the 29
min signal and the second harmonic of the superhump signal. The 29 min signal
shows variability on a 2-day time scale. Data gaps are masked. bottom: The
amplitudes of the 29 min (solid red line) and 80 min SH (dashed blue line)
oscillations from periodograms of a 1-day wide moving window. These
oscillations occur at 49 and 18 ${\rm d}^{-1}$, respectively. Gaps in the TESS
data have been masked. The dotted black line indicates a 3$\sigma$ detection
threshold for the oscillations. The 29 min oscillation is well-detected out to
BTJD$\approx 1991$.

##  4 Discussion

Figure 9: left: Periodogram of the TESS data during the outburst (BTJD$<1969$)
zoomed in on the 29 min peak (top). The primary signal is concentrated in an
unresolved peak at 29.34 mins (49.085 ${\rm d}^{-1}$). A weak, resolved peak
is also present at 29.57 mins (48.7 ${\rm d}^{-1}$). A periodogram of a
simulated light curve is shown at the bottom. The observed beat signal is
approximated by adding cosines with frequencies of 48.65 and 48.75 ${\rm
d}^{-1}$ (corresponding to periods of 29.60 and 29.54 minutes) to a cosine
with a frequency of 49.085 ${\rm d}^{-1}$. right: The time-resolved
periodogram of the TESS data (top) during outburst and the simulated light
curve (bottom). The simulated light curve shows a modulation similar to that
seen in the observations.

###  4.1 Behavior of the 29 min Periodicity During Outburst

Details of the 29 min signal variability are shown in Figure 8. The frequency
of the 29 min signal is relatively steady when compared with the SH signal.
However, there is clearly some variation in its strength during the brightest
phases of the outburst. The amplitude of the 29 min periodicity varies on a
2.3$\pm 0.2$-day cycle until the data gap at BTJD=1970. The oscillatory
amplitude is suggestive of an interference with a nearby frequency offset from
the main oscillation by 0.4 ${\rm d}^{-1}$. A periodogram of the outburst
(BTJD$<1969$) zoomed in on the 29 min signal is displayed in Figure 9. The
primary peak centered at 29.34$\pm 0.01$ min (49.085$\pm 0.005$ ${\rm
d}^{-1}$) is unresolved, that is, its width matches that of a constant
frequency sinusoid sampled with TESS time stamps. A weak, resolved signal at
29.54 min (48.75 ${\rm d}^{-1}$) is also detected and beats against the
primary peak to generate the 2.3-day modulation. As shown in Figure 9, a
simulation of the primary signal plus a beat does fairly well at reproducing
the observed 0.4 ${\rm d}^{-1}$ modulation.

The origin of a 2.3-day oscillation that could beat against the 29 min signal
is not explicitly obvious. One periodicity in the system that does operate on
this long time scale is the period of the dynamical SH instability relative to
the orbital period. That is, the difference between the SH period of 80.45 min
and the orbital period of 78.7 min, generates a precession frequency of the
eccentric disk corresponding to roughly 0.4 ${\rm d}^{-1}$, or a period of 2.5
days. This could be an explanation for the origin of the oscillation.

SH oscillations are generated primarily in the outer disk, while any impact of
a spinning WD or lpDNOs are thought to operate in the inner disk (Warner &
Woudt, 2008). Possibly a spiral instability in the disk during the brightest
phase of the superoutburst could connect the outer disk with the region around
the WD and generate a beat on the disk precession time-scale (e.g. Murray et
al., 1999).

###  4.2 Behavior of the 29 min Periodicity After Outburst

At the end of the superoutburst (BTJD$\approx 1971$), the amplitude of the 29
min signal drops by a factor of 3 while the SH amplitude fades by a factor of
20 (see Figure 8). After the brightest phase of the outburst ends, the
amplitude of the 29 min signal remains nearly constant for about eight days.
During this phase, the 29 min oscillation is the strongest periodic signal in
the TESS data.

For BTJD$>1972$, the flux of V844 Her fades exponentially for approximately 20
days as it returns to quiescence. The 29 min oscillation remains detectable
until BTJD$=1991$ in TESS sector 25. No clear modulation on the 2.3-day cycle
is detected after the outburst fades beyond $\approx 15$ mag.

###  4.3 Origin of the New Oscillation: All Things Considered

We summarize the possible sources of the 29 min signal here:

  * •

The signal comes from a mechanical or electronic signal originating on the
TESS satellite. Our tests show this is unlikely.

  * •

The signal comes from a star near V844 Her that is contributing light to the
extracted aperture. Our tests show this is unlikely.

  * •

V844 Her is an IP and the signal is the spin period of its magnetic WD. For
example, V1025 Cen and DW Cnc are IPs with short orbital periods and WD spin
periods near 30 m.

  * •

The signal is a Dwarf Nova Oscillation (DNO) or a long-period DNO (lpDNO)
(Warner, 2004). DNO typically have periods of around 20 s while lpDNOs are
four times longer. These periodicities tend to be shorter than the TESS fast
cadence, although they may be detectable through super-Nyquist sampling.

  * •

The signal comes from a spiral structure breaking the symmetry of the disk.
CVs with small stellar mass ratios (Lin & Papaloizou, 1979) or systems with
magnetic WDs (Murray et al., 1999) may develop spiral structures in their
disks.

  * •

The signal results from the WD spin or the beat frequency impacting the inner
disk or boundary layer. The magnetic field of the WD is likely weak compared
to typical IPs, so it is not clear how the WD rotation couples to the
accretion.

####  4.3.1 V844 Her is an Intermediate Polar?

IPs generally show optical/X-ray oscillations related to the spin period of
their magnetized WD. No periodic signal from V844 Her is detected during
quiescence at optical or X-ray wavelengths. The accretion properties of V844
Her do not appear similar to known IPs with short orbital periods. V844 Her
shows classic super-outbursts of SU UMa type dwarf novae. These outbursts
suggest a well-formed Keplarian accretion disk that undergoes episodes of
thermal and dynamical instability Kato (2022). In contrast, the IPs V1025 Cen
and DW Cnc tend to produce short outbursts ($<$ day) that may be the result of
magnetically gated accretion (Littlefield et al., 2022).

Our analysis of the X-ray luminosity and spectra of V844 Her, V1025 Cen, and
DW Cnc suggest that V844 Her is most similar to SU UMa type CVs, and unlikely
to be a classical IP.

We also compared the X-ray properties of V844 Her with WZ Sge, the prototype
of the sub-class of SU UMa dwarf novae. WZ Sge shows rapid oscillations and it
has been suspected of being an IP with a very rapidly rotating WD. A similarly
rapid signal could appear in the TESS data as a super-Nyquist peak with a
period around 30 minutes. However, we do not detect any high-frequency
oscillations in V844 Her that would correspond to the rapid variations seen in
WZ Sge.

####  4.3.2 V844 Her Exhibits Dwarf Nova Oscillations?

DNOs were identified as rapid oscillations with periods ranging from 5-40
seconds (Warner & Woudt, 2008). They have two time scales on which they vary:
one relating to optical brightness and the other to sudden, small changes in
period. The periods of DNOs are most consistent at maximum brightness during
outbursts, losing coherence as the outburst fades Hildebrand et al. (1981).
Such lapses in coherence can make signals difficult to detect using Fourier
transforms, but can be found using time-resolved power spectra. Less coherent
oscillations called QPOs (Patterson et al., 1977) are sometimes associated
with DNOs and tend to have frequencies 16 times lower than DNOs.

The 29 min signal is seen during outburst and during post-outburst fading.
This is consistent with the oscillation being a DNO, although, the observed
period of about 30 minutes is much longer than DNOs seen in other systems. The
oscillation seen at 29 min might be a high-frequency oscillation seen with the
super Nyquist sampling of TESS. Thus, the true signal originates at 671 ${\rm
d}^{-1}$ (128.8 seconds) or 769 ${\rm d}^{-1}$(112.4 seconds). Even these
periods near 2 minutes are longer than most observed DNO periodicities, so it
may be that we are detecting a long-period DNO (lpDNO). lpDNO tend to have
periods roughly four times longer than their associated DNO (Warner, 2004).
However, the ground-based detection of the 49 ${\rm d}^{-1}$ peak makes it
unlikely that TESS sampling is creating a super-Nyquist signal from an
oscillation close to the TESS cadence.

We conclude that the source of the 49 ${\rm d}^{-1}$ variation is unlikely to
be a DNO or a lpDNO.

####  4.3.3 V844 Her has a Spiral Disk Structure?

CVs have been shown to exhibit non-uniform emission due to tidally induced
spiral shocks (Lin & Papaloizou, 1979). In CVs with high mass ratios, the
outer disk is unable to expand to the 2:1 resonance that causes such shocks in
low mass ratios. However, the 2:1 resonance can occur within the tidal
truncation radius, causing temporary shocks to occur. This is one explanation
for the periodicity only being visible during super-outburst.

In IPs specifically, an asymmetric disk structure can alter the accretion on
the primary Murray et al. (1999). Tidally induced spiral arms propagate
through the disk and result in azimuthal asymmetry within the inner disk when
the arms extend to the disk-magnetosphere boundary. The accretion rate is
boosted as a magnetic pole sweeps past the spiral arm, which can produce power
at the spin-orbit beat frequency and related sidebands and harmonics. SU UMa
stars develop such a spiral structure during super-outburst, an explanation
for the 49 ${\rm d}^{-1}$ signal being detectable only during super-outburst.

Unlike SH oscillations, the new signal does not vary in frequency over the
superoutburst and it is not clear if a spiral structure would keep its
coherence over long periods covered by the TESS data.

The amplitude modulations of the new signal during the first phases of the
super-outburst are consistent with the precessional period of the eccentric
disk. This suggests a connection between the inner and outer disk that is
possible through a spiral wave.

A spot on the inner edge of the accretion disk has been used by Tovmassian et
al. (2007) to account for periodicities seen in FS Aur and V455 And that
appear unrelated to the orbital variations. For V844 Her, such an inner-edge
spot would develop only during episodes of enhanced mass transfer.

####  4.3.4 Low B-field Rotating WD?

Katz (1975) proposed that a WD magnetic field strength above about 0.1 MG
would lock the surface field to a crystallized core. This would preclude a
slipping equatorial belt of accreted gas from generating DNO phenomena
(Paczyński, 1978; Warner & Woudt, 2002) and could result in something similar
to a low-field IP. Warner & Woudt (2008) proposed that WZ Sge, and its 27.87 s
oscillations, is a good candidate for a weak field IP.

The steadiness of the 29 min signal seen in V844 Her suggests an origin from
solid-body rotation. However, the signal is only seen during outburst and as
it fades to quiescence. The WD spin signals from IPs are sometimes difficult
to see in quiescence. For example, CC Scl had a 389 s spin pulse discovered
during outburst, but it was not visible at optical wavelengths in quiescence.
Eventually, the UV light curve from $HST/COS$ did show the spin signal in
quiescence due to its higher amplitude at short wavelengths (Szkody et al.,
2017).

##  5 Conclusion

We detect a new photometric periodicity during a superoutburst of V844 Her
observed by TESS in sector 24. The variation is not an artifact of the data
and its origin is consistent with the position of V844 Her. With a period of
29 min, it is not directly related to the SH oscillations. The X-ray
properties of V844 Her are a poor match with IPs with similar orbital periods.
The precise cadence of TESS can result in super-Nyquist sampling of rapid
oscillations, suggesting that the observed 29 min peak could come from a DNO
or lpDNO with periods of 2.15 min or 1.87 min. No detection of a DNO or lpDNO
in V844 Her has been previously published.

The infrequency of superoutbursts in V844 Her, the low-amplitude of the
oscillation, and its relatively long period, has made ground-based
confirmation of this new oscillation difficult. Our analysis of AAVSO
photometry covering three nights during a superoutburst does support the
presence of the new signal. Thus, we consider it unlikely that TESS sampling
is generating a super-Nyquist signal. However, intensive photometry during
future outbursts will be important in determining the nature of the
oscillation.

The behavior of the 29 min signal is fairly complex over the super-outburst
and subsequent fading. While the SH oscillations vary in amplitude by more
than a factor of 10 over the brightest phases of the outburst, the amplitude
of the 29 min signal is relatively steady in comparison. During the initial
two weeks of the outburst, the amplitude of the 29 min signal modulates over a
2.3-day cycle that appears to be a beat frequency offset by 0.4 ${\rm d}^{-1}$
from the 29.34 min periodicity. The precession cycle of the eccentric disk
relative to the secondary star operates on an approximately 2.5 d period, but
it is not clear how the disk precession is physically connected with the 29
min variation.

During the final fading to quiescence, the 29 min becomes the dominant signal
in the TESS light curve.

Given the steady frequency of the 29 min signal in the TESS data, we suggest
that the oscillation is most likely caused by the rotation of the WD in V844
Her. A weak magnetic field on the WD may generate a photometric modulation
during outburst but it may be difficult to detect during periods of disk
quiescence. That is, V844 Her falls short of being an IP, but the asynchronous
rotation of the mildly magnetic WD may generate a spin or beat pulse
detectable through outburst and fading to quiescence. Deep photometry during
quiescence at blue or ultraviolet wavelengths would provide a test of this
hypothesis.

We acknowledge with thanks the variable star observations from the AAVSO
International Database contributed by observers worldwide and used in this
research. Some of the data presented in this paper were obtained from the
Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science
Institute. The specific observations analyzed can be accessed via
http://dx.doi.org/10.17909/yc7m-vr65 (catalog DOI). We acknowledge that this
research was funded by a College of Science Summer Undergraduate Research
Fellowship (COS-SURF) from the University of Notre Dame. This research was
partly funded through NASA grant 80NSSC22K0183. The full light curves of V844
Her obtained at MDM over four nights are displayed in Figure 10.

Figure 10: The MDM lightcurves of V844 Her from the four individual nights.
The cadence of the time series is 23s. The system is seen to vary in
quiescence with an amplitude of $\pm 0.2$ mag.

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