# New Time-Resolved, Multi-Band Flares In The GJ 65 System With gPhoton

Scott W. Fleming Space Telescope Science Institute, 3700 San Martin Dr,
Baltimore, MD 21218, USA  Chase Million Million Concepts LLC, 1355 Bardstown
Rd., No. 132, Louisville KY 40204  Rachel A. Osten Space Telescope Science
Institute, 3700 San Martin Dr, Baltimore, MD 21218, USA  Center for
Astrophysical Sciences, Department of Physics & Astronomy, Johns Hopkins
University, 3400 North Charles St., Baltimore, MD 21218, USA  Dmitrii Y.
Kolotkov Centre for Fusion, Space and Astrophysics, Department of Physics,
University of Warwick, Coventry CV4 7AL, UK  Institute of Solar-Terrestrial
Physics, Lermontov St., 126a, Irkutsk 664033, Russia  C. E. Brasseur Space
Telescope Science Institute, 3700 San Martin Dr, Baltimore, MD 21218, USA
SUPA Physics and Astronomy, University of St. Andrews, Fife, KY16 9SS,
Scotland, UK

(Accepted January 28, 2022)

###### Abstract

Characterizing the distribution of flare properties and occurrence rates is
important for understanding habitability of M dwarf exoplanets. The GALEX
space telescope observed the GJ 65 system, composed of the active, flaring M
stars BL Cet and UV Cet, for 15900 seconds ($\sim$4.4 hours) in two
ultraviolet bands. The contrast in flux between flares and the photospheres of
cool stars is maximized at ultraviolet wavelengths, and GJ 65 is the brightest
and nearest flaring M dwarf system with significant GALEX coverage. It
therefore represents the best opportunity to measure low energy flares with
GALEX. We construct high cadence light curves from calibrated photon events
and find 13 new flare events with NUV energies ranging from
$10^{28.5}-10^{29.5}$ ergs and recover one previously reported flare with an
energy of $10^{31}$ ergs. The newly reported flares are among the smallest M
dwarf flares observed in the ultraviolet with sufficient time resolution to
discern light curve morphology. The estimated flare frequency at these low
energies is consistent with extrapolation from the distributions of higher-
energy flares on active M dwarfs measured by other surveys. The largest flare
in our sample is bright enough to exceed the local non-linearity threshold of
the GALEX detectors, which precludes color analysis. However, we detect quasi-
periodic pulsations (QPP) during this flare in both the FUV and NUV bands at a
period of $\sim$50 seconds, which we interpret as a modulation of the flare’s
chromospheric thermal emission through periodic triggering of reconnection by
external MHD oscillations in the corona.

stars: flare – stars: individual (GJ65 AB (BL Cet, UV Cet)) – stars: late-type

††journal: ApJ††software: Astropy (Astropy Collaboration et al., 2013, 2018),
gPhoton (Million et al., 2016)

##  1 Introduction

###  1.1 Stellar Flares in the Ultraviolet

Stellar flares may have a substantial effect on the habitability of planets
that orbit them closely. Although a single stellar flare is unlikely to have a
lasting impact on a planet’s atmosphere (Segura et al., 2010), the cumulative
effects from repeated flares can drive atmospheric chemistry (e.g., Tarter et
al., 2007; Venot et al., 2016; Chadney et al., 2017; Kaltenegger, 2017; Loyd
et al., 2018b; Froning et al., 2019), cause atmospheric loss (e.g., Ribas et
al., 2016; Dong et al., 2018; Tilley et al., 2019), and could hinder (Lammer
et al., 2007; Atri, 2017; O’Malley-James, & Kaltenegger, 2017; Yamashiki et
al., 2019) or enhance (Ranjan & Sasselov, 2016; Ranjan et al., 2017)
biogenesis. Flare rates on the Sun follow a power-law as a function of flare
energy (Hannah et al., 2011; Schrijver et al., 2012), such that more energetic
flares happen less often than smaller energy flares. Our understanding of the
flare frequency distribution (FFD) is rapidly improving for G, K, and M dwarfs
thanks to both ground-based (Hilton, 2011; Davenport et al., 2012; Howard et
al., 2019; Chang et al., 2020) and space-based missions like Kepler/K2 (Hawley
et al., 2014; Maehara et al., 2015; Davenport, 2016; Gizis et al., 2017; Yang
et al., 2017; Raetz et al., 2020), HST (Osten et al., 2012; Loyd et al.,
2018a, b), and TESS (Doyle et al., 2019; Günther et al., 2020). Even with the
long baselines and minute-cadence observations afforded by space telescopes,
most detected flares and flare rate estimates from these large UV and optical
surveys have been at (non-bolometric) energies $\log{E}\gtrsim 30$. Flare
energy tends to scale directly with both peak brightness and duration in the
optical (Maehara et al., 2015; Namekata et al., 2017), so the ability of
space-based surveys like Kepler and TESS to detect low energy flares is
limited by relative magnitude sensitivity and cadence. Indeed, the cadence of
observations can impact the measurement accuracy of even large energy flares.
Yang et al. (2018) found that Kepler long-cadence data sampled at 30 minutes
compared to short-cadence data sampled at one minute resulted in energies
underestimated by 25% and systematically underestimated amplitudes and
overestimated durations by 50%. Raetz et al. (2020) compared short- and long-
cadence K2 light curves of flares on M dwarfs, and found that flare amplitudes
were underestimated by 30% and flare durations were overestimated by 60%.
However, these effects offset one another when deriving their flare energies,
which used an equivalent duration (area under the curve). Flares in the
ultraviolet (UV) may not follow as direct a relationship seen in optical
surveys, where the flares in UV may appear shorter in duration and not tied as
closely to energy across comparable integrated energy regimes (see Figure 21
in Brasseur et al., 2019).

Observations in the far-ultraviolet (FUV) and near-ultraviolet (NUV) provide
unique constraints to flare physics and any interactions they might have with
planetary atmospheres compared to other wavelength regimes. The UV fluxes
originate from the upper atmosphere of the star, namely, the chromosphere and
transition region leading to the corona. In the FUV, stellar fluxes can be
dominated by Lyman alpha emission (Linsky et al., 2013), which can
photodissociate $\mathrm{H_{2}O}$, $\mathrm{CH_{4}}$, and $\mathrm{CO_{2}}$ in
exoplanet atmospheres (Trainer et al., 2006). Other major lines come from C
IV, Si IV, He II, and Al II (Avrett, & Loeser, 2008; Dere et al., 2009;
Fontenla et al., 2016). In the NUV, the primary contributions come from the Mg
II h and k doublet, along with Al and ionized Fe lines (Peacock et al., 2019),
although the GALEX NUV band has low transmission near the Mg II lines, and
thus is more likely to be dominated by continuum emission (Robinson et al.,
2005). While these line emissions can be present when a flare is not
happening, the line emission increases during a flare due to the additional
hot plasma generated by a flare. Furthermore, a hot blackbody component from
the flare event contributes to the overall emission, which is not present
before or after the flare event. Observations across a wide range of
wavelengths, including X-ray, UV, optical, and radio probe different physics
during the flare events (Haisch et al., 1991; van den Oord et al., 1996;
Kowalski et al., 2012, 2013), especially if simultaneous observations of a
flare can be obtained. Previous studies have used photon events from GALEX to
search for intra-visit variable sources (Welsh et al., 2005), especially to
detect and characterize flares on individual stars (Robinson et al., 2005;
Welsh et al., 2006), and one survey detected 52 flare events on 49 stars using
1802 NUV images (Welsh et al., 2007). Doyle et al. (2018) reported detections
of quasi-periodic pulsations (QPP) in flares from six M dwarfs, including all
four of the M dwarfs that had flares reported in Welsh et al. (2006).

###  1.2 The GJ 65 System

The GJ 65 system is composed of two M dwarfs with an on-sky separation of
2.26$\arcsec$ (Gaia Collaboration et al., 2018), unresolved by the
4.2$\arcsec$ and 5.3$\arcsec$ full-width half maxima image resolutions of
GALEX in the FUV and NUV bands (Morrissey et al., 2007). The two components
have Gaia-based distance estimates of $2.687\pm 0.002$ and $2.703\pm 0.002$ pc
(Bailer-Jones et al., 2018). They orbit in an eccentric ($e\sim$0.6) 26.3-year
orbit and have a combined mass of $\sim 0.24\;\rm{M_{\odot}}$ (Mann et al.,
2019). Barnes et al. (2017) used Doppler image reconstructions to measure the
rotation rates of the two components (0.24 and 0.23 days, respectively).
Kervella et al. (2016) were able to measure the angular diameters of the two
components using interferometry, deriving radii of 0.165 and 0.159 $R_{\odot}$
to 4% relative precision. Using adaptive optics, the same authors derived
masses for the two components of 0.1225 and 0.1195 $M_{\odot}$, also at 4%
relative precision. Given these masses, the radii differ from model
predictions at the 10-15% level, a common observation for low-mass stars with
strong magnetic fields and stellar activity. Kochukhov, & Lavail (2017) used
spectro-polarimetric observations to study the magnetic topology of the two
components. Despite having very similar masses and radii, BL Cet’s total
magnetic energy is an order of magnitude smaller than UV Cet, and while BL Cet
exhibits a complex field structure, UV Cet has a strong, axisymmetric dipolar
magnetic field.

The GJ 65 stars are among the closest, brightest, active flare stars with a
large amount of GALEX coverage111The only other active M dwarfs within 5 pc
that have multiple hours of GALEX coverage is the Wolf 424 system, which has
$\sim$7500 seconds of coverage and a similar GALEX NUV magnitude. Like the GJ
65 system, it is also composed of two M dwarfs, and they orbit with a
comparable period to GJ 65 ($\sim$15.5 years). We find six flares with
energies between $28.8<\log(E)<30.1$, to be described in a future article.,
and thus presents the best opportunity to search for and study time-resolved,
short-duration stellar flares in the GALEX UV bands. High-cadence searches in
the optical, with time resolutions of seconds or even microseconds, have been
conducted on the GJ 65 system (Bopp & Moffett, 1973; Schmitt et al., 2016;
Beskin et al., 2017). The survey by Welsh et al. (2007) did not include GJ 65
system. From the visit level photometry catalogs, Miles & Shkolnik (2017)
detected a flare in the GJ 65 system, but did not analyze any photon event-
level data. Doyle et al. (2018) analyzed GJ 65, in the near-UV only, with the
gPhoton software using one-second time resolution bins, detecting a QPP in the
largest flare via a wavelet analysis. In this paper, we present results from a
time-resolved search for GJ 65 flares using all available GALEX archival
photometry.

In Section 2 we describe the data products and processing. In Section 3 we
describe our algorithms for detecting flare events within the GALEX light
curves. In Section 4 we present the detected flare events and further analyze
the relatively large flare previously found by Miles & Shkolnik (2017),
including a discussion on how the brightness of the large flare precludes an
analysis of the FUV-NUV color of the flare, and our detection and anaysis of
the QPP during the flare.

##  2 Observations and Data Processing

GALEX (Martin et al., 2005; Morrissey et al., 2007) collected data with
photon-counting micro-channel plate detectors in two ultraviolet bands. The
Far Ultraviolet (FUV) band extended from $\sim$1344 Å to $\sim$1786 Å, and the
Near Ultraviolet (NUV) band extended from $\sim$1771 Å to $\sim$2831 Å.
Observations were organized into “visits”: one or more sequences of
observations conducted while the spacecraft was behind Earth’s shadow, lasting
in total no more than approximately 30 minutes. GALEX had both imaging and
spectroscopic capabilities, and the imaging data were generally released to
the research community as integrated images with detected source catalogs. The
mission occasionally provided photon-level data to researchers by special
request. We use data available through the open-source gPhoton project
(Million et al., 2016), which re-created portions of the GALEX mission
pipeline to generate and archive calibrated photon events from all
observations taken through GALEX Data Release 7.

The present work analyzes dual-band observations of the GJ 65 system across
ten visits. Nine of these were $\sim$30 minute observations made within a span
of two days (18-19 November 2005). The tenth visit is a guest investigator
(GI) observation made on 09 October 2016 with an integration time of about 10
minutes. Two additional observations were made in single-band “AIS” observing
mode and have integration times of less than two minutes each. These visits
are too short for a meaningful flare measurement, even if a flare occurred. We
visually inspected light curves for these shorter visits, verified that no
obvious flare behavior was present, and then eliminated them from further
analysis. Removing these visits from the sample reduced the total effective
observation time by $\sim$5%. The total observation time for the ten
visits222Although gPhoton uses the uncalibrated photon events and the aspect
solution files to create the images and light curves analyzed here, the
mission-produced pipeline products corresponding to the visits we examined are
available at MAST via 10.17909/t9-638a-q564. used in this analysis (ignoring
the two AIS visits) is 15682 seconds ($\sim$4.36 hours).

###  2.1 Data Processing

####  2.1.1 Photometric Measurements

Our photometry is derived from photon events processed using a special branch
of gPhoton, “v1.28.9_nomask”. Due to our special treatment of hotspot masks
(see Section 2.1.2), we start from the raw photon events themselves, perform
calibration of the photon events, and extract light curves without using the
standard gAperture module. This branch of gPhoton is setup to allow such
analysis. Python notebooks333Notebook GitHub
repository:https://github.com/MillionConcepts/gfcat_gj65 DOI:
10.5281/zenodo.3870757 (catalog 10.5281/zenodo.3870757) are provided as
supplemental material that can be used to re-create our analysis (data
products, the flare table, and each figure) using this fork of the gPhoton
software. The light curves are extracted using an aperture radius of
$17.3\arcsec$ (equivalent to “APER7” in the GALEX catalogs) at a time bin of
30 seconds, except where noted. The bin size of 30 seconds is chosen such that
short-duration flares lasting only a few minutes will have more than one flux
bin during the event, while also providing sufficient counts in each time bin
to get reasonable signal-to-noise given the brightness of the GJ 65 system. At
the NUV magnitude of GJ 65 of $\sim$18, this bin size yields a 3-$\sigma$
error of $\sim$0.25 mag (see Fig. 11 from Million et al., 2016). We did not
include a background measurement in these calculations because the quantity of
interest for flare-detection is the change in magnitude (which automatically
accounts for a stationary sky) and the background flux is a very minor
contribution, approximately 27.5 AB Mag in NUV and 29 AB Mag in FUV at the
location of GJ 65 from the GALEX mission catalogs. Note that gPhoton outputs
flux densities measured in $\mathrm{erg\;s^{-1}\;cm^{-2}\;\text{\AA}^{-1}}$.

The initial photometric aperture location is based on the GAIA (Gaia
Collaboration et al., 2018) position, which we then adjust to better match the
position in the GALEX observations which were taken 10 years earlier than the
2015.5 epoch that Gaia coordinates are listed in. This initial photometric
aperture position is refined once for each visit by re-centering on the median
event position within the aperture. The re-centering corrects for the small
amount of scatter in GALEX astrometry between visits, and would also correct
for proper motion between visits if any were present (Morrissey et al., 2007).
This re-centering results in a change of the photometric aperture center
between 2.5 and 4 arcseconds from visit to visit, well within the GALEX
spatial resolution. Million et al. (2016) caution that pixel-to-pixel
variability in the instrument flat can be a significant source of additional
uncertainty in sub-visit light curves, and thus can produce false variable or
periodic signals. We compare each visit’s flux density as a function of time
with other output parameters from gPhoton to check for any correlated
variability, including the effective exposure times per bin and distance from
center of the field.

####  2.1.2 Turning Off the Hotspot Mask

Photon events that fall on regions of the detector covered by the GALEX
hotspot masks are excluded from calibration and reduction in gPhoton by
default. Therefore, the regions of the detector that are masked have an
effective response of exactly zero. This approach to hotspot masking generally
has a negligible effect on data quality in the mission-produced images and
catalogs because the contribution of the masked region was diluted over the
duration of an observation by the relative motion produced by spacecraft
dither and then corrected by a relative response map that accounted for the
effect of the mask. This does not work for shorter integration times; if the
light from a source intersects a masked detector region, its flux density will
be incorrectly measured. In sub-visit light curves, the interference of a
hotspot mask can produce significant non-astrophysical variability over the
period of the GALEX $\sim$120 second dither pattern (Boudreaux et al., 2017;
de la Vega, & Bianchi, 2018). The gPhoton software flags any light curve time
bin where the photometric aperture contains any photon events falling within
one pixel ($\sim$6″) of the flat field map of a masked region, and it is
recommended that researchers exercise additional skepticism when using any
flagged data.

The majority of the GALEX observations of GJ 65 have a masked hotspot close
enough to trigger this flagging. GALEX hotspots are known to vary over time,
which is to say that they may have been active during some periods of the
mission and not others. The mission hotspot mask was also optimized to remove
any possible spurious signal rather than to conserve usable detector area, and
a single hotspot mask was created for each band and applied uniformly over the
whole mission without regard to the temporal variation of hotspots. The
hotspot mask also only has one quarter of the spatial resolution of the final
GALEX imaging products, so there may be cases in which a hotspot passes
closely enough to a source of interest to potentially affect a measurement
even though any non-astrophysical signal from the hotspot would not leak into
a reasonably sized photometric aperture. This was the case for the
observations of GJ 65, so we modified the PhotonPipe module of the gPhoton
data reduction pipeline to aspect-correct photon events even if they are
covered by the hotspot mask, re-reduced the photon-level data from the raw
mission files, and then ported functions from the the gPhoton tools as needed
to create images and calibrated light curves from these files. This version of
the gPhoton software is available in the “v1.28.9_nomask” branch on GitHub.
Figure 1 demonstrates that for all visits of GJ 65 included in our analysis,
accurate photometry is still possible even with a nearby hotspot present. The
active hotspot appears in the images as annuli that trace the spiral dither
pattern. The hotspot near GJ 65 is especially visible in several of the NUV
images, and is denoted by the yellow arrow in the NUV Visit 3 panel for
reference. None of the visits analyzed here have the hotspot region pass
within the relatively large $17.3\arcsec$ radius photometric apertures,
centered on GJ 65 and denoted in blue. Thus, the default conservative flagging
of the photometry measured from locations near, but not within, hotspot mask
regions can safely be ignored here, and the photon events from within our
aperture (in blue) are not impacted.

Figure 1: Thumbnail images (FUV, left; NUV, right) of the first nine visits,
centered on GJ 65. Blue circles represent the photometric aperture of 17.3
arcseconds, equivalent to the GALEX MCAT ”APER7”. The blurred doughnut shapes
to the right are hotspots (NUV Visit 3 is first visit when the hotspot is most
visible, denoted with a yellow arrow). The effect of the largest flare on GJ
65’s brightness is readily apparent in the NUV during Visit 5 (center).

##  3 Flare Detections

###  3.1 Flare-Finding Algorithm

A variety of methods have been used for flare detection, and there is not a
clear consensus approach. One common strategy is to search for one or more
data points in the light curve that increase in flux density at some level of
significance, followed by visual inspection and validation by a human
researcher (e.g., Walkowicz et al., 2011; Davenport, 2016; Brasseur et al.,
2019). For single-band observations where counting statistics dominate, we
prefer a search algorithm that classifies any two consecutive data points that
are at least $3\sigma$ above a baseline level, or any one data point at
$5\sigma$ above the baseline level, as likely belonging to a flare. The flare
time range (start and end of the flare event) is then extended from these
detected peaks both forward and backward in time until the data are
indistinguishable from the “instantaneous non-flare flux” (INFF, see Section
3.2). The flare extent can be difficult to determine, especially for smaller
flares and those that do not follow a “fast rise, exponential decay” (FRED)
shape (see, e.g. Davenport et al., 2014). We define the flare range by
stepping the extensions backwards and forwards in time until two consecutive
points are less than $1\sigma$ above the INFF. This is similar to the method
used by Walkowicz et al. (2011) and Brasseur et al. (2019). All of the GALEX
visits of GJ 65 that we analyze here are dual-band, however, so we have
modified our search criteria to trigger on instances where at least two data
points in the NUV light curve rise to $3\sigma$ above the local baseline flux
density, _or_ that there is a simultaneous $3\sigma$ deviation in at least one
data point in both the FUV and NUV bands. This has the benefit of identifying
a few smaller events that are likely flares (because they occur simultaneously
in both bands) that would not be caught by a single-band search. An
algorithmic and visual search did not find any flares that are detected in FUV
but not in NUV. This matches expectations and previous results from flare
searches in the UV, where the vast majority of flares are detected in both FUV
and NUV when multi-band data are available. Although FUV-only flares are very
rare, recent results have shown at least one example of a significant FUV
flare (peak flux enhancement $>14000$) with optical response only increasing
by 0.9% (MacGregor et al., 2021).

We examined light curves from other sources in these GALEX visits to see if
any other sources exhibited similar flux density outliers within their light
curves. If multiple sources show similar levels of variability, then some of
our flare candidates may be caused by unknown systematic errors. We exclude
sources at the outer 20% of the GALEX field-of-view, since those often suffer
from edge effects. We also exclude sources at or very near to the local non-
linearity regime of the GALEX detectors. We find no other sources that exhibit
extremely large flux density outliers, and only a single source (a binary of
two similarly-bright components with a separation marginally resolved by
GALEX) that have significant variability at the 3-sigma level at all. Thus,
the intra-visit variability we see from GJ 65 is likely coming from the stars
themselves and is unlikely to be an unknown systematic related to the
processing of the photon events or instrument hardware.

The 30 minute maximum duration of GALEX visits is shorter than the duration of
many flares with energies of $\log{E}\gtrsim 32$, under reasonable assumptions
about flare light curve morphologies. For flares at or above these energies, a
single visit in GALEX will capture only a portion of the flare (most likely,
the long tail end of the flare), in which case the flux density during the
entire visit would likely be monotonically decreasing throughout the entire
visit. We do not see any evidence of this during the GALEX observations of GJ
65.

###  3.2 Instantaneous Non-Flare Flux

When searching for flares, the typical practice is to measure the change in
brightness due to a flare as offset from some “quiescent” flux. Over long time
baselines, it is possible to identify and account for non-flare stellar
variations due to other types of stellar activity, rotational spot modulation,
or transiting objects. For example, Günther et al. (2020) describes such an
approach for flare-finding in TESS. For active stars, such as the GJ 65
system, referring to a baseline flux as “quiescence” is inaccurate without a
long enough baseline to derive a flux value that takes into account intrinsic
variability over, e.g., the star’s magnetic cycles. For flare detection, the
measurement that is actually desired is the contribution of total stellar flux
made by all stellar activity except the flare event itself. We refer to this
as “instantaneous non-flare flux” (INFF); given perfect knowledge about
stellar behavior, the INFF would be equivalent to a light curve where all (and
only) contributions from flaring have been removed. Even this would be
technically inaccurate, because the pre-flare stellar fluxes may change due to
active region configurations related to specific flare events that are not
repeatable over time.

The ability to measure INFF is still impacted, in practice, by both the
limitations of the data (e.g. how well the bandpass is calibrated, rate of
flux sampling, and observation time baseline), and because it is likely that
flares can induce other phenomena that affect total luminosity, including
sustained increases in flux, QPPs, or additional flares (e.g., Pazzani, &
Rodono, 1981; Pearce, & Harrison, 1990; Panagi, & Andrews, 1995; Osten, &
Brown, 1999; Doyle et al., 2018). If only the decay phase of a large flare is
observed, it might be easily mistaken for some other type of astrophysical
variability such as a starspot rotating into view.

Our approach when defining the INFF for a visit is to identify and measure the
flux density during specific time windows that “look like” quiescence, i.e.
have a slope of approximately zero. We have calculated flare energies using
these measurements of INFF. Following the method of Davenport (2016), we use a
sigma-clipping algorithm to make an initial estimate of the INFF, which is
used to conduct a flare search in the manner described above. A new INFF
estimate was then made by running sigma-clipping again on light curves from
which flaring time periods were excised, and used as input to a final
algorithmic search for flaring. Uncertainties on the INFF “quiescence” reflect
counting statistics on the integrated value of all non-flare data points.

###  3.3 Detection Limit

Because it relies exclusively on the most extreme outlier, our flare detection
algorithm imposes an immediate lower limit on the size of any detectable
flare. The smallest detectable flare is one whose light curve deviates
precisely by $3\sigma$ from the INFF for exactly one time bin. For light
curves with a time resolution of 30 seconds, this flare would be reported with
a duration of $\sim$120 seconds. This is also the typical duration of “AIS” or
“scan mode” visits, which is why these have very little use for stellar flare
studies. The detection threshold and encapsulated energy will vary as a
function of the INFF. For a peak INFF AB magnitude of 17.77 in NUV, the
maximum detectable change in magnitude is 0.188 ($\sim$19%), with an
encapsulated energy in NUV of $\log{E}\sim$28.7 erg. On the lower end, an INFF
AB magnitude of 18.66 in NUV has a maximum detectable change in magnitude of
0.27 ($\sim$ 27%), with an encapsulated energy in NUV of $\log{E}\sim$29.02
erg.

###  3.4 Energy Calculation

Figures 2 and 3 show the FUV (blue) and NUV (black) visit-level light curves,
with the identified flare events highlighted in grey. Following Brasseur et
al. (2019), we calculate the energies of each flare event by integrating the
area under the curve from flare start to flare end as defined by our flare
finding algorithm, subtracted by the INFF value for each band. We convert the
integrated flux densities to fluence using GALEX effective widths in FUV and
NUV of $255.45\;\text{\AA}$ and $729.94\;\text{\AA}$, respectively (The SVO
Filter Profile Service, 2020). We assume a distance of 2.687 pc (Bailer-Jones
et al., 2018). The flare energy measurements are lower limits because of
uncertainty in the INFF measurement, but also because it is possible that a
small candidate flare event toward the beginning of a visit may actually be a
sub-component of a larger event that may have happened before the visit. More
commonly, the entire duration of a candidate flare event is not contained
within the visit, and is either truncated at the start or end of the visit.
For some flare events, the flux densities return to nearly the same INFF as
before the flare event, and the derived energy is quite close to the total,
but in other cases more of the flare’s tail is truncated, and thus more of the
total energy is missing.

Figure 2: Visit-level light curves for Visits 1-5 (top to bottom). FUV is in
blue, NUV is in black, and detected flare events are denoted by the grey
backgrounds. See the Appendix for more detailed plots of each visit and flare.
Figure 3: Visit-level light curves for Visits 6-9 (top to bottom). FUV is in
blue, NUV is in black, and detected flare events are denoted by the grey
backgrounds. See the Appendix for more detailed plots of each visit and flare.

Our energies are reported in the GALEX FUV and NUV bandpasses, and thus would
need to be scaled for comparison with energies from other surveys and
instruments. To derive an estimate of the fractional GALEX flare energy to
bolometric flare energy, we calculate the bolometric conversion factor
following Brasseur et al. (2019), resulting in $p_{bol}$ values of 0.021 and
0.133 for FUV and NUV, respectively. In brief, we calculate a blackbody
continuum spectrum at $T_{\mathrm{eff}}=10000$ K between 1400 and 10000 Å. We
then calculate the fraction of the blackbody flux within the GALEX FUV and NUV
bands, and then scale by an assumed ratio of continuum to bolometric flux of
0.6 following Osten & Wolk (2015). See the Python notebook associated with the
online version of this paper for details on the calculations. However, we
emphasize that these are approximate corrections, and for FUV the correction
factor is even more uncertain: the calculation assumes the dominant flux
contribution is from blackbody radiation within the bandpass, assumes a flare
blackbody temperature of 10000 K, and does not take into account the
transmission across the bandpass. Significant emission lines from C IV, He II,
and Al II mean that the emission in the GALEX FUV bandpass likely includes
non-blackbody contributions. Improvements to the bolometric conversion would
require spectra obtained during the flares to model the emission lines in the
FUV and NUV bandpasses. The assumption of a “typical” blackbody temperature of
10000 K for a flare continuum may not be appropriate in all cases given, e.g.,
the recent HST observation of a flare with an estimated color temperature of
40000 K (Froning et al., 2019).

Table 1: Summary of Detected Flares From The GJ 65 System

Flare | Visit | NUV Peak Time | Duration | log($E_{NUV}$) | log($E_{FUV}$) | NUV Strengtha
---|---|---|---|---|---|---
|  | (UTC) | (min.) | (erg) | (erg) |
1 | 1 | 2005-11-18 06:54:45 | 9.5 | $29.45\pm 27.92$ | $28.86\pm 27.84$ | 8.498467
2 | 2 | peak not measured | 5.5 | $28.95\pm 27.80$ | $28.00\pm 27.64$ | 1.761480
3 | 2 | 2005-11-18 08:35:49 | 10.5 | $28.88\pm 27.89$ | $28.34\pm 27.81$ | 1.293150
4 | 3 | 2005-11-18 11:54:02 | 12.0 | $29.17\pm 27.97$ | $28.64\pm 27.89$ | 1.397152
5 | 3 | 2005-11-18 11:48:02 | 7.5 | $28.95\pm 27.86$ | $28.52\pm 27.80$ | 1.660546
6 | 4 | 2005-11-18 18:22:56 | 5.0 | $29.42\pm 27.88$ | $29.02\pm 27.83$ | 3.686975
7 | 5 | 2005-11-18 20:01:01 | 5.0 | $28.73\pm 27.77$ | $27.91\pm 27.67$ | 1.329063
8b | 5 | 2005-11-18 20:12:01 | 18.0 | $31.31\pm 28.73$ | $30.80\pm 28.66$ | 150.754465
9 | 6 | 2005-11-19 00:56:50 | 5.5 | $28.73\pm 27.83$ | $28.53\pm 27.81$ | 1.194350
10c | 7 | 2005-11-19 05:52:08 | 6.0 | $29.48\pm 27.97$ | $28.23\pm 27.77$ | 5.832215
11 | 7 | 2005-11-19 05:54:38 | 7.5 | $29.05\pm 27.94$ | $28.52\pm 27.88$ | 1.253377
12 | 8 | peak not measured | 6.0 | $28.98\pm 27.91$ | $27.80\pm 27.75$ | 1.192360
13 | 8 | 2005-11-19 09:17:50 | 10.5 | $29.39\pm 28.05$ | $28.81\pm 27.97$ | 1.662115
14 | 9 | 2005-11-19 23:57:14 | 6.5 | $29.06\pm 27.81$ | $28.50\pm 27.73$ | 2.524152
15 | 9 | 2005-11-19 23:58:14 | 7.0 | $29.31\pm 27.88$ | $28.88\pm 27.83$ | 3.180030

  * a

This is computed as $\mathrm{\left(p-3\sigma_{p}\right)/i}$, where
$\mathrm{p}$ is the count rate at the flare’s peak and $\mathrm{i}$ is the
count rate at the INFF level, and is a measure of the strength of the flare
detection.

  * b

This flare exceed the local non-linearity threshold of the GALEX detectors
during the flare. The result is that the true flux densities are
underestimated here.

  * c

This flare is heavily truncated in both bands at the start of the visit,
nearly entirely in FUV, thus the flare parameters are all lower limits at
best. We do not include this event in the rest of our analysis, but list it
here for completeness.

###  3.5 Alternative Flare Energy Estimation

Several of the flare events identified by our algorithm do not exhibit a
“classical” flare lightcurve morphology, wherein the flux starts near the INFF
value and then undergoes a FRED-shaped evolution before returning to the INFF.
Multi-peaked flare events could be a single flare with a complex morphology
(“complex”), or they could be composed of several flares happening
concurrently on the stars’ surfaces (“compound”). Some previous work has
suggested that complex flare shapes are common at low energies (Brasseur et
al. (2019), Howard et al. (2021)). Low energy flares are also expected to be
more common, which would result in more compound flares. Our detection
approach described above and summarized in Table 1 defines a single flare
event as one bound by a return to the INFF flux level, regardless of the
shape. We were not able to come up with an alternative approach to flare
detection—given only the data in this sample—that could distinguish whether
any given flare event was classical, compound, or complex.

To explore the possibility that multi-peaked flares are caused by multiple,
individual flares happening concurrently, we have examined each flare event
detected by our algorithm for multiple peaks and manually split them into
smaller “flares” (Figs. 4 and 5). A summary of the energies of flares
extracted in this manner are presented in Table 2 and are used to generate a
second estimate of the flare frequency at low energy in Section 4.1. Some
groups have used Bayesian Markov Chain Monte Carlo (MCMC) methods to split
multi-peaked flare events into individual flares (Günther et al., 2020;
Kuznetsov & Kolotkov, 2021). These methods are promising, but still need to
make assumptions about the underlying shapes of the individual flares when
fitting the multi-peaked events. To match how energies are calculated when we
treat them as single flares, we estimate flare energies using the area under
the curve for each piece of the event. Note that flare numbers referenced in
this document and in figures refer to those in Table 1 throughout. To avoid
confusion, we append these manually subdivided flares with a ’b’ in Table 2.

Figure 4: Visit-level light curves for Visits 1-5 (top to bottom) with flare
ranges split manually (Visits 2 and 3). FUV is in blue, NUV is in black, and
detected flare events are denoted by the grey backgrounds.  Figure 5: Visit-
level light curves for Visits 6-9 (top to bottom) with flare ranges split
manually (Visits 7 and 8). FUV is in blue, NUV is in black, and detected flare
events are denoted by the grey backgrounds. Note that Visit 9 was already
manually split in the code as part of automated algorithm-based flare
detection. We did not split the second “bump” in the event in Visit 5 into a
separate flare because the NUV flux does not show significant variability
above the INFF value, which it should for real flare events since count rates
are higher in the NUV. We also did not split the second “bump” in the second
event in Visit 9 because the NUV flux is within 1-$\sigma$ of the neighboring
fluxes and thus is not an obvious new peak.  Table 2: Summary of Flares When
Split By Hand

Flare | Visit | NUV Peak Time | Duration | log($E_{NUV}$) | log($E_{FUV}$)
---|---|---|---|---|---
|  | (UTC) | (min.) | (erg) | (erg)
1b | 1 | 2005-11-18 06:54:45 | 9.5 | $29.45\pm 27.92$ | $28.86\pm 27.84$
2b | 2 | peak not measured | 5.5 | $28.95\pm 27.80$ | $28.00\pm 27.64$
3b | 2 | 2005-11-18 08:30:49 | 5.5 | $28.59\pm 27.75$ | $27.92\pm 27.67$
4b | 2 | 2005-11-18 08:30:19 | 5.0 | $28.56\pm 27.72$ | $28.12\pm 27.67$
5b | 3 | 2005-11-18 11:54:02 | 12.0 | $29.17\pm 27.97$ | $28.64\pm 27.89$
6b | 3 | 2005-11-18 11:48:02 | 4.0 | $28.69\pm 27.72$ | $28.28\pm 27.67$
7b | 3 | 2005-11-18 11:48:32 | 3.5 | $28.61\pm 27.69$ | $28.14\pm 27.62$
8b | 4 | 2005-11-18 18:22:56 | 5.0 | $29.42\pm 27.88$ | $29.02\pm 27.83$
9b | 5 | 2005-11-18 20:01:01 | 5.0 | $28.73\pm 27.77$ | $27.91\pm 27.67$
10ba | 5 | 2005-11-18 20:12:01 | 18.0 | $31.31\pm 28.73$ | $30.80\pm 28.66$
11b | 6 | 2005-11-19 00:56:50 | 5.5 | $28.73\pm 27.83$ | $28.53\pm 27.81$
12bb | 7 | 2005-11-19 05:52:08 | 6.0 | $29.48\pm 27.97$ | $28.23\pm 27.77$
13b | 7 | 2005-11-19 05:53:08 | 3.0 | $28.66\pm 27.73$ | $28.38\pm 27.69$
14b | 7 | 2005-11-19 05:52:08 | 4.0 | $28.67\pm 27.78$ | $27.80\pm 27.70$
15b | 8 | peak not measured | 6.0 | $28.98\pm 27.91$ | $27.80\pm 27.75$
16b | 8 | 2005-11-19 09:09:50 | 2.5 | $28.36\pm 27.69$ | $27.88\pm 27.61$
17b | 8 | 2005-11-19 09:09:20 | 1.5 | $27.91\pm 27.56$ | $27.83\pm 27.52$
18b | 8 | 2005-11-19 09:11:20 | 4.0 | $29.11\pm 27.86$ | $28.52\pm 27.78$
19b | 8 | 2005-11-19 09:09:50 | 2.5 | $28.92\pm 27.75$ | $28.27\pm 27.67$
20b | 9 | 2005-11-19 23:57:14 | 6.5 | $29.06\pm 27.81$ | $28.50\pm 27.73$
21b | 9 | 2005-11-19 23:57:44 | 6.5 | $29.31\pm 27.86$ | $28.88\pm 27.81$

  * a

This flare exceed the local non-linearity threshold of the GALEX detectors
during the flare. The result is that the true flux densities are
underestimated here.

  * b

This flare is heavily truncated in both bands at the start of the visit,
nearly entirely in FUV, thus the flare parameters are all lower limits at
best. We do not include this event in the rest of our analysis, but list it
here for completeness.

##  4 Flare Analysis

Detailed visit-level light curves with zoomed sections centered on each
detected flare are presented in Appendix A, Figs. 12, 13, 14, 15, 16, 17, 18,
19, and 20. Each light curve is binned at 30 seconds, and we do not include
any bins that contain less than 20 seconds effective exposure; when present,
these short-exposure bins typically occurred at the beginning or ends of
visits. UV Ceti is known to be a very active system, and we detect at least
one flare in every visit we analyzed in this work except the last (not shown
in Appendix A). The flare events are all within the UV energy range $\sim
28.5<\log{E}<29.5$ ergs with the exception of the largest flare (Flare 8 in
Visit 5) previously detected by Miles & Shkolnik (2017) at the visit-level. In
the following sections, we estimate the flare frequency in the
$28.5<\log{E}<29.5$ ergs range, where all but one of our detected flares
reside, and check if this rate is consistent with extrapolations of FFDs at
higher energies. Flare 8 by itself is remarkable because of how bright it is,
enabling a search for in-flare variability.

Flare 10 from Visit 7 is heavily truncated, where the peak likely occurred
before the GALEX visit started. The FUV channel started to collect data a
little later than the NUV, which makes for so little coverage that it is
essentially undetected in the FUV band. To make matters worse, the first NUV
bin and first two FUV bins are impacted by low effective exposure times and
are excluded as mentioned above. The first and last bins can sometimes be
unreliable due to how gPhoton defines bin boundaries, which may not always
align with the first or last valid photons for that particular visit. Checking
the time coverage for the first and last bins of gPhoton light curves is
always recommended, and those with very little effective exposure times are
best ignored. All these issues compound to make the identification of this
variability as a flare questionable at best. Even if this were an actual flare
event, the lack of coverage during the event would make the estimated energy
and duration very poor lower limits. Because of these issues, we have decided
to include this event as a possible flare detection in Table 1, but we do not
include it in our flare rate estimation.

###  4.1 Flare Rate

####  4.1.1 Flare Selection

Without spatially resolving a star’s surface, it can be difficult to determine
if a given flux increase is composed of one flare event, multiple distinct
flare events, or a chain reaction of physically related flare events. It can
also be difficult to say with certainty that a particular event is a stellar
flare when the event has an unusual shape, or the ratio of peak flux to INFF
is relatively small. For this paper, we prefer to define a “flare” as
variations in stellar flux density that trigger our flare search criteria. In
this case, a candidate flare is only included in the flare rate calculation if
both the INFF and local maximum, assumed to be the flare peak, were observed,
as well as some baseline before and after the peak to capture the rise to, and
decay from, peak flux. These criteria were chosen because the INFF, peak flux,
and slopes of the rise and decay phases are the minimum parameters required to
model a classical flare light curve. Some of the flares that pass these tests
do not return to the INFF value before the end of the visit, or have pre-flare
components that are above the INFF. The derived energies in these cases are
lower limits, but since in these cases the peak flux and a majority of the
event are captured, the majority of the flare energy should also be captured
in the GALEX data. However, compared to other flare surveys with much longer
continuous observing windows, the limited time baseline of each GALEX visit
makes it more difficult to estimate when a flare starts and ends. These
criteria do not apply to the alternative method, where a flare event is
manually split into individual flares (per Section 3.5); by construction, in
that case, the flux from individual flares has not returned to the INFF value.

When selecting flares to use for the flare frequency estimation from Table 1,
the following flare events are excluded. As previously described, Flare 10 is
a questionable flare event to begin with, and is heavily truncated even if it
is a flare, and thus is excluded from the flare rate analysis. In addition,
Flare 2 and Flare 12, where the local maximum occurs at the beginning of the
visit, are excluded. In these cases, the GALEX visit only captured the decay
phase of a (presumably) larger flare. Light curves with local maxima at the
end of the visit would also have been excluded, although none are present in
these data. We have chosen to decompose the light curve in Visit 9 into two
distinct, “fast rise, exponential decay” (FRED)-shaped flares (Flares 14 &
15). Although Flare 3 looks like it may also be two distinct FRED-like shapes,
only one of the peaks passes our search requirement of being $3\sigma$ above
the INFF simultaneously in both bands, so we decided not to decompose this
event. Many of the other flares are complex events, with several local maxima,
but we have chosen to not attempt to partition these into individual flares
because they are not clearly composed of a finite number of “classical FRED”
shapes. Any flare rate calculation will depend heavily on the criteria defined
to identify distinct flare events. This leaves a total of 11 flares to use for
estimating the flare frequency in the energy bin $28.5\leq\log{E}\leq 29.5$.

When selecting flares to use for the alternative flare frequency estimation
from Table 2, the following flare events are excluded. Flares 2b and 15b
correspond to Flare 2 and 12, and are excluded for the same reason. Flare 10b
corresponds to Flare 8 and is excluded because it is the one large flare
outside our energy bin we are considering. Flare 12b corresponds to Flare 10
that is heavily truncated, and is excluded for the same reason. Finally,
Flares 16b and 17b have estimated flare energies below the bin we are
considering, and thus are excluded. This leaves a total of 15 flares to use
for estimating the flare frequency when breaking down flare events manually.

####  4.1.2 Flare Recovery Testing

To determine the fraction of flares that may have been missed by our flare
search algorithm, we conducted a recovery test. We create 100,000 simulated
light curves containing flares using the Davenport et al. (2014) flare
template model. For each simulated light curve, we inject one, two, or three
flares within the visit. A baseline count rate for a source at an NUV
magnitude of 18 is assumed, which is the approximate brightness of GJ 65 in
the GALEX NUV band. To match the GJ 65 light curves here, our simulated light
curves use time bins of 30 seconds. We use a detection threshold of three
sigma to match our detection criteria here, but do not generate both FUV and
NUV light curves, since all of the detected flares for GJ 65 have FUV to NUV
flux ratios very close to unity. We then randomly select from uniform
distributions, for each flare: a peak flare magnitude ranging from NUV of
13-18, a start time during the central 1400-second observation baseline
(avoiding the first and last 200 seconds of the observing window), and a flare
full width at half maximum ranging from 1 to 300 seconds. Each simulated light
curve is then run through our flare detection algorithm.

Detected flare events are compared with the injected flares. We define a few
categories for each flare event. An injected flare is considered “detected” if
the peak of an event detected by our algorithm falls within two time bins of
the injected flare’s peak, and the calculated energy of the detected event is
within a factor of five of the injected flare’s energy. We choose this
tolerance factor because we are estimating the flare frequency in an energy
bin that covers a full order of magnitude ($28.5\leq\log{E}\leq 29.5$). If a
detected event’s peak is within two time bins of an injected flare’s peak, but
the energy is not within a factor of five, then it is counted as “detected
with wrong energy”. This is commonly the case when a large flare is near one
or more smaller flares: the time of peak flux matches the time of peak flux in
an injected flare, but our algorithm counts them all as one event and thus
derives a total energy that is far off from the injected energy. Any injected
flares that do not have times of peak flux near any detected flare events are
counted as “missed”. This category can include those smaller flares that occur
near a larger flare within the visit. A final category of “false positive” is
reserved for those flares that our detection algorithm identifies but do not
match the times of any injected flares.

Figs. 6 and 7 show sample visit light curves with injected flares. Fig. 6
provides a sample of a light curve with two injected flares well-separated in
time. In this case, the flux returns to the INFF value before the next flare
occurs, thus, our algorithm is able to correctly identify two individual
flares in this visit, and the estimated energies are within our tolerance
factor to count as being “detected”. Fig. 7 provides a sample of a light curve
with three injected flares that occur close enough in time such that the flux
level never returns back to the INFF level before the other flares occur. This
means that our flare detection algorithm treats this as a single “flare
event”, rather than the three “classically” shaped flares that were injected.
While many flares exhibit the FRED-shaped model, not all flares do, especially
at low energies in the ultraviolet (Brasseur et al., 2019). In these cases, is
a given flare event composed of a series of FRED-shaped flares occurring
concurrently, or a single flare event that does not follow the FRED-shape
morphology? Answering that question is beyond the scope of this work, but it
does impact our estimation of a flare frequency. Thus, we estimate flare
energies in two ways: following our algorithm that defines a single flare
event based on a return of the flux to the INFF value, and one where we force
energy calculations by splitting any multi-peaked flare events into individual
flares. These two methods cover the two cases: in the former, the assumption
made is that all flare events are from a single flare with a complex shape,
while in the latter, the assumption made is that every flare event with more
than one peak is composed of individual flares happening concurrently.

Figure 6: Example of a simulated visit light curve containing two flares
(peaks marked with vertical lines in the top panel.) In this case, the flares
are spaced within the visit such that our algorithm correctly identifies them
as individual flares (blue and orange shaded regions in the bottom panel), and
the energies match the injected flare energies within our tolerance factor (a
factor of 5.)  Figure 7: Example of a simulated visit light curve containing
three flares (peaks marked with vertical lines in the top panel.) Our
algorithm identifies this as a single “flare event” (blue shaded region in
bottom panel.) The peak time of the detected flare event matches the peak time
of the strongest injected flare, but the derived energy is larger than our
tolerance factor (a factor of 5) since multiple injected flares are
contributing flux.

To assess the impact of derived flare energies when there are multiple flares
occurring concurrently, we compare the distribution of injected flare energies
with the distribution of detected flare energies for the cases of one, two,
and three injected flares per visit. False positive flare detections were less
than 10% the total number of injected flares in all three cases. Fig. 8
compares these distributions, using a bin size of log(E) = 0.5, for the
injected flares (blue) and detected flares (orange). In visits where there is
a single injected flare, the estimated energies match well with the injected
energies, and the vast majority ($\sim 94\%$) of the flares are detected with
energies that match the injected flare’s energy within a factor of five. For
visits that contained two injected flares, only $\sim 43\%$ of the injected
flares were detected with energies within a factor of five, while $\sim 45\%$
of the flares were missed entirely. For visits containing three injected
flares, only $\sim 25\%$ of the flares were detected with energies within a
factor of five, and $\sim 63\%$ of the flares were missed entirely.

Figure 8: Comparison of the distributions of flare energies injected into the
light curves (blue) and those detected and estimated by our flare algorithm
(orange). Top-left: flares in light curves with only one flare injected. Top-
right: flares in light curves with two flares injected into the visit. Bottom-
left: flares in light curves with three flares injected into the visit. The
number of flares injected and detected are reported in the plot titles for all
three cases.

To further complicate the matter, GJ 65 is a binary system of two M dwarfs,
and the individual sources are not resolved by GALEX, so we are unable to
assign any specific flare to UV Ceti or BL Ceti. The two components have
similar spectral types and rotation rates, but very different magnetic field
behaviors and morphologies. Although UV Ceti is the more active component, we
are limited to estimating a flare rate for the GJ 65 system as a whole. Rather
than attempt to assign some fraction of the events to each star, we bound our
flare frequency estimation by assuming 100% of the events come from one of the
stars, and then by assuming the two stars split the events equally. Thus we
calculate an upper and lower estimate for the flare frequency.

We estimate the flare frequency between $28.5\leq\log{E}\leq 29.5$ by dividing
the total number of non-truncated flares detected within this energy range (11
using our algorithm, 15 when split by-hand), by the total observation time on
source (15682 seconds). This yields an estimated flare frequency of
$\log{\\#/\mathrm{hour}}=0.40\pm 0.11$ for the upper-bound case (where all
flares come from one of the stars in the system), and a lower-bound flare
frequency (where the detected flares are split evenly) of
$\log{\\#/\mathrm{hour}}=0.10\pm 0.15$. When split by hand into smaller
flares, the estimated flare frequencies are $\log{\\#/\mathrm{hour}}=0.54\pm
0.10$ for the upper bound case and $\log{\\#/\mathrm{hour}}=0.24\pm 0.14$ for
the lower-bound case. The quoted estimated uncertainties are $1\sigma$,
derived from standard counting statistics. Given the relatively large
additional uncertainties introduced by the assumptions made, we do not apply
the approximations for small-number counting statistics to further refine the
confidence intervals (Gehrels, 1986; Ebeling, 2003). The flare frequency
estimation is available as part of the Python notebooks associated with the
online version of this paper.

As an exercise, we can compare this estimated rate with the values expected
when extrapolating from other recent FFD calculations for M dwarfs. By no
means is our estimated flare rate a strong constraint on flare rates for mid-M
dwarfs at these low energies as a population, but it is still instructive to
see if our estimated flare frequency is in-line with results from much larger
surveys. There are a variety of sources we compare against. We use the “M3-M5
Active” FFD from Hilton (2011), the lone M star smaller than
$0.2\;\mathrm{M_{\odot}}$ from Davenport (2016), V541 Lyr = KIC 5683912
(although it may not be a dwarf based on spectroscopic data from Frasca et al.
(2016)), the “M4 Active” sample from Howard et al. (2019), and the M dwarf
FFDs from Günther et al. (2020) for TESS targets with
$2500\leq\mathrm{T_{eff}}\leq 3250$ K. Fig. 9 shows our estimated flare
frequencies for GJ 65 compared to FFD from these various sources based on
detected flares of higher energies and different optical passbands. Note that
we do not attempt to correct them all to bolometric luminosities to account
for differences in the filters, since in the NUV and optical none would change
the bolometric luminosity by more than an order of magnitude compared to any
other, and thus would have minimal impact on the log-log relation being
compared. Despite the approximations and uncertainties in the analysis, the
estimated flare frequency based on these low-energy GALEX flares from the GJ
65 system is comparable to the predicted values based on extrapolating these
other FFD determinations for similar M dwarfs down to these energies. Breaking
down flare events into smaller flares (dotted blue box in Fig. 9) does not
change the estimated flare frequency significantly, since the number of flares
in this energy bin only increases from 11 to 15.

Figure 9: Blue rectangular region: Estimated flare frequency based on detected
flares from the GJ 65 system assuming they all come from one star (upper
bound) or are split equally between the two (lower bound). The width of the
region is bounded by the approximate lowest and highest energies detected in
our flare sample (excluding Flare 8). The dashed blue box represents the flare
frequency estimate when breaking flare events into smaller flares by hand.
Other FFD from the literature are shown for comparison. No conversion between
the energies to account for the different filters is applied, since between
the NUV and optical none would change the derived bolometric energies by more
than an order of magnitude compared to each other.

###  4.2 Detailed Analysis of Flare 8

The eighth flare in our sample is the largest by orders of magnitude in both
peak flux and integrated energy, so it allows for much more detailed analysis.
We generate NUV and FUV light curves with 5-second bins for this visit, to
better study the evolution and shape of the flare. The GALEX microchannel
plate detectors have two sources of instrumental non-linearity: a global non-
linearity caused by the time it takes the electronics to assemble photon
lists, and a local non-linearity caused by limited current supply to small
regions near bright sources. For a detailed discussion, refer to Morrissey et
al. (2007), Section 4.4. The global non-linearity can be corrected to better
than 10% through calibration, but the local non-linearity is not reliably
corrected. Morrissey et al. (2007) conducted an analysis of bright white dwarf
standards, and identified count rates where the drop-off exceeds 10% (gPhoton
uses a threshold of 109 cps in FUV and 311 cps in NUV).

Flare 8 is bright enough to induce non-linear detector response. The NUV rate
exceeds the 10% local non-linearity threshold for $\sim$75 seconds on either
side of the flare’s maximum brightness (maximum count rate in NUV is $>800$
cps). From the predicted-to-measured count rates of bright white dwarfs
presented in Morrissey et al. (2007), the NUV count rate during peak flare
brightness would be suppressed by at least 30% (albeit with a large
uncertainty). In the FUV the 10% threshold is only exceeded for $\sim$25
seconds on either side of peak flare brightness, but at the maximum FUV count
rate ($\sim$159 cps) the count rate suppression would still be at the 25%
level based on the approximate formula given in Morrissey et al. (2007). These
estimates, based on Figure 8 from Morrissey et al. (2007), are highly
uncertain: the white dwarf calibrators show significant scatter around the
fitted relation, even between measurements at a single count rate (at an
expected count rate of 800 cps, which coincidentally matches the peak NUV
count rate during the GJ 65 flare, the measured count rates range from
$\sim$300-800 cps). The local non-linearity is known to depend on the change
in gain across the field-of-view, which is not well mapped using the
relatively small sample of targeted, bright white dwarf calibrators that
typically fell in the centers of the fields-of-view, and the timestamps of the
observations are not provided, and there have been no investigations on
whether the impact of local non-linearity changed over the course of the
mission.

Without recognizing that the count rates are in the non-linear regime, one
would derive a significant FUV-NUV color difference, and in fact, an FUV to
NUV ratio that changes during the flare itself. The time-evolution of the FUV
to NUV ratio during a flare can place strong constraints on the flare
mechanism and properties, especially on the effective temperature of the
flare’s blackbody component (Hawley et al., 2003). Even in the absence of
time-resolved spectra to study how individual lines change during a flare, one
could use information about the emissivity and the characteristics of the
flare to deduce some information. For flares with QPP detected in two bands,
one can compare the strengths of the detected signals with the fluxes in both
bands. A QPP signal strength that does not scale with the fluxes (i.e.,
signal-to-noise) from those bands is evidence that the signal is approximately
wavelength-independent across the bandpasses.

The flare spectral energy distribution consists of isolated emission lines and
a hot blackbody continuum feature. Different species have line emission
contribution in the FUV bandpass compared to the NUV, with very different
formation temperatures: in the FUV bandpass it is predominantly C IV and Si
IV, which form at temperatures near 100000 K, while in the NUV bandpass it is
Mg II, with formation temperature $\lesssim$ 30000 K (Fontenla et al., 2016).
A QPP signal that is stronger in the GALEX FUV than the GALEX NUV is evidence
that it arises from emission lines that dominate the FUV bandpass, while a
signal that is wavelength-independent or dominant in the NUV is evidence that
the QPP originates in the hot blackbody emission, especially since the GALEX
bandpass has little sensitivity near the Mg II lines and is dominated by
continuum emission. However, without an accurate correction (and associated
uncertainties to that correction) for local non-linearity to account for the
missing flux, such an analysis is not possible for Flare 8. While the branch
of gPhoton we used for this paper does not output quality flags as part of the
light curves, the main branch of gPhoton does, and readers are reminded to
always pay attention to these quality flags, which include checks on count
rates that exceed the 10% local non-linearity threshold.

####  4.2.1 Quasi-periodic Pulsations

While the effects of local non-linearity limit our ability to study the color
evolution of the flare, it does not preclude a search for QPPs. Detecting a
consistent signal in both the FUV and NUV bands is a good indicator: unless
the signal is strongly correlated with the dither pattern, there is nothing in
the GALEX hardware design that would suggest a signal would appear in both
bands by chance. de la Vega, & Bianchi (2018) conducted an extensive test of
gPhoton light curves to analyze false positives using several thousand bright,
blue sources, and found that false positives are nearly always correlated with
the dither pattern of the telescope. Thus, any signal detected in both bands
that is not correlated with position on the detector (in gPhoton, the “detrad”
parameter) is a strong candidate for a real signal, even if there is missing
flux due to local non-linearity.

The presence of in-flare variability is readily apparent even by visual
inspection of Flare 8. Such periodic variability could be caused by QPP (Parks
& Winckler, 1969; Rodono, 1974; Kupriyanova et al., 2010; Mathioudakis et al.,
2003; Simões et al., 2015; Pugh et al., 2016, and references therein), which
for stars other than the Sun, have been observed with periods ranging from a
few seconds to hundreds of seconds. In at least one case, multiple periods
have been detected during a single flare (Pugh et al., 2015). Welsh et al.
(2006) used time-tagged GALEX photon events to detect QPP with periods of
30-40 seconds from large flares from AF Psc, GJ 3685A, Cr Dra, and SDSS
J084425.9+513830.5, while Doyle et al. (2018) used a wavelet analysis on
gPhoton light curves to detect QPP in flares from six stars, including those
in Welsh et al. (2006).

As an initial quick check, we remove a smooth trend representing the unknown,
aperiodic flare shape using a Savitzky-Golay filter. The residuals are then
run through a Lomb-Scargle periodogram, where a clear peak around 48 seconds
is detected. We also run a periodogram on a large time period of the light
curve prior to the flare event, to test if there is intrinsic variability at
this frequency, but find no statistically significant peaks. To check if this
is an instrumental effect, we generate 5-second cadence light curves for three
of the closest known sources to GJ 65 (to check if there are any local
systematics) and also three of the closest known sources within one magnitude
of the peak brightness during the flare, in case the systematics only show up
for very high count rates. In no cases do we detect any statistically
significant peaks in the periodograms. Note that a similar test can not be
done using blank sky near GJ 65 itself, because the sky background in GALEX is
typically very low. At the position of GJ 65, the estimated sky background is
$\sim$0.59 cps within a 17.3″annulus. To check for the presence of a $\sim$50
second signal, one would want to use at most 25 second bins for Nyquist
sampling, resulting in $\sim$15 photon events per bin. At these count rates, a
signal at the 10% level like that found on GJ 65 would be lost in the photon
noise, thus tests must be done on known sources and not empty patches of sky.
Finally, we examine the frequency of the dither pattern to ensure this is not
an induced signal caused by the motion of the spacecraft during the
observation, and find no peak caused by the change of the spacecraft boresight
that matches the period of the QPP. All of these tests can be found in the
Python notebooks associated with the online version of this paper. Thus
confident that this variability is unique to GJ 65 and only present during the
flare itself, we conduct a more thorough analysis of the QPP.

We applied empirical mode decomposition (EMD; Huang et al., 1998; Huang & Wu,
2008) and Fourier transform methods444The IDL routines used for the analysis
can be accessed via github.com/Sergey-Anfinogentov/EMD_conf. Note, the project
is still under development so the interested reader is encouraged to contact
the software authors<EMAIL_ADDRESS>directly for the most recent
updates and guidance. for detection and analysis of QPP in Flare 8 observed in
the NUV and FUV bands. The use of two essentially independent methods for a
raw signal decomposition into intrinsic oscillatory components and their
analysis was motivated by the recent review of state-of-the-art techniques for
detecting QPP in solar and stellar flares by Broomhall et al. (2019), who
suggested that confidence in the QPP detections can be improved if more than
one detection method is employed. EMD allowed us to decompose the observed
flare light curves into five (FUV) and six (NUV) intrinsic quasi-oscillatory
modes and aperiodic trends (see Figs. 10 and 11). The flare aperiodic trends
were determined by summing up all EMD-revealed timescales longer than half a
length of the original signals. After removing the aperiodic trends, we
calculated Fourier power spectra for both observational signals and estimated
properties of the background noise and statistical significance of Fourier
peaks in comparison with it, adapting methods from Vaughan (2005) and Pugh et
al. (2017). The Fourier spectra for both signals are found to be fairly flat,
indicating the absence of correlated noise in the observations.

We assessed the statistical significance of detected EMD modes following the
scheme developed in Kolotkov et al. (2016). For this, we estimated the total
energy (as a sum of all instantaneous amplitudes squared) and the mean period
(using global wavelet analysis) of each individual EMD mode. In analogy with
the Fourier power spectrum, the dependence between the EMD modal power and
mean periods can be referred to as an “EMD power spectrum”. The concept of an
EMD power spectrum was previously used for the analysis of QPP in solar and
stellar flares in e.g. Kolotkov et al. (2015); Doyle et al. (2018); Kolotkov
et al. (2018); Jackman et al. (2019). Using properties of noise detected in
the Fourier analysis, we construct the upper and lower confidence intervals in
the EMD power spectrum governed by the $\chi^{2}$-distribution with the number
of degrees of freedom greater than two. In both the Fourier and EMD
approaches, periods of $48.6\pm 7.0$ s (FUV) and $49.2\pm 7.4$ s (NUV) were
found to be significant. The uncertainties for each mean modal period were
estimated using the half-level width of a best-fit Gaussian function in the
corresponding global wavelet spectra. Those uncertainties are connected with
the instantaneous period drift in each EMD mode rather than instrumental
effects. The non-periodic trends were excluded from this analysis. Thus, the
flare periodicities observed in the FUV and NUV bands are clearly consistent
between each other within the estimated uncertainties, which further
strengthens the confidence that the detected QPP are intrinsic to the star and
not a systematic error.

The statistical significance of the detected $\sim$50 second period is seen to
be substantially higher in the NUV band. This is seen in both the Fourier and
EMD analyses, which are intrinsically independent, thus ruling out the
possibility that it is caused by the method. On the other hand, in the EMD
power spectrum of the FUV signal, the first (shortest-period) mode near 20
seconds is seen at the 99% confidence level too, while the corresponding
Fourier peak is well below its level of significance. We note that the
shortest time scale modes in the EMD analysis usually have abnormally
distributed instantaneous amplitudes, hence their energies (sum of
instantaneous amplitudes squared) do not follow the $\chi^{2}$-law (Wu &
Huang, 2004). This makes the significance test performed in this study
inapplicable to the shortest-period modes. In addition, the distribution of
the modal energies in the EMD spectrum may be corrupted by the so-called “mode
leakage” problem, when limitations from the time resolution of the light curve
impact the ability of EMD to properly differentiate between neighboring modal
periods (Rilling & Flandrin, 2009).

Finally, the dither pattern of the observation during this flare induces a
sinusoidal signal with a period of 120 seconds (a plot of the detector
position over time for GJ 65 is available in a Python notebook associated with
the online version of this paper). Induced signals at, or aliased with, the
dither pattern frequency are an important source of systematic error when
using gPhoton data (de la Vega, & Bianchi, 2018), especially near the detector
edges or when at or near the local non-linearity threshold (which applies for
this flare). The strongest detected period at $\sim$50 seconds in both FUV and
NUV bands is far enough away from any aliases of the dither pattern that it is
highly unlikely these signals are induced by local non-linearity. In fact,
when conducting their wavelet analysis of GJ 65, Doyle et al. (2018) found a
46 second period in the rise and late decay phases of the flare (where the
count rate was below or barely above the local non-linearity threshold), and a
“weak $\sim$25 second period around flare maximum”, where the effects of
depressed flux due to local non-linearity would be at their most severe. While
Doyle et al. (2018) do not provide any uncertainty estimates for the detected
periods, we note the 46 second period is a very good match to the period found
in our analysis (and unlike Doyle et al. (2018), we analyzed both the FUV and
NUV bands), while their 25 second period found only when count rate was
highest may be the result of local non-linearity triggering off a 1:6 alias of
the dither pattern of the observations, and could also match our second
highest peak at $\sim$20 seconds. All this leads us to disregard the shortest-
period mode in Fig. 11 as an astrophysical source despite the formal
statistical significance from the EMD analysis, and if anything, we suspect it
may be caused by an induced signal due to local non-linearity during the peak
of the flare that relates to the dither pattern of the telescope.

####  4.2.2 QPP Physical Interpretation

The period of a QPP is linked to a characteristic length scale and a velocity,
for a given interpretation of the QPP mechanism (i.e. “sausage” or “kink”
magnetohydrodynamic (MHD) modes). MHD waves behave differently at the flare
loop tops and near the footpoints (Nakariakov et al., 2016). Standing, fast
magnetoacoustic kink oscillations weakly perturb the loop density, while the
perturbation of the loop velocity has nodes and antinodes near the footpoints
and at the apex, respectively. Fast sausage waves have stronger density
perturbations higher up in the corona. For compressive, slow magnetoacoustic
waves near the loop footpoints, the perturbation of velocity is zero and the
perturbation of density is maximized.

Provided the loop is large enough so that its apex is in the corona, kinks are
not likely to modulate the chromospheric source. Sausage modes can modulate
precipitation of accelerated electrons towards the footpoints by changing the
magnetic mirror ratio in the loop via the “Zaitsev-Stepanov” mechanism
(Kupriyanova et al., 2020). For solar coronal loops the periods of sausage
modes are usually 10-20 s. For standing slow modes (a variation of density
near the footpoints), oscillation periods are usually longer (at least several
minutes or more). A third possible mechanism for QPP are periodically
triggered magnetic reconnections in the corona. In this case, the coronal
reconnection site is unstable to an external oscillation like a kink
(Nakariakov et al., 2006), providing periodic precipitations of energetic
particles down to the chromosphere and heating the plasma again. The shortest
value of kink periods observed in the solar corona are about 1 min (Nechaeva
et al., 2019), not too far off from the $\sim$50 second periods observed here.
Out of these three possible mechanisms, periodic triggering of reconnection by
external MHD oscillation matches our observed QPP period best, but the others
are not necessarily excluded, especially when considering potential
differences in the QPP properties generated by these three mechanisms for M
dwarfs compared to the Sun.

Figure 10: QPP analysis of NUV light curve for Flare 8. Top left: Flare 8
light curve with the overall flare trend (the red dashed line), determined by
the empirical mode decomposition (EMD). Top right: Fourier power spectrum for
the detrended flare light curve (see the bottom left panel), with the power-
law fit (the blue dashed line) and the 99% confidence level (the red solid
line). Bottom right: Dependence of the total power (circles) against mean
period for each intrinsic oscillatory mode and flare trend determined in the
original signal (see the top left panel) with EMD (the “EMD power spectrum”).
The blue dashed line shows the overall slope of the spectrum. The red solid
lines show the corresponding 99% confidence intervals. Bottom left: The
original flare light curve with the flare trend subtracted (the black line)
and the oscillatory mode found to be statistically significant in the EMD
analysis (the blue line). The elapsed time in all panels is relative to the
start of the GALEX visit.  Figure 11: QPP analysis of FUV light curve for
Flare 8. The panel layout is the same as in Fig. 10.

##  5 Conclusion

The combination of high flare-to-star contrast in the UV, wide spatial
coverage of GALEX, and fast temporal sampling of the photon events enabled by
gPhoton make for a rich archive for flare science. The M5 dwarfs in the GJ 65
system are the brightest, active flare sources observed by GALEX for more than
a few minutes. GJ 65 is thus the best opportunity in the GALEX data to detect
and characterize low-energy M dwarf flares. We have described 14 previously
undetected flare events in the GALEX data, all with UV flare energies below
$10^{29.5}$ ergs. This is less than than the minimum-detectable flare energies
by space-based surveys from Kepler, K2, and TESS, but our estimated FFD is
broadly consistent with the predicted values based on extrapolated FFD from
those larger ground- and space-based surveys. We also time-resolve the largest
detected flare from GJ 65, previously detected by Miles & Shkolnik (2017) at
the visit level. Although the count rate exceeds the local non-linearity
threshold during the flare, using the simultaneous FUV and NUV observations
provided by GALEX, we detect strong, periodic variability during the flare
itself that is not correlated with the dither pattern of the telescope. Both
the FUV and NUV bands show a strong signal with a period of $\sim$50 seconds,
which is not seen in other nearby stars and is not correlated with known
instrumental systematics. We interpret this signal as a strong quasi-periodic
pulsation associated with the flare. Given the period of the QPP, the best
matching mechanism based on typical timescales from solar observations would
be a periodic triggering of reconnection caused by external MHD oscillation,
since the shortest timescale of such kinks observed in the Sun’s corona are
$\sim$1 min and most closely match the $\sim$50 second period here. However,
the extent to which a flare mechanism can be identified solely by comparing
timescales of Solar QPPs with observations of QPPs in M dwarfs is uncertain,
so we consider this interpretation to be suggestive rather than definitive.

GALEX observations of tens of thousands of other cool stars, in addition to
solar-like stars, are available in the gPhoton archive. Unlike GJ 65, most
stars were not observed multiple times by GALEX, but the nearly complete sky
coverage makes the GALEX archive a rich resource for UV flare science on a
massive scale. While GJ 65 might afford the best single source for low-energy
flare studies using the gPhoton archive, the sheer number of stars with more
than 10-minute long observations allows for ensemble investigations of flares
across a wide range of stellar types at a time resolution of seconds, a
sampling rate that is still inaccessible for the majority of targets being
observed from space-based surveys.

We thank the anonymous referee whose comments improved the quality of this
paper. This research is supported by NASA ADAP grant 80NSSC18K0084. We thank
Parke Loyd and Evgenya Shkolnik for discussions that greatly improved the
quality of the paper. This research is based on observations made with the
Galaxy Evolution Explorer, obtained from the MAST data archive at the Space
Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5–26555.
This research has made use of the SVO Filter Profile Service
(http://svo2.cab.inta-csic.es/theory/fps/) supported from the Spanish MINECO
through grant AYA2017-84089. DYK acknowledges support by the STFC consolidated
grant ST/T000252/1 and the Ministry of Science and Higher Education of the
Russian Federation. GALEX

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##  Appendix A Visit Light Curves and Detected Flares

Figures 12, 13, 14, 15, 16, 17, 18, 19 and 20 plot the detected flares from
the GJ 65 visits we analyzed. The top panels show the full visit light curves
from both the FUV and NUV bands. The bottom panels show a zoom-in on the flare
ranges themselves (each visit contains one or two flare events). The INFF
value in the NUV is shown for reference. In all cases, the FUV INFF values are
very similar to the NUV value.

Figure 12: Detected flares from Visit 1. Full visit (top), and zoomed plots
centered on each detected flare event (bottom). Figure 13: Detected flares
from Visit 2. Full visit (top), and zoomed plots centered on each detected
flare event (bottom). Figure 14: Detected flares from Visit 3. Full visit
(top), and zoomed plots centered on each detected flare event (bottom). Figure
15: Detected flares from Visit 4. Full visit (top), and zoomed plots centered
on each detected flare event (bottom). Figure 16: Detected flares from Visit
5. Full visit (top), and zoomed plots centered on each detected flare event
(bottom). Flare 7 is the strongest flare detected in gPhoton for GJ 65.
Although there is an apparent time evolution in the FUV-NUV flux ratio, the
count rate exceeds the local non-linearity threshold by a significant margin,
and thus any conclusions on FUV-NUV ratio cannot be made without applying a
robust, accurate correction for missing fluxes in both bands (see Sec. 4.2).
Figure 17: Detected flares from Visit 6. Full visit (top), and zoomed plots
centered on each detected flare event (bottom). Figure 18: Detected flares
from Visit 7. Full visit (top), and zoomed plots centered on each detected
flare event (bottom). Note: Flare 10 is truncated so much that we do not
include it in our analysis, but include it in Table 1 for completeness. The
apparent gap in the second flare event is caused by a time bin that falls
below our threshold for effective exposure time coverage (that particular bin
only has $\sim 16$ seconds of effective exposure time within the 30-second
bin). Figure 19: Detected flares from Visit 8. Full visit (top), and zoomed
plots centered on each detected flare event (bottom). Figure 20: Detected
flares from Visit 9. Full visit (top), and zoomed plots centered on each
detected flare event (bottom).