# The Nova KT Eri Is a Recurrent Nova With a Recurrence Time-Scale of 40-50
Years

Bradley E. Schaefer1, Frederick M. Walter2, Rebekah Hounsell3,4, & Yael
Hillman5
1Department of Physics and Astronomy, Louisiana State University, Baton Rouge,
Louisiana, 70820, USA
2Department of Physics and Astronomy, Stony Brook University, Stony Brook, New
York, 11794, USA
3University of Maryland, Baltimore County, Baltimore, MD 21250, USA
4NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
5Department of Physics, Ariel University, Ariel, POB 3, 4070000, Israel
E-mail<EMAIL_ADDRESS>
###### Abstract

KT Eridani was a very fast nova in 2009 peaking at $V$=5.42 mag. We marshal
large data sets of photometry to finally work out the nature of KT Eri. From
the TESS light curve, as confirmed with our radial velocity curve, we find an
orbital period of 2.61595 days. With our 272 spectral energy distributions
from simultaneous $BVRIJHK$ measures, the companion star has a temperature of
6200$\pm$500 K. Our century-long average in quiescence has $V$=14.5. With the
Gaia distance (5110${}^{+920}_{-430}$ parsecs), the absolute magnitude is
$M_{V_{q}}$=$+$0.7$\pm$0.3. We converted this absolute magnitude (corrected to
the disc light alone) to accretion rates, $\dot{M}$, with a full integration
of the $\alpha$-disc model. This $\dot{M}$ is very high at 3.5$\times$10-7
M⊙/year. Our search and analysis of archival photographs shows that no
eruption occurred from 1928–1954 or after 1969. With our analysis of the
optical light curve, the X-ray light curve, and the radial velocity curve, we
derive a white dwarf mass of 1.25$\pm$0.03 M⊙. With the high white dwarf mass
and very-high $\dot{M}$, KT Eri must require a short time to accumulate the
required mass to trigger the next nova event. Our detailed calculations give a
recurrence time-scale of 12 years with a total range of 5–50 years. When
combined with the archival constraints, we conclude that the recurrence time-
scale must be between 40–50 years. So, KT Eri is certainly a recurrent nova,
with the prior eruption remaining undiscovered in a solar gap of coverage from
1959 to 1969.

###### keywords:

stars: individual (KT Eri) – stars: novae, cataclysmic variables

††pubyear: 2021††pagerange: The Nova KT Eri Is a Recurrent Nova With a
Recurrence Time-Scale of 40-50 Years–References

##  1 Introduction

KT Eridani (Nova Eridani 2009) appeared as an ordinary nova, discovered by K.
Itagaki on 2009 November 25, roughly ten days after the optical maximum. The
entire fast rise, peak, and decline out to the time of discovery was covered
photometrically (Hounsell et al. 2010) with the Solar Mass Ejection Imager
(SMEI) instrument onboard the Coriolis satellite. KT Eri was a bright nova
(peaking near 5.42 mag), very fast (fading from peak by 3.0 mag in 13.6 days),
with a ‘P’ (plateau) class light curve, and a He/N spectral class. The
progenitor was quickly identified as a 15th mag star, for which Jurdana-Šepić
et al. (2012) sought prior nova events on 1012 Harvard plates from 1888 to
1962. KT Eri was also detected in the radio (O’Brien et al. 2010) and X-ray
(Bode 2010; Beardmore et al. 2010; Ness et al. 2015; Sun et al. 2020; Pei et
al. 2021).

KT Eri is an interesting and unusual nova in a variety of ways: (1) Hounsell
et al. (2010) measured the first well-sampled light curve of the entire
initial fast rise of any nova. (2) This light curve (see inset of Figure 4 of
Hounsell et al. 2010) shows the best example of a pre-maximum halt. (3) KT Eri
shows two distinct flat plateaus in its light curve, in defiance of all prior
examples and outside the formal classification scheme (Strope, Schaefer, &
Henden 2010). (4) KT Eri has been picked out by various groups as having
properties that are hallmarks of being a recurrent nova (RN).

Despite this interest, previously, little was known about the system, and
nothing fundamental. That is, the nature of the companion star, the distance,
the binary orbital period, and the nova-to-nova recurrence time-scale were not
known with any reliability. To illustrate, the literature contains
identification of the companion star as an A7 III giant star, an M III red
giant, or a low-mass faint red main sequence star. To further illustrate the
previously unknown nature of both the eruption and the companion, it has been
claimed to be an ordinary classical nova (CN) inside the Period Gap by the big
catalog of Ritter & Kolb (2003), an RN with a very long orbital period (e.g.,
Raj, Banerjee, & Ashok 2013), while the official VSX catalog lists it as a “Z
And" symbiotic star and a likely eclipsing binary.

##  2 Observations

###  2.1 Photometry

Nova eruptions are defined and recognized by their brightness variations.
Photometry of the system serves to measure many of the critical system
properties. For this purpose, our group has measured a very large data set
across in $BVRIJHK$ bands from 1888 to 2020. Further, we have collected
magnitudes from the literature and from various public domain data
collections. A full listing of our photometry sources is presented in Table 1.
The explicit measures from all these sources is given in Table 2, with 9627
lines in the on-line version of the table.

Table 1: KT Eri photometry data sources

Telescope | Reference | Start Date | Start JD | End JD | Band | Number
---|---|---|---|---|---|---
Harvard (HCO) | This paper | 1888 Oct 19 | 2410929.8 | 2447564.9 | B | 139 (1200a)
Sonneberg | This paper | 1950 Oct 13 | 2433567.5 | 2453380.5 | B | 0 (700a)
ASAS | [1]; Pojmanski (1997) | 2000 Nov 20 | 2451868.7 | 2455166.6 | V | 53
Catalina | [2]; Drake et al. (2014) | 2005 Sep 7 | 2453621.2 | 2456580.0 | CV | 303
SMEI | This paper; Hounsell et al. (2010) | 2009 Nov 11 | 2455147.5 | 2455162.7 | CV | 159
Liverpoool | This paper; Hounsell et al. (2010) | 2009 Nov 13 | 2455149.5 | 2455216.4 | CV | 437
AAVSO | [3]; [4] | 2009 Nov 25 | 2455161.0 | 2459277.0 | UBVRI | 20, 148, 729, 84, 68 (26194b)
Torun | Ilkiewicz et al. (2014) | 2009 Nov 27 | 2455162.5 | 2455592.4 | BVRI | 9, 9, 9, 9
SMARTS | This paper, Walter et al. (2012) | 2009 Dec 3 | 2455168.7 | 2458694.9 | BVRIJHK | 936, 639, 635, 639, 431, 429, 461
PTF | [5]; Rau et al. (2009) | 2010 Sep 21 | 2455461.0 | 2456282.7 | R | 55
APASS | [6]; [7]; Henden et al. (2012) | 2011 Jan 29 | 2455590.6 | 2455880.7 | BVgri | 4, 4, 4, 4, 4
Cembra | Munari & Dallaporta (2014) | 2011 Sep 30 | 2455834.7 | 2456373.3 | BVRI | 118, 157, 113, 156
Rozhen | Ilkiewicz et al. (2014) | 2012 Oct 25 | 2456226.4 | 2456226.4 | BVR | 1, 1, 1
ZTF | [8]; Bellm et al. (2019) | 2018 Mar 29 | 2458206.6 | 2458881.7 | gR | 100, 100
TESS Sector 5 | This paper | 2018 Nov 15 | 2458438.0 | 2458464.1 | CI | 1181
Las Cumbres | This paper | 2019 Dec 17 | 2458834.9 | 2458926.0 | BVRI | 15, 14, 13, 13
TESS Sector 32 | This paper | 2020 Nov 20 | 2459174.2 | 2459200.1 | CI | 1223 (102757c)

aThis is the approximate plate count including those for which dates were not
recorded, most of which have KT Eri being invisible below the plate limit

bNightly averages of 26194 magnitudes are tabulated to avoid swamping the data
file

cThe full light curve has 102757 fluxes with 20 second time resolution, with
the tabulated light curve binned to near 1800 second resolution

References: [1] http://www.astrouw.edu.pl/asas/?page=aasc [2]
http://nunuku.caltech.edu/cgi-bin/getcssconedb_release_img.cgi [3]
https://www.aavso.org/data-download [4] https://www.aavso.org/tags/kt-eri [5]
https://irsa.ipac.caltech.edu/cgi-bin/Gator/nph-
scan?mission=irsa&submit=Select&projshort=PTF [6] https://www.aavso.org/aavso-
photometric-all-sky-survey-data-release-1 [7] https://www.aavso.org/download-
apass-data [8] https://irsa.ipac.caltech.edu/cgi-bin/Gator/nph-
scan?projshort=ZTF

Table 2: KT Eri photometry (full table with 9627 lines available on-line as supplementary material) HJD | Year | Magnitude | Unit | Source
---|---|---|---|---
2413218.5846 | 1895.068 | 15.0 $\pm$ 0.15 | B | HCO (A 1268)
2421163.7970 | 1916.821 | 14.5 $\pm$ 0.15 | B | HCO (MC 11394)
2421272.5132 | 1917.118 | 14.5 $\pm$ 0.15 | B | HCO (MC 12366)
2421522.8347 | 1917.804 | 14.4 $\pm$ 0.15 | B | HCO (MC 13859)
2421545.7706 | 1917.867 | 14.7 $\pm$ 0.15 | B | HCO (MC 14282)
… |  |  |  |
2459249.0000 | 2021.094 | 15.3 $\pm$ 0.0 | V | AAVSO
2459257.0000 | 2021.116 | 15.3 $\pm$ 0.0 | V | AAVSO
2459260.0000 | 2021.124 | 15.4 $\pm$ 0.0 | V | AAVSO
2459268.0000 | 2021.146 | 15.2 $\pm$ 0.0 | V | AAVSO
2459277.0000 | 2021.170 | 15.0 $\pm$ 0.0 | V | AAVSO

####  2.1.1 Eruption Light Curve

The eruption light curve is presented in Figure 1. The fast rise, peak, and
initial decline are almost entirely covered by the light curves from the SMEI
satellite (Hounsell et al. 2010). The SMEI instrumental response was that of
an unfiltered CCD calibrated with V magnitudes of 17 bright stars around the
ecliptic (Buffington et al. 2007; Hick, Buffington, & Jackson 2007). The start
date of the eruption was 2009 November 13.12 UT (JD 2455148.62) at magnitude
8.44$\pm$0.09. The pre-maximum halt in the fast rise towards maximum occurred
at magnitude 6.04$\pm$0.07 starting on 2009 November 13.83 UT (JD
2455149.33$\pm$0.04) and lasted for roughly 0.14 days. Pre-maximum halts have
the theoretical explanation as a “temporary drop in the energy flux as
convection in the expanding, thinning envelope ceases to be efficient near the
envelope surface" (Hillman et al. 2014). The peak was at a magnitude of
5.42$\pm$0.02 on 2009 November 14.67 UT (JD 2455150.17$\pm$0.04). The peak
magnitude and time are placed into one summary table (Table 3), with this
serving as a collection place for all the critical properties of KT Eri.

Figure 1: Eruption light curve for KT Eri. All V-band observations are shown
by the green diamonds, and all B-band observations are shown as small blue
circles, with the data sources listed in Table 1. The two color light curves
are largely superposed on each other. The SMEI light curve shows a nicely-
resolved fast rise, a pre-maximum halt, the fast peak, and the rapid initial
decline. (A blow-up figure around the peak is shown in Hounsell et al. 2010.)
Startlingly, two plateaus are prominent in the light curve, with this being
unprecedented. The star returned to the pre-eruption quiescence level by
October 2011.

KT Eri took 6.6 days after maximum for the V-band light curve to decline by 2
mags, or $t_{2}$=6.6 days. The time needed to decline by 3 magnitudes from
peak, $t_{3}$, is 13.6 days for KT Eri. Specifying time-scales for large
magnitude drops will be required for evaluating the historical coverage for
prior nova eruptions. For this, $t_{5}$ is 61 days, $t_{6}$ is 80 days,
$t_{7}$=240 days, and $t_{8}$=277 days.

Table 3: Collected properties of KT Eri) Property | Value | Unit
---|---|---
Peak magnitude | 5.42$\pm$0.02 | mag
Peak date | 2455150.17$\pm$0.04 | JD
Light curve class | PP, very fast | -
Spectral class | He/N class | -
$t_{2}$ | 6.6$\pm$0.1 | days
$t_{3}$ | 13.6$\pm$0.5 | days
$t_{5}$ | 61$\pm$3 | days
$t_{6}$ | 80$\pm$3 | days
$t_{7}$ | 240$\pm$4 | days
$t_{8}$ | 277$\pm$4 | days
$t_{9}$ | 462$\pm$2 | days
$\langle V_{pre}\rangle$ | 14.5 (13.5 to 15.8) | mag
$\langle V_{post}\rangle$ | 15.06 (13.88 to 15.84) | mag
$V_{post}$-$V_{pre}$ |  $+$0.56 $\pm$ 0.3 | mag
Nova amplitude | 9.1$\pm$0.2 | mag
No eruptions | 1928–1954, after 1969 | year
$T$ companion star | 6200$\pm$500 |  $\degr$K
Radius of companion star | 3.7 $\pm$ 0.3 | R⊙
$K$ | 58.4$\pm$7.0 | km s-1
$\gamma$ | -142$\pm$5 | km s-1
Epoch of conjunction | 2455491.323$\pm$0.053 | HJD
Orbital period $P$ | 2.61595$\pm$0.00060 | days
Orbital inclination | 52$\pm$5 | $\degr$
Distance | 5110${}^{+920}_{-430}$ | parsecs
$E(B-V)$ | 0.082$\pm$0.003 | mag
$A_{V}$ | 0.254$\pm$0.008 | mag
Mass of companion star | 1.0 $\pm$ 0.2 | M⊙
$M_{WD}$ | 1.25$\pm$0.03 | M⊙
$M_{V_{peak}}$ | -8.38$\pm$0.25 | mag
Century-long $\langle V_{q}\rangle$ | 14.5$\pm$0.2 | mag
Range $\langle V_{q}\rangle$ | 14.0 to 15.3 | mag
Century-long $\langle M_{V_{q}}\rangle$ |  $+$0.70$\pm$0.3 | mag
Range $\langle M_{V_{q}}\rangle$ |  $+$0.2 to $+$1.5 | mag
Century-long $\langle\dot{M}\rangle$ | 3.5${}^{+1.8}_{-1.2}$$\times$10-7 | M⊙/year
Range $\langle\dot{M}\rangle$ | (0.83–8.2)$\times$10-7 | M⊙/year
$\tau_{rec}$ | 40–50 | years

The eruption light curve shows a prominent plateau, an interval where the
light curve suddenly stops its decline for a significant interval. That is,
from days 80–190 after maximum, KT Eri had a nearly constant brightness at
$V$$\approx$11.6. On this basis, we would classify KT Eri as being a ‘P’ class
nova light curve (see Strope et al. 2010). However, KT Eri also has a second
prominent plateau from 300–440 days after peak, where KT Eri is constant at a
magnitude of $V$=14.1. A second plateau in any nova light curve was completely
unprecedented at the time.111This was the first time in which any nova light
curve did not exactly fit into the light-curve-classification system. Even
though the number of plateaus required for a ‘P’ classification was not
specified, the possibility of a second plateau was not conceived. Only after
KT Eri’s eruption did both U Sco and V339 Del display two plateaus. A simple
solution for the classification system is that any nova with a second plateau
is still labelled as ‘P’. Alternatively, it might be helpful to distinguish
this two-plateau case, in which case we could define a subclass labelled as
‘PP’. The important point is that KT Eri displayed an entirely new phenomenon,
and such needs an explanation. Theoretical studies with full physics have
produced plateaus, and some of the models produce two plateaus (Hillman et al.
2014).

####  2.1.2 Pre-Eruption Light Curve

The pre-nova system of KT Eri was quickly identified as a $V$$\sim$15 mag star
exhibiting 1.8 mag of variability (Drake et al. 2009). Jurdana-Šepić et al.
(2012) examined 1012 archival photographic plates dating from 1888 to 1962. KT
Eri was invisible on 517 of these plates, with typical limits of 13th mag. KT
Eri was detected on 495 plates, mostly from 1925 to 1953, and only three
detections before 1925. The native plate sensitivity is close to the Johnson B
magnitude system, therefore with comparison stars in the Johnson B-band, the
magnitudes returned are closely in the modern B system. A primary goal was to
search for prior eruptions. (Various workers had pointed to similarities
between KT Eri and recurrent novae, and this provided a good motivation to
search for eruptions in the prior century.) No undiscovered nova events were
turned up. Unfortunately, the magnitudes are not quoted in the paper, nor
available elsewhere, and details (like a claimed photometric periodicity)
cannot be tested with the given light curve.

We have sought pre-eruption images of KT Eri in many archival sources
worldwide. Roughly 1200 useful plates were found at Harvard for the years
1888–1989, many of which were not deep enough to record KT Eri. Roughly 700
useful plates were found at Sonneberg for the years 1950–2009, with most of
the plates yielding non-detections. The goal was not to measure a light curve,
but rather was to quantify the lack of prior eruptions. Thus, all these plates
were looked at individually for KT Eri being bright, but only the dates and
limits of plates at the start and end of each observing season were noted.
Almost incidentally, 139 B magnitudes were measured for Harvard plates from
1888–1989.

Our Harvard light curve can be used to test for long term trends before
eruptions. (The Hibernation model predicts systematic pre-eruption
brightening, but the time-scale for this is tens-of-thousands of years, see
Hillman et al. 2020. Still, few nova can be tested back as far as KT Eri, then
it is worthwhile to look for anything surprising.) No long term pre-eruption
trends are seen. Another result from this light curve is that the claimed 737
day periodicity (Jurdana-Šepić et al. 2012) was not recovered. This is not
surprising because the claimed period is close to exactly-two-years, with this
being a common indication of a spurious periodicity related to the data
sampling.

Figure 2: Pre-eruption light curve for KT Eri. The Harvard $B$-band magnitudes
are displayed as blue diamonds, the ASAS $V$-band magnitudes are in dark green
diamonds, and the Catalina $CV$ magnitudes are shown by light green circles.
Importantly, for comparison with the $V$-magnitudes, the $B$-magnitudes need
to offset upward by $\langle$B-V$\rangle$=0.23, as taken from the post-
eruption data. One point from this figure is that KT Eri shows no significant
long term trends for over a century before its eruption. Another point is that
KT Eri varies greatly around its average of $\langle$V$\rangle$=14.5, from
around 13.5 to 15.8 mag in the $V$-system. Another point is that there are
yearly and decadal variations in the quiescent level.

We have collected pre-eruption magnitudes from Harvard, from ASAS, and the
Catalina Sky Survey, see Fig. 2. KT Eri displays extreme variability, roughly
from 13.5 to 15.8 mag in the $V$-band. Substantial changes are seen in the
yearly and decadal averages. For example, $\langle$B$\rangle$ is 14.19 in the
1920s, 14.31 in the 1930s, 14.75 in the 1940s, and 14.56 in the 1980s, while
$\langle$V$\rangle$ ranges from 14.47 in 2000-2001 to 15.09 in 2005-2009.
However, no sustained or systematic trend are apparent from 1895 to 2009.

The pre-eruption brightness level has a number of important applications for
the consideration of the evolution of novae and cataclysmic variables in
general. For these applications, it is likely best to use the average
brightness level. With this, the pre-eruption magnitudes are $B_{pre}$=14.55
from the Harvard plates and $V_{pre}$=14.62 from the ASAS magnitudes. The $B$
magnitudes can be converted to $V$ magnitudes with the post-eruption
$\langle$B-V$\rangle$=0.23. The average magnitude depends on how the
magnitudes are averaged. The likely best method is to average the decadal
averages, with this avoiding biases towards the level of years with large
number of magnitudes. With this, the mean pre-eruption magnitude is 14.5 with
an uncertainty of roughly 0.2 mag. The amplitude of the nova eruption
($V_{pre}$-$V_{peak}$) is 9.1$\pm$0.2 mag. This is a rather low amplitude,
pointing to a high mass accretion rate and pointing to an RN status.

####  2.1.3 KT Eri Nova Eruptions Before 2009

No prior event was discovered. Our detailed search can be used to greatly
limit the fraction of time from 1888 to 2009 over which any eruption could
have happened without discovery. We have archival data from every year that
show KT Eri to not be in outburst. During each observing season, we always
have enough deep plates to prove that KT Eri could not have erupted. But this
still leaves the possibility that KT Eri erupted when it is inside the ’solar
gap’, that is, the seasonal interval around the time of its yearly conjunction
with the Sun. These solar gaps last for usually 4-6 months centred on May of
each year.

The solar gaps start with the last plate of each observing season (typically
around March of each year) and ends with the first plate of the next observing
season (typically around September of each year). If KT Eri had a nova
eruption that peaked one day after the start of the solar gap, then the last
plate of the prior observing season would not have detected any eruption.
However, it is possible that such an eruption would be detected in the tail of
its eruption by the first plate taken at the end of the solar gap. For
example, if the next observing season started with a photographic plate with a
limiting magnitude of $B$=14.5 with no KT Eri, than any eruption must have
been $>$460 days earlier, and this proves that no undiscovered eruption could
have popped off during the solar gap. Important for this analysis is the
strong result that all known RN eruptions from the same star have essentially
identical light curves (Schaefer 2010). If the first photograph of an
observing season has a relatively poor limit, say only that $B$$>$12.0, then
the peak of the undiscovered KT Eri eruption would have to be more than 163
days earlier, and this might not fill the solar gap if its duration is longer
than 163 days. In general, each year’s solar gap might have effective coverage
with any nova event during the gap being discovered, or there might be a short
interval at the start of the solar gap during which KT Eri might have peaked
yet producing no evidence of the eruption in the archival record. These
situations are illustrated in Fig. 3 for the decade of the 1950s.

Figure 3: KT Eri in the 1950s. Archival photographic plates from Harvard and
Sonneberg were examined for any prior eruptions, but none was found. Plotted
here are the recorded Johnson-B magnitudes for positive detections of KT Eri
in quiescence (blue circles) and for upper limits (blue triangles). Solar gaps
in our coverage (due to the Sun passing by Eridanus) extend typically for 4–6
months centred on May of each year. For all the years from 1927–1954, KT Eri
could not have erupted anytime within the solar gap without having been
positively observed far above its quiescent level by the first image taken at
the end of the gap. But in some years, the first plate at the start of the
next observing season is either relatively late or not particularly deep, and
a KT Eri nova event could slip into the start of the solar gap and remain
undiscovered. In the 1950s, there is an interval of 46 days in 1955, 54 days
in 1956, and 100 days in 1958 during which KT Eri could possibly have peaked
and the eruption would remain undiscovered. The plot shows the 2009 B-band
light curve as a template for fitting into a gap, with the short-dashed gray
curves showing the earliest possible peak in the three gaps, and with the
long-dashed light curve showing the latest possible peaks for the three gaps.
The point of this plot is to show how the archival data can be used to sharply
constrain possible dates for prior eruptions.

We have tabulated the lengths of the solar gaps given all of our collected
archival data for KT Eri. For the majority of years, the gap has been closed.
That is, observations demonstrate that any eruption peak inside the solar gap
would have been detected by the plate seeing KT Eri in the tail of the
eruption as far brighter than the quiescent level. Some of these remaining
gaps are short, while the longest gaps are 297 days starting in 1894, 349 days
starting in 1997, and 292 days starting in 2004. From 1928 to 1954, there are
no gaps at all, and this will become critical for our analysis and
conclusions. From 1888 to 2021, the total number of gap days is 2542, which is
5.2 per cent of the time. The number of uncovered days (and the fraction of
the total time) is given in Table 4 for a number of year intervals.

Table 4: Number of days during which KT Eri might have peaked in an undiscovered eruption Year range | Days not covered | Fraction
---|---|---
1888–1908 | 733 | 10.0%
1909–1927 | 586 | 8.9%
1928–1954 | 0 | 0.0%
1955–1969 | 325 | 6.4%
1970–1999 | 497 | 4.7%
2000–2009 | 400 | 12.2%
2010–2021 | 0 | 0.0%

If KT Eri is an RN, then its recurrence time ($\tau_{rec}$) must be less than
100 years.222This threshold of one century is the long-used traditional value.
But there is no physics reason to chose any specific dividing line between CNe
and RNe, as the systems form a continuum of recurrence times. One century is a
nice round number that is appropriate for the observational situation of
usually not having more than a hundred years of time for detecting nova events
from any single system. From Table 4, we could have missed an old eruption
from 1909–1927, for 82$<$$\tau_{rec}$$<$100 years. There is no possibility
that any old eruption could have peak in 1928–1954, hence $\tau_{rec}$ cannot
be from 55 to 82 years. This archival constraint allow $\tau_{rec}$$<$55
years.

Within the RN hypothesis, any $\tau_{rec}$$<$40 years or so would require
three or more missed eruptions. For example, a 40 year recurrence time-scale
would require undiscovered eruptions around the years 1889, 1929, and 1969. In
this case, the 1889 eruption could easily have been missed, but the joint
probability will be less than 1 per cent that all three events will fall into
coverage gaps. (Indeed, for the case of a 40 year recurrence time-scale, the
1929 eruption would have to have come at least two years earlier to avoid the
1927–1954 interval with no eruption possible.) The Galactic RNe are consistent
with something like a 20 per cent jitter in eruption intervals (Schaefer
2010), with the sole exception of T Pyx with a large secular trend for slowing
down (Schaefer et al. 2013). For a 30 year recurrence time-scale, the
undiscovered eruptions would have been around the years 1889, 1919, 1949, and
1979. In this case, the 1889 eruption could easily have been missed, but the
1919 and 1979 eruptions should likely have been discovered, and the 1949
eruption would have certainly been caught. With three-or-more lost eruptions,
the probability will be greatly less than 1 per cent that all the eruptions
just happened to peak inside one of our coverage gaps. The possibility that
$\tau_{rec}$ is less than $\approx$40 years can be rejected as requiring an
unacceptably-low probability in the eruption times so as to avoid any of the
prior eruptions being discovered.

####  2.1.4 Post-Eruption Light Curve

The post-eruption era starts when the light curve has stopped its decline and
gone flat, with this certainly after the middle of 2011. We have collected
magnitudes from our own SMARTS program, from the AAVSO data base, from the
APASS data base with time stamps, and from Munari & Dallaporta (2014), see
Tables 1 and 2. The V-band magnitudes are plotted in Figure 4.

Figure 4: Post-eruption V-band light curve for KT Eri. Our SMARTS magnitudes are displayed with light green circles, the AAVSO magnitudes are shown with dark green diamonds, and the V-band magnitudes from Munari & Dallaporta (2014) are in brown crosses. The eruption light curve is certainly over by mid-2011. One of the points to take from this diagram is that KT Eri displays variability by over 1.7 mags, with frequent swings in brightness by over one magnitude on a time-scale of 1–3 months. Another point from this diagram is that there exists no long photometric periodicity after the eruption is over, as confirmed with power spectra from discrete Fourier transforms. Table 5: SMARTS colors for KT Eri in post-eruption quiescence Color | Faintest | Average | Brightest
---|---|---|---
$\langle V\rangle$ | 15.84 | 15.06 | 13.88
$\langle B-V\rangle$ | 0.31 | 0.23 | 0.20
$\langle V-R\rangle$ | 0.33 | 0.25 | 0.14
$\langle R-I\rangle$ | 0.34 | 0.27 | 0.18
$\langle I-J\rangle$ | 0.13 | 0.05 | 0.07
$\langle J-H\rangle$ | 0.43 | 0.28 | 0.16
$\langle H-K\rangle$ | -0.08 | -0.05 | -0.01

The light curve is startling for its large amplitude of variations. The total
range of variations is over 1.7 mag, with many instances of where the
brightness steadily increases or decreases by over 1.0 mag over durations from
1 to 3 months. To the best of our knowledge, this extreme variability is
unprecedented for any nova in quiescence.

For purposes of calculating absolute magnitude for later use, there are a
range of post-eruption magnitudes that we can chose from. The average
$V$-magnitude after 2011.5 is 15.06 mag. The range of post-eruption
$V$-magnitudes is roughly 13.9 to 15.9. The associated colors are presented in
Table 5 for the 9 faintest nights, for the decadal average, and for the seven
brightest nights. The RMS scatter is close to 0.05 mag for all the colors.
When KT Eri brightens, its light gets slightly bluer, as appropriate for
adding light from the accretion disc that is bluer than the light from the
companion star.

The post-eruption light curve can be used to test prior period claims and to
search for new possibilities. For example, Munari & Dallaporta (2014) report a
752 day periodicity of apparently eclipse-like minima. This was based on the
pre-eruption light curve of Jurdana-Šepić et al. (2012) plus just one post-
eruption ‘eclipse’ (in 2012.87). Unfortunately, their pre-eruption light curve
was not reproduced by our measures, many of the claimed ‘eclipse’ times
display apparent flares, and no ‘eclipses’ are seen. Further, the predicted
eclipses of 2016.98 and 2019.04 are at times of maximum light, while the
predicted eclipse for 2014.92 misses a wrong-shaped minimum by two months.
That is, the period of 752 days fails badly.

We have searched for any plausible periodicity from 0.1 days to 5 years in the
post-eruption data. The extreme variability appears as flares and dips with
time-scales of 1–6 months. Such dips and flares can provide alluring
possibilities for periodicities to appear to the human pattern-recognition
ability. And indeed, a discrete Fourier transform does show high and isolated
peaks. The highest peak is for a period of 436 days. But this peak is just
created by the beating of the three most prominent dips (each with much
photometry). With the random alignment of these three dips, the folded light
curve looks like a noisy sine wave. But this best periodicity fails completely
because most of the other times of minima are certainly not near any observed
minima, while one is well centred on the highest flare. What is going on is
that a light curve with a modest number of random flares (or dips) will always
have sharp and high peaks in the Fourier transform caused by random alignments
of the flare times. In the context of Gamma Ray Bursts, Schaefer & Desai
(1988) calculate the probabilities that shot noise will produce spurious
periodicities, with this formalism applicable for the post-eruption flares of
KT Eri. The result is that even the best periodicities for the post-eruption
data are insignificant, merely being the result of pattern recognition in
random flare dates.

We have also looked for photometric periods from 0.04 days to 5 days (the full
range of nova orbital periods, excluding those four RNe with red giant
companions). No such periodicity was found. The noise confusion limit starts
for a full amplitude of 0.12 mag. In all, no significant period was found for
KT Eri.

####  2.1.5 TESS Light Curve

The Transiting Exoplanet Survey Satellite (TESS) covers 75–80 per cent of the
sky down to roughly 19th mag, where all covered stars have generated light
curves with 20 to 1800 second time resolution, all continuously for 26-day
intervals. This is perfect for finding orbital periods of novae (Schaefer
2021b).

TESS observed KT Eri for two separate intervals, called Sectors. Sector 5
started on 2018 November 15, with a duration of 26.6 days. For this Sector, KT
Eri was not targeted, and hence the only data available are the Full Frame
Images, taken continuously with exposures of 1800 seconds. Sector 32 started
on 2020 November 20 with a duration of 26.0 days. For this Sector, KT Eri was
targeted, which means that the small images around the target (called Target
Pixel Files) were read out and saved every 20 seconds, all as a non-stop time
series for 26.0 days, although with a one-day gap in the middle between
orbits. This is good for seeking both orbital and spin periods.

We went from the primary TESS data to the final light curves by using standard
tools and processing pipelines (Jenkins et al. 2016). Much of this was run
with the Lightkurve program (Lightkurve Collaboration, 2018). All of the data
and analysis programs are freely available at
MAST333https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html. In
essence, this is simply to perform aperture photometry on KT Eri for each
image. These images for photometry are small Target Pixel Files when extracted
every 20 seconds onboard the satellite during Sector 32 or extracted from the
Full Frame Images downloaded to the ground every 1800 seconds during Sector 5.
The TESS pixels are squares 21 arc-seconds on a side, where a centered pixel
will ensquare 50 per cent of the flux. We have used a 3$\times$3 array for our
photometry aperture as this includes typically 99 per cent the starlight. For
the case of KT Eri, no nearby stars provide significant extra flux into the
photometry aperture. The background is determined from star-less regions also
recorded in each Target Pixel File. This background does change substantially
throughout each spacecraft orbit of 13.7 days, due to scattered light. The
reported flux, in units of electrons per second, is simply the flux in the
aperture minus the scaled flux for the background. With the stability of the
spacecraft environment, this leads to very good photometric precision.
Nevertheless, small effects still arise, typically at the 0.001 mag level,
although sometimes the uncertainties can be substantially higher. These
effects are imperfect background subtraction and small spacecraft pointing
drifts that change the fraction of the target light inside the photometry
aperture. Further, we have rejected a small fraction of the fluxes for cause,
including single magnitudes flagged as being of lower quality (e.g., exposures
during a spacecraft ‘momentum dump’), and brief intervals often at the start
or end of orbits where the flux of all the stars changes systematically. There
are several standard tools for correcting for these small instrumental
artifacts, and in the case of KT Eri, these are in good agreement. The fully-
corrected fluxes are labelled as ‘pdcsap_flux’ with units of electrons per
second. The spectral sensitivity of the TESS CCDs runs from 6000–10000 Å. The
mid-exposure times are Barycentric Julian Dates (BJD).

For Sector 32, the full-resolution 20-second exposure light curve has 102757
fluxes from BJD 2459174.23289 to 2459200.11816. With this full-resolution, the
light curve follows a smooth curve with superposed flares, where the scatter
arises from ordinary Poisson variations. The light curve shows ordinary
flickering on time-scales from minutes to days.

The light curve for Sector 32 is shown in Figure 5. For display purposes, the
light curve is shown where the 20-second exposures are averaged together into
bins of size 0.02 days. The reason is that this beats down the ordinary
Poisson variations, all while not hurting the visibility of any orbital
modulation. This same binned light curve is placed into Table 2, to avoid
swamping the file with 102757 lines.

Figure 5: TESS light curve for Sector 32. Importantly, this Sector shows a
prominent 2.6 day periodicity. The period is coherent, as can be seen by the
maxima and minima all lining up with the red-triangular time markers that are
spaced at 2.61595 days. (This is the accurate period from the radial velocity
curve. However, this period is not accurate enough to produce reliable phases
across the intervening 9 years.) The bottom time markers are for the minima,
while the top markers are offset by half the period and they follow the times
of the light curve peaks. The shape of the peaks looks to be triangular, but
the folded light curve shows an apparent sine wave. The amplitude of the
orbital photometric modulations varies by roughly a factor of 4$\times$. The
periodicity is also prominent as an isolated very-high peak in the Fourier
transform, as shown in the inset panel which plots power in units of the
average power versus the frequency in units of cycles/day. This provides
precedent that KT Eri has a large and intrinsic change in amplitude on a time-
scale of days to weeks.

With the full resolution light curve, we have sought coherent photometric
periodicities with Fourier transforms, as shown in the inset in Fig. 5. The
period range of our full search was from 30 seconds up to 10 days. Only one
significant period was found, near 2.6 days. This period is very highly
significant. The power spectrum is displayed in the inset to Fig. 5. This
period is prominent and easy to see in the data (Fig. 5). KT Eri has its
maxima and minima faithfully following the ephemeris for a 2.6 day
periodicity. There is no doubt about the significance and existence of this
periodicity. With a photometric period of 2.6 days and its coherence, this can
only be the orbital period.

What is the uncertainty in the orbital period? The formal calculations for
four different methods (a chi-square fit to a sine wave, a Fourier transform,
and two periodogram methods) all give error bars of $<$0.00035 days, despite
these four methods returning $P$ values over a range of 0.021 days. These
error bars are greatly too small because the methods assume that the Gaussian
noise from point-to-point is uncorrelated, whereas the TESS light curve has
the noise around the average orbital modulation dominated by many large flares
(i.e., flickering). What is happening is that the flickering will shift the
apparent times of minima and maxima both earlier and later, depending on the
random timing, by $\sim$10 per cent of the period. Schaefer (2021a) proved
with TESS light curves for four cataclysmic variables that the ubiquitous
jitter in the minimum-to-minimum times is caused by this random flickering
causing random jitter of individual minimum times. We know of no formalism or
calculation that can give the period error bars in the presence of flickering.
But we can make an approximate estimate. Considering the first and last
minima, with each uncertain by $\sim$10 per cent of the period, the time
difference will be uncertain by $\sim$14 per cent, or $\sim$0.37 days for KT
Eri. With Sector 32 having 10 cycles, the uncertainty in $P$ will be
$\sim$0.04 days. We do not know which of the four methods is best, all we can
do is take some middle value, which is near 2.64 days. In all, Sector 32 has a
realistic period estimate of 2.64$\pm$0.04 days.

The Sector 32 light curve shows a prominent periodicity with a constant
period, but the amplitude of the modulation apparently changes significantly.
The light curve swings up and down by roughly 40 counts/second round the third
cycle, whereas this amplitude is roughly 10 counts/second in the eighth cycle.
It looks like some sort of a beating phenomenon where the amplitude varies at
a beat frequency. This variable amplitude of KT Eri has good precedents, as
described below.

The light curve for TESS Sector 5 began on BJD 2458440.5154 and ended on BJD
2458463.9114. This time series has exposure times of 1800 seconds, and there
are 1050 fluxes. These are plotted in Figure 6, and listed in Table 2.

Figure 6: TESS light curve for Sector 5. Importantly, this Sector shows no
significant periodicity, not for 2.6 days nor any other period. This can be
seen in the inset panel showing the Fourier transform, with the same scale as
the inset for TESS 32 in Fig. 5.

For both sectors, the formal 1-sigma measurement error is close to 1.4
counts/second (derived from the propagation of the Poisson uncertainties),
with this being substantially smaller than the point-to-point scatter in the
light curve. We know of no systematic problem or further measurement error
that operates from point-to-point, hence the observed scatter in the light
curve can only be intrinsic to the star. That is, on time-scales of faster
than half-an-hour, KT Eri is fast flickering with a RMS amplitude of 6
count/second (0.03 mag).

The Sector 5 light curves shows a number of small amplitude ups and downs with
time-scales of a day or so. It is natural to look at the relative spacing of
the flares and dips and try to form a periodic progression. But these maxima
and minima do not follow anything like a 2.64 day period. And these maxima and
minima do not form any apparent periodicity that is sustained throughout
Sector 5. A Fourier transform (see inset in Fig. 6) does, of course, have a
highest peak, and for Sector 5 it is at 3.23 days. But this peak has a maximum
power of only 39, which translates into a insignificant period. (This can be
compared to Sector 32, whose peak rose to a power of 256 for a similar time
resolution.) The insignificance is emphasized by the fact that neither of the
two orbits (halves) of Sector 5 produce a Fourier peak anywhere near to 3.23
days. To further emphasize the insignificance of this ‘best’ period, such
modulations are not apparent in the ups and downs of the light curve in Figure
6. So, Sector 5 is not showing the 2.64 day period, nor any other period.

####  2.1.6 Variable Amplitude

Superposed on the fast flickering, both sectors show ups and downs on days-
long time scales. In Sector 5, the average flux is 214 counts/second, and the
full amplitude of variation is roughly 30 counts/second (0.14 mag), all with
no significant periodicity. The formal amplitude limit at a period of 2.6 days
is close to zero, while even for a range of nearby periods, the signal is $<$3
counts/second ($<$0.014 mag for full amplitude). In Sector 32, the average
flux is 187 counts/second, with variations whose amplitude varies from 10 to
40 counts/second (0.06 to 0.24 mag). These variations are periodic with
$P$=2.64 days, and the amplitude appears to vary systematically in a manner
that looks like it could arise from some beating between two close periods.
Why are there these stark differences in variability amplitude between Sectors
5 and 32?

The changing amplitude cannot be a simple beating phenomenon. The reason is
that any ordinary interplay between two periods must have the duration of near
zero amplitude always at a constant. But Sector 32 shows a low amplitude for
only a few days, whereas Sector 5 shows a low amplitude for at least 23 days.

Could the changing amplitude arise from some extra light (say, from the disc)
being added in to swamp the periodic signal? Sector 5 is brighter on average
than Sector 32 by 25 counts/second, however the upper limit on the periodic
signal ($<$1.3 counts/second) is greatly below the range of periodic signals
from Sector 32 (10 to 40 counts/second). Adding extra light does not explain
the low amplitude in Sector 5.

To explain the low periodic amplitude in Sector 5, similar systems can provide
precedents. We know of only five novae that display highly variable amplitude
in their orbital modulations, and these are all with similar binary systems.
These five nova systems are in the very narrow class of novae with subgiant
companions with orbital periods between 1.2 and 3.5 days, many of which are
RNe. (1) The RN V394 CrA has periodic modulations on the orbital period (a
well-measured 1.5 days) that occasionally go away444We have extracted the TESS
light curve for Sector 13, and prominent eclipses appear with a period of 1.5
days. The amplitude goes from 0.045 mag on the first day, steadily decreasing
in amplitude for the next six orbits until there is no visible modulation at
all for the next 12 days, only to have the minima reappear with increasing
depth for the last three orbits.. This was known from extensive photometry
over many years from Cerro Tololo, with the variable amplitude being
perplexing. Even in the old days, it was recognized that the amplitude was
largest when V394 CrA was faintest, and the dips went away only when the star
was near its brightest (Schaefer 2010). V394 CrA provides a perfect precedent
for an RN with an orbit a bit longer than one-day having starkly variable
amplitudes, with 12-day-long intervals of zero amplitude, all tied to the
accretion rate, with the zero-amplitude intervals when the accretion rate is
highest. (2) Our second precedent is the recurrent nova V2487 Oph (Schaefer,
Pagnotta, & Zoppelt 2022). We observed this with the K2 mission of the Kepler
satellite and discovered an orbital period of 1.24 days. Over the 69 day
observing interval, the amplitude started out at a middle level, increased
steadily to day 15 (with amplitude near 0.08 mag), then steadily decreased in
amplitude to day 40, with a zero amplitude from day 40 until day 53, whereupon
the amplitude rose to near the maximum by the end of the run on day 69. V2487
Oph is a perfect precedent for a recurrent nova with a period just longer than
one-day for which the orbital modulations varied in amplitude from 0.08 mag
down to zero, with intervals of zero amplitude lasting for two weeks. (3) Our
third precedent is the recurrent nova U Sco with a very well measured orbital
period of 1.23 days and deep eclipses. During the late tail of the 2010
eruption, when the disc was reforming, deep intermittent ‘eclipses’ were seen
at all orbital phases (Schaefer et al. 2010). This was interpreted as the fast
varying splash from the accretion stream making a transient high outer edge of
the disc which caused the eclipse of the inner bright region near the white
dwarf. U Sco is a precedent and prior realization that an RN, with orbital
period just longer than one-day, has a variable height of the outer edge of
the disc, making for rapidly changing amplitude of the orbital modulation. (4)
Our fourth precedent, and the only non-RN system, is V407 Lup, a nova from
2016. The TESS light curves from Sector 12 and 38 have a period of 3.57 days
(Schaefer 2021b). Inside both sectors, the amplitude appears to vary
substantially, although with relatively few orbits in each Sector, this is
difficult to be exacting. Between the two Sectors, the amplitude changes from
2.6 to 0.8 counts/second. V407 Lup is not an RN because its accretion rate is
too low. (5) Our fifth precedent for the Sector 5 orbital amplitude being zero
is KT Eri itself, in Sector 32. That is, KT Eri has already displayed
amplitude changes from 0.24 mag down to 0.06 mag. KT Eri itself provides the
precedent that such systems have highly variable photometric oscillations on
the orbital period, and it is not surprising that Sector 5 can show an
interval with zero amplitude.

This is prior and strong precedent that a very narrowly defined class of nova
systems has large variations in the amplitudes of their orbital modulations.
These precedents are all for nova systems with orbital periods from 1.2 to 3.5
days, and a reasonable idea would be that the conditions necessarily have a
narrow range of disc sizes over which the effects are observable. We know of
no cases of large changes in amplitude outside of this very narrow range of
periods. However, for nova systems inside the 1.2$<$$P$$<$3.5 day range, V2109
Oph, and V392 Per (Schaefer 2021b), as well as GK Per do not display variable
amplitudes.

###  2.2 Spectral Energy Distribution

Munari & Dallaporta (2014) report a spectral energy distribution (SED) for KT
Eri in quiescence. Their seven input magnitudes were their own post-eruption
BVRI measures plus the pre-eruption JHK measures from the 2MASS survey. They
also point out that the WISE infrared magnitudes showed KT Eri only during the
tail of the eruption, and these points could not be added to the SED for
quiescence. Their SED plot shows a power law with modest curvature. They fit
the SED as being that of an A7 III star at 5 kpc distance. This fit has three
major problems: First, the optical and infrared parts of the SED were taken a
decade apart, and KT Eri varies greatly by up to two magnitudes during
quiescence, hence their overall shape of the SED is inevitably skewed with a
likely-large offset from the optical to infrared in the reported SED. Second,
the spectral model includes no disc contribution to the SED, yet the disc
component is very bright, dominating over the companion star. Third, their SED
covers the frequency region where the disc light is switching from the
$F_{\nu}\propto\nu^{1/3}$ slope to the Rayleigh-Jeans region with a slope for
$F_{\nu}\propto\nu^{2}$, while the disc spectrum shows curvature that looks
much like that displayed in Figure 3 of Munari & Dallaporta (2014). That is,
their fit is not measuring the temperature of a blackbody-like companion star,
but rather is telling us about the accretion disc.

We have constructed our own SEDs, with all three of these problems being
solved. Critically, we have complete sets of $BVRIJHK$ photometry from 272
nights with KT Eri in quiescence (from July 2011 to April 2019). All
magnitudes from each night were taken within a ten minute interval, indeed
with many pairs of magnitudes taken simultaneously. With this, we have
constructed SEDs for many individual instances, for seasonal averages, for KT
Eri at its brightest, and for KT Eri at its faintest. With the averaging of
many nights data together, the photometric error bars become small, allowing
for good spectral model fits. Further, we have made model fits as a realistic
$\alpha$-disc plus a companion star.

Our SEDs are constructed from the SMARTS data set, with the ANDICAM instrument
on the Cerro Tololo 1.3-m telescope. (ANDICAM uses a dichroic mirror such that
the optical and infrared images are taken simultaneously.) The RMS scatter of
magnitudes for seasonal averages in all of the bands is typically one-third of
a magnitude, hence the uncertainties on the average magnitudes are usually
around 0.05 mag. The conversion from magnitudes to fluxes (in units of Jansky)
uses the calibrations adopted in Schaefer (2010). The extinction correction
was made with $E(B-V)$=0.08 mag, and hence $A_{V}$=0.25 mag, as taken from
Ragan et al. (2009). Many of our SEDs are plotted in Fig. 7.

Figure 7: KT Eri spectral energy distribution in post-eruption quiescence.
These SEDs show the flux levels ($F_{\nu}$ in Janskys) as a function of the
central photon frequencies ($\nu$ in Hertz) for the K, H, J, I, R, V, and B
bands (from left to right). These SEDs are the summation of the disc light
plus the blackbody light from the companion star. The top red curve shows the
average SED for the 7 brightest nights (all with $V$$<$14.21), and the bottom
red curve shows the average SED for the 9 faintest nights (all with
$V$$>$15.77) The middle curves show the seasonal average SEDs from 2011/2012
to 2018/2019. KT Eri has an extreme amplitude of variation in quiescence. The
curvature and the peak near the R-band are from the blackbody of the companion
star. These SEDs are fit to a model with a standard $\alpha$-disc model plus a
blackbody for the companion star. In the faint-state, the effective
temperature is 6200$\pm$500 K.

Our SEDs show the huge range of variation for KT Eri. At the top is the SED
for the 7 brightest nights (with $V$$<$14.21), for which the accretion disc
dominates over the companion star. At the bottom is the SED for the 9 faintest
nights (with $V$$>$15.77), for which the blackbody spectrum of the companion
star is seen on top of the power law of the accretion disc. Between these
extremes are 8 SEDs for the seasonal averages from 2011/2012, 2012/2013, … ,
2018/2019. The shape of the SEDs has a steady progression from the companion-
star-dominated faint state to the accretion-disc-dominated bright state.

Our SED model consists of a disc component plus a companion star component.
The disc component is taken as the standard $\alpha$-disc model (Frank, King,
& Raine 2002). For this, we have performed the full integration over blackbody
annuli from the white dwarf surface to the outer edge of the disc near the
Roche surface. The primary unknown fitting parameter is the accretion rate,
$\dot{M}$, but its use here is merely to get a realistic curvature in the
model SED. This calculated disc flux is then multiplied by an arbitrary
normalization factor that absorbs many uncertainties (including the
inclination and distance). The companion star is represented by a simple
blackbody of temperature $T$, with the normalization allowed to freely vary.
This model has four fitting parameters, the two normalization constants for
the power law and the blackbody, plus the blackbody $T$ and the disc
$\dot{M}$. Our fitting procedure is to adopt a value for $T$ and $\dot{M}$
over a large grid of values, vary the two normalization factors until the chi-
square is minimized, then the best grid position can be recognized. Our use of
the two arbitrary normalization factors means that the fit is to the shape of
the SED by adding two distinct shapes (for the disc and for the companion),
with this allowing the recognition of the relative sizes of the two
components. Further, this allows us to pick out the companion star’s component
and recognize the Wien peak and measure the surface temperature.

The model fit for KT Eri at its faintest will provide the best measure of $T$.
In this extreme state, the observed brightness has an average of $V$=15.84.
This best-fitting value is 6200 K. The error bar is uncertain due to not
knowing all the intrinsic variations, as well as possible variants on the disc
model (like truncating the disc far inside the Roche surface), but it appears
to be roughly $\pm$500$\degr$. From B to I to K bands, the model places the
companion star as 1.4$\times$, 3.1$\times$, and 2.5$\times$ the brightness of
the disc. With KT Eri in its extreme faintest state, the disc light only
provides roughly one-third of the system light. In the V-band, the correction
from the observed magnitude to a disc-only magnitude is 1.25 mag.

An important point from the SED gives the fundamental nature of the companion
star. With $T$=6200$\pm$500 K, the companion is too hot to be a main sequence
star in any cataclysmic variable. For any such companion, the star must have
already evolved off the main sequence, and the consequent orbital period must
be larger than 0.5 days or so.

Further, the size of the companion can also be measured from the SED with a
calculation of its blackbody radius. For the Gaia distance and our SMARTS SED
with KT Eri at its faintest, subtracting out the disc light modeled as an
$\alpha$-disc, the radius is roughly 3 R⊙. This is the size of a subgiant star
of the measured temperature, therefore, the companion star must have evolved
far off the main sequence.

The SED for KT Eri in its average state is taken as that of the 2018/2019
observing season (see Fig. 7). This middle SED has the observed V-magnitude of
15.00. This SED was fit with the same model, with the $T$ and the blackbody
normalization factor held constant with the fit for KT Eri at its faintest. We
got a surprisingly close fit by only varying the $\dot{M}$, where the
accretion apparently increased by a factor of 14$\times$ from the faintest
state to the middle state. By our fits adding up differently shaped components
in the SED, we can distinguish what fraction of the light comes from the disc
and companion as a function of the band. From the B to I to K bands, the ratio
of the fluxes from the companion star to the accretion disc is 0.23$\times$,
0.57$\times$, and 0.80$\times$ respectively. In its average middle state, KT
Eri has the accretion disc dominating roughly by a factor of 2:1. For critical
use later, in the V-band, the correction from the observed magnitude to the
disc-only magnitude is 0.34 mag.

KT Eri in its extreme high-state is taken from the 7 brightest nights out of
all our 272 post-eruption simultaneous SEDs. For these nights, the average is
$V$=13.88, without extinction correction. This SED (of course with extinction
correction) is displayed as the top red curve in Fig. 7. Our model fit uses
the parameters for the companion star as unchanged from the values derived for
the extreme-faint state. The disc parameters were freely varied until the sum
of the two components matched the observed shape of the SED. This allows us to
distinguish the relative fluxes from the disc and the companion. To match the
shape of the SED, the disc component must dominate greatly over the companion
star’s blackbody. Our specific best-fitting ratio of the fluxes from the
companion star to the accretion disc is 0.09$\times$, 0.21$\times$, and
0.28$\times$ for the B, I, and K bands respectively. That is, roughly the disc
dominates over the companion by roughly 4:1. In the V-band, the fraction of
light in the disc makes for a difference in the observed magnitude and the
disc-only magnitude of 0.14 mag. This correction will become important later
in this paper for use in determining the accretion rate.

###  2.3 Radial Velocity Curve

Munari, Mason, & Valisa (2014) present 67 radial velocities (from 19 nights)
for the He II 4686 Å line. The radial velocities vary from -259 to -38 km s-1.
However, the velocities change greatly from exposure to exposure on short time
scales. For example, on one night, the radial velocity changed by 65 km/s in
16 minutes. This makes it likely that non-orbital velocity variations (from
measurement error or intrinsic to the star) are at this level. With this
scatter being similar to the $K$ velocity and with only 19 times of
measurements, no significant periodicity was found in a Fourier transform. The
power spectrum shows many low peaks, with many near the top power, and no
period is significant.

We have also constructed a radial velocity curve for the He II 4686 Å line
with our SMARTS spectra (Walter et al. 2012). We have 109 measures from 108
nights from early 2010 to late 2011, all with the RC Spectrograph on the Cerro
Tololo 1.5-m telescope, as reported in Table 6. A Fourier transform shows a
highly significant peak at a period of 2.61575 days. (There is a peak with
significantly lower power for the period 1.611084 days, with this being an
artifact from the window function, where the two frequencies add up to exactly
one-per-day. Our highest peak corresponds exactly with the second highest peak
in the fourth highest cluster of peaks in the Fourier transform of the Munari
et al. data.) A formal chi-square fit with a sinewave gives
2.61595$\pm$0.00060 days.

The folded radial velocity curve is consistent with a circular orbit, with the
middle value ($\gamma$) equal to $-$142$\pm$5 km s-1. The epoch of crossing
$\gamma$, going more positive, is JD 2455491.323$\pm$0.053, with this
corresponding to the conjunction with the white dwarf in front of the
companion star. The K amplitude is 58.4$\pm$7.0 km s-1.

Table 6: KT Eri radial velocity data for He II 4686 Å line HJD | Velocity (km/s) |  | HJD | Velocity (km/s)
---|---|---|---|---
2455206.500 | -116 |  | 2455511.650 | -203
2455210.565 | -214 |  | 2455513.679 | -163
2455211.586 | -156 |  | 2455515.695 | -113
2455212.531 | -86 |  | 2455516.623 | -230
2455215.582 | -69 |  | 2455522.587 | -193
2455217.551 | -79 |  | 2455524.741 | -195
2455222.551 | -69 |  | 2455527.574 | -250
2455223.553 | -116 |  | 2455532.551 | -193
2455224.523 | -71 |  | 2455537.546 | -246
2455228.521 | -124 |  | 2455543.535 | -138
2455229.500 | -190 |  | 2455544.542 | -168
2455232.526 | -100 |  | 2455549.525 | -125
2455234.527 | -161 |  | 2455550.525 | -179
2455245.500 | -125 |  | 2455553.550 | -183
2455246.527 | -33 |  | 2455560.558 | -219
2455249.518 | -103 |  | 2455562.546 | -97
2455251.527 | -37 |  | 2455591.531 | -90
2455255.509 | -177 |  | 2455593.539 | -95
2455261.552 | -44 |  | 2455597.550 | -180
2455264.521 | 26 |  | 2455602.527 | -141
2455265.514 | -197 |  | 2455605.518 | -183
2455269.501 | 73 |  | 2455607.553 | -104
2455273.500 | -36 |  | 2455609.597 | -92
2455276.494 | -98 |  | 2455615.564 | -115
2455279.489 | -131 |  | 2455616.518 | -154
2455279.500 | -23 |  | 2455619.524 | -96
2455282.489 | -16 |  | 2455623.526 | -139
2455285.484 | -16 |  | 2455625.504 | -79
2455286.519 | -191 |  | 2455626.539 | -154
2455287.481 | -72 |  | 2455628.501 | -95
2455290.480 | -78 |  | 2455633.496 | -117
2455299.491 | -139 |  | 2455637.541 | -180
2455304.500 | -171 |  | 2455641.489 | -89
2455312.468 | -195 |  | 2455647.493 | -143
2455392.942 | -129 |  | 2455651.489 | -57
2455396.930 | -199 |  | 2455655.386 | -200
2455405.500 | -155 |  | 2455764.932 | -232
2455411.917 | -224 |  | 2455768.904 | -148
2455416.898 | -218 |  | 2455772.902 | -238
2455425.867 | -184 |  | 2455783.895 | -209
2455428.893 | -141 |  | 2455785.861 | -185
2455431.836 | -144 |  | 2455801.815 | -246
2455451.795 | -217 |  | 2455818.816 | -173
2455456.764 | -208 |  | 2455820.794 | -233
2455460.837 | -152 |  | 2455824.804 | -182
2455471.721 | -176 |  | 2455830.764 | -257
2455476.705 | -177 |  | 2455834.712 | -134
2455481.748 | -179 |  | 2455838.803 | -299
2455484.832 | -179 |  | 2455840.784 | -166
2455488.676 | -157 |  | 2455844.724 | -97
2455489.801 | -141 |  | 2455854.717 | -225
2455499.743 | -99 |  | 2455858.659 | -104
2455501.822 | -109 |  | 2455864.707 | -208
2455507.776 | -121 |  | 2455871.614 | -54
2455509.750 | -145 |  |  |

##  3 Analysis

###  3.1 Orbital Period

KT Eri has many published photometric periodicities. These include 35.09
seconds, 0.0938 days, 56.7 days, 210 days, 376 days, 737 days, 750 days, and
752 days, as well as quasi-periodic oscillations at 3530, 3809, 6560, and
10440 seconds. These claims were all dubious to begin with, and critically,
all have been subsequently disproven with further data extending the light
curves. The long periods were derived from much the same data set, being
variations and aliases of each other. and are suspiciously close to multiples
of the primary sampling period of one year. Critically, these periods are not
reproduced when the same data source is independently examined with Fourier
transforms, and the spectrum in quiescence does not show a red giant companion
as required for such long periods. The claimed quasi-periodic oscillations
have the observations only covering 1.2–2.1 cycles, with just two
maxima/minima recorded, and a periodicity was claimed. We have used the TESS
light curve to search for significant broad-band power over a wide range of
frequencies, and no significant periodicity was found. The reported X-ray
periodicity of 35.09 seconds was never significant, even by the reckoning of
the claimants, as post facto data selection of a fraction of the light curve
was required to get the confidence level of the periodicity up to 90 per cent,
i.e. a 1.6-sigma detection even without accounting for the selection. We have
searched the TESS light curve for periodicities or quasi-periodicities from
30–40 seconds, with none being found down to the noise limit of 0.0029 mag.
The 56.7 day claim was based on only 3.5 cycles of data, and the 210 day claim
was reported despite the authors stating "this detection does not appear to
have high significance". KT Eri has a poor history for claimed periodicities.

For KT Eri, both TESS and radial velocity data have produced highly confident
measures of the orbital period. These independently agree that the orbital
period is near 2.6 days. The radial velocity curve ensures that the orbital
period is not double the optical modulation period due to ellipsoidal effects.
The two measures of $P$ are consistent to within their uncertainties. We adopt
the more precise period from the radial velocity curve,
$P$=2.61595$\pm$0.00060 days.

This new $P$ measure has a variety of deep implications: (1) One implication
is that the companion star must be an evolved star as required to fill up its
large Roche lobe. For a white dwarf mass of 1.25 M⊙ and a companion mass of
1.0 M⊙, the Roche lobe radius is 3.7 R⊙, while the two star centres in the
binary are separated by 10.4 R⊙. This radius is too small for a red giant and
too large for any of the usual low-mass main sequence companion stars. A 6200
K star of that size would be a subgiant ‘recently’ evolved off the main
sequence. (2) A second implication of our new long-period is that we have no
understanding of why KT Eri has such a high accretion rate. Models of
cataclysmic variable evolution (e.g., magnetic-braking) are not applicable to
binaries with $P$$>$7 hours, and the $P$=2.6 days of KT Eri means that the
dominant source of angular momentum loss in the binary is unknown. Is the
accretion driven by the angular momentum loss in the binary, or by the
evolutionary expansion of the companion? And why does KT Eri have such a high
accretion rate, while other similar systems (e.g., GK Per) have greatly lower
rates? (3) A third implication is to realize we have no detailed idea of the
evolution of KT Eri. Most nova systems have periods between 0.05 days and 0.5
days (with nearly-main-sequence companion stars), while no published model of
cataclysmic variable evolution applies to systems with evolved companion
stars. Presumably, the system started out as an ordinary detached binary, the
more massive star evolved to become a white dwarf, later the companion started
evolving off the main sequence, the Roche lobe overflow started, hence
reaching the situation seen today. With the observed high $\dot{M}$, the
current state of KT Eri cannot last for longer than a few million years. The
ultimate fate of KT Eri depends critically on whether $M_{WD}$ is increasing
towards the Chandrasekhar limit. (4) A fourth implication is that a 2.6 day
period makes KT Eri look a lot like an RN. Amongst Galactic RNe, 80 per cent
have unusually long orbital periods (Schaefer 2010), whilst only 13 per cent
of CNe have periods longer than 0.6 days (Pagnotta & Schaefer 2014). (And we
expect that many of the long-period CNe are simply RNe with the second
eruptions in the prior century having been missed.) On the face of it, this
makes for a reasonably high expectation that KT Eri is a recurrent nova.

###  3.2 Orbital Inclination

The inclination of the binary’s orbital plane is needed for a variety of
calculations. Ribeiro et al. (2013) presented a model reproducing the fine
structure in the emission line profiles during the eruption. That is, the
ejecta has some reasonable presumed symmetry tied to the orbital plane, with
the orientation of the axis of symmetry likely pointing along the pole of the
binary orbit. Their morpho-kinematical study of the H$\alpha$ line profiles
points to a dumbbell structure with a 4:1 axis ratio and an inclination angle
of $58^{+6}_{-7}$ degrees. This is a reasonable estimate, although it could be
easy to dismiss this value as being produced by an arbitrary and simplistic
model for the ejecta.

Further, three constraints can be placed on the inclination: (1) The first
constraint is that no eclipses are seen in the TESS light curve. For the
expected stellar masses with an orbital period of 2.6 days, this translates
into a limit that the inclination must be less than 69$\degr$. For all
plausible stellar masses, this limit varies by only 2$\degr$. (2) The second
constraint is that the TESS light curve shows the orbital modulations to have
a full amplitude of 0.115 mag. Such an amplitude rules out the binary orbit
appearing nearly face-on. A calculation of the amplitude expected as a
function of inclination would require a very detailed geometry model plus a
full knowledge of the irradiation of the companion star. We are not able to do
this calculation, yet it is reasonable to realize that the constraint will be
that the inclination must be larger than some threshold like 30$\degr$. (3)
The third constraint is our radial velocity curve, with $K$=58.4$\pm$7.0 km
s-1 and P=2.615 days. For the most likely values with $M_{WD}$= 1.25$\pm$0.03
M⊙ (see Section 3.7) and $M_{comp}$= 1.0$\pm$0.2 M⊙ (see Section 3.8), the
inclination is then 41$\pm$9 degrees.

For purposes of adopting an inclination for use with the analysis of the
radial velocity curve to constraint the stellar masses in Sections 3.7 and
3.8, we cannot use the third constraint. For this purpose, the first two
constraints are not useful, and best value to use is just the 58${}^{+6}_{-7}$
degree inclination from Ribeiro et al. (2013).

For purposes of knowing the binary inclination to calculate the accretion
rate, we are allowed to adopt our independent white dwarf mass of
1.25$\pm$0.03 M⊙, and a plausible range of companion mass (0.8–1.2 M⊙). With
two useful inclination measures, $58^{+6}_{-7}$ degrees and 41$\pm$9 degrees,
we adopt a weighted average to get a final inclination of 52$\pm$5 degrees.

###  3.3 Extinction

The only reported extinction measure for KT Eri is $E(B-V)$=0.08 mag (Ragan et
al. (2009). Schlafly & Finkbeiner (2011) report that the extinction all the
way through our Milky Way galaxy along the line of sight to KT Eri has
$E(B-V)$=0.0821$\pm$0.0027. KT Eri is certainly at a distance far past
essentially all our galaxy’s dust, and hence this upper limit is really a
direct measure. With this, the extinction in the V-band is
$A_{V}$=0.254$\pm$0.008 mag.

###  3.4 Distance

Before Gaia, the distance to KT Eri was poorly constrained. The only basis
published was the so-called Maximum-Magnitude Rate-of-Decline (MMRD) relation
(e.g., Munari & Dallaporta 2014), but these are well known to be wrong by up
to nearly 10$\times$ in distance for similar systems (Schaefer 2018).
Fortunately, the Gaia spacecraft555https://archives.esac.esa.int/gaia has
recently measured an accurate parallax. The Gaia EDR3 data release (Gaia
Collaboration 2021; Lindegren et al. 2021) quotes the parallax as $\pi$ =
0.196$\pm$0.024 milli-arcseconds. With the usual simple calculation, the
distance is $(1000pc)/\pi$ with the parallax in milli-arseconds, for a
distance of 5100$\pm$620 pc. However, to best translate the parallax into a
distance, we must use the ‘exponentially decreasing space density’ (EDSD)
priors in a Bayesian calculation prescribed by the Gaia Team (Luri et al.
2018). This uses an exponential length, $L$, for which the vertical scale
height of 150 pc (corrected for the galactic latitude) is appropriate for the
disk population of cataclysmic variables (Patterson 1984), which gives $L$=280
pc (Schaefer 2018). With this expected $L$ value pulling to closer distances,
the EDSD calculation gives a distance of $D$=4350 pc, with a one-sigma range
from 4040 pc to 4860 pc. Bailer-Jones et al. (2021) return a similar result
($D$=4056$\pm$440 pc) for assuming that KT Eri follows a spatial distribution
like in their detailed galactic model.

However, this distance is greatly larger than the prior expectation of $L$=280
pc. This likely points to the standard prior expectation for KT Eri as being
wrong due to the nova not following the distribution of all the other disk
novae. But we cannot just adopt $L=(1000pc)/\pi$, because this would be a
circular bias. Perhaps the most reasonable approach is to use the additional
prior information that the peak absolute magnitudes of novae are in the range
$-$7.0$\pm$1.4 (Schaefer 2018). With extinction correction, this points to a
distance of 2700 pc (with a one-sigma range of 1400–5100 pc). For $L$=2700 pc,
then the EDSD calculation gives $D$=5110${}_{-430}^{+920}$ pc, and this is
what we adopt.

###  3.5 Absolute Magnitudes

The absolute magnitude is important for determining the accretion rate in KT
Eri. Fortunately, we have a good distance from Gaia and the extinction has
small uncertainty. This gives $M_{V}$=$V$-13.80$\pm$0.25.

With $V_{peak}$=5.42$\pm$0.02, then $M_{V_{peak}}$ equals -8.38$\pm$0.25. This
is quite ordinary for nova eruptions, although a bit on the luminous side
(Schaefer 2018).

For the application of finding the average $M_{V}$ over the eruption cycle, it
is best to use the average V-magnitudes from 1895 to 2021 in quiescence. The
B-magnitudes are converted to V-magnitudes with the average post-eruption
$\langle B-V\rangle$=0.23. The V-band magnitudes were 14.77 in 1895, 14.30 in
the 1910s, 13.96 in the 1920s, 14.08 in the 1930s, 14.52 in the 1940s, 14.85
in the early 1950s, 14.33 in the 1980s, 14.47 in the early 2000s, 15.09 in the
last half of the 2000s before the eruption, and 15.06 in the decade after the
end of the eruption. With the vagaries of sampling, it is difficult to come up
with a formal average or uncertainty. For example, if we took a straight
average, then this would heavily bias to faint magnitudes because the post-
eruption decade has a very high density of magnitudes while it just happens to
be systematically fainter than pre-eruption intervals. A fairer method to find
the century-long average magnitude would be to average the decadal averages.
Even this has a variety of reasonable calculations, for example by using the
average or median, and whether or not we combine the separate values from the
early and late decade starting in 2000. Fortunately, all these methods return
a middle or average value of $\langle V_{q}\rangle$=14.50 for the entire
century-long light curve. With the large variability in the intrinsic light
curve and our sampling, the various ways to calculate the error bar are not
convincing, yet such attempts return values close to $\pm$0.20. This century-
long average magnitude of 14.5$\pm$0.2 translates to an absolute visual
magnitude of $\langle M_{V_{q}}\rangle$=0.7$\pm$0.3.

In Sections 3.6 and 3.9, we will be needing a range of absolute magnitude that
is representative of the variations. Above in this paper, we have presented an
array or maximum and minimum values of $\langle V_{q}\rangle$ for various time
intervals and for averaged or extreme magnitudes. For purposes of calculating
the recurrence time scale, the extremes are not appropriate, the decadal
averages are hiding the times of high and low accretion, while we cannot
select just the pre-eruption or post-eruption intervals. What is needed is
something like the magnitudes from 1895–2021 (outside eruption) for which only
10 per cent are fainter and only 10 per cent are brighter. Again, we need to
avoid doing straight counts in the light curve, as such would bias the range
for those time intervals with a high density of magnitudes. But monthly,
yearly, or decadal groupings would average out much of the variability being
measured. With and without various weighting schemes, the dividing magnitude
for the faintest 10 per cent is always near $V$=15.3, and the dividing
magnitude for the brightest 10 per cent is roughly $V$=14.0. We are taking the
typical range of variations in quiescence to be 14.0–15.3 mag. The
corresponding range of absolute magnitude is from $+$0.2 to $+$1.5 mag.

For purposes of calculating the accretion rate, we need the absolute magnitude
of the disc alone, $M_{V_{disc}}$. The correction from $M_{V_{disc}}$ to
$M_{V_{disc}}$ was calculated with the SED fits for a blackbody plus
$\alpha$-disk (Section 2.2). The century-long average (with $\langle
V_{q}\rangle$=14.5) is between the middle-SED case (with $\langle
V_{q}\rangle$=15.00) and the brightest-SED case (with $\langle
V_{q}\rangle$=13.88). With an interpolation from our SED fits, the correction
from the total magnitude to the disc-only magnitude is 0.25 mag. This
correction is taking out the light from the companion star. If we only count
the disc light in the century-long average case, the magnitude would be
$V$=14.75. The corresponding $\langle M_{V_{disc}}\rangle$ is then +0.95 with
an error bar near $\pm$0.3 mag.

The range of $M_{V_{disc}}$ is of relevance for seeing the effects of the
variability of $\dot{M}$ for KT Eri. From our SED fits (see Section 2.2), the
magnitude corrections to get the disc light alone are roughly +0.15 and +0.5
mag respectively. The typical variations in $M_{V_{disc}}$ is from +0.35 to
+2.0 mag.

The magnitudes and absolute magnitudes are tabulated in Table 7. This allows
us to keep the values for the three states in order. Further, this table
illustrates the line of analysis, where the observed $V$-magnitudes are
converted to absolute magnitudes, then the absolute magnitudes for the disc-
light alone are separated out, then converted to an accretion rate and finally
a recurrence time scale.

KT Eri in quiescence is at the top end of the $M_{V_{q}}$ distribution for
novae. Patterson et al. (2021) shows that the historical nova are from +3.0 to
+6.0, with recurrent novae having $M_{V_{q}}$ around +1.0. Schaefer (2018)
found that 88 per cent of the CNe in the gold sample have $M_{V_{q}}$ less
luminous than +3.0. This result is pointing to KT Eri as a strong RN
candidate.

Table 7: Calculation of $\tau_{rec}$ from observed magnitudes | Faintest | Average | Brightest
---|---|---|---
$V_{q}$ (mag) | 15.3 | 14.5$\pm$0.2 | 14.0
$M_{V_{q}}$ (mag) |  $+$1.5 |  $+$0.7$\pm$0.3 |  $+$0.2
$M_{V_{disc}}$ (mag) |  $+$2.0 |  $+$0.95$\pm$0.3 |  $+$0.35
$\dot{M}$ ($10^{-7}$ M⊙/year) | 0.83 | 3.5${}^{+1.8}_{-1.2}$ | 8.2
$\log$[$\dot{M}$] | -7.08 |  $-$6.46$\pm$0.19 |  $-$6.09
$\tau_{rec}$ (years) | 50 | 12$\pm$7 | 5

###  3.6 The Accretion Rate

The optical light from KT Eri is dominated by the accretion disc. The
luminosity of the accretion disc is proportional to the mass accretion rate.
Unfortunately, it is effectively impossible to directly measure the accretion
luminosity because much of the flux comes out in the invisible ultraviolet.
Instead, the traditional solution is to use the $M_{V_{disc}}$ as a good proxy
for $\dot{M}$. Fortunately, the physics of cataclysmic variable accretion
discs is well known as for the how to translated the $M_{V_{disc}}$ into
$\dot{M}$ (e.g., Smak 1989; Frank et al. 2002; Dubus, Otulakowska-Hypka, &
Lasota 2018). None of these references provides a conversion from
$M_{V_{disc}}$ to $\dot{M}$ for the specific case of KT Eri, therefore, we
have performed the identical calculation. This is simply an integral across
annuli in the standard $\alpha$-disc, each annulus having blackbody emission
at a temperature falling off from the centre of the disc. The standard
equations appear many places (e.g., equations 5.43 and 5.45 of Frank et al.
2002). This integral was performed numerically, resulting in a $F_{\nu}$ value
in Janskys for 5500 Å at a distance of 10 parsecs, with this then being
converted to $M_{V_{disc}}$. The most critical inputs are $\dot{M}$, MWD, and
the inclination. Other inputs are the period, the companion mass, and the
fraction of the white dwarf’s Roche lobe filled by the accretion disc, with
these three parameters used only to get a radius for the outer edge of the
accretion disc, while the $M_{V_{disc}}$ has only negligible dependency on
these three parameters for the situation of KT Eri. As an ordinary check on
our calculations, we are able to reproduce the results displayed in Smak
(1989). Our procedure is to use the best system parameters (from Table 3),
introduce variations within the stated uncertainty range as quoted, and vary
the $\dot{M}$ until the target $M_{V_{disc}}$ is reached. Our derived
accretion rates are given in Table 7.

The most important conversion is from the century-long average $\langle
M_{V_{disc}}\rangle$=$+$0.95$\pm$0.30 to the $\langle\dot{M}\rangle$ as
averaged over the entire eruption cycle. With this, the average accretion rate
over the eruption cycle is 3.5${}^{+1.8}_{-1.2}$$\times$10-7 M⊙/year. With
frequently used logarithmic values, the rate is -6.46$\pm$0.18. But the real
uncertainty will be larger, due to the various uncertainties in the model
input for translating $M_{V}$ into $\dot{M}$. These errors can be estimated by
looking at the variations in $\log$$\dot{M}$ for each input parameter. The
largest variations come from the error bars in $\langle M_{V_{disc}}\rangle$,
as already expressed with the $\pm$0.18. Varying the inclination over its
allowed range of 47°to 57°, resulting in deviations of $\log$$\dot{M}$ by up
to 0.07. Variations in $\log$$\dot{M}$ are smaller than $\pm$0.02 for changes
in $M_{WD}$, mass of the companion star, and the fraction of the Roche surface
filled by the outer edge of the disc. Added in quadrature, the error bars are
$\pm$0.19. The final value for the eruption-cycle-averaged
$\log$[$\langle\dot{M}\rangle$] is -6.46$\pm$0.19. This is the relevant
accretion rate for calculating the nova recurrence time-scale.

It is also useful to calculate the accretion rate for the extremes for the
typical range in $M_{V_{disc}}$ from +0.35 to +2.0 mag. For these two
extremes, the accretion rate varies from 0.83$\times$10-7 to 8.2$\times$10-7
M⊙/year. The range of values of $\log$$\dot{M}$ is from -7.08 to -6.09 (with
units of solar masses per year).

These $\dot{M}$ values are high, very high. These accretion rates are higher
than that of any other known nova. The upper part of the derived $\dot{M}$
range is nominally within the zone of the ‘Nomoto plot’ (Nomoto 1982) for
which there is stable and continuing hydrogen burning on the surface of the
white dwarf (see Fig. 8). (The hatched zone is not from the Shen & Bildsten
full-physics calculation, but rather they took the analytic calculations from
Nomoto et al. 2007.) And for accretion rates $\gtrsim$6$\times$10-7 M⊙/year,
the expectation is that the outer parts of the white dwarf will expand to red
giant size, presumably creating a common envelope situation. A possible
explanation for this high mass transfer rate, may be what is called: ‘thermal
time-scale mass transfer’ (Ivanova & Taam 2004). This can occur when the
envelope of the donor becomes even just slightly out of thermal equilibrium,
causing the envelope to expand. A sub-giant donor, just coming off the main-
sequence, will have such a bloated envelope on its way to becoming a red
giant. Since the accretion rate is highly sensitive to the radius of the donor
(e.g., Ritter 1988), a bloating envelope will increase the Roche lobe
overflow, and thus, enhance the rate of mass transfer, possibly explaining the
high accretion rate we deduce here for KT Eri. Another possibility for a
temporarily, thermally-induced, enhanced mass transfer, can be the irradiation
of the donor from a previous nova eruption, causing the donor’s envelope to
slightly expand from the heat blast, and then slowly relax (Hillman et al.,
2020, Hillman, 2021). The operative scenario for systems like KT Eri is
largely unknown, and there is no detailed physics for the accretion.
Unfortunately, for application to KT Eri, these theory predictions assume a
steady accretion rate, while KT Eri has a rate that varies by an order of
magnitude on most time-scales. With the physical processes being non-linear,
the theory cannot reach any conclusion for KT Eri. We are not aware of any
published models or precedents for how a star in this zone should appear or
behave, much less one that is inside the zone only part of the time. For KT
Eri, some evidences give information on the accretion. First, we see no sign
of a heavy stellar wind. Second, KT Eri is a long-lasting supersoft X-ray
source (Sun et al. 2020), which could point to sustained nuclear burning on
the white dwarf. Third, any episodic excursions to hydrogen burning cannot
burn most of the accumulated hydrogen, because there was a normal nova
eruption in 2009 during which strong hydrogen lines appear, while the helium
lines are not enhanced (Munari et al. 2014).

After the recurrent-nova-nature of KT Eri is established (see below), the
front line for study of this system turns to the nature of the accretion, with
this hopefully providing some sort of a ground-truth for systems with such
high accretion. With an eye towards the future of the KT Eri system, its
evolution depends sensitively on the original main sequence mass of the
companion star, with the end result possibly being a double white dwarf
binary, an accretion induced collapse of the white dwarf, a Type Ia supernova,
or a common envelope with a merger (see Fig. 4 of Ivanova & Taam 2004).
Regardless of the uncertainties in the nature of the ‘stable hydrogen burning’
regime, KT Eri has an accretion rate that is very very high.

Figure 8: The ‘Nomoto plot’ showing $\tau_{rec}$ as a function of $M_{WD}$ and
$\dot{M}$. The blue ellipse in the upper right shows the possible positions
for KT Eri, with the vertical spread due to the range of intrinsic changes of
$\dot{M}$ and the horizontal width due to the uncertainty in the white dwarf
mass. As KT Eri changes its accretion rate, the instantaneous position on this
graph moves up and down within the ellipse. Curves of constant $\tau_{rec}$
are shown as dotted lines running diagonally, with the 30-year-recurrence line
in the upper right. Just below this is the $\tau_{rec}$=100 year line that
provides the threshold for the definition of a recurrent nova. KT Eri is above
this threshold in all cases, hence KT Eri is a recurrent nova. While the nova
moves from top to bottom within the ellipse, the operative level to trigger
the eruption is at an unknown position that must be somewhere inside the
ellipse. From archival plates, there were no prior undiscovered nova eruptions
from 1927–1954 or after 1969, within the blue ellipse of possibilities,
$\tau_{rec}$ can only be from 40 to 50 years (as shown by the blue region
cutting across the the bottom of the blue ellipse). The thick and thin solid
diagonal black lines show the trigger mass, Mtrigger in units of solar masses.
The hatched region across the top nominally has steady hydrogen burning on the
white dwarf. This Nomoto plot has the base diagram copied from Figure 7 of
Shen & Bildsten (2009), with solar abundances and the 3He mass fraction
($X_{3}$) equal to $10^{-4}$.

###  3.7 White Dwarf Mass

The mass of the white dwarf, $M_{WD}$, is critical for many of the central
questions for KT Eri. We have three methods to estimate $M_{WD}$:

The radial velocity curve has information on $M_{WD}$. From Section 2.3,
$K$=58.4$\pm$7.0 km s-1 and P=2.615 days, for a mass function of
0.054${}^{+0.022}_{-0.017}$ M⊙. For the nominal expected values of
$M_{comp}$=1.0 M⊙ and an inclination of 58$\degr$, the white dwarf is much
more massive than the Chandrasekhar limit at 2.36 M⊙. If the input are
individually push to their acceptable limits666$K$ to 65.4 km s-1, inclination
to 51$\degr$, and $M_{comp}$ to 0.8 M⊙, then the Chandraeskhar limit is still
never approached. If all three inputs are simultaneously pushed to their
limits, then the white dwarf mass can be 0.98 M⊙, which is certainly too low.
In all, the radial velocity curve does not provide any useful lower limit on
$M_{WD}$. Still, with the distributions for the inputs, a value just below the
Chandrasekhar limit is the most likely.

I. Hachisu (University of Tokyo) and M. Kato (Keio University) have a long
series of papers reporting their derivation of the white dwarf masses for many
classical and recurrent novae (including Hachisu & Kato 2016; 2018; 2019 and
Hachisu, Kato, & Schaefer 2003). Their method is to make a detailed physics
model of the entire system that addresses the multi-color light curves,
including those in the optical, infrared, and X-ray. Their methods yield
results that closely match independent measures of $M_{WD}$. One of their
papers (Hachisu & Kato 2018) specialized in deriving $M_{WD}$ for very-fast
novae (just like KT Eri), including many recurrent novae. On a query by email,
Hachisu tells us that the KT Eri $M_{WD}$ had already been calculated. Their
best fitting value is 1.26 M⊙, with an uncertainty of roughly 0.02 M⊙.

Shara et al. (2018) presented a set of calculations for $M_{WD}$ and
$\tau_{rec}$ for 82 CNe and 10 RNe in our own galaxy. The observational basis
for this was the light curves and tabulated properties in the catalog of
Strope et al. (2010) and the comprehensive RN review of Schaefer (2010). The
only required input is the eruption amplitude ($V_{q}$-$V_{peak}$) and
$t_{2}$. For this, they used model light curve calculations, such as in Yaron
et al. (2005) to produce model amplitudes and $t_{2}$ for a grid of models
with varying $M_{WD}$ and $\dot{M}$. This encapsulates the primary variables,
with secondary conditions having small import. (Still, extreme conditions are
not covered. For example, the helium envelope of V445 Pup means that the model
cannot readily apply. Similarly, the extremely small and large eruption
amplitudes of V888 Cen and CP Pup are outside the grid.) The grid was
constructed for models with varying $M_{WD}$ and $\dot{M}$ as input, but can
then be made into a grid of model amplitude and $t_{2}$. An observed nova is
placed on to the grid. The white dwarf mass and the recurrence time-scale for
the model at that grid point (with interpolation as needed) is extracted. The
derived $M_{WD}$ values are in good agreement with the masses measured from
radial velocity curves.

We have applied this particular procedure for KT Eri. The input is $t_{2}$=6.6
days and that the amplitude varies from 8.7 to 9.6 mag, depending on when the
quiescence is measured. The white dwarf mass is determined to be 1.21–1.27 M⊙,
with this range representing the range of input amplitudes. The uncertainty is
$\pm$0.05 M⊙.

A substantial potential problem arises because the accretion rate in KT Eri is
extremely variable throughout quiescence, with this leading to possibly large
and non-linear effects. The theory models used for the KT Eri estimates all
assumed a constant accretion rate. With a fast changing $\dot{M}$, the thermal
structure and diffusion rates in the accreted envelope will likely change
greatly from that of a constant-$\dot{M}$ case, and there is no guarantee that
the resultant $t_{2}$ and amplitude will be anywhere near to that of the
constant-$\dot{M}$ case. This uncertainty is likely to be particularly large
for estimating the recurrence time-scale, therefore, we are not quoting any
$\tau_{rec}$ value. Still, we expect that our estimate of $M_{WD}$ should lie
somewhere between the values for the two extremes in amplitude. For this third
method, $M_{WD}$ lies between 1.21–1.27 M⊙.

With judicious weighing of our three estimates, we adopt $M_{WD}$ as
1.25$\pm$0.03 M⊙.

###  3.8 Companion Star Mass

The mass of the companion star is poorly constrained, both for KT Eri and for
other similar novae. Here are the various constraints: (1) For novae with
periods pointing to evolved companions, the estimated masses, in solar masses,
are 0.88 for U Sco, 1.05 for QZ Aur, 0.87 for BT Mon (Ritter & Kolb 2003), and
1.05 for V3890 Sgr (Mikołajewska et al. 2021), all with mass ratios around
0.8. For KT Eri, with a mass ratio of 0.8, the companion to be roughly 1.0 M⊙.
(2) The mass ratio of KT Eri cannot be higher than some limit like 1.0, or the
accretion would runaway with a fast exponential increase, and the companion
must have something less than 1.25 M⊙. (3) The core mass of a subgiant star
has to be roughly 0.6 M⊙, and the companion can only be substantially larger.
(4) The companion has a temperature of 6200$\degr$, which would point to the
star being more massive than our Sun given its subgiant status, and providing
that irradiation is not changing the effective temperature much. (5) Our
radial velocity curve for KT Eri places only weak constraints on the
subgiant’s mass. For the best values from Table 3 plus the 58${}^{+6}_{-7}$
degree inclination (see Section 3.2), the companion mass is 0.70$\pm$0.14 M⊙.
But it is easy to push to lower inclinations to allow companion star masses
$>$1.25 M⊙. In all, the approximate mass is 1.0$\pm$0.2 M⊙.

###  3.9 Recurrence Time-Scale

The recurrence time-scale between nova eruptions, $\tau_{rec}$, is the system
property that determines whether KT Eri is a recurrent nova or not. A cutoff
of 100 years is a traditional, arbitrary, and useful definition for RNe as a
way of cutting the continuum of $\tau_{rec}$ for novae. Much of our data
collection and analysis has turned into a quest to measure a reliable value
for $\tau_{rec}$. The easiest way to measure $\tau_{rec}$ is to find two
eruptions and use the intervening time interval. But such is not possible for
most cataclysmic variables, because the probabilities of discovering a second
eruption is almost always low. If the vagaries of chance observations does not
come up lucky, then $\tau_{rec}$ information must come from elsewise.

For KT Eri, we use two sources of information. First, we use our examination
of archival sky photographs worldwide to constrain the possible times of prior
eruptions. Second, we use our $M_{WD}$ and $\dot{M}$ values to derive
$\tau_{rec}$.

For first source of information on $\tau_{rec}$ is the archival plates, as
discussed in Section 2.1.3. KT Eri did not have any eruptions from 1928 to
1954, and any eruptions after 1969 are very unlikely. KT Eri can only have a
$\tau_{rec}$$>$82 years or 40$<$$\tau_{rec}$$<$55 years.

Our second method to get $\tau_{rec}$ is to calculate it from the our $M_{WD}$
and $\dot{M}$ values. The trigger mass ($M_{trigger}$) is the amount of
material that must be accreted onto the white dwarf for which a thermonuclear
runaway is triggered. With some average accretion rate,

$\tau_{rec}=M_{trigger}/\langle\dot{M}\rangle.$ (1)

The runaway is triggered when the pressure at the base of the newly accreted
layer of material reaches a critical value,

$P_{crit}=(GM_{WD}M_{trigger})/(4\pi R_{WD}^{4}).$ (2)

The white dwarf radius, $R_{WD}$ is a well known function of $M_{WD}$. Shen &
Bildsten (2009) point to $P_{crit}$ values within a factor-of-3 of
1$\times$1019 dyne cm-2. They find that the metallicity dependence is weak,
scaling only as Z-0.2. Still $P_{crit}$ varies with $\dot{M}$ and $M_{WD}$,
but not by a lot. For $P_{crit}$ as a constant appropriate for the middle of
the CN/RN boundary, then the CN/RN distinction applies closely for the KT Eri
case. $P_{crit}$ can be evaluated for all the ten known Galactic RNe, for
which $\tau_{rec}$ values are roughly known. (For some RNe, like for U Sco,
the $\tau_{rec}$ is known to 10 per cent and is stable in time.) With this,
$P_{crit}$ is varied until the ten RNe have nearly correct recurrence time-
scales. This value is within $\sim$20 per cent of 0.7$\times$1019 dyne cm-2.
(This choice gives 8 years for U Sco, 50 years for T CrB, 17 years for RS Oph,
and all below 100 years.) This is a short path to calculating $\tau_{rec}$
from $M_{WD}$ and $\dot{M}$ for KT Eri.

With the century-averaged accretion rate of
$\log$[$\langle\dot{M}\rangle$]=$-$6.46$\pm$0.19, a 1.25 M⊙ white dwarf with a
radius of 3540 kilometers, and the $P_{crit}$=0.7$\times$1019 dyne cm-2,
$\tau_{rec}$ is 12$\pm$5 years. Varying the white dwarf mass from 1.22 to 1.28
M⊙, the recurrence time varies from 16 to 8 years. For the century-long
average brightness level, the derived recurrence time scale is 12$\pm$7 years.
This assumes that the trigger threshold is steadily accreting at its average
rate.

A substantial worry for all these theory calculations is the effect of the
highly-variable accretion rate on to the white dwarf. Alternating episodes of
high and low accretion might well return a substantially different trigger
condition than for some middling-and-constant accretion. It is easy to imagine
that the runaway would start during high accretion rates with a different-
from-average trigger threshold, and it is easy to imagine that the low
accretion rate intervals would allow the accreted layer to relax to a
condition farther from the trigger threshold. Fortunately, the effects that we
can imagine are all bounded by the maximum and minimum accretion rates. That
is, the effects of the variable accretion rate will never be more than that of
a steady maximal accretion, and the effects will never be less than that of a
steady minimal accretion. While being somewhere between the maximum and the
minimum, the best estimate can now only be for the average accretion rate.
Even with all our imagined effects of the variable accretion, the $\tau_{rec}$
value must still be between the values derived for the high and low accretion
states. This is why we have been carefully tracking the range of $V_{q}$
through to $\langle\dot{M}\rangle$. For $\log$[$\dot{M}$] of -6.09 and -7.08,
the recurrence times is between 5 and 50 years. Our best measure of
$\tau_{rec}$ is 12 years, but a range of 5–50 years is within our
uncertainties.

The above calculation with a constant $P_{crit}$ is easy to calculate, simple
to understand, and closely approximates the underlying physics. Further, the
above calculations have the huge advantage that they match the existence of
the ten known Galactic RNe, and their known $\tau_{rec}$ values. Still, the
straight forward calculation of $\tau_{rec}$ has not covered all the physics
effects. To cover the exact physics, Shen & Bildsten (2009) have detailed
models of all the nuclear reaction rates, realistic convection models within
the accreted layer, and much more. Further, they present their results such
that their model $\tau_{rec}$ can be evaluated for the $M_{WD}$ and $\dot{M}$
case of KT Eri. These results are shown in their fig. 7, which is reproduced
in our Fig. 8. On top of this plot, a blue ellipse delineate the allowed
location of KT Eri based on our measured $M_{WD}$ and $\dot{M}$. The
$\tau_{rec}$ values are displayed as the diagonal dotted lines in the Shen &
Bildsten plot. This graph provides a confirmation of our simpler calculation.
In particular, the best-fitting position has a recurrence time of close to 12
years, while the range of allowed $\tau_{rec}$ is the same. This is all just a
confirmation of our above simpler calculation. In the end, for the theory
calculation from our measured $M_{WD}$ and $\dot{M}$, the calculated
$\tau_{rec}$ of KT Eri is 12 years, with an extreme possible range of 5–50
years. So, by this alone, KT Eri is an RN.

But we still have to combine our two sources of information on $\tau_{rec}$.
The best estimate value of 12 years violates the limits from the archival
record. The real value must come from the long-end of the allowed range. The
$>$82 year range allowed by the archival data is eliminated by the theory
calculation. In Fig. 8, the ellipse should be cutoff for recurrence times of
$<$40 years and $>$55 years, as required by the archival data. We are left
with only 40$<$$\tau_{rec}$$<$50 years. Our final answer is that we infer that
KT Eri has a recurrence time-scale of 40–50 years.

##  4 Is KT Eri a Recurrent Nova?

The recognition of RNe is important for a wide range of applications
concerning the evolution of novae. Only ten Galactic RNe are known, and each
system is individually of high importance. Now we can ask whether KT Eri is
the eleventh Galactic recurrent nova?

The prior operational definition of RNe was something like ‘a binary with a
white dwarf that has two or more observed thermonuclear nova eruptions’. All
classical novae recur, even if on time-scales up to several million years
(Yaron et al. 2005), some sort of a mandated threshold for $\tau_{rec}$ is
needed. The round number of one century is appropriate and traditional. A
better formal definition of RNe is that they are a ‘binary with a white dwarf
that undergoes thermonuclear nova eruptions with $\tau_{rec}$$<$100 years’.

Previously, the only way to prove that $\tau_{rec}$$<$100 years has been to
spot two or more nova events from the same system. But this is inefficient, as
the discovery rate for second eruptions on a previously know system is
amazingly low (Schaefer 2010). Many nova systems with only one observed
eruption are actually RNe for which all of the other eruptions in the century
have been missed (Pagnotta & Schaefer 2014).

Table 8: Proxy Criteria for Recognizing RN candidates # | Criterion | KT Eri | RN?
---|---|---|---
1 | Nova Amplitude $<$ $14.5-4.5\log(t_{3})$ | 9.2 $<$ 9.5 | Yes
2 |  $P$$>$0.6 days |  $P$=2.6 days | Yes
3 |  $J-H$$>$0.7 & $H-K$$>$0.1 |  $J-H$=0.11 & $H-K$=0.07 | No - but OK
4 | H$\alpha$ FWHM > 2000 km s-1 | 3300 km s-1 | Yes
5 | High-Excitation lines (He II and/or Fe X) | He II | Yes
6 | P class (plateau in light curve) | P or PP | Yes
7 |  $M_{WD}$$>$1.20 M⊙ | MWD=1.25 M⊙ | Yes
8 |  $M_{V_{q}}$$<$3 |  $M_{V_{q}}$=0.70 | Yes

###  4.1 The Eight Proxy Criteria

Over the past many decades, many workers have pointed to a wide variety of
nova properties that were claimed to indicate that the system was actually an
RN. Pagnotta & Schaefer (2014) have systematized the previous six RN-criteria,
and applied it to all available nova systems. These six criteria are itemized
in Table 8. Criteria 4, 5, 6, and the speed class ($t_{3}$) are just proxies
for recognizing a high mass white dwarf. Criteria 2, 3, and the eruption
amplitude are just proxies for recognizing a high accretion rate.

For KT Eri, all six criteria are evaluated, with the results shown in Table 8.
KT Eri easily passes all but one of the criteria. (Criteria 3 is just a proxy
for having an evolved companion which forces the large $P$, and hence this
criterion is satisfied more fundamentally by passing Criterion 2.) KT Eri is a
very good RN candidate.

We propose two new proxy criteria (see Table 8), where RNe should have
$M_{WD}$>1.20 M⊙ and RNe should have $M_{V_{q}}$$<$3.0 mag. Both of these
criteria are individually satisfied by all known RNe in our galaxy, and are
individually satisfied by 5 known CNe with $M_{WD}$>1.27 M⊙ and $M_{V_{q}}$
more luminous than 2.5 mag.

###  4.2 The Recurrence Time -Scale for KT Eri

A recurrent nova is defined as a system with nova events that has
$\tau_{rec}$$<$100 years. This paper is putting forth a new method for
recognizing RNe, and that is to use the observed $\dot{M}$ and $M_{WD}$ to
calculate $\tau_{rec}$.

This new method has the strength that it can be applied to most nova systems.
And there is no need to wait for a century and hope that the next eruption is
not missed. This new method has the strength that the empirical calibration of
$P_{crit}$ with the known Galactic RNe matches up with the deep theory results
from the nuclear reaction rate models. We know of no way to impeach these
results outside of the usual propagation of uncertainties on the input.

The long train of observations and analysis in this paper has all been leading
up to applying this method for KT Eri. We found that $M_{WD}$=1.25$\pm$0.03 M⊙
and that the century-long average $\dot{M}$ is 3.5$\times$10-7 M⊙/year. This
results in a best estimate of $\tau_{rec}$=12$\pm$7 years, although with a
possible range from 5–50 years. This calculation is constrained by the
archival data which demonstrates that $\tau_{rec}$ cannot be faster than 40
years and cannot be 55–82 years. With these, the primary result of our paper
is that the recurrence time-scale of KT Eri is 40–50 years. KT Eri is
certainly a recurrent nova, even though only one of its eruptions has been
discovered.

##  5 The Nature of KT Eri

Figure 9: Close-up view of the KT Eri binary. This picture is constructed with
the correct sizes and distances for the stars, the positioning of the hotspot
and accretion disc, and the viewing angle. To set the scale, the companion
star has a radius of 3.7 R⊙. The subgiant companion star has a temperature of
6200 K, while the irradiated polar regions appear brighter and hotter. With
the long orbital period, the accretion disc is very large, and the outer
regions are relatively cool. As the binary revolves, the extra light from the
upper irradiated region will change in aspect, making for the brightness
modulation on the orbital period. In its average state, the disc outshines the
companion star by 2:1. The extreme variability of KT Eri likely results in a
mottled disc.

An artistic visual picture of KT Eri is in Fig. 9, a realistic picture created
by R. Hynes using his BinSim program777http://www.phys.lsu.edu/ rih/binsim/.
Let us also give a verbal picture of the nature of KT Eri. The binary has a
period of 2.6 days, with the star centres separated by 10.4 R⊙, and is viewed
from a middle inclination. The companion star has evolved off the main
sequence and is now a subgiant star near 3.7 R⊙ in radius with a temperature
of 6200 K. The companion star is losing mass through its inner Roche lobe at a
very very high rate (3.5$\times$10-7 M⊙/year). This accretion rate changes up
and down by up to 10$\times$ on all time-scales from minutes to decades. When
the accretion rate is higher than average, KT Eri enters the ‘steady hydrogen
burning’ regime, although the understanding of this state is poor due to the
rapid variability. The accretion flow is through the usual disc, with no
evidence for any magnetic field on the white dwarf. The white dwarf is just
below the Chandrasekhar mass, at 1.25$\pm$0.03 M⊙. The nova event of 2009 had
a very high ejection velocity, a fast decline time, a ‘PP’ plateau class light
curve, and high excitation lines, all because the white dwarf is very massive.
The combination of a very high accretion rate plus a very high white dwarf
mass requires that the nova recurrence time-scale must be 40–50 years, and KT
Eri is a recurrent nova.

KT Eri is still ‘displaying’ mysteries. A detailed theory model is needed for
how this system can have such a high accretion rate. A theoretical
understanding is needed for the large changes in the amplitude of the orbital
modulations. The extreme variability in this one system needs an explanation.
Detailed physics calculations are needed for what a system looks like in the
‘stable hydrogen burning’ regime when the variability is so extreme.

##  6 Acknowledgments

We thank I. Hachisu and M. Kato for forwarding their calculation of the white
dwarf mass of KT Eri. We thank M. Shara for helpful discussions on white dwarf
masses. Rob Hynes provided the realistic BinSim image of the KT Eri system.
Research on novae at Stony Brook University has been supported by NSF grant
AST1611443. Access to the SMARTS observing facilities has been made possible
in part by research support from Stony Brook University. The material is based
upon work supported by NASA under award number 80GSFC21M0002. This research
has made use of the APASS database, located at the AAVSO web site; funding for
APASS has been provided by the Robert Martin Ayers Sciences Fund. This
research made use of Lightkurve, a Python package for Kepler and TESS data
analysis (Lightkurve Collaboration, 2018). The radial velocity analysis used
software written in IDL. This work has made use of data from the European
Space Agency (ESA) mission Gaia, processed by the Gaia Data Processing and
Analysis Consortium (DPAC), with funding for the DPAC provided by national
institutions, in particular the institutions participating in the Gaia
Multilateral Agreement.

##  7 Data Availability

All of the photometry data used in this paper are explicitly given in Table 2,
and is publicly available from the references and links in Table 1.

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