Helium-deficient ER UMa-type Dwarf Nova below the Period Minimum with a Hot Secondary

We present the discovery of a peculiar dwarf nova KSP-OT-201712a using high-cadence, multicolor observations made with the Korea Microlensing Telescope Network. KSP-OT-201712a exhibits a rare presence of outbursts during standstills, as well as strong Hα emission for a dwarf nova below the period minimum with an orbital period of 58.75 ± 0.02 minutes. The outburst cycles are ∼6.6 days within standstills but increase to ∼15 days outside of them. Both B − V and V − I colors become bluer and redder as the outburst luminosities increase and decrease, respectively, for the outburst within standstill, while they evolve in the opposite directions outside of the standstills. The presence of strong double-peaked Hα and weak He i emission lines with He/H flux ratio of 0.27, together with absorption lines of Mg b and Na D in the source, leads to the estimation T eff ≃ 4570 ± 40 K, [Fe/H] ≃ 0.06 ± 0.15 dex, and log g ≃ 4.5 ± 0.1 for its secondary. KSP-OT-201712a is the second He-deficient dwarf nova below the period minimum, while the temperature of the secondary is measured for the first time in such objects. We identify it to be an ER UMa-type dwarf nova, suggesting that the evolution of dwarf novae across the period minimum is accompanied by large mass transfers. The high temperature of the secondary indicates that the system started its mass transfer when the secondary was about 93% of its main-sequence age. The system will evolve to a helium cataclysmic variable or to AM CVn once its hydrogen envelope is exhausted before it explodes as a Type Ia supernova.


INTRODUCTION
Dwarf novae are low-mass binaries composed of a white dwarf (WD) and a secondary mass donor together with an accretion disk (Warner 1995).Their orbital periods are ≲10 hours (Ritter & Kolb 2003), indicating that they are at a late dynamical evolutionary stage of binary systems and their orbits shrink due to gravitational radiation or magnetic braking as they evolve until the orbital periods become close to the period minimum about 75 minutes (Paczynski & Sienkiewicz 1981;Rappaport et al. 1983;Knigge et al. 2011;Goliasch & Nelson 2015).Some dwarf novae are expected to evolve to AM Canum Venaticorum (AM CVn) objects (Kennedy et al.Corresponding author: Youngdae Lee hippo206@gmail.com2015; Burdge et al. 2022;Belloni & Schreiber 2023), which are WD + WD binaries with an extremely short (≲ 40 minutes) orbital period.AM CVn systems are considered to be progenitors of some Type Ia supernovae as well as sources of substantial gravitational wave radiation (Han & Podsiadlowski 2004;Bildsten et al. 2007;El-Badry et al. 2021a).It is believed that dwarf novae with a high central density of the secondary star at the onset of mass transfer evolve to AM CVn than those with a low central density.According to Podsiadlowski et al. (2003), low-mass binaries with a central hydrogen abundance in mass, X c , smaller than 0.4 can evolve to AM CVn systems.Dwarf novae with a more evolved secondary star typically show a relatively large helium to hydrogen abundance ratio at the center of the secondary star.

Lee et al.
Dwarf nova outbursts are triggered by thermal instability in the accretion disk, with their properties determined by the mass transfer from the secondary star and binary properties (Cannizzo & Kenyon 1987;Osaki 1996).Dwarf novae are generally categorized into three groups based on the observed outburst properties: U Gem (Geminorum), SU UMa (Ursae Majoris), and Z Cam (Camelopardalis) types.About 13% of dwarf novae are U Gem type that shows both short (∼ 5 days) and long (∼ 12 days) outbursts, and their orbital periods are typically larger than the period gap of 2-3 hours (Smak 2000;Otulakowska-Hypka et al. 2016).SU UMa types amount to about 70% of the entire dwarf nova population showing the presence of normal and superoutbursts with their orbital periods smaller than the period gap (Otulakowska-Hypka et al. 2016).The short outbursts from U Gem and normal outbursts from SU UMa are almost identical.There exist small differences between the long and superoutbursts in that the latter contain superhumps of magnitude variation of about 0.2 mag and plateaus during their decline phase (Warner 1995).
Z Cam types are very rare (about 5%) compared to U Gem and SU UMa types.Their outburst light curves are similar to those of U Gem types but featured with post-outburst "standstills" when the mass-transfer rate approaches the critical value Ṁcrit ∼ 8 × 10 17 g s −1 depending on disk radius, viscosity, orbital period and mass ratio of the system (Meyer & Meyer-Hofmeister 1983;Otulakowska-Hypka et al. 2016;Buat-Ménard et al. 2001a).Although standstills in Z Cam types typically show very small magnitude variations, there has been a growing number of Z Cam types that show the presence of outbursts towards the end of standstills (Simonsen 2011; Szkody et al. 2013;Kato et al. 2019;Kato 2019).The orbital periods of Z Cam types are known to be larger than the period gap as U Gem types (Otulakowska-Hypka et al. 2016).One notable exception is the peculiar case of NY Serpentis (NY Ser), a dwarf nova which shows characteristics of both SU UMa type-like superoutbursts and Z Cam type-like standstills together (Kato et al. 2019).ER UMa types also show standstills and large mass-transfer rate (MGAB-V859, ZTF18abgjsdg, BO Cet; Kato & Kojiguchi 2021;Kato et al. 2021), appearing to be Z Cam types below the period gap.
Only a limited number of dwarf novae with an orbital period smaller than the so-called period minimum of ∼ 75 minutes (Breedt et al. 2012;Kennedy et al. 2015), have been found: EI Psc (Thorstensen et al. 2002), ZTF J1813+4251 (Burdge et al. 2022), KSP-OT-201701a (Lee et al. 2022), OV Boo (Patterson et al. 2008), V485 Cen (Augusteijn et al. 1996;Olech 1997), CSS120422 (Carter et al. 2013), V418 Ser (Kennedy et al. 2015), and CSS100603 (Breedt et al. 2012).Most of these objects are helium dwarf novae with strong helium and hydrogen emission lines and are believed to be in the evolutionary path to AM CVn.In the case of KSP-OT-201701a, the helium to hydrogen flux ratio is notably smaller than those of the other objects, indicating that it is in an earlier evolutionary stage to AM CVn than the others (Lee et al. 2022), although the properties of its secondary star remain largely unknown.Because of the lack of observed examples, however, the details of how short-period dwarf novae evolve toward the AM CVn phase are poorly understood.
In this paper, we provide an illustrative case of KSP-OT-201712a that sheds new light on the early evolutionary stage of a short-period dwarf nova to an AM CVn, revealing the properties of the secondary.

KSP-OT-201712a: DISCOVERY AND LIGHT CURVES
As part of the Korea Microlensing Telescope Network (KMTNet) Supernova Program (KSP; Moon et al. 2016) aimed at detecting infant/early supernovae (Afsariardchi et al. 2019;Moon et al. 2021;Ni et al. 2022Ni et al. , 2023a,b),b), we monitored the 4-square degree field around the lenticular galaxy NGC 2380 in the BV I bands with an average cadence of 8 hours for each band between December 2017 and March 2019 using the three 1.6-m telescopes of the KMTNet located at Chile, South Africa and Australia (Kim et al. 2016).All our images are 60 sec exposures reaching an average detection limit of 21.5 mag.In addition to infant/early supernovae, KSP has also discovered other types of optical transients, including several novae and dwarf novae of interest (Antoniadis et al. 2017;Brown et al. 2018;Lee et al. 2019Lee et al. , 2022)).
We discovered a dwarf nova KSP-OT-201712a at the coordinate (α, δ) J2000 = (111.0321• , -26.3318 • ) 1 on December 25, 2017 (UT).This object was also observed by the Wide-field Infrared Survey Explorer (WISE) with a single exposure (Wright et al. 2010) and the Zwicky Transient Facility (ZTF) with low-and high-cadence time-series observations in r band for about 2 years from 2018 November (Bellm et al. 2019).We performed DAOPHOT-based point spread function photometry (using DAOPHOT II; Stetson 1987).For the photometric calibration of our KSP BV I images, we used about 300 BV i standard stars near the source in the AAVSO Photometric All Sky Survey (APASS) database and made I = i ′ − 0.4 mag (Park et al. 2017;Lee et al. 2019).B-band KMTNet instrumental magnitudes required a color correction and were corrected by ≃ 0.27 × (B − V ) (see Park et al. 2017, for details).Extinction corrections A B = 1.57mag, A V = 1.18 mag, and A I = 0.72 mag were applied (see Section 4).Throughout this paper, we use extinctioncorrected magnitudes and colors unless otherwise specified.
Figure 1 shows the extinction-uncorrected V -band light curves of KSP-OT-201712a revealing the abundance of outburst activities from the source.In the left panel, we identify at least six outbursts that we name O1-O6 between MJD 58110 and 58160.We summarize the observed properties of them as follows: (1) The six outbursts are overlapped in which the next outburst starts before the previous one reaches the quiescent brightness (see below).( 2) The peak brightness of each outburst increases until O3 after which it decreases, and the average outburst cycle is about 6.6 days.(3) Their rising rates are 0.79, 0.57, 0.32, 0.43, 0.44 and 0.36 mag day −1 for O1-O6, respectively, with the primary peak O3 having the smallest value.(4) The amplitudes of these outbursts, which are defined as the magnitude difference between the start of outburst rise and peak, are 1.52, 1.47, 1.34, 1.22, 0.85, and 1.02 mag for O1-O6, respectively.(5) The intermediate phases, which we identify to be "standstills" ( §5.1), showing almost constant brightness occur between overlapped outbursts (see cyan shaded areas in Figure 1 and 2) and typically last about 2 days.The brightness of the intermediate phase after O2 is shown as a guideline (blue dashed line).(6) The minimum brightness of the object is 18.6 mag, or 17.42 mag with extinction correction ( §4), which we adopt as quiescent magnitude shown as the black dashed line.
In the right panel of Figure 1 during the period of MJD 58380-58550, the source is featured with complicated, but different from those in the left panel, outburst activities with varying amplitudes ranging from 0.5 mag to ≳ 2 mag.Although the lack of observations in some intervals during the period makes it difficult to clearly identify outburst peaks, we identify at least two peaks which we name O7 and O8 (black dots).In particular, the O8 outburst, which peaks at MJD 58507.3748,occurs between two quiescent phases with peak amplitude and rising rate of 1.60 mag and 0.28 mag day −1 , respectively.Using the O8 outburst peak, we estimate the distance to the source to be about 1.32 kpc (see § 4).The red dots in Figure 1 are the r-band magnitudes of the source observed by the Zwicky Transient Facility (ZTF; Bellm et al. 2019).The ZTF observations are both with high (40 seconds) and low (> 1 day) cadences with part of them covering the intervals when there are no KMTNet observations.The outburst (O ZTF ) around MJD 58493 is largely detected by ZTF solely since the KMTNet observations were made for only its tail phase.The subset in Figure 1 shows the ZTF light curve of O ZTF in which the source magnitudes increase at a rate of 0.37 mag day −1 as typically found in dwarf nova outbursts (e.g.Otulakowska-Hypka et al. 2016).The outburst cycle between O ZTF and O8, where there are no significant observational gaps from the combined KMT-Net and ZTF observations, is about 15 days, which is equivalent to the cycle between the O7 and O ZTF outbursts.
Figure 2 shows the extinction-corrected color evolution of KSP-OT-201712a in which its B −V and V −I colors vary in a similar manner.In the overlapping O2-O5 outbursts, the colors become bluest at their peak brightness as typically found in outbursts of other dwarf novae (Cannizzo & Kenyon 1987).On the contrary, the colors of O7 and O8, as well as those of O1 and O6, show an almost opposite behavior with redward evolutions towards the peak brightness, attaining maximum redness a few days after the peak.

SPECTROSCOPY
Spectroscopic observations of KSP-OT-201712a were made with Gemini Multi-object Spectrographs South (GMOS-S) at two epochs of 2018 January 16 (UT, MJD 58134.2016)and 24 (UT, MJD 58142.1823).Four 400sec exposures were obtained for the blue channel (3970-7060 Å) with a 1.5 ′′ width slit during the first epoch, while four 280-sec exposures were obtained for each of the blue channel and red channel (5405-10000 Å) during the second epoch.The spectral resolutions measured in FWHM were 2.73 Å at 4610 Å and 3.98 Å at 7640 Å for the blue and red channels, respectively.The Gemini IRAF2 package was used to conduct basic data reduction of the observed spectra, including image preprocessing, wavelength calibration, and flux calibration.
Figure 3 shows the extinction-corrected integrated GMOS-S spectrum of KSP-OT-201712a, revealing a continuum shape that appears consistent with that of a late-type star as well as a very prominent Hα line and notable absorption lines of Mg b, Na D, and Na I. We note that He i emission at 5876 Å and Hα emission are weakly and strongly detected in this source, respec- tively.The He/H flux ratio of KSP-OT-201712a is 0.27 which is smaller than known dwarf novae (>0.5) below the period minimum (Kennedy et al. 2015).In order to estimate stellar parameters of the secondary, we use the Medium-resolution Isaac Newton Telescope Library of Empirical Spectra (MILES), an empirical stellar library constructed by 985 observed stars (Sánchez-Blázquez et al. 2006).The grids of the stellar parameters in the library are in the range of 2747 < T eff [K] < 36000, −0.2 < log g < 5.5, and −2.86 < [Fe/H] [dex] < 1.65, and they are densely sampled around [Fe/H] ∼ 0.0 dex, log g ∼ 4.0, and T eff ∼3500-7000 K with mean grid spacing of ∆T eff = 32 K, ∆log g = 0.06, and ∆[Fe/H] = 0.01 dex.We find the best-fit library model to the observed spectrum of KSP-OT-201712a in the wavelength range of 4000 Å-7400 Å to be that of T eff = 4570 ± 40 K, [Fe/H] ∼ 0.06 ± 0.15 dex, and log g = 4.5 ± 0.1 with a reduced chi-square value of 0.99.We exclude the wave-length ranges for the emission lines and telluric lines in our fitting.We measure the radial velocities of the observed Hα and Na D lines by conducting double Gaussian fits to the individual spectra (see Figure 3 (b)-(d)).For the Hα line, we first determine the separation between the peak wavelengths of the two Gaussians to be 5.92 Å and 7.24 Å for the first 4 spectra obtained on January 16, 2018 and the remaining 8 spectra obtained on January 24, 2018, respectively.In this process, all fitting parameters are set free.We then fix the separation between two Gaussian components to these values (i.e., 5.92 Å for the first 4 spectra and 7.24 Å for the other 8 spectra) and conduct another double Gaussian fit to obtain the peak wavelengths of the two Gaussian components, as was done in previous studies of dwarf nova emission lines (e.g.Patterson et al. 2008;Green et al. 2020).For the Na D lines, we fix the wavelength separation of the two  Gaussian components to be its intrinsic value of 5.97 Å to obtain the other fitting parameters of the peak wavelengths and intensities.A Long-Scargle analysis3 of the fitted wavelengths of the Hα and Na D lines of the 12 spectra gives 58.78 minutes (or 24.5 cycles day −1 ) as the binary orbital period of KSP-OT-201712a.
By adopting this as the initial value for the orbital period in the sinusoidal fitting of the Hα velocity evolution, we measure the orbital period of KSP-OT-201712a to be 58.75 ± 0.02 minutes as shown in the bottom panel of Figure 3.Note that we obtain the same orbital period (58.70 ± 0.03 minutes) when we conduct the same fitting to Na D velocities, but with less statistical significance due to the increased uncertainties of their veloci-ties.The radial velocity amplitude derived for KSP-OT-201712a from the observed Hα lines is 11.9 ± 2.9 km s −1 , which is relatively small but still belongs to the range previously observed in other dwarf novae below the period minimum (Augusteijn et al. 1996;Patterson et al. 2008;Breedt et al. 2012;Kennedy et al. 2015;Green et al. 2020).The small amplitude is likely due to a small inclination angle of the source.

DISTANCE AND EXTINCTION
KSP-OT-201712a has been observed by the GAIA satellite (Gaia Collaboration et al. 2016, 2018) to have a parallax of 0.714 ± 0.064 mas, providing its distance of 1.40 ± 0.13 kpc.
The peak luminosities of dwarf nova outbursts are known to be correlated with their binary orbital periods (e.g., Warner 1995;Patterson 2011).Using the orbital period of 58.75 minutes for KSP-OT-201712a ( § 3), and we obtain 5.42 ± 0.47 mag as the peak V -band absolute magnitude of the source based on the relation between luminosities and periods in Patterson (2011, see equation 3 for normal outbursts).The peak V -band apparent magnitude of the O8 outburst, which is a well-isolated outburst between quiescence (Figure 1), is 17.20 ± 0.02 mag, we attribute the difference of 11.78 mag to the distance and extinction to the source.If we combine this and the 3D E(B−V ) model by Green et al. (2019) in the direction of KSP-OT-201712a, the best-fit combination of distance and extinction values are 1.32 ± 0.10 kpc and E(B − V ) = 0.38 ± 0.10 mag (see Figure 4).The peak magnitude of the O7 outburst, which is 17.80±0.02mag, corresponds to the distance of 1.56 ± 0.02 kpc and E(B − V ) of 0.46 ± 0.01 mag.These are slightly larger that those of the O8 outburst.Given that O8 outburst was observed with higher cadence around the peak than O7 outburst, we adopt the distance obtained using the O8 outburst in our study.This distance estimation is very similar to that from the parallax measurement, confirming that the isolated outburst O8 is likely a typical normal outburst of dwarf novae.We adopt 1.32 ± 0.10 kpc as the distance to KSP-OT-201712a in this paper.
In addition, the extinction value E(B −V ) = 0.38 ± 0.10 mag is also in good agreement with the observed Balmer decrement of Hα and Hβ from the source (Figure 3) where the ratio Hα/Hβ ≃ 4.68 translates into E(B − V ) ≃ 0.42 mag by the model of Cardelli et al. (1989) in the case of a temperature T = 10 4 K and an electron density n e = 10 2 cm −3 , intrinsic Balmer decrement of Hα/Hβ = 2.86 (Osterbrock 1989).As the extinction to KSP-OT-201712a in this paper, we use A B = 1.57,A V = 1.18, and A I = 0.72 mag which are calculated with the E(B − V ) = 0.38 ± 0.10 mag, R V = 3.1 mag, and the extinction curve of Cardelli et al. (1989).mass-transfer rate, and the observed outburst cycles and amplitudes (Figure 1), we classify the source to be an ER UMa-type dwarf nova as follows.Standstills, which have been observed in ER UMa types for short-period dwarf novae, are intermediate phases following an outburst peak with flat brightness that is about 0.7 mag fainter than the peak brightness (Buat-Ménard et al. 2001b;Szkody et al. 2013).Their duration ranges from as short as a few weeks to as large as more than a year (Ohshima 2023).During the multiple outbursts O1-O6, the brightness of KSP-OT-201712a stalls at intermediate magnitudes of about two days that are 0.8-1 mag fainter than the peak magnitudes after each outburst peak, consistent with the behavior of short-interval standstills observed in other ER UMa type dwarf novae.We, therefore, identify them to be standstills.In terms of outburst pattern, the ∼6 and ∼15 days of the observed outburst cycles of O1-O6 and O7-O8, respectively, for KSP-OT-201712a and their amplitudes of ∼1.24 mag (O1-O6) and ∼1.60 mag (O7-O8), on the other hand, belong to the cycle ranges of 3-15 days and amplitudes of 1-4 mag that have been observed in ER UMa types (Otulakowska-Hypka et al. 2016).Its orbital period of ≃59 minutes is considerably smaller than the observed range of 1.25-1.58hours for ER UMa types (Otulakowska-Hypka et al. 2016), and in fact, KSP-OT-201712a is an ER UMa dwarf nova with the shortest orbital period as far as we are aware.Standstills, which have been observed in ER UMa types and its long-period version of Z Cam types, are known to be caused by a large mass-transfer rate (Buat-Ménard et al. 2001b;Ohshima 2023).However, a dwarf nova with a cluster of recurring standstills (as seen in the O1-O6 period of KSP-OT-201712a), maintaining the minimum brightness substantially above the quiescent level, is extremely rare since dwarf novae return to a quiescent phase after a standstill (Ohshima 2023).Even in the case of the few dwarf novae that show a standstill followed by an outburst activity instead of immediately returning to a quiescent phase (Simonsen 2011; Szkody et al. 2013;Kato et al. 2019;Kato 2019), the outburst activity is very simple and composed of a single outburst.KSP-OT-201712a is, therefore, a unique dwarf nova showing the presence of a cluster of standstills, i.e., O1-O6, above the quiescent level.
The origin of standstills is relatively unknown, although attempts have been made to attribute it to changes in mass-transfer rate from the secondary (e.g., Hameury & Lasota 2014) or to limit-cycle oscillations between standstills from the inner-disk area and outbursts caused by thermal instability from the outer-disk (e.g., Kato 2019).What initiates the required changes in the mass-transfer rate and the limit-cycle oscillations, however, remains uncertain.We note that the relatively periodic (∼6.6 days) burst activities of O1-O6 of KSP-OT-201712a can be more readily explainable by the limit-cycle oscillation process in the frame of thermal disk instability (Cannizzo & Kenyon 1987).
It is known that there exists a good correlation between the average V -band magnitudes and the mass accretion rates of dwarf novae (e.g., Paczynski & Schwarzenberg-Czerny 1980;Dubus et al. 2018).Applying the correlation to the observed brightness of the outbursts of KSP-OT-201712a, we obtain the expected accretion rates in the range of ∼0.4-2.6:0.9 (O1), 1.9 (O2), 2.6 (O3), 1.6 (O4), 1.4 (O5), 0.6 (O6), 0.4 (O7) and 0.5 (O8), all in unit of 10 17 g s −1 .The inferred critical mass is ∼ 0.35 × 10 17 g s −1 using its orbital period of 59 minutes and the relation Ṁcrit ∼ 3.5 × 10 16 P 1.6 orb g s −1 from Dubus et al. (2018).This value is similar to the expected accretion rates of the four outbursts of O1, O6, O7 and O8, while it is somewhat smaller than those of the other four outburst of O2, O3, O4 and O5.This is consistent with the presence of standstills in the latter four outbursts.
In Figure 2, the B −V and V −I colors of KSP-OT-201712a show different evolutions between O2-O5 and O7-O8 outbursts in which the former become bluest at their brightness peaks, as most of the other outbursts observed in dwarf novae (Pichardo Marcano et al. 2021, e.g.,), while the latter do the opposite pattern.O1, which precedes O2-O5 outbursts, is similar to O7-O8 in color.The colors of an accretion disk during outbursts are largely determined by the internal heat wave transfer and the accretion rate of cold material from outside.A small accretion rate creates outbursts at the inner part of the accretion and tends to be followed by a slow internal heat wave transfer to the outside of the accretion disk (Cannizzo et al. 1986).The observed colors of O7-O8, as well as those of O1 and O6 which are closer to O7-O8 than O2-O5 ( §2), suggest that the internal heat wave transfer rate is less efficient than the accretion rate of cold material, leading to a redward evolution, consistent with their small accretion rate.In the case of the O2-O5 outbursts, their large accretion rate is more compatible with outbursts at the outer part of the accretion disk and an efficient outside-in heat wave transfer, leading to a blueward evolution if the heat wave transfer effect is more dominant than the accretion rate of cold material in their colors.

Evolution of KSP-OT-201712a
Short-period dwarf novae below the period minimum with a low He/H flux ratio are of important consequence to our understanding of how low-mass binaries evolve to He CVs or AM CVn, the two ultimate phases of dwarf novae prior to Type Ia SN explosions, from the longperiod dwarf nova phase (Bildsten et al. 2007).Note that only a handful of dwarf novae have been observed below the period minimum (∼75 minutes), and most of them have a large He/H flux ratio (>0.5) due to the small amount of hydrogen in their secondary stars (e.g., Kennedy et al. 2015).Little has been known about short-period dwarf novae that still have a substantial amount of hydrogen (= a low He/H flux ratio) from an early evolutionary phase of low-mass binaries below the period minimum.As we reported previously in Lee et al. (2022), until now, KSP-OT-201701a has been the only short-period dwarf nova under the period minimum with a small He/H flux ratio of 0.26.Although the discovery of KSP-OT-201701a did confirm the presence of a transitional phase between long-period dwarf novae and He CVs in the evolutionary track of low-mass binaries, its spectrum was dominated by the emission from the accretion disk.This made it impossible to conduct further investigation into the physical conditions of the source such as the size and temperature of its secondary star which is expected to play a pivotal role in their evolution (e.g., Thorstensen et al. 2002).KSP-OT-201712a, with an orbital period of 58.75 minutes and He/H flux ratio of ∼0.27, is therefore the second dwarf nova with the transitional nature of a short period and low He/H flux ratio and the first one with a measured surface temperature of the secondary, providing a unique opportunity to study its density condition and mass transfer history during this intermediate phase in the evolution of lowmass binaries (Podsiadlowski et al. 2003).Figure 5 (a) compares the orbital period and He/H ratio of KSP-OT-201712a with those of other dwarf novae, showing that the source and KSP-OT-201701a together correspond to the transitional phase between long-and short-period dwarf.
It is known that dwarf novae with higher effective temperatures at a given orbital period have evolved donor stars (Thorstensen et al. 2002).The measured ∼4570 K temperature of the secondary star of KSP-OT-201712a is greater than the 3000-3500 K range in which dwarf novae whose orbital periods are slightly greater than the period minimum have been measured (Beuermann et al. 1998;Thorstensen et al. 2002), while it is lower than ∼6700 K for He CVs (Burdge et al. 2022).In the case of He CVs, which is a more evolved short-period dwarf nova with a larger He/H flux ratio than KSP-OT-201712a, the measured temperatures of ∼6700 K for the secondaries are in good agreement with the theoretical prediction made by stellar evolution code MESA (Modules for Experiments in Stellar Astrophysics; Paxton et al. 2011Paxton et al. , 2013Paxton et al. , 2015Paxton et al. , 2018Paxton et al. , 2019)).No such comparison between theoretical predictions and observational examples has been made for short-period dwarf novae with a low He/H flux ratio so far to the best of our knowledge.
Figure 5 (b) shows the evolutionary tracks of the effective temperature of the secondary of KSP-OT-201712a that we calculate using MESA (version r22.11.1; following a description of El-Badry et al. 2021b) for four different cases of the initial mass transfer age.As shown in the figure, we find that the mass transfer in KSP-OT-201712a started when its age was about 93% of the main sequence age.Theoretically, the secondary stars of dwarf novae passing through the period minimum are generally expected to start mass transfer when their ages are over ∼80% of the main sequence age (Goliasch & Nelson 2015;El-Badry et al. 2021b;Burdge et al. 2022).We, therefore, find that the temperature of the secondary star of KSP-OT-201712a is within the range that is compatible with the theoretical predictions and that its age was in fact about 13% older than the minimum main-sequence age for mass transfer to start and pass through the period minimum.Following our binary evolutionary model that corresponds to KSP-OT-201712a, the source is expected to evolve to the AM CVn phase with an orbital period of as short as 20 minutes after which its period bounces back a bit when the thermal time scale of the secondary star becomes larger than gravitational radiation time scale (Rappaport et al. 1982).(a) Observed orbital periods and He/H ratios of dwarf novae: red squares for long-period dwarf novae; circles for short-period dwarf novae; and red star for KSP-OT-201712a.The green shared area shows the period gap.blue dotted vertical line indicates the period minimum of 76 minutes.The arrowed red dashed curve roughly represents the expected evolutionary path of a dwarf nova with an evolved secondary as its orbital period decreases.The AM CVn systems, which are a group of dwarf novae with small orbital periods, small mass ratios, and no H emission, are located at the top-left corner.The orbital periods and He/H ratios of other dwarf novae are from Lee et al. (2022).(b) Calculated effective temperatures of the secondary star of KSP-OT-201712a by MESA (see text) as a function of orbital period: the blue curve is for the case in which the initial mass transfer started when its age was 8% of the main sequence.The green, red, and cyan curves are the same as the blue curve but for the cases of 90, 93, and 96%, respectively.The red star marks the position of KSP-OT-201712a.
KSP-OT-201712a is a unique example showing that standstills can persist in a dwarf nova to the dynamical evolutionary stage after the passage of the period minimum with atypical outbursts embedded in standstills.To the best of our knowledge, no dwarf novae below the period minimum have been observed with standstills.Also, standstills in general appear as a middle stage from an outburst to the quiescent phase, which is different from the standstill in KSP-OT-201712a.The secondary of KSP-OT-201712a still has a significant hydrogen envelope revealed by the strong Hα emission (Figure 3), and the mass-accretion rate of the system is still largely supported by the presence of standstills and short outburst cycles (Figure 1).The secondary will gradually exhaust its hydrogen envelope via mass transfer and the system will enter a dwarf nova phase that has outburst cycles without standstills (Lee et al. 2022).Only a handful of dwarf novae have been observed below the period minimum, and more samples are required to understand the evolution of short-period dwarf novae.
6. SUMMARY AND CONCLUSION KSP-OT-201712a is the first He-deficient dwarf nova below the period minimum with a measured temperature for a secondary.We summarize the results as follows.
• The source exhibits peculiar light curves for a dwarf nova with outbursts embedded in standstills, which identifies it to be an ER-UMa type undergoing substantial mass transfer.The outburst cycle during the standstills is ∼ 6.6 days but it increases to ∼ 15 days outside of them.
• The outburst colors become bluest near the peaks during the standstills, but they evolve in the opposite direction outside of the standstills.We attribute this to the difference in the mass transfer rate, in which outside-in outburst processes with an increased mass transfer are responsible for the outburst within the standstills while inside-out outburst processes with a smaller mass transfer are responsible for those outside of the standstills.
• Using radial velocity curves obtained from time series spectroscopy, we estimate its orbital period to be 58.75 ± 0.02 minutes, which is below the period minimum.The spectral energy distribution of the source appears to be very similar to that of a late-type star, apparently dominated by its secondary.While its double-peaked Hα emission is very strong, He emission is weak, giving the He/H flux ratio of ∼ 0.27 and making the source a Hedeficient dwarf nova.By analyzing the absorption lines of Na D, Mg b, and Na I, we obtain the following parameters for its secondary: T eff ≃ 4570 ± 40 K, [Fe/H] ≃ 0.06 ± 0.15 dex and log g ≃ 4.5 ± 0.1.Its orbital period and outburst peak, as well as its measured proper motion, are consistent with the source being at the distance of 1.32 ± 0.10 kpc.
• Long-period dwarf novae above the period minimum typically show strong Hα but weak He emission, while short-period dwarf novae below the period minimum have weak Hα emission but strong He emission.KSP-OT-201712a is a Hedeficient (or, small He/H flux ratio), short-period dwarf nova below the period minimum showing a transitional nature evolving from a long-period dwarf nova to a short-period one.The hot secondary suggests that the mass transfer in KSP-OT-201712a started when its age was about 93% of the main sequence age with a large central density.
It is expected that KSP-OT-201712a will eventually evolve into an AM CVn.

Figure 1 .
Figure1.The observed V -and r-band light curves of KSP-OT-201712a by the KMTNet and ZTF are shown in filled black and red circles, respectively.The panel on the left-hand side is for the period of MJD = 58110-58160, whereas the panel on the right-hand side is for MJD = 58380-58550.On the left-hand panel, we identify six outbursts that show a clear rise and decay across peak brightness which we name O1-O6 from left to right.On the right-hand panel, we identify at least two such outbursts of O7 and O8 from the KMTNet data.Although there exist more outburst activities, only these two outbursts are clearly identified by observations of their peak brightnesses.During the period of MJD = 58475-58495, ZTF also detected outburst activities of the source in the r band (filled red circles), consisting of four separate 2-hour and one 40-minute (MJD ∼ 58490 day) observations conducted at about 40-second cadence and showing an r-band magnitude variation of 18.2-16.8mag.The first three 2-hour ZTF observations overlap with the O7 outburst identified by the KMTNet data.The fourth 2-hour observation occurred at MJD ∼ 58493.30day when there was no KMTNet observation, and we named this OZTF.The inset in the right-hand side shows how the r-band magnitude changes during OZTF.The two horizontal dashed lines represent the quiescent magnitude (V = 18.6 mag; black) of the source and V = 17.4 mag (blue) which is the brightness of the standstill just after the O2 outburst.The shaded cyan vertical area on the left-hand plot corresponds to the interval of the standstills therein.The inset in the left-hand side provides an enlarged view of part of the light curve to highlight the shape of the standstills.The two dashed orange vertical lines mark the epochs of spectroscopic observations of the source.Extinction is not corrected.Magnitude errors are about 0.02 mag around V = 18.6 mag.

Figure 2 .
Figure 2. (Top-left panel) The B −V (middle plot) and V −I (bottom plot) color evolution of KSP-OT-201712a synchronous with that of the V -band light curve (top plot) during the period of MJD = 58110-58166 which corresponds to the left-hand panel in Figure 1.All magnitudes are extinction corrected.(Top-right panel) Same as the top-left panel, but for the first one-third period (MJD = 58380-58437 days) of the right panel in Figure 1.(Bottom-left panel) Same as the top-right panel but for the second one-third period (MJD = 58437-58494 days).(Bottom-right panel) Same as the top-right panel, but for the final one-third period (MJD = 58494-58550 days).The shaded cyan vertical areas and the blue horizontal dashed lines are the same in Figure 1.The red vertical dotted lines indicate the peak epochs of the O1-O8 outbursts.

Figure 3 .
Figure 3. (Top panel) Extinction-corrected and stacked GMOS-S spectrum (grey color) of KSP-OT-201712a compared with a model spectrum (green color) from the MILES library for a star with T eff = 4570 K, [Fe/H] = 0.06 dex, and log g = 4.5.Notable emission and absorption features are marked with arrows.(Middle panels) A sequence of the enlarged individual spectra centered on Hβ emission, Na D absorption, and Hα emission features from left to right, respectively, arranged in time sequence from top spectrum to bottom spectrum.(Bottom panel) The radial velocity curves of KSP-OT-201712a obtained by Hα emission (blue circles) and Na D absorption (red circles) compared with the best-fit sinusoidal curves shown in blue and red lines, respectively.

Figure 4 .
Figure 4.The solid curve represents the distribution of the expected E(B −V ) values as a function of distance in the direction of KSP-OT-201712a from the 3D extinction model of Green et al. (2019).The dashed curve represents the distribution of the E(B −V ) values that satisfy the known relation between the orbital periods and the absolute peak magnitudes of dwarf novae for KSP-OT-201712a.
Figure 5.(a) Observed orbital periods and He/H ratios of dwarf novae: red squares for long-period dwarf novae; circles for short-period dwarf novae; and red star for KSP-OT-201712a.The green shared area shows the period gap.blue dotted vertical line indicates the period minimum of 76 minutes.The arrowed red dashed curve roughly represents the expected evolutionary path of a dwarf nova with an evolved secondary as its orbital period decreases.The AM CVn systems, which are a group of dwarf novae with small orbital periods, small mass ratios, and no H emission, are located at the top-left corner.The orbital periods and He/H ratios of other dwarf novae are fromLee et al. (2022).(b) Calculated effective temperatures of the secondary star of KSP-OT-201712a by MESA (see text) as a function of orbital period: the blue curve is for the case in which the initial mass transfer started when its age was 8% of the main sequence.The green, red, and cyan curves are the same as the blue curve but for the cases of 90, 93, and 96%, respectively.The red star marks the position of KSP-OT-201712a.