# The Z Camelopardalis-type star AY Piscium: stellar and accretion disk
parameters

Jan Kára Astronomical Institute, Faculty of Mathematics and Physics, Charles
University, V Holešovičkách 2, CZ-180 00 Praha 8, Czech Republic  Sergey
Zharikov Universidad Nacional Autónoma de México, Instituto de Astronomía, AP
106, Ensenada, 22800, BC, México  Marek Wolf Astronomical Institute, Faculty
of Mathematics and Physics, Charles University, V Holešovičkách 2, CZ-180 00
Praha 8, Czech Republic  Ainash Amantayeva  Al-Farabi Kazakh National
University, Al-Farabi Ave., 71, 050040, Almaty, Kazakhstan  Gulnur Subebekova
Al-Farabi Kazakh National University, Al-Farabi Ave., 71, 050040, Almaty,
Kazakhstan  Serik Khokhlov Al-Farabi Kazakh National University, Al-Farabi
Ave., 71, 050040, Almaty, Kazakhstan  Aldiyar Agishev Al-Farabi Kazakh
National University, Al-Farabi Ave., 71, 050040, Almaty, Kazakhstan  Jaroslav
Merc Astronomical Institute, Faculty of Mathematics and Physics, Charles
University, V Holešovičkách 2, CZ-180 00 Praha 8, Czech Republic

###### Abstract

We present a new study of the Z Cam-type eclipsing cataclysmic variable AY
Piscium with the aim of determining the fundamental parameters of the system
and the structure of the accretion flow therein. We use time-resolved
photometric observations supplemented by spectroscopy in the standstill, to
which we applied our light-curve modeling techniques and the Doppler
tomography method, to update system parameters. We found that the system has a
massive white dwarf $M_{\rm WD}=0.90(4)$ M☉, a mass ratio $q=0.50(3)$, and the
effective temperature of a secondary $T_{2}=4100(50)$ K. The system
inclination is $i=74\fdg 8(7)$. The orbital period of the system
$P_{\mathrm{orb}}=0.217320523(8)\;\mathrm{d}$ is continuously increasing with
the rate of $\dot{P}_{\mathrm{orb}}=+7.6(5)\times 10^{-9}$ d year-1. The mass
transfer rate varies between 2.4$\times$10-10 M⊙ year-1 in quiescence up to
1.36$\times$10-8 M⊙ year-1 in outburst. The accretion disk transitions from
the cooler, flared, steady-state disk to a warmer state with a practically
constant and relatively high disk height. The mass transfer rate is about
1.6$\times$10-9 M⊙ year-1 in the standstill. The Balmer emission lines show a
multi-component structure similar to that observed in long-orbital-period
nova-like systems. Out of standstill, the system exhibits outburst bimodality,
with long outbursts being more prominent. We conclude that the Balmer emission
lines in AY Psc are formed by the combination of radiation from the irradiated
surface of the secondary, from the outflow zone, and from winds originating in
the bright spot and the disk’s inner part.

binaries: close – novae, cataclysmic variables – stars: individual: AY Psc –
stars: fundamental parameters – stars: dwarf novae

††software:  Matplotlib (Hunter, 2007), NumPy (Harris et al., 2020), SciPy
(Virtanen et al., 2020), astropy (Astropy Collaboration et al., 2013, 2018,
2022), Fast maximum entropy Doppler mapping (Spruit, 1998), PyDoppler
(Hernandez Santisteban, 2021), IRAF (Tody, 1986, 1993), CVlab (Zharikov et
al., 2013)

##  1 Introduction

Non-magnetic cataclysmic variables (CVs) are interacting binary star systems
in which a Roche-lobe–filling secondary (a late-type main-sequence star or a
brown dwarf) transfers matter onto a white dwarf (WD) primary (Warner, 1995)
forming an accretion disk around the WD. Typical orbital periods of CVs are
between 76 minutes and 10 hours (Ritter & Kolb, 2003). These systems are
divided into several classes and subclasses generally based on their optical
light curve behavior, e.g., Dwarf novae (DNe), Nova-likes (NLs), VY Scl (also
referred to as ‘anti-dwarf novae’), Z Cam, and V Sge systems. DNe systems show
semi-periodic outbursts, and some of them also exhibit more energetic
superoutbursts. They can be divided into several subclasses depending on the
orbital period, the presence of superhumps, and the characteristic of outburst
behavior (for the general information on DNe and superhumps, see e.g., Warner
(1995)). SU UMa-type dwarf novae ($P_{orb}\lesssim 2.2$ hours) show superhumps
during their long outbursts (superoutbursts) whose period is generally a few
percent longer than the orbital period. It is generally accepted that
superhumps are caused by the 3:1 resonance (Whitehurst, 1988). In contrast to
SU UMa-type systems, DNe with longer orbital periods ($>3$ hours) do not show
superhumps. Among the CVs with the shortest orbital periods are the WZ Sge-
type systems, which were originally proposed as a subgroup of SU UMa-type
systems with outbursts of high amplitude ($\sim 8\,\mathrm{mag}$) and long
recurrence times (up to decades) (Bailey, 1979; Kato, 2015).

NLs remain mostly in a high luminosity state and they can be also divided into
different sublcasses. The most prominent of them are SW Sex- and VY Scl-types
stars. SW Sex-type systems show distinctive spectroscopic characteristic
(Thorstensen et al., 1991) from the rest of NLs and mostly cluster in the 3-4
h orbital period range (Rodríguez-Gil et al., 2007). The VY Scl stars are a
subclass of NLs whose light curves are characterized by occasional drops from
steady high states into low states lasting up to several hundred days. The Z
Cam systems are a subclass of the DNe, which in addition to outburst activity,
exhibit standstills, during which the system luminosity stays at a high state
for a long time, similarly to NLs. The mechanisms of transition between
outburst cycles and standstills in Z Cam stars, and why VY Scl stars enter a
low mass transfer state, are not well understood. It is hypothesized that VY
Scl stars might be Z Cam stars in extended standstills (see Warner, 1995,
section 4.1 and references therein). On the side of long-period CVs, there are
the V Sge-type systems (Steiner & Diaz, 1998; Diaz, 1999). The V Sge stars’
orbital periods range from 5 to 12 hours, and their orbital light curves are
either low-amplitude sinusoidal or high-amplitude asymmetric with primary and
secondary eclipses. Their spectra show the ratio of the equivalent widths of
He II 4686 Å to H$\beta$ usually greater than 2 and indicate the presence of a
strong wind in the systems (Steiner & Diaz, 1998).

The subject of this paper is a detailed spectroscopic and photometric study of
the eclipsing CV AY Piscium, hereafter AY Psc (also SDSS J013655.46+071629.2,
2MASS J01365544+0716293, PG 0134+070, $V\simeq 16.3$ mag). The source was
identified as a CV by Green et al. (1982). Szkody et al. (1989) found that AY
Psc is an eclipsing system with an orbital period of $P=5.22$ h. Later, an
orbital ephemeris was provided by Diaz & Steiner (1990) who also revised the
orbital period of $P=0.2173209\;\mathrm{d}=5.2157\;\mathrm{h}$ . They reported
flickering with a semi-amplitude of about 0.08 mag present in the light curve
along the whole orbital cycle.

The system parameters were derived for the first time by Szkody & Howell
(1993, hereafter SH93) using spectroscopic observations and later by Howell &
Blanton (1993) using photometric observations. They found that the system
contains a massive $\sim$ 1.11-1.31 M☉ white dwarf, a $\sim$ 0.53-0.59 M☉
companion, and that the system inclination is about 74∘. Those estimates
locate AY Psc in a harbor of potential SN Ia progenitors.

Mercado & Honeycutt (2002) classified AY Psc as a Z Cam-type star based on the
presence of dwarf-nova outbursts as well as occasional standstills. Gülsecen
et al. (2009) reported an extensive photometric analysis of AY Psc based on
observation obtained during a large number of nights in 2003–2005. They
confirmed the stability of the system’s orbital period in the long term and
found evidence of variable negative superhumps in the system. Han et al.
(2017) continued to study the long-term photometric behaviour of AY Psc. They
reported that the system shows outbursts with an amplitude of $\sim 2.5$ mag,
during which the system reaches the maximal brightness $V\simeq 14.6$ mag.
Outbursts repeated themselves with a period of $\sim 18.3(7)$ days.

The first time-resolved spectroscopy of AY Psc was reported by SH93. The
object had 15.8 mag in the V-band, which is close to the low state level. They
covered about 70 % of an orbit in the wavelength range of 4250-4950 Å with a
spectral resolution of about 2.8 Å. The presented spectra show complex Balmer
line profiles and the absence of the He II $\lambda$4686 line. The full width
zero intensity (FWZI) of H$\beta$ was between 30 and 40 Å. No other time-
resolved spectroscopy was reported in the literature.

Three additional spectra were acquired by the LAMOST project (Han et al.,
2020). The spectra were obtained close to the high brightness state ($V_{\rm
AAVSO}\simeq 14.6$ mag). They are significantly different compared to the low
state spectra of SH93 and exhibit broad single-peaked Balmer emission lines
and several weak neutral helium emission lines (e.g., HeI $\lambda$4914,
$\lambda$5876, $\lambda$6678). There are also strong He II $\lambda$4686 and
Bowen blend lines (C III/N III $\lambda$4634-4651). Some absorption features
at He I $\lambda$4026 and $\lambda$4471, Fe I $\lambda$5018, Fe II
$\lambda$4924, Mg I$~{}\lambda$5178 and Na D lines were also found. The FWZI
and equivalent width (EW) of H$\beta$ and H$\alpha$ lines in LAMOST spectra
were 42.1Å /5.0Å and 120.7Å /17.6Å, respectively.

The Gaia parallax of AY Psc from DR3 (Gaia Collaboration, 2022) is
$\pi=1.37(4)$ mas, which gives a distance of $d=$ 730(20) pc. The interstellar
absorption in the direction of AY Psc is $E(B-V)=0.05\pm 0.03$ (Schlafly &
Finkbeiner, 2011), three-dimensional map of interstellar dust by Green et al.
(2015) gives for the same direction and for the object’s distance absorption
of $E(g-r)=0.04^{+0.05}_{-0.01}$.

AY Psc is the only confirmed Z Cam-type DN that shows deep eclipses (0.75-1.75
mag)111EM Cyg, another Z Cam-type system, exhibits eclipses of depth about
0.15 mag (Liu et al., 2021) caused by the system inclination of $i=67\pm 2$
(North et al., 2000) at which only a small part of the accretion disk is
obscured by the secondary., which provides an opportunity for a thorough
analysis of a system belonging to this subclass of DNe. The aims of the
presented paper are to determine the fundamental parameters of the system
based on the analyses of the light curves obtained in different states of the
system, study the structure of the accretion flow therein, and the origin of
the sources that form emission line profiles. This will be useful to better
understand the mechanism of switching between outburst activity and
standstills in Z Cam systems.

##  2 Observations

Figure 1: Top: Long-term light curve of AY Psc collected by AAVSO, ASAS, ASAS-
SN, ZTF, and our photometry obtained at OAN SPM, Ondřejov, La Silla and TSHAO,
only out-of-eclipse measurements are shown. Grey dashed lines mark the times
of the spectroscopic observations obtained at OAN SPM. The triangles mark the
nights when photometric observations used for light-curve modeling were
obtained, their color corresponds to the eclipse light curves discussed below.
These light curves were obtained at HJDs $2\,458\,041$, $2\,459\,470$, and
$2\,458\,156$ and show the light curve of AY Psc in quiescence, outburst, and
standstill, respectively. Middle and bottom panels: LAMOST spectrum of AY Psc
(middle panel) and cutouts of normalized LAMOST spectrum centered on
H${\beta}$ and He II (bottom, left), and H${\alpha}$ and He I (bottom, right).
The air wavelength positions of the emission lines are marked by red lines.
Table 1: Log of observations Photometry
---
HJD | Civil date | Filter | Exposure time | Number of frames | Observatory
$-2\,400\,000$ |  |  | [s] |  |
$58\,041$ | 2017 Oct 14 | C | $60$ | $91$ | Ondřejov
$58\,156$ | 2018 Feb 6 | C | $60$ | $50$ | Ondřejov
$58\,847$ | 2019 Dec 29 | C | $60$ | $48$ | Ondřejov
$59\,184$ | 2020 Nov 30 | R | $30$ | $57$ | La Silla
$59\,471$ | 2021 Sep 13 | V | $60$ | $308$ | OAN SPM
$59\,472$ | 2021 Sep 14 | V | $60$ | $296$ | OAN SPM
$59\,473$ | 2021 Sep 15 | V | $60$ | $350$ | OAN SPM
$59\,474$ | 2021 Sep 16 | V | $60$ | $314$ | OAN SPM
$59\,494$ | 2021 Oct 6 | V | $60$ | $386$ | OAN SPM
$59\,497$ | 2021 Oct 9 | V | $60$ | $244$ | OAN SPM
$59\,498$ | 2021 Oct 10 | V | $60$ | $240$ | OAN SPM
$59\,511$ | 2021 Oct 23 | C | $60$ | $54$ | Ondřejov
$59\,515$ | 2021 Oct 27 | C | $60$ | $44$ | Ondřejov
$59\,528$ | 2021 Nov 9 | V | $60$ | $105$ | TSHAO
$59\,571$ | 2021 Dec 22 | C | $60$ | $49$ | Ondřejov
$59\,586$ | 2022 Jan 6 | C | $60$ | $32$ | Ondřejov
$59\,857$ | 2022 Oct 4 | C | $60$ | $45$ | Ondřejov
$59\,874$ | 2022 Oct 21 | C | $60$ | $33$ | Ondřejov
$59\,898$ | 2022 Nov 14 | C | $60$ | $46$ | Ondřejov
Spectroscopy
HJD | Civil date | Spectral range | Exposure time | Number of Spectra | Observatory
$-2\,400\,000$ |  |  | [s] |  |
$59\,471$ | 2021 Sep 13 | 6026 Å- 7258 Å | $1\,200$ | $15$ | OAN SPM
$59\,472$ | 2021 Sep 14 | 6026 Å- 7258 Å | $1\,200$ | $15$ | OAN SPM
$59\,473$ | 2021 Sep 15 | 6026 Å- 7258 Å | $1\,200$ | $15$ | OAN SPM
$59\,474$ | 2021 Sep 16 | 6026 Å- 7258 Å | $1\,200$ | $15$ | OAN SPM

Over the past years, we have accumulated new AY Psc data, including our own
photometric and spectroscopic measurements obtained at several observatories
as well as available data or information previously published in the
literature. A log of the newly obtained observations is given in Table 1.

###  2.1 Photometry

Table 2: New mid-eclipse times of AY Psc determined from ground-based observations $\mathrm{BJD}_{\mathrm{min}}$ – | Epoch | Error | Filter | Observatory
---|---|---|---|---
2 400 000 |  | [day] |  |
52 966.17334 | 24 585 | 0.0005 | C | Exmouth
52 968.12946 | 24 594 | 0.0005 | C | Exmouth
52 969.21630 | 24 599 | 0.0005 | C | Exmouth
52 972.04142 | 24 612 | 0.0005 | C | Exmouth
52 986.16834 | 24 677 | 0.0005 | C | Exmouth
52 987.03754 | 24 681 | 0.0005 | C | Exmouth
52 988.12446 | 24 686 | 0.0005 | C | Exmouth
53 272.15809 | 25 993 | 0.0005 | C | Exmouth
53 273.24509 | 25 998 | 0.0005 | C | Exmouth
53 287.15469 | 26 062 | 0.0005 | C | Exmouth
53 291.06605 | 26 080 | 0.0005 | C | Exmouth
53 291.28355 | 26 081 | 0.0005 | C | Exmouth
53 292.15251 | 26 085 | 0.0005 | C | Exmouth
53 294.10878 | 26 094 | 0.0005 | C | Exmouth
53 297.15130 | 26 108 | 0.0005 | C | Exmouth
53 663.12073 | 27 792 | 0.0005 | C | Exmouth
53 670.29257 | 27 825 | 0.0005 | C | Exmouth
53 675.07403 | 27 847 | 0.0005 | C | Exmouth
53 675.29136 | 27 848 | 0.0005 | C | Exmouth
53 676.16109 | 27 852 | 0.0005 | C | Exmouth
53 677.24797 | 27 857 | 0.0005 | C | Exmouth
53 678.11698 | 27 861 | 0.0005 | C | Exmouth
58 041.48048 | 47 939 | 0.0001 | C | Ondřejov
58 156.22572 | 48 467 | 0.0001 | C | Ondřejov
58 778.85019 | 51 332 | 0.0005 | r | ZTF
58 779.93694 | 51 337 | 0.0005 | r | ZTF
58 847.30611 | 51 647 | 0.0001 | C | Ondřejov
59 184.58819 | 53 199 | 0.0001 | R | La Silla
59 470.79944 | 54 516 | 0.0001 | V | OAN SPM
59 471.01677 | 54 517 | 0.0001 | V | OAN SPM
59 471.88628 | 54 521 | 0.0001 | V | OAN SPM
59 472.97279 | 54 526 | 0.0001 | V | OAN SPM
59 473.84180 | 54 530 | 0.0001 | V | OAN SPM
59 493.83522 | 54 622 | 0.0001 | V | OAN SPM
59 496.87772 | 54 636 | 0.0001 | V | OAN SPM
59 497.96454 | 54 641 | 0.0001 | V | OAN SPM
59 511.43831 | 54 703 | 0.0001 | C | Ondřejov
59 515.34967 | 54 721 | 0.0002 | C | Ondřejov
59 528.17230 | 54 780 | 0.0001 | V | TSHAO
59 571.20157 | 54 978 | 0.0001 | C | Ondřejov
59 586.19618 | 55 047 | 0.0002 | C | Ondřejov
59 857.41284 | 56 295 | 0.0001 | C | Ondřejov
59 898.26921 | 56 483 | 0.0001 | C | Ondřejov

New ground-based photometry222 All data were reduced using the apphot IRAF
task except Ondřejov Observatory and La Silla Observatory. The heliocentric
correction was applied. The magnitude errors, ranging from 0.01 to 0.02 mag
(OAN SPM, La Silla, and TSHAO) and 0.01-0.05 mag (Ondřejov) were estimated
from the magnitude dispersion of comparison stars with similar brightness. of
AY Psc was obtained at four different observatories: Observatorio Astronomico
Nacional San Pedro Mártir (Mexico, hereafter OAN SPM), Ondřejov Observatory
(Czech Republic, hereafter Ondřejov), La Silla Observatory in Chile, and Tien
Shan Astronomical Observatory (Kazakhstan, hereafter TSHAO). Below we describe
the details of these observations shortly for each observatory. These newly
obtained data, together with recently available ones, were used for new mid-
eclipse times determination presented in Table 2. New times of primary
eclipses and their uncertainties were generally determined by fitting the
light curve by Gaussians or polynomials of the third or fourth order. The
least-squares method to the lower part of the light curve was applied. The
times were converted from heliocentric Julian date (HJD) to barycentric Julian
date (BJD) using a conversion tool created by Eastman et al.
(2010)333Available at https://astroutils.astronomy.osu.edu/time/hjd2bjd.html.

Table 3: Mid-eclipse times of AY Psc based on TESS observations

$\mathrm{BJD}_{\mathrm{min}}$ – | Epoch |  $\mathrm{BJD}_{\mathrm{min}}$ – | Epoch |  $\mathrm{BJD}_{\mathrm{min}}$ – | Epoch |  $\mathrm{BJD}_{\mathrm{min}}$ – | Epoch
---|---|---|---|---|---|---|---
2 400 000 |  | 2 400 000 |  | 2 400 000 |  | 2 400 000 |
$59\,447.76307$ | $54\,410$ | $59\,453.19610$ | $54\,435$ | $59\,461.67160$ | $54\,474$ | $59\,467.10444$ | $54\,499$
$59\,447.98041$ | $54\,411$ | $59\,453.41342$ | $54\,436$ | $59\,461.88885$ | $54\,475$ | $59\,467.32195$ | $54\,500$
$59\,448.19767$ | $54\,412$ | $59\,453.63074$ | $54\,437$ | $59\,462.10625$ | $54\,476$ | $59\,467.53927$ | $54\,501$
$59\,448.41506$ | $54\,413$ | $59\,453.84804$ | $54\,438$ | $59\,462.32357$ | $54\,477$ | $59\,467.75658$ | $54\,502$
$59\,448.63237$ | $54\,414$ | $59\,454.06539$ | $54\,439$ | $59\,462.54087$ | $54\,478$ | $59\,467.97388$ | $54\,503$
$59\,448.84974$ | $54\,415$ | $59\,454.28269$ | $54\,440$ | $59\,462.75841$ | $54\,479$ | $59\,468.19123$ | $54\,504$
$59\,449.06702$ | $54\,416$ | $59\,454.50002$ | $54\,441$ | $59\,462.97553$ | $54\,480$ | $59\,468.40855$ | $54\,505$
$59\,449.28440$ | $54\,417$ | $59\,454.71735$ | $54\,442$ | $59\,463.19286$ | $54\,481$ | $59\,468.62585$ | $54\,506$
$59\,449.50173$ | $54\,418$ | $59\,454.93467$ | $54\,443$ | $59\,463.41019$ | $54\,482$ | $59\,468.84319$ | $54\,507$
$59\,449.71902$ | $54\,419$ | $59\,455.15189$ | $54\,444$ | $59\,463.62749$ | $54\,483$ | $59\,469.06051$ | $54\,508$
$59\,449.93629$ | $54\,420$ | $59\,455.36932$ | $54\,445$ | $59\,463.84483$ | $54\,484$ | $59\,469.27774$ | $54\,509$
$59\,450.15360$ | $54\,421$ | $59\,455.58664$ | $54\,446$ | $59\,464.06213$ | $54\,485$ | $59\,469.49525$ | $54\,510$
$59\,450.37090$ | $54\,422$ | $59\,455.80384$ | $54\,447$ | $59\,464.27937$ | $54\,486$ | $59\,469.71252$ | $54\,511$
$59\,450.58833$ | $54\,423$ | $59\,456.02126$ | $54\,448$ | $59\,464.49680$ | $54\,487$ | $59\,469.92979$ | $54\,512$
$59\,450.80557$ | $54\,424$ | $59\,456.45593$ | $54\,450$ | $59\,464.71416$ | $54\,488$ | $59\,470.14719$ | $54\,513$
$59\,451.02299$ | $54\,425$ | $59\,456.89053$ | $54\,452$ | $59\,464.93149$ | $54\,489$ | $59\,470.36450$ | $54\,514$
$59\,451.24022$ | $54\,426$ | $59\,457.10794$ | $54\,453$ | $59\,465.14873$ | $54\,490$ | $59\,470.58199$ | $54\,515$
$59\,451.45753$ | $54\,427$ | $59\,457.54246$ | $54\,455$ | $59\,465.36606$ | $54\,491$ | $59\,470.79916$ | $54\,516$
$59\,451.67482$ | $54\,428$ | $59\,458.41193$ | $54\,459$ | $59\,465.58337$ | $54\,492$ | $59\,471.01640$ | $54\,517$
$59\,451.89218$ | $54\,429$ | $59\,458.62915$ | $54\,460$ | $59\,465.80070$ | $54\,493$ | $59\,471.23359$ | $54\,518$
$59\,452.10962$ | $54\,430$ | $59\,458.84644$ | $54\,461$ | $59\,466.01802$ | $54\,494$ | $59\,471.45103$ | $54\,519$
$59\,452.32682$ | $54\,431$ | $59\,459.06377$ | $54\,462$ | $59\,466.23533$ | $54\,495$ | $59\,471.66836$ | $54\,520$
$59\,452.54415$ | $54\,432$ | $59\,459.28105$ | $54\,463$ | $59\,466.45264$ | $54\,496$ | $59\,472.53763$ | $54\,524$
$59\,452.76147$ | $54\,433$ | $59\,460.15036$ | $54\,467$ | $59\,466.67006$ | $54\,497$ | $59\,472.75504$ | $54\,525$
$59\,452.97879$ | $54\,434$ | $59\,461.45431$ | $54\,473$ | $59\,466.88728$ | $54\,498$ |  |

Note. We assumed accuracy of $0.0005\;\mathrm{d}$ for all mid-eclipse times
determined from the light curve observed by TESS.

####  2.1.1 OAN SPM

Time-resolved photometry of AY Psc was obtained using the direct CCD image
mode of the 0.84-m telescope of OAN SPM. The object was observed repeatedly
during seven photometric nights on October 13–16 and November 6–10, 2021. The
time of individual exposure in the V-band was 60 seconds, and each run lasted
about 5–8 hours. The images were bias-corrected and flat-fielded before
aperture photometry was carried out.The photometric data were calibrated using
the field standard stars from Henden & Honeycutt (1995).

Figure 2: Light curves of AY Psc showing primary eclipses obtained at OAN SPM
during 7 nights in October and November 2021, all light curves were obtained
during standstill

.

Figure 3:  Phase-folded light curve of AY Psc in V-band at OAN SPM (top) and
TESS magnitude (bottom), both light curves were obtained during standstill.
The light curves were phase-folded orbital
$P_{\mathrm{orb}}=0.21732002\;\mathrm{d}$, the phase $\varphi=0.0$ corresponds
to the inferior conjunction of the secondary. The out-of-eclipse TESS
magnitude was estimated using the ticgen software package (Jaffe & Barclay,
2017; Stassun et al., 2018) with out-of-eclipse brightness in V filter as an
input parameter. The blue circles mark the individual measurements, the orange
circles represent the phase-averaged light curve computed as median values in
evenly-spaced bins with a width of $\Delta\varphi=0.004$ orbital phase.

####  2.1.2 Ondřejov

Time-resolved CCD photometry of AY Psc has also been obtained at the Ondřejov
Observatory in the years 2017–2022. The Mayer 0.65-m ($f/3.6$) reflecting
telescope with the CCD camera MI G2-3200 without a photometric filter (marked
by ”C” in Tables 1 and 2) was used. The Aphot444Developed at the Ondřejov
Observatory by M. Velen and P. Pravec., synthetic aperture photometry and
astrometry software, was used for data reduction. The quality of the nights
was photometric or with light clouds. Therefore, differential photometry was
performed using suitable comparison stars also from Henden & Honeycutt (1995).

####  2.1.3 La Silla and TSHAO

Two additional time series were obtained at La Silla and TSHAO observatories.
In the first case, the Danish 1.54-m telescope was used in remote access on
December 1, 2020. The R filter and 30-second exposure time were used, and the
conditions were photometric. The Aphot software was used for data reduction.

In TSHAO, the photometric data were obtained using the 1-m telescope on
November 9, 2021, in the V- band and with 60 seconds exposures. The
observations were obtained under photometric weather conditions.

####  2.1.4 Exmouth

The original unfiltered CCD photometry obtained by A. Liu at Norcape
Observatory, Exmouth, Western Australia, during the 2003–2005 seasons (48
nights together) and used primarily for search in a superhump period of AY Psc
(Gülsecen et al., 2009) was kindly provided to us by H. Gülsecen, Istanbul
University.

####  2.1.5 ASAS, ASAS-SN, ZTF, AAVSO

We have also employed photometric measurements of AY Psc obtained by the All-
Sky Automated Survey555http://www.astrouw.edu.pl/asas/ (ASAS; $V$ filter;
Pojmanski, 1997), All-Sky Automated Survey for Supernovae666https://asas-
sn.osu.edu/ (ASAS-SN; V and g filters; Shappee et al., 2014; Kochanek et al.,
2017), the Zwicky Transient Facility (ZTF)
survey777https://www.ztf.caltech.edu/ztf-public-releases.html (IRSA, 2022) (r
and g filters; Masci et al., 2019) and the database of American Association of
Variable Star Observers888https://www.aavso.org (AAVSO; V filter; Kloppenborg,
2022). The photometric data were subjected to visual inspection and used for
the construction of the long-term light curve. Using the data from the ZTF
survey, we derived two additional mid-eclipse times, and they are also given
in Table 2.

####  2.1.6 TESS

AY Psc was also measured by the TESS satellite in a 2-minute cadence during
two consecutive periods (Sectors 42 and 43) in August and September 2021
during a standstill. We also used these data999The TESS data used in this
paper can be found in MAST: https://doi.org/10.17909/5fq3-s930 (catalog
https://doi.org/10.17909/5fq3-s930). for mid-eclipse time determination.
However, the poor coverage of the light curve during eclipses reduced the
achievable precision, a fact which was taken into account in further analysis,
where we assumed an accuracy of $0.0005$ d for all times of eclipses. The
times of eclipses and corresponding epochs are given in Table 3.

###  2.2 Spectroscopy

We obtained new time-resolved spectroscopic observations of the H$\alpha$
line. All new observations were obtained during a standstill. We also used the
spectra obtained by the LAMOST project101010http://www.lamost.org/dr8/v2.0/
(R=1800 at $\lambda=5500$ Å) (Han et al., 2020), which are shown in Fig.1,
middle and bottom panels.

####  2.2.1 Time-resolved H$\alpha$ spectroscopy

The new spectroscopic data of AY Psc were obtained using the Boller & Chivens
long-slit spectrograph attached to the 2.12-m telescope of the OAN
SPM111111http://www.astrossp.unam.mx. A total of 60 spectra were obtained
during four consecutive nights, log of the observations is listed in Table 1.
The Boller & Chivens spectrograph covered spectral range 6026–7258 Å with the
spectral resolving power of $R\approx$ 5500\. We obtained 15 spectra with
exposure time of $1\,200\;\mathrm{s}$ each night, the duration of each
observing run was $4.9\;\mathrm{h}$. The weather conditions during the
observing run were photometric. They were controlled by simultaneous
photometric observations of the object. The spectral data were reduced in the
standard way using the apextract and onedspec IRAF tools. Standard procedures,
including bias and flat-field correction, cosmic ray removal, and wavelength
calibration, were applied.

##  3 The AY Psc light curve analysis

All long-term photometry of the AY Psc collected at different sites is
presented in Fig. 1. The light curve clearly demonstrates the periods of DNe
activity of the system and the time/duration of standstills. Individual V-band
time-series OAN SPM data obtained in 2021 during standstills are given in Fig.
2. Flickering with an amplitude of about 0.15 mag is well-visible in out-of-
eclipse phases of the light curve. The depth of the eclipse of the disk by the
secondary was about 1.10(15) mag. In contrast with the absence of the bright
spot contribution in the photometric data reported by SH93, we clearly see
some hints of it in our data (see the light curve before the eclipse in Fig.
2, HJD-2459400: 72.9–73.0 and 96.8–96.9), and in some light curves from
Gülsecen et al. (2009). The light curve in standstill folded on the orbital
period is presented in the top panel of Fig. 3 in comparison with similar TESS
data. The blue points show raw data, and the orange points show the average
light curve, which was computed as median values in evenly-spaced bins with a
width of $\Delta\varphi=0.004$. The depth of the main eclipse in the TESS data
is about 0.7(3) mag. It is less than in the V band, as the spectral range of
TESS is centered on longer wavelengths. There is also a faint hint of a
secondary eclipse ($\varphi=0.5$) in the smoothed TESS light curve.

###  3.1 Long-term variability

Figure 4: Example of an outbursting phase as covered by ASAS-SN an AAVSO data
(top), only out-of-eclipse measurements are shown, average light curves of
long and short outbursts (bottom left and center, respectively) and histogram
showing the distribution of FWHM of analyzed outbursts (bottom right). The
average light curves were constructed using ASAS-SN and AAVSO data obtained
out fo eclipse, which were shifted by an arbitrary time value so that the
shapes of the outbursts are outlined. The average light curves consist of 27
and 11 separate outburst light curves for long and short outbursts,
respectively. The grey vertical lines show our definition of moments of the
beginning of outbursts, reaching a maximal brightness, the end of the plateau
phase of the long outbursts, and the moment when the disk returns to
quiescence.

Examples of outburst behavior are shown in Fig. 4, where in the top panel, we
present outbursts detected in the time interval between HJD 2 457 550–2 457
775. Based on their shape and duration, the outbursts can be divided into two
different classes designated as ’long’ and ’short’ outbursts. This bimodality
in outburst duration is present in many DNe (Szkody & Mattei, 1984), most
prominently in SU UMa DNe, which exhibit outbursts and superoutbursts
(Otulakowska-Hypka et al., 2016). The average light curves of both classes are
presented in the lower panels of Fig. 4. The light curves were formed by a
combination of data of outbursts obtained from the AAVSO and ASAS-SN
databases, which were shifted by an arbitrary time value so that the shape of
an outburst is outlined. The time when the outburst reaches its maximal
brightness was chosen as the reference point and set as time zero. We analyzed
38 outbursts observed during active states for which good observational
coverage was found in AAVSO and ASAS-SN databases. We classified 27 of them
(71%) as long outbursts and 11 (29%) as short outbursts. The right-bottom
panels of Fig. 4 show the distribution of full width at half maximum (FWHM) of
outbursts, and in Table 4, we summarised their main characteristics. Most of
the observed outbursts were long outbursts, which is in contrast with most
other Z Cam DNe, for which short outbursts are more common (Collinson & Isles,
1979; Szkody & Mattei, 1984; Oppenheimer et al., 1998), and also with other
DNe exhibiting long and short outbursts (Otulakowska-Hypka et al., 2016, see
fig. 12 therein).

The amplitudes of outbursts are $A_{\mathrm{O}}\simeq$ 2.5 mag for the long
outbursts and $A_{\mathrm{O}}\simeq$ 2.0 mag for the short outbursts.
Typically, the system reaches the maximal brightness during an outburst in 4–5
days. In the case of long outbursts, the system remains in a plateau phase for
several days (from 6 to 9) before the brightness starts to decrease. In the
case of short outbursts, the decrease in brightness follows right after
reaching their maximum, and the plateau phase is absent. The decrease rate of
short outbursts is stable at about 0.3 mag d-1. In the case of the long
outbursts, the rate varies between 0.3 mag d-1 and 0.5 mag d-1. The average
time in low brightness state at $V=17.0\pm 0.2$ mag is about 1–5 days.

The outbursts’ occurrence during the active phase is quasi-periodic. The power
spectrum of AAVSO observations between HJD 2 455 380–2 455 990 (2010 July 2 -
2012 March 3) gives outburst recurrent time of
$T_{\mathrm{O}}=18.2(4)\>\mathrm{d}$ and the power spectrum of AAVSO, ASAS-SN
and ZTF observations between HJD 2 457 000–2 458 380 (2014 December 8 - 2018
September 18) gives $T_{\mathrm{O}}=19.1(2)\>\mathrm{d}$, both power spectra
are shown in Fig. 5.

Figure 5: Power spectrum of observations obtained on HJD 2 455 380–2 455 990
based on AAVSO data (top panel) and power spectrum of observations obtained on
HJD 2 457 000–2 458 380 based on AAVSO, ASAS-SN and ZTF data (bottom panel).

So far, there have been three standstills observed - the first one occurred
between HJD 2 456 160–2 456 995 (2012 August 20 - 2014 December 3) and lasted
about 835 days. The second was between HJD 2 457 231–2 457 275 2015 July 27 -
2015 September 9 and lasted only $\sim$44 days, and the most recent one
started on HJD 2 458 402 (2018 November 10) and did not come to an end at the
time of writing. The most recent standstill is the longest one so far, with a
length greater than $1500$ days. There are, however, gaps in the observational
data lasting $\sim 100$ days around the times of solar conjunctions (see Fig.
1), and it is, therefore, possible that standstills could be interrupted
during these gaps by a short active phase or that some short standstills were
not detected. The brightness of the system during standstill is $V\approx$
15.4 mag, that is $\sim$ 1.7 mag bellow the maximal brightness of outbursts.
The standstill states are occasionally interrupted by the occurrence of
outbursts or outburst/dip pairs. The maximal brightness during these outbursts
is the same as of the ones occurring during active states, but they occur only
sporadically.

Table 4: The outburst characteristics Parameters | Unit | Short | Long
---|---|---|---
$T_{\mathrm{d}}$ | d | $11$ | $16-19$
FWHM | d | $6$ | $10-14$
$A$ | mag | $2.0$ | $2.5$
$\dot{m}_{\mathrm{i}}$ | mag d-1 | $-0.5$ | $-0.5$
$\dot{m}_{\mathrm{d}}$ | mag d-1 | $0.3$ | $0.3-0.5$
$T_{\mathrm{max}}$ | d | $0$ | $6-9$

Figure 6: Left: Eclipse light curves of AY Psc obtained during 2017–2022 at
Ondřejov (filled-in symbols) and OAN SPM (empty stars). The color of light
curves corresponds to the color of triangles in the top panel of Fig. 1. The
plot demonstrates how the system brightness and the eclipse depth and shape
varied throughout our observational campaign. Right: The relation between the
eclipse depth (horizontal axis) and out-of-eclipse brightness (vertical axis)
in different activity states based on Ondřejov, OAN SPM both marked by filled-
in symbols), and Exmouth (marked by empty symbols) observations. The linear
fit of all points is marked by the black line. Fitting was performed using the
orthogonal distance regression method to account for uncertainties in both $V$
and $\Delta\mathrm{V}$.

In Fig. 6 left, we collected eclipse profiles in different brightness states
of the system obtained with low photometric errors ($\lesssim 0.03$ mag). The
C magnitudes were transformed to the V-band using corresponding V-band
magnitudes of several field stars and verified by comparison with nearly
simultaneous AAVSO observations. Fig. 6 right shows a relation between the
out-of-eclipse system brightness and the eclipse depth for the active state
and standstill. To accommodate for out-of-eclipse changes in brightness and
for different phase coverage of the eclipse light curves, only the phase
interval $\varphi\in$ [$-$0.1; 0.1] was used to determine the out-of-eclipse
brightness and the eclipse depth. The out-of-eclipse brightness was determined
as the brightest measured magnitude from this phase interval, and the eclipse
depth was determined as the difference between the faintest and the brightest
magnitude. During the active state, the eclipse depth gets smaller as the out-
of-eclipse brightness increases (Fig. 6, purple symbols) and shows a tendency
for a linear dependence between them. The dependence is shown by a solid line
described by relation

$\Delta V=0.20(4)\times V-2.16(54),$ (1)

which was determined as the best linear fit of the presented data using the
orthogonal distance regression method (Boggs & Rogers, 1990) which, unlike
least square method, takes into account uncertainties of both quantities of
the fitting function. Similar behavior was also observed in some NL systems
(Subebekova et al., 2020). The eclipse depth during standstill (the green
symbols at Fig. 6) is about $1.1$ mag, however, with a smaller dispersion of
about $\sim 0.2$ mag.

###  3.2 Ephemeris

Figure 7: The historical $O\\!-\\!C$ diagram for the mid-eclipse times of AY
Psc since its discovery. The diagram was constructed using the linear
ephemeris given by Equation 5, which is represented by the grey horizontal
line in the plot. The minima previously published by Diaz & Steiner (1990) and
Han et al. (2017) are denoted by green squares, newly-derived mid-eclipse
times from light curves of Gülsecen et al. (2009) are denoted by yellow
diamonds, and our new minima are denoted by orange circles. The continuous
blue curve corresponds to the best quadratic fit of the data described by
Equation 6, and the grey dashed line represents the best linear fit derived by
Han et al. (2017).

The first linear light elements of AY Psc were derived by Diaz & Steiner
(1990):

$\mathrm{Pri.Min.}=\mathrm{HJD}\;2\,447\,623.3463+0\fd 2173209\times E,$ (2)

where HJD $2\,447\,623.3463$ is the initial epoch in heliocentric Julian date,
$0\fd 2173209$ is the orbital period of the system and $E$ stands for the
number of epochs. The elements were later improved by Gülsecen et al. (2009):

$\mathrm{Pri.Min.}=\mathrm{HJD}\;2\,452\,966.1728(4)+0\fd 217320(1)\times E.$
(3)

Finally, based on a four-year scale, Han et al. (2017) derived the light
elements as

$\mathrm{Pri.Min.}=\mathrm{HJD}\;2\,447\,623.34628(2)+0\fd 21732061(1)\times
E.$ (4)

They also noted that the residuals from this ephemeris show some deviations
and the orbital period does not seem to be constant. Several additional
eclipse timings for AY Psc have been reported in the literature. Besides those
minima given in Table 2 and Table 3, we used previous mid-eclipse times
obtained by Diaz & Steiner (1990) and Han et al. (2017). A total of 155 CCD
times were included in our period study, and we derived new linear ephemeris

$\begin{array}[]{l}\mathrm{Pri.Min.}=\mathrm{BJD}\;2\,447\,623.34668(13)\,+\\\
\hskip 45.5244pt+0\fd 217320641(3)\times E,\end{array}$ (5)

where the initial epoch is given in barycentric Julian date. The data,
however, are better described by a quadratic ephemeris and, therefore a
quadratic ephemeris with a period increase was derived:

$\begin{array}[]{l}\mathrm{Pri.Min.}=\mathrm{BJD}\;2\,447\,623.34700(8)\,+\\\
\hskip 45.5244pt+\,0\fd 217320523(8)\times E\,+\\\ \hskip
45.5244pt+\,2.3(1)\,10^{-12}\times E^{2},\end{array}$ (6)

where $0\fd 217320523$ is the orbital period at epoch $E=0$ and $2.3\,\times
10^{-12}$ d is the quadratic term describing the non-linear changes in the
$O\\!-\\!C$ diagram. The period increase was also reported by Bruch (2023),
who used eclipse timings listed by Diaz & Steiner (1990) and Han et al.
(2017), eclipse epoch given by Gülsecen et al. (2009) and TESS data to derive
quadratic term of $3.69(2)\,\times 10^{-12}$ d. The quadratic term in Equation
6 indicates a slow continuous period increase with a rate of
$dP/dt=+7.6(5)\times 10^{-9}\mathrm{\;d\;year}^{-1}$. The complete $O\\!-\\!C$
diagram since the discovery of AY Psc as a variable star is plotted in Fig. 7.
Our new observations extended the time span by over 1800 days corresponding to
8300 epochs. Excluding a part of data with a high scatter around the epoch of
$\sim 25~{}000$ does not change our quadratic fit out of its 1$\sigma$
uncertainty. It should be noted that determination of the center of the
eclipse of the WD is difficult using only observations with a low time
resolution, for which it is not possible to define the times of the eclipse
ingress and egress. The observed minimum brightness does not exactly
correspond to the mid-eclipse of the WD. Nevertheless, it is clearly visible
that these times have not followed a simple linear ephemeris during the past
30 years. Assuming a conservative mass transfer between components, the period
increase, and stellar masses determined below, one can compute an upper limit
of a long-term averaged mass transfer rate from the secondary component to WD
$\dot{M}$ using the equation

$\dot{M}=\frac{\dot{P}}{3P}\,\frac{q\,M_{1}}{1-q},$ (7)

where $M_{1}$ is the mass of the primary and $q$ is the mass ratio (see
Warner, 1995, equation 9.5b). Equation 7 gives $\dot{M}=1.05(15)\times
10^{-8}\mathrm{\;M}_{\sun}\mathrm{\;year}^{-1}$.

Figure 8: The contribution of different components to the total flux. The top side of the plot presents an artistic view of the system in corresponding orbital phases. The lack of continuity in the bright spot curve is due to a pixelation of our model.  Figure 9: Upper part: Results of the light curve fit of AY Psc eclipses in quiescence/low (left), standstill (middle) and in outburst/high (right) state. Mid-eclipse times of the displayed light curves are BJD 2458041.48048, BJD 2459471.01677, and BJD 2458156.22572, respectively. The blue points show the observational data presented in Fig. 6, left. The orange squares mark the modeling light curves corresponding to the best fits. The $(O\\!-\\!C)/\sigma$ residuals for the fits are given. Note the different values on the vertical axis. Bottom: Models of AY Psc in quiescence (left), standstill (middle) and in outburst (right). The colors mark the effective temperature in Kelvin of the system elements (right bar). The upper panels correspond to orbital phase $\varphi=0$, the middle ones are views on the geometry of the system at the orbital phase of $\varphi=0.25$ from the inclination angle $i=0.0$, and the lower panels correspond o $\varphi=0.25$ and inclination angle $i=90.0$ degree.  Table 5: System parameters from modeling of light curves of eclipses. |  |  | System brightness state
---|---|---|---
Adopted parameters | low∗ | high⋆ | standstill⋄
$P_{\mathrm{orb}}$ | 18 776.49 s
$E(B-V)$ | 0.05
Distance | 730 pc
Variable and their best values |  |
$i$ [degree] | 74$\fdg$8(7) | fixed | fixed
$M_{\mathrm{WD}}$ [M☉] | 0.90(4) | fixed | fixed
${T}_{\mathrm{WD}}$ [K] | 27 600(12 000) | fixed | fixed
$T_{2}$ [K] | 4100(50) | fixed | fixed
$q$ | 0.50(3) | fixed | fixed
$\dot{M}$ [$10^{-10}$ M☉ year-1] (model) | 2.4(1) | 96.8 | 9.1
Parameters of the disk |  |
$R_{\mathrm{d,in}}\equiv R_{\mathrm{WD}}$ [R☉] | 0.009 | fixed | fixed
$R_{\mathrm{d,out}}$ [R☉] | 0.67(1) | 0.67 | 0.67
$z_{\mathrm{d,out}}$ [R☉] | 0.047(5) | 0.049 | 0.061
$\gamma_{\mathrm{disk}}$ | 1.223(0.500) | 0.00 | 0.48
EXP | 0.250(1) | 0.238 | 0.228
The bright spot/line |  |  |
length spot ($\varphi_{\mathrm{min}}+\varphi_{\mathrm{max}}$) | 128$\fdg$9(9.5) | 139$\fdg$3 | 129$\fdg$4
width spot [%] | $9.5_{-8}^{+5}$ | 22.9 | 13.2
Z excess spot ($z_{\mathrm{s,max}}/z_{\mathrm{d,out}}$) | 1.27(0.55) | 1.65 | 1.01
Spot Z slope | 3.9(1.5) | 1.4 | 2.5
Shift spot ($\varphi_{\mathrm{min}}$) | -30$\fdg$3$(3.0)$ | -20$\fdg$7 | -42$\fdg$5
Shift $T_{\mathrm{s,max}}$ ($\varphi(T_{\mathrm{s,max}})$) | -6.8$\fdg$0(2.0) | -0$\fdg$2 | -11$\fdg$3
Temp. excess spot ($T_{\mathrm{s,max}}/T_{\mathrm{d,out}}$) | 2.7(3) | 1.2 | 1.8
Spot Temp. slope (left) | $0.18_{-0.07}^{+0.15}$ | 1.32 | 1.0
Spot Temp. slope (right) | $0.41_{-0.1}^{+0.2}$ | 0.25 | 0.4
$\chi^{2}$/dof | 0.74/31 | 0.79/29 | 0.94/47
Calculated parameters |  |
$\dot{M}$ [$10^{-10}$ M☉ year-1] (eq.9) | 2.4 | 135.7 | 15.8
$a$ [R☉] | 1.68
$M_{2}$ [M☉] | 0.45
$R_{2}$ [R☉] | 0.54

###  3.3 Eclipse light-curve modeling and system parameters

The AY Psc system shows strong activity, and the time in quiescence is
significantly shorter than the length of outbursts or standstills (see Section
3.1). The quiescence lasts in a range of about 5–23 orbital periods. The full
time of outbursts and the time in the plateau phase of outbursts lasts on
average up to $\sim$80 and $\sim$40 orbital periods, respectively. In contrast
to the active state of AY Psc, the standstill duration is very long when
compared with the orbital period of the systems (months or even years).
Generally, the disk in the system is not in a steady state if we consider its
evolution along whole time intervals of quiescence or during outbursts. It is
more likely to resemble the steady state during a standstill. Such fast
activity of the system complicates the analyses of the physical properties of
the accretion disk significantly. Nevertheless, the eclipse light curve
profile (ELCP) in different states of the system allows us to probe intensity
or effective temperature distribution along the disk radius and to try to
determine the system parameters. To do this, we attempt to reproduce the
collected photometric observations of the system eclipse light curves in
quiescence, standstill, and during an outburst using the tool developed by
Zharikov et al. (2013). The detailed description of the model can be found in
our recent papers of Subebekova et al. (2020) and Kára et al. (2021). Here we
note only that the light curve is a superposition of flux contribution of four
main components: the white dwarf primary, the secondary star, and the
accretion disk with the bright spot formed at the disk/stream impact region.
The depth and shape of the eclipse depend on the flux from the secondary and
the brightness distributions on the disk and the bright spot. The bright spot
affects more the descending branch of ELCP, i.e., before reaching the minimum.
The side of ELCP after the minimum is formed mainly by contribution from the
disk and partly by the underlying secondary. Only after the orbital phase of
$\varphi\approx 0.05$ does the bright spot affect the total flux of ELCP
significantly. Fig. 8 shows the contributions of different components to the
resulting eclipse light curve. Below, we give only the specifications of the
model connected with the considered case.

10 Figure 10: Posterior distributions of some parameters (see Table 5) of the
fit for the AY Psc light curve in the low brightness state. The grey scale
shows normalized $\chi^{-2}$. The blue dashed lines mark the best fit values
of parameters. The white long-dashed lines correspond to 1$\sigma$ errors of
parameters.  Figure 11:  Temperature (top panel) and height of accretion disk
(bottom panel) from the model fitting. The 1$\sigma$ uncertainties of the disk
height are marked in the bottom panel by light-shaded areas. The orange,
green, and blue lines correspond to the high, standstill, and low state of the
system.

Foremost, we take into account that the disk contribution in the total flux
from the system is lower in quiescence than in outbursts or standstills. The
flux from the far side of the secondary is always the same, but its
contribution to the total flux is significantly larger in quiescence.
Therefore, we used the eclipse light curve in the low-brightness state of the
system obtained on October 14, 2017 (the eclipse time
$\mathrm{BJD}\;2\,458\,041.48048$, the last light-curve point was obtained at
$\mathrm{HJD}\;2\,458\,041.51871$) to find the system parameters. We verified
our calibration of the flux in the $V$-band using AAVSO data obtained close to
our observations at $\mathrm{JD}\;2\,458\,041.59532$ where $V=16.73(11)$ mag
was measured about two hours after the used eclipse. We adopted the published
values of the orbital period, the distance, and the interstellar extinction as
the fixed parameters. All other parameters of the model, described below and
presented in Table 5, were free.

We assume that the disk radiates as a black body at the local effective
temperature with radial distribution across the disk given by the equation:

$\begin{array}[]{lll}T_{\rm eff}(r)&=&T_{0}\left\\{\left(\frac{r}{R_{\rm
WD}}\right)^{-3}\,\left(1-\left[\frac{R_{\rm
WD}}{r}\right]^{1/2}\right)\right\\}^{EXP},\\\ T_{0}&=&\left[\frac{3GM_{\rm
WD}\dot{M}}{8\pi\sigma R_{\rm WD}^{3}}\right]^{1/4},\end{array}$ (8)

where $M_{\mathrm{WD}}$ and $R_{\mathrm{WD}}$ are the mass and the radius of
the WD, respectively, $\dot{M}$ is the mass-transfer rate, $G$ is the
gravitational constant and $\sigma$ is the Stefan–Boltzmann constant. In the
standard accretion disk model the radial temperature gradient $EXP$ = 0.25
(Warner, 1995, equation 2.35), but we allow it to slightly deviate from this
value, similarly to how it was done in Linnell et al. (2010). Generally, this
departure from the standard temperature distribution can be presented as the
multiplication of the standard steady-state model $T_{\rm eff,SSD}(r)\propto
r^{-3/4}$ to a slowly changing function $f(r)\propto r^{\delta}$ reflecting
the order of a deviation from the steady-state disk. The mass transfer rate
corresponding to the luminosity state of the disk can be obtained from the
relation

$L_{\rm disk}=\frac{1}{2}\frac{GM_{\rm WD}\dot{M}}{R_{\rm WD}},$ (9)

where $L_{\rm disk}$ is the total disk luminosity calculated as

$L_{\rm disk}=\sum_{i}^{N}S_{i}\sigma T_{\rm eff,i}^{4},$ (10)

where $N$ is the number of elements in the model of the accretion disk,
$S_{i}$ and $T_{\rm eff,i}$ are an area and an effective temperature of an
$i$-element, respectively. The disk limb-darkening also includes the following
Eddington approximation (Mayo et al., 1980; Paczynski & Schwarzenberg-Czerny,
1980). We also used the complex model for the bright spot described in detail
in Kára et al. (2021, see fig. 9 therein) where all definitions of parameters
can be found. Clearly, the true bright spot configuration is more complicated,
and our models only give general impressions about brightness distribution in
the stream/disk impact region. The free parameters of this fit were: the mass
of the primary ($M_{\mathrm{WD}}$), the mass ratio
($q=M_{2}/M_{\mathrm{WD}}$), the mass transfer rate ($\dot{M}$), the system
inclination ($i$), the outer radius of the accretion disk
($R_{\mathrm{d,out}}$), the disk thickness at the outer radius
($z_{\mathrm{d,out}}$), the effective temperature of the secondary ($T_{2}$),
and the accretion disk with a thickness

$z_{\mathrm{d}}(r)=z_{\mathrm{d}}(r_{\mathrm{out}})(r/r_{\mathrm{out}})^{\gamma_{\mathrm{disk}}},$
(11)

where $\gamma_{\mathrm{disk}}$ is a free parameter for which we used the
standard value of $\gamma_{\mathrm{disk}}=9/8$ (Warner, 1995, equation 2.51b)
as the initial value. We fit only the orbital phase range of
$\varphi\in[-0.05;+0.12]$ which is less affected by out-of-eclipse flickering
of the disk, as can be seen on Fig. 2.

As the first approach, we found by hand an approximate solution of the light
curves with steady-state parameters of the disk. The mass transfer rate, in
this case, can be considered as an average in the disk corresponding to the
current luminosity state of the system. After that, we searched for the
minimum of the $\chi^{2}$ function with free parameters mentioned above (see
also Table 5) using the gradient-descent method. The values of the best-fit
model are presented in Table 5. The error of each fitted parameter was
calculated with the Gaussian approximation of the $\chi^{2}$ function when
other parameters were set at the best values. The result of the fit and the
observed-minus-calculated $(O\\!-\\!C)/\sigma$ residuals are shown in Fig. 9,
left panels. As an example, in Fig. 10, we show two-dimensional error maps for
some parameters.

We found that the selected eclipsing light curve in quiescence was reproduced
by the accretion disk with parameters close to steady-state disk ($EXP$ =
0.250 and $\gamma_{\mathrm{disk}}\simeq 9/8$, see Fig. 10, two bottom lines).
The expected flux from the secondary is about $V=18.2$ mag, which is slightly
lower than the magnitudes at the eclipse minimum (see Fig. 6) in the
quiescence. As we noted before, the main difference between ELCP in different
system states is the depth of the eclipse. Applying our light curve modeling
technique to the high 121212 the eclipse time
$\mathrm{BJD}\;2\,458\,156.22572$ and standstill 131313 the eclipse time
$\mathrm{BJD}\;2\,459\,471.01677$ states (Fig. 9, middle and right panels)
with the system parameters obtained for the low state, we found a departure of
the accretion disk from the steady-state: The light curves in high brightness
states were reproduced by the models with effective temperatures which are
different from steady-state distribution and the height along disk radius is
flatter (see Fig. 11).

The mass transfer rate corresponding to the luminosity of the source changes
drastically between the low and the high states at about two orders of
magnitude. The mass transfer rate in high state $\dot{M}\approx 1.4\times
10^{-8}\mathrm{\;M}_{\sun}\mathrm{\;year}^{-1}$ is larger than the one derived
from the orbital period changes, which is $\dot{M}\approx 1.1\times
10^{-8}\mathrm{\;M}_{\sun}\mathrm{\;year}^{-1}$. As the former corresponds to
a mass accretion rate during a short event, namely the maximum of an outburst,
and the latter corresponds to a long-term averaged value, this discrepancy can
be expected.

The mass transfer rate in standstill is $\approx 2\times 10^{-9}$ M☉ year-1.
This mass transfer rate is slightly below the critical mass transfer rate
above which a cataclysmic variable is hot and stable ($\approx 7\times
10^{-9}$ M☉ year-1; Dubus et al., 2018), however, it is in the range of
$\dot{M}$ estimations for Z Cam systems (Dubus et al., 2018, see fig. 3
therein). The model uncertainties of the fits in the high brightness state and
standstill have the same order of values as in quiescence.

##  4 Spectroscopy and Doppler tomography

###  4.1 AY Psc spectra

Table 6: Radial velocity solution Method |  $\upsilon_{\rm cor}$ [$\mathrm{km\,s}^{-1}$] |  $K$ [$\mathrm{km\,s}^{-1}$] | $\varphi_{0}$
---|---|---|---
H$\alpha$, this paper | $34.8(8.0)$ | $147.0(10.5)$ | $0.12(1)$
H$\beta$, SH93 | $67(17)$ | $131(20)$ | $0.05(3)$
Figure 12: Normalised average spectrum from OAN SPM and normalized LAMOST
spectrum. The wavelength range corresponds to the spectral range of OAN SPM
data.  Figure 13: H$\alpha$ radial velocities found using the diagnostic
diagrams. The orange line marks the best fit of the data.

Figure 14: Doppler maps for H$\alpha$ line (left panels), and observed and
reconstructed trailed spectra (centre and right panels, respectively). The top
left panel shows the Doppler map constructed using the raw data. The middle
left and the bottom left panels present the Doppler maps in which we removed
the L1 and L1 + spot components, respectively (see description in the text).
The color of the Doppler maps corresponds to arbitrary units of emission
intensity (the yellow-blue-red-black palette corresponds to a change from a
low to high intensity). The dashed circle marks the tidal limitation radius of
the accretion disk. The red and orange dashed lines in the reconstructed
trailed spectra of raw H$\alpha$ line (top right panel) mark the radial
velocities of the ‘L1’ and ‘spot’ components, respectively.  Figure 15:
Example of a three-Gaussian fits of the H$\alpha$ emission line profile at the
orbital phase $\varphi=0.85$. The blue curve corresponds to the observed line
profile. The green, brown, and yellow lines represent ‘L1’, ‘spot’, and
background components (see the text), respectively. The dashed orange line is
the sum of those three components.  Figure 16: Doppler map for He I line (left
panel), observed and reconstructed trailed spectra (right two panels). The
color of the Doppler maps corresponds to arbitrary units of emission
intensity, the dashed circle marks the tidal limitation radius of the
accretion disk. The corresponding orbital phase is marked.

Our time-resolved spectroscopy was obtained around the H$\alpha$ line when the
source was in the standstill state. In the observed spectral region, there are
strong H$\alpha$ and relatively weak He I 6678 Å emission lines. The phase-
averaged normalized spectrum from OAN SPM is shown in Fig. 12 together with
the same spectral region of the LAMOST spectrum for comparison. We covered
about four full orbital periods with uniform spectra distributed along the
orbital phase. The phase-averaged H$\alpha$ line profile looks practically
symmetric. Its FWZI and EW are 105.5 Å and 35.2 Å, respectively. We also
measured radial velocities of H$\alpha$ line using the double-Gaussian method
described by Schneider & Young (1980) and Shafter (1983). We used Gaussians
with the width of $1.5$ Å and separated by $19.5$ Å. The resulting radial
velocity curve is shown in Fig. 13. We fitted the radial velocity curve with a
model curve described by formula

$\upsilon=\upsilon_{\rm cor}-K\sin\,[2\pi(\varphi-\varphi_{0})],$ (12)

where $\upsilon_{\rm cor}$ is the systemic velocity, $K$ is the semi-amplitude
of the radial velocity curve, and $\varphi$ is the orbital phase calculated
relative to the epoch $T_{0}$ = HJD 2 459 470.79867 which corresponds to the
conjunction of the red and white dwarfs ($\varphi_{0}$=0), when the L1 point
velocity changes from negative to positive values. The best fit is shown in
Fig. 13, and its parameters are listed in Table 6. We found a good agreement
of our results with those reported by SH93, which are given in Table 6.
Nevertheless, detailed analyses of variations of the H$\alpha$ line profile
required us to apply a multi-components model presented below.

Table 7: Multi-component model parameters Parameter | Unit | Component
---|---|---
|  | (1) | (2)
|  | ‘L1’ | ‘spot’
$\upsilon_{\rm cor}$ | km s-1 | $34.8$ | $34.8$
$K$ | km s-1 | $-145$ | $360$
$\varphi_{0}$ | – | 0.0 | 0.196
$A$ | – | 0.3 | 0.5
$\sigma$ | Å | 2.2 | 3

###  4.2 Doppler tomography of the multi-component emission H$\alpha$ line

We generated Doppler maps from our time-resolved spectra of the object using
the code developed by Spruit (1998) which uses the maximum entropy method to
compute the Doppler maps. The Roche lobe, position of the components, and
stream were overplotted on the Doppler maps using a Python3 module PyDoppler
by Hernandez Santisteban (2021). The orbital phases ($\varphi\sim$ -0.05–0.05)
around the eclipse minimum $\varphi_{0}=0$ were excluded from computations,
and the zeroth orbital phase was well defined from the simultaneous
photometric observations. The possible displacement between the zeroth orbital
phase, when the secondary stays strictly between the primary and an observer,
and a minimum of an eclipse does not exceed $\sim 0.005$ orbital phase, as
follows from our light-curve modeling estimate. The system parameters from
Section 3.3 are used to overlay the secondary Roche lobe and position of the
primary, the center of mass, and the ballistic and Kepler stream trajectories.
By circle, we show a tidally truncated radius ($R_{d,out,max}=0.69R_{\odot}$)
of the disk which we estimated using Equation (2) from Neustroev & Zharikov
(2020).

The Doppler map of the H$\alpha$ line (Fig. 14, top-left) and trailed spectra,
based on the raw data, clearly show the presence of at least two spectral
components. One, located in the Doppler map at coordinates $V_{X}\approx$ 0 km
s-1, $V_{Y}\approx$ 100 km s-1, is bright, narrow and related to the
Lagrangian point L1. Another more extended component is located at
$V_{X}\approx$ -300 km s-1, $V_{Y}\approx$ -100 km s-1, close to the standard
bright spot position and named hereafter as the ‘spot’ component. Both of them
are located outside the accretion disk, whose outer radius is shown by the
black dashed circle. They are placed above a very broad and heterogeneous
background, the origin of which is discussed below. In the trailed spectra,
the ‘L1’ components do not seem to vary with the orbital phase in its width
and amplitude except for the time of the eclipse. Another component varies in
its amplitude and width during the orbital phase and has its maximal
brightness just before the eclipse and a minimum at $\varphi\simeq 0.6$.

To determine the parameters of those spectral features, we fitted both those
components in such a way as to exclude their contribution from the trailed
spectrum. For each component, we used a simple Gaussian profile characterized
by its peak flux $A$ and the standard deviation $\sigma$, and the radial
velocities $\upsilon$ dependent on the orbital phase:

$\displaystyle\mathrm{flux}(\lambda)$ $\displaystyle=$ $\displaystyle
A\exp{\left[-\frac{1}{2}\left(\frac{\lambda-\lambda_{0}}{\sigma}\right)^{2}\right]},$
$\displaystyle\lambda_{0}$ $\displaystyle=$ $\displaystyle
6562.82\;\left(1+\frac{\upsilon}{c}\right)\,[\AA],$ (13)

where $\upsilon$ is defined by Equation (12). As the first step, an eye
estimation was applied to determine the parameters of the ‘L1’ component. We
accepted that the best fit means that the result of the component removal
gives a similar flux from the position of the ‘L1’ component and its nearby
vicinity. Afterwards, the parameters of the ‘spot’ component at $V_{X}\approx$
-300 km s-1, $V_{Y}\approx$ -100 km s-1 in the Doppler map were determined by
least-square fitting the spectra with a model consisting of three Gaussians
representing both components and the rest of the emission line while using the
parameters of the ‘L1’ component taken from the first step. An example of the
model can be seen in Fig. 15. The output of the fits is presented in Table 7.
We successively removed each component from the raw Doppler map to probe the
origin of the background. The result of the removal is shown in the middle and
the bottom panels of Fig. 14 where we removed the L1 component (middle panel)
and both components (L1 + ”spot”) together (bottom panel). The last step of
this procedure is not unambiguous. Nevertheless, the Doppler map at the bottom
panel clearly shows the presence of an extended ragged background. Its shape
depends on the model parameters, however, in all cases, we found that this
background is concentrated around/close to the WD position ($V_{\rm X}=0$ km
s-1, $V_{\rm Y}=-130$ km s-1) and has FWZI $\approx\pm 600$km s-1. There is
also an additional stand-out excess of the flux in the background at $V_{\rm
X}\approx 250$ km s-1, $V_{\rm Y}\approx 0$ km s-1. We note that the maps do
not show the usual ‘doughnut’ structure commonly observed from accretion disks
in CVs. In addition, we constructed a Doppler map for He I 6678 line in Fig.
16. The map shows only the emission from the L1 region.

We interpret the obtained results as follows:

  1. 1.

the ‘L1’ component is formed at the irradiated side of the secondary close to
the L1 point;

  2. 2.

the ‘spot’ component ($V_{\rm X}\approx$ -300 km s-1, $V_{\rm Y}\approx$-100
km s-1) is located close to a standard position of the bright spot, however,
keeps out of Keplerian velocities of the disk or ballistic and Keplerian
trajectories of the stream. Thus we propose that this component is more likely
to be linked with radiation formed by a bright spot wind where, during a
standstill, our photometric modeling gives the temperature about 8200 K (see
Fig. 9);

  3. 3.

the background is created mainly by the wind originating from the central hot
part of the accretion disk and partly from an ‘outflow zone’ of the accretion
disk as it was observed in some NLs (Bisikalo & Kononov, 2010; Hernandez et
al., 2017; Subebekova et al., 2020). The presence of He II in LAMOST spectra
of AY Psc also supports the wind origin of the H$\alpha$ line background by
analogy with V Sge-systems (Steiner & Diaz, 1998).

##  5 Discussion

There are nineteen well-defined Z Cam stars until now (Simonsen et al., 2014).
They have orbital periods from about 3 to 8.5 hours with an average of 5.3
hours, which is close to the orbital period of AY Psc. The mentioned period
range is also filled by other types of non-magnetic CVs (Warner, 1995) such as
U Gem-type DNe, VY Scl-type, NLs SW Sex, RW Sex / RW Tri types, and V Sge-type
systems. It is commonly accepted that the observational diversity of those
types of CVs is caused by a difference in the mass transfer rate and,
correspondingly, by the state/temperature of the accretion disk. The last
statement can be clearly seen in Fig. 17 where the Gaia color index
$G_{\mathrm{BP}}-G_{\mathrm{RP}}$ (the top panel) and the absolute magnitude
$G_{\mathrm{abs}}$ (the bottom panel) versus orbital periods are shown. The
NLs look brighter $G_{\rm abs,\;NL}=5.0(5)$ and bluer $(G_{\rm BP}-G_{\rm
RP})_{\rm NL}\sim 0.3(2)$ in comparison with DNe ($G_{\rm abs,\;DNe}=8(1)$,
$(G_{\rm BP}-G_{\rm RP})_{\rm DNe}\sim 1.3(2)$. The Z Cam-type objects fill
the space between them with $G_{\rm abs,~{}Z~{}Cam}=6.5(5)$, $(G_{\rm
BP}-G_{\rm RP})_{\rm~{}Z~{}Cam}\sim 0.7(2)$. A high dispersion in color
indices and absolute magnitudes is caused by the absence of exact values of
inclinations of most of the systems (see the right histograms of both panels).
Nevertheless, the indicated trend is clearly visible. It is also interesting
that eclipsing NLs with known parameters (V347 Pup, RW Tri, UX UMa, 1RXS
J064434.5+334451) in the period range of 4–5 hours have slightly less massive
primaries ($\sim 0.7$ M☉) and a slightly hotter ($\sim$M0V/3900K$\pm$400K)
secondaries in comparison with DNe (U Gem, CW Mon, GY Cnc, and others $\sim
1.0$ M☉, $\sim$M3.5V/3300K$\pm$270K) (Ritter & Kolb, 2003; Wenger et al.,
2000, see data and the latest references for these objects
therein141414http://simbad.u-strasbg.fr/simbad/). The average secondary mass
is about 0.4 M☉ in both cases. The estimate of a spectral class of the
secondary in Z Cam systems looks similar to NLs with a large dispersion
(M0[$\pm 3$]V, see Table 8). Nevertheless, they appear hotter than secondaries
in most CVs of the same orbital periods (Fig. 18). Unfortunately, until now,
the number of systems with well-determined fundamental parameters is low, and
the above-mentioned tendency must be fully confirmed.

In the list of confirmed Z Cam systems, only AY Psc shows deep eclipses that,
together with the time-resolved spectroscopic data and the Gaia distance,
provide a possibility to determine the system parameters. From the light curve
fitting of AY Psc we found that the mass of the WD primary is $M_{\rm
WD}=0.90(4)$ M☉, the mass ratio is $q=0.50(4)$, and the system inclination is
$i=$ 74$\fdg$8(7). At the practically same inclination angle, we obtained less
massive components in the system comparison with masses presented by Howell &
Blanton (1993) whose estimations were based on the analytical technique
applied for analysis of the eclipse profile (see references therein). Our
system parameters exclude AY Psc as a potential SN Ia progenitor. The WD
primary has a temperature of about 30 000 K, and the red dwarf temperature is
higher than can be expected for the secondaries from the orbital period vs.
secondary spectral class relation (Knigge et al., 2011). Nevertheless, the
characteristics of AY Psc are very similar to other Z Cam-systems with close
orbital periods, such as AT Cnc (Nogami et al., 1999) and RX And (Sepinsky et
al., 2002; Sion et al., 2001).

We also found that in the low state, the eclipsing light curve can be well
described by a steady-state disk with an accretion rate of 2.4$\times$10-10 M☉
year-1. The object out-of-eclipse magnitude shows dispersion about $\sim$0.5
mag in the low brightness state. Also, the disk is close to the instability
condition and goes into an outburst at a relatively short time scale. This
means that the estimation of the mass transfer rate from the analysis of the
particular eclipse light curve gives only the order of magnitude of $\dot{M}$
value for quiescence. However, similar accretion rates in quiescence were
found for other Z Cam systems, e.g., RX And (Sepinsky et al., 2002) and EM Cyg
(Dai & Qian, 2010). The outer part of the quiescence disk has an effective
temperature in the range of $\sim$3000–5000 K, and its brightness distribution
looks like in a steady-state disk.

Figure 17: Different types of CVs displayed in orbital periods vs. Gaia color
indexes (top) and absolute magnitudes diagram. Orbital periods were taken from
catalog of Ritter & Kolb (2003), the color index was adopted from the Gaia
catalog (see Gaia Collaboration et al., 2016, 2018). Figure 18:  Spectral
types and effective temperatures of the donors of CVs (blue dots) plotted vs.
their orbital periods (an update of the Beuermann et al. (1998) list). The
green line corresponds to the periods of semi-detached systems with main-
sequence donors and 0.7 M☉ accretor, the numbers mark the corresponding mass
of main-sequence stars. The red dots show the Z Cam systems listed in Table 8,
and AY Psc is shown as a purple asterisk.

The disk in outburst and standstill is significantly hotter. The effective
temperature departs from the steady-state disk dependence, and the optical
depth, where the continuum is formed, extends in the z-direction especially
more significantly in the outburst maximum. The He II emission $\lambda$4686
in outburst spectra supports the idea of forming of wind from the disk in
outbursts and standstill. It is also the distinguishing feature of high-mass
transfer ($>10^{-9}$ M⊙ year-1) V Sge-type systems (Steiner & Diaz, 1998)
which represent a state of binary evolution dominated by wind mass loss. The
example of such an object with an orbital period close to AY Psc is V617 Sgr
(Cieslinski et al., 1999) in which a strong wind from the stream/disk impact
region is proposed (Steiner et al., 1999, see fig. 6 therein). The effective
temperature of the primary more probably varies with the change of the system
state as it was found, for example, in RX And (Sepinsky et al., 2002). Still,
its contribution to optical flux in an outburst or standstill is negligible
compared to the flux from the inner part of the disk. Thus, using the constant
value for the light curve fitting in the outburst and standstill does not
affect obtained results.

Table 8: List of known Z Cam-type CVs with the orbital period between 0.17 – 0.26 day and estimate of the secondary star type (Ritter & Kolb, 2003).  System |  $V$ [mag] | Period [day] | Sp. Type | Ref.
---|---|---|---|---
WW Cet | 13.9 | 0.175800 | M2.5V | 1
ES Dra | 16.2 | 0.176600 | M1-3V | 2
HS2325+8205 * | 16.4 | 0.194335 | M2-4V | 3
HX Peg | 15.8 | 0.200800 | K6 | 4
AT Cnc | 15.3 | 0.201100 | K7-M0V | 5
RX And | 14.0 | 0.209893 | K5V | 6
AY Psc | 15.3 | 0.217321 | K7V | 7
AH Her | 13.9 | 0.258116 | K7V | 8

The Doppler map and emission line trailed spectra of AY Psc in standstill are
similar to those observed in other NLs, e.g. LX Ser (Kaitchuck et al., 1994),
RW Sex (Hernandez et al., 2017), 1RXS J064434.5+334451 (Hernandez et al.,
2017), V347 Pup (Thoroughgood et al., 2005), V341 Ara (Castro Segura et al.,
2021), BP Lyn (Still, 1996), HBHA 4705-03 (Yakin et al., 2013), AC Cnc
(Thoroughgood et al., 2004), V363 Aur(Kaitchuck et al., 1994), RW Tri
(Subebekova et al., 2020), and some DNe, e.g. EM Cyg (North et al., 2000), AH
Her, SS Cyg (North et al., 2002), and CzeV404 Her (Kára et al., 2021). While
in most of them, the low-resolution spectra show only the one-peaked Balmer
emission lines, the higher-resolution spectroscopy reveals a structure with
two or more components. Using the terminology proposed by Hernandez et al.
(2017) for NLs, the ‘narrow’ low-velocity component, if is present, usually
originates from the disk-illuminated side of the secondary and is identical to
the ‘L1’ component here. Other wider component(s) have not been related to
Keplerian motions in the accretion disk and, more probably, are formed by
winds from the bright spot and/or the central part of the accretion disk and
from the outflow zone of the disk (Hernandez et al., 2017; Subebekova et al.,
2020; Hernández et al., 2021). The specific view of the Doppler map with
‘wide’ component(s) depends on the physical conditions where they are formed.
It is a very interesting subject, but its full discussion is out of the scope
of the presented paper. A ‘doughnut’ structure associated with the Balmer
emission from the accretion disk is absent in all objects mentioned in this
section.

The interesting feature of some long orbital period CVs is the relation
between the depth of an eclipse and out-of-eclipse brightness of objects
(Subebekova et al., 2020, and references therein). We showed that AY Psc also
suits this relation. The proposed model can be easily explained by the change
in temperature distribution followed by the variation of the disk height along
its radius. Nonetheless, it cannot be excluded that some additional effects as
tidal torque by the secondary on a misaligned accretion disk are also possible
(Montgomery, 2009).

##  6 Conclusions

We performed time-resolved photometric and spectroscopic observations of the
eclipsing Z Cam-type CV AY Psc. Based on the fitting of the eclipse light
curves in different states of the system and time-resolved spectroscopy
obtained in a standstill state, we determined:

  1. 1.

The system contains a hot massive white dwarf $M_{\mathrm{W}D}=0.90(4)$ M☉.
The mass of the secondary is $M_{2}=0.45(5)$ M☉. However, its effective
temperature is $T_{2}=4100$(50) K. It corresponds to the spectral type of K7V.
We note that it is significantly hotter than the effective temperature of the
main-sequence star with the corresponding mass whose radius must also be less
than 25% size of the secondary. The last means that the secondary is an
evolved star with a flayed shell. The system inclination is $i=74\fdg 8(7)$.

  2. 2.

The mass accretion rate and the disk structure change between quiescence,
standstill, and outburst. The mass accretion rate increases from quiescence to
outburst maximum, and the disk becomes hotter and its shape flatter.

  3. 3.

The H$\alpha$ emission line shows a multi-component structure similar to those
observed in other long orbital period NLs and DNe. We conclude that the
H$\alpha$ emission line is formed by the superposition of radiation from the
irradiated surface of the secondary, the wind from the bright spot and hot
central part of the accretion disk, and from the outflow zone.

  4. 4.

We found that AY Psc shows two distinct types of outbursts during its cycles,
which differ in the shape of their light curve and their duration: long and
short outbursts. The long outbursts exhibit a plateau phase after reaching
their peak brightness, which is a shape typical for superoutbursts of SU UMa-
type systems and long outbursts of U Gem and Z Cam CVs (see Otulakowska-Hypka
et al., 2016, fig. 1). Individual long outbursts differ in the duration of the
plateau phase and subsequent decline rate. Short outbursts do not exhibit a
plateau phase, and they have a shape typical for normal outbursts of DNe. Long
outbursts were detected more prominently, and no pattern in the occurrence of
any particular outburst type was found in the available data. The prominence
of long outbursts over short outbursts is unusual, as typically long outbursts
have longer occurrence cycles than short outbursts (Otulakowska-Hypka et al.,
2016).

  5. 5.

We calculated a new ephemeris of AY Psc using data covering over 30 years of
observations. Instead of a simple linear ephemeris fit proposed by previous
studies, the updated $O-C$ diagram shows a quadratic ephemeris fit
corresponding to the increase of the orbital period with a rate of
$dP/dt={+7.6}\times 10^{-9}\mathrm{\;d\;year}^{-1}$. Nevertheless, even when
we take the quadratic ephemeris into consideration, the $O-C$ diagram shows a
large scatter. This can be caused by a variation of mid-eclipse times due to a
change of the accretion disk radius and/or azimuthal movements of the bright
spot position at the edge of the accretion disk (Schaefer, 2021). The increase
of the orbital period could be an effect of the dynamical evolution of the
system, namely the effect of changes on the masses of the primary and the
secondary due to mass transfer. Another possibility is an effect of a third
body in the system that cannot be ruled out as the observed parabolic behavior
could be caused by a cyclical change of the period longer than the time-span
of current observations (see Chavez et al., 2020; Fang et al., 2020; Liu et
al., 2021, for examples of CVs with proposed third bodies).

We think that this object is a unique laboratory to study the response of the
accretion disk on mass transfer variations. New precise time-resolved
simultaneous photometric and spectroscopic observations during active and
standstill states are needed in the future to understand the mechanism of
transition between them better.

We are grateful to the anonymous referee for the useful and valuable
suggestions that allowed us to improve the manuscript. The authors thank Prof.
H. Gülsecen, Istanbul University, Turkey, who kindly provided us with his
original photometry of AY Psc. Based upon observations carried out at the
Observatorio Astronómico Nacional on the Sierra San Pedro Mártir (OAN SPM),
Baja California, México. S.Z. acknowledges PAPIIT grants IN102120 and
IN119323. The research of J.K., M.W., and J.M. was also supported by the
project Cooperatio - Physics of Charles University in Prague. This research
has been funded in a part by the Science Committee of the Ministry of Science
and Higher Education of the Republic of Kazakhstan (grant No. AP19678376 ).
S.K. acknowledges Al-Farabi Kazakh National University for a postdoc position.
This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular, the institutions
participating in the Gaia Multilateral Agreement. We acknowledge with thanks
the variable star observations from the AAVSO International Database
contributed by observers worldwide and used in this research. The following
internet-based resources were used in research for this paper: the SIMBAD
database and the VizieR service operated at CDS, Strasbourg, France; NASA’s
Astrophysics Data System Bibliographic Services. This paper includes data
collected by the TESS mission. Funding for the TESS mission is provided by
NASA’s Science Mission Directorate. The TESS data presented in this paper were
obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space
Telescope Science Institute. The specific observations analyzed can be
accessed via https://doi.org/10.17909/5fq3-s930 (catalog
https://doi.org/10.17909/5fq3-s930). STScI is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS5–26555.
Support to MAST for these data is provided by the NASA Office of Space Science
via grant NAG5–7584 and by other grants and contracts. Based on observations
obtained with the Samuel Oschin 48-inch Telescope at the Palomar Observatory
as part of the Zwicky Transient Facility project. ZTF is supported by the
National Science Foundation under Grant No. AST-1440341 and a collaboration
including Caltech, IPAC, the Weizmann Institute for Science, the Oskar Klein
Center at Stockholm University, the University of Maryland, the University of
Washington, Deutsches Elektronen-Synchrotron and Humboldt University, Los
Alamos National Laboratories, the TANGO Consortium of Taiwan, the University
of Wisconsin at Milwaukee, and Lawrence Berkeley National Laboratories.
Operations are conducted by the COO, IPAC, and UW.

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