# The emergence of a neutral wind region in the orbital plane of symbiotic
binaries
during their outbursts

Augustin Skopal Astronomical Institute, Slovak Academy of Sciences,
059 60 Tatranská Lomnica, Slovakia

###### Abstract

Accretion of mass onto a white dwarf (WD) in a binary system can lead to
stellar explosions. If a WD accretes from stellar wind of a distant evolved
giant in a symbiotic binary, it can undergo occasional outbursts in which it
brightens by several magnitudes, produces a low- and high-velocity mass-
outflow, and, in some cases, ejects bipolar jets. In this paper, we complement
the current picture of these outbursts by the transient emergence of a neutral
region in the orbital plane of symbiotic binaries consisting of wind from the
giant. We prove its presence by determining H0 column densities ($N_{\rm H}$)
in the direction of the WD and at any orbital phase of the binary by modeling
the continuum depression around the Ly$\alpha$ line caused by Rayleigh
scattering on atomic hydrogen for all suitable objects, i.e., eclipsing
symbiotic binaries, for which a well-defined ultraviolet spectrum from an
outburst is available. The $N_{\rm H}$ values follow a common course along the
orbit with a minimum and maximum of a few times $10^{22}$ and $10^{24}$ cm-2
around the superior and inferior conjunction of the giant, respectively. Its
asymmetry implies an asymmetric density distribution of the wind from the
giant in the orbital plane with respect to the binary axis. The neutral wind
is observable in the orbital plane due to the formation of a dense disk-like
structure around the WD during outbursts, which blocks ionizing radiation from
the central burning WD in the orbital plane.

stars: binaries: symbiotic – scattering – stars: winds, outflows

††facilities: IUE(SWP, LWP), AAVSO

##  1 Introduction

Currently, symbiotic stars (SySts) are understood as the widest interacting
binaries comprising a cool giant as the donor and a compact star, mostly a
white dwarf (WD), as the accretor. Their orbital periods are typically as long
as a few years (S-type systems containing a normal giant, see Belczyński et
al., 2000; Gromadzki et al., 2013), but for systems containing a Mira variable
(D-type systems, see Webster & Allen, 1975; Kenyon et al., 1988; Seal, 1990)
they can be significantly longer, but mostly they are unknown (e.g., Schmid &
Schild, 2002; Matthews & Karovska, 2006; Hinkle et al., 2013). SySts are
detached binaries Mürset & Schmid (1999); their activity is thus triggered via
the wind mass transfer. The accretion process is responsible for the WD’s
temperatures of $1-2\times 10^{5}$ K and luminosities of $10^{1}-10^{4}$
$L_{\odot}$ (Muerset et al., 1991; Skopal, 2005).

According to the light variations in the optical, we distinguish between the
quiescent and active phases of SySts. During quiescent phases, a SySt releases
its energy at a constant rate. The hot and luminous accreting WD ionizes the
neighboring part of the wind from the giant giving rise to the nebular
emission (e.g., Boyarchuk et al., 1966), while its portion around the cool
giant remains neutral. The boundary between the ionized and neutral regions is
given by the balance between the flux of ionizing photons from the hot
component and the flux of neutral particles from the cool giant, the shape of
which determines the ionization structure of SySts during the quiescent phase
(see e.g., Fig. 6 of Seaquist et al., 1984). This configuration causes the
characteristic feature in the light curves of SySts during their quiescent
phases – a periodic wave-like variation as a function of the orbital phase
(see light curves presented by, e.g., Belyakina, 1992; Dmitrienko, 2000;
Skopal, 2008). On the other hand, active phases of SySts result from unstable
nuclear burning on the WD surface that gives rise to transient outbursts
indicated by brightening of a few magnitudes in the optical. The most
characteristic outbursts for SySts are of ‘Z And-type’ that result from an
increase in the accretion rate above that sustaining the stable burning
(Skopal et al., 2017, 2020). They show 1–3 mag (multiple) brightening(s)
evolving on the time-scale of a few months to years/decades (e.g., Brandi et
al., 2005; Leibowitz & Formiggini, 2008; Sekeráš et al., 2019) with signatures
of a mass outflow (e.g., Fernandez-Castro et al., 1995; Esipov et al., 2000;
Skopal, 2006; McKeever et al., 2011). The periodic wave-like variation in the
light curve disappears and, in the case of eclipsing systems, deep narrow
minima caused by eclipses of the hot component by the red giant, appear in the
light curve (e.g., Belyakina, 1976, and Appendix B for our targets) – one of
the most prominent indications of the change in the ionization structure of
the hot component during active phases (see below).

During outbursts, the stellar radiation from the hot component and the nebular
radiation markedly change. For systems with a high orbital inclination, the
hot component temperature significantly declines, often showing spectral
features of an A–F type star in the optical (Mikolajewska & Kenyon, 1992,
1996; Munari et al., 1992; Quiroga et al., 2002; Brandi et al., 2005). Such a
warm WD pseudophotosphere with an effective radius of several solar radii
(Skopal, 2005) becomes a significant source of optical radiation. Therefore,
its eclipse by the red giant will cause narrow minima in the light curve (see
e.g., Fig. 4 of Skopal, 2008). Munari et al. (1997a), while studying the
active phase of YY Her, pointed out that its hot component cannot always be
spherically symmetric, as they indicated its occasionally low temperature
($\sim$1.5$\times 10^{4}$ K) in the simultaneous presence of a hot subdwarf
radiation ($\sim$105 K) in the system. Similarly, during the active phase of
AS 338, Esipov et al. (2000) indicated a low hot component temperature
($<$1.5$\times 10^{4}$ K) in the optical with the simultaneous presence of an
extended H II region indicating the presence of a high-temperature region
($\sim$105 K) in the ‘pseudosphere’. In this respect, the authors pointed out
the similarity with other classical SySts. Another interesting effect,
considering the aim of this work, was the appearance of a substantial amount
of neutral hydrogen on the line of sight to the hot component of YY Her after
its short-duration outburst in December 1981 (Munari et al., 1997a). Also,
Quiroga et al. (2002) found that the nebula in AR Pav is probably bounded on
all sides by significant amount of neutral material at least near the orbital
plane. In contrast, for non-eclipsing systems, seen $\sim$ pole-on, the
temperature increases to around 2$\times 10^{5}$ K (e.g., Tomov et al., 2016;
Skopal et al., 2020). In both cases, eclipsing and non-eclipsing, the nebular
continuum increases by a factor of $\sim$10 relative to quiescent phases
(Skopal, 2005; Skopal et al., 2017). The nature of these dramatic changes
between the quiescence and the activity was clarified by disentangling the
ultraviolet (UV) to near-infrared spectra of S-type symbiotic stars (Skopal,
2005). This revealed that all eclipsing systems develop a two-temperature type
of the hot component spectrum during active phases: The cool spectrum is
produced by a $1-3\times 10^{4}$ K warm pseudophotosphere, while the hot one
is represented by highly ionized emission lines and a strong nebular
continuum. The former is not capable of producing the measured nebular
emission, which thus signals the presence of a strong ionizing source in the
system – the essential condition for its interpretation: The hot component has
a disk-like structure, whose flared outer rim (which is the warm WD’s
pseudophotosphere) occults the central ionizing source in the line of sight,
while the nebula above/below the disk is ionized (see Fig. 27 of Skopal (2005)
and Fig. 6 of Cariková & Skopal (2012)). On the other hand, non-eclipsing
systems, seen $\sim$ pole-on, show an increase in the WD temperature ($\sim
2\times 10^{5}$ K) and the nebular emission from the very beginning of the
outbursts (e.g., Skopal et al., 2017).

The key phenomenon, the emergence of the disk-like structure around the WD
during active phases, allows us to measure the column density of neutral
hydrogen between the observer and the warm WD’s pseudophotosphere ($N_{\rm
H}^{\rm obs}$) for eclipsing SySts at any orbital phase of the binary (see
Figs. 8, 10, 19 and 21 of Skopal, 2005). This is because the flared disk
blocks the ionizing photons from the central hot WD in the orbital plane.
Consequently, the lack of ionizing photons allows the giant’s wind to remain
neutral in the orbital plane.

Accordingly, measuring $N_{\rm H}^{\rm obs}$ from Rayleigh scattering on H
atoms around the Ly$\alpha$ line (e.g., Isliker et al., 1989) along the whole
orbit, and for all suitable objects (Sect. 2.1) represents the main aim of
this paper. In this way, we revealed the transient emergence of a neutral wind
region in the orbital plane, and its asymmetry with respect to the binary axis
(Sect. 3). In Sect. 4 we discuss how our results aid us in understanding the
geometric and ionization structure of SySts, while in Sect. 5 we summarize our
findings and propose tasks for future investigation.

##  2 Observations and methods

###  2.1 Selection of targets

According to the ionization structure of hot components during active phases
(see above), the number of objects suitable for the objective of this paper is
restricted only to the eclipsing systems, for which a well-defined far-UV
spectrum from the active phase is available. This allows us to model the
effect of Rayleigh scattering around the Ly$\alpha$ line. Only in such the
case, it is possible to expect comparable $N_{\rm H}^{\rm obs}$ for different
objects at any orbital phase, because their values depend on the orbital
inclination. For systems that may no longer be eclipsing but have a relatively
high orbital inclination, up to values given by the vertical extension of the
WD’s pseudophotosphere, lower $N_{\rm H}^{\rm obs}$ values can be expected.
For even lower inclinations, when the line of sight passes only through the
ionized region, no neutral hydrogen is measurable. Moreover, the wind density
dispersion with the orbital inclination can be accentuated by focusing of the
giant’s wind to the orbital plane (see Shagatova et al., 2016) that results in
its dilution around the giant’s poles (see Shagatova et al., 2021).

Accordingly, we first inspected the historical light curves of SySts available
from the literature, and, on the basis of our own experience with photometric
monitoring of these objects for more than 30 years (Sekeráš et al., 2019) we
found that BF Cyg, CH Cyg, CI Cyg, YY Her, BX Mon, AR Pav, AX Per, FN Sgr, PU
Vul, AS 338 and AS 296 show eclipses during outbursts. Second, searching the
archive of the International Ultraviolet Explorer (IUE) we found that the
spectra of Z And, CD-43∘14304, TX CVn, BF Cyg, CH Cyg, CI Cyg, YY Her, AR Pav,
AX Per, PU Vul, AS 338 and AS 296 show signatures of the Rayleigh scattering
attenuation around the Ly$\alpha$ line during active phases that signals a
large amount of H atoms on the line of sight. The intersection of both sets of
objects then should represent those that best suit the goals of this study.
However, some systems from these groups cannot be included in the final set of
our targets. They are discussed in Appendix C.

As a result, targets for which comparable $N_{\rm H}^{\rm obs}$ at any orbital
phase of the binary can be expected are the eclipsing systems: BF Cyg, CI Cyg,
YY Her, AR Pav, AX Per and PU Vul. Log of their IUE spectra is introduced in
Table 1, and Appendix D summarizes their basic characteristics.

Table 1: Log of the low-resolution IUE spectra of our targets and corresponding column densities $N_{\rm H}^{\rm obs}$ (see text and Fig. 1). Object | Spectrum | Date (UT)† | Julian Date† | $\varphi^{\star}$ | $N_{\rm H}^{\rm obs}$
---|---|---|---|---|---
|  | yyyy-mm-dd | JD 2 44… |  | (cm-2)
BF Cyga | SWP31540+LWP11376 | 1987-08-11 | 7019.35 | 0.145 | $(2.5\pm 1.0)\times 10^{23}$
| SWP32341+LWP12109 | 1987-11-16 | 7116.00 | 0.273 | (9.0 +2.4/-1.9)$\times 10^{22}$
| SWP33113+LWP12886 | 1988-03-19 | 7239.88 | 0.436 | $(3.5\pm 1.1)\times 10^{22}$
| SWP39163+LWP18251 | 1990-06-30 | 8072.58 | 0.536 | $(4.8\pm 1.5)\times 10^{22}$
| SWP39188+LWP18302 | 1990-07-06 | 8079.35 | 0.545 | $(6.0\pm 1.8)\times 10^{22}$
| SWP40055+LWP19153(4) | 1990-11-05 | 8201.25 | 0.706 | (4.0 +1.2/-1.5)$\times 10^{22}$
CI Cygb | SWP03816+LWR03396 | 1979-01-05 | 3879.35 | 0.392 | $(7.0\pm 2.7)\times 10^{22}$
| SWP05485+LWR04757 | 1979-06-11 | 4035.74 | 0.576 | $(3.0\pm 1.3)\times 10^{22}$
| SWP05672+LWR04916 | 1979-06-29 | 4054.03 | 0.597 | $(3.5\pm 1.4)\times 10^{22}$
| SWP07818+LWR06831 | 1980-01-30 | 4269.40 | 0.850 | $(1.6\pm 0.7)\times 10^{23}$
| SWP08757 | 1980-04-14 | 4344.17 | 0.937 | (2.5 +0.9/-0.8)$\times 10^{24}$
| SWP09664+LWR08408 | 1980-08-01 | 4453.21 | 0.065 | $(1.5\pm 0.7)\times 10^{24}$
| SWP09830+LWR08542 | 1980-08-18 | 4469.96 | 0.085 | (1.0 +0.6/-0.4)$\times 10^{24}$
| SWP09942+LWR08651 | 1980-08-28 | 4480.44 | 0.097 | (6.0 +1.6/-2.6)$\times 10^{23}$
| SWP10602+LWR09303 | 1980-11-14 | 4558.37 | 0.188 | $(2.5\pm 0.8)\times 10^{23}$
| SWP11003+LWR09671 | 1981-01-08 | 4613.44 | 0.253 | (1.0 +0.5/-0.3)$\times 10^{23}$
| SWP14755+LWR11318 | 1981-08-14 | 4830.93 | 0.508 | $(6.0\pm 2.6)\times 10^{22}$
| SWP15713+LWR12127 | 1981-12-11 | 4950.19 | 0.648 | $(3.0\pm 1.3)\times 10^{22}$
YY Herc | SWP15652+LWR12080 | 1981-12-04 | 4943.46 | 0.265 | (1.4 +0.4/-0.6)$\times 10^{23}$
AR Pavd | SWP17070+LWR13346 | 1982-05-30 | 5119.91 | 0.008 | eclipse
| SWP10415+LWR09095 | 1980-10-19 | 4532.05 | 0.035 | eclipse
| SWP10497+LWR09184 | 1980-10-29 | 4541.85 | 0.051 | eclipse
| SWP10510+LWR09199 | 1980-10-30 | 4543.45 | 0.054 | $(3.0\pm 1.3)\times 10^{24}$
| SWP10520+LWR09207 | 1980-11-01 | 4544.90 | 0.056 | $(3.0\pm 1.3)\times 10^{24}$
| SWP10524+LWR09212 | 1980-11-02 | 4545.74 | 0.058 | $(2.5\pm 1.3)\times 10^{24}$
| SWP10527+LWR09217 | 1980-11-03 | 4546.70 | 0.059 | $(2.5\pm 1.3)\times 10^{24}$
| SWP17331+LWR13580 | 1982-07-01 | 5152.09 | 0.061 | (2.5 +0.8/-1.3)$\times 10^{24}$
| SWP22434+LWP02903 | 1984-03-07 | 5766.70 | 0.078 | $(2.0\pm 0.7)\times 10^{24}$
| SWP45099+LWP23467 | 1992-07-08 | 8812.01 | 0.116 | (5.0 +1.5/-2.5)$\times 10^{23}$
| SWP22707+LWP03139 | 1984-04-10 | 5800.76 | 0.134 | $(4.0\pm 1.4)\times 10^{23}$
| SWP05828+LWR05077 | 1979-07-17 | 4071.74 | 0.274 | (7.5 +1.8/-3.3)$\times 10^{22}$
| SWP13956+LWR10570 | 1981-05-10 | 4735.37 | 0.371 | $(5.0\pm 2.0)\times 10^{22}$
| SWP01561 | 1978-05-16 | 3645.37 | 0.568 | (5.0 +3.5/-2.5)$\times 10^{22}$
| SWP02236+LWR02023 | 1978-08-08 | 3728.89 | 0.706 | $(3.0\pm 1.3)\times 10^{22}$
| SWP03310+LWR02917 | 1978-11-11 | 3824.39 | 0.864 | (2.0 +1.7/-0.7)$\times 10^{23}$
| SWP09646+LWR08393 | 1980-07-30 | 4451.29 | 0.901 | (1.9 +0.7/-0.8)$\times 10^{24}$
| SWP16711+LWR12974 | 1982-04-07 | 5067.04 | 0.920 | (1.0 +0.6/-0.4)$\times 10^{24}$
| SWP16857+LWR13104 | 1982-04-29 | 5088.99 | 0.956 | eclipse
| SWP16938+LWR13208 | 1982-05-09 | 5098.88 | 0.973 | eclipse
| SWP16949+LWR13235 | 1982-05-13 | 5102.93 | 0.980 | eclipse
AX Pere | SWP03755+LWR03332 | 1978-12-31 | 3873.65 | 0.598 | (5.0 +2.5/-1.5)$\times 10^{22}$
| SWP03814+LWR03332 | 1979-01-05 | 3879.19 | 0.606 | (4.5 +2.5/-1.5)$\times 10^{22}$
Table 1: continued

PU Vulf | SWP33833+LWP13531 | 1988-06-29 | 7342.30 | 0.570 | $(5.6\pm 1.8)\times 10^{22}$
---|---|---|---|---|---
| SWP33930+LWP13669 | 1988-07-16 | 7359.45 | 0.574 | $(5.8\pm 1.9)\times 10^{22}$
| SWP34406+LWP14173 | 1988-10-03 | 7437.82 | 0.590 | $(3.9\pm 1.5)\times 10^{22}$
| SWP35960+LWP15328 | 1989-04-08 | 7624.82 | 0.628 | $(3.0\pm 0.9)\times 10^{22}$
| SWP36301+LWP15549 | 1989-05-19 | 7666.20 | 0.636 | $(2.9\pm 1.2)\times 10^{22}$
| SWP37185+LWP16416 | 1989-09-25 | 7794.53 | 0.663 | $(3.8\pm 1.4)\times 10^{22}$
AS 338g | SWP37290+LWP16522 | 1989-10-09 | 7809.16 | 0.670 | $<5\times 10^{23}$
AS 296h | SWP34080+LWP13843 | 1988-08-13 | 7387.15 | 0.321 | (1.0 +2.1/-0.6)$\times 10^{23}$
| SWP34725+LWP14446 | 1988-11-11 | 7477.07 | 0.458 | $<3\times 10^{23}$
| SWP38353+LWP17523 | 1990-03-13 | 7963.90 | 0.197 | $(3.0\pm 2.3)\times 10^{23}$

Notes:
† the dates correspond to the start of the observation with the SWP camera,
⋆ orbital phase as given by the ephemerides below:
a JDspec.conj. = 2 445 395.1 + 757.2$\times$E (Fekel et al., 2001), EB-V =
0.35, $d=3.4$ kpc (Muerset et al., 1991),
b JDecl. = 2 441 838.8 + 852.98$\times$E (Skopal et al., 2012), EB-V = 0.35
(Skopal, 2005), $d=1.6$ kpc (Seaquist et al., 1993),
c JDecl. = 2 440 637 + 592.8$\times$E (Skopal, 1998), $d=6.3$ kpc (Skopal,
2005), EB-V = 0.20 (Munari et al., 1997a),
d JDecl. = 2 411 266.1 + 604.45$\times$E (Skopal, 2005), EB-V = 0.26, $d=4.9$
kpc (Schild et al., 2001),
e JDecl. = 2 447 551.26 + 680.83$\times$E (Skopal et al., 2011), EB-V = 0.27
(Kenyon & Webbink, 1984), $d=1.7$ kpc (Skopal et al., 2001),
f JDecl. = 2 444 550 + 4897$\times$E (Shugarov et al., 2012), EB-V = 0.30,
$d=4.7$ kpc (Kato et al., 2012),
g JDecl. = 2 446 650 + 434.1$\times$E (Siviero et al., 2007), EB-V = 0.50,
$d=6$ kpc (Esipov et al., 2000),
h JDecl. = 2 448 492 + 658$\times$E (Munari et al., 1995), EB-V = 1.0, $d=1$
kpc (Munari et al., 1992).

###  2.2 Measuring $N_{\rm H}^{\rm obs}$ from Rayleigh scattering

Rayleigh scattering represents the process, where the atom is excited by an
incident photon to the intermediate state and is immediately stabilized by a
transition to the same bound state, re-emitting a photon of the original
energy (e.g., Nussbaumer et al., 1989). For hydrogen, the effect is best
observable around the Ly$\alpha$ line as a continuum depression with zero
residual intensity and extended wings. The strength of Rayleigh scattering is
determined by the number of scatterers on the path between the emitting source
and the observer, i.e., on the value of $N_{\rm H}^{\rm obs}$, and its profile
is given by the cross-section, $\sigma_{\rm Ray}(\lambda)$, which yields the
optical depth, $\tau_{\rm Ray}=\sigma_{\rm Ray}(\lambda)N_{\rm H}^{\rm obs}$.
Therefore, fitting the far-UV continuum of an object attenuated by Rayleigh
scattering, we can obtain the corresponding value of $N_{\rm H}^{\rm obs}$. It
is important to emphasize that the Rayleigh scattering effect is dominant in
modeling the continuum depression around the Ly$\alpha$ line111It is meant
relative to other line broadening effects in the neutral part of the giant’s
wind. during quiescent phases (e.g., Isliker et al., 1989; Vogel, 1991; Dumm
et al., 1999; Crowley et al., 2005), and also in our case, during active
phases, because the width of possible ‘atmospheric’ Ly$\alpha$ absorption
profile from/above the warm WD pseudophotosphere can be neglected (see
Appendix F).

According to the configuration of SySts, we assume that the UV continuum of
eclipsing systems during outbursts consists of the stellar continuum from the
warm WD’s pseudophotosphere and the nebular continuum from the ionized
circumbinary matter (see Sect. 1). We compare the former with the blackbody
radiation at a temperature $T_{\rm BB}$, and approximate the latter by
contributions from free-bound and free-free transitions in hydrogen plasma
radiating at the electron temperature $T_{\rm e}$. Then, using Eqs. (5) and
(11) of Skopal (2005), the reddening-free UV continuum of a SySt,
$F(\lambda)$, measured at the Earth, can be written in the form,

$F(\lambda)=\theta_{\rm WD}^{2}\pi B_{\lambda}(T_{\rm BB})\,e^{-\sigma_{\rm
Ray}(\lambda)\,N_{\rm H}^{\rm obs}}+\,k_{\rm
N}\times\varepsilon_{\lambda}({\rm H},T_{\rm e}),$ (1)

where $\theta_{\rm WD}=R_{\rm WD}^{\rm eff}/d$ is the angular radius of the
warm WD’s pseudophotosphere, given by its effective radius $R_{\rm WD}^{\rm
eff}$ (i.e., the radius of a sphere with the same luminosity) and the distance
$d$. The Rayleigh cross-section for scattering by hydrogen in its ground state
can be expressed as (see Nussbaumer et al., 1989),

$\sigma_{\rm Ray}(\lambda)=\sigma_{\rm
e}\Big{[}\sum_{k}\frac{f_{1k}}{(\lambda/\lambda_{1k})^{2}-1}\Big{]}^{2},$ (2)

where $\sigma_{\rm e}=6.65\times 10^{-25}$ cm2 is the Thomson cross-section,
$f_{1k}$ are the oscillator strengths of the hydrogen Lyman series and
$\lambda_{1k}$ are the corresponding wavelengths. In calculating $\sigma_{\rm
Ray}(\lambda)$ we used all bound states tabulated by Wiese et al. (1966),
i.e., $k$ = 2 to 40. The second term on the right is the nebular continuum
given by its volume emission coefficient, $\varepsilon_{\lambda}({\rm
H},T_{\rm e})$, scaled with the factor $k_{\rm N}=EM/4\pi d^{2}$, where $EM$
is the emission measure of the nebula. The variables determining the model
continuum are, $\theta_{\rm WD}$, $T_{\rm BB}$, $N_{\rm H}^{\rm obs}$, $k_{\rm
N}$ and $T_{\rm e}$. They are obtained by comparing Eq. (1) with the continuum
fluxes selected from the dereddened spectra of our targets. In selecting
suitable flux points of the true continuum, we proceeded as follows.

First, we considered the influence of the line blanketing effect, which
represents an additional source of absorption in the neutral wind, mostly by
Fe II transitions (see Shore & Aufdenberg, 1993). This so-called iron curtain
can strongly depress the level of the continuum at 1500 to 1800 Å and 2300 to
2800 Å (see e.g., BF Cyg, PU Vul, AR Pav in Appendix A and B). To eliminate
this effect we used a template of three representative low-resolution IUE
spectra with a low, modest and strong influence of the continuum by the iron
curtain (see Fig. 1 of Skopal, 2005). With the aid of these observations and
theoretical calculations of, e.g., Shore & Aufdenberg (1993) and Horne et al.
(1994), we selected spectral regions with the lowest effect of the intervening
absorption. Second, we took into account the often very different errors of
the measured fluxes for different spectra, which are also wavelength
dependent. For example, in the short-wavelength part of the spectrum,
especially below 1200 Å, the standard deviation of the flux measurement can be
compared to the flux itself 222However, there are spectra that are quite well
exposed even below 1200 Å. In these cases the model matches also the short-
wavelength wing of the continuum depression (e.g., PU Vul and BF Cyg, see
Appendix A).. Fortunately, the use of only the fluxes of the long-wavelength
wing of the Rayleigh attenuated continuum is sufficient to determine the
values of $N_{\rm H}^{\rm obs}$ (e.g., Vogel, 1991; Fernandez-Castro et al.,
1995). Furthermore, the very extended absorption profile for $N_{\rm H}^{\rm
obs}\gtrsim 2\times 10^{22}$ cm-2 causes a measurable Rayleigh scattering
effect even for $\lambda>1300$ Å (see Fig. 5 in Appendix F), where the
spectrum is in most cases sufficiently well determined to allow us to at least
estimate the corresponding value of the H0 column density. However, for some
strongly underexposed spectra, it was possible to estimate only the upper
limit of $N_{\rm H}^{\rm obs}$ or its wide range. Therefore, according to the
quality of the used spectra, we proceeded to determine the $N_{\rm H}^{\rm
obs}$ values as follows:

(i) For well-exposed spectra, according to the signal-to-noise ratio and for
simplicity, we set the errors to 7 – 10% for all selected continuum fluxes. In
these cases, we calculated a grid of models (1) for reasonable ranges of the
fitting parameters and selected that corresponding to a minimum of the reduced
$\chi^{2}$ function333The corresponding software and application example are
available at https://doi.org/10.5281/zenodo.7695015.

(ii) In cases where the spectrum is underexposed, mostly in the far-UV region
and/or heavily affected by the iron curtain absorptions, we compared the
spectrum to a set of plausible synthetic models, ($\lambda,B_{\lambda}(T_{\rm
BB})exp[-\sigma_{\rm Ray}(\lambda)N_{\rm H}^{\rm
obs}],\varepsilon_{\lambda}({\rm H},T_{\rm e}$), and selected the best match
by eye.

(iii) Finally, for severely underexposed spectra of AS 338 and AS 296, we
estimated only the upper limits or wide ranges of H0 column densities (see
Appendix C and examples in the bottom row of Fig. 3). Some example models for
our targets are shown in Fig. 3 (Appendix A). Examples of the selected
continuum fluxes for better- (PU Vul) and poorly-exposed (AR Pav) far-UV
spectra with the corresponding models are illustrated in Fig. 7 (Appendix G).

The most important parameter for the purpose of this paper is the column
density $N_{\rm H}^{\rm obs}$ (Table 1), and, in particular, its dependence on
the orbital phase (Fig. 1). Its uncertainty is estimated at $\sim$20 to
$\sim$60 %, depending on the signal-to-noise ratio and the influence of other
emission features around the Ly$\alpha$ transition. For illustration, the
models corresponding to the upper and lower value of $N_{\rm H}^{\rm obs}$ are
depicted by dotted lines in Figs. 3 and 4. In addition, we also investigated
the possible dependence of the $N_{\rm H}^{\rm obs}$ determination on
interstellar reddening. Our analysis suggests that uncertainties in the
$E_{\rm B-V}$ color excess may cause additional errors in the $N_{\rm H}^{\rm
obs}$ determination of about 10% (see Appendix G). Table 1 and Fig. 1 indicate
the total $N_{\rm H}^{\rm obs}$ errors. For completeness, Table 3 (Appendix E)
presents the values of other parameters determining the UV continuum. Their
uncertainties would be estimated at $\sim$10 to $\sim$50% of their best values
(see Sect. 3.3 of Skopal, 2005).

##  3 Results

###  3.1 Indication of the neutral wind region in the orbital plane during
outbursts

The main result of this study is depicted in Fig. 1: The $N_{\rm H}^{\rm obs}$
values for our targets show a strong dependence on the orbital phase, with a
difference of about two orders of magnitude between the values around the
inferior and superior conjunction of the giant. High values of $N_{\rm H}^{\rm
obs}$ at any position of the binary reflects the presence of a neutral region
in the orbital plane, because our targets are seen $\sim$edge-on. Its
emergence is transient, being connected solely with active phases (Sect. 3.2,
Appendix B). The values for eclipsing systems (i.e., BF Cyg, CI Cyg, YY Her,
AR Pav, AX Per and PU Vul) follow a common course that suggests similar
properties of the neutral zone for these objects. In contrast, during
quiescent phases of eclipsing systems, the neutral hydrogen zone is limited
only to the vicinity of the inferior conjunction of the giant, where it
represents the neutral wind from the giant (e.g., Vogel, 1991; Dumm et al.,
1999; Shagatova & Skopal, 2017). Therefore, a comparison of H0 column
densities from quiescent and active phases at these positions (see Fig. 2,
panel b and e) suggests that our $N_{\rm H}^{\rm obs}$ values also represent
the densities of the stellar wind from the giant.

The case of measuring the H0 column densities in the direction to the WD,
while the source of neutral hydrogen is associated with the red giant, will
give a large difference between their values measured around the inferior and
the superior conjunction of the giant, which is in agreement with our result
(see Fig. 1). Thus, the high-amplitude orbital-dependent variation of $N_{\rm
H}^{\rm obs}$ values confirms that we measure H0 column densities of the
neutral wind from the red giant444If the broad Ly$\alpha$ line profile was
formed in the WD atmosphere, there would be no reason to measure the
dependence of the $N_{\rm H}^{\rm obs}$ values on the orbital phase (see the
last paragraph of Appendix F)..

Figure 1:  Column densities of atomic hydrogen, $N_{\rm H}^{\rm obs}$, between
the observer and the WD, measured for our targets (Sect. 2.1) during active
phases as a function of the orbital phase $\varphi$ ($\varphi=0$ corresponds
to the inferior conjunction of the giant). For better visualization, the
values are plotted over two orbital cycles. Eclipsing objects (black solid
symbols) follow a common course. The blue line indicates their fit with a 4th-
degree polynomial. Open gray symbols denote values for objects discussed in
Appendix C, i.e., for those with poorly defined UV spectra (AS 338, AS 296) or
not eclipsing, but with a high orbital inclination (Z And, TX CVn, CD-43∘14304
(CD-43∘ in the legend)). Values for the latter were taken from Skopal (2005).
All data measured in this work are summarised in Table 1, and examples of the
corresponding continuum models are shown in Appendix A.

###  3.2 The cause of the neutral region during outbursts

The emergence of the neutral wind region in the orbital plane is conditioned
by the formation of an optically thick disk-like structure around the WD in
the orbital plane during outbursts (see Sect. 1). Consequently, the disk
blocks the ionizing radiation from the central burning WD within its vertical
extension from the orbital plane, which makes the wind of the giant neutral in
the orbital plane, thus making it detectable by eclipsing systems in any
orbital phase. During active phases, the wind from the giant represents a cool
absorbing gas veiling the WD’s pseudophotosphere in the orbital plane.
Therefore, the $N_{\rm H}^{\rm obs}$ values of this medium show a clear
dependence on the orbital phase, with a high amplitude (Fig. 1, Sect. 3.1).

The presence of the neutral giant’s wind in the orbital plane is primarily
indicated by the deep continuum depression in the spectrum around the
Ly$\alpha$ line due to Rayleigh scattering on H0 atoms, and by broad
absorption bands due to iron curtain (see Fig. 3)555The prominence of the iron
curtain in the spectrum varies from object to object, depending mainly on the
temperature of the WD’s pseudophotosphere., the features that are absent
during quiescent phases around the whole orbit. For our targets, we
demonstrate the corresponding change of the UV spectrum between the quiescent
and active phase in Fig. 4 (Appendix B).

###  3.3 Wind asymmetry

Figure 1 shows the asymmetric distribution of $N_{\rm H}^{\rm obs}$ values
along the orbit with a minimum of $\sim 4\times 10^{22}$ cm-2 between
$\varphi\sim$0.6 and $\sim$0.7 and a maximum of a few times $10^{24}$ cm-2
just before and after eclipses ($\varphi\sim 0.95$ and $\sim 0.03$). The
asymmetry is also evidenced by the steeper values of $N_{\rm H}^{\rm obs}$
before the eclipse ($0.85<\varphi<0.95$) than after the eclipse
($\varphi>0.05$), and a small local maximum around $\varphi=0.5$. Such the
asymmetric distribution of $N_{\rm H}^{\rm obs}$ along the orbit implies the
asymmetric density distribution of the giant’s wind in the near-orbital-plane
region with respect to the binary axis. This property of the wind was
previously indicated also for quiescent eclipsing SySts SY Mus and EG And by
the same type of the asymmetric distribution of H0 column densities, although
they are measurable only around the inferior conjunction of their giants in
quiescent phases (Dumm et al., 1999; Shagatova et al., 2016, here Fig. 2b,
Sect. 4.1). Recently, this sort of asymmetric shaping of the wind in the
orbital plane was confirmed by modeling the UV light curves of SY Mus
(Shagatova & Skopal, 2017), and by the H$\alpha$ line profile variation along
the orbit of EG And (Shagatova et al., 2021). Therefore, the orbital-dependent
asymmetry of $N_{\rm H}^{\rm obs}$ values measured for more objects and during
the active phases (Fig. 1) suggests that the asymmetric distribution of the
giant’s wind in the orbital plane with respect to the binary axis may possibly
be a common property of winds from giants in SySts.

Its origin could in principle be similar to that simulated and measured for
detached high-mass X-ray binaries consisting of a hot O/B (super)giant and a
neutron star or a black hole, where a similar type of orbital-related
asymmetry in NH is attributed to tidal streams and accretion wakes, distorted
by the orbital motion (e.g., Blondin et al., 1990, 1991; Manousakis et al.,
2012; Kretschmar et al., 2021; Rahin & Behar, 2023). Modeling of our $N_{\rm
H}^{\rm obs}(\varphi)$ values in this way, but for parameters of S-type SySts,
should clarify the cause of their asymmetric distribution throughout the
orbit.

Figure 2: The symbiotic phenomenon in a nutshell. Characteristic UV spectra
(top panels), hydrogen column densities $N_{\rm H}^{\rm obs}$ (middle panels),
and sketch of the corresponding ionization structure (bottom panels) for
eclipsing SySts (see keys) during quiescent and active phases are shown in the
left and right columns, respectively. During the quiescent phase, the
ionization structure is given by the location of $N_{\rm H}^{\rm obs}$ values
only in the vicinity of the inferior conjunction of the giant (pole-on view;
see Shagatova & Skopal, 2017), while during the active phase a biconical
ionization structure is constrained by the H0 wind region in the orbital plane
(edge-on view; Sect. 4.2). The two-velocity type of mass outflow during
outbursts is denoted by arrows of different sizes (Sect. 4.2). In both cases,
the asymmetric profile of $N_{\rm H}^{\rm obs}(\varphi)$ (panels b and e)
imprints the asymmetric wind from the giant. Spectra from the quiescent phase
(panel a) are introduced in Table 4 (Appendix E). Description of SED models as
in Appendix A, and column densities in panel e as in Fig. 1. The data and
models in panel b are from the literature (see Sect. 4.1), i.c. denotes the
continuum depression caused by the iron curtain (see Sect. 2.2), and p is in
units of the binary components separation. Other denotations are obvious.

##  4 Discussion

Here we describe how our findings complement the overall picture of the
symbiotic phenomenon. For this purpose, we present the characteristic UV
spectra of SySts, the measured H0 column densities as a function of the
orbital phase, and discuss how they relate to the ionization structure of
SySts during both, the quiescent and active phases. Figure 2 summarizes our
view.

###  4.1 Quiescent phase

During quiescent phases, the far-UV spectrum is dominated by the Rayleigh-
Jeans tail of a very hot source of the stellar radiation ($T_{\rm BB}\gtrsim
10^{5}$ K), while the near-UV is usually dominated by the nebular continuum
(e.g., Muerset et al., 1991; Skopal, 2005). The effect of Rayleigh scattering
on hydrogen atoms, and overall decrease of the continuum level is measured
only for eclipsing systems in the vicinity of the inferior conjunction of the
giant as a result of the passage of light from the WD through the absorbing
medium of the neutral wind from the giant (e.g., Isliker et al., 1989; Horne
et al., 1994). Here, an example of BF Cyg is depicted in Fig. 2a. Figure 2b
then shows all $N_{\rm H}^{\rm obs}$ values of eclipsing SySts determined
during their quiescent phases: SY Mus and EG And (Dumm et al., 1999; Shagatova
et al., 2016), BF Cyg (Pereira & Landaberry, 1996), and RW Hya (Dumm et al.,
1999). Accordingly, the observed distribution of H0 column densities along the
orbit suggests that the neutral zone is located around the giant and beyond it
in the direction away from the WD, and is distributed asymmetrically with
respect to the binary axis, while the rest of the binary environment around
the WD is ionized. Example of SY Mus that corresponds to the $N_{\rm H}^{\rm
obs}(\varphi)$ model depicted in Fig. 2b (red line, Shagatova et al., 2016) is
shown in Fig. 2c (adapted according to Shagatova & Skopal, 2017). A simplified
calculation of the ionization H0/H+ boundary during quiescent phase is
introduced by Seaquist et al. (1984) and Nussbaumer & Vogel (1987).

###  4.2 Active phase

During active phases, the UV spectrum of eclipsing SySts can be fitted by a
low-temperature stellar-type of radiation ($T_{\rm BB}\approx 1-3\times
10^{4}$ K) emitted by the warm WD’s pseudophotosphere often dominating the
far-UV, and a strong nebular continuum pronounced in the near-UV (see examples
in Appendix A and B). The former is strongly attenuated around the Ly$\alpha$
line by Rayleigh scattering on H0 atoms at any orbital phase, and shows
signatures of the iron curtain absorptions, while the latter increases
compared to the quiescent phase (Fig. 2d, and Appendix A and B). The
corresponding high values of $N_{\rm H}^{\rm obs}$ along the orbit (Fig. 1)
indicate the presence of the neutral region in the orbital plane (Sect.
3)666During outbursts of non-eclipsing systems, the neutral wind region in the
orbital plane is indicated by significant broadening and high fluxes of the
Raman-scattered O VI 6825 Å line relative to the quiescent phase. This is
because the new neutral hydrogen in the orbital plane increases the Raman
scattering efficiency (see Skopal et al., 2020).. Such the neutral zone
determines a biconical shaping of the ionized region distributed above/below
it with the tops at the burning WD (see Fig. 2f). In this case, the nebular
radiation is produced by the ionized wind from the WD (Skopal, 2006). Such an
ionization structure is responsible for observing two different types of
spectra depending on the orbital inclination. This suggests a classification
of outbursts into two types – the warm- and hot-type (see also Skopal, 2005;
Skopal et al., 2020):

(i) Outbursts in systems with a high orbital inclination (i.e., seen $\sim$
edge-on) show the two-temperature type of the hot component spectrum (see
Sect. 1). These outbursts are classified as the ‘warm-type’, because the
stellar component of radiation is emitted by the warm ($1-3\times 10^{4}$ K)
WD’s pseudophotosphere. During the warm-type of outbursts, the two-velocity
type of mass outflow from the hot component is indicated. A rather slow
outflow is indicated by the absorption component in P-Cygni line profiles
created in the expanding optically thick wind from the WD in the orbital
plane, while a fast outflow is indicated by the broad emission wings produced
by the fast optically thin ionized wind from the WD over the remainder of the
star (see Fig. 2f, and Skopal et al., 2006, in detail). All our targets show
signatures of the warm-type of outbursts.

(ii) Outbursts in systems with a low orbital inclination (i.e., seen $\sim$
pole-on) show the spectrum characterized by the immediate occurrence of strong
nebular radiation that dominates the optical. These outbursts are classified
as ‘hot-type’, because the stellar component of radiation is emitted by the
hot ($\sim 2\times 10^{5}$ K) WD’s pseudophotosphere, the contribution of
which is negligible in the optical (e.g., Skopal et al., 2020). The strong
nebular radiation is emitted by the enhanced ionized wind from the WD (Skopal,
2006). Here, the well-observed SySts, AG Dra, AG Peg, LT Del and V426 Sge show
features of the hot-type of outbursts (e.g., González-Riestra et al., 2008;
Leedjärv et al., 2016; Skopal et al., 2017; Ikonnikova et al., 2019; Skopal et
al., 2020).

##  5 Conclusion and future work

We have found that a deep and wide absorption is formed around the Ly$\alpha$
line during outbursts of all eclipsing symbiotic binaries around the whole
orbit, for which there are relevant observations (Sect. 2.1). Modeling this
feature by Rayleigh scattering on atomic hydrogen we determined the
corresponding H0 column densities in the direction of the WD (Fig. 1). The
high values of $N_{\rm H}^{\rm obs}$ measured at any orbital phase indicate
the presence of a neutral region in the orbital plane. Their large-amplitude
orbital-dependent variation indicates that this region consists of the wind
from the giant (Sect. 3.1). It is observable due to the emergence of a dense
disk-like structure around the WD during outbursts (Skopal, 2005; Cariková &
Skopal, 2012) that blocks the ionizing photons from the central hot WD in the
orbital plane (Sect. 3.2). The asymmetric course of $N_{\rm H}^{\rm
obs}(\varphi)$ values implies an asymmetric density distribution of the wind
from the giant in the orbital plane with respect to the binary axis (Sect.
3.3). Finally, the emergence of the neutral near-orbital-plane region changes
significantly the ionization structure of the symbiotic binary during active
phases: The ionized region is distributed above/below it, having the tops at
the burning WD (Sect. 4.2, Fig. 2f).

The unique distribution of neutral hydrogen in the orbital plane of symbiotic
binaries as indicated for different objects during different stages of their
activity (Fig. 1, Appendix B) suggests common properties of stellar winds from
their giants. Our findings can aid us in further theoretical modeling and can
be conducive to the explanation of more violent classical nova outbursts. For
example:

  1. 1.

Modeling $N_{\rm H}^{\rm obs}$ values along the whole orbit for more objects
during active phases should confirm and generalize the substantial focusing of
the wind from the giant in S-type SySts towards the orbital plane as found for
quiescent SySts SY Mus and EG And by Shagatova et al. (2016, 2021).

  2. 2.

The $N_{\rm H}^{\rm obs}$ values measured around the orbit will serve as a
benchmark for testing the theoretical modeling of the wind morphology of wide
interacting binaries containing an evolved giant (e.g., Bermúdez-Bustamante et
al., 2020; El Mellah et al., 2020; Lee et al., 2022). In particular, modeling
the morphology of a massive slow wind blowing from red giants in S-type SySts
with terminal velocity of a few times 10 km s-1 (e.g., Dumm et al., 1999), at
rates of a few times ($10^{-7}-10^{-6}$) $M_{\odot}\,{\rm yr}^{-1}$ (e.g.,
Seaquist et al., 1993; Shagatova et al., 2016), which is disrupted by the
accreting WD, in a similar way to what has been done for massive X-ray
binaries (see references in Sect. 3.3), should lead to a better understanding
of the mass-transfer problem in symbiotic binaries.

  3. 3.

The emergence of a slowly expanding disk-like structure around the exploding
WD appears to be common also for more violent outbursts of classical novae,
where it is indicated by direct radio imaging (Chomiuk et al., 2014) and is
constrained by modeling the energy distribution in the nova spectrum Skopal
(2019). During outbursts of SySts, the flared disk blocks the ionizing
radiation from the center resulting in the creation of the neutral near-
orbital-plane region throughout the binary. During the classical nova
explosions, the disk represents a vital element to explain the $\gamma$-ray
emission measured near the optical maximum as a result of shocks developing
between the first slow and secondary fast outflow (e.g., Li et al., 2017).
Also, the disk structure facilitates the creation of dust and its persistence
during extreme conditions of the super-soft X-ray phase (e.g., Skopal, 2019).

I thank my colleague Ján Budaj for having calculated for me the Ly$\alpha$
profiles discussed in Appendix F. This work was supported by a grant of the
Slovak Academy of Sciences, VEGA No. 2/0030/21, and by the Slovak Research and
Development Agency under contract No. APVV-20-0148. This research is based on
observations made with the International Ultraviolet Explorer, obtained from
the MAST data archive at the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5-26555. The data presented in this paper were
obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space
Telescope Science Institute. The specific observations analyzed can be
accessed via https://doi.org/10.17909/0mkj-f579 (catalog 10.17909/0mkj-f579).

##  Appendix A Indication of neutral hydrogen in the orbital plane of
eclipsing symbiotic stars during their active phases

Figure 3 of this appendix shows examples of SED models in the ultraviolet for
the investigated objects at different orbital phases (see Sect. 2.2).

Figure 3:  Examples of IUE spectra (in magenta) of our targets (Sect. 2.1)
during active phases observed at different orbital phases $\varphi$ and their
SED model (black line, Eq. (1)). The model consists of the nebular (green
lines) and the stellar continuum from the hot component (blue line; Sect.
2.2). A strong depression of the continuum around the Ly$\alpha$ line (gray
area) is caused by Rayleigh scattering of the WD radiation on hydrogen atoms
with column densities, $N_{\rm H}^{\rm obs}$ (Table 1). The bottom row shows
examples of AS 338 and AS 296, whose spectra are underexposed (see Appendix
C). Models for very different $N_{\rm H}^{\rm obs}$ estimated for AS 296 are
plotted with dotted lines. Additional depression of the continuum is caused by
the iron curtain absorptions (Sect. 2.2), here denoted by ‘i.c.’.

##  Appendix B Spectral energy distribution during quiescent and active phases
of our targets

Figure 4 of this appendix compares the profile of the ultraviolet continuum
for the investigated objects during the quiescent and active phases (Sect.
3.1).

Figure 4:  Comparison of SEDs for our targets during quiescent and active
phases. Meaning of lines (magenta, black, green, blue, and dotted) and
denotation by i.c. as in Appendix A. Panels for BF Cyg, CI Cyg, AX Per and YY
Her (a, b, c and e) are compiled according to Skopal (2005), and that for PU
Vul is adapted from Skopal (2014). In panel f we used photometry of Munari et
al. (1989, 1992, 1995). The dramatic change of the spectrum during the
transition from quiescent to active phase is caused by the creation of a disk-
like structure around the WD during outbursts, and subsequent formation of the
neutral wind region in the orbital plane (Sect. 3.2). Here, the former is
evidenced by the emergence of deep eclipses in the light curves (top panels),
while the latter is indicated by Rayleigh scattering on atomic hydrogen around
the Ly$\alpha$ line (gray area). Note that AR Pav was observed only during the
active phase, so its UV spectrum from quiescence is not available. Instead, we
show here an example of AS 296, although its far-UV spectrum is not well
determined (see Appendix C).

##  Appendix C Discussion of the selection of the final set of targets

In this appendix, we explain why some of the systems suggested in Sect. 2.1 as
candidates cannot be included in the resulting set of our targets. First, we
verify if non-eclipsing systems from the second group (i.e., showing the far-
UV continuum depression; Z And, TX CVn and CD-43∘14304) have also a high
orbital inclination. Second, we comment on some eclipsing systems from the
first set (i.e., showing the optical eclipses), whose far-UV spectra are
underexposed (BX Mon, AS 338, and AS 296), and disputed object CH Cyg. The
following comments are relevant:

Z And and TX CVn sporadically show eclipses in their optical light curves
during active phases, suggesting that their orbital inclination $i$ is quite
high (see Skopal et al., 2004). A high $i$ for both systems is also
constrained by the two-temperature type of their UV spectrum (see Figs. 3 and
6 of Skopal, 2005) – a typical spectral feature of symbiotic binaries with a
high $i$ that emerges during active phases (Sect. 1). In addition, an analysis
of the 2003 eclipse of Z And suggested $i>76^{\circ}$ (Skopal, 2003). On the
basis of polarimetric observations, Isogai et al. (2010) derived
$i=74^{\circ}\pm 14^{\circ}$, and analyzing the Rayleigh scattering effect
during quiescence, Skopal & Shagatova (2012) obtained
$i=59^{\circ}-2^{\circ}/+3^{\circ}$, which was later refined to
$63.6^{\circ}-12.2/+6.9^{\circ}$ by Shagatova (2017). A high value of $i$ for
Z And is independently supported by the obscuration of the O I] $\lambda$1641
Å emission line around the inferior conjunction of the giant (Shore &
Wahlgren, 2010; Skopal & Shagatova, 2012). As concerns to CD-43∘14304, there
are no relevant observations to estimate directly its $i$. Here, a relatively
high value of $i$ is suggested by the ionization structure during active
phases that is constrained for CD-43∘14304 by the two-temperature type of the
UV spectrum shown by its model SED (see Fig. 5 of Skopal, 2005). That these
three systems have a high $i$, but they are not strictly eclipsing, explains
why the corresponding $N_{\rm H}^{\rm obs}$ values are lower than those
measured for eclipsing systems (see Fig. 1), as expected according to the
ionization structure during active phases.

As concerns to BX Mon, its very faint far-UV continuum does not make it
possible to evaluate the effect of Rayleigh scattering. We excluded CH Cyg,
because its activity is accretion-powered, and thus does not show typical
features of Z And-type outbursts (e.g., Mikolajewska et al., 1988; Tarasova &
Skopal, 2021). In addition, its basic configuration (binary or triple system)
and orbital inclination are uncertain – possible eclipses observed during 1992
and 1994 (Skopal et al., 1996) never repeated again (see Hinkle et al., 2009,
for a review). That is probably why the Rayleigh scattering effect was
observed only during a short period (from $\sim$1993 to $\sim$1995), although
CH Cyg is active from $\sim$1977 (see its light curve777e.g.,
https://www.aavso.org/LCGv2/). Further, FN Sgr was observed in the UV only
during quiescence (e.g., Brandi et al., 2005).

Finally, spectra of AS 338 and AS 296 are strongly underexposed in the far-UV,
which precludes a correct determination of $N_{\rm H}^{\rm obs}$ by Rayleigh
scattering (see Fig. 3, bottom row panels). This is because the light from
both stars is strongly reddened with the color excess $E_{\rm B-V}$ = 0.5
(Esipov et al., 2000) and 1.0 (Munari et al., 1992) for AS 338 and AS 296,
respectively. Therefore, if we attribute the total attenuation of the far-UV
radiation to Rayleigh scattering, we obtain only the upper limits of $N_{\rm
H}^{\rm obs}$, or very uncertain values (see Fig. 1).

##  Appendix D Characteristic parameters of targets

In this appendix, we briefly summarize the basic characteristics of the
selected targets that are suitable for the aim of this paper – the eclipsing
symbiotic binaries with a well-exposed far-UV spectrum acquired during the
active phase (see Sect. 2.1).

Recent ephemerides of the eclipses and/or the inferior conjunction of the red
giant, distances, and the $E_{\rm B-V}$ interstellar reddening parameter of
the targets are found in Table 1, while Table 2 of this appendix lists the
physical parameters of their main radiation sources. In addition, Table 3
(Appendix E) presents these parameters for the hot component and the nebula,
we obtained by modeling their UV SEDs in this paper (Sect. 2.2), while Table 4
of Appendix E collects these parameters for the spectra from quiescent phases,
plotted in Figs. 2 and 4. Below we briefly describe their photometric
observations with regard to the appearance of eclipses in their light curves
during active phases.

BF Cyg: In $\sim$1894 BF Cyg experienced a nova-like explosion (Jacchia,
1941), after which its brightness was gradually declining for about 70 years,
occasionally showing brightenings lasting for several years (Z And-type of
outbursts), with maxima of around 1920, 1956, 1968-74, 1990, and 2006
(Leibowitz & Formiggini, 2006; Skopal et al., 1997; Munari et al., 2006;
Sekeráš et al., 2019). During the 1989-94 active phase, Skopal (1992) reported
for the first time the appearance of a primary minimum in the $UBV$ light
curves (eclipse), which was relatively narrow and rectangular in profile,
located around the position of the inferior conjunction of the giant. Later,
the eclipsing nature of BF Cyg was also confirmed by observing the effect of
Rayleigh scattering near the eclipse during the quiescent phase (Pereira &
Landaberry, 1996). The following development of the wave-like orbital-related
variation during 1995 – 2005 reflects a quiescent phase of BF Cyg (see Fig. 4a
of Appendix B here).

CI Cyg: The eclipsing nature of CI Cyg is best documented by its major active
phase that began in 1975 (Belyakina, 1976), when narrow minima, eclipses,
developed in the light curve during the first four 855.25-d cycles from the
maximum, with the subsequent change to a broad wave-like variation since
$\sim$1984 (see Fig. 2 of Belyakina & Prokofeva, 1991, and Fig. 4b of Appendix
B here). This is a textbook example of the typical photometric features of the
active and quiescent phases of SySts reflecting the very different ionization
structure of the hot component (see Sects. 1 and 4.2; Figs. 2c and 2f for a
summary).

YY Her: Munari et al. (1997b) identified four Z And-type outbursts with
additional six brightenings in the historical (1890–1996) light curve of YY
Her. The authors also found four deep and sharp minima in the light curve,
located near the zero orbital phase (i.e., at the light minima in their
quiescent light curve). However, they rejected their eclipsing nature because
they did not find any reason for this interpretation compared to the eclipses
observed in SySts. On the other hand, they found no other reasonable
explanation for these minima. During the 1993-98 main active phase, the visual
light curve of YY Her showed a relatively narrow V-shaped minimum in 1994.43,
around the zero orbital phase, suggesting a high orbital inclination, but less
than 90∘ (see e.g., Fig. 16 of Skopal, 2005). The eclipsing nature of YY Her
was confirmed by measuring the eclipse effect in the $U$-light curve during
1997 (Tatarnikova et al., 2000). The transition to the quiescent phase was
similar to that observed for AX Per or CI Cyg (see Fig. 1 of Tatarnikova et
al., 2001). After entering the quiescent phase, only a few brighter periods
have been recorded (Munari et al., 2013, 2021).

AR Pav: The eclipsing nature of AR Pav was already revealed by the first
photographic observations made between 1889 and 1936.5 by Mayall & Shapley
(1937), who classified it as an unusual eclipsing P Cyg type binary with an
orbital period of 605 days. Later, optical spectroscopy showed that AR Pav is
a symbiotic binary (see Kenyon, 1986, and references therein). Observing
changes in the eclipse profile and systematic changes in their timing from
cycle to cycle, a strong out-of-eclipse variability (e.g., Andrews, 1974;
Bruch et al., 1994; Skopal et al., 2000; Sekeráš et al., 2019), and also the
spectroscopic variability in the UV/optical domain (e.g., Schild et al., 2001;
Quiroga et al., 2002) reflect continuous activity of AR Pav. The persistent
presence of narrow deep minima – eclipses – in the light curve and current
activity indicate that AR Pav is in a long-lasting active phase.

AX Per: The historical light curve of AX Per (since 1887) is characterized by
long quiescent phases, occasionally interrupted by Z And-type outbursts of
typically several years, usually showing more than one brightening (see e.g.,
Figs. 1 in Skopal et al., 2011; Leibowitz & Formiggini, 2013). The eclipsing
nature of AX Per was unambiguously revealed during the 1988-1994 active phase
by the appearance of narrow minima around the inferior conjunction of the
giant (Skopal & Komárek, 1990; Skopal, 1991). Figure 4c of Appendix B shows
this part of the light curve together with the following development of the
quiescent phase since $\sim$1995\. The nature of low stages between outbursts
as the quiescent phase of symbiotic star was proven by Kenyon (1982), who
revealed the wave-like variation in the light curve between the $\sim$1950 and
$\sim$1978 outbursts with a period of 681.6 days, which he ascribed to the
orbital period.

PU Vul is a symbiotic nova, discovered during its outburst in 1979 by Kozai et
al. (1979) and Argyle et al. (1979). From $\sim$1977 to $\sim$1979, PU Vul
brightened by $\sim$5 magnitudes in the $m_{\rm pg}/B$ band. Subsequently,
from 1980.1 to 1981.4 the light curve of the nova showed a narrow (relative to
the orbital period; see below) $\sim$5 mag deep minimum, after which continued
at a bright stage (a supergiant phase) up to $\sim$1987.5 when PU Vul began a
gradual fading till $\sim$1999 (the nebular phase). Meanwhile, the light curve
showed another relatively narrow but only $\sim$0.5 mag deep minimum around
1994.25 (see Fig. 1 of Tatarnikova et al., 2018, and references therein).
Vogel & Nussbaumer (1992) interpreted the first deep minimum as an eclipse of
the outbursting star by the M giant companion. The appearance of the second
1994 eclipse allowed Nussbaumer & Vogel (1996) to estimate the orbital period
of the binary to be 4900$\pm$100 days, later refined by Shugarov et al. (2012)
to 4897$\pm$10 days using three primary minima. Since $\sim$2000, the
development of a broad wave in the light curve with minima around the inferior
conjunction of the giant (Tatarnikova et al., 2018)888See also the current
AAVSO light curve: https://www.aavso.org/LCGv2/. indicates that PU Vul is
currently in the quiescent phase.

Table 2: Characteristic parameters of the radiation sources of our targets.
Red Giant: Spectral type $ST$, radius $R_{\rm RG}$ ($R_{\odot}$), luminosity
$L_{\rm RG}$ ($L_{\odot}$). Hot component: Effective radius $R_{\rm WD}^{\rm
eff}$ ($R_{\odot}$), temperature $T_{\rm BB}$(104 K), luminosity $L_{\rm WD}$
($L_{\odot}$), during quiescent (Q) and active (A) phases. Nebula: Emission
measure $EM$ ($10^{60}\,{\rm cm^{-3}}$).

| Red Giant | Hot Component | Nebulac |
---|---|---|---|---
| ————————— | —————————————————- |  |
Object | $ST$ | $R_{\rm RG}$ | $L_{\rm RG}$ | $R_{\rm WD}^{\rm eff}$ | $T_{\rm BB}$ | $L_{\rm WD}$ | $EM$ | Reference†
|  |  |  | Q/A | Q/A | Q/A | Q/A |
BF Cyg | M 5 | 150 | 2700 | 0.79/7.1 | 5.5/2.15 | 5200/16800a | 3.1/12 | 1, 2, 3, 11
CI Cyg | M 5.5 | 180 | 3400 | 0.11/0.67 | 11.5/2.8 | 1700/1540a | 0.48/1.1 | 2, 3, 4
YY Her | M 4 | 110 | 1600 |  $<$0.14/0.89 |  $>$10.5/2.2 |  $>$2100/3800a | 1.1/0.7-1.3 | 2, 3e
AR Pav | M 5 | 139 | 2300 | –/1.9 | –/2.2 | –/6400a | –/4.6 | 2, 3, 5, 12
AX Per | M 4.5 | 102 | 1200 | 0.07/0.42 |  $\sim$10/0.6 | 400-900/$\sim$1200a | 0.25/0.30-0.71 | 2, 3
— | M 5.6 | 115 | 1500 | –/6.2-11 | –/0.53-0.63 | –/600-1400a | –/0.35-0.82d | 6
PU Vul | M 6-7 | 282 | 3820 |  $\approx$0.03/8.2b |  $\approx$20/2b |  $\approx$1000/9700b | –/11b | 7, 8, 9, 10

Notes:
a the luminosity of the $10^{5}$ K hot ionising source that generates the
observed $EM$ during active phases (Skopal et al., 2017),
b as on October 3, 1988 (see Table 3),
c symbiotic nebulae radiate at characteristic electron temperature $T_{\rm e}$
= 13 000 – 19 000 K during quiescent phases (Muerset et al., 1991; Skopal,
2005), while during active phases, an additional high-temperature nebula with
$T_{\rm e}\gtrsim$30 000 K is indicated (see Figs. 3, 5, 8, 10, 16, 19 and 21
of Skopal, 2005, and Table 3 in Appendix E here),
d the out-of-eclipse values,
e as on December 5, 1981, for the active phase,
† References: 1 - Muerset et al. (1991), 2 - Mürset & Schmid (1999), 3 -
Skopal (2005), 4 - Skopal et al. (2012), 5 - Schild et al. (2001), 6 - Skopal
et al. (2011), 7 - Kato et al. (2012), 8 - Shugarov et al. (2012), 9 - Chochol
et al. (1998), 10 - Cúneo et al. (2018), 11 - Mikolajewska et al. (1989), 12 -
Quiroga et al. (2002).

##  Appendix E Physical parameters of the ultraviolet continuum

Table 3 of this appendix presents other physical parameters of our targets
given by the variables of Eq. (1) that determines the continuum models for
active phases, while Table 4 lists these parameters for the spectra from
quiescent phases that are used in Figs. 2 and 4. The modeling is introduced in
Sect. 2.2.

Table 3: Parameters from model SEDs during active phases (Table 1): $R_{\rm WD}^{\rm eff}$, $T_{\rm BB}$, $T_{\rm e}$, $EM$ for the given date of observation, and a minimum of the $\chi^{2}_{\rm red}$ function.  Object | Date | $R_{\rm WD}^{\rm eff}$ | $T_{\rm BB}$ | $T_{\rm e}$ | $EM$ |  $\chi^{2}_{\rm red}$ / d.o.f.
---|---|---|---|---|---|---
| yyyy-mm-dd | ($R_{\odot}$) | (K) | (K) | (1060 cm-3) |
BF Cyg | 1987-08-11 | 1.7$\pm 0.2$ | 25000$\pm 2000$ | 30000$\pm 5000$ | 3.0$\pm 0.5$ | $\dagger$
| 1987-11-16 | 2.0$\pm 0.2$ | 25000$\pm 2000$ | 20000$\pm 3000$ | 3.4$\pm 0.5$ | $\dagger$
| 1988-03-19 | 1.1$\pm 0.1$ | 45000$\pm 5000$ | 18000$\pm 2000$ | 2.6$\pm 0.3$ | 1.4 / 21
| 1990-06-30 | 6.3$\pm 0.8$ | 21500$\pm 2000$ | 42000${}^{b}\pm 5000$ | 6.9$\pm 0.7$ | $\dagger$
| 1990-07-06 | 6.5$\pm 0.6$ | 21000$\pm 2000$ | 30000${}^{b}\pm 5000$ | 8.4$\pm 0.8$ | $\dagger$
| 1990-11-05 | 5.8$\pm 0.5$ | 25000$\pm 2000$ | 42000${}^{b}\pm 5000$ | 11$\pm 1$ | $\dagger$
CI Cyg | 1979-01-05 | 0.50$\pm 0.05$ | 28000$\pm 2000$ | 20000a | 0.64$\pm 0.07$ | $\dagger$
| 1979-06-11 | 0.60$\pm 0.1$ | 25000$\pm 4000$ |  $\sim$15000 |  $\sim$0.37 | $\star$
| 1979-06-29 |  $\sim$0.54 |  $\sim$25000 |  $\sim$15000 |  $\sim$0.40 | $\star$
| 1980-01-30 | 0.52$\pm 0.07$ | 25000$\pm 2000$ | 20000$\pm 2000$ | 0.43$\pm 0.06$ | $\dagger$
| 1980-04-14 |  $\sim$0.44 |  $\sim$25000 |  $\sim$40000b |  $>$0.26 | $\times$
| 1980-08-01 | 0.44$\pm 0.07$ | 25000$\pm 3000$ | 20000$\pm 3000$ | 0.37$\pm 0.06$ | $\dagger$
| 1980-08-18 | 0.49$\pm 0.08$ | 25000$\pm 3000$ | 20000$\pm 3000$ | 0.40$\pm 0.07$ | $\dagger$
| 1980-08-28 | 0.46$\pm 0.05$ | 28000$\pm 2000$ | 15000a/40000b | 0.61$\pm 0.05$ | $\dagger$
| 1980-11-14 | 0.38$\pm 0.05$ | 28000$\pm 3000$ | 25000$\pm 3000$ | 0.52$\pm 0.07$ | $\dagger$
| 1981-01-08 | 0.34$\pm 0.04$ | 28000$\pm 2000$ | 25000$\pm 3000$ | 0.46$\pm 0.05$ | $\dagger$
| 1981-08-14 |  $\sim$0.36 |  $\sim$28000 |  $\sim$25000 |  $\sim$0.46 | $\star$
| 1981-12-11 | 0.51$\pm 0.05$ | 25000$\pm 2000$ | 20000$\pm 2000$ | 0.25$\pm 0.04$ | $\dagger$
YY Her | 1981-12-04 | 1.1$\pm 0.2$ | 22000$\pm 2000$ | 15000$\pm 2000$ | 0.66$\pm 0.2$ | 1.8 / 17
AR Pav | 1980-10-30 | 2.7$\pm 0.3$ | 16000$\pm 1500$ | 14000a/40000b | 3.2$\pm 0.4$ | 1.4 / 14
| 1980-11-01 | 2.7$\pm 0.3$ | 16000$\pm 1500$ | 15500a/40000b | 3.3$\pm 0.4$ | 1.4 / 15
| 1980-11-02 | 3.1$\pm 0.3$ | 16000$\pm 1500$ | 15500a/40000b | 3.3$\pm 0.4$ | 1.5 / 17
| 1980-11-03 | 3.0$\pm 0.3$ | 16000$\pm 1500$ | 15500a/40000b | 4.0$\pm 0.5$ | 1.4 / 17
| 1982-07-01 | 3.5$\pm 0.4$ | 16000$\pm 1500$ | 17000a/40000b | 4.0$\pm 0.5$ | 1.8 / 17
| 1984-03-07 | 4.4$\pm 0.5$ | 16000$\pm 1500$ | 17000$\pm 2000$/40000b | 3.7$\pm 0.5$ | 1.6 / 12
| 1992-07-08 | 3.9$\pm 0.5$ | 16000$\pm 1500$ | 17000a/40000b | 2.6$\pm 0.3$ | 1.2 / 11
| 1984-04-10 | 5.5$\pm 0.5$ | 15500$\pm 1500$ | 13500a/40000b | 4.3$\pm 0.5$ | 1.8 / 13
| 1979-07-17 | 3.5$\pm 0.5$ | 19000$\pm 2000$ | 15800a/40000b | 3.9$\pm 0.4$ | $\dagger$
| 1981-05-10 | 2.6$\pm 0.3$ | 20000$\pm 2000$ | 15500$\pm 2000$/40000b | 4.0$\pm 0.5$ | 0.90 / 18
| 1978-05-16 |  $\sim$3.6 |  $\sim$17000 | – | – | $\times$
| 1978-08-08 | 2.9$\pm 0.5$ | 17500$\pm 2000$ | 15500a/40000b | 3.5$\pm 0.7$ | 2.0 / 15
| 1978-11-11 | 3.8$\pm 0.5$ | 16000$\pm 2000$ | 14000a/40000b | 3.3$\pm 0.4$ | $\dagger$
| 1980-07-30 | 4.6$\pm 0.7$ | 16000$\pm 2000$ | 15000a/40000b | 5.3$\pm 0.6$ | $\dagger$
| 1982-04-07 | 3.2$\pm 0.4$ | 16000$\pm 2000$ | 40000b |  $\sim$3.2 | 0.39 / 127
AX Per | 1978-12-31 | 0.90$\pm 0.2$ | 20000$\pm 2000$ | 15000$\pm 2000$ | 0.41$\pm 0.06$ | $\dagger$
| 1979-01-05 | 0.90$\pm 0.1$ | 20000$\pm 1000$ | 15000$\pm 2000$ | 0.40$\pm 0.05$ | 0.80 / 18
PU Vul | 1988-06-29 | 6.0$\pm 0.7$ | 23000$\pm 2000$ | 15000$\pm 2000$ | 12$\pm 2$ | 2.4 / 18
| 1988-07-16 | 9.8$\pm 1.1$ | 19000$\pm 1500$ | 14000$\pm 2000$ | 1.3$\pm 0.3$ | 1.5 / 21
| 1988-10-03 | 8.2$\pm 1.0$ | 20000$\pm 2000$ | 20500$\pm 3000$ | 11$\pm 2$ | 3.9 / 212
| 1989-04-08 | 7.2$\pm 0.8$ | 22000$\pm 2000$ | 20000b | 5.3$\pm 1$ | 2.4 / 16
| 1989-05-19 | 5.5$\pm 0.6$ | 24000$\pm 2000$ | 31000$\pm 3000$ | 9.9$\pm 2$ | 1.5 / 15
| 1989-09-25 | 4.2$\pm 0.5$ | 27000$\pm 3000$ | 24000$\pm 3000$ | 5.4$\pm 0.7$ | 0.88 / 15
Table 3: continued

AS 338 | 1989-10-09 |  $\approx$2.9 |  $\approx$15000 |  $\approx$15000 |  $\approx$0.4 | $\star$
---|---|---|---|---|---|---
AS 296 | 1988-08-13 |  $\approx$8.7 |  $\approx$13000 |  $\approx$10000 |  $\approx$0.1 | $\star$
| 1988-11-11 |  $\approx$4.9 |  $\approx$15000 |  $\approx$15000 |  $\approx$0.1 | $\star$
| 1990-03-13 |  $\approx$4.7 |  $\approx$16000 |  $\approx$20000 |  $\approx$0.1 | $\star$

Notes:
a – fixed value,
b – high-temperature nebula ($T_{\rm e}$ fixed) filling in the residual light
around Ly$\alpha$,
$\dagger$ – from a comparison with a set of synthetic models (Sect. 2.2),
$\star$ – underexposed spectrum,
$\times$ – only SWP spectrum available

Table 4: As in Table 3, but for the spectra from quiescent phases that are
plotted in Figs. 2 and 4.

Object | Spectrum | Date | Julian Date | $R_{\rm WD}^{\rm eff}$ | $T_{\rm BB}$ | $T_{\rm e}$ | $EM$ | Note
---|---|---|---|---|---|---|---|---
|  | yyyy-mm-dd | JD 2 44… | ($R_{\odot}$) | (K) | (K) | (1060 cm-3) |
BF Cyg | SWP13477+LWR10132 | 1981-03-13 | 44676.84a | 0.37 | 100000b |  $\sim$5000 |  $\sim$0.22 | $\dagger$
| SWP28734+LWP08681 | 1986-07-22 | 46633.58 | 0.48 | 100000b |  $\sim$22000 |  $\sim$3.3 | $\dagger$
| SWP58385+LWP32695 | 1996-09-26 | 50352.80 | 0.44 | 95000 | 22800 | 2.5 | Sk05c
CI Cyg | SWP36321+LWP15571 | 1989-05-22 | 47669.04 | 0.088 | 115000 | 24000 | 0.31 | Sk05
YY Her | SWP09773+LWR08493 | 1980-08-12 | 44464.18 |  $<$0.14 |  $>$105000 | 21500 | 1.1 | Sk05
AX Per | SWP24278+LWP04619 | 1984-10-23 | 45997.21 |  $<$0.10 |  $>$66000 | 25000 | 0.25 | Sk05
PU Vul | SWP45415+LWP23757 | 1992-08-23 | 48858.25 |  $<$0.64 |  $>$79000 |  $\sim$25000 |  $\sim$9.6 | Sk14
AS 296 | SWP16380+LWR12630 | 1982-02-19 | 45020.11 | 0.22 | 100000b |  $\sim$20000 |  $\sim$0.72 |  $\dagger$/$\star$

Notes:
a – orbital phase $\sim$0.1; $N_{\rm H}^{\rm obs}\sim 2\times 10^{23}$ cm-2,
b – fixed value,
c – for the distance $d=3.4$ kpc (Table 1),
$\dagger$ – from a comparison with a set of synthetic models (Sect. 2.2),
Sk05 – according to Skopal (2005),
Sk14 – according to Skopal (2014),
$\star$ – underexposed spectrum

##  Appendix F Ly$\alpha$ line profiles from spherically symmetric expanding
shell

In this appendix, we test whether the Ly$\alpha$ absorption line profile that
can be formed in the expanding wind from the WD during the active phases could
be as broad as the attenuation due to Rayleigh scattering on H0 atoms in the
wind from the red giant.

For this purpose, we used the code SHELLSPEC Budaj & Richards (2004) that
solves a simple radiative transfer along the line of sight in the moving
circumstellar medium (CM) assuming local thermodynamic equilibrium (LTE) and
single scattering approximations. The LTE model determines the basic CM
structure, temperature, mass density, and electron density as functions of
depth.

Here, the CM has the form of spherically symmetric wind from the WD, whose
optically thick/thin interface represents the WD’s pseudophotosphere
(originally suggested for classical novae outbursts by Kato & Hachisu, 1994).
Synthetic Ly$\alpha$ line profiles are calculated using an object SHELL in the
SHELLSPEC code. The radius of the inner, $R_{\rm in}$, and outer, $R_{\rm
out}$, sphere is set to 1 and 5 $R_{\odot}$, respectively. We assume that the
line profile is formed in the wind from the WD that conforms to wind
properties derived from observations during active phases: The mass-loss rate,
$\dot{M}$ of a few times $10^{-6}$ $M_{\odot}\,{\rm yr}^{-1}$ (e.g., Skopal,
2006), and the pseudophotosphere expansion velocity of $\approx 200$ km s-1
(e.g., McKeever et al., 2011) are considered. The latter is given by radial
velocities of absorption components in P Cygni profiles of hydrogen Balmer
lines measured mainly at the beginning of outbursts. For simplicity, its value
was assumed to be constant, and for turbulent motions, we adopted a constant
velocity of 10 km s-1.

Next, we choose the initial temperature and density at the inner radius of the
shell, $T_{\rm in}$ and $\rho_{\rm in}$, deep inside the pseudophotosphere
(i.e., where the optical depth in the continuum is $\gg$1), and find what
temperature $T_{1}$ and density $\rho_{1}$ correspond to the wind medium with
an optical thickness of 1, assuming it to represent the WD’s
pseudophotosphere. Its radius, $R_{1}$ is given by the mass continuity
equation that determines the densities of the expanding wind. The input
parameters, $T_{\rm in}$ and $\rho_{\rm in}$ were chosen so that the resulting
parameters, $T_{1}$, $\rho_{1}$, $\dot{M}$, and $R_{1}$, were comparable to
those determined from observations (Tables 3 and 5).

As the emitted flux at the radial distance, $r$ from the WD could basically
satisfy the proportionality, $\sigma T^{4}\propto r^{-2}$, we first provided
calculations using the temperature gradient, $T(r)/T_{\rm in}=(r/R_{\rm
in})^{-1/2}$. For suitable parameters, $T_{\rm in}=30000-40000$ K and
$\rho_{\rm in}$ = a few times $10^{-10}-10^{-9}$ g cm-3, all the corresponding
profiles have a dominant emission component (see Fig. 5 a, green profiles),
$R_{1}$ is of a few solar radii, $T_{1}$ between 14000 and 24000 K, and
$\dot{M}$ of a few times $10^{-6}-10^{-5}$ $M_{\odot}\,{\rm yr}^{-1}$ (Table
5).

In order to obtain the absorption component in the Ly$\alpha$ profile, we
assumed a steeper temperature gradient, $T(r)/T_{\rm in}=(r/R_{\rm in})^{-1}$.
The corresponding profiles, calculated for reasonable initial values of
$T_{\rm in}$ and $\rho_{\rm in}$, are shown in Fig. 5, where they are compared
with the attenuation of the UV continuum around the Ly$\alpha$ line due to
Rayleigh scattering on $5\times 10^{22}$ and $1\times 10^{23}$ hydrogen atoms
per cm2. Despite the fact that we chose rather lower values of $N_{\rm H}$
(see Fig. 1), the attenuation effect by Rayleigh scattering is clearly
dominant. The specific very broad wings from Rayleigh scattering are
significantly broader than the ‘atmospheric’ profile of the Ly$\alpha$
line999Note that the gas pressure at the expanding pseudophotosphere is zero,
so the broadening of spectral lines by the Stark effect does not apply..

Finally, it is important to note that if the width of the ‘atmospheric’
Ly$\alpha$ absorption profile was dominant, it would not be possible to
measure the orbital phase dependence of $N_{\rm H}^{\rm obs}$. Instead, the
$N_{\rm H}^{\rm obs}$ values would be scattered along the orbital phase, as
they would be dependent on the properties of the WD’s pseudophotosphere, i.e.,
on the object and its current activity. This is not observed. In our case, the
optically thick pseudophotosphere plays only the role of blocking ionization
photons from the central WD, which has nothing to do with its properties.

Table 5: Input parameters, $T_{\rm in}$, $\rho_{\rm in}$, and resulting
parameters, $T_{1}$, $\rho_{1}$, $\dot{M}$, $R_{1}$, for modeling the
Ly$\alpha$ profile formed in the wind from the WD above its pseudophotosphere
using the code SHELLSPEC. Parameters and modeling are described in Appendix F.
Corresponding profiles are shown in Fig. 5.

Model | $T_{\rm in}$ | $\rho_{\rm in}$ | $T_{1}$ | $\rho_{1}$ | $\dot{M}$ | $R_{1}$
---|---|---|---|---|---|---
No. | (K) | (${\rm g\,cm^{-3}}$) | (K) | (${\rm g\,cm^{-3}}$) | ($M_{\odot}\,{\rm yr}^{-1}$) | ($R_{\odot}$)
1a | 30000 | $1\times 10^{-10}$ | 24000 | $4.4\times 10^{-11}$ | $1.9\times 10^{-6}$ | 1.5
2a | 30000 | $4\times 10^{-10}$ | 17000 | $3.9\times 10^{-11}$ | $7.7\times 10^{-6}$ | 3.2
3a | 30000 | $2\times 10^{-9}$ | 14000 | $9.5\times 10^{-11}$ | $3.9\times 10^{-5}$ | 4.6
4b | 40000 | $9\times 10^{-11}$ | 25000 | $3.5\times 10^{-11}$ | $1.7\times 10^{-6}$ | 1.6
5b | 40000 | $1\times 10^{-10}$ | 21000 | $2.8\times 10^{-11}$ | $1.9\times 10^{-6}$ | 1.9
6b | 40000 | $1.5\times 10^{-10}$ | 13000 | $1.7\times 10^{-11}$ | $2.9\times 10^{-6}$ | 3.0
7b | 50000 | $1\times 10^{-10}$ | 33000 | $4.4\times 10^{-11}$ | $1.9\times 10^{-6}$ | 1.5
8b | 50000 | $2\times 10^{-10}$ | 21000 | $3.5\times 10^{-11}$ | $3.9\times 10^{-6}$ | 2.4
9b | 50000 | $3\times 10^{-10}$ | 17000 | $3.6\times 10^{-11}$ | $5.8\times 10^{-6}$ | 2.9
10b | 60000 | $2\times 10^{-10}$ | 26000 | $3.8\times 10^{-11}$ | $3.9\times 10^{-6}$ | 2.3
11b | 60000 | $4\times 10^{-10}$ | 19000 | $3.9\times 10^{-11}$ | $7.7\times 10^{-6}$ | 3.2
12b | 60000 | $8\times 10^{-10}$ | 15000 | $5.0\times 10^{-11}$ | $1.5\times 10^{-5}$ | 4.0

Notes:
a – models for temperature gradient, $T(r)/T_{\rm in}=(r/R_{\rm in})^{-1/2}$,
b – $T(r)/T_{\rm in}=(r/R_{\rm in})^{-1}$.

Figure 5:  Comparison of the UV continuum attenuation due to Rayleigh
scattering on H0 atoms for two values of $N_{\rm H}$ (grey area) with the
Ly$\alpha$ line profile that may form in the expanding wind from the WD. The
modeling of the Ly$\alpha$ line is described in Appendix F. The model
parameters are summarized in Table 5. The dotted line represents the
unattenuated continuum of the pseudophotosphere with a temperature $T_{\rm
BB}=22000$ K.

##  Appendix G On the effect of interstellar extinction on modeling the UV
continuum

The strong attenuation of radiation by interstellar dust particles around the
wavelength of 2175 Å is often used to determining the characteristic
interstellar absorption from the UV spectrum. Since the profile of the true
continuum can be determined with an accuracy of about 10%, this uncertainty
also limits the value of the color excess so that the corrected profile of the
continuum around 2175 Å does not show a local extreme.

Figure 6 shows what the effect of interstellar reddening looks like in the
range of IUE spectra. It plots the Planck function for $T_{\rm BB}=22000$ K,
attenuated by Rayleigh scattering on $5\times 10^{22}$ (panel a) and $1\times
10^{24}$ (b) hydrogen atoms, both dereddened with $E_{\rm B-V}\pm 0.05$ mag,
where $E_{\rm B-V}$ is the correct value of the color excess. The value of
$N_{\rm H}^{\rm obs}$ is given by the width of the absorption core and the
extension of its wings due to Rayleigh scattering (Sect. 2.2). Since the
extinction curve is wavelength-dependent, increasing toward shorter
wavelengths, one can expect that $N_{\rm H}^{\rm obs}$ values determined from
the (broad) continuum depression around the Ly$\alpha$ line can be affected
also by the uncertainty in $E_{\rm B-V}$. Moreover, the determination of lower
values of $N_{\rm H}^{\rm obs}$ that attenuate a narrower range of the
spectrum will be probably less affected by a change in color excess than high
$N_{\rm H}^{\rm obs}$ values that attenuate a wider range of the spectrum.

Therefore, in order to test how the uncertainties of the color excess affect
the determination of $N_{\rm H}^{\rm obs}$, we selected one spectrum with a
narrow absorption and another one with very broad absorption, which are
typical for the superior and inferior conjunction of the red giant,
respectively. Specifically, we modeled the spectrum of PU Vul exposed on
October 3, 1988 ($\varphi=0.59$, $N_{\rm H}^{\rm obs}=3.9\times 10^{22}$ cm-2)
and the spectrum of AR Pav taken on April 7, 1982 ($\varphi=0.92$, $N_{\rm
H}^{\rm obs}=1.0\times 10^{24}$ cm-2) dereddened with different values of
$E_{\rm B-V}$. For PU Vul we used $E_{\rm B-V}=0.30\pm 0.04$, although Kato et
al. (2012) give an uncertainty of only $\pm$0.02, and for AR Pav we adopted
$E_{\rm B-V}=0.26\pm 0.03$ according to models of Kenyon & Webbink (1984). The
corresponding SED models are shown in Fig. 7, and their parameters are
introduced in Table 6.

In the case of PU Vul (a narrower absorption), $N_{\rm H}^{\rm obs}$ decreases
with increasing $E_{\rm B-V}$ for acceptable $\chi^{2}_{\rm red}$ (Table 6).
This is because dereddening the spectrum with a larger value of $E_{\rm B-V}$
will increase the height of the absorption core relative to its long-
wavelength wing, leading to a narrowing of the absorption core and thus a
decrease of the corresponding $N_{\rm H}^{\rm obs}$. According to our models
of PU Vul, $E_{\rm B-V}$ uncertainties of $\sim$13% correspond to errors in
$N_{\rm H}^{\rm obs}$ of less than 10% (see Table 6).

In the case of AR Pav, the SED modeling revealed the opposite behavior. This
is due to the fact that a strong component of the hot nebular continuum
contributes to the far-UV, which shifts the absorption core well above the
zero value (see Fig. 7, right). As a result, dereddening the spectrum with a
higher value of $E_{\rm B-V}$ will increase the level of the far-UV spectrum
more than its mid-UV part, which leads to relative smoothing of the absorption
core that corresponds to a higher value of $N_{\rm H}^{\rm obs}$. Here, the
uncertainties in $E_{\rm B-V}$ of $\pm$0.03 mag ($\sim$12%) cause errors in
$N_{\rm H}^{\rm obs}$ of 10 – 20%. However, the uncertainly of 20%,
corresponding to the model for $E_{\rm B-V}=0.029$, is overestimated because
of the worse model – the flux-points near $\lambda$2175 Å are above the model
which increases the value of $\chi^{2}_{\rm red}$ (see Fig. 7 and Table 6).
Finally, we also tested a model with $E_{\rm B-V}=0.35$ that can be found in
the literature (i.e., the uncertainty of $\sim$35%). However, the points near
$\lambda$2175 Å were $\sim$25% above the model, and $\chi^{2}_{\rm red}$
increased by a factor of $\sim$2 (Table 6).

According to these examples, we assume that interstellar reddening
uncertainties may cause additional errors in the $N_{\rm H}^{\rm obs}$
determination of about 10%.

Figure 6:  Effect of interstellar extinction in the range of IUE spectra shown
for the Planck function ($T_{\rm BB}=22000$ K) attenuated with $N_{\rm H}^{\rm
obs}=5\times 10^{22}$ (a) and $1\times 10^{24}$ cm-2 (b), and dereddened with
$E_{\rm B-V}\pm 0.05$ mag (see text). Meaning of lines and the gray area as in
Fig. 3.

Figure 7:  A possible effect of interstellar extinction on the determination
of $N_{\rm H}^{\rm obs}$ illustrated for PU Vul (left) and AR Pav (right). The
former and the latter represent the cases with relatively small and high
values of $N_{\rm H}^{\rm obs}$ measured around the superior and the inferior
conjunction of the red giant, respectively. The crosses represent the flux
points that we modeled. The large spread of selected points near to
$\lambda$2175 Å for PU Vul is responsible for the high $\chi^{2}_{\rm red}$
value, while the small spread of these points for AR Pav (circled)
demonstrates the sensitivity of the spectrum in this region to interstellar
extinction. Meaning of lines and the gray area as in Fig. 3. Corresponding
parameters are summarized in Table 6.  Table 6: The best-fit parameters
corresponding to SED models of PU Vul and AR Pav plotted in Fig. 7. Models are
calculated for different values of the color excess $E_{\rm B-V}$. Denotation
and meaning as in Tables 1 and 3.

Object | $E_{\rm B-V}$ | $N_{\rm H}^{\rm obs}$ | $R_{\rm WD}^{\rm eff}$ | $T_{\rm BB}$ | $T_{\rm e}$ | $EM$ |  $\chi^{2}_{\rm red}$ / d.o.f.
---|---|---|---|---|---|---|---
| (mag) | (cm-2) | ($R_{\odot}$) | (K) | (K) | (1060 cm-3) |
PU Vul | 0.26 | $4.2\times 10^{22}$ | 7.5 | 19500 | 19000 | 9.3 | 4.4 / 212
| 0.28 | $4.0\times 10^{22}$ | 8.1 | 19500 | 20000 | 9.7 | 4.1 / 212
| 0.30 | $3.9\times 10^{22}$ | 8.2 | 20000 | 20000 | 11 | 3.9 / 212
| 0.32 | $3.8\times 10^{22}$ | 9.0 | 20000 | 22000 | 11 | 3.8 / 212
| 0.34 | $3.5\times 10^{22}$ | 9.8 | 20000 | 22000 | 12 | 3.8 / 212
AR Pav | 0.23 | $0.9\times 10^{24}$ | 3.5 | 15000 | 40000a | 2.4 | 0.40 / 127
| 0.26 | $1.0\times 10^{24}$ | 3.2 | 16000 | 40000a | 3.2 | 0.39 / 127
| 0.29 | $1.2\times 10^{24}$ | 2.8 | 17500 | 40000a | 4.2 | 0.46 / 127
| 0.35 | $1.2\times 10^{24}$ | 2.7 | 19000 | 40000a | 7.0 | 0.99 / 127

Notes:
a – fixed value

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