# A search for period changes of eight short-period Type II Cepheids

Alemiye M. Yacob,1,2,3 Leonid N. Berdnikov,4 Elena N. Pastukhova,5 Alexei Y.
Kniazev,3,4,6Patricia A. Whitelock 3,7
1 Astronomy and Astrophysics Department, Entoto Observatory and Research
Center (EORC),
Space Science and Geospatial Institute (SSGI), P.O. Box 33679, Addis Ababa,
Ethiopia
2 Addis Ababa University (AAU), P.O.Box 1176, Addis Ababa, Ethiopia
3 South African Astronomical Observatory (SAAO), P.O. Box 9, 7935 Observatory,
Cape Town, South Africa
4 Sternberg Astronomical Institute (SAI) of the Moscow State University,
Universitetskii pr. 13, 119992 Moscow, Russia
5Institute of Astronomy, Russian Academy of Sciences, Pyatnitskayaul. 48,
119017 Moscow, Russia
6Southern African Large Telescope (SALT) Foundation, P.O. Box 9, 7935
Observatory, Cape Town, South Africa
7 Department of Astronomy, University of Cape Town, 7701 Rondebosch, South
Africa E-mail<EMAIL_ADDRESS>(AMY)Research visitor @ SAAO, SA

(Accepted 2022 July 28. Received 2022 July 28; in original form 2022 June 28)

###### Abstract

In this study, we investigate the period changes of eight short-period Type II
Cepheids of the BL Her subtype, i.e., with periods in the 1-4 day range. The
$O-C$ diagrams for these stars are constructed using all suitable
observational data from ground and space surveys. This spans a time interval
of over one century and includes digitized photographic plates as well as
photometry from the literature. The $O-C$ diagrams show parabolic evolutionary
trends, which indicate the presence of both increasing and decreasing periods
for these eight short period stars. These period changes are in good agreement
with the recent theoretical evolutionary framework and stellar evolution
models for BL Her stars. The pulsation stability test proposed by Lombard and
Koen also suggests that the changes in the periods are real.

###### keywords:

stars: variables: Cepheids – stars: Population II – stars: evolution – stars:
low-mass– methods: data analysis

††pubyear: 2022††pagerange: A search for period changes of eight short-period
Type II Cepheids–7

##  1 Introduction

Type II Cepheids (T2Cs) are old, low-mass and radially pulsating variable
stars with luminosities below the classical Cepheids and above the RR Lyraes
(RRLs) in the Hertzsprung-Russell diagram (e.g., Wallerstein, 2002).

T2Cs are in the post-horizontal branch evolutionary phase of low-mass stars,
where double shell (hydrogen and helium) burning occurs in thin shells outside
the inert carbon-oxygen core. As it ascends the asymptotic giant branch (AGB)
the star expands rapidly and becomes cooler and brighter. It experiences shell
flashes at the boundary between the core and the helium shell. During these
shell flashes the radius decreases temporarily; thus, the star moves to higher
temperatures and into the instability strip (IS). As these stars leave the
horizontal branch (HB) and evolve further up the AGB, they cross the IS at
higher luminosity than RRLs and become T2Cs (see, e.g., Bhardwaj, 2022;
Catelan & Smith, 2015, and reference therein).

Based on their pulsation periods T2Cs are classified as BL Herculis (BLHs) for
periods between 1 and 4 days, W Virginis (WVs) for periods greater than four
and less than 20 days, and RV Tauri (RVs) stars for period greater than 20
days (e.g., Soszyński et al., 2018).

The three grouping of T2Cs represent various stages of post-horizontal branch
evolution. In each evolutionary stage, predicted stellar properties can be
compared with observations. Short-period T2Cs stars crossing the IS show
increasing periods as they evolve redward from the HB to the AGB. The
intermediate-period WVs, evolving at higher luminosities on the AGB, suffer
helium shell flashes and are making temporary excursions from the AGB into the
IS, showing either increasing or decreasing periods. RVs stars, with long
periods, are post-AGB stars undergoing thermal pulses that send them blueward
into the IS and show only decreasing periods (Gingold, 1976; Bono et al.,
1997b; Wallerstein, 2002).

The period change is one of the essential properties of pulsating stars
obtained directly from observational data that can be used to constrain and
test stellar structure models and to probe stellar evolution. The period
change is thus one of the parameters that can detect evolutionary effects on
human time-scales.

Several studies have been conducted to investigate the pulsation and
evolutionary status of T2Cs as described in reviews by Wallerstein (2002) and
Neilson et al. (2016). A number of theoretical evolutionary track grids and
pulsation models have been developed (see e.g., Gingold, 1976; Bono et al.,
1997a, b; Bono et al., 2016, 2020; Smolec, 2016; Dotter, 2008; Dell’Omodarme
et al., 2012) that can be used to compute the pulsation properties including
period changes, period distributions, crossing modes and other characteristics
of T2Cs in their post-HB evolution.

From theoretical considerations we would expect short-period T2Cs (BLH) stars,
to be dominated by increasing periods as the they move redward from the hot
edge to the cool edge of the IS (e.g., Gingold, 1976; Bono et al., 2016;
Sandage et al., 1994; Wallerstein, 2002).

Several period change studies of BLH stars in globular clusters (Osborn, 1969;
Wehlau & Bohlender, 1982; Jurcsik et al., 2001; Osborn et al., 2019) and in
the field (Christianson, 1983; Diethelm, 1996; Provencal, 1986) have found
that the majority of BLH stars do indeed show period increases while a
minority, within observational uncertainties and limited data, show no period
change. However, the changes are broadly consistent with theoretically
predicted period changes (Neilson et al., 2016; Smith, 2013).

For BLH stars, the most apparent evolutionary trend is redward evolution with
an increasing period. However, Gonzales (1994) discovered one example that
demonstrated blue-ward advancement with a decreasing period. Furthermore, the
current theoretical framework (Bono et al., 2020) predicts that BLH stars can
experience both negative and positive period changes during their post-HB
evolution. This prediction was based on gravo-nuclear instabilities at the
onset of He-shell burning, following the exhaustion of helium in the core. The
existence of these ‘gravo-nuclear loops’(GNLs) causes BLH stars to stay longer
inside the IS and make fast period changes (Bono et al., 1997a, b). Such
scenarios would suggest that BLHs could show alternately increasing and
decreasing periods on quite short timescales. The period changes found in our
study of BLH stars support the existence of GNLS, and if interpreted in terms
of breathing pulses they could provide new insight into the very uncertain
mixing processes which are crucial for stellar evolution (see also Sweigart et
al., 2000).

In this work, we revise and study the period changes of eight BLH stars, with
periods between 1 and 2 days, which are usually called Above Horizontal Branch
(AHB) stars (Diethelm, 1983) during their post-HB evolution. We also
investigate the evolutionary changes in period of BLHs from records dating
back over a century and compare them to those predicted by the theory of
stellar evolution. The eight BLH stars, in order of increasing period, are
V716 Oph, BF Ser, CE Her, BL Her, XX Vir, KZ Cen, V745 Oph, and V439 Oph; they
are listed in Table 1.

This paper is structured as follows: in section 2 we describe the data
sources, methods and analyses used for this study. In section 3 we present and
discuss the result of our work by comparing it with theoretical models and
previous observational analyses. Finally, section 4 provides a summary and
conclusion.

##  2 Data, Methods and Analysis

For this research, we used all suitable ($B$, $V$, and $g^{\prime}$) band data
we could find in the literature, from ground- and space-based surveys,
including digitized photographic plates. Specifically, we used: (i)
photographic (PG) data from Digital Access to a Sky Century at Harvard (DASCH)
(Grindlay et al., 2012), and from the Sternberg Astronomical Institute (SAI);
(ii) CCD data (filters $V$ and $g^{\prime}$) from the All Sky Automated
Surveys (ASAS-3) (Pojmanski, 2002), the All Sky Automated Surveys of
SuperNovae (ASAS-SN) (Kochanek et al., 2017), INTEGRAL-OMC (Alfonso-Garzón et
al., 2012), Catalina Sky Survey (CSS) (Drake et al., 2013), PAN-STARSS
(Chambers et al., 2016), HIPPARCOS (Perryman et al., 1997); (iii)
photoelectric (PHE) (filters $B$ and $V$), visual (VIS) and photovisual (PGV)
data from the literature. The photographic data, from DASCH, SAI and others,
obtained from the literature are assumed to be identical to $B$-band
photometry for the purpose of this analysis.

We present the general information for the stars from the general catalogue of
variable stars (GCVS) (Samus’ et al., 2017) in Table 1. All other data sources
used for this study are listed in Table 2.

The data obtained from different sources are combined and sorted in order of
Heliocentric Julian Date (HJD). They are then divided into seasonal batches,
generally covering intervals of at least 3-months each year, although this
obviously depends on the individual data sets and the length of the gaps
between them. For the PG data there are sometimes gaps of several years
between data-sets. The seasonal light-curves generated for each data-batch
were then used to construct the $O-C$ curves.

To search for any period changes we employed the observed minus calculated
($O-C$) time of maximum as illustrated in an $O-C$ diagram. The observed
light-curves ($O$) were constructed for each star at each season and then
compared with a reference light-curve ($C$) to calculate the difference
between the times of maximum light ($O-C$). The $O-C$ residuals were
determined using the Hertzsprung (1919) method, with the algorithm developed
by Berdnikov (1992). At the same time we correct for the shifts in the time of
maxima between observations made through different filters. We use the method
by Lombard & Koen (1993) to confirm that the pulsation period changes are
real.

Assuming that the change in a period is linear with time, we can calculate the
maximum light elements for all stars using the following quadratic elements
(Sterken, 2005) :

$\displaystyle HJD_{\textrm{max}}=M_{\textrm{o}}+PE+QE^{2},$ (1)

where $P$ is the period at the adopted epoch, $M_{\textrm{o}}$, $Q$ is a
parabolic term and $E$ is the number of the cycle. The quadratic coefficient
$Q$ relates to $O-C$ with the following equation :

$\displaystyle Q=\frac{1}{2}\frac{dp}{dt}P_{\textrm{mid}}E^{2},$ (2)

where $dP/dt$ is the rate of period change and $P_{\textrm{mid}}$ is the mid-
epoch period.

The quadratic coefficient $Q$ can be used to measure the values of period
change ($dP/dt$) in seconds per year ($s/yr$) or in days per million years
($d/Myr$) using the following relations in Eqn. 3 and 4, respectively, using
sidereal years:

$\displaystyle\frac{dP}{dt}=365.25\times 24\times 60\times
60\times(\frac{2Q}{P_{\textrm{mid}}}),$ (3)

$\displaystyle\frac{dP}{dt}=730.5\times
10^{6}\times(\frac{Q}{P_{\textrm{mid}}}).$ (4)

Table 1: Summary of information for the BLH stars from the GCVS. Star | Period | Max $V$ | Min $V$
---|---|---|---
| [d] | [mag] | [mag]
V716 Oph | 1.116 | 11.28 | 12.60
BF Ser | 1.165 | 11.05 | 12.56
CE Her | 1.209 | 11.53 | 12.92
BL Her | 1.307 | 9.70 | 10.62
XX Vir | 1.348 | 11.55 | 12.78
KZ Cen | 1.520 | 11.80 | 12.77
V745 Oph | 1.595 | 12.70 | 13.90
V439 Oph | 1.893 | 11.73 | 12.70
Table 2: Summary of the Data Sources Star Name | JD & Year Intervals | No. of Observ. | Type of Observation | References
---|---|---|---|---
V716 Oph | 2411544 - 2458589 | 2041 | PG | DASCH
| 1890 - 2019 | 199 | PG | Mandel (1970); Kinman et al. (1984); Kinman (1965)
|  | 117 | PG | SAI
|  | 17 | CCD ($g^{\prime}$) | PAN-STARSS
|  | 126 | CCD ($V$) | INTEGRAL- OMC
|  | 176 | PHE ($B$,$V$) | Kwee & Diethelm (1984); Diethelm (1986); Lin (1983)
|  |  |  | McNamara & Pyne (1994); Bookmeyer et al. (1977)
|  | 330 | CCD ($V$) | CSS
|  | 1448 | CCD ($g^{\prime}$,$V$) | ASAS-SN
|  | 509 | CCD ($V$) | ASAS3 2411549
BF Ser | 2411549 - 2458589 | 2226 | PG | DASCH
| 1890 - 2019 | 780 | PG VIS | Ashbrook (1950); Soloviev (1952); Mandel (1970); Nikulina (1966)
|  | 69 | PG | SAI
|  | 11 | CCD ($g^{\prime}$) | PAN-STARSS
|  | 132 | CCD ($V$) | INTEGRAL-OMC
|  | 126 | CCD ($V$) | HIPPARCOS
|  | 128 | PHE ($B$,$V$) | Henden (1996); Diethelm & Tammann (1982); Harris (1980)
|  |  |  | Ashbrook (1950); Soloviev (1952); Bookmeyer et al. (1977)
|  | 367 | CCD ($V$) | CSS
|  | 1510 | CCD ($g^{\prime}$,$V$) | ASAS-SN
|  | 355 | CCD ($V$) | ASAS3
CE Her | 2411586 - 2458589 | 1584 | PG | DASCH
| 1890 - 2019 | 247 | PG | VIS
|  | 9 | CCD ($g^{\prime}$) | PAN-STARSS
|  | 118 | CCD ($V$) | INTEGRAL-OMC
|  | 189 | PHE ($B$,$V$) | Loomis et al. (1988); Chambers et al. (2016)
|  |  |  | Harris(1980); Diethelm & Tammann (1982)
|  | 101 | CCD ($V$) | CSS
|  | 1591 | CCD ($g^{\prime}$,$V$) | ASAS-SN
Bl Her | 2411508 - 2458589 | 4449 | PG | DASCH
| 1890 - 2019 | 504 | PG & PGV | Mandel(1970)
|  | 54 | CCD (V) | INTEGRAL-OMC
|  | 123 | CCD ($V$) | HIPPARCOS
|  | 658 | PHE ($B$,$V$) | Mitchell et al. (1964); Moffett & Barnes (1984)
|  |  |  | Arellano Ferro et al. (1998); Alexander et al. (1987); Meakes et al. (1991)
|  |  |  | Michałowska-Smak & Smak (1965); Preston & Kilston (1967)
|  |  |  |  Ignatova & Vozyakova (2000); Szabados (1977); Harris(1980)
|  | 1647 | CCD ($g^{\prime}$,$V$) | ASAS-SN
|  | 495 | CCD ($V$) | ASAS3
XX Vir | 2411529-2458589 | 1832 | PG | DASCH
| 1890 - 2019 | 639 | PG & VIS |  Oosterhoff (1936); Mandel (1970)
|  | 13 | CCD ($g^{\prime}$) | PAN-STARSS
|  | 68 | CCD ($V$) | INTEGRAL-OMC
|  | 214 | PHE ($B$,$V$) | Bookmeyer et al. (1977), Loomis et al. (1988)
|  |  |  | Harris (1980); Mitchell et al. (1964); McNamara & Pyne (1994)
|  | 302 | CCD ( $V$) | CSS
|  | 1548 | CCD ($g^{\prime}$,$V$) | ASAS-SN
KZ Cen | 2411167 - 2458590 | 1527 | PG | DASCH
| 1889 - 2019 | 190 | PHE ($B$,$V$) | Petersen & Hansen (1984); Irwin (1961); Diethelm (1986)
|  | 1907 | CCD ( $g^{\prime}$,$V$ ) | ASAS-SN
|  | 617 | CCD($V$) | ASAS3
V439 Oph | 2410929 - 2458589 | 1626 | PG | DASCH
| 1888 - 2019 | 236 | PGV & VIS | Mandel (1970); Tsesevich (1952)
|  | 258 | PG | SAI
|  | 10 | CCD ($g^{\prime}$) | PAN-STARSS
|  | 26 | CCD ($V$) | INTEGRAL-OMC
|  | 61 | PHE ($B$,$V$) |  Sturch (1966); Henden (1980);Diethelm & Tammann (1982); Diethelm (1986)
|  | 1019 | CCD($g^{\prime}$,$V$) | ASAS-SN
|  | 177 | CCD($V$) | ASAS3
V745 Oph | 2412263 -2458589 | 1217 | PG | DASCH
| 1892 - 2019 | 193 | PGV & VIS | Mandel(1970)
|  | 12 | CCD($g^{\prime}$) | PAN-STARSS
|  | 80 | CCD ($V$) | INTEGRAL-OMC
|  | 41 | PHE ($B$,$V$) |  Kwee & Diethelm (1984); Diethelm (1986)
|  | 114 | CCD ($V$) | CSS
|  | 1567 | CCD ($g^{\prime}$,$V$) | ASAS-SN

##  3 Results and Discussion

We have calculated for the eight BLHs: the quadratic elements, the rates of
period change and the corrections for maxima in the $B$\- and
$g^{\prime}$-bands, as listed in Tables 3 and 4. We constructed the $O-C$
diagrams for each star with all available data and performed the corresponding
period change test to confirm whether the period changes are real or not. The
resulting $O-C$ diagrams and the period change test graphs are presented in
Figures 1 and 2, respectively.

In the $O-C$ diagrams, we see convex parabolas (e.g., BL Her in Fig. 1)
indicating increasing periods and concave parabolas (e.g., V745 Oph in Fig. 1)
indicating decreasing periods. Thus we have examples of both increasing and
decreasing periods within this sample of eight stars.

The results from the seasonal light-curves for all our objects are presented
in the appendix (supplementary materials) Table LABEL:tab:table7. Columns 1, 2
and 3 give the times of maximum light and their errors; column 4 gives the
type of observations used; columns 5 and 6 contain the epoch number E and the
$O-C$ residual; columns 7 and 8 contain the number of observations N and the
data sources, respectively. The data from Table A1 are shown on the $O-C$
diagrams (Fig. 1) as open squares for the Harvard photographic measurements
and as dots for all the remaining observations, with vertical bars indicating
the limits of the errors in the $O-C$ residuals. The parabolic elements
obtained for the stars are listed in Table 3.

It is well known that the brightness maxima for pulsating variables generally
occur later at longer wavelengths. This differences in the light curves from
different filters was first noted by Arp (1955), who demonstrated that the
times of maximum and minimum in the $V$-band ($M_{\textrm{V}}$) light-curves
lag behind those in the $B$-band ($M_{\textrm{PG}}$) light-curves. When
different passbands are simultaneously present in the observational data set,
the primary passband should be selected in order to determine the shifts in
the times of maximum light in other bands. In our case, among the three bands
used ($V$, $B$, and $g^{\prime}$), the $V$-band is our primary reference.
Accordingly, we make the phase shift in the times of maximum for the $B$\- and
$g\textquoteright$-bands with respect to the $V$-bands, which is reported in
days. The phase shifts are expressed as
$\Delta\phi($B,V$)=\phi_{\textrm{$B-V$}}$ and
$\Delta\phi(\text{$g^{\prime},V$})=\phi_{\textrm{$g^{\prime}-V$}}$. These
corrections for maxima in the $B$\- and $g^{\prime}$-bands are given in Table
4. We applied them when constructing Fig.1 and determining the elements (Table
4) which refer to the $V$-band. The quadratic elements (Table 3) make it
possible to calculate the rate of change in the period ($dP/dt$), which is
given in column 5 of Table 4, together with its error.

Assuming a constant rate of change for the periods We applied parabolic fits
to the $O-C$ diagrams. We do see irregular changes, that do not fit the
parabolic pattern, in some of the diagrams (V716 Oph, BF Ser, BL Her, Ce Her &
XX Vir); these changes could be the result of random fluctuation in the
periods. Such random fluctuations have been observed in classical Cepheid
variables. The Eddington & Plakidis (1929) method can be used to test for
random, cycle-to-cycle changes in period, and it is usually applied to long-
period Cepheids. For short period Cepheids, the Lombard & Koen (1993) method
is useful to check whether the period change is real or due to random
fluctuations.

For the BLHs we used the Lombard & Koen method for every star to check whether
the measured $O-C$ residuals indicate real period changes. For this purpose,
we calculated the differences $\Delta(O-C)_{i}$ of successive $O-C$ residuals
from Table LABEL:tab:table7, $\Delta(O-C)_{i}=(O-C)_{i+1}-(O-C)_{i}$, and
plotted $D_{i}=\Delta(O-C)_{i}/(E_{i+1}-E_{i})$ against
$E^{\prime}_{i}=(E_{i}+E_{i+1})/2$ (Fig.2). The differences, $D_{i}$, which
describe the period changes in the epoch interval $E_{i}-E_{i+1}$, correspond
to the behaviour of the O$-$C residuals in Fig. 1. As shown in Fig. 2, the
differences $D_{i}$ in pulsation period show decreases and increases as a
function of time.

From our period derivative results, we found a decreasing period for three
stars, namely BF Ser, BL Her, and XX Vir, and an increasing period for the
remaining five stars, namely V716 Oph, CE Her, KZ Cen, V745 Oph, and V439 Oph.
The period-change graph for V716 Oph, illustrated in Fig. 2, is almost flat,
making it difficult to see if there is any significant change at all.
Nevertheless, our analysis indicated an increasing period of $0.022\pm 0.0048$
d/Myr. In a prior study by Diethelm (1996), XX Vir and BF Ser showed no period
changes and constant period change, respectively, over 70 years. However, in
the current study, we found decreasing periods over the 129-year span. For
V716 Oph and CE Her our result and Diethelm’s show increasing periods,
although there are slightly different period changes. For the remaining stars,
we found positive (KZ Cen, V439 Oph, & V745 Oph) and negative (BL Her) period
changes. The measured rate of period change in all eight BLH stars is in the
range $10^{-5}$ and $10^{-8}$ days per year, which is the same order of
magnitude as estimated by Sandage et al. (1994), Wehlau & Bohlender (1982),
Diethelm (1996) and Osborn et al. (2019) for stars evolving from the HB
towards the AGB. In addition, the parabolic trends of the $O-C$ diagrams
suggests that the observed rate of period change can be understood as real
evolutionary changes.

Table 3: The quadratic elements  Stars |  $HJD_{max}=M_{\textrm{o}}+PE+QE^{2}$, where $M_{\textrm{o}}$ adopted epoch,
---|---
|  $P$ is the period at adopted epoch and $Q$ is parabolic term
V716 Oph | $2435904.8889+1.1159169E+0.34152\times 10^{-10}E^{2}$
BF Ser | $2437226.1635+1.1654399E-0.55228\times 10^{-10}E^{2}$
CE Her | $2436639.7693+1.2094373E+0.15322\times 10^{-9}E^{2}$
BL Her | $2436482.0464+1.3074548E-0.68189\times 10^{-9}E^{2}$
XX Vir | $2436163.5888+1.3482049E-0.68355\times 10^{-10}E^{2}$
KZ Cen | $2435356.4024+1.5199792E+0.24842\times 10^{-8}E^{2}$
V745 Oph | $2435965.8617+1.5951035E+0.52379\times 10^{-7}E^{2}$
V439 Oph | $2435842.2304+1.8929943E+0.19312\times 10^{-8}E^{2}$
Table 4: Corrections for maxima in the $B$\- and $g^{\prime}$-bands and rate of period change. Stars | Difference between $V$\- & $B$-bands | Difference between $V$\- & $g^{\prime}$-bands | New Element | Rate of Period change
---|---|---|---|---
|  $\Delta\phi(B,V)$[d] |  $\Delta\phi(g^{\prime},V)$[d] |  | ($s/year$)
V716 Oph | 0.0006 | 0.0048 | 2435904.8889 + 1.1159169 E | 0.00193 $\pm$ 0.00042
BF Ser | -0.0037 | 0.0067 | 2437226.1635 + 1.1654399 E | -0.00299 $\pm$ 0.00031
CE Her | -0.0044 | -0.0020 | 2436639.7693 + 1.2094373 E | 0.008 $\pm$ 0.00068
BL Her | 0.00070 | -0.0069 | 2436482.0464 + 1.3074548 E | -0.03292 $\pm$ 0.00050
XX Vir | 0.00999 | 0.00608 | 2436163.5888 + 1.3482049 E | -0.0032 $\pm$ 0.00029
KZ Cen | -0.0016 | -0.0018 | 2435356.4024 + 1.5199792 E | 0.10315 $\pm$ 0.00119
V745 Oph | -0.0147 | -0.0135 | 2435965.8617 + 1.5951035 E | 2.07251 $\pm$ 0.00770
V439 Oph | 0.0050 | 0.0249 | 2435842.2304 + 1.8929943 E | 0.06439 $\pm$ 0.00346

###  3.1 Comparison with theoretical prediction of period change by Bono et
al. 2020

Several studies have been conducted to examine the evolutionary status of
post-horizontal branch stars by constructing models and deriving
evolutionarytracks for stars leaving the HB (e.g. Gingold, 1976; Bono et al.,
1997a, b; Dotter, 2008; Dell’Omodarme et al., 2012). The evolutionary models
of blue HB stars with depleted core helium show three different evolutionary
paths depending on their mass on the HB (Bono et al., 2016). The first path is
for low mass stars ($M$/$M_{\odot}\lesssim 0.515$), these do not enter the IS
and never reach the AGB. They move into their white dwarf cooling sequence and
are usually referred to as AGB-Manquè stars. The second path is for more
massive stars ($0.52\lesssim M$/$M_{\odot}\lesssim 0.62$), these evolve
redward through the IS, above the HB as they move towards their AGBs. They are
known as Post-Early AGB (PEAGB). The third path is for higher mass stars
($0.62\lesssim M$/$M_{\odot}\lesssim 0.80$), which evolve along the AGB and
into the Post-AGB phase (PAGB). They also experience thermal pulses and are
therefore known as thermally pulsating AGB (TPAGB) stars. The BLH stars are
thus classified as PEAGB stars that evolve redward en route to the AGB by
crossing the IS (Bono et al., 2020).

According to the evolutionary analysis of T2Cs by Gingold (1976, 1985), BLHs
on their way to the AGB experience blue-loops, known as ‘blue-noses ’, after
crossing the IS. Before the BLHs reach the AGB the ‘blue-nose’causes two
additional crossings of the IS. Gingold argues that the reason for these three
successive excursions is a readjusting of the hydrogen and helium-burning
shells before the stars reached the AGB. However, recent evolutionary studies
and HB evolutionary models with updated physics inputs do not support the
scenario proposed by Gingold (Bono et al., 2016).

Bono et al. (1997a, b) proposed a model that involves several GNLs in the
Hertzsprung-Russell diagram that the BLH star encounters before it reaches the
AGB. They pointed out that the ignition of the helium-shell in PEAGB BLH stars
is dramatically different from the normal evolutionary process. Following core
helium exhaustion helium-shell burning started immediately, causing the
structure to expand rapidly and creating a large discontinuity of energy
sources in both the hydrogen and helium shells, that resulted in GNLs. The
helium-burning shell undergoes a series of gravo-nuclear instabilities before
the star resumes its normal evolutionary path to the AGB.

Sweigart et al. (2000) investigated the GNLs reported by Bono et al. (1997a,b)
during the onset of helium-shell burning at the end of the HB phase. They
discovered the occurrence of GNLs, characterized by relaxation oscillations
within the helium shell, that led to loops in the evolutionary tracks.
Sweigart et al. showed that the onset of helium-burning produces GNLs in the
shell immediately following core-helium exhaustion, and indicated their strong
dependence on the helium profile. They also argued that the treatment of
convective boundaries following core helium burning (CHeB) impacts on the
presence of GNLs. Constantino et al. (2016) further demonstrating that at the
end of CHeB, the helium-shell encountered convective overshooting at the
convective boundary, whereby the GNLs appeared during the early AGB phase.
Both the Sweigart et al. and Constantino et al. studies supported the
existence and effects of GNLs during early AGB evolution.

Bono et al. (2020) recently presented a theoretical framework that examines
the evolutionary and pulsation properties of T2Cs based on HB evolutionary
models. They predicted that BLH stars would show both positive and negative
period changes. The prediction assumes the occurrence of multiple GNLs at the
onset of He-shell burning. Such loops could also result in increased time
spent within the IS and rapid period changes for the BLH stars in this short
period regime.

In our study, we found both positive and negative period changes for BLH stars
during their PEAGB phases in agreement with the Bono et al. (2020)
predictions.

The detection of period changes that agree with the current theoretical
framework proposed by Bono et al. (2020) has significance in modelling the
GNLs, and many also contribute to providing detailed information about the
occurrence of breathing pulses relevant to understanding Helium-burning mixing
process that are important to our understanding of stellar evolution.

Figure 1:  The $O-C$ diagrams for eight stars relative to the linear (top) and
quadratic (bottom) elements (Table 4). The open squares represent the Harvard
photographic observations, while dots are used for all other measurements;
vertical bars indicating the limits of errors in the residuals.

Figure 2: The period change in epoch interval ($D_{\textrm{i}}$) in days
versus the epoch number ($E^{{}^{\prime}}_{\textrm{i}}$), showing the period
change corresponding to the $O-C$ residuals.

###  3.2 Comparison with predicted period change of evolutionary track model
and results of Osborn et al. 2019

####  3.2.1 Comparison with predicted period changes and crossing modes

Osborn et al. (2019) conducted a period change analysis for metal-poor BLH
stars identified in the M13 globular cluster. They calculated the observed
rate of period change for three BLH stars using $O-C$ method, and found
increasing periods for all of them.

To compare the results of the measured period changes with evolution models
Osborn et al. constructed colour-magnitude diagrams for M13 showing BLH and
RRL stars overlaid with post-horizontal branch tracks from the models of the
Pisa group (Dell’Omodarme et al., 2012). To understand the evolutionary stages
and determine the pulsation period change rate, the Pisa evolutionary tracks
are divided into three phases related to the ’blue loop’. These are: pre-loop,
the first redward evolution (FRE) for the crossing of the IS, where the star’s
period is expected to increase; blueward evolution (BE), where the period
decreases; and post-loop as the second redward evolution (SRE), where the
period increases as the star resumes its evolution towards the AGB.

Osborn et al. estimated the rates of period change ($dP/dt$) using the Pisa
models and presented a graph of $dP/dt$ versus $P$ (their fig. 9). From this
diagram, all M13 stars are found to be located in the SRE phases, and the
measured period changes of BLH stars are in qualitative agreement with
theoretical predictions of post-HB evolution. Osborn et al. argued that this
$dP/dt-P$ diagram, with Pisa evolutionary tracks, can be extended and used for
other BLH stars to estimate their evolutionary stage and directions while
crossing the IS. Accordingly, Osborn et al. determined the crossings made for
18 BLH stars with published period changes, on the $dP/dt-P$ diagram.

Based on the Osborn et al. work, we compared our results with the Pisa models,
using evolutionary tracks with $Y=0.25$, and indicate the crossing mode of our
stars (red diamonds) in the $dP/dt-P$ diagram as shown in Fig. 3 (Osborn et al
2019, private communication 2022).

From Fig. 3, we are able to locate our stars in the FRE, BE and SRE stages,
along with the other 18 BLH stars. The crossing modes for each evolutionary
stage are presented in Table 5; one star is in the FRE, four in the SRE and
three in the BE stages. For comparison and future use we include published
period change rates for BLHs with our result in Table 6.

Figure 3: The theoretical rates of period change ($dP/dt$) as a function of
period ($P$) for different masses ($M$) and helium abundances ($Y$),
calculated from the Pisa stellar evolution models and taken from Osborn et al.
(2019). They are over-plotted with the observed rate of period change of our
BLH stars (red diamonds). Also shown are the period change rates of M13 V1, V2
and V6 (black squares), together with other T2Cs listed in Table 6 (gray
circles). The ordinate shows the rate of change of the period, in days per
million years, while the abscissa shows the pulsation period, in days. Models
with $Y=0.25$ are shown as red squares, with $Y=0.27$ as green squares and
with $Y=0.33$ as blue ones. These models used $\alpha$-elements enhancement
[$\alpha$/Fe]${}=+0.3$ and a mixing length parameter of ML${}=1.7$. Models for
the same $M$ and $Y$ are connected by lines of the appropriate colour; the
lines can be considered evolutionary tracks in the $P$ \- $dP/dt$ plane, and
the regions corresponding to the three phases of evolution produced by loops
are labelled FRE, BE and SRE. Tracks with masses corresponding to the M13
Cepheids are emphasised using thick lines labelled with mass, the labels
having same colour as the appropriate track.

####  3.2.2 Comparison with crossing times

Osborn et al. also estimated the crossing times, as a more quantitative method
of comparing theory with observations, for stars evolving in the IS. Since the
percentage of the crossing time spent in each evolutionary phase should
correlate with the percentages of stars found in the sample, they calculated
the proportion of the crossing time spent in each evolutionary phase (FRE, BE,
and SRE). They compared this to the percentages of stars found in those stages
in the sample, as presented in table 10 from Osborn et al. (2019). They found
an absence of quantitative agreement between theory and observation,
especially for BE stars. They speculated that this was due to their small
sample size and proposed an in-depth examination of a larger sample of stars.

Although we have only 3 BE stars, that is more than Osborn et al. and our
sample is large enough to compare crossing times quantitatively. Taking the 22
BLH stars from Table 6, where 14 are in SRE, 5 in FRE and 3 in BE crossing
modes, the percentage of stars in each phase is 64% SRE, 23% FRE and 14% BE.
These numbers can be compared with the theoretical values of 78%, 13% and 9%
(Osborn et al. (2019) table 10, for the canonical Y=0.25). This is reasonable
agreement given the sample size. Obviously a larger sample would allow a more
precise comparison.

Table 5: The evolutionary crossing modes of the eight BLH stars based on the $dP/dt-P$ diagram of Osborn et al. (2019) illustrated in Fig 3 Stars | Period | Rate of period change | Crossing modes
---|---|---|---
| [d] |  $dP/dt$[d/Myr] |
V716 Oph | 1.1159169 | 0.022 $\pm$ 0.0048 | SRE
BF Ser | 1.1654399 | -0.035 $\pm$ 0.0035 | BE
CE Her | 1.2094373 | 0.092 $\pm$ 0.0078 | SRE
BL Her | 1.3074548 | -0.381 $\pm$ 0.0057 | BE
XX Vir | 1.3482049 | -0.037 $\pm$ 0.0033 | BE
KZ Cen | 1.5199792 | 1.193 $\pm$ 0.0137 | SRE
V745 Oph | 1.5951035 | 23.987 $\pm$ 0.0891 | FRE
V439 OPH | 1.8929943 | 0.745 $\pm$ 0.0400 | SRE
Table 6: Published period changes of BLH stars, including the current work shown in Fig.3, for comparison with Osborn et al. (2019) Star |  Period($P$) |  Rate of period change($dP/dt$) | Error |  Years of span ($\vartriangle T$) | Crossing modes | Source
---|---|---|---|---|---|---
| [d] | [d/Myr] | [d/Myr] | [yr] |  |
V716 Oph | 1.116 | 0.03[1];0.022[2] | 0.0048 [2] | 76 [1] ;129[2] | SRE |  1 Diethelm (1996) ;2This paper
$\omega$ Cen V43 | 1.157 | 0.56 | 0.14 | 79 | SRE | Jurcsik et al. (2001)
BF Ser | 1.165 | 0.0[1];$-$0.035[2] | 0.0035 | 60[1];129[2] | BE |  1 Diethelm (1996); 2This paper
CE Her | 1.209 | 0.2[1] ;0.092[2] | 0.0078[2] | 65[1];129[2] | SRE |  1 Diethelm (1996) ; 2This paper
BL Her | 1.307 |  $-$0.381 | 0.0057 | 129 | BE | This paper
$\omega$ Cen V92 | 1.345 | 13.94 | 0.56 | 100 | FRE | Jurcsik et al. (2001)
XX Vir | 1.348 | 0.0[1];$-$0.037[2] | 0.0033[2] | 72[1] ;129[2] | BE |  1 Diethelm (1996);2This paper
$\omega$ Cen V60 | 1.349 | 4.85 | 0.92 | 100 | FRE | Jurcsik et al. (2001)
M15 V1 | 1.438 | 4.67 | 0.23 | 72 | FRE | Wehlau & Bohlender (1982)
M13 V1 | 1.459 | 0.52 | 0.09 | 114 | SRE | Osborn et al. (2019)
KZ Cen | 1.519 | 1.193 | 0.0137 | 130 | SRE | This paper
V745 Oph | 1.595 | 23.987 | 0.0891 | 127 | FRE | This paper
M22 V11 | 1.690 | 0.01 | 0.19 | 83 | SRE | Wehlau & Bohlender (1982)
M14 V76 | 1.890 | 7.43 | 1.0 | 48 | FRE | Wehlau & Froelich (1994)
V439 Oph | 1.893 | 0.745 | 0.0400 | 131 | SRE | This paper
EK Del | 2.047 | 0.6 | – | 61 | SRE | Diethelm (1990, 1996)
M13 V6 | 2.113 | 0.80 | 0.06 | 114 | SRE | Osborn et al. (2019)
UY Eri | 2.213 | 0.8 | – | 66 | SRE | Diethelm (1996)
$\omega$ Cen V61 | 2.274 | 1.13 | 0.16 | 100 | SRE | Jurcsik et al. (2001)
M14 V2 | 2.794 | 0.34 | 0.3 | 48 | SRE | Wehlau & Froelich (1994)
$\omega$ Cen V48 | 4.474 | 15.45 | – | 79 | SRE | Jurcsik et al. (2001)
M13 V2 | 5.111 | 9.2 | 0.7 | 115 | SRE | Osborn et al. (2019)

##  4 Summary and Conclusions

We investigate the period changes of eight BLH stars with periods between 1
and 2 days using all previously published data and all relevant observational
survey data, including digitized photographic plates.

The $O-C$ diagrams for the stars studied show parabolic evolutionary trends,
which indicate the presence of both increasing and decreasing periods for
these BLHs over a baseline of more than a century. The derived period changes
for such stars are in good agreement with the recent theoretical evolutionary
framework proposed by Bono et al. (2020), and with the Pisa group evolutionary
tracks from Dell’Omodarme et al. (2012) as presented by Osborn et al. (2019).

Our study found three BLH stars with decreasing periods, a significant
increase over those reported by Gonzalez (1994). A more extensive study (in
preparation) will further increase the number of BLH stars and improve the
sample size for future studies.

We were able to determine the crossing mode of these stars by comparing with
evolutionary tracks, as illustrated by Osborn et al. (2019). We found one star
in FRE, four stars in SRE and three stars in BE crossing modes, respectively.
The existence of decreasing periods for BLHs is important for the following
reasons:

  * •

It provides observational evidence for BE crossings with decreasing periods
for BLHs, which were previously only known to have increasing periods and to
be evolving redward.

  * •

It fits with the recent theoretical evolutionary framework proposed by Bono et
al. (2020).

  * •

It supports the presence of GNLs predicted by Bono et al. (1997a, b) and
provides observational evidence for breathing pulse as suggested by Sweigart
et al. (2000).

  * •

The availability of a sample of BE stars provides quantitative agreement
between theory and observation, especially for BE stars, thus the proportion
of crossing times spent and the number of stars available in each evolutionary
phase across the IS are approximately matched.

## Acknowledgements

We thank the anonymous referee for valuable comments that improved the paper
significantly. AMY acknowledges and thanks the South African Astronomical
Observatory (SAAO) in Capetown, South Africa, and the Sternberg Astronomical
Institute (SAI) of Moscow State University in Russia for the continuous
support provided by research administrators and staff during his research
visit. AMY thanks and is indebted to Space Science and Geospatial Institute
(SSGI) in Ethiopia for all financial and logistical support. AMY acknowledges
and thanks Prof. Wayne Osborn from Central Michigan University, and Prof.
Grzegorz Kopacki, from Wroclaw University Astronomical Institute, for
providing the $dP/dt$-$P$ diagram & information calculated from Pisa, stellar
evolution model. This work makes use of the observational data available from
the catalogue of Digital Access to a Sky Century at Harvard (DASCH), All Sky
Automated Surveys (ASAS-3), All Sky Automated Surveys of SuperNovae (ASAS-SN),
INTEGRAL-OMC, Catalina Sky Survey(CSS), PAN-STARSS, HIPPARCOS and data from
Sternberg Astronomical Institute (SAI).

## Data Availability

The data underlying this article are available in the article as well as the
data source cited in the article and references therein.

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##  Appendix A supplementary materials

###  A.1 Times of maximum light

The results of reduction of the seasonal light-curves for all stars are
presented in Table LABEL:tab:table7. Columns 1, 2 and 3 give the times of
maximum light and their errors; column 4 gives the type of observations used;
columns 5 and 6 contain the epoch number (E) and the $O-C$ residual; columns 7
and 8 contain the number of observations (N) and the data sources,
respectively.

Table 7: Times of maximum light  Max, HJD | Year | Uncertainty | Filter | E |  O – C, days | N | Reference
---|---|---|---|---|---|---|---
V716 Oph |
2413238.3811 | 1895-02-13 | 0.0018 | $PG$ | $-20312$ | $-0.0028$ | 31 | DASCH
2415142.1364 | 1900-05-02 | 0.0050 | $PG$ | $-18606$ | $-0.0017$ | 69 | DASCH
2417078.2595 | 1905-08-20 | 0.0030 | $PG$ | $-16871$ | $0.0055$ | 106 | DASCH
2419917.1566 | 1913-05-29 | 0.0061 | $PG$ | $-14327$ | $0.0099$ | 92 | DASCH
2423221.3956 | 1922-06-15 | 0.0038 | $PG$ | $-11366$ | $0.0190$ | 95 | DASCH
2424211.2217 | 1925-03-01 | 0.0037 | $PG$ | $-10479$ | $0.0268$ | 45 | Lin (1983)
2425483.3594 | 1928-08-24 | 0.0025 | $PG$ | $-9339$ | $0.0193$ | 122 | DASCH
2427502.0525 | 1934-03-05 | 0.0018 | $PG$ | $-7530$ | $0.0186$ | 196 | DASCH
2428479.5831 | 1936-11-07 | 0.0022 | $PG$ | $-6654$ | $0.0060$ | 89 | DASCH
2429280.8172 | 1939-01-17 | 0.0023 | $PG$ | $-5936$ | $0.0118$ | 162 | DASCH
2429795.2446 | 1940-06-14 | 0.0019 | $PG$ | $-5475$ | $0.0014$ | 133 | DASCH
2430436.8968 | 1942-03-18 | 0.0018 | $PG$ | $-4900$ | $0.0014$ | 190 | DASCH
2431442.3390 | 1944-12-17 | 0.0027 | $PG$ | $-3999$ | $0.0025$ | 151 | DASCH
2432153.1769 | 1946-11-28 | 0.0022 | $PG$ | $-3362$ | $0.0013$ | 168 | DASCH
2432886.3309 | 1948-11-30 | 0.0023 | $PG$ | $-2705$ | $-0.0021$ | 120 | DASCH
2433587.1205 | 1950-11-01 | 0.0027 | $PG$ | $-2077$ | $-0.0083$ | 80 | DASCH
2435157.2222 | 1955-02-18 | 0.0059 | $PG$ | $-670$ | $-0.0017$ | 25 | Mandel (1970)
2435370.3651 | 1955-09-19 | 0.0037 | $PG$ | $-479$ | $0.0010$ | 25 | DASCH
2436961.6478 | 1960-01-28 | 0.0042 | $PG$ | $947$ | $-0.0137$ | 32 | SAI (this paper)
2437470.5153 | 1961-06-20 | 0.0030 | $PG$ | $1403$ | $-0.0043$ | 33 | Kinman (1965)
2437514.0366 | 1961-08-02 | 0.0091 | $PG$ | $1442$ | $-0.0038$ | 57 | Mandel (1970)
2439977.9790 | 1968-05-01 | 0.0007 | $B$ | $3650$ | $-0.0059$ | 38 | Bookmeyer et al. (1977)
2439977.9808 | 1968-05-01 | 0.0007 | $V$ | $3650$ | $-0.0047$ | 38 | Bookmeyer et al. (1977)
2440237.9849 | 1969-01-16 | 0.0044 | $PG$ | $3883$ | $-0.0086$ | 24 | SAI (this paper)
2441639.5786 | 1972-11-18 | 0.0006 | $V$ | $5139$ | $-0.0073$ | 49 | Kwee & Diethelm (1984)
2441639.5793 | 1972-11-18 | 0.0004 | $B$ | $5139$ | $-0.0059$ | 49 | Kwee & Diethelm (1984)
2441663.0125 | 1972-12-11 | 0.0041 | $PG$ | $5160$ | $-0.0070$ | 59 | SAI (this paper)
2443129.3337 | 1976-12-16 | 0.0044 | $PG$ | $6474$ | $-0.0006$ | 67 | DASCH
2443985.2392 | 1979-04-21 | 0.0012 | $PG$ | $7241$ | $-0.0034$ | 34 | Kinman (1965)
2445581.0046 | 1983-09-03 | 0.0044 | $PG$ | $8671$ | $0.0009$ | 43 | DASCH
2446646.7067 | 1986-08-04 | 0.0011 | $B$ | $9626$ | $0.0023$ | 78 | McNamara & Pyne (1994)
2446646.7075 | 1986-08-04 | 0.0012 | $V$ | $9626$ | $0.0024$ | 78 | McNamara & Pyne (1994)
2446893.3229 | 1987-04-07 | 0.0046 | $PG$ | $9847$ | $0.0008$ | 71 | DASCH
2452032.1278 | 2001-05-02 | 0.0049 | $V$ | $14452$ | $0.0077$ | 47 | ASAS-3
2452479.6133 | 2002-07-24 | 0.0036 | $V$ | $14853$ | $0.0105$ | 22 | ASAS-3
2452801.0035 | 2003-06-10 | 0.0027 | $V$ | $15141$ | $0.0167$ | 68 | ASAS-3
2453134.6579 | 2004-05-09 | 0.0023 | $V$ | $15440$ | $0.0119$ | 43 | ASAS-3
2453533.0388 | 2005-06-11 | 0.0016 | $V$ | $15797$ | $0.0105$ | 68 | ASAS-3
2453848.8423 | 2006-04-23 | 0.0049 | $V$ | $16080$ | $0.0095$ | 35 | ASAS-3
2454252.8081 | 2007-06-01 | 0.0021 | $V$ | $16442$ | $0.0134$ | 76 | ASAS-3
2454443.6346 | 2007-12-09 | 0.0047 | $V$ | $16613$ | $0.0180$ | 212 | CSS
2454612.1333 | 2008-05-25 | 0.0014 | $V$ | $16764$ | $0.0133$ | 94 | ASAS-3
2454983.7338 | 2009-06-01 | 0.0016 | $V$ | $17097$ | $0.0135$ | 51 | ASAS-3
2455623.1539 | 2011-03-02 | 0.0034 | $V$ | $17670$ | $0.0132$ | 117 | CSS
2456396.4852 | 2013-04-13 | 0.0020 | $V$ | $18363$ | $0.0141$ | 62 | ASAS-SN
2456837.2716 | 2014-06-28 | 0.0007 | $V$ | $18758$ | $0.0133$ | 117 | ASAS-SN
2457148.6129 | 2015-05-06 | 0.0003 | $V$ | $19037$ | $0.0137$ | 193 | ASAS-SN
2457457.7216 | 2016-03-10 | 0.0004 | $V$ | $19314$ | $0.0135$ | 125 | ASAS-SN
2457599.4446 | 2016-07-29 | 0.0007 | $V$ | $19441$ | $0.0150$ | 100 | ASAS-SN
2457837.1316 | 2017-03-24 | 0.0007 | $V$ | $19654$ | $0.0118$ | 100 | ASAS-SN
2457956.5361 | 2017-07-22 | 0.0005 | $V$ | $19761$ | $0.0131$ | 108 | ASAS-SN
2458159.6261 | 2018-02-10 | 0.0002 | $g$ | $19943$ | $0.0063$ | 120 | ASAS-SN
2458212.0735 | 2018-04-03 | 0.0006 | $g$ | $19990$ | $0.0056$ | 100 | ASAS-SN
2458262.2951 | 2018-05-23 | 0.0008 | $V$ | $20035$ | $0.0109$ | 139 | ASAS-SN
2458295.7679 | 2018-06-26 | 0.0003 | $g$ | $20065$ | $0.0062$ | 100 | ASAS-SN
2458428.5614 | 2018-11-06 | 0.0004 | $g$ | $20184$ | $0.0055$ | 100 | ASAS-SN
2458572.5147 | 2019-03-30 | 0.0007 | $g$ | $20313$ | $0.0056$ | 83 | ASAS-SN
BF Ser |
2415910.2467 | 1902-06-09 | 0.0019 | $PG$ | $-18290$ | $-0.0247$ | 87 | DASCH
2418492.8713 | 1909-07-05 | 0.0020 | $PG$ | $-16074$ | $-0.0149$ | 115 | DASCH
2420613.9758 | 1915-04-26 | 0.0016 | $PG$ | $-14254$ | $-0.0110$ | 145 | DASCH
2421911.1180 | 1918-11-13 | 0.0022 | $PG$ | $-13141$ | $-0.0034$ | 131 | DASCH
2425049.6437 | 1927-06-18 | 0.0015 | $PG$ | $-10448$ | $-0.0073$ | 145 | DASCH
2427593.7936 | 1934-06-05 | 0.0017 | $PG$ | $-8265$ | $-0.0126$ | 168 | DASCH
2428828.0099 | 1937-10-21 | 0.0016 | $PG$ | $-7206$ | $0.0029$ | 210 | DASCH
2430147.2848 | 1941-06-01 | 0.0017 | $PG$ | $-6074$ | $-0.0002$ | 166 | DASCH
2431831.3479 | 1946-01-10 | 0.0014 | $PG$ | $-4629$ | $0.0023$ | 164 | DASCH
2433011.9401 | 1949-04-05 | 0.0050 | $PG$ | $-3616$ | $0.0039$ | 29 | Nikulina (1966)
2433214.7330 | 1949-10-25 | 0.0019 | $PG$ | $-3442$ | $0.0102$ | 182 | DASCH
2435577.0678 | 1956-04-13 | 0.0030 | $PG$ | $-1415$ | $-0.0016$ | 64 | Nikulina (1966)
2436439.5109 | 1958-08-24 | 0.0051 | $PG$ | $-675$ | $0.0160$ | 29 | Mandel (1970)
2438431.2295 | 1964-02-05 | 0.0024 | $PG$ | $1034$ | $-0.0021$ | 114 | DASCH
2440154.9139 | 1968-10-25 | 0.0009 | $B$ | $2513$ | $-0.0033$ | 72 | Bookmeyer et al. (1977)
2440160.7372 | 1968-10-31 | 0.0006 | $V$ | $2518$ | $-0.0029$ | 74 | Bookmeyer et al. (1977)
2442287.6756 | 1974-08-28 | 0.0030 | $PG$ | $4343$ | $0.0034$ | 53 | SAI (this paper)
2444039.3146 | 1979-06-14 | 0.0020 | $V$ | $5846$ | $-0.0095$ | 12 | Harris (1980)
2444068.4526 | 1979-07-13 | 0.0041 | $V$ | $5871$ | $-0.0074$ | 19 | Diethelm & Tammann (1982)
2444069.6219 | 1979-07-15 | 0.0040 | $B$ | $5872$ | $-0.0079$ | 18 | Diethelm & Tammann (1982)
2444872.6172 | 1981-09-25 | 0.0019 | $PG$ | $6561$ | $-0.0006$ | 155 | DASCH
2446997.2153 | 1987-07-20 | 0.0029 | $PG$ | $8384$ | $0.0006$ | 70 | DASCH
2448285.0207 | 1991-01-28 | 0.0016 | $V$ | $9489$ | $-0.0008$ | 64 | Hipparcos
2448652.1313 | 1992-01-30 | 0.0021 | $V$ | $9804$ | $-0.0038$ | 61 | Hipparcos
2449726.6609 | 1995-01-09 | 0.0016 | $V$ | $10726$ | $-0.0098$ | 22 | Henden (1996)
2449726.6670 | 1995-01-09 | 0.0019 | $B$ | $10726$ | $-0.0079$ | 22 | Henden (1996)
2452773.1211 | 2003-05-13 | 0.0016 | $V$ | $13340$ | $-0.0094$ | 60 | ASAS-3
2453120.4214 | 2004-04-24 | 0.0022 | $V$ | $13638$ | $-0.0102$ | 37 | ASAS-3
2453506.1819 | 2005-05-15 | 0.0017 | $V$ | $13969$ | $-0.0103$ | 58 | ASAS-3
2453668.1734 | 2005-10-24 | 0.0037 | $V$ | $14108$ | $-0.0149$ | 44 | CSS
2453855.8108 | 2006-04-30 | 0.0018 | $V$ | $14269$ | $-0.0133$ | 37 | ASAS-3
2454245.0662 | 2007-05-24 | 0.0020 | $V$ | $14603$ | $-0.0149$ | 45 | ASAS-3
2454419.8814 | 2007-11-15 | 0.0016 | $V$ | $14753$ | $-0.0156$ | 71 | CSS
2454608.6875 | 2008-05-22 | 0.0013 | $V$ | $14915$ | $-0.0108$ | 62 | ASAS-3
2454881.4002 | 2009-02-18 | 0.0008 | $V$ | $15149$ | $-0.0111$ | 132 | INTEGRAL-OMC
2454932.6815 | 2009-04-11 | 0.0025 | $V$ | $15193$ | $-0.0090$ | 47 | CSS
2454962.9723 | 2009-05-11 | 0.0023 | $V$ | $15219$ | $-0.0197$ | 35 | ASAS-3
2455497.9136 | 2010-10-28 | 0.0019 | $V$ | $15678$ | $-0.0153$ | 68 | CSS
2456229.8125 | 2012-10-29 | 0.0029 | $V$ | $16306$ | $-0.0127$ | 84 | CSS
2456416.2827 | 2013-05-03 | 0.0007 | $V$ | $16466$ | $-0.0129$ | 70 | ASAS-SN
2456845.1613 | 2014-07-06 | 0.0008 | $V$ | $16834$ | $-0.0161$ | 140 | ASAS-SN
2457156.3337 | 2015-05-13 | 0.0004 | $V$ | $17101$ | $-0.0162$ | 143 | ASAS-SN
2457510.6279 | 2016-05-02 | 0.0005 | $V$ | $17405$ | $-0.0157$ | 260 | ASAS-SN
2457813.6409 | 2017-03-01 | 0.0004 | $V$ | $17665$ | $-0.0170$ | 120 | ASAS-SN
2457926.6911 | 2017-06-22 | 0.0011 | $V$ | $17762$ | $-0.0145$ | 90 | ASAS-SN
2458148.1151 | 2018-01-29 | 0.0004 | $g$ | $17952$ | $-0.0241$ | 120 | ASAS-SN
2458212.2137 | 2018-04-03 | 0.0003 | $g$ | $18007$ | $-0.0247$ | 100 | ASAS-SN
2458233.1998 | 2018-04-24 | 0.0006 | $V$ | $18025$ | $-0.0165$ | 171 | ASAS-SN
2458307.7802 | 2018-07-08 | 0.0004 | $g$ | $18089$ | $-0.0243$ | 130 | ASAS-SN
2458543.1984 | 2019-02-28 | 0.0004 | $g$ | $18291$ | $-0.0249$ | 155 | ASAS-SN
CE Her |
2414721.2099 | 1899-03-07 | 0.0041 | $PG$ | $-18123$ | $0.0680$ | 59 | DASCH
2418255.1516 | 1908-11-09 | 0.0035 | $PG$ | $-15201$ | $0.0338$ | 159 | DASCH
2424349.4865 | 1925-07-17 | 0.0037 | $PG$ | $-10162$ | $0.0140$ | 181 | DASCH
2428028.5842 | 1935-08-14 | 0.0022 | $PG$ | $-7120$ | $0.0033$ | 213 | DASCH
2429626.2417 | 1939-12-28 | 0.0022 | $PG$ | $-5799$ | $-0.0059$ | 198 | DASCH
2432087.4413 | 1946-09-23 | 0.0036 | $VIS$ | $-3764$ | $-0.0059$ | 122 | Mandel (1970)
2432091.0693 | 1946-09-27 | 0.0026 | $PG$ | $-3761$ | $-0.0116$ | 385 | DASCH
2434408.3507 | 1953-01-30 | 0.0077 | $PG$ | $-1845$ | $-0.0121$ | 33 | Mandel (1970)
2436732.8861 | 1959-06-13 | 0.0038 | $PG$ | $77$ | $-0.0153$ | 88 | Mandel (1970)
2440410.7957 | 1969-07-08 | 0.0027 | $V$ | $3118$ | $0.0008$ | 26 | Bookmeyer et al. (1977)
2440410.8044 | 1969-07-08 | 0.0014 | $B$ | $3118$ | $0.0042$ | 26 | Bookmeyer et al. (1977)
2441280.3892 | 1971-11-24 | 0.0083 | $PG$ | $3837$ | $0.0035$ | 121 | DASCH
2444043.9623 | 1979-06-19 | 0.0026 | $V$ | $6122$ | $0.0176$ | 11 | Harris (1980)
2444070.5692 | 1979-07-16 | 0.0049 | $V$ | $6144$ | $0.0169$ | 25 | Diethelm & Tammann (1982)
2444070.5712 | 1979-07-16 | 0.0029 | $B$ | $6144$ | $0.0136$ | 25 | Diethelm & Tammann (1982)
2444717.6238 | 1981-04-23 | 0.0047 | $PG$ | $6679$ | $0.0172$ | 68 | DASCH
2446461.6325 | 1986-01-31 | 0.0003 | $V$ | $8121$ | $0.0227$ | 127 | Loomis et al. (1988)
2446543.8861 | 1986-04-23 | 0.0034 | $PG$ | $8189$ | $0.0291$ | 155 | DASCH
2454840.6304 | 2009-01-09 | 0.0018 | $V$ | $15049$ | $0.0387$ | 117 | INTEGRAL-OMC
2454851.5157 | 2009-01-20 | 0.0024 | $V$ | $15058$ | $0.0391$ | 101 | CSS
2456450.3894 | 2013-06-06 | 0.0010 | $V$ | $16380$ | $0.0367$ | 111 | ASAS-SN
2456854.3438 | 2014-07-15 | 0.0003 | $V$ | $16714$ | $0.0390$ | 122 | ASAS-SN
2457136.1447 | 2015-04-23 | 0.0003 | $V$ | $16947$ | $0.0410$ | 100 | ASAS-SN
2457316.3495 | 2015-10-20 | 0.0005 | $V$ | $17096$ | $0.0396$ | 100 | ASAS-SN
2457486.8843 | 2016-04-08 | 0.0004 | $V$ | $17237$ | $0.0437$ | 100 | ASAS-SN
2457606.6190 | 2016-08-06 | 0.0004 | $V$ | $17336$ | $0.0441$ | 121 | ASAS-SN
2457830.3652 | 2017-03-17 | 0.0005 | $V$ | $17521$ | $0.0445$ | 100 | ASAS-SN
2457930.7502 | 2017-06-26 | 0.0005 | $V$ | $17604$ | $0.0461$ | 99 | ASAS-SN
2458106.1191 | 2017-12-18 | 0.0006 | $V$ | $17749$ | $0.0466$ | 99 | ASAS-SN
2458143.6141 | 2018-01-25 | 0.0003 | $g$ | $17780$ | $0.0490$ | 100 | ASAS-SN
2458228.2769 | 2018-04-19 | 0.0004 | $g$ | $17850$ | $0.0513$ | 100 | ASAS-SN
2458281.4914 | 2018-06-11 | 0.0005 | $g$ | $17894$ | $0.0505$ | 99 | ASAS-SN
2458329.8671 | 2018-07-30 | 0.0005 | $V$ | $17934$ | $0.0487$ | 111 | ASAS-SN
2458360.1031 | 2018-08-29 | 0.0005 | $g$ | $17959$ | $0.0488$ | 119 | ASAS-SN
2458559.6627 | 2019-03-17 | 0.0005 | $g$ | $18124$ | $0.0512$ | 117 | ASAS-SN
BL Her |
2414401.5576 | 1898-04-22 | 0.0085 | $PG$ | $-16888$ | $-0.1912$ | 66 | DASCH
2416207.1700 | 1903-04-02 | 0.0061 | $PG$ | $-15507$ | $-0.1739$ | 253 | DASCH
2417308.0764 | 1906-04-07 | 0.0059 | $PG$ | $-14665$ | $-0.1444$ | 197 | DASCH
2418474.3252 | 1909-06-16 | 0.0056 | $PG$ | $-13773$ | $-0.1452$ | 197 | DASCH
2419687.6708 | 1912-10-12 | 0.0060 | $PG$ | $-12845$ | $-0.1177$ | 186 | DASCH
2420805.5699 | 1915-11-04 | 0.0052 | $PG$ | $-11990$ | $-0.0924$ | 271 | DASCH
2422471.2907 | 1920-05-26 | 0.0062 | $PG$ | $-10716$ | $-0.0691$ | 205 | DASCH
2423963.1071 | 1924-06-26 | 0.0046 | $PG$ | $-9575$ | $-0.0587$ | 220 | DASCH
2424960.7070 | 1927-03-21 | 0.0064 | $PG$ | $-8812$ | $-0.0468$ | 134 | DASCH
2426129.5730 | 1930-06-02 | 0.0061 | $PG$ | $-7918$ | $-0.0453$ | 197 | DASCH
2427320.6767 | 1933-09-05 | 0.0044 | $PG$ | $-7007$ | $-0.0330$ | 278 | DASCH
2428340.4854 | 1936-06-20 | 0.0042 | $PG$ | $-6227$ | $-0.0390$ | 294 | DASCH
2430102.9532 | 1941-04-18 | 0.0027 | $PG$ | $-4879$ | $-0.0204$ | 693 | DASCH
2431806.5820 | 1945-12-17 | 0.0035 | $PG$ | $-3576$ | $-0.0052$ | 508 | DASCH
2433178.1195 | 1949-09-18 | 0.0057 | $PG$ | $-2527$ | $0.0122$ | 277 | DASCH
2434639.8492 | 1953-09-19 | 0.0084 | $PG$ | $-1409$ | $0.0075$ | 59 | Mandel (1970)
2435000.7199 | 1954-09-15 | 0.0075 | $PG$ | $-1133$ | $0.0207$ | 130 | DASCH
2435017.6993 | 1954-10-02 | 0.0015 | $B$ | $-1120$ | $0.0031$ | 124 | Mitchell et al. (1964)
2435034.6988 | 1954-10-19 | 0.0023 | $V$ | $-1107$ | $0.0049$ | 125 | Mitchell et al. (1964)
2436157.7909 | 1957-11-15 | 0.0078 | $PG$ | $-248$ | $-0.0059$ | 111 | Mandel (1970)
2436744.8402 | 1959-06-25 | 0.0063 | $PGV$ | $201$ | $-0.0047$ | 87 | Mandel (1970)
2437699.2797 | 1962-02-03 | 0.0087 | $PG$ | $931$ | $-0.0062$ | 65 | Mandel (1970)
2437873.1682 | 1962-07-27 | 0.0036 | $B$ | $1064$ | $-0.0092$ | 25 | Michałowska-Smak & Smak (1965)
2437873.1740 | 1962-07-27 | 0.0041 | $V$ | $1064$ | $-0.0043$ | 25 | Michałowska-Smak & Smak (1965)
2438218.3485 | 1963-07-07 | 0.0049 | $PGV$ | $1328$ | $0.0021$ | 122 | Mandel (1970)
2438218.3485 | 1963-07-07 | 0.0049 | $PGV$ | $1328$ | $0.0021$ | 122 | Mandel (1970)
2439325.7700 | 1966-07-19 | 0.0054 | $V$ | $2175$ | $0.0094$ | 48 | Preston & Kilston (1967)
2439325.7715 | 1966-07-19 | 0.0076 | $B$ | $2175$ | $0.0118$ | 48 | Preston & Kilston (1967)
2441788.9933 | 1973-04-16 | 0.0033 | $B$ | $4059$ | $-0.0113$ | 23 | Szabados (1977)
2441788.9986 | 1973-04-16 | 0.0038 | $V$ | $4059$ | $-0.0069$ | 23 | Szabados (1977)
2442774.8126 | 1975-12-28 | 0.0058 | $PG$ | $4813$ | $-0.0129$ | 67 | DASCH
2443322.6237 | 1977-06-28 | 0.0028 | $V$ | $5232$ | $-0.0262$ | 28 | Alexander et al. (1987)
2444014.2700 | 1979-05-20 | 0.0032 | $V$ | $5761$ | $-0.0236$ | 14 | Harris (1980)
2444381.6592 | 1980-05-22 | 0.0009 | $B$ | $6042$ | $-0.0283$ | 69 | Moffett & Barnes (1984)
2444381.6594 | 1980-05-22 | 0.0007 | $V$ | $6042$ | $-0.0290$ | 69 | Moffett & Barnes (1984)
2444541.1771 | 1980-10-28 | 0.0054 | $PG$ | $6164$ | $-0.0199$ | 79 | DASCH
2445355.7032 | 1983-01-21 | 0.0008 | $B$ | $6787$ | $-0.0381$ | 271 | Alexander et al. (1987)
2445589.7339 | 1983-09-12 | 0.0008 | $V$ | $6966$ | $-0.0427$ | 243 | Alexander et al. (1987)
2445906.1406 | 1984-07-24 | 0.0057 | $PG$ | $7208$ | $-0.0391$ | 74 | DASCH
2447044.9237 | 1987-09-06 | 0.0051 | $PG$ | $8079$ | $-0.0492$ | 79 | DASCH
2448373.2769 | 1991-04-26 | 0.0022 | $V$ | $9095$ | $-0.0710$ | 123 | HIPPARCOS
2448973.3938 | 1992-12-16 | 0.0019 | $V$ | $9554$ | $-0.0759$ | 30 | Arellano Ferro et al. (1998)
2448973.3948 | 1992-12-16 | 0.0014 | $B$ | $9554$ | $-0.0739$ | 30 | Arellano Ferro et al. (1998)
2450846.9550 | 1998-02-02 | 0.0014 | $B$ | $10987$ | $-0.0965$ | 36 | Ignatova & Vozyakova (2000)
2450846.9562 | 1998-02-02 | 0.0021 | $V$ | $10987$ | $-0.0962$ | 36 | Ignatova & Vozyakova (2000)
2452817.2783 | 2003-06-26 | 0.0017 | $V$ | $12494$ | $-0.1085$ | 57 | ASAS-3
2453146.7530 | 2004-05-21 | 0.0025 | $V$ | $12746$ | $-0.1124$ | 32 | ASAS-3
2453518.0686 | 2005-05-27 | 0.0020 | $V$ | $13030$ | $-0.1140$ | 34 | ASAS-3
2453588.6711 | 2005-08-06 | 0.0024 | $V$ | $13084$ | $-0.1141$ | 31 | ASAS-3
2453859.3043 | 2006-05-03 | 0.0029 | $V$ | $13291$ | $-0.1240$ | 27 | ASAS-3
2453898.5334 | 2006-06-12 | 0.0009 | $V$ | $13321$ | $-0.1186$ | 191 | ASAS-3
2454248.9298 | 2007-05-28 | 0.0021 | $V$ | $13589$ | $-0.1200$ | 30 | ASAS-3
2454607.1584 | 2008-05-20 | 0.0031 | $V$ | $13863$ | $-0.1340$ | 26 | ASAS-3
2454641.1614 | 2008-06-23 | 0.0017 | $V$ | $13889$ | $-0.1249$ | 56 | ASAS-3
2454834.6730 | 2009-01-03 | 0.0013 | $V$ | $14037$ | $-0.1166$ | 54 | INTEGRAL-OMC
2456829.8073 | 2014-06-21 | 0.0009 | $V$ | $15563$ | $-0.1583$ | 197 | ASAS-SN
2457199.8099 | 2015-06-26 | 0.0010 | $V$ | $15846$ | $-0.1654$ | 167 | ASAS-SN
2457463.9088 | 2016-03-16 | 0.0014 | $V$ | $16048$ | $-0.1723$ | 100 | ASAS-SN
2457601.1871 | 2016-07-31 | 0.0010 | $V$ | $16153$ | $-0.1768$ | 152 | ASAS-SN
2457865.2877 | 2017-04-21 | 0.0009 | $V$ | $16355$ | $-0.1821$ | 150 | ASAS-SN
2457992.1089 | 2017-08-26 | 0.0011 | $V$ | $16452$ | $-0.1840$ | 89 | ASAS-SN
2458041.7941 | 2017-10-15 | 0.0029 | $g$ | $16490$ | $-0.1821$ | 44 | ASAS-SN
2458176.4653 | 2018-02-26 | 0.0014 | $g$ | $16593$ | $-0.1788$ | 95 | ASAS-SN
2458239.2226 | 2018-04-30 | 0.0017 | $g$ | $16641$ | $-0.1793$ | 96 | ASAS-SN
2458290.2033 | 2018-06-20 | 0.0009 | $V$ | $16680$ | $-0.1894$ | 161 | ASAS-SN
2458334.6661 | 2018-08-04 | 0.0012 | $g$ | $16714$ | $-0.1800$ | 99 | ASAS-SN
2458392.1973 | 2018-09-30 | 0.0014 | $g$ | $16758$ | $-0.1768$ | 87 | ASAS-SN
2458564.7738 | 2019-03-22 | 0.0024 | $g$ | $16890$ | $-0.1844$ | 90 | ASAS-SN
XX Vir |
2413761.7782 | 1896-07-21 | 0.0035 | $PG$ | $-16616$ | $-0.0239$ | 24 | DASCH
2416467.6346 | 1903-12-19 | 0.0031 | $PG$ | $-14609$ | $-0.0148$ | 100 | DASCH
2420293.8485 | 1914-06-10 | 0.0027 | $PG$ | $-11771$ | $-0.0064$ | 114 | DASCH
2424887.1914 | 1927-01-06 | 0.0029 | $PG$ | $-8364$ | $0.0022$ | 138 | DASCH
2427227.6690 | 1933-06-04 | 0.0019 | $PG$ | $-6628$ | $-0.0040$ | 185 | DASCH
2427632.1310 | 1934-07-13 | 0.0007 | $PG$ | $-6328$ | $-0.0034$ | 329 | Oosterhoff (1936)
2429264.8106 | 1939-01-01 | 0.0020 | $PG$ | $-5117$ | $0.0000$ | 310 | DASCH
2430435.0536 | 1942-03-16 | 0.0020 | $PG$ | $-4249$ | $0.0011$ | 80 | Mandel (1970)
2430997.2563 | 1943-09-29 | 0.0018 | $PG$ | $-3832$ | $0.0023$ | 295 | DASCH
2432480.2737 | 1947-10-21 | 0.0025 | $PG$ | $-2732$ | $-0.0057$ | 115 | DASCH
2433450.9861 | 1950-06-18 | 0.0025 | $PG$ | $-2012$ | $-0.0008$ | 90 | DASCH
2437107.3153 | 1960-06-21 | 0.0009 | $B$ | $700$ | $-0.0034$ | 42 | Mitchell et al. (1964)
2437107.3268 | 1960-06-21 | 0.0011 | $V$ | $700$ | $-0.0054$ | 42 | Mitchell et al. (1964)
2439997.8686 | 1968-05-21 | 0.0004 | $B$ | $2844$ | $-0.0015$ | 25 | Bookmeyer et al. (1977)
2439997.8824 | 1968-05-21 | 0.0013 | $V$ | $2844$ | $-0.0012$ | 25 | Bookmeyer et al. (1977)
2440895.7741 | 1970-11-05 | 0.0038 | $PG$ | $3510$ | $-0.0004$ | 25 | DASCH
2443826.7780 | 1978-11-14 | 0.0059 | $V$ | $5684$ | $-0.0075$ | 8 | Harris (1980)
2444340.4364 | 1980-04-10 | 0.0034 | $PG$ | $6065$ | $-0.0018$ | 114 | DASCH
2446404.5375 | 1985-12-05 | 0.0015 | $B$ | $7596$ | $-0.0024$ | 61 | McNamara & Pyne (1994)
2446404.5517 | 1985-12-05 | 0.0018 | $V$ | $7596$ | $-0.0016$ | 61 | McNamara & Pyne (1994)
2446482.7432 | 1986-02-21 | 0.0008 | $V$ | $7654$ | $-0.0060$ | 76 | Loomis et al. (1988)
2446866.9654 | 1987-03-12 | 0.0039 | $PG$ | $7939$ | $-0.0088$ | 67 | DASCH
2454050.2157 | 2006-11-10 | 0.0028 | $V$ | $13267$ | $-0.0079$ | 101 | CSS
2455379.5506 | 2010-07-02 | 0.0021 | $V$ | $14253$ | $-0.0030$ | 92 | CSS
2456214.0831 | 2012-10-13 | 0.0034 | $V$ | $14872$ | $-0.0093$ | 62 | CSS
2456313.8416 | 2013-01-21 | 0.0015 | $V$ | $14946$ | $-0.0180$ | 57 | ASAS-SN
2456900.3120 | 2014-08-30 | 0.0004 | $V$ | $15381$ | $-0.0168$ | 170 | ASAS-SN
2457175.3484 | 2015-06-01 | 0.0011 | $V$ | $15585$ | $-0.0142$ | 128 | ASAS-SN
2457435.5496 | 2016-02-17 | 0.0005 | $V$ | $15778$ | $-0.0165$ | 110 | ASAS-SN
2457569.0225 | 2016-06-29 | 0.0009 | $V$ | $15877$ | $-0.0160$ | 103 | ASAS-SN
2457810.3492 | 2017-02-25 | 0.0005 | $V$ | $16056$ | $-0.0179$ | 111 | ASAS-SN
2457922.2501 | 2017-06-17 | 0.0009 | $V$ | $16139$ | $-0.0180$ | 118 | ASAS-SN
2458139.3023 | 2018-01-20 | 0.0008 | $g$ | $16300$ | $-0.0268$ | 110 | ASAS-SN
2458191.8833 | 2018-03-14 | 0.0004 | $g$ | $16339$ | $-0.0258$ | 110 | ASAS-SN
2458249.8624 | 2018-05-11 | 0.0006 | $V$ | $16382$ | $-0.0195$ | 161 | ASAS-SN
2458280.8638 | 2018-06-11 | 0.0004 | $g$ | $16405$ | $-0.0268$ | 162 | ASAS-SN
2458508.7091 | 2019-01-25 | 0.0004 | $g$ | $16574$ | $-0.0281$ | 100 | ASAS-SN
2458568.0307 | 2019-03-25 | 0.0006 | $g$ | $16618$ | $-0.0276$ | 104 | ASAS-SN
2458568.0307 | 2019-03-25 | 0.0006 | $g$ | $16618$ | $-0.0276$ | 104 | ASAS-SN
KZ Cen |
2412139.3277 | 1892-02-10 | 0.0349 | $PG$ | $-15275$ | $0.6057$ | 18 | DASCH
2414024.0446 | 1897-04-09 | 0.0176 | $PG$ | $-14035$ | $0.5483$ | 20 | DASCH
2415533.2679 | 1901-05-28 | 0.0148 | $PG$ | $-13042$ | $0.4323$ | 37 | DASCH
2416591.1134 | 1904-04-20 | 0.0116 | $PG$ | $-12346$ | $0.3722$ | 61 | DASCH
2417802.4834 | 1907-08-14 | 0.0144 | $PG$ | $-11549$ | $0.3187$ | 37 | DASCH
2418483.3956 | 1909-06-25 | 0.0266 | $PG$ | $-11101$ | $0.2803$ | 24 | DASCH
2419717.5425 | 1912-11-11 | 0.0288 | $PG$ | $-10289$ | $0.2040$ | 14 | DASCH
2420465.4008 | 1914-11-28 | 0.0090 | $PG$ | $-9797$ | $0.2325$ | 33 | DASCH
2420997.3634 | 1916-05-13 | 0.0224 | $PG$ | $-9447$ | $0.2023$ | 21 | DASCH
2421594.7083 | 1918-01-01 | 0.0121 | $PG$ | $-9054$ | $0.1954$ | 34 | DASCH
2422237.6385 | 1919-10-06 | 0.0107 | $PG$ | $-8631$ | $0.1744$ | 44 | DASCH
2423401.8983 | 1922-12-13 | 0.0193 | $PG$ | $-7865$ | $0.1301$ | 28 | DASCH
2424108.7184 | 1924-11-19 | 0.0256 | $PG$ | $-7400$ | $0.1599$ | 49 | DASCH
2424665.0129 | 1926-05-29 | 0.0277 | $PG$ | $-7034$ | $0.1419$ | 20 | DASCH
2425534.3823 | 1928-10-14 | 0.0110 | $PG$ | $-6462$ | $0.0833$ | 57 | DASCH
2426826.3695 | 1932-04-28 | 0.0104 | $PG$ | $-5612$ | $0.0880$ | 33 | DASCH
2427750.5052 | 1934-11-09 | 0.0138 | $PG$ | $-5004$ | $0.0764$ | 55 | DASCH
2428461.8158 | 1936-10-20 | 0.0122 | $PG$ | $-4536$ | $0.0367$ | 52 | DASCH
2429036.3619 | 1938-05-17 | 0.0121 | $PG$ | $-4158$ | $0.0306$ | 46 | DASCH
2429382.9298 | 1939-04-29 | 0.0100 | $PG$ | $-3930$ | $0.0433$ | 55 | DASCH
2429744.6756 | 1940-04-25 | 0.0098 | $PG$ | $-3692$ | $0.0341$ | 47 | DASCH
2430235.6173 | 1941-08-29 | 0.0078 | $PG$ | $-3369$ | $0.0225$ | 112 | DASCH
2430823.8547 | 1943-04-09 | 0.0148 | $PG$ | $-2982$ | $0.0279$ | 41 | DASCH
2431211.4461 | 1944-04-30 | 0.0092 | $PG$ | $-2727$ | $0.0246$ | 79 | DASCH
2431576.2239 | 1945-04-30 | 0.0114 | $PG$ | $-2487$ | $0.0074$ | 60 | DASCH
2431944.0651 | 1946-05-03 | 0.0124 | $PG$ | $-2245$ | $0.0136$ | 69 | DASCH
2432453.2514 | 1947-09-24 | 0.0081 | $PG$ | $-1910$ | $0.0069$ | 133 | DASCH
2433017.1442 | 1949-04-10 | 0.0124 | $PG$ | $-1539$ | $-0.0127$ | 49 | DASCH
2433617.5746 | 1950-12-02 | 0.0125 | $PG$ | $-1144$ | $0.0260$ | 31 | DASCH
2435228.7452 | 1955-05-01 | 0.0301 | $V$ | $-84$ | $0.0210$ | 7 | Irwin (1961)
2435228.7566 | 1955-05-01 | 0.0657 | $B$ | $-84$ | $0.0300$ | 7 | Irwin (1961)
2444059.8938 | 1979-07-05 | 0.0175 | $PG$ | $5726$ | $0.0877$ | 42 | DASCH
2445073.7337 | 1982-04-14 | 0.0005 | $V$ | $6393$ | $0.1040$ | 171 | Petersen & Hansen (1984)
2445073.7339 | 1982-04-14 | 0.0005 | $B$ | $6393$ | $0.1017$ | 170 | Petersen & Hansen (1984)
2445969.0148 | 1984-09-25 | 0.0128 | $PG$ | $6982$ | $0.1148$ | 43 | DASCH
2446051.1029 | 1984-12-16 | 0.0018 | $V$ | $7036$ | $0.1265$ | 9 | Diethelm (1986)
2446051.1037 | 1984-12-16 | 0.0013 | $B$ | $7036$ | $0.1248$ | 9 | Diethelm (1986)
2446744.2247 | 1986-11-09 | 0.0129 | $PG$ | $7492$ | $0.1353$ | 33 | DASCH
2446871.9139 | 1987-03-17 | 0.0093 | $PG$ | $7576$ | $0.1462$ | 77 | DASCH
2451979.2030 | 2001-03-10 | 0.0045 | $V$ | $10936$ | $0.3075$ | 80 | ASAS-SN
2452543.1264 | 2002-09-25 | 0.0084 | $V$ | $11307$ | $0.3187$ | 22 | ASAS-SN
2452859.2930 | 2003-08-07 | 0.0026 | $V$ | $11515$ | $0.3296$ | 159 | ASAS-SN
2453485.5410 | 2005-04-25 | 0.0047 | $V$ | $11927$ | $0.3461$ | 66 | ASAS-SN
2453815.3988 | 2006-03-20 | 0.0052 | $V$ | $12144$ | $0.3684$ | 68 | ASAS-SN
2454218.2128 | 2007-04-27 | 0.0051 | $V$ | $12409$ | $0.3879$ | 65 | ASAS-SN
2454575.4186 | 2008-04-18 | 0.0038 | $V$ | $12644$ | $0.3986$ | 82 | ASAS-SN
2454926.5579 | 2009-04-05 | 0.0054 | $V$ | $12875$ | $0.4227$ | 64 | ASAS-SN
2456966.4488 | 2014-11-04 | 0.0009 | $V$ | $14217$ | $0.5015$ | 180 | ASAS-SN
2457167.0958 | 2015-05-24 | 0.0009 | $V$ | $14349$ | $0.5112$ | 76 | ASAS-SN
2457416.3860 | 2016-01-28 | 0.0009 | $V$ | $14513$ | $0.5249$ | 140 | ASAS-SN
2457557.7502 | 2016-06-18 | 0.0010 | $V$ | $14606$ | $0.5309$ | 88 | ASAS-SN
2457782.7184 | 2017-01-29 | 0.0009 | $V$ | $14754$ | $0.5422$ | 140 | ASAS-SN
2457908.8838 | 2017-06-04 | 0.0009 | $V$ | $14837$ | $0.5493$ | 156 | ASAS-SN
2458130.8059 | 2018-01-12 | 0.0008 | $g$ | $14983$ | $0.5545$ | 100 | ASAS-SN
2458177.9291 | 2018-02-28 | 0.0008 | $g$ | $15014$ | $0.5583$ | 100 | ASAS-SN
2458188.5724 | 2018-03-11 | 0.0009 | $V$ | $15021$ | $0.5617$ | 202 | ASAS-SN
2458222.0082 | 2018-04-13 | 0.0010 | $g$ | $15043$ | $0.5580$ | 99 | ASAS-SN
2458290.4128 | 2018-06-20 | 0.0007 | $g$ | $15088$ | $0.5635$ | 172 | ASAS-SN
2458480.4191 | 2018-12-27 | 0.0007 | $g$ | $15213$ | $0.5725$ | 150 | ASAS-SN
2458536.6604 | 2019-02-22 | 0.0006 | $g$ | $15250$ | $0.5745$ | 150 | ASAS-SN
2458576.1820 | 2019-04-02 | 0.0009 | $g$ | $15276$ | $0.5767$ | 148 | ASAS-SN
V745 Oph |
2413362.5270 | 1895-06-18 | 0.1197 | $PG$ | $-14178$ | $10.4186$ | 4 | DASCH
2413789.9750 | 1896-08-18 | 0.0139 | $PG$ | $-13910$ | $10.3788$ | 6 | DASCH
2414591.2173 | 1898-10-28 | 0.0148 | $PG$ | $-13407$ | $9.2839$ | 7 | DASCH
2415187.6688 | 1900-06-17 | 0.0113 | $PG$ | $-13033$ | $9.1665$ | 4 | DASCH
2415880.6617 | 1902-05-11 | 0.0529 | $PG$ | $-12598$ | $8.2893$ | 5 | DASCH
2416270.9350 | 1903-06-05 | 0.0110 | $PG$ | $-12353$ | $7.7621$ | 7 | DASCH
2417410.5773 | 1906-07-19 | 0.0184 | $PG$ | $-11638$ | $6.9052$ | 5 | DASCH
2418309.7250 | 1909-01-03 | 0.0082 | $PG$ | $-11074$ | $6.4143$ | 5 | DASCH
2420217.5768 | 1914-03-26 | 0.0085 | $PG$ | $-9877$ | $4.9269$ | 7 | DASCH
2421483.6332 | 1917-09-12 | 0.0190 | $PG$ | $-9083$ | $4.4709$ | 5 | DASCH
2423707.1064 | 1923-10-14 | 0.0103 | $PG$ | $-7688$ | $2.7742$ | 10 | DASCH
2424409.0761 | 1925-09-15 | 0.0210 | $PG$ | $-7248$ | $2.8983$ | 7 | DASCH
2424710.3520 | 1926-07-13 | 0.0144 | $PG$ | $-7059$ | $2.6996$ | 10 | DASCH
2425735.4703 | 1929-05-03 | 0.0147 | $PG$ | $-6416$ | $2.1661$ | 8 | DASCH
2427039.8129 | 1932-11-28 | 0.0115 | $PG$ | $-5598$ | $1.7138$ | 7 | DASCH
2427648.8494 | 1934-07-30 | 0.0060 | $PG$ | $-5216$ | $1.4206$ | 38 | DASCH
2427990.0895 | 1935-07-06 | 0.0058 | $PG$ | $-5002$ | $1.3085$ | 28 | DASCH
2428326.5944 | 1936-06-07 | 0.0066 | $PG$ | $-4791$ | $1.2465$ | 30 | DASCH
2428698.1951 | 1937-06-13 | 0.0073 | $PG$ | $-4558$ | $1.1880$ | 17 | DASCH
2429093.5450 | 1938-07-14 | 0.0067 | $PG$ | $-4310$ | $0.9522$ | 23 | DASCH
2429436.3147 | 1939-06-21 | 0.0117 | $PG$ | $-4095$ | $0.7745$ | 16 | DASCH
2429757.0430 | 1940-05-07 | 0.0098 | $PG$ | $-3894$ | $0.8870$ | 12 | DASCH
2429843.0930 | 1940-08-01 | 0.0102 | $PG$ | $-3840$ | $0.8014$ | 15 | DASCH
2430170.0167 | 1941-06-24 | 0.0091 | $PG$ | $-3635$ | $0.7288$ | 19 | DASCH
2430170.0167 | 1941-06-24 | 0.0091 | $PG$ | $-3635$ | $0.7288$ | 19 | DASCH
2430498.4792 | 1942-05-18 | 0.0129 | $PG$ | $-3429$ | $0.5999$ | 9 | DASCH
2430830.1848 | 1943-04-15 | 0.0067 | $PG$ | $-3221$ | $0.5240$ | 8 | DASCH
2431260.8527 | 1944-06-19 | 0.0078 | $PG$ | $-2951$ | $0.5138$ | 16 | DASCH
2431613.0968 | 1945-06-06 | 0.0095 | $PG$ | $-2730$ | $0.2400$ | 13 | DASCH
2431986.4350 | 1946-06-14 | 0.0076 | $PG$ | $-2496$ | $0.3239$ | 20 | DASCH
2432351.6846 | 1947-06-15 | 0.0063 | $PG$ | $-2267$ | $0.2947$ | 25 | DASCH
2432699.3630 | 1948-05-27 | 0.0115 | $PG$ | $-2049$ | $0.2405$ | 14 | DASCH
2433072.6334 | 1949-06-05 | 0.0071 | $PG$ | $-1815$ | $0.2566$ | 17 | DASCH
2433463.2384 | 1950-06-30 | 0.0119 | $PG$ | $-1570$ | $0.0612$ | 11 | DASCH
2433814.1969 | 1951-06-16 | 0.0124 | $PG$ | $-1350$ | $0.0968$ | 8 | DASCH
2434085.2465 | 1952-03-13 | 0.0139 | $PG$ | $-1180$ | $-0.0212$ | 8 | DASCH
2434085.2465 | 1952-03-13 | 0.0139 | $PG$ | $-1180$ | $-0.0212$ | 8 | DASCH
2436910.2533 | 1959-12-07 | 0.0031 | $PGV$ | $591$ | $0.0801$ | 7 | Mandel (1970)
2437718.9536 | 1962-02-23 | 0.0050 | $PGV$ | $1098$ | $0.0628$ | 8 | Mandel (1970)
2437900.7784 | 1962-08-24 | 0.0030 | $VIS$ | $1212$ | $0.0458$ | 19 | Mandel (1970)
2438647.3305 | 1964-09-08 | 0.0034 | $PGV$ | $1680$ | $0.0893$ | 14 | Mandel (1970)
2440413.3918 | 1969-07-10 | 0.0106 | $PG$ | $2787$ | $0.3472$ | 9 | DASCH
2441287.6601 | 1971-12-02 | 0.0095 | $PG$ | $3335$ | $0.4986$ | 9 | DASCH
2441761.5661 | 1973-03-20 | 0.0045 | $V$ | $3632$ | $0.6823$ | 40 | Kwee & Diethelm (1984)
2441780.7308 | 1973-04-08 | 0.0060 | $B$ | $3644$ | $0.6823$ | 37 | Kwee & Diethelm (1984)
2442441.2786 | 1975-01-28 | 0.0143 | $PG$ | $4058$ | $0.8571$ | 10 | DASCH
2442934.2248 | 1976-06-04 | 0.0241 | $PG$ | $4367$ | $0.9163$ | 8 | DASCH
2443314.0155 | 1977-06-19 | 0.0143 | $PG$ | $4605$ | $1.0722$ | 8 | DASCH
2443314.0155 | 1977-06-19 | 0.0143 | $PG$ | $4605$ | $1.0722$ | 8 | DASCH
2443778.2868 | 1978-09-26 | 0.0090 | $PG$ | $4896$ | $1.1683$ | 12 | DASCH
2444569.7789 | 1980-11-26 | 0.0122 | $PG$ | $5392$ | $1.4890$ | 8 | DASCH
2444817.0688 | 1981-07-31 | 0.1301 | $PG$ | $5547$ | $1.5378$ | 5 | DASCH
2445279.8278 | 1982-11-06 | 0.0091 | $PG$ | $5837$ | $1.7166$ | 18 | DASCH
2445839.8933 | 1984-05-19 | 0.0096 | $PG$ | $6188$ | $1.9007$ | 17 | DASCH
2446232.5267 | 1985-06-16 | 0.0179 | $PG$ | $6434$ | $2.1386$ | 13 | DASCH
2446612.3828 | 1986-06-30 | 0.0133 | $PG$ | $6672$ | $2.3600$ | 13 | DASCH
2446987.3897 | 1987-07-10 | 0.0082 | $PG$ | $6907$ | $2.5174$ | 8 | DASCH
2447617.7538 | 1989-04-01 | 0.0122 | $PG$ | $7302$ | $2.8156$ | 8 | DASCH
2453876.0563 | 2006-05-20 | 0.0206 | $V$ | $11223$ | $6.7395$ | 23 | INTEGRAL-OMC
2454566.1551 | 2008-04-09 | 0.0159 | $V$ | $11655$ | $7.7534$ | 18 | INTEGRAL-OMC
2454645.3459 | 2008-06-27 | 0.0030 | $V$ | $11705$ | $7.1891$ | 16 | CSS
2454841.9214 | 2009-01-10 | 0.0164 | $V$ | $11828$ | $7.5667$ | 13 | CSS
2455101.8873 | 2009-09-27 | 0.0243 | $V$ | $11991$ | $7.5308$ | 14 | INTEGRAL-OMC
2456049.9321 | 2012-05-02 | 0.0384 | $V$ | $12585$ | $8.0838$ | 16 | CSS
2456115.5025 | 2012-07-07 | 0.0104 | $V$ | $12626$ | $8.2550$ | 23 | ASAS-SN
2456115.7236 | 2012-07-07 | 0.0068 | $V$ | $12626$ | $8.4761$ | 24 | CSS
2456342.3866 | 2013-02-18 | 0.0249 | $g$ | $12768$ | $8.6344$ | 8 | Chambers et al. (2016)
2456465.1982 | 2013-06-21 | 0.0029 | $V$ | $12845$ | $8.6230$ | 70 | ASAS-SN
2456790.8710 | 2014-05-13 | 0.0031 | $V$ | $13049$ | $8.8946$ | 70 | ASAS-SN
2456901.0270 | 2014-08-31 | 0.0029 | $V$ | $13118$ | $8.9885$ | 67 | ASAS-SN
2457110.1646 | 2015-03-28 | 0.0034 | $V$ | $13249$ | $9.1674$ | 93 | ASAS-SN
2457229.8946 | 2015-07-26 | 0.0024 | $V$ | $13324$ | $9.2646$ | 95 | ASAS-SN
2457461.3797 | 2016-03-13 | 0.0024 | $V$ | $13469$ | $9.4597$ | 121 | ASAS-SN
2457606.6689 | 2016-08-06 | 0.0027 | $V$ | $13560$ | $9.5945$ | 125 | ASAS-SN
2457844.5385 | 2017-04-01 | 0.0027 | $V$ | $13709$ | $9.7936$ | 115 | ASAS-SN
2457969.0712 | 2017-08-03 | 0.0035 | $V$ | $13787$ | $9.9082$ | 126 | ASAS-SN
2458184.6170 | 2018-03-07 | 0.0027 | $g$ | $13922$ | $10.1150$ | 139 | ASAS-SN
2458218.1310 | 2018-04-09 | 0.0046 | $V$ | $13943$ | $10.1318$ | 67 | ASAS-SN
2458282.0089 | 2018-06-12 | 0.0025 | $g$ | $13983$ | $10.2056$ | 135 | ASAS-SN
2458304.3379 | 2018-07-04 | 0.0034 | $V$ | $13997$ | $10.2031$ | 71 | ASAS-SN
2458379.3699 | 2018-09-17 | 0.0041 | $V$ | $14044$ | $10.2652$ | 22 | ASAS-SN
2458419.3105 | 2018-10-27 | 0.0044 | $g$ | $14069$ | $10.3282$ | 62 | ASAS-SN
2458567.7945 | 2019-03-25 | 0.0034 | $g$ | $14162$ | $10.4676$ | 58 | ASAS-SN
V439 Oph |
2413120.8627 | 1894-10-19 | 0.0087 | $PG$ | $-11615$ | $0.2469$ | 13 | DASCH
2415417.0420 | 1901-02-01 | 0.0061 | $PG$ | $-10402$ | $0.2257$ | 29 | DASCH
2416798.8860 | 1904-11-14 | 0.0048 | $PG$ | $-9672$ | $0.1850$ | 40 | DASCH
2422273.3222 | 1919-11-10 | 0.0063 | $PG$ | $-6780$ | $0.0855$ | 140 | DASCH
2426172.8662 | 1930-07-15 | 0.0060 | $PG$ | $-4720$ | $0.0640$ | 42 | DASCH
2426574.1821 | 1931-08-20 | 0.0082 | $VIS$ | $-4508$ | $0.0559$ | 50 | Tsesevich (1952)
2427543.3797 | 1934-04-15 | 0.0062 | $PG$ | $-3996$ | $0.0506$ | 88 | DASCH
2428151.0264 | 1935-12-14 | 0.0058 | $PG$ | $-3675$ | $0.0466$ | 111 | DASCH
2428944.1601 | 1938-02-14 | 0.0080 | $PG$ | $-3256$ | $0.0163$ | 84 | DASCH
2429814.9538 | 1940-07-04 | 0.0057 | $PG$ | $-2796$ | $0.0332$ | 119 | DASCH
2430337.4285 | 1941-12-08 | 0.0088 | $PG$ | $-2520$ | $0.0419$ | 17 | SAI (this paper)
2431105.9344 | 1944-01-16 | 0.0057 | $PG$ | $-2114$ | $-0.0074$ | 157 | DASCH
2432177.3898 | 1946-12-22 | 0.0087 | $PG$ | $-1548$ | $0.0140$ | 78 | DASCH
2432894.8408 | 1948-12-09 | 0.0065 | $PG$ | $-1169$ | $0.0207$ | 94 | DASCH
2433739.1133 | 1951-04-02 | 0.0078 | $PG$ | $-723$ | $0.0183$ | 86 | DASCH
2437439.8443 | 1961-05-20 | 0.0052 | $PGV$ | $1232$ | $-0.0614$ | 122 | Mandel (1970)
2438810.4112 | 1965-02-18 | 0.0057 | $B$ | $1956$ | $-0.0119$ | 21 | Sturch (1966)
2438818.0126 | 1965-02-26 | 0.0035 | $V$ | $1960$ | $0.0081$ | 22 | Sturch (1966)
2442056.9553 | 1974-01-09 | 0.0051 | $PG$ | $3671$ | $0.0493$ | 46 | DASCH
2443673.5826 | 1978-06-14 | 0.0062 | $B$ | $4525$ | $0.0607$ | 22 | Henden (1980)
2443675.4881 | 1978-06-15 | 0.0027 | $V$ | $4526$ | $0.0636$ | 20 | Henden (1980)
2443775.7689 | 1978-09-24 | 0.0045 | $PG$ | $4579$ | $0.0254$ | 98 | SAI (this paper)
2444065.4552 | 1979-07-10 | 0.0114 | $V$ | $4732$ | $0.0742$ | 6 | Diethelm & Tammann (1982)
2444067.3706 | 1979-07-12 | 0.0204 | $B$ | $4733$ | $0.1061$ | 8 | Diethelm & Tammann (1982)
2446058.7600 | 1984-12-24 | 0.0076 | $PG$ | $5785$ | $0.0669$ | 120 | DASCH
2457083.7467 | 2015-03-02 | 0.0026 | $V$ | $11609$ | $0.2532$ | 162 | ASAS-SN
2457468.0424 | 2016-03-20 | 0.0033 | $V$ | $11812$ | $0.2714$ | 90 | ASAS-SN
2457602.4414 | 2016-08-01 | 0.0034 | $V$ | $11883$ | $0.2679$ | 93 | ASAS-SN
2457914.7930 | 2017-06-10 | 0.0022 | $V$ | $12048$ | $0.2756$ | 181 | ASAS-SN
2458223.3601 | 2018-04-14 | 0.0044 | $V$ | $12211$ | $0.2848$ | 90 | ASAS-SN
2458276.3162 | 2018-06-06 | 0.0012 | $g$ | $12239$ | $0.2371$ | 90 | ASAS-SN
2458327.4767 | 2018-07-27 | 0.0032 | $V$ | $12266$ | $0.2868$ | 103 | ASAS-SN
2458367.1816 | 2018-09-05 | 0.0022 | $g$ | $12287$ | $0.2389$ | 84 | ASAS-SN
2458564.0546 | 2019-03-21 | 0.0015 | $g$ | $12391$ | $0.2406$ | 118 | ASAS-SN