# Anomalous Cepheids discovered in a sample of Galactic short period Type II
Cepheids

Serb. Astron. J. ˝ 183 (2011), 1 - 25

Editorial

M. I. Jurkovic1,2

1Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia

E–mail<EMAIL_ADDRESS>
2Konkoly Thege Miklós Astronomical Institute, Research Centre for Astronomy
and Earth Sciences, Hungarian Academy of SciencesH-1121 Budapest, Konkoly
Thege Miklós út 15-17.

(Received: xxxx xx, 2018; Accepted: xxxx xx, 2018)

SUMMARY: We revisited the short period Type II Cepheids (T2Cs), called the BL
Herculis (BLHs), in the Galactic Field to derive a homogeneous analysis of
their Fourier parameters. Only V-band data were compiled to make sure that it
was directly comparable between the known variables of the OGLE-III catalogue
and the 59 individual objects classified as short period Type II Cepheids in
the General Catalogue of Variable Stars (GCVS) we had in our sample. The
derived Fourier parameters were used to make the distinction between different
classes of variables. From the 59 stars we found 19 BLHs, 19 fundamental mode
Anomalous Cepheids (ACs) (8 of them were already known from the Catalina Sky
Survey (CSS)), 1 first overtone AC, 2 were found to be possible peculiar W
Virginis (pWVir), 11 classical Cepheids (DCEPs), and 7 stars were not
pulsating variables at all. As a result we created a list of bright BLH stars
in the Galactic Field, and separated the ACs, as well as other objects that
were misclassified. The number of true BLHs decreased in our sample by more
than 50%. We gathered the metallicity from spectroscopic measurements
published in the literature. While the number of actual measurements is low,
it is highly suggestive that ACs are metal poor. The mean metallicity from 8
measurements in 4 stars (UY Eri having 5 different [Fe/H] data points) is
-1.12 dex, but if the higher value metallicity outliers of UY Eri are left out
the mean metallicity becomes -1.88 dex, regardless if the AC is in the Milky
Way itself or in a cluster. On the other hand, BLHs seem to have a Solar-like
metallicity of 0 dex averaged from 21 measurements of 10 stars.

Key words. Stars: variables: Cepheids – Stars: Population II

##  1 1\. INTRODUCTION

The short period Type II Cepheids (T2Cs), called BL Herculis (BLH) subtype,
are low mass ($\approx$ 0.5 - 0.6 M⊙) pulsating stars, with periods between 1
- 4 days. BLHs pulsate only in the fundamental mode (F). A summary of these
objects was given in Wallerstein (2002) and Catelan & Smith (2015). In the
past the General Catalogue of Variable Stars
(GCVS111http://www.sai.msu.su/gcvs/gcvs/, Samus et al. 2009a, Samus et al.
2018) was the biggest source of the classification of variable stars, but with
the emergence of the big sky observing programs their lists became somewhat
outdated, so we decided to revisit the BLHs subtype to see how they compare
with the other datasets. In the GCVS the BLHs are marked with ”CWB” and
candidates with ”CWB:”. The boarder between the short period and longer period
W Virginis (CWA) stars was put at 8 days, which got outdated by the results of
the T2Cs from the Optical Gravitational Lensing Experiment III (OGLE-III)
catalogue (Soszyński et al. 2008, 2010b, 2011b). In the latest OGLE-IV
catalogue composed of stars in the Galactic bulge (Soszyński et al. 2017) the
border between BLHs and WVir stars was moved from 4 to 5 days for the Bulge.

Anomalous Cepheids (ACs) are stars which have similar period range ($0.24-4$
days), but their masses are higher 1.2-1.8 M⊙. In the instability strip (IS)
of the Herztsprung-Russell diagram (HRD) they are just above the T2Cs, see
Bono et al. (1997b), Fiorentino et al. (2006), Groenewegen and Jurkovic
(2017b). ACs pulsate in the fundamental mode (F) and in the first overtone
(1O). In the OGLE-III catalogue we have seen (Soszyński et al. 2008, 2010b,a)
that T2Cs and ACs form a different Period-Luminosity ($PL$) relations in the
LMC and SMC. Groenewegen and Jurkovic (2017a,b) confirmed this in their papers
calculating the luminosities ($L$), effective temperatures ($T_{\rm eff}$),
masses ($M$), radii ($R$) and the bolometric $PL$ relation for the T2Cs and
ACs in the LMC and SMC. The number ACs identified in the LMC and SMC in the
OGLE-IV catalogue is 174 F and 76 1O pulsators. In Soszyński et al. (2017) the
number of identified ACs in the Galactic bulge has risen to 20 (19 F and 1
1O).

In Catelan and Smith (2015) it is stated that most of ACs have been discovered
in dwarf spheroidal galaxies, in the Magellanic Clouds (MCs), and a few in
globular clusters, but only a handful in the Milky Way (MW). The whole
subgroup of ACs is also know as BLBOO in the GCVS, and it was named after the
variable BL Bootis, which was considered to be the only AC in the MW, and it
turned out to be a member of the galactic globular cluster NGC 5466. The
discovery was made by Zinn and Dahn (1976), and studied in detail e.g. by
McCarthy and Nemec (1997), Nemec and McCarthy (1998). Szabados et al. (2007)
published a detailed study of XZ Ceti, confirming it to be a 1O AC, making it
the second AC discovered in the MW.

Articles in the literature about T2Cs might further complicate the
understanding of the classification, since the derived properties of these
variables were interpreted differently. We give a short overview of these
papers, but a longer summary is given in Catelan and Smith (2015). Diethelm
(1983) has published a classification of pulsating stars based on the shape of
their light curves. V716 Oph, BF Ser, CE Her, VX Cap, XX Vir, EK Del, UY Eri
and UX Nor were labelled RR Lyrae Type d (RRd). Petersen and Diethelm (1986)
concluded that the properties of the T2Cs known at that time is not uniform,
and the stars known as RRds are singled out as forming a different group. To
make things more complicated the nomenclature of the RR Lyrae (RRL) variables
has added a subclass also called RRd, which describes an RRL simultaneously
pulsating in the F and 1O, with a period ratio of $0.745$, and the upper limit
of the RRL variables is established to be at 1 day (e.g. see Catelan and Smith
(2015)).

The Catalina Sky Survey (CSS), see Drake et al. (2014a), published their
catalogue and they have detected 64 ACs in total Drake et al. (2014b). The
following six stars overlap with our BLH sample: FY Vir, BF Ser, VX Cap, XX
Vir, V1149 Her, and V716 Oph. Then in 2017 they published a new Catalina
Southern Survey (Drake et al. 2017) with additional 153 ACs, and two more
stars overlapped with our sample: V563 Cen and BI Tel. Most recently Soszyński
et al. (2017) added 20 new ACs detected in toward the Galactic center by the
OGLE-IV program.

Wallerstein (2002) dealt with the question of metallicities of T2Cs. Most of
the data available at that point were estimated from different photometric
systems (Diethelm 1990, Harris 1981). Nevertheless, there was a separation
between a group of stars that were very metal-poor, and the once that had
metallicities larger than $-$0.3.

We have looked into 128 stars in the GCVS, but found V-band data for only 59
stars that were previously classified in the GCVS as CWB stars. Applying the
Fourier analysis, and comparing our results to the V-band dataset of ACs and
T2Cs in the LMC from OGLE-III we reclassified the above mentioned 59 stars
comparing their Fourier parameters to the OGLE-III sample. We have made clear
which of these objects are known cluster members (open and globular), since
their evolution can be linked to the history of the evolution of the clusters
that is separate from the individual stars in the Galaxy. The
spectroscopically measured metallicites, as well as, other derived physical
parameters were gathered from the literature. These two variable types are
important to be separated, since they do have significantly different ages, as
a result of having different initial masses, and the clearance on their true
numbers in the MW should be useful to future research in variety of fields,
for example in the evolutionary modelling of stars or understanding the star
formation history of our Galaxy. T2Cs are old objects making it possible to
constrain some early star forming regions to a specific metallicity content
helping future galactic evolution modelling. Because the origin of ACs is
still not clear - they could be either a result of interacting binaries or
they could have come from single star evolution - their contribution to
galactic archaeology is not that straightforward, but because they are found
in dwarf spheroidal and irregular galaxies as well as spiral galaxies (such as
the MW or the LMC) and sometimes in globular cluster and they are metal-poor
they could give an insight to the intermediate-age (1-6 Gyrs) star formation
mechanism in these systems.

##  2 2\. THE DATA

The comparison sample was taken from the OGLE-III catalog for the LMC BLHs and
ACs. The Fourier parameters published in the online catalogue are derived from
the I-band data, so we have collected the OGLE-III Soszyński et al. (2008,
2010b) V-band data and did the Fourier analysis ourselves.

In the Milky Way we have stared with the 128 star classified in the GCVS as
short period T2Cs or possible T2Cs. We were able to find datasets for 59 stars
in that list. We have collected the available data from the All Sky Automated
Survey (ASAS-3222http://www.astrouw.edu.pl/asas/),see Pojmanski (1997), in
V-band for 34 stars. This search did not include all the objects in the GCVS
list, so additional light curve data were collected from various publicly
available databases: CSS333http://nesssi.cacr.caltech.edu/DataRelease/ (Drake
et al. 2009, 2014), INTEGRAL444https://sdc.cab.inta-csic.es/omc/ and
individual published papers, such as Berdnikov (2008), Henden (1980), Kwee and
Diethelm (1984), Schmidt and Reiswig (1993), Schmidt et al. (2005), Soszyński
et al. (2011b), and in one case data from the American Association of Variable
Star Observers (AAVSO555https://www.aavso.org/). We have added the source of
the data for each star in the Appendix Table A.1.

While there are other sources (for example the
SuperWASP666http://www.superwasp.org/), with very good data, we could not use
it for our comparative Fourier analysis, because they were collected in a
broad band or no filter.

##  3 3\. THE FOURIER ANALYSIS AND CLASSIFICATION PROCEDURE

We have used the Period04 program (Lenz and Breger 2004), which uses this
equation (Eq. 1):

$A=Z+\sum A_{i}sin(2\Pi(\omega_{i}t+\phi_{i})).$ (1)

We have proceeded to get the Fourier parameters, defined by these equations:

$R_{i1}=\frac{A_{i}}{A_{1}},$ (2)

and

$\phi_{i1}=\phi_{i}-i\phi_{1},$ (3)

where $i=2,3$, for the light curve analysis.

This kind of Fourier decomposition was presented by Petersen and Diethelm
(1986) based on the amplitude ratio ($R_{i1}$) and phase differences
($\phi_{i1}$) defined in Simon and Lee (1981). It is a useful tool for the
automation of the classification.

With the publication of the OGLE-III data, a long spanning precise photometric
information became available, making it possible to compare other stars to the
known variables of the OGLE sample. We have concentrated our attention on the
LMC dataset, because the Wessenheit index vs. log P for T2Cs and the F and 1O
ACs separate very clearly (this is true for the SMC too, but we omitted that
sample, because the number of AC was much smaller than in the LMC). When we go
back to the Fourier parameters, we can be assured that this is a good
indication of the type, and this is the sample we have compared our 59 Field
stars against. All the Fourier parameters were converted to match the once
from the OGLE-III catalogue.

The calculated values of the Fourier parameters are given in Appendix, see
Tables A.1, A.2 and A.3. The Fourier parameters are plotted in Figs. 1a, 1b,
1c, 1d. The ACs from the OGLE-III LMC sample and from the MW are plotted with
purple, while the BLH from both datasets are green, to help the reader
distinguish between the types of the Fourier parameter plots. The DCEPs are
dark grey, and the possible pWVirs stars are orange.

In addition to the Fourier parameters we have looked into the amplitudes of
the detected harmonics ($A_{2}$ and $A_{3}$). Figs. 2 and 3 show how the T2Cs
and ACs separate for the LMC and Galactic stars (the color coding is the same
as in Figs. 1a, 1b, 1c and 1d). ACs have higher harmonic frequency amplitudes
than T2Cs. There are a few stars that are overlapping. In the case of BQ CrA
and V745 Oph this can be a consequence of the noisy data set that was used for
the Fourier analysis. In the case of UY Eri the discrepancy in the Figs. 2 and
3 is attributable to the behaviour of the star.

The classification is based on an iterative process. Since the the OGLE BLHs
and ACs are separated on their period-luminosity relation, we took their
Fourier parameters as a comparison sample. To make sure that all the Fourier
parameters are homogeneous we have used only V-band data for each examined
star. The first step was to see where the OGLE LMC and MW stars overlap on all
the six Fourier parameter plots. The $\phi_{21}$ parameter was the least
helpful in distinguishing these types. This method,, however, does not give a
clear classification for each object, since the Fourier parameters overlap in
some cases. For this reason we did not apply any statistical criteria for the
classification. Instead, when the classification of an object was not clear we
looked at the light curve shape visually to confirm the result, and
furthermore reviewed the previously published literature for individual stars
to verify the result. The BLHs and ACs separated most clearly on the Figs. 2
and 3. In the cases where we felt that a star showed some peculiarities we
have expanded our finding in individual paragraph.

(a)

(b)

(c)

(d)

Fig. 1. The logarithm of the periods are plotter against the Fourier
parameters $R_{21}$, $R_{31}$, $\phi_{21}$ and $\phi_{31}$ with their errors.
The same color indicates the same classes for variables from the OGLE LMC and
from the MW. The OGLE LMC BLHs are plotted in green crosses, the MW BLHs are
green squares. The purple crosses represent the OGLE LMC AC F stars, the OGLE
LMC AC 1O purple stars, the MW AC F are plotted as purple filled squares and
MW AC 1O star is plotted as a purple circle. The MW DCEP are plotted as dark
grey circles. Orange dotted triangles stand for possible pWVir stars.

Fig. 2. Log $P$ vs. $A_{2}$ for the stars in the LMC. The description is the
same as in Fig. 1.

Fig. 3. Log $P$ vs. $A_{3}$ for the stars in the Field. The description is the
same as in Fig. 1.

(a) FY Aqr

(b) V563 Cen

(c) FY Vir

(d) PP Tel

(e) V716 Oph

(f) DF Hyi

(g) BH Cet

(h) BF Ser

(i) BI Tel

(j) V2733 Oph

(k) CE Her

(l) VX Cap

(m) XX Vir

(n) V1149 Her

(o) MQ Aql

(p) UY Eri

(q) UX Nor

Fig. 4. The phased light curves of ACs in the MW with photometric errors.

##  4 4\. RESULTS

Here we give the results of our analysis, separating each star into the their
variable class, and giving additional details about them when necessary. It is
important treat variable stars which are members of a globular or an open
cluster separately from the individual stars in the MW, because we need to
differentiate initial conditions at the birth of these stars, and the
evolutionary processes that take place in these objects from those in the
Galaxy. Contaminating the Galactic sample with these variables is going to
influence our understanding of MW evolution itself, and lessen our knowledge
about the clusters.

###  4.1 4.1. The anomalous Cepheids

Soszyński et al. (2011a) and Soszyński et al. (2011b) show in their variable
star distribution that the 1 days limit they have adopted for making a
differentiation between the RRLs and T2Cs is well founded in the observations.
The ACs bridge the span of both these variable types, as well as the DCEPs.
The problem in the MW sample is that it is much more difficult to disentangle
each of these variables on a $PL$ relation, since the reddening is changing
significantly in different directions. This is why examination of the
properties of the light curves is the best way to proceed.

The CSS (Drake et al. 2014a) used the Stetson variability index ($J_{WS}$) to
identify the variability of the observed objects, and than applied a Lomb-
Scargle periodogram analysis for the variables. The total number of ACs they
have found is 64, and most of them are newly discovered variables, but six
overlap with our sample: FY Vir, V716 Oph, BF Ser, VX Cap, XX Vir, V1149 Her.
We confirmed these stars. In Drake et al. (2017) CSS published a list of 156
ACs in which two more stars were overlapping: V563 Cen and BI Tel. From our
Fourier parameter plots we have found additional fundamental mode ACs: FY Aqr,
PP Tel, DF Hyi, BQ CrA, BH Cet, V2733 Oph, CE Her, MQ Aql, V745 Oph, UY Eri,
UX Nor, and one possible first overtone AC: V742 Cyg, see Figs. 4 and 5.

We present the list of ACs with their positions (RA (h:m:s), DEC (d:m:s),
eq=J2000) taken from Simbad777http://simbad.u-strasbg.fr, the derived median V
magnitude with additional data from the literature $T_{\rm eff}$, $logg$,
[Fe/H], and the classification from the CSS in Table 1.

The detailed Fourier parameters can be found in appendix Table A.1.

The phased light curves of AC stars are presented in Fig. 4.

There are individual objects that we needed to expand on, because their
interpretation needs further explaining.

FY Vir

The phased light curve of FY Vir ($P$=1.082 days) seen in Fig. 4c shows a well
defined modulation.

V742 Cyg

Zejda et al. (2012) states that V742 Cyg ($P$=0.936 days) is a member of the
open cluster Dolidze 37. The data for our analysis was published by Schmidt
and Reiswig (1993). In the VizieR catalog the data for V742 Cyg was wrongly
published under the name ”V741 Cyg”, which is a known eclipsing binary of
Algol type with a period of $P$=4.649850 days. The correctly phased light
curve can be see in Fig. 5. Vasil’Yanovskaya (1978), Schmidt (1990), and
Schmidt (1991) all discussed that V742 Cyg shows a significant period
variation (with a period around $P$=0.93979 days) that is different from the
Blazhko effect in RRL stars. Based on the Fourier parameters it is an AC,
possibly a 1O AC, making this star the first possible AC to be discovered in
an open cluster.

Fig. 5. V742 Cyg phased light curve with a $P$=0.936 days.

V716 Oph

V716 Oph ($P$=1.116 days) is a member of the globular cluster $\omega$
Centauri (NGC 5139), Dinescu (2002). The estimated age of $\omega$ Cen is
11.52$\times$109 yrs. Resulting from our Fourier parameters V716 Oph is an AC,
confirming the results of Drake et al. (2014a).

BI Tel

The classification of this object has been shifting during the years. Layden
(1994) lists BI Tel ($P$=1.166 days) as an ”RRab” type RRL, and get the
[Fe/H]=-1.96 dex for the metallicity. Than with the ASAS-3 observations, the
classification changed to ”DCEP-FU” (Pojmanski et al. 2005), to be
reclassified, again, to an ”RR Lyrae FM” by Richards et al. (2012). Our
Fourier parameters show it to be an AC.

BQ CrA and V745 Oph

BQ CrA ($P$=1.128 days) and V745 Oph ($P$=1.596 days) have light curves that
show a lot of scatter (see Fig. 6), so their new classification may be wrong,
and needs further confirmation.

(a) BQ CrA

(b) V745 Oph

Fig. 6. The phased light curves of BQ CrA (left) and V745 Oph (right) showing
significant scatter from ASAS-3 data.

Table 1. The identified ACs among the BLHs in the MW.

Name RA (h:m:s) DEC (d:m:s) $<V>$ [mag] $P$ [days] $T_{\rm eff}$ [K] $logg$
[cgs] [Fe/H] [dex] References CSS V742 Cyg 20:02:32.77 +37:46:34.8 15.886
0.936 FY Aqr 22:16:34.99 -03:48:55.41 12.359 1.023 V563 Cen 14:49:50.89
-38:53:08.4 14.798 1.077 AC FY Vir 12:14:13.52 +06:01:17.1 16.419 1.082 AC PP
Tel 20:16:56.51 -51:15:11.4 13.622 1.091 V716 Oph 16:30:49.47 -05:30:19.5
12.169 1.116 6550 2.500 -1.870 Soubiran et al. (2016) AC DF Hyi 01:40:49.20
-67:29:41.9 14.336 1.123 BQ CrA 18:37:01.38 -38:04:34.5 13.132 1.128 BH Cet
00:50:02.80 -17:36:26.9 15.490 1.138 BF Ser 15:16:28.50 +16:26:39.69 12.093
1.165 AC BI Tel 18:18:17.56 -53:22:19.8 12.814 1.166 - - -1.96 Layden (1994)
AC V2733 Oph 17:31:21.880 -17:43:39.51 14.469 1.172 CE Her 17:41:56.55
+15:04:30.2 12.170 1.209 VX Cap 21:06:22.51 -18:49:39.8 14.859 1.327 AC XX Vir
14:16:48.59 -06:17:15.06 12.326 1.348 AC V1149 Her 16:03:43.36 +50:13:33.43
13.995 1.409 - - -2.32 Allende Prieto et al. (2000) AC MQ Aql 19:40:55.69
+12:37:10.1 13.812 1.481 V745 Oph 17:20:02.93 +03:48:56.0 13.942 1.596 UY Eri
03:13:39.13 -10:26:32.40 11.294 2.213 6800 1.800 -1.430 Soubiran et al. (2016)
6389 6280 9978 3.25 2.58 4.15 0.01 0.10 0.30 Schmidt et al. (2011) 6000 1.5
-1.8 Maas et al. (2007) UX Nor 16:27:44.70 -56:47:08.1 13.644 2.386

XX Vir

Dr Dana Casetti in private communication confirmed that XX Vir ($P$=1.348
days) is not a member $\omega$ Centaur globular cluster. We agree that XX Vir
is an AC, as identified in Drake et al. (2014a).

UY Eri

The results of the three different articles (Maas et al. 2007, Schmidt et al.
2011, Soubiran et al. 2016) that measured metallicity for UY Eri ($P$=2.213
days) are summarized in Table 1. The big differences in the [Fe/H] values make
conclusions about this star open for further discussion. While on most of the
Fourier parameter plots UY Eri is among AC, in amplitude figures (see Figs. 2
and 3) it seems to be among the BLHs. Further measurements are needed to
resolve the question about the nature of this star.

###  4.2 4.2. The short period Type II Cepheids - BL Herculis subtype

Summarizing the results from the Fourier parameter plots we list the BLHs with
additional information: positions (RA (h:m:s), DEC (d:m:s), eq=J2000 from
Simbad888http://simbad.u-strasbg.fr, the derived median V magnitude, and
$T_{\rm eff}$, log g, [Fe/H] from the literature) in Table 2. All, but two,
stars had their [Fe/H] determined from direct spectroscopic measurements. The
exceptions are V527 Sgr ($M$=1.025 M⊙, $R$=1.366 R⊙) and V1287 Sco ($M$=0.963
M⊙, $R$=2.933 R⊙), for which the parameters were derived with a combination of
photometric observations and a MW stellar population synthesis program (Sharma
et al. 2011) for the EPIC K2 stars (Huber et al. 2016).

There are some BLH stars in our sample that need more detailed discussion,
which we give in the following paragraphs.

BL Her

The literature dealt with BL Her ($P$=1.307 days) in quite some detail. The
behaviour of the Hα line was analysed by Gillet et al. (1994), while Fokin and
Gillet (1994) compared the measurements with a non-linear model, to find a
good agreement and confirmation of the presence of the 2:1 resonance predicted
by the pulsation model of T2Cs. The emission in the Hα line was reported in
Schmidt et al. (2003) confirming previous findings of Gillet et al. (1994) and
Vinko et al. (1998) (and references within). The numerous measurements of the
$T_{\rm eff}$, log g and [Fe/H] from spectra are listed in Table 2.
Furthermore, a Baade-Wesselink analysis carried out by Balog et al. (1997) on
BL Her gave the following results: $R$=9.4 $\pm$ 2 R⊙. Using the surface-
brightness method for deriving radii of stars Arellano Ferro and Rosenzweig
(2000) derived $R$=15.4 $\pm$ 1.5 R⊙, while Groenewegen and Jurkovic (2017b)
used the period-radius relation to get $R$=8.066 R⊙, putting it outside the
region of the BLHs. On the Fourier parameters figures the position of BL Her
is not unambiguous, either. The true nature of BL Her is still open for
discussion, despite the fact that this star named the whole subgroup.

KZ Cen

The Fourier parameters and light curve shape puts KZ Cen ($P$=1.520 days)
among BLHs, but the metallicity given in Table 2 is 0.67, which is too high
for this subtype, so this makes KZ Cen great candidate for further
spectroscopic measurements.

Table 2. The list of BLHs.

Name RA (h:m:s) DEC (d:m:s) $<V>$ [mag] P [days] $T_{\rm eff}$ [K] log g [cgs]
[Fe/H] [dex] References Notes BX Del 20:21:18.97 +18:26:16.28 12.412 1.092
6250 1.0 -0.2 Maas et al. (2007) BV Cha 13:02:21.18 -79:45:26.4 12.284 1.238
VY Pyx 08:54:29.63 -23:31:18.57 7.245 1.240 5750 1.5 -0.4 Maas et al. (2007)
V527 Sgr 19:16:10.99 -20:55:55.8 14.918 1.255 5816 4.159 -0.042 Huber et al.
(2016) using Sharma et al. (2011) BL Her 18:01:09.22 +19:14:56.70 10.219 1.307
6121 - - Muñoz Bermejo et al. (2013) 6256 - - McDonald et al. (2012) 6500 2.0
-0.1 Maas et al. (2007) 6497 6464 - -0.17 Ammons et al. (2006) 6350 2.5 0.0
Caldwell and Butler (1978) V5614 Sgr 17:55:43.81 -29:44:50.2 16.656 1.354 HQ
CrA 18:11:53.74 -37:39:15.0 14.741 1.415 Madore and Fernie (1980): blue
companion? KZ Cen 12:01:55.19 -46:16:41.48 12.293 1.520 6261 6021 - 0.67
Ammons et al. (2006) V2022 Sgr 18:40:39.0 -25:22:50 13.516 1.529 SW Tau
04:24:32.97 +04:07:24.08 9.721 1.584 7036 7482 6322 3.10 3.54 1.92 0.20 0.22
0.12 Schmidt et al. (2011) 6250 2.0 0.2 Maas et al. (2007) NW Lyr 19:15:56.34
+34:27:08.08 12.520 1.601 VZ Aql 19:05:02.96 -06:50:58.7 14.002 1.685 V1437
Sgr 18 03 33.63 -30 01 14.9 15.603 1.748 V714 Cyg 19:41:48.62 +37:59:33.8
14.148 1.888 RT TrA 16:34:30.89 -63:08:00.81 9.841 1.946 5996 5868 - 0.48
Ammons et al. (2006) C-rich 6200 6040 6360 2.0 2.5 2.3 0.34 0.54 0.43
Wallerstein et al. (2000) V439 Oph 17:43:33.27 +03:35:36.08 12.172 1.893
5547.61 -0.493 Luo et al. (2016) GK Cen 13:46:20.94 -49:35:50.1 12.929 1.950
V477 Oph 17:59:08.16 +05:38:26.2 13.946 2.016 V1287 Sco 16:36:52.85
-28:05:34.2 13.480 2.036 5428 3.542 -0.343 Huber et al. (2016) using Sharma et
al. (2011) period increase AT Tel 18:50:02.64 -51:38:04.6 14.216 1.970 V553
Cen 14:46:33.64 -32:10:15.25 8.458 2.061 5600 3.100 -0.500 Soubiran et al.
(2016) C-rich 5635 5654 - 0.16 Ammons et al. (2006) - - 0.04 Wallerstein and
Gonzalez (1996) 5600 3.1 -0.5 Wallerstein et al. (1979) V5608 Sgr 17:54:09.11
-29:39:59.0 16.374 2.212 V617 Ara 17:10:08.31 -60:39:43.4 11.792 2.522 DCEP in
Simbad V465 Oph 17:52:07.5 -01:05:07 13.312 2.844 BE CrA 18:54:54.03
-40:23:15.3 13.957 3.337 V5609 Sgr 17:54:55.57 -29:57:31.0 16.919 3.542

V2022 Sgr

V2022 Sgr ($P$=1.529 days) was observed by Diethelm (1983), who found a period
of $P$=1.533 days, while Kwee and Diethelm (1984) observed it in UBV-bands
determining a $P$=1.533171 days. Provencal (1986) has observed that the period
has increased up to $P$=1.5530160 days.

In Jurkovic (2015) V2022 Sgr was misclassified. The confusion came from the
reference on the ”The ASAS Catalogue of Variable Stars” which directs to this
object: 184041-2523.7. This object is indeed a variable star with a period of
$P$=290.71001 $\pm$ 0.52327 days. The right ASAS ID for V2022 Sgr is
184039-2523.0, and it appears correctly in the ”ASAS All Star Catalogue”.

We can confirm that V2022 Sgr is a BLH, with a variable period, using data
from Kwee and Diethelm (1984).

V1437 Sgr

V1437 Sgr ($P$=1.748 days) is a probable member of NGC 6522 (V8) globular
cluster according to the newest catalogue of variables in clusters by Clement
(2017) (for details see Clement et al. (2001)). This is also confirmed by
Samus et al. (2009b). Udalski et al. (1994) in the VizieR catalogue (Udalski
1996) the OGLE star identifier for this object is BWC V1, and gives a type for
the variability type ”ACEP”, and it is also remarked that this star was
identified by Blanco (1984) as a ”CW” and marked V58. The light curve is (and
I, V measurements) can be found in Soszyński et al. (2011b), where it is, once
again, classified as a T2C-BLH. We confirm this latest result with the Fourier
parameters.

RT TrA

RT TrA ($P$=1.946 days) is a carbon rich star (Lloyd Evans 1983, Wallerstein
et al. 2000, Wallerstein 2002), as is V553 Cen, with a light curve (Diethelm
1983) that puts its among BLH (see Fig. 7a), but with a bump on the ascending
branch. It looks similar to a BLH star with a similar period, but this feature
makes it different. The Fourier parameters (as with the V553 Cen) the
$R_{21}$, $R_{31}$ is very close to 0. The evolutionary models do not give an
answer for the existence of such C-rich stars, as it is detailed in
Wallerstein (2002).

(a) Phased RT TrA light curve from ASAS-3 data ($P$=1.946 days).

(b) Phased light curve of V553 Cen from ASAS-3 data ($P$=2.061 days).

Fig. 7. The phased light curves of the C-rich BLH stars.

V477 Oph

V477 Oph ($P$=2.016 days) is a member of the open cluster Collinder 359
according to (Zejda et al. 2012). If it is truly a cluster member this star
can not be a BLH star, because the age of the cluster is much younger
($\approx$ 30-60 $\times$ 106 years, see Bobylev (2008)) than any BLH star
should be.

V553 Cen

Wallerstein and Gonzales (1996) has confirmed from a detailed spectroscopic
study that V553 Cen ($P$=2.061 days) is indeed a C- and N-rich short period
T2C, and in Wallerstein (1979) presented the measured $T_{\rm eff}$=5600 K,
$logg$=3.1, and [Fe/H]=-0.50 (see Table 2). It is in the same time a O-poor
star, and has a moderate Na content. The idea of this BLHs star being in a
binary system was tested by Wallerstein and Gonzales (1996), but no evidence
has been found that would support that. The only strange thing that is
different from the other BLHs is that the $R_{21}$ and $R_{31}$ parameters are
almost zero, a feature seen in the other C-rich star in the sample, RT TrA.
Fig. 7 shows both RT TrA and V553 Cen showing very similar light curve shapes.

###  4.3 4.3. The (p) W Virginis subtype Type II Cepheids

The peculiar W Virginis (pWVir) stars are a special class among the W Virginis
(WVir) with periods between 4 and 20 days. Many of the pWVir in the OGLE-III
LMC sample are binary systems. They might overlap with the DCEPs on the $PL$
relations, because they are usually brighter than regular WVir stars. The
phased light curves of UY CrA and IT Cep are shown in Fig. 8.

UY CrA

The INTEGRAL data of UY CrA ($P$=6.995 days) is quite noisy, but we could
derive the Fourier parameters, which puts this star among DCEP/pWVir stars,
although the shape of the light curve would support the suggestion that it
would be more likely that it a DCEP.

IT Cep

From the Fourier parameters IT Cep ($P$=7.349 days) can be classified as
pWVir. Ammons et al. (2006) lists the $T_{\rm eff}$=6622 and 6497 K, and a
[Fe/H]=0.16 [dex].

(a) UY CrA phased with $P$=6.995 days.

(b) IT Cep phased with $P$=7.349 days.

Fig. 8. The phased light curves of the suspected pWVir/DCEP stars - UY CrA on
the left and IT Cep on the right.

###  4.4 4.4. The classical Cepheids

Classical Cepheids (DCEPs) are intermediate mass (4-20 M⊙) stars pulsating in
F, 1O and second overtone (2O) modes with periods from 1 to 100 days (Catelan
and Smith 2015). The DCEPs that were found during our investigation (combining
the Fourier parameters, and the light curve shapes) were summarized in Table 3
(RA (h:m:s), DEC (d:m:s), eq=J2000 from Simbad999http://simbad.u-strasbg.fr,
and derived media V magnitude). Where available we give the known $T_{\rm
eff}$, $logg$ and [Fe/H] from spectroscopic measurements, as well as other
physical parameters found in the literature when describing individual stars.

In the cases of V5626 Sgr (OGLE BUL-SC30 604452, OGLE BLG-CEP-25, $P$=1.33916
days) and V1529 Sco (OGLE BUL-SC4 404186, OGLE BLG-CEP-14, OGLE DIA BUL-SC4
170, $P$=1.53185 days) we relay on the classification given in Soszyński et
al. (2011b) stating that these stars are DCEPs. In the following we provide
some details about some of the stars.

Table 3. The identified DCEPs among short period BLHs in the GCVS.

Name RA (h:m:s) DEC (d:m:s) $<$V$>$ [mag] $P$ [days] $T_{\rm eff}$ [K] $logg$
[cgs] [Fe/H] [dex] References Notes V351 Cep 22:33:41.35 +57:19:05.89 9.430
2.807 DQ And 00:59:34.47 +45:24:24.20 11.715 3.201 6596.19 - 0.418 Luo et al.
(2016) 6366 5665 6068 2.82 1.93 1.79 -0.08 -0.40 -0.02 Schmidt et al. (2011)
5500 1.5 -0.5 Maas et al. (2007) FM Del 20:33:44.26 +16:16:17.5 13.957 3.337
Le Borgne and Klotz (2014): DCEP BD Cas 00:09:51.39 +61:30:50.55 11.110 3.651
6200 6075 2.50 -0.07 Andrievsky et al. (2013) - - -0.07 Acharova et al. (2012)
6069 6601 6278 2.40 4.70 1.72 -0.03 0.02 -0.09 Schmidt et al. (2011) - - -0.07
Luck et al. (2011) V572 Aql 20:02:32.69 +00:42:50.05 11.207 3.756 6250 1.0
-0.2 Maas et al. (2007) QY Cyg 19:58:51.54 +37:38:50.1 14.645 3.893 Schmidt et
al. (2005): DCEP V383 Cyg 20:28:58.16 +34:08:06.36 10.909 4.612 V675 Cen
14:24:50.90 -34:39:45 12.411 4.629 Berdnikov et al. (2014):DCEP V394 Cep
22:02:40.90 +59:27:09.04 14.008 5.688 AB Ara 16:42:08.99 -57:18:44.8 13.355
5.96 ASAS, VSX, Fernie (1968) and Berdnikov et al. (2015): DCEP TX Del
20:50:12.69 +03:39:08.36 9.158 6.166 6217 1.8 0.24 Andrievsky et al. (2013) -
- 0.24 Acharova et al. (2012) 5738 5485 1.32 1.06 0.23 0.11 Schmidt et al.
(2011) - - 0.24 Luck et al. (201) 5500 0.5 0.1 Maas et al. (2007) 5553 5593 -
0.29 Ammons et al. (2006) 5900 1.6 -0.18 Galazutdinov and Klochkova (1995)

V351 Cep

V351 Cep ($P$=2.807 days, unclear) is a member of the galactic open cluster
[KPR2005] (Zejda et al. 2012), which age was approximated to be 0.012 $\times$
109 years. Galazutdinov and Klochkova (1995) from spectroscopic analysis, as
well as taking into account previous photometric analysis especially from
Arellano Ferro (1984), V351 Cep is not a DCEP, but it is not a T2C either, so
they conclude that it is most probably an AC. However, Acharova et al. (2012)
calculated the mass and age (as well as [Fe/H]=0.02) of V351 Cep to be 5.1 M⊙
and 82 Myr old. Making this star too massive to be an AC. Balog et al. (1997)
has suspected that V351 Cep is an s-Cepheid which pulsates in first overtone
based on ”small-amplitude sinusoidal light curve, radius as large as about
50-60 R⊙, low galactic latitude”.

The V-band data for the Fourier analysis was collected from Henden (1980) (19
data points) and Szabados (1977) (32 data points). The classification is not
clear. It can be either a BLH or a DCEP, but if it is a BLH then all the other
measurements (see above the mass and radius) would be incorrect. In
conclusion, the true nature of V351 Cep is still open for discussion.

DQ And

Szabados (1977) analysing light curve of DQ And ($P$=3.201 days) in V says
that the presence of the bump in the descending branch and its high galactic
latitude excludes the possibility that this is a DCEP. In the Schmidt et al.
(2005) paper the V-band photometric observations do not show a bump on the
descending branch, so the Szabados (1977) argument does not stand. However,
Jurkovic et al. (2016) showed that this star in the span of 12 Gyrs has had a
ellipsoidal orbit going from to bellow the Galactic plane. At this present
moment it can be seen as a Halo object, but in the case of DQ And this does
not mean that it is an old low-mass object. The position of DQ And on the $PR$
relation in Groenewegen and Jurkovic (2017b), using the radius from Balog et
al. (1997): $R$=35 $\pm$ 6 R⊙, as well as the derived Fourier parameters in
this paper, from the Schmidt et al. (2005) data, put it among the DCEPs.

BD Cas

Andrievsky et al. (2013) have estimated the $T_{\rm eff}$ of BD Cas ($P$=3.651
days) to be 6200 and 6075 K. Acharova et al. (2012) derived the following
element abundances from spectroscopic measurements: [O/H]=-0.09 and
[Fe/H]=-0.07 [dex], from modelling calculated the age of BD Cas to be 4.9 Myr,
and the mass 4.9 M⊙. In addition Schmidt et al. (2005) concluded, after much
consideration, that BD Cas is an overtone pulsator. In our Fourier analysis of
the INTEGRAL data we see that the parameters align with the DCEPs.

TX Del, T2C or DCEP

Here we give an overview of the information available about TX Del ($P$=6.166
days), and while we would put is among DCEPs, we can not exclude the
possibility that might be a T2C showing interesting features due to it being
in a binary. Laney and Stobie (1995), Balog and Vinko (1995) and Balog et al.
(1997) conclude from the Baade-Wesselink analysis that the radius of the star
is too big for a T2C, one has to be careful with this assessment, again,
because of the presence of a secondary component. Galazutdinov and Klochkova
(1995) presented an extensive spectroscopic analysis and concluded that it
shows all the hallmark of a classical Cepheid, but because of the binary
nature and a possible interaction between the components. The automated
classification of the Hipparcos variables (Dubath et al. 2011) has it as
”DCEP”. Acharova et al. (2012) has the mass estimate at $M$=6.4 M⊙, and age 60
Myr, making it impossible to be T2C. Maas et al. (2007) points to Andrievsky
et al. (2002) to say that this is a first-overtone Type I Cepheid, and it is
clear from its chemical element abundance that it has gone through a mass
transfer, nevertheless the authors stay with a conclusion that TX Del is a
T2C.

##  5 5\. STARS THAT ARE NOT PULSATING VARIABLES IN THE SAMPLE

NY Her

NY Her ($P$=0.076 days) is a SU UMa type dwarf novae as it was described in
Kato et al. (2013). We confirm their findings on the AAVSO dataset of NY Her
as shown on Fig. 9a.

V4110 Sgr

Fig. 9b shows our analysis of the OGLE I-band data of V4110 Sgr ($P$=1.125
days). The period that we found was $P$=1.1254 days. It has a strange jump in
amplitude, which comes back to the previous level. It would be highly unlikely
for a pulsating star to show such a behaviour, if it was real. This feature,
on the other hand, could be a result of a measurement error, so we can not
give a definite conclusion. Another thing to notice is that V4110 Sgr is
flagged to be in a crowded field, and a neighbouring star OGLEII DIA BUL-SC01
V3246 (RA: 270.757455, DEC: -29.766070, and the median I-band magnitude is
15.899 $\pm$ 0.047 mag) is a BY Draconis variables type of variable star
(rotating stars with star spots, and other chromospheric activity). Blanco
(1984) has V4110 Sgr observed from 1977 to 1981 (it was originally classified
as a CW star by Gaposchkin), and it showed a variable period (in 1977
$P$=1.1247, in 1979 $P$=1.1345, and in 1980 $P$=1.108 days).

CT Sge

CT Sge ($P_{GCVS}$=1.7179 days) has V-band data in ASAS catalogue, but the
period given by the GCVS team, $P$=1.7179 days, and the period from the
Fourier analysis does not phase the light curve. We were not able to phase the
light curve using the the above periods, nor could we establish a new one from
the Fourier analysis.

DI And

DI And ($P_{GCVS}$=3.385584882 days) was originally classified in the GCVS as
an ”IS” star, which changed to ”CWB:” after Khruslov (2005) published it’s
results, noting that ”the shape of the descending branch is not quite
typical”. WASP has a long data set, which we looked at (see Fig. 9c). We are
not aware of any known T2C nor DCEP of this period to have an even remotely
similar light curve shape. Morrison et al. (2001) gives us the information
that it is not a binary. The possible types of variability that could result
in a similar light curve shape could be a star with spots, a chromospherically
active star or a rotating star.

UW For

UW For ($P_{\rm ASAS}$=4.277943728 days) is an eclipsing binary system, as it
was described by the ASAS with a period of $P$=4.27774 days.

The phased light curve (see Fig. 9d) shows the two minima in the eclipse. We
do not exclude the possibility that after removing the eclipse from the light
curve there could be other variability left in the system.

KT Com

KT Com ($P_{\rm ASAS}$=8.140512308 days) is listed as a semi-detached (ESD) or
detached (ED) binary system. Using this classification Szczygiel et al. (2008)
has calculated the bolometric luminosity $L$=33.418 [ergs/sec], X-ray
luminosity $L_{\rm X-ray}$=29.765 [ergs/sec], and distance, d=39.1256 [pc].
Independently Soubiran et al. (2016) gives an effective temperature $T_{\rm
eff}$=5924 K for this star. In the ”The International Variable Star Index”
(VSX) of the The American Association of Variable Star Observers
(”AAVSO”)101010http://www.aavso.org/vsx/ KT Com is a variable star of RS Canum
Venaticorum-type binary system, with a period of P=4.07 days, but the given
reference, Kiraga (2012), lists this star as a rotation variable. We conclude
that KT Com is not a BLH, but instead it is most probably a binary system.

V403 Cyg (no period)

Koch (1974) listed V403 Cyg as a strong interacting binary, but there is no
light curve that would support this claim. The GCVS listed Suzuki and Huruhata
(1938) for the identification, and it is listed as a binary in Coughlin et al.
(2014), yet again there were no data to support it. SuperWASP has a lot of
data points, but it does not show any sign of binarity and it can not be
phased with the given period of PGCVS=0.80477 days. This is too short for a
BLH, but it is in the range of ACs. Taken into account that Hanson et al.
(2004) has classified it as an RRL, it is very possible that indeed it is an
AC, but further observations would be needed to confirm this claim. We could
not determine what kind of variable this star is.

(a) NY Her phased with $P$=0.076 days from the AAVSO data.

(b) V4110 Sgr OGLE II I-band phased light curve with $P$=1.125 days.

(c) DI And phased light curve from SuperWASP data with $P$=3.386 days.

(d) UW For phased light curve with $P$=4.278 days using ASAS-3 data.

(e) KT Com phased light curve with a period $P$=8.141 days using ASAS-3 data.

Fig. 9. Stars that are not pulsating variables.

##  6 6\. THE DISCUSSION OF METALLICITY

The collected spectroscopic data of the published $T_{\rm eff}$, log g, [Fe/H]
confirms a result from Diethelm (1990), described in Wallerstein (2002) about
the metallicities. Diethelm (1990) has estimated the photometric metallicities
of the than known short period T2Cs, and it became obvious that from the 45
stars in his list, 30 had [Fe/H]${}_{\rm VBLU}>$ -0.3, and 8 had
[Fe/H]${}_{\rm VBLU}<$ -1.0. Comparing our list of AC with these results we
saw that 7 out of 8 were indeed AC. The metallicities that are in Tables 1 and
2 are directly measured from spectra, and they also show the same distribution
of [Fe/H]. In the case of the ACs we have only data for four stars, and they
are very metal poor. The average of all the eight measurements of four stars
is $<$[Fe/H]$>$=-1.12 dex, but if we leave out the outlier of UY Eri by
Schmidt et al. (2011) then the it becomes $<$[Fe/H]$>$=-1.88 dex. While the
number of measured metallicities is small, we do suggest that it is correct to
conclude that this low metallicity is fundamental to the evolution of these
objects. This was already known from observations in dwarf spherical and dwarf
irregular galaxies (for example Sculptor, Sextans, LeoII, Ursa Minor, Draco,
Fornax, LeoI) and in smaller numbers in globular clusters, such as BL Boo in
NGC 5466, and in the Milky Way summarized in Fiorentino and Monelli (2012).
Bono (1997b) and Fiorentino and Monelli (2012), as well as others, have used
these observational boundaries to constrain their theoretical calculations
confirming that ACs are metal-poor stars with an mean mass of 1.2 - 1.5 M⊙.

The BLH stars, on the other hand, turned out to have Solar metallicities on
average, $<$[Fe/H]$>$=0.00 dex. We got this by combining all the twenty one
measurements of ten stars. BLHs are not metal poor, despite being old objects.

In order to see how these result reflect on the Herztsprung-Russell diagram
(HRD) of the BLH stars in the MW we have calculated the luminosities (L) from
the Groenewegen and Jurkovic (2017b). We used the $M_{bol}$=0.12-1.78*logP
formula to calculate the bolometric magnitudes, and than we converted that to
luminosities. The Teff values are given in Table 2, which were measured from
spectroscopy. In the cases were there were multiple measurements for $T_{\rm
eff}$ we have used the mean value of all the values. In the same table we give
the values of pulsational periods in days, derived from our Fourier analysis.
The number of BLH stars was limited to ten stars, since only for these were
the spectroscopy was available, and we give all the relevant data in Table 4.
In Fig. 10 we have compared our computed $L$ and $T_{\rm eff}$ with models of
horizontal branch (HB) stars from the BaSTI111111http://basti.oa-
teramo.inaf.it/ evolutionary model database. The models were calculated for
the Solar metallicity of [M/H]=0.058 to match our findings, and previously
assumed metallicity value for metal-poor stars of [M/H]=-1.488. The masses of
the modelled stars were $M$=0.500 M⊙, $M$=0.520 M⊙, $M$=0.530 M⊙ and $M$=0.550
M⊙. These mass ranges are in agreement with estimates from Bono (1997a) of
approx. 0.52-0.53 M⊙ and Groenewegen and Jurkovic (2017a) of 0.49 M⊙. All of
our stars fall in the region of Solar metallicity models, with the majority
being on the track for the $M$=0.500 M⊙ model, and going towards the track of
the $M$=0.520 M⊙ model. The metal-poor model of $M$=0.550 M⊙ is very close to
the Solar metallicity model of $M$=0.500 M⊙, but the independently measured
spectroscopic metallicities as well as the newest mass estimates seem to
strengthen our finding that BLH stars have Solar-like metallicities.

Table 4. The mean effective temperature ($<T_{\rm eff}>$) from the
spectroscopic measurements shown in Table 2, the pulsational period ($P$), the
bolometric magnitude form $M_{bol}$=0.12-1.78*logP (Groenewegen and Jurkovic
2017b), and the calculated luminosities ($L$) for the Galactic BLH stars.

Name $<T_{\rm eff}>$ (K) log$<T_{\rm eff}>$ (K) $P$ (days) log$P$ (days)
$M_{bol}$ (mag) $L$ (L⊙) log$L$ (L⊙) BX Del 6250 3.796 1.092 0.038 0.052 75.03
1.87 VY Pyx 5750 3.760 1.240 0.093 -0.046 82.13 1.91 V527 Sgr 5816 3.765 1.255
0.099 -0.056 82.84 1.92 KZ Cen 6141 3.788 1.520 0.182 -0.204 94.94 1.98 SW Tau
6772.5 3.831 1.584 0.200 -0.236 97.77 1.99 V439 Oph 5547 3.744 1.893 0.277
-0.373 111.00 2.05 V1287 Sco 5428 3.735 2.036 0.309 -0.430 116.91 2.08 V553
Cen 5629.7 3.750 2.061 0.314 -0.440 117.93 2.07 RT TrA 6092.8 3.785 1.946
0.289 -0.395 113.21 2.05 BL Her 6364.7 3.804 1.307 0.116 -0.087 85.27 1.931

Fig. 10. The BLH stars from the MW plotted with a metal-poor and a Solar
metallicity models. The models are from the BaSTI database (Pietrinferni et
al. 2004). The black circles represent the data for BLH stars shown in Table
4. In the case on the metal-poor models ([M/H]=-1.488) the masses of are shown
with the following colors and symbols: red plus signs $M$=0.500 M⊙, green
crosses $M$=0.520 M⊙, blue star $M$=0.530 M⊙ and pink doted square $M$=0.550
M⊙. For the Solar metallicity models ([M/H]-0.058) the masses are shown as:
cyan square $M$=0.500 M⊙, yellow dotted circle $M$=0.520 M⊙, grey filled
triangle $M$=0.530 M⊙, orange dotted triangle $M$=0.550 M⊙.

##  7 7\. CONCLUSIONS

Fourier parameters of 59 stars from the GCVS short period T2Cs list, known as
BLHs, as well as 33 BLHs and 29 ACs from the LMC OGLE-III catalogue for
comparison, using V-band datasets, were derived. Among the 59 stars we have
found 19 F ACs, 1 1O AC, 26 BLHs, 2 pWVir/DCEP, 11 DCEPs, and 7 other types of
variables.

The BLHs and ACs can be distinguished using the $R_{21}$, $R_{31}$ and
$\phi_{31}$ Fourier parameters. The $\phi_{21}$ parameter is not useful fr his
purpose, because almost all the points clumped together. Interestingly, Figs.
2 and 3, representing the amplitude of the two and three times of the
fundamental frequency, showed a very clear separation between the ACs and the
BLHs. These Fourier parameters can be used as new comparison sample for the
stars measured by the Kepler space telescope, since its broad band filter
corresponds broadly with the V-band.

In total 19 F ACs and one 1O AC was discovered in the examined sample. FY Vir,
V563 Cen, V716 Oph, BF Ser, BI Tel, VX Cap, XX Vir and V1149 Her were detected
as ACs in the CSS (Drake et al. 2014a, 2017) using a different method of
detection, and we confirmed their classification through the Fourier
parameters. We add further 12 F ACs (FY Aqr, PP Tel, DF Hyi, BQ CrA, BH Cet,
V2733 Oph, CE Her, MQ Aql, V745 Oph, UY Eri, UX Nor), and one 1O AC (V742 Cyg)
to the previously known once. We list some of our findings:

(i) V742 Cyg is a 1O AC, and a supposed member of Dolidze 37 open cluster,
making it a first objects of this type to be discovered in an open cluster,
but further observations would be needed to confirm this result;

(ii) FY Vir shows signs of Blazhko effect-like modulation.

BLH star are shown to have Solar-like metallicities if the AC are properly
separated from the sample. The AC, despite being more massive, seem to have
low-metallicities.

These results can be useful for other research fields as well, such as
Galactic archaeology and evolution modelling, as well for individual
measurements of these objects, and for the improvement of the precision of the
$PL$ relation, as it will become even more important with the new Gaia data
(Gaia Collaboration 2016).

Acknowledgements – I would like to express my deepest gratitude to G. B.,
Martin Groenewegen, Róbert Szabó, Emese Plachy, Branislav Vukotić, László
Molnár, and all the colleagues with whom I have consulted for all of their
help and patience. This research had financial support from the Ministry of
Education, Science and Technological Development of the Republic of Serbia
through the project 176004. This project has been supported by the NKFIH
K-115709 grant of the Hungarian National Research, Development and Innovation
Office. This research has made use of NASA’s Astrophysics Data System. This
research has made use of the SIMBAD database, operated at CDS, Strasbourg,
France (Wenger et al. 2000). Based on data from the OMC Archive at CAB (INTA-
CSIC), pre-processed by ISDC. The CSS survey is funded by the National
Aeronautics and Space Administration under Grant No. NNG05GF22G issued through
the Science Mission Directorate Near-Earth Objects Observations Program. The
CRTS survey is supported by the U.S. National Science Foundation under grants
AST-0909182. This research has made use of the NASA/ IPAC Infrared Science
Archive, which is operated by the Jet Propulsion Laboratory, California
Institute of Technology, under contract with the National Aeronautics and
Space Administration. This work has made use of data from the European Space
Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the
Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consor tium). Funding for the DPAC
has been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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ANOMALNE CEFEIDE OTKRIVENE U UZORKU GALAKTIQKIH KRATKOPERIODIQNIH CEFEIDA TIPA
$\mathbf{II}$

M. I. Jurkovic1,2

1Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia

E–mail<EMAIL_ADDRESS>
2Konkoly Thege Miklós Astronomical Institute, Research Centre for Astronomy
and Earth Sciences, Hungarian Academy of SciencesH-1121 Budapest, Konkoly
Thege Miklós út 15-17.

UDK …

Uredjivaqki prilog

Ponovo smo posetili kratkoperiodiqne cefeide tipa II, zvane BL Herculis
(BLHs), u Galatiqkom polju da bismo izveli homogenu analizu njihovih Furije
parametara.

Koristili smo iskljuqivo podatke sakupljene u V filtru da bismo obezbedili da
se promeljive iz OGLE-III kataloga mogu direktno uporediti sa 59 zvezda, koje
su bile klasifikovane kao kratkoperiodiqne cefeide tipa II u Generalnom
Katalogu PromeΨivih Zvezda u naxem uzorku.

Od 59 zvezda naxli smo da je 19 BLH tip, 19 su anomalne cefeide (ACs) koje
pulsiraju u fundamentalnoj modi (8 od ovih je veﬄ prethodno bilo klasifikovano
od strane Katalina Nebeskog Pregleda, 1 je anomalna cefeida koja pulsira u
prvoj nad modi, za 2 prepostavljamo da su naroqitog W Virginis tipa (pVVVir)),
11 su klasiqne cefeide (DCEPs), a 7 nisu pulsairajuﬄe zvezde uopxte. Kreirali
smo listu sjajnih BLH zvezda u Galaksiji i razdvojili smo ACs, kao i druge
objekte, koji su bili pogreqno klasifikovani. Broj stvarnih BLH zdezda u naqem
uzorku se smanjio za viqe od 50%. Sakupili smo metaliqnosti dobijene iz
spektroskopskih merenja koji su bili publikovani u literaturi. Iako je broj
stvarnih merenja mali, veoma je verovatno da su ACs niske metaliqnosti.
Proseqna metaliqnost iz 8 merenja 4 zvezda (UY Eri ima 5 razliqitih merenja
[Fe/H]) je $-1.12$ dex, ali ako izostavimo vrednosti metaliqnosti koje su
drastiqno razlikuju kod UY Eri zvezde onda proseqna metaliqnost postaje
$-1.88$ dex, bez obzira na to da li se AC nalazi unutar samog Mleqnog puta ili
u nekom od obliznjih jata. Sa druge strane, qini se da BLH zvezde imaju
metaliqnost sliqnu Suncu, $0.00$ dex, koja je raqunata iz 21 merenja radjenih
za 10 zvezda.

## APPENDIX

In Tables A1, A2 and A3 we give the Fourier parameters of the investigated
stars in the Milky Way, the Fourier parameters of the ACs in the LMC using the
V-band data from the OGLE-III survey and the Fourier parameters of the BLHs in
the LMC using the V-band data from the OGLE-III survey, respectively.

Table A.1. The Fourier parameters of the investigated stars in the Milky Way.

Name | $f_{0}$ | log P[days] | $A_{1}$ | $A_{1err}$ | $A_{2}$ | $A_{2err}$ | $A_{3}$ | $A_{3err}$ | $R_{21}$ | $R_{21err}$ | $R_{31}$ | $R_{31err}$ | $\phi_{1}$ | $\phi_{1err}$ | $\phi_{2}$ | $\phi_{2err}$ | $\phi_{3}$ | $\phi_{3err}$ | $\phi_{21}$ | $\phi_{21err}$ | $\phi_{31}$ | $\phi_{31err}$ | Source
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
V742 Cyg | 1.06785011 | -0.0285102967 | 0.33 | 0.01 | 0.12 | 0.01 | 0.04 | 0.01 | 0.36 | 0.04 | 0.12 | 0.04 | 0.613 | 0.005 | 0.77 | 0.02 | 0.78 | 0.16 | 4.97 | 0.02 | 2.74 | 0.16 | Schmidt and Reiswig (1993)
FY Aqr | 0.977620241 | 0.0098298152 | 0.287 | 0.005 | 0.118 | 0.005 | 0.091 | 0.005 | 0.41 | 0.02 | 0.32 | 0.02 | 0.751 | 0.003 | 0.873 | 0.007 | 0.009 | 0.009 | 3.896 | 0.007 | 1.605 | 0.009 | Pojmanski (1997)
V563 Cen | 0.928577098 | 0.0321820318 | 0.437 | 0.007 | 0.206 | 0.008 | 0.153 | 0.007 | 0.47 | 0.02 | 0.35 | 0.02 | 0.621 | 0.003 | 0.635 | 0.006 | 0.666 | 0.009 | 4.043 | 0.007 | 1.914 | 0.009 | Drake et al. (2014a)
FY Vir | 0.924247177 | 0.0342118673 | 0.404 | 0.006 | 0.174 | 0.007 | 0.154 | 0.007 | 0.43 | 0.02 | 0.38 | 0.02 | 0.378 | 0.003 | 0.155 | 0.006 | 0.909 | 0.007 | 4.076 | 0.007 | 1.728 | 0.008 | Drake et al. (2014a)
PP Tel | 0.916880399 | 0.0376873115 | 0.36 | 0.02 | 0.20 | 0.02 | 0.14 | 0.02 | 0.55 | 0.07 | 0.40 | 0.06 | 0.841 | 0.009 | 0.10 | 0.02 | 0.30 | 0.02 | 4.19 | 0.02 | 1.74 | 0.03 | Pojmanski (1997)
BX Del | 0.915927138 | 0.0381390731 | 0.359 | 0.007 | 0.12 | 0.02 | 0.064 | 0.006 | 0.35 | 0.06 | 0.18 | 0.02 | 0.727 | 0.003 | 0.96 | 0.07 | 0.98 | 0.03 | 4.77 | 0.07 | 1.87 | 0.03 | Pojmanski (1997)
V716 Oph | 0.896124749 | 0.0476315282 | 0.491 | 0.008 | 0.231 | 0.005 | 0.161 | 0.004 | 0.47 | 0.01 | 0.329 | 0.009 | 0.579 | 0.002 | 0.541 | 0.002 | 0.529 | 0.004 | 3.984 | 0.003 | 1.841 | 0.005 | Pojmanski (1997)
DF Hyi | 0.890678094 | 0.0502792289 | 0.51 | 0.03 | 0.28 | 0.03 | 0.17 | 0.05 | 0.55 | 0.07 | 0.33 | 0.09 | 0.852 | 0.009 | 0.01 | 0.02 | 0.27 | 0.17 | 3.52 | 0.02 | 1.38 | 0.17 | Pojmanski (1997)
BQ CrA | 0.89886751759 | 0.0521979414 | 0.27 | 0.04 | 0.21 | 0.04 | 0.16 | 0.04 | 0.77 | 0.19 | 0.59 | 0.16 | 0.41 | 0.03 | 0.19 | 0.06 | 0.81 | 0.08 | 3.91 | 0.07 | 0.46 | 0.08 | Pojmanski (1997)
BH Cet | 0.878962235 | 0.0560297842 | 0.420 | 0.004 | 0.198 | 0.004 | 0.136 | 0.004 | 0.47 | 0.01 | 0.323 | 0.009 | 0.145 | 0.001 | 0.679 | 0.003 | 0.229 | 0.005 | 4.019 | 0.003 | 1.854 | 0.005 | Drake et al. (2014a)
BF Ser | 0.858045833 | 0.0664895134 | 0.482 | 0.006 | 0.245 | 0.006 | 0.162 | 0.006 | 0.51 | 0.01 | 0.34 | 0.01 | 0.312 | 0.002 | 0.039 | 0.004 | 0.790 | 0.006 | 4.186 | 0.004 | 2.233 | 0.006 | Pojmanski (1997)
BI Tel | 0.857323302 | 0.0668604377 | 0.472 | 0.007 | 0.238 | 0.007 | 0.148 | 0.007 | 0.50 | 0.02 | 0.31 | 0.02 | 0.776 | 0.002 | 0.950 | 0.005 | 0.139 | 0.008 | 4.066 | 0.005 | 1.947 | 0.008 | Pojmanski (1997)
V2733 Oph | 0.853554943 | 0.0687685183 | 0.60 | 0.04 | 0.25 | 0.05 | 0.09 | 0.03 | 0.42 | 0.09 | 0.15 | 0.05 | 0.78 | 0.01 | 0.99 | 0.06 | 0.15 | 0.24 | 4.28 | 0.06 | 1.98 | 0.24 | Pojmanski (1997)
CE Her | 0.826825468 | 0.0825861546 | 0.37 | 0.01 | 0.18 | 0.01 | 0.14 | 0.01 | 0.48 | 0.04 | 0.38 | 0.04 | 0.875 | 0.006 | 0.49 | 0.01 | 0.48 | 0.01 | 6.22 | 0.01 | 2.26 | 0.01 | Pojmanski (1997)
BV Cha | 0.807728303 | 0.0927346991 | 0.380 | 0.002 | 0.139 | 0.003 | 0.106 | 0.002 | 0.365 | 0.008 | 0.279 | 0.007 | 0.851 | 0.001 | 0.205 | 0.003 | 0.468 | 0.005 | 4.731 | 0.003 | 2.608 | 0.005 | Pojmanski (1997)
VY Pyx | 0.806485292 | 0.0934035485 | 0.118 | 0.001 | 0.019 | 0.001 | 0.005 | 0.001 | 0.16 | 0.01 | 0.04 | 0.01 | 0.655 | 0.002 | 0.85 | 0.01 | 0.45 | 0.22 | 4.97 | 0.01 | 6.16 | 0.22 | Pojmanski (1997)
V527 Sgr | 0.797035422 | 0.0985223772 | 0.36 | 0.01 | 0.12 | 0.02 | 0.03 | 0.01 | 0.32 | 0.05 | 0.08 | 0.04 | 0.949 | 0.006 | 0.32 | 0.02 | 0.42 | 0.04 | 4.25 | 0.02 | 0.46 | 0.04 | Kwee and Diethelm (1984)
BL Her | 0.764852872 | 0.1164220982 | 0.342 | 0.002 | 0.121 | 0.002 | 0.082 | 0.002 | 0.353 | 0.006 | 0.241 | 0.007 | 0.798 | 0.001 | 0.101 | 0.003 | 0.408 | 0.004 | 4.740 | 0.003 | 3.223 | 0.004 | Pojmanski (1997)
VX Cap | 0.750502164 | 0.1246480512 | 0.479 | 0.005 | 0.227 | 0.005 | 0.130 | 0.005 | 0.47 | 0.01 | 0.27 | 0.01 | 0.222 | 0.002 | 0.891 | 0.003 | 0.531 | 0.006 | 4.446 | 0.004 | 2.393 | 0.007 | Drake et al. (2014a)
V5614 Sgr | 0.738490213 | 0.1316552559 | 0.31 | 0.01 | 0.12 | 0.01 | 0.07 | 0.01 | 0.37 | 0.04 | 0.22 | 0.04 | 0.898 | 0.005 | 0.34 | 0.01 | 0.79 | 0.02 | 4.96 | 0.02 | 3.74 | 0.02 | Soszyński et al. (2011b)
XX Vir | 0.741726923 | 0.1297559568 | 0.392 | 0.006 | 0.193 | 0.006 | 0.132 | 0.006 | 0.49 | 0.02 | 0.34 | 0.02 | 0.465 | 0.002 | 0.343 | 0.005 | 0.248 | 0.007 | 4.163 | 0.005 | 2.215 | 0.007 | Pojmanski (1997)
V1149 Her | 0.709424427 | 0.140938619 | 0.336 | 0.004 | 0.173 | 0.004 | 0.123 | 0.004 | 0.514 | 0.0126 | 0.37 | 0.01 | 0.481 | 0.002 | 0.392 | 0.003 | 0.317 | 0.005 | 4.274 | 0.004 | 2.356 | 0.005 | Drake et al. (2014a)
HQ CrA | 0.706485722 | 0.1508966108 | 0.39 | 0.02 | 0.12 | 0.01 | 0.01 | 0.01 | 0.31 | 0.04 | 0.03 | 0.03 | 0.040 | 0.006 | 0.43 | 0.02 | 0.69 | 0.19 | 3.79 | 0.02 | 0.43 | 0.19 | Kwee and Diethelm (1984)
MQ Aql | 0.675328868 | 0.1704846853 | 0.29 | 0.02 | 0.18 | 0.02 | 0.17 | 0.02 | 0.64 | 0.10 | 0.59 | 0.09 | 0.21 | 0.01 | 0.75 | 0.02 | 0.46 | 0.02 | 3.58 | 0.03 | 2.01 | 0.03 | Pojmanski (1997)
KZ Cen | 0.657879317 | 0.1818537671 | 0.384 | 0.004 | 0.144 | 0.005 | 0.053 | 0.004 | 0.38 | 0.01 | 0.14 | 0.01 | 0.311 | 0.002 | 0.991 | 0.005 | 0.46 | 0.01 | 3.881 | 0.00 | 0.15 | 0.01 | Pojmanski (1997)
V2022 Sgr | 0.653820108 | 0.184541727 | 0.38 | 0.01 | 0.14 | 0.08 | 0.05 | 0.08 | 0.37 | 0.21 | 0.13 | 0.20 | 0.952 | 0.006 | 0.54 | 0.01 | 0.60 | 0.14 | 5.59 | 0.02 | 1.56 | 0.14 | Kwee and Diethelm (1984)
SW Tau | 0.631499487 | 0.1996269979 | 0.353 | 0.004 | 0.115 | 0.004 | 0.0305 | 0.004 | 0.33 | 0.01 | 0.09 | 0.01 | 0.026 | 0.002 | 0.515 | 0.005 | 0.15 | 0.02 | 4.474 | 0.005 | 3.584 | 0.020 | Pojmanski (1997)
V745 Oph | 0.626497323 | 0.2030807804 | 0.25 | 0.02 | 0.09 | 0.03 | 0.05 | 0.02 | 0.37 | 0.12 | 0.18 | 0.07 | 0.42 | 0.01 | 0.27 | 0.25 | 0.34 | 0.07 | 4.18 | 0.25 | 3.58 | 0.07 | Pojmanski (1997)
NW Lyr | 0.624493109 | 0.2044723495 | 0.40 | 0.03 | 0.16 | 0.03 | 0.08 | 0.03 | 0.40 | 0.07 | 0.20 | 0.07 | 0.890 | 0.010 | 0.29 | 0.02 | 0.42 | 0.06 | 4.75 | 0.03 | 1.54 | 0.06 | Schmidt et al. (2005)
V971 Aql | 0.615557473 | 0.2107313919 | 0.363 | 0.005 | 0.091 | 0.005 | 0.07 | 0.005 | 0.25 | 0.01 | 0.19 | 0.01 | 0.657 | 0.002 | 0.827 | 0.009 | 0.71 | 0.01 | 4.791 | 0.009 | 1.52 | 0.01 | Pojmanski (1997)
VZ Aql | 0.593633762 | 0.2264814072 | 0.6 | 0.09 | 0.42 | 0.05 | 0.20 | 0.06 | 0.65 | 0.12 | 0.30 | 0.09 | 0.09 | 0.04 | 0.91 | 0.07 | 0.31 | 0.16 | 6.15 | 0.07 | 3.40 | 0.16 | INTEGRAL
V1437 Sgr | 0.572075542 | 0.2425466193 | 0.41 | 0.01 | 0.16 | 0.01 | 0.09 | 0.01 | 0.38 | 0.03 | 0.21 | 0.03 | 0.983 | 0.005 | 0.41 | 0.01 | 0.69 | 0.02 | 4.33 | 0.02 | 1.51 | 0.03 | Soszyński et al. (2011b)
V714 Cyg | 0.529782964 | 0.2759020112 | 0.42 | 0.01 | 0.15 | 0.01 | 0.11 | 0.01 | 0.36 | 0.03 | 0.27 | 0.03 | 0.383 | 0.004 | 0.18 | 0.01 | 0.94 | 0.02 | 4.19 | 0.01 | 1.83 | 0.02 | Schmidt et al. (2005)
V439 Oph | 0.52826286 | 0.2771499217 | 0.30 | 0.02 | 0.05 | 0.02 | 0.04 | 0.02 | 0.16 | 0.07 | 0.15 | 0.08 | 0.47 | 0.06 | 0.38 | 0.15 | 0.84 | 0.34 | 4.34 | 0.16 | 5.78 | 0.35 | Schmidt et al. (2005)
RT TrA | 0.513842147 | 0.2891702764 | 0.323 | 0.001 | 0.034 | 0.001 | 0.031 | 0.001 | 0.105 | 0.004 | 0.095 | 0.004 | 0.9926 | 0.0006 | 0.503 | 0.006 | 0.693 | 0.006 | 4.821 | 0.005 | 1.350 | 0.007 | Pojmanski (1997)
GK Cen | 0.512882982 | 0.289981711 | 0.267 | 0.007 | 0.049 | 0.006 | 0.031 | 0.007 | 0.18 | 0.02 | 0.12 | 0.02 | 0.796 | 0.004 | 0.09 | 0.02 | 0.23 | 0.03 | 4.72 | 0.02 | 2.189 | 0.04 | Pojmanski (1997)
AT Tel | 0.507627684 | 0.2944547012 | 0.285 | 0.03 | 0.12 | 0.02 | 0.06 | 0.02 | 0.43 | 0.09 | 0.19 | 0.07 | 0.34 | 0.01 | 0.94 | 0.03 | 0.50 | 0.24 | 3.19 | 0.04 | 6.13 | 0.24 | Pojmanski (1997)
V477 Oph | 0.496086274 | 0.3044427891 | 0.34 | 0.02 | 0.12 | 0.04 | 0.06 | 0.02 | 0.37 | 0.13 | 0.19 | 0.06 | 0.93 | 0.01 | 0.33 | 0.20 | 0.23 | 0.10 | 4.50 | 0.20 | 5.84 | 0.10 | Pojmanski (1997)
V1287 Sco | 0.491265871 | 0.3086834059 | 0.22 | 0.06 | 0.14 | 0.05 | 0.08 | 0.03 | 0.63 | 0.27 | 0.39 | 0.16 | 0.51 | 0.13 | 0.97 | 0.12 | 0.04 | 0.07 | 1.21 | 0.18 | 0.01 | 0.15 | Pojmanski (1997)
V553 Cen | 0.485305739 | 0.3139845729 | 0.230 | 0.002 | 0.012 | 0.003 | 0.020 | 0.003 | 0.05 | 0.01 | 0.09 | 0.01 | 0.284 | 0.002 | 0.005 | 0.177 | 0.57 | 0.06 | 4.31 | 0.17 | 1.37 | 0.06 | Pojmanski (1997)
V5608 Sgr | 0.45193215 | 0.3449267623 | 0.38 | 0.01 | 0.066 | 0.009 | 0.0376 | 0.009 | 0.17 | 0.03 | 0.10 | 0.03 | 0.842 | 0.004 | 0.22 | 0.03 | 0.20 | 0.05 | 4.93 | 0.03 | 4.23 | 0.05 | Soszyński et al. (2011b)
UY Eri | 0.451814735 | 0.3450396096 | 0.269 | 0.002 | 0.111 | 0.002 | 0.038 | 0.002 | 0.415 | 0.009 | 0.143 | 0.007 | 0.952 | 0.001 | 0.369 | 0.003 | 0.789 | 0.009 | 4.494 | 0.004 | 2.723 | 0.009 | Pojmanski (1997)
UX Nor | 0.419109544 | 0.3776724493 | 0.38 | 0.02 | 0.21 | 0.02 | 0.13 | 0.02 | 0.56 | 0.07 | 0.35 | 0.06 | 0.62 | 0.01 | 0.69 | 0.02 | 0.86 | 0.03 | 4.45 | 0.02 | 3.25 | 0.03 | Pojmanski (1997)
V617 Ara | 0.396512214 | 0.4017434303 | 0.231 | 0.003 | 0.061 | 0.003 | 0.028 | 0.003 | 0.27 | 0.01 | 0.12 | 0.01 | 0.996 | 0.002 | 0.446 | 0.007 | 0.91 | 0.01 | 4.426 | 0.007 | 2.65 | 0.01 | Pojmanski (1997)
V351 Cep | 0.356303349 | 0.4481800956 | 0.149 | 0.007 | 0.022 | 0.007 | 0.011 | 0.006 | 0.15 | 0.05 | 0.08 | 0.04 | 0.959 | 0.008 | 0.12 | 0.05 | 0.08 | 0.12 | 2.85 | 0.05 | 4.42 | 0.12 | Szabados (1977) Henden (1980)
V465 Oph | 0.351651936 | 0.4538869873 | 0.40 | 0.01 | 0.14 | 0.01 | 0.07 | 0.01 | 0.34 | 0.03 | 0.17 | 0.03 | 0.673 | 0.004 | 0.83 | 0.01 | 0.97 | 0.03 | 4.65 | 0.01 | 2.83 | 0.03 | Pojmanski (1997)
DQ And | 0.312444362 | 0.5052273077 | 0.316 | 0.005 | 0.133 | 0.005 | 0.078 | 0.006 | 0.42 | 0.02 | 0.25 | 0.02 | 0.505 | 0.003 | 0.433 | 0.007 | 0.37 | 0.01 | 4.228 | 0.007 | 2.22 | 0.02 | Schmidt et al. (2005)
BE CrA | 0.299683177 | 0.5233376359 | 0.47 | 0.03 | 0.18 | 0.06 | 0.10 | 0.03 | 0.38 | 0.14 | 0.21 | 0.06 | 0.584 | 0.006 | 0.67 | 0.21 | 0.85 | 0.09 | 4.76 | 0.21 | 3.73 | 0.09 | Pojmanski (1997)
FM Del | 0.299679663 | 0.5233427283 | 0.47 | 0.03 | 0.18 | 0.06 | 0.10 | 0.03 | 0.37 | 0.14 | 0.21 | 0.06 | 0.597 | 0.006 | 0.65 | 0.20 | 0.79 | 0.08 | 4.45 | 0.20 | 3.16 | 0.08 | Pojmanski (1997)
BD Cas | 0.273901489 | 0.5624056068 | 0.160 | 0.002 | 0.016 | 0.002 | 0.007 | 0.002 | 0.10 | 0.01 | 0.05 | 0.01 | 0.080 | 0.002 | 0.54 | 0.03 | 0.74 | 0.06 | 3.98 | 0.03 | 0.02 | 0.06 | INTEGRAL
V5609 Sgr | 0.282290865 | 0.5493031755 | 0.302 | 0.010 | 0.112 | 0.010 | 0.056 | 0.009 | 0.37 | 0.03 | 0.19 | 0.03 | 0.714 | 0.005 | 0.01 | 0.01 | 0.27 | 0.03 | 5.25 | 0.01 | 3.96 | 0.03 | Soszyński et al. (2011b)
QY Cyg | 0.256861546 | 0.5903009078 | 0.19 | 0.03 | 0.14 | 0.03 | 0.15 | 0.03 | 0.70 | 0.20 | 0.78 | 0.20 | 0.30 | 0.02 | 0.88 | 0.03 | 0.74 | 0.03 | 3.40 | 0.04 | 2.22 | 0.04 | INTEGRAL
V383 Cyg | 0.216813043 | 0.6639145951 | 0.248 | 0.006 | 0.076 | 0.006 | 0.039 | 0.007 | 0.31 | 0.03 | 0.16 | 0.03 | 0.646 | 0.004 | 0.71 | 0.01 | 0.81 | 0.03 | 4.21 | 0.01 | 2.33 | 0.03 | Berdnikov (2008), AAVSO
V675 Cen | 0.216011549 | 0.6655230288 | 0.298 | 0.009 | 0.114 | 0.006 | 0.05 | 0.02 | 0.38 | 0.02 | 0.17 | 0.07 | 0.317 | 0.003 | 0.57 | 0.01 | 0.18 | 0.22 | 1.15 | 0.01 | 4.60 | 0.22 | Pojmanski (1997)
V394 Cep | 0.175807826 | 0.7549617964 | 0.371 | 0.006 | 0.15 | 0.03 | 0.060 | 0.008 | 0.39 | 0.07 | 0.16 | 0.02 | 0.065 | 0.004 | 0.59 | 0.19 | 0.07 | 0.02 | 4.45 | 0.19 | 2.33 | 0.02 | INTEGRAL
AB Ara | 0.167854242 | 0.7750676788 | 0.34 | 0.01 | 0.13 | 0.01 | 0.04 | 0.01 | 0.39 | 0.03 | 0.13 | 0.03 | 0.639 | 0.005 | 0.79 | 0.01 | 0.97 | 0.06 | 4.82 | 0.01 | 3.46 | 0.06 | Pojmanski (1997)
TX Del | 0.162177362 | 0.7900097682 | 0.294 | 0.002 | 0.072 | 0.002 | 0.022 | 0.002 | 0.245 | 0.009 | 0.076 | 0.008 | 0.776 | 0.001 | 0.091 | 0.006 | 0.36 | 0.02 | 4.960 | 0.006 | 3.32 | 0.19 | Pojmanski (1997)
UY CrA | 0.142949436 | 0.8448175538 | 0.52 | 0.02 | 0.13 | 0.02 | 0.14 | 0.02 | 0.25 | 0.05 | 0.27 | 0.04 | 0.019 | 0.007 | 0.43 | 0.03 | 0.05 | 0.03 | 4.00 | 0.03 | 3.10 | 0.033 | INTEGRAL
IT Cep | 0.136081047 | 0.8662023579 | 0.232 | 0.005 | 0.077 | 0.004 | 0.016 | 0.004 | 0.33 | 0.02 | 0.07 | 0.02 | 0.587 | 0.003 | 0.70 | 0.01 | 0.73 | 0.05 | 4.87 | 0.01 | 2.96 | 0.05 | Schmidt et al. (2005)

Table A.2. The Fourier parameters of the ACs in the LMC using the V-band data
from the OGLE-III survey.

OGLE-LMC-ACEP | $f_{0}$ | log P[days] | $A_{1}$ | $A_{1err}$ | $A_{2}$ | $A_{2err}$ | $A_{3}$ | $A_{3err}$ | $R_{21}$ | $R_{21err}$ | $R_{31}$ | $R_{31err}$ | $\phi_{1}$ | $\phi_{1err}$ | $\phi_{2}$ | $\phi_{2err}$ | $\phi_{3}$ | $\phi_{3err}$ | $\phi_{21}$ | $\phi_{21err}$ | $\phi_{31}$ | $\phi_{31err}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
3 | 2.61930268 | -0.4181856873 | 0.379 | 0.015 | 0.128 | 0.031 | 0.052 | 0.018 | 0.338 | 0.082 | 0.136 | 0.046 | 0.705 | 0.005 | 0.704 | 0.151 | 0.967 | 0.232 | 3.417 | 0.151 | 2.214 | 0.232
6 | 1.17707809 | -0.0708052759 | 0.256 | 0.011 | 0.12 | 0.009 | 0.053 | 0.017 | 0.469 | 0.038 | 0.204 | 0.065 | 0.564 | 0.004 | 0.647 | 0.011 | 0.782 | 0.287 | 4.834 | 0.011 | 3.713 | 0.287
7 | 1.11555371 | -0.0474904849 | 0.44 | 0.03 | 0.165 | 0.026 | 0.099 | 0.033 | 0.376 | 0.063 | 0.224 | 0.076 | 0.183 | 0.008 | 0.721 | 0.027 | 0.462 | 0.253 | 3.803 | 0.028 | 2.602 | 0.253
8 | 1.33497031 | -0.125471607 | 0.2 | 0.007 | 0.062 | 0.006 | 0.021 | 0.004 | 0.307 | 0.028 | 0.103 | 0.021 | 0.04 | 0.005 | 0.29 | 0.064 | 0.887 | 0.05 | 2.888 | 0.064 | 1.678 | 0.05
14 | 0.436427013 | 0.3600883762 | 0.348 | 0.01 | 0.149 | 0.038 | 0.063 | 0.01 | 0.426 | 0.109 | 0.18 | 0.029 | 0.916 | 0.011 | 0.328 | 0.232 | 0.751 | 0.027 | 4.691 | 0.232 | 3.167 | 0.029
16 | 0.646943545 | 0.189133616 | 0.421 | 0.009 | 0.211 | 0.013 | 0.143 | 0.009 | 0.501 | 0.033 | 0.339 | 0.023 | 0.082 | 0.003 | 0.423 | 0.01 | 0.821 | 0.01 | 3.2 | 0.01 | 0.475 | 0.011
17 | 1.07527992 | -0.0315215358 | 0.335 | 0.015 | 0.135 | 0.017 | 0.089 | 0.015 | 0.403 | 0.052 | 0.264 | 0.044 | 0.492 | 0.007 | 0.353 | 0.084 | 0.411 | 0.026 | 3.883 | 0.085 | 2.729 | 0.027
19 | 1.09962029 | -0.0412427448 | 0.449 | 0.007 | 0.192 | 0.007 | 0.125 | 0.006 | 0.427 | 0.016 | 0.279 | 0.014 | 0.421 | 0.002 | 0.184 | 0.005 | 0.973 | 0.008 | 3.723 | 0.006 | 1.333 | 0.009
20 | 2.6184651 | -0.4180467898 | 0.345 | 0.009 | 0.126 | 0.039 | 0.047 | 0.008 | 0.366 | 0.114 | 0.135 | 0.023 | 0.687 | 0.004 | 0.626 | 0.224 | 0.565 | 0.08 | 3.155 | 0.224 | 0.031 | 0.08
21 | 0.771695927 | 0.1125537919 | 0.381 | 0.004 | 0.181 | 0.004 | 0.15 | 0.003 | 0.474 | 0.011 | 0.393 | 0.009 | 0.671 | 0.002 | 0.727 | 0.005 | 0.807 | 0.003 | 3.992 | 0.005 | 1.859 | 0.004
22 | 1.56018852 | -0.193177078 | 0.296 | 0.018 | 0.132 | 0.017 | 0.095 | 0.011 | 0.446 | 0.061 | 0.322 | 0.041 | 0.192 | 0.008 | 0.664 | 0.017 | 0.486 | 0.064 | 3.33 | 0.019 | 2.577 | 0.065
23 | 1.38229242 | -0.1405999265 | 0.25 | 0.003 | 0.122 | 0.004 | 0.057 | 0.003 | 0.486 | 0.014 | 0.226 | 0.012 | 0.744 | 0.002 | 0.911 | 0.004 | 0.987 | 0.009 | 4.229 | 0.004 | 1.614 | 0.009
24 | 1.25871428 | -0.0999271593 | 0.288 | 0.013 | 0.13 | 0.011 | 0.092 | 0.012 | 0.45 | 0.042 | 0.319 | 0.043 | 0.867 | 0.007 | 0.011 | 0.015 | 0.351 | 0.022 | 3.314 | 0.016 | 1.58 | 0.022
26 | 0.575126634 | 0.2402365198 | 0.339 | 0.005 | 0.167 | 0.005 | 0.108 | 0.005 | 0.492 | 0.015 | 0.319 | 0.015 | 0.666 | 0.002 | 0.775 | 0.005 | 0.858 | 0.007 | 4.354 | 0.006 | 2.264 | 0.007
32 | 0.759864208 | 0.1192640116 | 0.248 | 0.005 | 0.112 | 0.027 | 0.069 | 0.005 | 0.451 | 0.11 | 0.278 | 0.02 | 0.549 | 0.005 | 0.479 | 0.15 | 0.472 | 0.016 | 3.97 | 0.15 | 2.05 | 0.016
35 | 2.24191287 | -0.3506187301 | 0.339 | 0.007 | 0.128 | 0.034 | 0.038 | 0.007 | 0.376 | 0.099 | 0.112 | 0.019 | 0.055 | 0.004 | 0.511 | 0.219 | 0.008 | 0.082 | 4.09 | 0.219 | 2.157 | 0.083
36 | 0.794929717 | 0.0996712674 | 0.178 | 0.013 | 0.061 | 0.012 | 0.031 | 0.014 | 0.341 | 0.07 | 0.173 | 0.075 | 0.438 | 0.007 | 0.271 | 0.023 | 0.146 | 0.047 | 4.058 | 0.024 | 2.092 | 0.047
38 | 0.748949532 | 0.1255474463 | 0.285 | 0.013 | 0.134 | 0.039 | 0.094 | 0.014 | 0.469 | 0.138 | 0.329 | 0.052 | 0.862 | 0.01 | 0.138 | 0.25 | 0.376 | 0.085 | 4.173 | 0.25 | 1.827 | 0.086
39 | 1.00765091 | -0.0033101014 | 0.331 | 0.011 | 0.143 | 0.034 | 0.108 | 0.015 | 0.43 | 0.102 | 0.325 | 0.044 | 0.898 | 0.007 | 0.221 | 0.229 | 0.54 | 0.025 | 4.248 | 0.229 | 2.189 | 0.026
40 | 1.04104059 | -0.0174676629 | 0.3 | 0.008 | 0.117 | 0.008 | 0.084 | 0.007 | 0.389 | 0.027 | 0.278 | 0.025 | 0.206 | 0.004 | 0.8 | 0.01 | 0.421 | 0.015 | 4.012 | 0.011 | 1.913 | 0.015
41 | 1.13876929 | -0.0564357467 | 0.308 | 0.007 | 0.121 | 0.008 | 0.083 | 0.019 | 0.392 | 0.025 | 0.269 | 0.062 | 0.159 | 0.004 | 0.705 | 0.008 | 0.243 | 0.276 | 4.009 | 0.009 | 1.68 | 0.276
44 | 0.764227056 | 0.116777591 | 0.45 | 0.005 | 0.237 | 0.005 | 0.16 | 0.005 | 0.527 | 0.012 | 0.356 | 0.011 | 0.814 | 0.002 | 0.055 | 0.003 | 0.293 | 0.005 | 4.249 | 0.004 | 2.209 | 0.005
46 | 0.791317111 | 0.1016494432 | 0.328 | 0.004 | 0.097 | 0.004 | 0.095 | 0.004 | 0.296 | 0.012 | 0.289 | 0.011 | 0.054 | 0.002 | 0.284 | 0.004 | 0.045 | 0.006 | 2.676 | 0.004 | 2.405 | 0.006
48 | 0.646873474 | 0.1891806574 | 0.398 | 0.004 | 0.21 | 0.004 | 0.136 | 0.004 | 0.528 | 0.01 | 0.34 | 0.009 | 0.63 | 0.002 | 0.681 | 0.003 | 0.74 | 0.004 | 4.223 | 0.003 | 2.211 | 0.004
49 | 1.55087039 | -0.1905755043 | 0.226 | 0.01 | 0.108 | 0.009 | 0.08 | 0.01 | 0.477 | 0.045 | 0.354 | 0.045 | 0.399 | 0.007 | 0.2 | 0.015 | 0.935 | 0.021 | 4.103 | 0.017 | 1.504 | 0.022
51 | 1.41125232 | -0.1496046689 | 0.226 | 0.008 | 0.055 | 0.008 | 0.051 | 0.011 | 0.242 | 0.036 | 0.224 | 0.049 | 0.068 | 0.007 | 0.289 | 0.041 | 0.051 | 0.109 | 2.54 | 0.042 | 2.193 | 0.109
52 | 0.792038365 | 0.1012537814 | 0.413 | 0.029 | 0.202 | 0.024 | 0.171 | 0.047 | 0.488 | 0.067 | 0.413 | 0.117 | 0.232 | 0.01 | 0.791 | 0.029 | 0.479 | 0.192 | 3.621 | 0.03 | 1.78 | 0.193
53 | 0.529628975 | 0.2760282635 | 0.437 | 0.01 | 0.205 | 0.008 | 0.108 | 0.006 | 0.468 | 0.02 | 0.247 | 0.015 | 0.104 | 0.005 | 0.67 | 0.011 | 0.149 | 0.02 | 4.475 | 0.012 | 2.124 | 0.02
57 | 0.584789332 | 0.2330005586 | 0.403 | 0.004 | 0.236 | 0.004 | 0.171 | 0.003 | 0.585 | 0.01 | 0.424 | 0.007 | 0.156 | 0.001 | 0.815 | 0.002 | 0.457 | 0.003 | 4.726 | 0.002 | 3.072 | 0.003
60 | 0.783862684 | 0.1057600098 | 0.475 | 0.006 | 0.245 | 0.006 | 0.159 | 0.006 | 0.516 | 0.013 | 0.335 | 0.012 | 0.201 | 0.002 | 0.819 | 0.004 | 0.441 | 0.006 | 4.188 | 0.004 | 2.125 | 0.006
62 | 0.94421245 | 0.0249302774 | 0.485 | 0.008 | 0.208 | 0.007 | 0.129 | 0.008 | 0.429 | 0.016 | 0.266 | 0.017 | 0.414 | 0.002 | 0.214 | 0.007 | 0.016 | 0.009 | 3.996 | 0.007 | 1.727 | 0.009
63 | 1.11978242 | -0.049133645 | 0.331 | 0.016 | 0.115 | 0.014 | 0.055 | 0.01 | 0.348 | 0.044 | 0.166 | 0.03 | 0.208 | 0.005 | 0.811 | 0.016 | 0.716 | 0.036 | 4.051 | 0.017 | 3.717 | 0.036
65 | 0.756691193 | 0.1210813207 | 0.468 | 0.006 | 0.234 | 0.006 | 0.145 | 0.006 | 0.501 | 0.014 | 0.309 | 0.012 | 0.425 | 0.002 | 0.283 | 0.004 | 0.137 | 0.006 | 4.294 | 0.005 | 2.284 | 0.006

Table A.3. The Fourier parameters of the BLHs in the LMC using the V-band data
from the OGLE-III survey.

OGLE-LMC-T2CEP | $f_{0}$ | log P[days] | $A_{1}$ | $A_{1err}$ | $A_{2}$ | $A_{2err}$ | $A_{3}$ | $A_{3err}$ | $R_{21}$ | $R_{21err}$ | $R_{31}$ | $R_{31err}$ | $\phi_{1}$ | $\phi_{1err}$ | $\phi_{2}$ | $\phi_{2err}$ | $\phi_{3}$ | $\phi_{3err}$ | $\phi_{21}$ | $\phi_{21err}$ | $\phi_{31}$ | $\phi_{31err}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
7 | 0.804721291 | 0.0943545081 | 0.363 | 0.008 | 0.098 | 0.01 | 0.045 | 0.007 | 0.27 | 0.028 | 0.123 | 0.018 | 0.246 | 0.003 | 0.889 | 0.012 | 0.871 | 0.035 | 4.07 | 0.013 | 3.984 | 0.035
9 | 0.567734944 | 0.2458543742 | 0.413 | 0.01 | 0.169 | 0.011 | 0.087 | 0.011 | 0.408 | 0.028 | 0.209 | 0.025 | 0.738 | 0.005 | 0.884 | 0.011 | 0.886 | 0.018 | 4.142 | 0.012 | 1.098 | 0.019
24 | 0.80212731 | 0.095756697 | 0.37 | 0.014 | 0.096 | 0.013 | 0.033 | 0.014 | 0.258 | 0.036 | 0.089 | 0.038 | 0.023 | 0.006 | 0.448 | 0.027 | 0.207 | 0.275 | 4.099 | 0.028 | 4.022 | 0.275
30 | 0.254110433 | 0.5949775038 | 0.256 | 0.016 | 0.082 | 0.028 | 0.04 | 0.016 | 0.321 | 0.11 | 0.155 | 0.062 | 0.269 | 0.007 | 0.142 | 0.395 | 0.97 | 0.226 | 5.372 | 0.395 | 4.174 | 0.226
48 | 0.691842499 | 0.1599927633 | 0.426 | 0.026 | 0.147 | 0.046 | 0.064 | 0.033 | 0.345 | 0.11 | 0.15 | 0.076 | 0.968 | 0.003 | 0.318 | 0.293 | 0.422 | 0.378 | 3.968 | 0.293 | 0.114 | 0.378
49 | 0.309093736 | 0.5099097961 | 0.176 | 0.009 | 0.048 | 0.012 | 0.011 | 0.007 | 0.272 | 0.065 | 0.061 | 0.037 | 0.931 | 0.008 | 0.392 | 0.076 | 0.891 | 0.29 | 4.906 | 0.076 | 3.766 | 0.29
53 | 0.95877363 | 0.0182839193 | 0.447 | 0.015 | 0.203 | 0.01 | 0.088 | 0.027 | 0.454 | 0.027 | 0.196 | 0.06 | 0.793 | 0.009 | 0.076 | 0.018 | 0.345 | 0.187 | 4.649 | 0.02 | 2.936 | 0.187
60 | 0.808680959 | 0.0922227826 | 0.433 | 0.008 | 0.106 | 0.012 | 0.025 | 0.007 | 0.244 | 0.027 | 0.057 | 0.017 | 0.585 | 0.005 | 0.57 | 0.011 | 0.865 | 0.345 | 4.08 | 0.012 | 3.834 | 0.345
61 | 0.846373695 | 0.0724378428 | 0.316 | 0.005 | 0.063 | 0.006 | 0.027 | 0.005 | 0.199 | 0.017 | 0.083 | 0.015 | 0.715 | 0.003 | 0.88 | 0.013 | 0.138 | 0.024 | 4.403 | 0.013 | 3.112 | 0.025
68 | 0.621385688 | 0.2066387538 | 0.218 | 0.005 | 0.053 | 0.005 | 0.024 | 0.005 | 0.243 | 0.022 | 0.111 | 0.02 | 0.029 | 0.004 | 0.508 | 0.015 | 0.582 | 0.032 | 4.398 | 0.016 | 6.255 | 0.033
69 | 0.979185356 | 0.0091350901 | 0.179 | 0.017 | 0.051 | 0.013 | 0.045 | 0.016 | 0.282 | 0.074 | 0.249 | 0.091 | 0.015 | 0.011 | 0.59 | 0.1 | 0.172 | 0.28 | 5.089 | 0.101 | 3.947 | 0.281
71 | 0.867929397 | 0.0615156017 | 0.431 | 0.006 | 0.139 | 0.006 | 0.027 | 0.007 | 0.322 | 0.013 | 0.061 | 0.015 | 0.659 | 0.002 | 0.77 | 0.007 | 0.829 | 0.111 | 4.412 | 0.007 | 2.217 | 0.111
73 | 0.323840472 | 0.4896688762 | 0.384 | 0.019 | 0.131 | 0.014 | 0.067 | 0.013 | 0.34 | 0.039 | 0.175 | 0.035 | 0.488 | 0.005 | 0.535 | 0.161 | 0.558 | 0.02 | 5.077 | 0.162 | 3.728 | 0.02
76 | 0.475216778 | 0.3231082346 | 0.427 | 0.02 | 0.138 | 0.023 | 0.085 | 0.029 | 0.321 | 0.055 | 0.199 | 0.068 | 0.771 | 0.009 | 0.059 | 0.061 | 0.197 | 0.197 | 4.823 | 0.062 | 2.421 | 0.197
77 | 0.82386308 | 0.0841449589 | 0.151 | 0.005 | 0.039 | 0.005 | 0.011 | 0.004 | 0.255 | 0.032 | 0.07 | 0.027 | 0.183 | 0.005 | 0.863 | 0.049 | 0.446 | 0.263 | 4.692 | 0.049 | 2.497 | 0.263
85 | 0.293677425 | 0.5321294364 | 0.298 | 0.006 | 0.09 | 0.006 | 0.033 | 0.005 | 0.301 | 0.021 | 0.11 | 0.016 | 0.257 | 0.003 | 0.097 | 0.008 | 0.913 | 0.031 | 5.244 | 0.008 | 4.046 | 0.032
89 | 0.85667704 | 0.0671828726 | 0.373 | 0.02 | 0.077 | 0.022 | 0.029 | 0.009 | 0.207 | 0.06 | 0.077 | 0.024 | 0.327 | 0.058 | 0.051 | 0.24 | 0.91 | 0.059 | 4.075 | 0.247 | 2.711 | 0.082
90 | 0.676157034 | 0.1699524297 | 0.224 | 0.006 | 0.038 | 0.007 | 0.033 | 0.007 | 0.168 | 0.029 | 0.144 | 0.028 | 0.746 | 0.004 | 0.03 | 0.08 | 0.75 | 0.052 | 4.948 | 0.081 | 0.072 | 0.052
92 | 0.382183436 | 0.4177281394 | 0.347 | 0.02 | 0.088 | 0.029 | 0.039 | 0.014 | 0.253 | 0.084 | 0.112 | 0.04 | 0.44 | 0.006 | 0.425 | 0.252 | 0.372 | 0.248 | 4.989 | 0.252 | 3.467 | 0.248
102 | 0.789875542 | 0.1024413336 | 0.436 | 0.006 | 0.123 | 0.005 | 0.044 | 0.005 | 0.283 | 0.012 | 0.101 | 0.011 | 0.214 | 0.002 | 0.858 | 0.007 | 0.545 | 0.019 | 4.275 | 0.007 | 2.541 | 0.02
105 | 0.67145576 | 0.1729825963 | 0.408 | 0.005 | 0.14 | 0.006 | 0.055 | 0.006 | 0.343 | 0.013 | 0.135 | 0.014 | 0.889 | 0.002 | 0.157 | 0.006 | 0.193 | 0.035 | 3.951 | 0.006 | 0.163 | 0.035
107 | 0.827030392 | 0.0824785305 | 0.239 | 0.008 | 0.054 | 0.015 | 0.022 | 0.008 | 0.225 | 0.062 | 0.091 | 0.031 | 0.997 | 0.005 | 0.392 | 0.395 | 0.881 | 0.122 | 4.073 | 0.395 | 2.455 | 0.123
116 | 0.508472942 | 0.2937321528 | 0.284 | 0.006 | 0.038 | 0.006 | 0.036 | 0.007 | 0.134 | 0.021 | 0.125 | 0.023 | 0.205 | 0.004 | 0.922 | 0.024 | 0.468 | 0.028 | 4.786 | 0.024 | 2.219 | 0.028
138 | 0.717571438 | 0.1441348561 | 0.312 | 0.007 | 0.06 | 0.009 | 0.028 | 0.009 | 0.19 | 0.029 | 0.089 | 0.026 | 0.361 | 0.004 | 0.146 | 0.067 | 0.489 | 0.051 | 4.237 | 0.067 | 5.698 | 0.051
145 | 0.29962254 | 0.5234255186 | 0.13 | 0.004 | 0.024 | 0.004 | 0.006 | 0.004 | 0.179 | 0.03 | 0.041 | 0.025 | 0.365 | 0.004 | 0.214 | 0.073 | 0.098 | 0.157 | 4.611 | 0.073 | 3.162 | 0.157
148 | 0.374289368 | 0.4267925092 | 0.343 | 0.006 | 0.097 | 0.026 | 0.054 | 0.007 | 0.283 | 0.075 | 0.157 | 0.021 | 0.872 | 0.004 | 0.306 | 0.218 | 0.692 | 0.039 | 5.103 | 0.218 | 3.621 | 0.039
160 | 0.569254354 | 0.244693639 | 0.338 | 0.012 | 0.094 | 0.012 | 0.071 | 0.017 | 0.277 | 0.035 | 0.21 | 0.05 | 0.796 | 0.004 | 0.012 | 0.013 | 0.063 | 0.172 | 4.208 | 0.014 | 1.102 | 0.172
163 | 0.590452294 | 0.2288151858 | 0.238 | 0.01 | 0.036 | 0.01 | 0.05 | 0.013 | 0.149 | 0.041 | 0.207 | 0.054 | 0.192 | 0.008 | 0.844 | 0.166 | 0.3 | 0.123 | 4.466 | 0.166 | 1.416 | 0.123
171 | 0.643185732 | 0.1916635982 | 0.171 | 0.006 | 0.025 | 0.006 | 0.042 | 0.007 | 0.146 | 0.036 | 0.245 | 0.041 | 0.239 | 0.007 | 0.664 | 0.051 | 0.277 | 0.029 | 2.74 | 0.051 | 0.378 | 0.03