Peculiar double-periodic pulsation in RR Lyrae stars of the OGLE collection. II. Short-period stars with dominant radial fundamental mode

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by  Zdenek Prudil

MNRAS000,1–12(2016) Preprint4January2017 CompiledusingMNRASLATEXstylefilev3.0
Peculiar double-periodic pulsation in RR Lyrae stars of the
OGLE collection. II. Short-period stars with dominant
radial fundamental mode.
Z. Prudil1,2⋆, R. Smolec3, M. Skarka4, H. Netzel5
1 Astronomisches Rechen-Institut, Zentrumfu¨r Astronomie der Universit¨atat Heidelberg, M¨onchhofstr. 12-14,
7 69120 Heidelberg, Germany
1 2 Department of Theoretical Physicsand Astrophysics, Masaryk University,Kotl´aˇrska´ 2, 611 37 Brno, Czech Republic
0 3 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka18, 00-716 Warszawa, Poland
2 4 Konkoly Observatory,MTA Research Centre for Astronomy and Earth Sciences, Konkoly Thege u´t 15-17, H-1121 Budapest, Hungary
5 Warsaw UniversityObservatory, Al. Ujazdowskie 4, 00–478 Warszawa, Poland
n
a
J

3
Accepted.Received;inoriginalform

]
R
ABSTRACT
S
Wereportthediscoveryofanewgroupofdouble-periodicstarsintheOGLEGalactic
.
h bulgephotometry.In38starsidentifiedasfundamentalmodeRRLyraeand4classified
p
as the first-overtone RR Lyrae, we detected additional shorter periodicity. Periods of
-
o the dominant variability in the newly discovered group are 0.28 < PD < 0.41days.
r Periodratios(0.68−0.72)aresmallerthantheperiodratiosoftheGalacticbulgeRRd
st stars. The typical amplitude ratio (of the additional to the dominant periodicity) is
a 20%forthestarsidentifiedasfundamentalmodeRRLyraeand50%forstarsclassified
[ as the first-overtone RR Lyrae. Ten stars from our sample exhibit equidistant peaks

in the frequency spectrum, that suggest the Blazhko-type modulation of the main
1
v pulsation frequency and/or the additional periodicity. The Fourier coefficients R21
1 and R31 are one of the lowest among fundamental mode RR Lyrae stars, but among
5 the highest for the first-overtonepulsators.For the phase Fourier coefficients ϕ21 and
7 ϕ31,ourstarslieinbetweenRRabandRRcstars.Discussedstarswerecomparedwith
0 the radial, linear pulsation models. Their position in the Petersen diagramcannot be
0 reproducedassumingthattworadialmodes areexcitedandtheirphysicalparameters
.
1 are similar to that characteristic for RR Lyrae stars. The non-radial mode scenario
0 also faces difficulties. We conclude that the dominant variability is most likely due
7 to pulsation in the radial fundamental mode including stars classified as the first
1 overtonemodepulsators.Atthispoint,wecannotexplainthenatureoftheadditional
: periodicity. Even more, classification of the stars as RR Lyrae should be treated as
v
i tentative.
X
Key words: sort stars: horizontal branch – stars: oscillations – stars: variables:
r
a RR Lyrae – methods: data analysis
1 INTRODUCTION which were previously considered to pulsate purely radi-
allyinthefundamental(Fmode,RRab),first-overtone(1O
Recent studies of RR Lyrae stars based on ultra-
mode,RRc),orinbothmodessimultaneously(F/1Omodes,
precise, quasi-continuous space observations (MOST,
RRd),werefoundtoshowadditionalpulsationalmodeswith
CoRoT and Kepler) and top-quality long-term ground-
low amplitude.
based measurements represented by the Optical Gravi-
Gruberbaueret al. (2007) discovered AQ Leo (RRd
tational Lensing Experiment (OGLE Udalskiet al. 2008;
star) to be the first example of the most numerous
Udalski, Szyman´ski& Szyman´ski2015)completelychanged
group of stars showing additional variability (lower in-
our view on these stars revealing the true complexity of
their pulsational behaviour. Some of the RR Lyrae stars, dex ‘A’) with period PA ∈ (0.6,0.64)P1O in MOST
data. This peculiar periodicity, with amplitude in the
mmag regime, was detected in photometry collected by
⋆ E-mail:[email protected] space telescopes CoRoT and Kepler (see e.g. references
(cid:13)c 2016TheAuthors
2 Prudil et al.
Szab´oet al. 2014; Moskalik et al. 2015), but mainly in suchsignal,thestarwassassignedtoacandidategroupand
the OGLE Galactic bulge data where more than 260 analysedmanuallyinthesamewayasinourpreviousstudy
such stars of both RRc and RRd types were identified Smolec et al. (2016):
(Netzel, Smolec & Moskalik 2015a,b). The most plausible Wefollowedastandardconsecutivepre-whiteningtech-
recent explanation for the peculiar PA variability counts nique (fitting sine series). We considered only well resolved
with the non-radial modes trapped in the outer part of the significant peaks (S/N > 4.0) with separation larger than
envelope (Dziembowski 2016). Beside these so called 0.61- 2/∆T, where ∆T is data length. If necessary, the outliers
stars, first-overtone pulsators also show additional period- wereomitted(4σ clipping)andseculartrendswereremoved
icity with P1O/PA ∼0.686 (Netzel, Smolec & Dziembowski usinglow-orderpolynomialsorsplinefunctions.Wealsoan-
2015; Netzel & Smolec 2016), which has not yet been ex- alyzedbothmagnitudeandflux-scaleddatatoavoid confu-
plained.Recentlyanothernewsubclass ofdouble-modeRR sionof possibleartificialpeakswith thecombinationpeaks.
Lyraeshadbeenidentified(Soszyn´skiet al.2016).These22 Combination peaks, if present in theflux-scaled data, are a
anomalous RRd stars discovered in the Magellanic system, convincingevidencethattwodetectedfrequenciesareintrin-
haveperiodratiosintherange0.725−0.738.Inmostcases, sic to the star. Their presence is essential for marking the
the fundamental mode is the dominant periodicity among star as a candidate. The stars without combination peaks
these stars. RRd stars with atypical period ratios detected were accepted only if they shared similar properties with
earlierintheGalactic bulge(Smolecet al.2015)andinM3 otherstarswithinourgroup(periodratio,shapeofthelight
(Jurcsik et al.2014)canalsobeclassifiedasanomalousRRd curve). For details of all steps of the analysis see sect. 2 in
stars. (Smolecet al. 2016).
In the first paper of the series (Smolec et al. 2016) In addition, to the automatic procedure, we manually
we report the discovery of another group of fundamen- analysed all stars located in the same region of period-
tal mode RR Lyrae stars showing additional mode with amplitude diagram as newly discovered double-periodic
PA/PF ∈(0.70;0.75)1 and with long fundamentalmodepe- stars3, to ensurecompletness of our sample.
riod. This period ratio and pulsational models suggest that
thesestars could be an extremecase of RRdstars.
Inthispaper,wepresentresultson38starscatalogued 3 RESULTS
by OGLE as RRab stars and on 4 stars identified as RRc
variableswithpulsationperiods0.28<PD <0.41days.Our Fromatotalsampleof36190singleperiodicRRLyraestars
intheOGLE-IVGalacticbulgecatalog,wereportadiscov-
stars seem to be adjacent to the sequence formed by the
ery of extra periodicity in 42 stars. In 14 of our stars, ad-
Galactic bulge classical RRd stars in the Petersen diagram
withshorterperiodsandlowerperiodratios(0.68−0.72)(see ditional periodicity was reported by Soszyn´skiet al. (2014,
2011),butnotdiscussedatall.Itwasonlymentionedinthe
Fig. 1). In the Sect.2 we provide a short summary about
remarks fileavailableatOGLEftparchive4.Fromthissam-
used methods. The Sect.3 contains a comparison of our
newly identified double-periodic stars with other RR Lyrae ple,38starshavebeenclassifiedbySoszyn´skiet al.(2014)as
thefundamental-modestars,and4starsasthefirst-overtone
subtypes together with brief notes on selected stars. In ad-
pulsators. In all stars, theperiod ratio of thetwo periodici-
dition, we examine the properties of our newly discovered
group and discuss several stars in detail. In section 4 we ties falls in the ≈(0.68−0.72) range. The extra variability
alwayshasashorterperiodandalower amplitudethanthe
discuss the pulsation nature of the newly discovered group.
dominantmode.Inaddition,inOGLE-BLG-RRLYR-14135
Section 5 summarises our results. The appendix contains a
onemoreperiodicitywasdetectedwithperiodratio0.74623.
short list ofstarswith an additionalvariability,thatdonot
In the top plot of Fig. 1, we compare known double-
fall into our group but were detected during the conducted
periodicRRLyraestarsfromourGalaxy,withanewlydis-
analysis.
covered group (black stars). Several double-periodic stars,
identifiedasRRab,haveasimilarperiodratioasthedouble-
periodic pulsators found by Netzel, Smolec & Dziembowski
2 DATA ANALYSIS
(2015, marked with green triangles). The latter stars are
After identification of the first long-period, double-periodic very different, however. The light curve of the dominant
RR Lyrae stars (Smolec et al. 2016), we searched for addi- variability in these stars is among the most typical for the
tional double-periodic stars with period ratio close to 0.7 first overtone RR Lyrae stars and additional variability is
among all RRab and RRc stars observed by OGLE-IV2 in alwaysofalongerperiodwithsignificantlylower amplitude
theGalacticbulge(36190starsintotal).Weusedautomatic (around4%ofthefirstovertonemodeamplitude).Further-
procedure pysca (Herzberg & Glogowski 2014) employing more, these stars form a well defined and sharp sequence
nonlinear-least squares methods and the Lomb-Scargle al- in thePetersen diagram, while our stars do not. The newly
gorithm for identification of the suspicious periodicity. We discoveredstarssharesomesimilaritieswithdouble-periodic
looked for an additional signal (with S/N > 4.0) in range stars found by Smolec et al. (2016) (magenta points in the
from νD+0.3c/d up to 2νD−0.3c/d to avoid possible con- Petersendiagram).Smolec et al.(2016)identifiedadditional
taminationwithstarsexhibitingBlazhkoeffect.Ifwefound periodicityamongfundamentalmodestars,wheretheextra
modehasaverylowamplitude(downto8.5%ofthefunda-
mentalmode).Ourgroup,ontheotherhand,standsonthe
1 A few stars in this period-ratio range were identified in Ke-
pler/K2byMolnar(2016).
2 ForfurtheranalysisweusedcombinedOGLE-IVandOGLE-III 3 PD=h0.28;0.42idaysandAI =h0.35;0.65imag.
datasetswhereveritwaspossible. 4 ftp://ftp.astrouw.edu.pl/ogle/ogle4/OCVS/blg/rrlyr/remarks.txt
MNRAS000,1–12(2016)
Peculiar double-periodic pulsation in RR Lyr stars 3
0.80 pentagons in top Fig. 1). The second periodicity PA2 =
0.215331(2)days with period ratio PA2/PD = 0.71586 fits
intoour newly discovered group.
0.75 The basic properties of newly found double periodic
stars aresummarized in Tab.1. Thecolumnscontain mean
Shortperiod0.7stars brightness I, period of the dominant, PD, and additional,
/PSL 0.70 SPOmiGetoLrlEueck-IoeVwt.-iacBzl.ue(lt2g.0ea1Rl6.R)(2d013) PfoAll,opweinrigodciocliutymtnosgectohnetraiwnitahmtphleitirudpeesrioofdtrhaetidoo,mPAin/aPnDt.vTahrie-
P 0.68-Netzeletal.(2015) ability, AD, and the amplitude ratio of both periodicities,
0.61-0.64-Netzeletal.(2015a,b) AA/AD. The last column, ‘remarks’, contains notes on in-
0.65 dividual objects. The stars with unresolved signal near PD
(possible period change or long period Blazhko effect) are
marked with ‘a’. Ten stars from our sample exhibit signa-
tures of the Blazhko effect (quasi-periodic modulation of
0.60 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 the light curve, for review, see Szab´o (2014)). These stars
log(PL[days]) are marked as ‘blD/A’, with regards whether the dominant
and/or additional mode exhibits the Blazhko modulation.
0.75 Stars that showed no combination frequencies were marked
with ‘c’. The letter ‘d’ marks stars with non-stationary ad-
0.74
ditional periodicity. In a few stars, we have detected har-
monic of theadditional variability and mark them with ‘e’.
0.73
Thenoteaboutadditional periodicity in remarks filein the
0.72 OGLEftparchiveismarkedby‘f’.InthetoppanelofFig.2
L we show a distribution of amplitude ratios for our stars. In
/P0.71 averagetheamplituderatiovaryinthe(5−90%)rangewith
PS most typical value 25 per cent. Stars from our group, pre-
0.70 viously classified as RRcstars, have higher amplitude ratio
in comparison with therest of our group of double-periodic
0.69 variables.Thisismostlikelycausedbyaloweramplitudeof
thedominantperiodicityinstarsidentifiedasfirst-overtone
0.68
variables.Inthebottompanelofthisfigure,weshowperiod-
amplitude dependence for the dominant variability. We ex-
0.67−0.55 −0.50 −0.45 −0.40 −0.35 plicitly divided our stars into two groups based on OGLE
log(PL[days])
classification. It is clearly visible that we have two groups,
stars identified as RRabpulsators in one and six stars clas-
Figure 1. The Petersen diagram for newly discovered double-
sified as RRcand RRabvariables in thesecond.
periodic stars (black stars). PL and PS are longer and shorter
period, respectively. The top panel displays several groups of Shapes of the light curves can be quantitatively
double-periodicstarsincomparisonwithourgroup.Themagenta described using the Fourier decomposition parameters
circles represent double-periodic stars found by Smolecetal. (Simon & Lee1981).InFig.3,wecomparethedifferencesin
(2016). The yellow pentagons stand for several F+1O HADS ourstars,RRcandRRabstarsfromtheOGLE-IVGalactic
stars found in the Galactic disk by Pietrukowiczetal. (2013). bulge catalog Soszyn´skiet al. (2014). We see, that the vast
In addition, green triangles and blue circles correspond to
majority of our stars with extra periodicity fall in the re-
the stars found by Netzel,Smolec&Dziembowski (2015) and
gion between RRc and RRab stars in the period-amplitude
Netzel,Smolec&Moskalik(2015a,b).Thebottompanelprovides
diagram. Four of our stars, identified by the OGLE team
narrowcontextbetweenOGLE-IVGalacticbulgeRRdstars(red
as RRc,fall in themiddle of RRcgroup, which likely moti-
squaresinbothplots)andourgroup.
vatedtheirclassification.However,theirFourierparameters
are different, as we discuss in the following. Stars from the
newly discovered group have, on average, shorter periods
other side of the period spectrum for RR Lyraes. Further-
thanRRabstarsandlargeramplitudesthanRRcstars.For
more,starsfromourgrouphavesomewhatlargeramplitudes
for the additional variability (around 25% of the dominant the Fourier amplitude ratios, R21 and R31, our stars popu-
late the region between RRc and RRab stars. The Fourier
periodicity, see the top panel of Fig. 2). The stars with ad-
ditional variability are similar to RRd stars (red squares), phases ϕ21 and ϕ31 for our stars follow linear progression
separating RRab and RRc stars. In addition, phase coeffi-
but the period ratio is lower around 0.7 (see bottom panel
cientsare among thelowest in thefirst-overtonestars.
of Fig. 1).
The only outlier in the Petersen diagram is OGLE- To explore the true nature of the dominant variability
BLG-RRLYR-14135. This star was identified as a funda- among these stars, we prewhitened the data with all com-
mental mode pulsator and two extra periodicities were ponents of the frequency spectra except kνD. The observa-
found. The first additional variability has period PA1 = tions with removed additional periodicity phased with the
0.2244660(9)daysandperiodratioPA1/PD =0.74623. This dominantperiod,aredisplayedinFig.4.Thecorresponding
period ratio is close, but significantly smaller than in High- legend shows OGLE id and pulsation period of the domi-
amplitude δ Scuti (hereafter referred to as HADS, yellow nant variability. All of the displayed light curves resemble
MNRAS000,1–12(2016)
4 Prudil et al.
Table 1.Basic properties of discussed double-periodicstars. Subsequent columns provide star’s id,mean I-bandbrightness, pulsation
period of the dominant mode, the period of the additional mode, period ratio, amplitude of the dominant mode, amplitude ratio, and
remarks.AllstarswereidentifiedbyOGLEasRRabstars,exceptthelastfour.
Name I[mag] PD[days] PA[days] PA/PD AD[mag] AA/AD Remarks
OGLE-BLG-RRLYR-00595 16.770 0.28183 0.19971 0.70863 0.11414 0.287
OGLE-BLG-RRLYR-00617 18.419 0.33811 0.24171 0.71491 0.16522 0.412
OGLE-BLG-RRLYR-01401 16.892 0.31304 0.21390 0.68330 0.21913 0.056
OGLE-BLG-RRLYR-01529 16.926 0.36332 0.25456 0.70064 0.17671 0.235 blD,f
OGLE-BLG-RRLYR-02147 16.716 0.35221 0.25067 0.71171 0.17831 0.197 a,f
OGLE-BLG-RRLYR-02217 16.387 0.36557 0.25700 0.70301 0.11729 0.174 f
OGLE-BLG-RRLYR-02943 17.448 0.33669 0.22978 0.68247 0.18827 0.049 a
OGLE-BLG-RRLYR-02990 17.814 0.35305 0.24763 0.70139 0.15975 0.205
OGLE-BLG-RRLYR-03090 17.197 0.32432 0.23087 0.71185 0.16619 0.184 blA
OGLE-BLG-RRLYR-05851 18.105 0.35469 0.24563 0.69253 0.19680 0.108
OGLE-BLG-RRLYR-07688 17.596 0.31544 0.21815 0.69159 0.19433 0.242
OGLE-BLG-RRLYR-08621 16.242 0.33001 0.22940 0.69513 0.19538 0.124
OGLE-BLG-RRLYR-09117 16.607 0.30968 0.21910 0.70750 0.18466 0.212 blD,blA,e,f
OGLE-BLG-RRLYR-12880 16.679 0.34004 0.23906 0.70302 0.21009 0.129 blD,d,e,f
OGLE-BLG-RRLYR-13745 16.391 0.35677 0.24762 0.69404 0.17592 0.213 blA
OGLE-BLG-RRLYR-14063 16.239 0.37532 0.26343 0.70188 0.15565 0.155 e,f
OGLE-BLG-RRLYR-14135 17.571 0.30080 0.22447 0.74623 0.17557 0.173
17.571 0.30080 0.21533 0.71586 0.17557 0.086
OGLE-BLG-RRLYR-14481 16.271 0.40971 0.28202 0.68835 0.17284 0.255 a
OGLE-BLG-RRLYR-15657 15.993 0.36659 0.25402 0.69294 0.18889 0.289
OGLE-BLG-RRLYR-15842 14.995 0.36544 0.25341 0.69345 0.17214 0.042 a
OGLE-BLG-RRLYR-16999 16.216 0.32582 0.23142 0.71026 0.17399 0.227 blA
OGLE-BLG-RRLYR-18798 18.138 0.36868 0.26039 0.70628 0.18446 0.316
OGLE-BLG-RRLYR-19058 17.703 0.30608 0.21404 0.69929 0.17930 0.195
OGLE-BLG-RRLYR-19121 17.455 0.35760 0.24818 0.69402 0.15869 0.209 blD,f
OGLE-BLG-RRLYR-20645 17.743 0.35648 0.24628 0.69088 0.17467 0.198
OGLE-BLG-RRLYR-21400 17.922 0.35273 0.25389 0.71979 0.15273 0.354 f
OGLE-BLG-RRLYR-22305 18.465 0.34065 0.23816 0.69914 0.20571 0.240 blA
OGLE-BLG-RRLYR-24360 17.920 0.32650 0.23003 0.70452 0.17587 0.207
OGLE-BLG-RRLYR-24500 18.329 0.33858 0.24043 0.71011 0.17638 0.213 c
OGLE-BLG-RRLYR-27203 17.687 0.32119 0.22332 0.69527 0.16233 0.258 blD
OGLE-BLG-RRLYR-28160 17.055 0.32689 0.23295 0.71261 0.16598 0.256 f
OGLE-BLG-RRLYR-29286 18.138 0.38828 0.27080 0.69744 0.17443 0.176 c
OGLE-BLG-RRLYR-30418 17.993 0.36410 0.25938 0.71238 0.18504 0.124
OGLE-BLG-RRLYR-30470 17.244 0.38117 0.26376 0.69198 0.19405 0.131
OGLE-BLG-RRLYR-30974 17.637 0.28973 0.20427 0.70505 0.20601 0.202
OGLE-BLG-RRLYR-32721 17.046 0.32617 0.23016 0.70565 0.18223 0.210 blA
OGLE-BLG-RRLYR-32923 18.246 0.34929 0.24503 0.70150 0.16659 0.274 c
OGLE-BLG-RRLYR-35838 16.065 0.31627 0.21852 0.69092 0.20416 0.235 f
OGLE-BLG-RRLYR-19847 18.264 0.31772 0.22438 0.70624 0.11475 0.502 c,f
OGLE-BLG-RRLYR-30908 18.610 0.28746 0.20314 0.70668 0.10017 0.396 f
OGLE-BLG-RRLYR-31754 18.009 0.31732 0.22598 0.71216 0.08845 0.906 e,f
OGLE-BLG-RRLYR-34006 17.973 0.31207 0.21946 0.70323 0.08899 0.511 f
a-unresolvedsignalatPD;blD -peak(s)oftheBlazhkoeffectinthevicinityofdominantmode;blA -peak(s)fortheBlazhkoeffect
inthevicinityofadditionalmode;c-nocombinationfrequency;d-non-stationaryPA;e-harmonicsofPA;f-listedin
remarks fileinOGLEarchive
triangular shape characteristic for the fundamental mode of the lower- and higher- frequency side peaks, A− and
pulsators. A+, respectively, in the case they were detected in the
Based on plots 3 and 4 we suspect that the cause of frequency spectrum. In addition, we enclose a list of fre-
thedominantperiodicity is thesame and thusfundamental quencies of detected modulation side peaks. The periods
pulsation mode seems to be the most probable for all stars of the Blazhko modulation range from 7days up to al-
from our sample (see Section 4 for the discussion). most500days.Insevenstars,tripletstructuresaredetected
Several stars from our double-periodic group seem to in thefrequencyspectrum.OGLE-BLG-RRLYR-12880and
manifest the Blazhko modulation (listed in Tab. 2). The OGLE-BLG-RRLYR-09117 exhibit two Blazhko modula-
columns contain OGLE identification, specification which tions. The OGLE-BLG-RRLYR-09117 displays modulation
periodicity is modulated (PA or PD), period of theBlazhko withthesameperiodofthedominantandadditionalperiod-
modulation PB. Furthermore, we provide the amplitudes icity.Amongthemajorityofthestarsweseeapreferencefor
MNRAS000,1–12(2016)
Peculiar double-periodic pulsation in RR Lyr stars 5
1.0
Discovereddouble-periodicstars
20 0.8
ag]0.6
m
[0.4
s AI0.2
r 15
a 0.0
t
s
f 0.7
o 0.6
mber 10 R21000...543
u 0.2
N 0.1
5 0.0
0.5
0.4 RRabstars
RRcstars
0.3
00.0 0.2 0.4 0.6 0.8 1.0 R310.2
AA/AD 0.1
0.24 0.0
RRabstars
4.5
0.22 RRcstars ad]34..50
0.20 [r3.0
ϕ2122..05
0.18 1.5
]
g
a 4
m 0.16 3
A[D 0.14 rad] 012
[
0.12 ϕ31−−21
−3
0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55
0.10 P[days]
0.008.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 Figure 3. The Fourier decomposition parameters for the newly
PD[days] discovereddouble-periodicstars(blackstars)withadditionalpe-
riodicityfilteredout.Forcomparison,theFouriercoefficients for
RRabstars(graydots)andRRcstars(bluedots)areincluded.
Figure 2. The distribution of amplitude ratio and the period-
amplitude diagram for newly discovered double-periodic stars.
The top-panel shows a histogram of amplitude ratios between
dominant and additional periodicity. The bottom panel displays • Ten stars from our sample exhibit the Blazhko modu-
period-amplitude diagram for the dominant periodicity among lation, and either the dominant, additional or both period-
discovereddouble-periodicstarswithregardtotheirOGLEclas- icities are modulated.
sification.
3.1 Remarks on the most well-observed stars
symmetryofthesidepeaks,ortheA+ componentishigher.
This section contains notes on a few of the most well-
Only in OGLE-BLG-RRLYR-03090 solely the A− compo-
observedstarsfrom theOGLEphotometrythatexhibitex-
nent is detected. It is worth noting that all stars listed in
tra periodicity. For each star, we present periods for the
Tab.2 were previously classified as the fundamental mode
dominant and the additional variability together with their
pulsators.
period ratio. In addition, we provide a list of combination
To summarize, we have discovered a new and distinct
frequencies that appeared in the frequency spectrum and
classofdoubleperiodicpulsatorswiththefollowing charac-
otherpossible peculiarities of an individualobject.
teristics:
OGLE-BLG-RRLYR-05851. The pulsa-
• Period of thedominant variability 0.28−0.41days. tion period is close to the average within our
• The additional periodicity is shorter. group, PD = 0.35468824(22)days, in addition we
• The period ratios are in therange of 0.68−0.72. found PA = 0.2456316(12)days. The period ratio
• Typical amplitude ratio is 25%. PA/PD = 0.69253 fall into the lower boundary of our
• Triangularshapeoflightcurvessuggestsdominantfun- group. This star has one of the lowest amplitudes for the
damentalmode for all stars from oursample. additional periodicity (only 10 percent of the amplitude of
• Values of R21 and R31 lie between typical values for thefundamentalmode).Inthefrequencyspectrum(Fig.5),
RRcand RRabstars. we found five harmonics for the fundamental mode and
• The ϕ21 and ϕ31 coefficients form a linear progression two combination frequencies νD + νA and 2νD + νA. In
between RRcand RRabstars. Fig. 5 we notice an obvious difference in the frequency
MNRAS000,1–12(2016)
6 Prudil et al.
−0.3
−0.2
−0.1
0.0
0.1
0.2 00595(0.28183d) 00617(0.33811d) 01401(0.31304d) 01529(0.36332d) 02147(0.35221d) 02217(0.36557d)
−0.4
−0.3
−0.2
−0.1
0.0
0.1
0.2 02943(0.33669d) 02990(0.35305d) 03090(0.32432d) 05851(0.35469d) 07688(0.31544d) 08621(0.33001d)
0.3
−0.4
−0.3
−0.2
−0.1
0.0
0.1
0.2
0.3 09117(0.30968d) 12880(0.34004d) 13745(0.35677d) 14063(0.37532d) 14135(0.30080d) 14481(0.40971d)
] −0.3
g −0.2
a −0.1
m 0.0
[ 0.1
I 0.2
∆ 0.3 15657(0.36659d) 15842(0.36544d) 16999(0.32582d) 18798(0.36868d) 19058(0.30608d) 19121(0.35760d)
−0.3
−0.2
−0.1
0.0
0.1
0.2
0.3 19847(0.31771d) 20645(0.35648d) 21400(0.35273d) 22305(0.34065d) 24360(0.32650d) 24500(0.33858d)
−0.4
−0.3
−0.2
−0.1
0.0
0.1
0.2 27203(0.32119d) 28160(0.32689d) 29286(0.38828d) 30418(0.36410d) 30470(0.38117d) 30908(0.28746d)
−0.4
−0.2
0.0
0.2
0.4 30974(0.28973d) 31754(0.31732d) 32721(0.32617d) 32923(0.34929d) 34006(0.31207d) 35838(0.31627d)
−0.6−0.4−0.20.0 0.2 0.4 0.6−0.6−0.4−0.20.0 0.2 0.4 0.6−0.6−0.4−0.20.0 0.2 0.4 0.6−0.6−0.4−0.20.0 0.2 0.4 0.6−0.6−0.4−0.20.0 0.2 0.4 0.6−0.6−0.4−0.20.0 0.2 0.4 0.6
Phase
Figure 4.Lightcurvesofthesamplestars,phasedwiththedominantperiodicitywiththeadditionalvariabilityfilteredout.
spectrum for OGLE-III and OGLE-IV. We did not detect ditionalperiodicityandthefundamentalmode,respectively
any combination frequencies in OGLE-III data. This could (see Tab.2).
be caused by lower amplitude of the additional periodicity The numerous and high-quality data allowed
in theOGLE-III data. us to use the time-dependent Fourier analysis
OGLE-BLG-RRLYR-09117. The most often ob- (Kova´cs,Buchler & Davis 1987) using merged OGLE-
served star in our sample, with the fifth shortest pulsation II, OGLE-III and OGLE-IV data (see Fig. 7). The top
period PD = 0.30967728(3)days. The additional variabil- panel shows available photometric data. Changes in ampli-
ity has a period PA =0.21909756(19)days and period ratio tude and phase for a given periodicity are displayed in the
PA/PD =0.70750 is typicalfor our group. middleandbottompanel.Inthebottomplot,weclearlysee
Thefrequencyspectrum(Fig.6)containseightharmon- phase changes in the dominant and additional periodicity.
icsforthefundamentalmode,additionalperiodicityandits While for the later, the change is not so pronounced, the
harmonic, and 14 combination frequencies in the following variation in the dominant mode can be modeled using a
formkνD+νA (k=1,...,6),νA−νD,2νA−νD,kνD+2νA parabolic function,which gives usgrowing pulsation period
(k=0,...,4) andkνD−νA (k=2,...,5).Inaddition,this with a rate of 1.5 · 10−6daysper1000days.
star, as theonly one from our sample, exhibitstheBlazhko OGLE-BLG-RRLYR-12880.Thestarwasidentified
modulationwiththesameperiodinbothperiodicities,with as the fundamental mode pulsator, with pulsation period
period PB = 252.8(7)days. In the frequency spectrum, we PD = 0.3400408(1)days, furthermore we found extra peri-
seea triplet anddoubletstructurein thevicinityof thead- odicity PA =0.2390565(5)days. The period ratio PA/PD =
MNRAS000,1–12(2016)
Peculiar double-periodic pulsation in RR Lyr stars 7
Table 2. List of double-periodic stars exhibiting the Blazhko modulation. Columns contain information about modulated periodicity,
whetherdoubletortripletstructureispresentandcompletelistofidentifiedsidepeaks.
OGLE-id mod.periodicity PB[days] A−[mag] A+[mag] listofadditionalmodulationside-peaks
OGLE-BLG-RRLYR-01529 PD 21.80(2) 0.007(1) 0.013(1) 2νD+νB,3νD+νB
OGLE-BLG-RRLYR-03090 PA 121.8(5) 0.021(2) - νD+νA−νB,2νD+νA−νB
OGLE-BLG-RRLYR-09117 PD 252.8(7) 0.0016(3) 0.0019(3) νD+νB,νD−νB,2νD+νB
PA 252.8(7) 0.0017(3) 0.0041(3) νD+νA+νB,2νD+νA+νB,νD+νA−νB,
2νD+νA−νB,3νD+νA+νB,νD+2νA+νB,
νA−νD+νB
OGLE-BLG-RRLYR-12880 PD 70.85(8) 0.017(4) 0.019(7) νD−νB1,νD+νB1,2νD−νB1,2νD+νB1,
3νD−νB1,3νD+νB1,4νD−νB1,4νD+νB1,
5νD−νB1,6νD−νB1,5νD+νB1
PD 75.24(9) 0.0056(4) 0.0055(4) νD−νB2,νD+νB2,2νD−νB2,2νD+νB2,
3νD+νB2,3νD−νB2
OGLE-BLG-RRLYR-13745 PA 334.9(8) 0.020(1) 0.028(1) νD+νA+νB,νD+νA−νB,2νD+νA+νB,
νA−νD+νB,2νD+nuA−νB,3νD+νA−νB,
νA−νD−νB,3νD+νA+νB,4νD+νA−νB,
3νD+2νA−νB
OGLE-BLG-RRLYR-16999 PA 507(11) - 0.035(3)
OGLE-BLG-RRLYR-19121 PD 482(5) 0.022(2) 0.018(2) νD+νA−νB,νD+νA+νB,2νD+νA−νB,
2νD+νA+νB
OGLE-BLG-RRLYR-22305 PA 7.947(4) - 0.030(6) νD+νA+νB
OGLE-BLG-RRLYR-27203 PD 37.09(4) 0.022(3) 0.019(3) 2νD+νB
OGLE-BLG-RRLYR-32721 PA 495(16) - 0.026(3)
0.025 0.05
e[mag]00..001250 νA νD+νA O2GνLDE-+IVνA e[mag]00..0034 OGνLAE--IVνD νA 3νD-νA νD+4ννAD-νA
ud0.010 ud0.02 2νD-νA 2νA
plit0.005 plit0.01
m m
A0.000 A0.00
0.025 0.05
e[mag]00..001250 OGLE-III e[mag]00..0034 OGνLAE--IIνID νA 3νD-νA νD+νA
d d
u0.010 u0.02
plit0.005 plit0.01
m m
A0.0000 2 4 6 8 10 A0.000 2 4 6 8 10
Frequency[c/d] Frequency[c/d]
Figure 5. The top panel shows the frequency spectrum of the Figure 6. The same as Fig.5 but for the OGLE-BLG-RRLYR-
OGLE-IVdataforOGLE-BLG-RRLYR-05851afterprewhitening 09117.
withdominantfrequencyanditsharmonics.Additionalvariabil-
ityandcombinationfrequenciesofbothperiodicitiesaremarked.
Other significant peaks are their daily aliases. The bottom fig- spectrum computed from OGLE-III. This could be caused
ure shows the frequency spectrum of the same star but for the bylower amplitudeof theadditional periodicity.
OGLE-III data. Dashed red lines mark frequencies of the main
OGLE-BLG-RRLYR-30908. One of the four stars
pulsationfrequencyanditsharmonics.
classified as RRc variable in our sample with pulsation pe-
riod PD = 0.28746404(55)days, the second shortest period
among discovered stars and additional periodicity with pe-
0.70302 is similar to the other stars in our sample, but the riod of PA = 0.20314449(70)days. Thus the period ratio
amplitude ratio AA/AD = 0.1292 is somewhat lower. The PA/PD =0.70668 fall in the middle of our group. The am-
frequency spectrum (see Fig. 8) contains six harmonics for plituderatioAA/AD =0.3958isthelowest amongthestars
thefundamentalmodeand oneharmonic for theadditional identifiedbySoszyn´skiet al.(2014)asthefirst-overtonepul-
periodicity(νA and2νA).Inaddition,wedetectedfollowing satorsinourgroup.Thefrequencyspectrum(seeFig.9top
combinations:kνD+νA(k=1,...,5),νA−νDand2νA+2νD. plot) of this star contains three harmonics of the dominant
Two Blazhko modulations were detected in the vicinity of periodicity.Wefoundtwocombinationfrequenciesofthead-
the fundamental mode, with periods PB1 = 70.85(8)days ditional variability with the dominant periodicity, νD+νA
and PB2 =75.24(9)days. In the frequency spectrum we see and νA−νD.
aresiduaatthekνA,whichsuggestchangesinperiodofthe OGLE-BLG-RRLYR-31754. Anotherstar from our
additionalvariability.Similarly asinFig.5,inFig.8wesee sampleoriginally classifiedasRRcwithdominantpulsation
lower number of combination frequencies in the frequency period PD = 0.31731570(42)days and with additional pe-
MNRAS000,1–12(2016)
8 Prudil et al.
16.1 16.2
16.2 OGLE-II-III-IV-09117-I[mag] 16.3
16.3 16.4
16.4 16.5
1166..56 16.6
16.7 16.7
16.8 16.8
16.9 16.9
17.0 17.0
200
220 AA[mmag] 60 50
55 195
210 50 190 45
200 45 40
190 40 185
180 35 180 35
AD[mmag] 30 30
170 25 175
6.92 1.5
3.70 φD[rad] φA[rad] 1.00 6.90 11..34
3.69 0.95 6.88 1.2
3.68 0.90 6.86 11..10
3.67 6.84 0.9
0.85 6.82 0.8
3.66 6.80 0.7
0 1000 2000 3000 4000 5000 6000 7000 5200 5400 5600 5800 6000 6200 6400 6600
HJD-2450000[days] HJD-2450000[days]
Figure 7. Time-dependent analysis of amplitude and phase changes of the two periodicities in OGLE-BLG-RRLYR-09117. The top
panels show available photometric data in the OGLE catalogue. The middle and bottom panels display amplitude and phase changes
forboth variabilities.Squared symbolscharacterize thedominant periodicity. Its amplitude andphase correspondto theleft-handside
verticalaxes.Circularsymbolscharacterizetheadditionalvariability.Itsamplitudesandphasecorrespondtotheright-handsidevertical
axes. The left-hand panels show data analysed on season-to-season basis, while the right-hand panels show analysis of OGLE-IV data
withresolution≈50days.
Amplitude[mag]00000000........000000003001122350505050 OGνLAE--IνVD νA νD+νA mplitude[mag]00000.....0000012345 νA-νD νA νDO+GLνEA-IV
Amplitude[mag]00000000........0000000030011223505050500 OGLE-I2II 4νA 6 νD+ν8A 10 Ae[mag]0000....000106800 OGνLAE--IνV2D 4 νA 6 νD8+νA 2νA 10
d
Frequency[c/d] u0.04
mplit0.02
F12i8g8u0r.e 8.Thesameas Fig.5but forthe OGLE-BLG-RRLYR- A0.000 2 4 6 8 10
Frequency[c/d]
Figure 9. The frequency spectra for the OGLE-BLG-RRLYR-
riodicity PA = 0.22598012(25)days (period ratio PA/PD = 30908 (top panel) and for the OGLE-BLG-RRLYR-31754 (bot-
0.71216). TheamplituderatioAA/AD =0.9058 isthehigh- tom panel) after prewhitening with dominant frequency and its
est among stars in our group. The frequency spectrum dis-
harmonics.Additionalperiodicityandcombinationfrequenciesof
plays two harmonics for the dominant periodicity and one both variabilities are marked. Other significant peaks are their
for the additional variability (see Fig. 9 bottom plot). Fur- daily aliases. Only OGLE-IV data were available. Dashed red
thermore,frequencyspectrumofthisstarcontainsfollowing lines mark frequencies of the main pulsation frequency and its
combinations: νD+νA, 2νD+νA, νD+2νA, νA−νD. harmonics.
Based on figuresdisplayingfrequencyspectruminsub-
section 3.1andscarceappearanceofthemark‘a’inTab.1,
it is worth mentioningthat thedominantperiodicity is sta-
MNRAS000,1–12(2016)
Peculiar double-periodic pulsation in RR Lyr stars 9
ble in the vast majority of cases. Only in four instances, (still, typically lower than in the“classical”RRd stars), so
we detected residual power at the kνD after the prewhiten- their position in the Petersen diagram is easily reproduced
ing,whichsuggests changesintheperiod and/oramplitude assumingexcitationofradialfundamentalandfirst-overtone
(mark ‘a’ in Tab. 1). modes. In addition, Blazhko-like modulation is commonly
detectedinanomalousRRdstars.Variablesdiscussedinthis
paperclearly do not belong to thisgroup.
The other possibility we now consider, is that the dis-
4 DISCUSSION
cussed stars are the so-called binary evolution pulsators
We have discovered a new group of double-periodic vari- (BEPs). The first, and so far the only member of this
ables. Majority of these stars are identified in the OGLE group, is OGLE-BLG-RRLYR-02792. The star was cata-
catalogasRRab–RRLyrstarspulsatingintheradialfun- logued as RRab, member of the eclipsing binary system
damental mode. The characteristic, asymmetric light curve (Soszyn´skiet al. 2011). Its dynamical mass is only 0.26M⊙
shape(Fig.4)leavesnodoubt–itmustcorrespondtopulsa- however (Pietrzyn´skiet al. 2012), definitely too low for
tion. The large amplitude and non-linear, triangular shape RR Lyr variable. BEPs are stars that evolved in the bi-
ofthelightcurveimmediatelysuggeststheradialfundamen- narysystemand,afterexperiencingthemasslossevent,en-
talmode.Aglimpse attheFourierparameterplots(Fig.3) ter the classical instability strip. The non-linear model sur-
pointshowever,thatthisisnotthelightcurveshapethatis vey conducted by Smolec et al. (2013) shows that such ob-
typicalforRRabstarswithsuchshortpulsationperiods.In jectsmayindeedshowlarge-amplituderadialpulsationthat
fact,genuineRRabstarswithperiodsshorterthan0.43days may mimic RR Lyr variability. In fact, models presented
are scarce in the Galactic bulge and nearly not present for inSmolec et al.(2013) seem tosupportthehypothesisthat
periods shorter than 0.35days. The light curves do not re- thediscusseddouble-periodicstarsareBEPs.Theexpected
sembletheRRclightcurveseither.TheFourierparameters fundamentalmode light curvesat theblueedgeof theclas-
correspondingtothedominantvariabilitylieinbetween the sical instability strip have simple triangle-like form (fig. 11
parameters typicalfor RRaband RRcstars. inSmolec et al.2013).TheFourierparametersofhotBEPs
The secondary variability in the discussed stars, is al- fall in between RRab and RRc stars (their fig. 13; begin-
ways of shorter period and of lower amplitudeas compared ning of the model sequences). Also, close to the blue edge,
to the dominant variability. The corresponding light curve bothlow orderradialmodesmaybesimultaneously excited
shape is a pure sine wave in nearly all the cases, i.e. we do (their fig. 3) and beat pulsation is thus possible. The lin-
not detect the harmonics of the additional variability. The earpulsationmodelsdisprovethisscenarioaswell.Wehave
secondaryperiod istooshort tobeconnectedwith rotation computeda grid of models with masses in the0.2−0.4M⊙
orwiththebinarityeffects.InthePetersendiagram(Fig.1), range,withluminosities inthe20−70L⊙ rangeandmetal-
the newly identified group forms a rather large cloud that licity range the same as considered in Fig. 10 (other model
touches theRRd sequence at its extreme, short-period tail. parameters arethesame asin Smolec et al. 2016). Wenote
We note in passing, that this tail is observed only in the that little is known about expected physical parameters of
Galacticbulge,andexplainedasduetohighmetallicityRRd BEPs, as only one object was observed so far (see how-
variables (Soszyn´skiet al. 2011). Could the discussed stars everKarczmarek et al.2017).Therangeofthephysicalpa-
be extreme cases of RRd variables, with the radial funda- rameters given above, is motivated by the model study by
mental and radial first-overtone modes excited? Such pos- Smolec et al.(2013),andassuresthatmodelperiodsarenot
sibility can be easily verified with linear pulsation calcula- farfromthoseobservedinRRLyrstars.Themodelsassume
tions. Theresultsare presentedin Fig. 10. Weused exactly homogeneousenvelopewith chemical composition thesame
the same set of models as in Smolec et al. (2016) and the as in RR Lyr-typemodels. For 0.2M⊙ and 0.3M⊙ models,
readerisreferredtoitssect.4.1foralltechnicaldetails.The periodsoftheunstableradialmodesaresignificantlylonger
filled symbols mark the models in which both radial modes than observedin ourstars. Period ratios for 0.4M⊙ models
are simultaneously unstable – a necessary condition for the are plotted in Fig. 11. The models have longer periods and
non-resonantbeat pulsation. Opensymbols totheleft, cor- higher period ratios, and are far from the region in which
respond to the models in which only the first-overtone is double-periodicstarsreside. Clearly,thediscussedstars are
unstable and open symbols to the right, correspond to the notfundamentalandfirst-overtonedouble-moderadialpul-
models in which only the fundamental mode is unstable. sators.Atleast,notassumingtheirphysicalparametersare
Although the models cover a wide range of metallicities, close to expected for RR Lyr stars or BEPs (that mimic
masses and luminosities, it is clear that our group cannot RR Lyr stars). Other combinations of radial modes do not
correspond to RRd pulsation. Only for the highest (solar) fit thediscussed group as well.
metallicity,thehighestmass(0.7M⊙),andthelowest lumi- Wenotethatsimpletriangularlightcurveshapeischar-
nosity (40L⊙), the models in which both radial modes are acteristic for fundamental mode HADS stars. Fourier pa-
simultaneously unstable approach the part of the Petersen rametersofthesestarsaresimilaraswell(seefig.8andfigs.
diagram in which thenew, double-periodicvariables reside. 4-7 in Poretti 2001, note that cosine convention is adopted
The extreme RRd scenario must be dropped. The models in that paper). Periods of these stars are typically below
also indicate, that for the considered range of physical pa- 0.2days however, while in our stars they are longer than
rameters, it is even hard to get the unstable fundamental 0.28days.Periodratiosintheradialmulti-modeHADSstars
mode at such short periods. arealsovastlydifferent,seee.g.fig.10inPietrukowicz et al.
Recently,Soszyn´skiet al.(2016)identifiedanewgroup (2013).
of anomalous RRd variables. These stars however, have Assuming that the dominant variability do correspond
longer fundamental mode periods and higher period ratios to the radial fundamental mode (large amplitude and non-
MNRAS000,1–12(2016)
10 Prudil et al.
linear light curve shape make this hypothesis most plau-
sible), the additional variability may correspond to non- 0.75 [Fe/H]=-2.5 0.5M⊙
radialpulsationmode.Low-degreemodesmaybeexcitedin
0.74 [Fe/H]=-1.5
RRLyrmodels(VanHoolst, Dziembowski & Kawaler1998;
[Fe/H]=-1.0
Dziembowski & Cassisi 1999), preferentially in the vicinity 0.73
of the radial modes. Although the frequency spectrum of [Fe/H]=-0.5
F
such modes is very dense, their growth rates do display a /PO 0.72 [Fe/H]=0.0
local maximum close to the position of the radial modes. P1 0.71
In particular, for ℓ = 1 modes, the growth rates approach
that of the radial first-overtone mode and their frequency 0.7
is higher than radial first-overtone frequency [see e.g. fig. 1
in Van Hoolst, Dziembowski & Kawaler (1998) or fig. 1 in 0.69 40L⊙ 50L⊙ 70L⊙
Dziembowski (2016)]. This would lead to the period ratios 0.68
a bit lower than observed for RRd variables, which is what
wewant.Fig.10seemstodisprovethisscenarioagain.Non- 0.75 0.6M⊙
radial modes of ℓ=1 are unstable only if the first-overtone
0.74
is unstable, which occurs at longer fundamentalmode peri-
odsthanobserved inthediscussedstars. Also, it would not 0.73
be clear why the non-radial mode is excited instead of the
F
neighbouring,strongly driven radial first-overtone. /PO 0.72
At the moment we have no explanation for the nature P1 0.71
of thediscussed double-periodicvariables.
0.7
0.69
5 CONCLUSIONS
0.68
Wepresent thediscovery of a newgroup of double-periodic
stars in the OGLE Galactic bulge photometry. In 38 stars 0.75 0.7M⊙
identified in the OGLE catalog as the fundamental mode
0.74
RRLyraestarsandin4starsidentifiedasthefirst-overtone
pulsators (RRc), we detect additional variability of lower 0.73
amplitudeand of a shorter period. The period ratios in the F
P 0.72
discoveredstars(0.68−0.72) arelowerthanintheGalactic /O
bulgeRRd stars (0.725−0.750). P1 0.71
Althoughourstarsdonotformasharpsequenceinthe
Petersen diagram, they occupy a well-defined region. Also, 0.7
their light curves are very similar and different from the
0.69
light curves of single-periodic RRab and RRc stars. This is
best demonstrated with the help of Fourier decomposition 0.68
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
parameters. The Fourier coefficients R21, R31, ϕ21 and ϕ31
P (days)
for discovered stars differ from typical values for stars in F
RRab and RRc group. For the Fourier parameters R21 and
R31,ourgroupliessomewhereinthemiddle,betweensingle
Figure 10.Modelledradialmode periodratios confronted with
periodicRRcandRRabstars.Thenewlydiscovereddouble-
thenew double-periodicvariablesinthePetersen diagram.RRd
periodicstarshavehighervaluesofthesecoefficientsincom-
starsfromtheGalacticbulgearealsoplottedforreference(small
parison with RRc stars. The similar difference applies for
dots).Threepanelscorrespondtodifferentmodelmasses,asindi-
the phase coefficients ϕ21 and ϕ31 where our group creates cated inthetoprightcorners.Modelsequences areplotted with
some kind of a transition between the fundamental mode differentsymbols,dependingonthemodels’luminosityandwith
and first-overtonepulsators. In addition, stars in our group differentcolors,dependingonthemodels’metallicity,asindicated
havethelowestvaluesofthesecoefficientsamongRRcstars. inthetoppanel.Filledsymbolscorrespondtothemodelsinwhich
Our findings suggest that the original OGLE classification fundamental modeandfirst-overtonearesimultaneouslylinearly
asRRaborRRcisquestionableinourstars.Tenstarsfrom unstable. Opensymbols correspondto the modelsinwhichonly
oursample show properties typical for Blazhko-typemodu- onemodeislinearlyunstable.
lation(equidistantpeaksinthefrequencyspectrum).Inthe
majority of modulated stars, themodulation sidepeaksare
symmetrical, or we observethat higherfrequencyside peak with larger amplitude (AD > 0.15mag, all stars originally
is of higher amplitude. classified as RRab, except two) and with lower amplitude
Theadditionalperiodicityisalwaysofloweramplitude. (AD < 0.12mag, four stars originally classified as RRc and
Exceptforonecase,amplituderatiosarebelow0.6;themost twoasRRab).Originoftheapparentgapinthedistribution
typical value is 0.2 (see the top panel of Fig. 2). Consid- of amplitudesof thedominant variability is unclear.
ering the amplitude of the dominant variability (see the We find it very challenging to explain the nature of
lower panel of Fig. 2), our stars divide into two groups: the discovered group. Although these stars were identified
MNRAS000,1–12(2016)