VI-Band Follow-Up Observations of Ultra-Long-Period Cepheid Candidates in M31

3 MB·English

by  Chow-Choong Ngeow

Draftversion January13,2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
VI-BAND FOLLOW-UP OBSERVATIONS OF ULTRA-LONG PERIOD CEPHEID CANDIDATES IN M31
Chow-Choong Ngeow1, Chien-Hsiu Lee2,3, Michael Ting-Chang Yang1, Chi-Sheng Lin1, Hsiang-Yao Hsiao1,
Yu-Chi Cheng1, Zhong-Yi Lin1, I-Ling Lin1, Shashi M. Kanbur4 and Wing-Huen Ip1
Draft version January 13, 2015
ABSTRACT
The ultra-long period Cepheids (ULPCs) are classical Cepheids with pulsation periods exceeding
5
≈80 days. The intrinsic brightness of ULPCs are ∼1 to ∼3 mag brighter than their shorter period
1
counterparts. Thismakesthemattractiveinfuturedistancescaleworktoderivedistancesbeyondthe
0
limit set by the shorter period Cepheids. We have initiated a program to search for ULPCs in M31,
2
using the single-band data taken from the Palomar Transient Factory, and identified eight possible
n
candidates. In this work,we presented the VI-band follow-up observations of these eight candidates.
a
Based on our VI-band light curves of these candidates and their locations in the color-magnitude
J
diagramand the Period-Wesenheitdiagram,we verify two candidates as being truly ULPCs. The six
1 other candidates are most likely other kinds of long-period variables. With the two confirmed M31
1
ULPCs,wetestedthe applicabilityofULPCsindistancescaleworkbyderivingthedistancemodulus
] of M31. It was found to be µM31,ULPC = 24.30±0.76 mag. The large error in the derived distance
R modulus, together with the large intrinsic dispersion of the Period-Wesenheit (PW) relation and the
smallnumberofULPCsinagivenhostgalaxy,meansthatthequestionofthesuitabilityofULPCsas
S
standardcandlesisstillopen. FurtherworkisneededtoenlargethesampleofcalibratingULPCsand
.
h reduce the intrinsic dispersion of the PW relation before re-considering ULPCs as suitable distance
p indicators.
- Subject headings: Cepheids — variablesstars —galaxies: individual(M31)—distance scale —stars:
o
distances
r
t
s
a 1. INTRODUCTION riods longer than ∼80 days.
[
Most studies of extragalactic distance determination
Cepheidvariablesspanaclassofpulsatingstarswithin
use the Large Magellanic Cloud (LMC) as a distance
1 the instability strip in the Hertzsprung-Russell dia-
v gram. Their well-known period-luminosity (PL) rela- anchor. Since the LMC has irregularity in its three-
6 tion (also known as the Leavitt law, as first presented dimensional shape and low metallicity, many authors
5 inLeavitt & Pickering1912)makesCepheids goodstan- suggestinsteadusingM31asasteppingstonetocosmic-
4 distance determination(see, e.g.,Clementini et al. 2001;
dard candles. They constitute the first rung of the
2 Vilardell et al.2010,andreferencestherein). Themerits
extra-galactic distance scale ladder. Previous stud-
0 of M31 include the following: it has a simple geometry;
ies have shown that the Cepheid PL relation can be
. potentialM31distance-indicatorstarsarebrightenough
1 used to determine distances out to the order of 10-
toberesolved;itisalocalcounterparttothespiralgalax-
0 30 Mpc (e.g., Freedman et al. 2001; Riess et al. 2011)
ies that are used to determine the extragalacticdistance
5 using the Hubble Space Telescope (HST). When cou-
1 pled with other secondary distance indicators, such as (see, e.g., Freedman et al. 2001); and it is a local bench-
: type Ia supernovae and the Tully-Fisher relation, one mark to calibrate the Tully-Fisher relation. Despite its
v proximity, M31 has not been considered as a distance
is able to determine distances to galaxies that are well
i
X within the Hubble flow. However, the cosmic distance anchor (see, e.g., Riess et al. 2011), because a distance
anchor has to have a precise distance estimate and har-
r ladder suffers from several uncertainties at each lad-
a der rung. Thus, Bird et al. (2009) have proposed the borafairamountofdistanceindicatorssuchasCepheids.
M31 has not yet met these two criteria because (1) its
use of very luminous Cepheids, the so-called ultra-long-
current distance estimate has larger uncertainty (∼ 4%,
period Cepheids (hereafter ULPCs), to extend distance
estimation beyond ≈ 100 Mpc. Besides the potential Vilardell et al.2010)comparedtootherdistanceanchors
(for example, LMC at ∼ 2% level; see Pietrzyn´ski et al.
to be used as distance indicators, ULPCs can also be
2013), and (2) there was no large sample of well stud-
usedtoconstrainandenhanceourunderstandingofstel-
ied Cepheids in the literature. Nevertheless, recent
lar pulsation and evolution theories for intermediate- to
studies of M31 eclipsing binaries (Lee et al. 2014b) and
high-mass stars crossing the instability strip (Bird et al.
Cepheids (Fliri & Valls-Gabaud 2012; Riess et al. 2012;
2009; Fiorentino et al. 2012). Bird et al. (2009) defined
Kodric et al. 2013, 2014) have demonstrated the poten-
ULPCstobefundamental-mode(FU)Cepheidswithpe-
tial of establishing M31 as a distance anchor in the near
future. Given the increasing importance of M31 in fu-
1Graduate Institute of Astronomy, National Central Univer-
ture distance scale work, it makes sense to search for
sity,Jhongli32001,Taiwan
2Max Planck Institute for Extraterrestrial Physics, D-85748 and identify ULPCs in M31: such studies could provide
Garching,Germany a “one-step” calibration of the Hubble constant, similar
3UniversityObservatoryMunich,D-81679Munich,Germany
to the role of NGC 4258 in Riess et al. (2011).
4DepartmentofPhysics,SUNYOswego,Oswego,NY13126,
USA Ground-based CCD observations of Cepheids in M31
2 Ngeow et al.
Clementini+
30:00.0
POMME
42:00:00.0 Vilardell+
POINT-AGAPE
DIRECT
30:00.0 WeCAPP
NMS
41:00:00.0
40:30:00.0
54:00.0 52:00.0 0:50:00.0 48:00.0 46:00.0 44:00.0 42:00.0 40:00.0 38:00.0
Figure 1. Footprints forsomeoftheprevioussurveys,assummarizedinTable1,superimposedonaPTFimageofM31. Notethat one
CCD(upper row,thirdfromtheleft)isinoperable.
originate either from dedicated surveys to search for were detected in these studies.
Cepheids and (detached) eclipsing binaries, or as by- Therefore, we have initiated a program to search for
products from intense monitoring of M31 to detect ULPCsinM31byusingdatafromthePalomarTransient
micro-lensing events. Examples of the former case in- Factory(PTF;Law et al.2009;Rau et al.2009). Thisis
cludeFreedman & Madore(1990),Magnier et al.(1997), becausethePTFdatacancovertheentirediskofM31,as
and Vilardell et al. (2006, 2007), as well as the DI- shown in Figure 1. In addition, PTF observes M31 rou-
RECT project (see Kaluzny et al. 1998, and subsequent tinely with cadence up to one day. These twoconditions
papers in the series). For the micro-lensing experi- make PTF an ideal data set to search for the ULPCs
ments, these include the AGAPE (Ansari et al. 2004), in M31. Our search results were published in Lee et al.
the Nainital Microlensing Survey (Joshi et al. 2010), (2013, hereafter Paper I) and Lee et al. (2014a). Using
the POINT-AGAPE Survey (An et al. 2004), the We- image subtraction techniques, eight ULPC candidates
CAPP survey (Fliri et al. 2006), and the POMME Sur- were identified. Figure 2 displays the postage stamp im-
vey(Fliri & Valls-Gabaud2012). Inaddition,time-series ages for these candidates based on PTF data. As men-
observationsoftwoM31fields,usingtheLargeBinocular tioned in Paper I, time series VI-band data is needed
Telescope, have also detected a number of short-period to further confirmor disprovethe ULPC nature of these
Cepheids (Clementini et al. 2011). Recently, Riess et al. candidates. In this work, we report the VI-band follow-
(2012) combined data from the POMME Survey and up observations for all these eight candidates. Section
HSTobservationsfor68Cepheids,andderiveatruedis- 2 describes the follow-up observations, data reduction,
tance of 752±27 kpc to the M31. Kodric et al. (2013) and the calibrationof the light curves. Analysis of these
presented a catalog of M31 Cepheids, including funda- light curves and the results are presented in Section 3,
mental and first overtone Cepheids (as well as Type II followed by our conclusions in Section 4.
Cepheids), basedonthe firstyearofthe PanoramicSur-
vey Telescope and Rapid Response System (PS1, Pan- 2. THEFOLLOW-UPOBSERVATIONS
STARRS1) PAndromeda Survey. A summary of these
The VI-band follow-up observations were carried out
surveys and projects is presented in Table 1, and the
with the P60 Telescope (P60; Cenko et al. 2006) at the
coverage for some of the surveys is shown in Figure 1.
PalomarObservatoryandtheLulin1mTelescope(LOT;
These studies are limited in that most of the observa-
Kinoshita et al. 2005) at Lulin Observatory. These ob-
tions,withtheexceptionofthePOMMESurveyandthe
servations began in 2012 October and ended in 2013
PAndromeda Survey, cover only part of M31, and most November. P60 is equipped with a 2k×2k CCD with
of them concentrate on the disk (see Figure 1). Further-
a pixel scale of 0.379 arcsec per pixel, while LOT used
more, no Cepheids with periods longer than ∼ 80 days a 1k × 1k CCD with a pixel scale of 0.512 arcsec per
VI-Band Follow-Up Observations of ULPC Candidates 3
Table 1
SummaryofModern-dayCepheidObservations inM31.
Project/Surveya Telescopeb FieldCenterc Field-of-View Pix. Scaled Obs. TimeSpane Ref.f
DedicatedSurveystoSearchforCepheids(andEclipsingBinaries)
Freedman&Madore 3.6mCFHT 10fieldscoveringBaade’sFieldI,III&IV 2′×3′g ··· 1985-1988 1
Magnieretal. 2.5mINT 9fieldsalongspiralarms 12.5′×12.5′ 0.367 1993(9) 2
1.3mMDM (sameasabove) 10.9′×10.9′ 0.637 1993(11) 2
Vilardelletal. 2.5mINT α=00h44m46s δ =+41o38′20′′ 33.8′×33.8′ 0.33 1999-2003(21) 3,4
DIRECT:M31B TwoTel.h α=11o.20δ =+41o.59 11′×11′ 0.32 1996-1997 (∼43) 5
DIRECT:M31A TwoTel.h α=11o.34δ =+41o.37 11′×11′ 0.32 1996-1997 (∼44) 6
DIRECT:M31C TwoTel.h α=11o.10δ =+41o.42 11′×11′ 0.32 1996-1997 (∼53) 7
DIRECT:M31D TwoTel.h α=11o.03δ =+41o.27 11′×11′ 0.32 1996-1997 (∼58) 8
DIRECT:M31F TwoTel.h α=10o.10δ =+40o.72 11′×11′ 0.32 1996-1997 (∼51) 9
DIRECT:M31Y 1.2mFLWO α=10o.97δ =+41o.69 11′×11′ 0.33 1999-2000 (∼25) 10
By-productsfromMicro-lensingExperiments
AGAPE 2.0mTBL 6+1fieldscentered atM31, 14′×10′i 0.30 1994-1996 (∼69) 11
orientedalongthemainaxis
NMS 1.0mST α=00h43m38s δ =+41o09.1′ 13′×13′ 0.37 1998-2002(>150) 12,13
POINT-AGAPE 2.5mINT α=00h43m10s δ =+40o58′15.0′′ 33′×33′ 0.33 1999-2001(∼180) 14
α=00h44m00s δ =+41o34′00.0′′ 33′×33′ 0.33 1999-2001(∼180) 14
WeCAPP 1.2mCAO α=00h42m44s.3δ =+41o16′07.5′′ 17.2′×17.2′ 0.50 2000-2001 15
0.8mWO mosaicCAO’sFOVwith4pointings 8.3′×8.3′ 0.49 1999-2008 15
POMME 3.6mCFHT α=00h43m50s δ =+41o45′0′′ 1o×1o 0.187 2004(∼50) 16
α=00h41m50s δ =+40o44′0′′ 1o×1o 0.187 2005(∼50) 16
OtherTime-seriesObservations
Clementinietal. 8.4mLBT α=00h48m13.11s δ =+40o19′09.4′′ 23′×23′ 0.225 2007(∼8) 17
α=00h49m08.31s δ =+42o16′09.4′′ 23′×23′ 0.225 2007(∼8) 17
PAndromeda 1.8mPS1 α=00h42m44.33s δ =+41o16′07.5′′ ∼2.6o×∼2.6o 0.258 2010-2011(∼183) 18
a AGAPE = AndromedaGravitational AmplificationPixelExperiment;NMS = Nainital MicrolensingSurvey; POINT-AGAPE = Pixel-lensingObser-
vations with the Isaac Newton Telescope-Andromeda Galaxy Amplified Pixels Experiment; WeCAPP = Wendelstein Calar Alto Pixellensing Project;
POMME=PixelObservationsofM31withMEgacam
b CFHT= Canada-France-Hawaii Telescope(Hawaii, USA);INT =Issac Newton Telescope(Spain);MDM =McGraw-Hill Telescopeat theMichigan-
Dartmouth-MIT(MDM)Observatory;FLWO=F.L.WhippleObservatory(Arizona,USA);TBL=BernardLyotTelescope(France);WO=Wendelstein
Observatory(Germany); CAO =Calar AltoObservatory (Spain);ST= SampurnanandTelescope(India); LBT= Large BinocularTelescope(Arizona,
USA);PS1=Pan-STARRS1Telescope(Hawaii,USA)
c R.A.anddecl. offieldcenterisinJ2000.
d CCDpixelscalein”/pixel.
e Numberintheparenthesisisthenumberofobservingnightswhenavailable.
f Reference: 1. Freedman&Madore (1990); 2. Magnieretal. (1997); 3. Vilardelletal. (2006); 4. Vilardelletal. (2007); 5. Kaluznyetal. (1998); 6.
Staneketal.(1998);7. Staneketal.(1999);8. Kaluznyetal.(1999);9. Mochejskaetal.(1999);10. Bonanosetal.(2003);11. Ansarietal.(2004);12.
Joshietal.(2003);13. Joshietal.(2010);14. Anetal.(2004);15. Flirietal.(2006);16. Fliri&Valls-Gabaud(2012);17. Clementinietal.(2011);18.
Kodricetal.(2013)
g TheFOVforeachofthe10CCDfields.
h ThetwotelescopesusedintheDIRECTprojectare: 1.3mMDMand1.2mFLWO.
i ThisisthetotalFOV;theFOVforindividualfieldsis4′×4.5′.
7-1326 8-0272 8-0326 8-1176 8-1180 8-1498 9-0530 4-1047
Figure 2. Postage-stampimagesoftheeightULPCcandidatesreportedinPaperI.TheupperrowshowsthePTFR-bandimages,while
the lower row shows the PTFg-band images. Note that the R- and g-band images are fromdifferent epochs. Allstamps have aFOV of
30′′×30′′. Thegreencircleswitharadiusof5′′ indicatethelocations ofthecandidates.
4 Ngeow et al.
Table 2
VI-bandLightCurvesfortheCandidates.
Candidate Telescope Band MJD m σm
8-0326 LOT V 56218.62510 18.819 0.031
8-0326 LOT V 56224.71680 18.931 0.034
8-0326 LOT V 56224.71403 18.935 0.033
8-0326 LOT V 56235.64163 19.026 0.038
··· ··· ··· ··· ··· ···
Note. —(Thistableisavailableinitsentiretyinmachine-readable
andVirtualObservatory(VO)forms.)
bright (V ∼ 16.3mag. to ∼ 19.9mag.) and isolated
LGS
stars taken from the M31 Local Group Survey catalog
(LGS; Massey et al. 2006). These LGS stars were vi-
sually inspected to ensure they were located within the
P60and LOTimages,as wellasawayfromanycrowded
regions in the images. About ∼ 15 to ∼ 25 LGS stars
in the “master” catalog were used to construct the PSF
modelforeachimagebyexecutingtheIRAFsubroutines
Figure 3. SeeingdistributionsintheV (upperpanel)andIbands DAOPHOT.PHOT, DAOPHOT.PSTSELECT and DAOPHOT.PSF.
(lower panel) for the P60 and LOT images. For the P60 observa- Sky coordinates for all the stars in the “master” cat-
tions, besides a pair of VI-band images, an additional V-band
alogs were then converted to pixel coordinates and
image was also taken on the nights between 2012 November and
2013March. saved as a coordinate file. Finally, DAOPHOT.PHOT and
DAOPHOT.ALLSTAR were run with the input coordinate
pixel. Observations for both telescopes were obtained
fileandPSFmodelto obtainthe instrumentalPSFpho-
in queue mode when there was available observing time
tometry for the stars in the “master” catalog.
in suitable weather conditions. Imaging data from P60
was reduced with a dedicated pipeline as described in
2.1. Light Curves from Differential Photometry
Cenko et al. (2006). For LOT images, subroutines in
IRAF5 wereusedtoreducethedataintheusualmanner The VI-band light curves for the eight candidates
were constructed using differential photometry tech-
(bias and dark subtraction, and flat-fielded with mas-
niques given in Broeg et al. (2005). Instead of using a
ter flat images). The LOT I-band images suffered from
single star as a comparison star (cs) to obtain differen-
a fringing problem. To remove the fringe patterns, we
tial photometry, the technique presented in Broeg et al.
mediancombinedthe I-bandimagesforcandidates with
an internal ID 4-10476 and created a master fringe im- (2005) used a number of stars(either all stars in the im-
ages or a subset of suitable constant stars) to construct
age. We selected the images for this candidate because
an artificial comparisonstar:
it is located far away from the M31 bulge and disk (see
Figure 1 in Paper I). Hence, the images do not have a
strong background gradient. The master fringe image ∆m=mc−<m>cs = mc−Xwimcis, (1)
was smoothed by a “boxcar” averaging algorithm avail-
i
ablefromIRAF,andthenscaledandsubtractedfromall
of the LOT I-band images. Astrometric refinement for wheremcwastheinstrumentalmagnitudesforourcandi-
both P60- and LOT-reduced images were performed us- datesineither the V orI band,andwi werethe weights
ing astrometry.net(Lang et al. 2010). Figure 3 shows for individual comparisonstars such that Piwi =1. At
theseeingdistributionsofalltheimagestakenfromboth the first stage, we constructed differential photometry
telescopes. It can be seen that some images with large lightcurvesforapairofLGSstarsinour“master”cata-
seeingcouldbe affectedby badweather. After visualin- logs,asmentionedinthe previoussection,bytakingone
spection, images thatwere affected by bad weatherwere of them as a comparison star. We then removed those
discarded. This left 568 and 386 images from P60 and LGS stars that exhibited a large scatter in the differ-
LOT, respectively. ential light curves. This left a subset of good LGS stars
Photometry based on point-spread function fitting beforeequation(1)wasappliedtoeachofourcandidates.
(hereafter PSF photometry) for the candidates and Since the calibrated VI-band magnitudes were available
suitable stars in each frame were obtained from for these comparison stars from the LGS catalog, light
IRAF/DAOPHOTsubroutines. For each candidate, we first curvesconstructedfromequation(1)werecalibratedvia
created a “master” catalog (with ∼ 50 stars) that in- the following equation:
cluded: (1) the location of the ULPC candidate itself;
(le2c)tefadinbtassetdarosnitnhethbeesvticseineiitnygoimf athgees)c;aannddid(a3t)ersetlaatriv(esley- mcalibrate=∆m+Xwimcis,LGS, (2)
i
5 IRAF is distributed by the National Optical Astronomy Ob- where w were the same weights as in equation (1), and
i
sfoerrvRaetoseraiersc,hwinhiAchstarorenoompeyr,aItnecd.,buyndtehrecAoosspoecriaattiivoenaogfreUemnievnetrswitiitehs mcis,LGSweretheVI-bandmagnitudesfromtheLGScat-
theNationalScienceFoundation. alog. The calibrated VI-band light curves for the eight
6 SeePaperIforthemeaningofinternalID. candidates are given in Table 2, and displayed in panel
VI-Band Follow-Up Observations of ULPC Candidates 5
(a) and (b) of Figures 4-7.
Table 3
3. ANALYSISANDRESULTS RevisedPeriodsandMeanMagnitudesfortheCandidates.
3.1. Period Search and Folded Light Curves Candidate Period(days) <V > <I> W
The new VI-band light curves suggested that periods
for the candidates need to be revised from Paper I. For M31ULPCCandidates
eachpairoftheVI-bandlightcurves,wefirstsubtracted 8-0326 74.427±0.120 18.684 17.256 15.043
the arithmetic mean of the light curve, followed by nor- 8-1498 83.181±0.178 18.856 17.783 16.120
malizationofthe lightcurve using the peak-to-peakam-
plitude. We then applied the well-documented Lomb- M31non-ULPCCandidates
Scargle algorithm to search for periodic signals by com- 8-1176 125.313±4.832 19.095 17.367 14.689
biningthesemean-subtractedandnormalizedpairofVI- 7-1326 132.608±4.543 19.357 17.356 14.254
8-0272 169.262±4.461 20.464 18.176 14.630
band light curves (as shown in panel (c) of Figures 4-7) 4-1047 216.169±0.907 18.625 17.548 15.879
to eachof the candidates. We only searchedfor periodic 9-0530 221.779±17.695 20.218 19.092 17.347
signals around ∼ ±30 or ∼ ±50 days from the periods 8-1180 222.124±5.959 19.780 17.246 13.318
reported in Paper I (with the exception of candidate 8-
0272, for which a shorter period range was searched for The VI-band light curves for the other six candidates
periodicsignals). Theperiodscorrespondingtothehigh- are given in Figures 6 and 7. These curves do not dis-
est peaks in the Lomb-Scargle periodogram were taken play light curves that are expected for Cepheids. In the
as the periods for these candidates. They are indicated followingsub-sections,thetwocandidateswithCepheid-
by a vertical dashed line in panel (d) of Figures 4-7, as like light curves are referred to as “M31 ULPC candi-
well as listed in the second column of Table 3. We also dates,” while the other six candidates will be referredto
ran a Monte-Carlo simulation to quantify the errors on as “M31 non-ULPC candidates.” Further confirmation
thecorrespondingperiodicsignals. Assumingthe photo- or falsification of their ULPC nature will be detailed in
metric errorsare Gaussian,about10,000simulatedlight the nextsub-section. We note thatthe two “M31ULPC
curves were generated using the Box-Muller method for candidates”havewell-determinedperiods(witherrorsof
eachofthecandidates. TheLomb-Scarglealgorithmwas theorderof∼0.2%),whiletheperiodsforthe“M31non-
then applied to these light curves in a similar fashion to ULPC candidates,” with the exception of the candidate
the combined VI-band light curves. The errors on the with an internal ID of 4-1047, have a much larger error
derived periods were then estimated as the rms of the (from ∼ 2.6% to ∼ 8%). Furthermore, as mentioned in
corresponding peaks in the power spectra. Paper I, these two “M31 ULPC candidates” have pre-
Using the periods given in Table 3, we folded the VI- viously been classified as Cepheids in the literature (for
band light curves for these eight candidates. The folded example,in Magnier et al.1997, but they haveincorrect
VI-band light curves were then fitted with a low-order periods).
Fourier decomposition (for example, see Simon & Lee ThetwoM31ULPCcandidateshaveperiodsof∼74.4
1981) in the following form: and ∼ 83.2 days, respectively. According to the defini-
tion by Bird et al. (2009), a ULPC should havea period
longerthan80days. Hence,the∼74.4daysULPCfound
i=2,3,4
inthisworkmaynotbeclassifiedasULPC.However,an
m(φ)=m0+ X Aicos(2iπφ+Φi) (3) 80 day period cut is rather arbitrary, and we prefer to
i=1 identifytheULPCsbasedonthediscussiongiveninSec-
where φ ∈ [0,1] were phases of the pulsating cycles. tion 3.2. Furthermore, initial period detection searches
for this candidate gave results in excess of 80 days in
The fitted light curves, shown as black curves in panels
Paper I, and was refined to a shorter period with other
(e) and (f) of Figures 4-7, were used to derive the VI-
period-search algorithms and VI-band light curve data.
band mean magnitudes (by converting the fitted light
Therefore, we retained this candidate in the sample of
curves to intensity, taking the average, and converting
M31 ULPCs.
back to magnitude), as well as the extinction-free We-
senheit function W. In order to be consistent with pre-
3.2. Verification of the ULPC Candidates
viousworks(Bird et al.2009;Fiorentino et al.2012),we
adopted the same Wesenheit function in the form of Besides the shapes of the VI-band light curves, we
W =I−1.55(V−I)fromUdalski et al.(1999a). Theco- verify/falsify the ULPC nature of our eight candidates
efficientof1.55intheWesenheitfunctionisbasedonthe by comparing them to the known ULPCs (given in
extinction law from Schlegel et al. (1998). The derived Fiorentino et al. 2012) in the color-magnitude diagram
mean magnitudes and the values of Wesenheit function (CMD) and the Period-Wesenheit diagram (PWD), col-
are listed in Table 3. lectively presented in Figure 8. Using the CMD and
The shape of the ULPC VI-band light curves are PWD to identify Cepheids has been done, for exam-
similar to the classical Cepheids (Bird et al. 2009; ple, in Udalski et al. (1999b) and Kodric et al. (2013).
Ngeow et al. 2013), for which light curves exhibit the Only those Cepheids identified with periods longer than
characteristic “saw-tooth” shape with a quick rise to ∼80dayswillbere-classifiedasULPC(Bird et al.2009;
maximum light followed by a slow decline to minimum Fiorentino et al.2012). Whenmakingsuchcomparisons,
light. Based on our VI-band light curves, only two of wehaveadoptedthedistancemodulusofM31asµ =
M31
the candidates (8-0326 and 8-1498) exhibit Cepheid-like 24.46mag, recommended by de Grijs & Bono (2014), to
light curves, as shown in Figures 4 and 5, respectively. convert the observed magnitudes of these candidates to
6 Ngeow et al.
(a) (d)
(b) (e)
(c) (f)
Figure 4. (a)ObservedV-bandlightcurveforcandidate8-0326,wherethegreenopencirclesandredfilledsquaresarefortheP60and
LOT data, respectively. (b) Observed I-band light curve for the same candidate. (c) the combined VI band light curve that was used
inperiodsearch; seethe text (Section 3)for details. (d)The Lomb-Scargleperiodogram, at which the correspondingperiod atthe peak
oftheperiodogram (indicates byaverticaldashed line),istheadopted periodlistedinTable3. (e)TheV-bandfoldedlightcurveusing
theperiodgiveninTable3. (f)TheI-bandfoldedlightcurveforthesamecandidate. Theblackcurvesin(e)and(f)representthefitted
lightcurvesbasedonlow-orderFourierdecomposition.
(a) (d)
(b) (e)
(c) (f)
Figure 5. SameasFigure4,butforcandidate 8-1498.
the absolute magnitudes. We also included the LMC sistentwithULPCsineithertheCMDorPWDdiagram,
FU Cepheids and long-period variables (LPV) based but not in both. For example, candidates 4-1047 and 9-
on the OGLE-III database, taken from Soszynski et al. 0530fall within the ULPC instability strip, but they are
(2008) and Soszynski et al. (2009) respectively, in these outsidethe±3σboundaryofthePeriod-Wesenheit(PW)
diagrams. Again, we adopted µ = 18.49 mag relation. Similarly,candidates7-1326,8-0272and8-1176
LMC
(de Grijs et al.2014)whenconvertingtheobservedmag- arelocatedwithinthe±3σboundaryofthePWrelation,
nitudestoabsolutemagnitudes. WeenlargedFigure8by however they are too red in the CMD to be considered
onlyshowingtheknownULPCsandoureightcandidates as ULPC. Since the main goal of this work is to verify
in Figure 9. Figures 8 and 9 reveal that the two “M31 the ULPCnature ofourcandidatesinM31,determining
ULPCcandidates”areindeedULPC,asbothofthemfall the nature of these six non-ULPC candidates is beyond
in the parameter spaces defined by the known ULPCs. the scope of this paper, and they will not be discussed
The remaining six “M31 non-ULPC candidates” are fal- further.
sified as ULPC based on their location in the CMD and It is expected that a galaxy would have small num-
PWD diagrams,eventhough a few of them may be con- ber of ULPCs for two reasons. Firstly, ULPCs are
VI-Band Follow-Up Observations of ULPC Candidates 7
(a) (d)
(b) (e)
(c) (f)
(a) (d)
(b) (e)
(c) (f)
(a) (d)
(b) (e)
(c) (f)
Figure 6. SameasFigure4,butforcandidate 4-1047,8-0272&9-0530.
8 Ngeow et al.
(a) (d)
(b) (e)
(c) (f)
(a) (d)
(b) (e)
(c) (f)
(a) (d)
(b) (e)
(c) (f)
Figure 7. SameasFigure4,butforcandidate7-1326,8-1176&8-1180. Wefoundthatanadditionalzero-pointoffsetof+0.078,+0.089
and+0.078isneededtobeaddedtoP60dataforthesecandidates withinternalID7-1326,8-1176and8-1180,respectively.
VI-Band Follow-Up Observations of ULPC Candidates 9
Figure 8. Comparisonof oureightcandidates to theknownULPCslistedinFiorentinoetal.(2012),as wellasthe LMCCepheids and
long-periodvariables (LPV) fromthe OGLE-III database, inthe observed CMD (leftpanel) and PWD (rightpanel). We included LPVs
to aid in falsifying the ULPC nature of our candidates. The LPVs were classified as small amplitude red giants (OSARG), semi-regular
variables(SRV),andMirabytheOGLEteam(Soszynski etal.2009). NotethatthesaturationlimitinOGLE-IIIdataisaround∼13mag
to∼13.5mag. ThistranslatestoMV ∼−5.0magto∼−5.5mag.
Figure 9. Observed CMD (left panel) and PWD (right panel) only showing the ULPCs. Since the predicted boundary of the ULPC
instabilitystripfromtheoretical calculations isnot yet available, weused the color range availablefrom known ULPCs (Fiorentinoetal.
2012), 0.6 < (V −I) < 1.6, to represent the (crude) boundary of the instability strip (shown as vertical lines in the left panel). The
solidlineintherightpanelisthePeriod-WesenheitrelationadoptedfromFiorentinoetal.(2012),andthedashedlinesrepresentthe±3σ
boundary(whereσ=0.34mag).
Table 4
M31CepheidswithPeriodsGreater than∼75daysbutLessthan80days.
NameorID Period(days) α(J2000) δ(J2000) Reference
vn.4.2.678 78.00 11.06420 41.56927 Riessetal.(2012)
PSOJ010.5806+40.8319 74.79 10.58066 40.83192 Kodricetal.(2013,onlyforCepheidsclassifiedas“FU”)
intermediate- to high-mass stars with masses between ond,theseintermediate-tohigh-massstarsneedtocross
∼15M⊙ ang∼20M⊙ (Bird et al.2009;Fiorentino et al. theinstabilitystripinordertopulsateandthetimethat
2012). Hence, their number should be lower than their they spend inside the instability strip is relatively short
shorter period counterparts that have lower mass. Sec- as compared to their evolutionary age. Based on the
10 Ngeow et al.
list compiled in Fiorentino et al. (2012), the number of
ULPCs in a given galaxy ranges from one (NGC 6822),
two(M81andIZw18),three(SMCangNGC300),four
(LMC, NGC 1309 and NGC 3021), five (NGC 55), and
nine (NGC 3370). Then, it is not a surprise that only
two ULPCs were found in M31. Another reason for de-
tecting a small number of ULPCs in M31 could be due
to characteristics of PTF data. For example, the one
CCDthatisoutofcommissioncoversaportionofM31’s
disk (see Figure 1), and the stars in M31’s bulge region
are not resolvable in PTF images. Further discussionon
the effect of PTF data canbe found in Paper I, and will
notbe repeatedhere. A few additionalULPCs mightbe
discovered from the three years of the Pan-STARRS1’s
PAndromedaSurvey(M.Kodricetal. 2014,privatecom-
munication). On the other hand, if the period cut of
∼ 80 days that defines ULPC is lowered to ∼ 75 days,
then there are a few more very long-period Cepheids
in M31 that could be classified as ULPCs. These are
listed in Table 4. They were not reported in Paper I be-
cause their periods are lowerthan the searchcriterionof Figure 10. Top: comparison of the two Period-Wesenheit rela-
P > 80 days. Furthermore, there is no VI-band photo- tionsadoptedfromBirdetal.(2009)andFiorentinoetal.(2012);
Bottom: difference in the derived distance modulus from these
metric data available for these Cepheids currently.
twoPeriod-WesenheitrelationsasafunctionoftheULPCperiods.
3.3. Distance Scale Application
(2014). Notethatthesampleofmetal-poorULPCs(12+
In the previous sub-section, we adopted a distance log[O/H] < 8.4 dex) in Fiorentino et al. (2012) is the
modulus for M31 in order to verify the ULPC nature of same as the sample given in Bird et al. (2009). The de-
our candidates. In this sub-section, we reverse the prob- riveddistancemodulusisµ =24.74±0.68mag
M31,ULPC
lembyusingthetwoconfirmedULPCstodeterminethe when using the PW relation given in Bird et al. (2009).
distance modulus of M31, i.e., µ=W −MW. The abso- The distance moduli derived using the PW relations
lutemagnitudeMW ofthetwoULPCscanbedetermined given in Fiorentino et al. (2012) and Bird et al. (2009)
from the latest PW relation as given in Fiorentino et al. differed by 0.44 mag, albeit with large uncertainties.
(2012): MW =−2.66log(P)−3.68, with a dispersion of ThisreflectsoneofthecurrentproblemsinusingULPCs
σ =0.34. Since the PW relation is a statistical relation, to derivedistances: the calibrationof the ULPC PW re-
the dispersion of this relation (σ) will dominate the er- lations is still uncertain with many discrepant results.
ror term of the derived distance modulus for individual The slope of the PW relation derived in Bird et al.
ULPCs. Hence, we have adopted the dispersion of the (2009), based on 18 ULPCs in metal-poor host galaxies,
PWrelationasthe errorinthe calculateddistancemod- isessentiallyzerobutwithalargeerror(−0.05±0.54). In
uliforthetwoM31ULPCs: µ(8-0326)=23.70±0.34mag contrast, the PW slope given in Fiorentino et al. (2012)
andµ(8-1498)=24.91±0.34mag. Since the weights for is −2.66(though no erroron the slope is quoted in their
these two distance moduli are the same, taking an aver- paper). The intercepts of these two Period-Wesenheit
age of them reduces to the case of an unweighted mean. relationsevendisplayeda largerdifference: −9.06±1.12
This procedure yielded µM31,ULPC = 24.30±0.76 mag, versus−3.68. ThetoppanelinFigure10comparesthese
where the error on the averaged distance modulus is two PW relations, while the bottom panel of the same
calculated using the small number statistics given in figureshowsthedifferenceofthederiveddistancemodu-
Keeping (1962, p. 202). The large error on the deter- lusbasedonthesetwoPWrelations: thiscanbeaslarge
mined distance modulus is mainly due to the combina- as ∼ 0.5 mag. This disagreement between the two PW
tion of small number statistics (as there are only two relations suggests more work is needed in the future to
ULPCs found in M31) and the large dispersion of the properlycalibratethe ULPCPWrelation. Nevertheless,
PW relation for ULPCs. the distance modulus derived from the Fiorentino et al.
G.Fiorentino(2014,privatecommunication)suggested (2012) PW relation will be adopted in this work, be-
usingthePWrelationderivedfromULPCsinmetal-rich cause this Period-Wesenheit relation is derived from a
galaxies (hereafter metal-rich ULPCs). However, the larger sample of ULPCs than can be found in the lit-
sample of metal-rich ULPCs given in Fiorentino et al. erature. Figure 11 shows a comparison of the adopted
(2012), i.e. thosewith 12+log[O/H]>8.4dex,only oc- distance modulus (based on the two M31 ULPCs) to
cupiedanarrowrangeinlog(P). Thiscausesthederived other distance moduli given in literature. Our calcu-
PWrelationto be unreliable. Instead, we have averaged lated distance modulus is consistent with some of re-
the absolute Wesenheit magnitudes for this sample of cent determinations, including the recommended value
metal-rich ULPCs, yielding M = −8.84 mag. Using of 24.46±0.10 mag (de Grijs & Bono 2014).
W
this absolute Wesenheit magnitude,the deriveddistance We note that the Wesenheit magnitudes and the dis-
modulus to M31 with our two ULPCs is µ = tance moduli for these two ULPCs differ by ∼ 1 mag.
M31,ULPC
24.42±0.68 mag with a (unbiased) standard deviation This is not due to the “depth effect,” as one ULPC is
of 0.76. The value of this distance modulus is almost locatedatthe near-side andanother ULPC is locatedat
identical to the value recommended in de Grijs & Bono the far-side of M31 (see Figure 12). Assuming the size