On the distance of the Magellanic Clouds using Cepheid NIR and optical-NIR Period Wesenheit Relations

3.9 MB·English

by  L. Inno

Draft version January 31, 2013
PreprinttypesetusingLATEXstyleemulateapjv.08/22/09
ON THE DISTANCE OF THE MAGELLANIC CLOUDS USING CEPHEID NIR AND OPTICAL–NIR
PERIOD–WESENHEIT RELATIONS
L. Inno1,2, N. Matsunaga3, G. Bono1,4, F. Caputo4, R. Buonanno1,5, K. Genovali1, C.D. Laney6,7, M. Marconi8,
A.M. Piersimoni5, F. Primas2, M. Romaniello2
(Dated: drafted January 31, 2013 / Received / Accepted)
Draft version January 31, 2013
ABSTRACT
We present the largest near-infrared (NIR) data sets, JHK , ever collected for classical Cepheids
S
in the Magellanic Clouds (MCs). We selected fundamental (FU) and first overtone (FO) pulsators,
3
andfound4150(2571FU,1579FO)CepheidsforSmallMagellanicCloud(SMC)and3042(1840FU,
1
1202 FO) for Large Magellanic Cloud (LMC). Current sample is 2–3 times larger than any sample
0
used in previous investigations with NIR photometry. We also discuss optical VI photometry from
2
OGLE-III. NIR and optical–NIR Period-Wesenheit (PW) relations are linear over the entire period

n range (0.0 < logP ≤ 1.65) and their slopes are, within the intrinsic dispersions, common between
FU
a the MCs. These are consistent with recent results from pulsation models and observations suggesting
J
that the PW relations are minimally affected by the metal content. The new FU and FO PW

0 relations were calibrated using a sample of Galactic Cepheids with distances based on trigonometric
3 parallaxes and Cepheid pulsation models. By using FU Cepheids we found a true distance moduli of

18.45±0.02(random)±0.10(systematic)mag(LMC)and18.93±0.02(random)±0.10(systematic)mag
]
(SMC). These estimates are the weighted mean over 10 PW relations and the systematic errors
R
account for uncertainties in the zero–point and in the reddening law. We found similar distances
S
usingFOCepheids(18.60±0.03(random)±0.10(systematic)mag[LMC]and19.12±0.03(random)±
.
h 0.10(systematic) mag [SMC]). These new MC distances lead to the relative distance, ∆µ = 0.48±
p 0.03 mag (FU, logP =1) and ∆µ =0.52±0.03 mag (FO, logP =0.5),which agrees quite well with
- previous estimates based on robust distance indicators.
o
Subject headings: Magellanic Clouds — stars: variables: Cepheids — stars: distances — stars:
r
t oscillations
s
a
[
1. INTRODUCTION MC Cepheids play a crucial role in many astrophysical
2 Recent detailed investigations indicate that 2%–3% of problems,thenumberofhomogeneousoptical(B,V,R,I)
v the systematic error affecting the Hubble constant esti- and near-infrared (NIR; J,H,KS) data sets is quite lim-
6 mate is due to the Cepheid distance to the Large Magel- ited.
7 The most extensive surveys in the optical bands (V,I)
lanic Cloud (LMC Freedman & Madore 2010a; Riess et
3 wereperformedbymicro–lensingexperiments(MACHO,
al. 2011; Freedman et al. 2012). Moreover, the Magel-
4 EROS, OGLE). The MACHO project collected R, I
lanicClouds(MCs)arefundamentalbenchmarkstocon-
. band data for ∼1900 Cepheids in the LMC (Skrutskie
2 straintheaccuracyandtheprecisionofthemostpopular
et al. 2006; Alcock et al. 2000; Welch et al. 1999),
1 primarydistanceindicators(Pietrzyn´skietal.2010;Mat-
while EROS collected V,R band data for ∼300 and
2 sunagaetal.2009,2011). Thedecreaseofafactortwoin
1 metallicity between the LMC and the Small Magellanic ∼600 Cepheids in the LMC and in the SMC, respec-
: Cloud(SMC)makesthesegalaxiesalsoexcellentlabora- tively (Beaulieu & Marquette 2000). The most com-
v pletesampleofMCCepheidswascollectedbyOGLE-III
tories to constrain the possible dependence of different
i
X standard candles on the metal content. Although, the (Soszyn´skietal.2008, 2010). TheircatalogincludesV,I
band light curves for more ∼7000 Cepheids (LMC: 2000
r
a 1Dipartimento di Fisica, Universit`a di Roma Tor Ver- fundamental [FU], 1000 first overtone [FO]; SMC: 2500
gata, via della Ricerca Scientifica 1, I-00133 Rome, Italy; FU, 1500 FO). Accurate distance determinations to the
[email protected] MCs based on optical Period–Wesenheit (PW) relations
2European Southern Observatory, Karl-Schwarzschild-Str. have also been provided by Udalski et al. (1999), Bono
2,D-85748GarchingbeiMunchen,Germany
3Kiso Observatory, Institute of Astronomy, School of Science, et al. (2002), Groenewegen & Salaris (2003) and Ngeow
TheUniversityofTokyo10762-30,Mitake,Kiso-machi,Kiso-gun,3 et al. (2009). More recently, Di Criscienzo et al. (2012)
Nagano97-0101,Japan provided a detailed theoretical investigation concerning
4INAF–OAR, via Frascati 33, I-00040 Monte Porzio Catone,
thePWrelationsintheSloanDigitalSkySurveybands.
Rome,Italy
5INAF-Osservatorio Astronomico di Collurania, via M. The NIR data bases for MC Cepheids are significantly
Maggini,I-64100Teramo,Italy smaller: Laney&Stobie(1986,1994)collectedNIRlight
6Department of Physics and Astronomy, N283 ESC, Brigham curves for 44 MC Cepheids (21 LMC, 23 SMC), while
YoungUniversity,Provo,UT84601,USA
Welch et al. (1987) for 91 SMC Cepheids. More recently
7South African Astronomical Observatory, P.O. Box 9, Obser-
vatory7935,SouthAfrica Perssonetal.(2004,hereinafterP04)collectedNIRlight
8INAF-Osservatorio Astronomico di Capodimonte, via curves for 92 LMC Cepheids. More recently, accurate
Moiarello16,I-80131Napoli,Italy K band photometry (12 phase points per variable) was
2 Inno et al.
collected by Ripepi et al. (2012, hereinafter R12) in two the single-epoch measurements to the mean magnitudes
LMCfieldslocatedaround30Doradus(172FU,152FO) based on the template (0.12 versus 0.05 mag). The total
and the South Elliptical Pole (11 Cepheids). They pro- errorbudgetofthemeanmagnitudesestimatedusingthe
vided,byusingalsoliteraturedata,accurateestimatesof template light curve is given by σ2 =σ2 +σ2 +σ2 ,
Period–Luminosity (PL), PW, and Period-Luminosity- whereσ2 istheintrinsicphotomeλtiricermroir,wictahl atyrpphi-
Color relations for both FU and FO Cepheids. One of mi
cal value of ∼0.03 at 16 mag in J,H,K ; σ2 is the error
the key advantages in using NIR data is that the pulsa- S cal
due to the transformation into the 2MASS photometric
tion amplitude decreases for increasing wavelength and
system, it is of the order of 0.01 mag for UKIRT, LCO
theestimateofthemeanmagnitudebecomeseasier. The
andIRSFsystems; σ2 isthescatterduetotherandom
previouslargestsetofsingleepochmeasurementsforMC rph
phase sampling, it is given by the template algorithm
Cepheids was collected by Groenewegen (2000) (LMC:
and it is ∼0.05 mag (Soszyn´ski et al. 2005).
713 FU, 450 FO; SMC: 1200 FU, 675 FO) using 2MASS
For the FO Cepheids the mean magnitude is based
and DENIS data sets. The same approach was also
on the single epoch measurements, since template light
followed by Nikolaev et al. (2004) using MACHO and
curves are not available for these pulsators. It is worth
2MASS data sets (LMC: 1357 FU, 749 FO) and more
mentioning,thatthemeanmagnitudesofthesepulsators
recently by Ngeow et al. (2009) using the 2MASS data
are less affected by their random sampling, since their
set(LMC:1761FU)andthemid-infraredSAGESpitzer
luminosity amplitude is on average three times smaller
(Meixner et al. 2006) data set (LMC: 1759 FU).
thanforFUCepheids(Freedman&Madore2010b). The
Inthisinvestigation,weprovidenewMCdistancesus-
errors of the FO mean magnitudes were estimated using
ing a new sample of single-epoch J,H,K measurements
S the above relation, but the term σ2 gives the typical
ofasignificantfractionofMCCepheids(∼80%)detected rph
byOGLE.Inparticular, inSection2wediscusstheNIR semi-amplitudeofFOlightcurves(∼0.10mag). Weplan
and optical data sets we adopted in this investigation to address the discussion concerning the template light
together with the criteria to select both FU and FO curve for FO Cepheids and their errors in a forthcoming
Cepheids. In Section 3 we present the PW relations, paper.
whileinSection3.1wefocusourattentiononthelinear-
ity and the metallicity dependence of NIR and optical- 3. PERIODWESENHEITRELATIONS
NIR PW relations. Empirical and theoretical absolute The Wesenheit indices, introduced by Madore (1982),
calibrations of the PW relations are addressed in Sec- are pseudo-magnitudes closely related to apparent mag-
tion 3.2. The summary of the results and more detailed nitudes, but minimally affected by uncertainties on red-
discussion concerning pros and cons of the two indepen- dening. On the basis of two magnitudes, m and m ,
λ1 λ2
dentcalibrationsaregiveninSection4,whileinSection5 we can define a Wesenheit index:
we briefly outline some possible future avenues concern- (cid:20) (cid:21)
A(λ )
ing the developments of this project. W(λ ,λ )=m − 1 ×(m −m );
2 1 λ1 E(m −m ) λ2 λ1
λ2 λ1
2. DATASETSANDDATASELECTION (1)
The Cepheid intrinsic parameters are taken from the where λ > λ and A(λ1) is the total to selective
OGLE-III catalog (Soszyn´ski et al. 2008, 2010). We 1 2 E(mλ2−mλ1)
extinction for the given filters –{λ = V,I,J,H,K }–
adoptedthefollowingCepheidparameters: pulsationpe- i S
and for the adopted reddening law. The clear advantage
riod, position (right ascension and declination), mean
inusingtheWesenheitindicesisthattheyareminimally
V and I band magnitude, I band amplitude, epoch
affected by uncertainties affecting reddening corrections
of maximum and pulsation mode. The optical OGLE-
for Galactic and extragalactic Cepheids. Once we fix
III Cepheid catalog was cross-correlated with the NIR
the reddening law (Cardelli et al. 1989) and we assume
catalog of the IRSF/SIRIUS Near-Infrared Magellanic
R = A(V) =3.23, we obtain the following selective
Clouds Survey provided by Kato et al. (2007). The V A(B)−A(V)
single-epoch J,H,K magnitudes for the OGLE-III FU absorption ratios, namely A /A =0.61; A /A =0.29;
S I V J V
Cepheids were extracted by Matsunaga et al. (2011). In A /A =0.18; A /A =0.12 mag.
H V KS V
this investigation we also included FO Cepheids. We By combining the five optical–NIR (VIJHK ) mean
S
ended up with a sample of 3042 LMC (1840 FU, 1202 magnitudes, we can compute 10 Wesenheit indices for
FO) and 4150 SMC (2571 FU, 1579 FO) Cepheids with each Cepheid in the sample, and in turn, 10 PW rela-
three NIR (J,H,K ) single-epoch measurements. The tions of the form W(λ ,λ ) = a+b×logP, where P
S 2 1
IRSF/SIRIUS J,H,K measurements were transformed is the pulsation period in days. We decided to analyze
S
intothe2MASSNIRphotometricsystemfollowingKato separately FU and FO Cepheids to overcome possible
et al. (2007). systematicuncertaintiesthatthe’fundamentalization’of
The mean magnitudes of FU Cepheids were esti- theFOperiodsmightintroduceintheestimateofthePL
mated using the NIR template light curves provided by relations(Feast&Catchpole1997;Marengoetal.2010).
Soszyn´ski et al. (2005). To assess the accuracy of this Therefore, we computed independent PW relations for
method,wecomparedourestimatesofmeanmagnitudes FU and FO Cepheids. We performed a linear fit of the
with the mean magnitudes for LMC Cepheids based on datatoidentifypossibleoutliers. Wehaveincludeddata
finely sampled light curves (P04). The template light up to 4σ from the central location by using the robust
curves and the mean magnitude by P04 were also trans- Biweight location estimator (Fabrizio et al. 2011). We
formed into the 2MASS NIR photometric system follow- ended up with a sample of ∼4000 SMC (∼2500, FU;
ing Carpenter (2001). Figure 1 shows that the intrinsic ∼1500, FO) and ∼3000 LMC (∼1800, FU; ∼1100, FO)
dispersiondecreasesbyafactoroftwowhenmovingfrom Cepheids. For approximately three dozen Cepheids with
Distance to the MCs 3
period (cid:38) 20 days the I band is saturated in the OGLE- due to depth effects. The anonymous referee explicitly
IIIdata-set,andthereforewecannotapplythetemplate. asked a quantitative analysis concerning the linearity of
TheNIRmeanmagnitudesfortheseCepheidsweretaken the PW relations for both FU and FO SMC Cepheids.
from P04 and transformed into the 2MASS photometric To our knowledge there is no clear physical reason why
system (see green dots in Figure 2). FU and FO NIR PW relations should show a break,
WethenperformedalinearregressionoftheNIRdata therefore, we decided to constrain the possible occur-
and the results for the three PW relations are showed in rence using different breaks in period. We split the en-
Figure 2 (see also Table 1). From top to bottom each tire Cepheid sample by adopting a break in period at
panelshowsFU(redandgreendots)andFO(bluedots) logP=0.45. This means that we assume as short-period
LMC (left) and SMC (right) Cepheids. The PW rela- Cepheids those with logP ≤0.45, while the long–period
tions are over–plotted as black lines. Data plotted in ones are those with 0.45< logP ≤1.65 (FU) and with
Figure 2 display four relevant findings concerning the 0.45<logP ≤0.65 (FO). The zero–points and the slopes
NIRPWrelations. (1)TheFUandtheFOPWrelations for FU NIR PW relations listed in Table 3 show that
are linear over the entire period range. (2)The intrinsic their errors are a factor of 3–4 larger than the errors of
dispersion of the SMC PW relations are a factor of two the linear regressions based on the entire sample. This
larger than for the LMC PW relations. The difference trendisexpected,sincethenumberofCepheidsincluded
is mainly caused by depth effects in the former system in the two new linear regressions decreases from a factor
(van den Bergh 2000). (3)For each PW relation the dif- of three (long–period) to 50% (short–period). On the
ference in the slope between LMC and SMC Cepheids is other hand, the dispersions of the new PW relations are
small. Data listed in Tables 1 and 2 indicate that it is, eithersimilar(short–period)oronaveragesmaller(long–
on average, smaller than 0.8σ , where σ is the sum period). The new FO PW relations show similar trends
tot tot
in quadrature of the dispersion of LMC and SMC PW concerningtheintrinsicerrorsonthezero–points,onthe
relations. slopes and on the dispersions.
This indicates a minimal dependence of the NIR PW The break in period is defined somewhat arbitrarily,
relations on the metal content. (4)The width in tem- therefore,wedecidedtoperformthesametest,butusing
perature of the FO instability strip is narrower than the a break at logP=0.40 and logP=0.35. Current empir-
instability strip for FU Cepheids (Bono et al. 2000), but ical evidence suggests that optical PL relations of SMC
the intrinsic dispersions are not significantly different. Cepheids show a break in period at logP≈0.4 (Sandage
The lack of a template light curve for FO Cepheids in- et al. 2009), while for LMC Cepheids the break seems to
creases the dispersion of their mean magnitudes. beatlogP≈1(Sandageetal.2004). Theresultsconcern-
Theabovefindingssupportrecenttheoretical(Bonoet ing the new NIR PW relations are listed in Table 3 and
al. 2010) and empirical (Majaess et al. 2011) investiga- indicate that the short–period PW relations are quite
tions. The main advantage of the current approach is similartotheglobalPWrelations,i.e.,thePWrelations
that the results rely on NIR single epoch measurements covering the entire period range. This trend is –once
thatare2–3timeslargerthananypreviousinvestigation again– expected, since more than 2/3 of the Cepheid
(Groenewegen 2000). In order to constrain the possible sample is in the short–period range. The evidence that
occurrenceofsystematicerrorsintheNIRPWrelations, linear regressions with an arbitrary break in period, give
we also computed the optical–NIR PW relations using PW relations with either similar or marginally smaller
the V, I mean magnitudes provided by OGLE-III. Fig- dispersion is also expected. This is the consequence of
ures 3 and 4 show the optical–NIR PW relations for FU the increase in the degrees of freedom of the linear re-
(red dots) and FO (blue dots) LMC and SMC Cepheids, gressions. However, this does not mean that the PW re-
respectively. Once again, we found that the PW rela- lationswithabreakinperiodareabetterrepresentation
tions are linear and the slopes are minimally affected by of observations. To address this issue on a more quan-
the difference in metal content (see Table 1). Current titative basis, we devised a new empirical test based on
results concerning the linearity of NIR and optical–NIR the relative distance between SMC and LMC. The MC
PW relations support previous findings by Ngeow et al. relative distance is quite solid, since different standard
(2005) and Madore & Freedman (2009). candles provide similar estimates.
ByadoptingbothNIRandoptical–NIRPWrelations,
3.1. Linearity of PW Relations
wefoundthattherelativedistancemodulusbasedonFU
Toconstrainonamorequantitativebasisthelinearity Cepheids and at logP=1 is ∆µ=0.48±0.03 mag. This
of NIR PW relations we estimated the distance of in- evaluation agrees quite well with similar estimates avail-
dividual Cepheids from the least squared solution. The ableintheliterature(seeSection4). Tofurtherconstrain
residuals for FU Cepheids plotted in the top panels of the intrinsic accuracy of the NIR PW relations with a
Figure 5 do not show any trend as a function of the breakinperiod,wecomputedthreenewPW(J,K )rela-
S
pulsation period. To further constrain this evidence, we tionsforLMCCepheids. FollowingSandageetal.(2004),
performed a linear fit to the residuals and we found that we adopted a break in period at logP=1. The zero–
the zero–points, the slopes and the means attain van- points and the slopes of the new NIR PW relations are
ishing values. Moreover, the dispersions are typically listed in Table 4. We estimated the MC relative dis-
smaller than 0.2 mag. The same outcome applies to tances by using the short–period and the long–period
the FO Cepheids (see bottom panels of Figure 5). Note PW relations. The relative distances based on the for-
that the residuals of FO PW relations are larger than meroneswereestimatedatlogP=0.3,whilethosebased
the residuals of the FU PW relations, since for the for- on the latter ones were estimated at logP=1.0. The re-
mer ones we lack template light curves. The residuals sults listed in Table 5 indicate –as expected– that the
referred to SMC are larger than the residuals of LMC MC relative distances based on short–period PW rela-
4 Inno et al.
tions agree quite well with the MC relative distances indicate that current Magellanic and Galactic NIR PW
based on global PW relations. The main difference is relations do agree within 1σ. The difference in the slope
that the relative distance based on short–period PW re- between our SMC and Galactic PW(J,K ) relations is,
S
lations have intrinsic errors, estimated by propagating on average, smaller than 0.3σ (N12) and 0.4σ (S11a).
the errors on both the coefficients and the dispersion of Theanonymousrefereesuggestedtoperformthesame
the individual PW relations, that are on average a fac- comparison for the optical PW(V,I) relation. The top
tor of two larger than those ones based on the global panel of Figure 6 shows the difference between the slope
PW relations. The same outcome applies to the MC rel- of the PW(V,I) relations we estimated for LMC (black
ative distances based on the long–period PW relations. line) and SMC (green line) Cepheids with similar PW
However, their intrinsic errors are larger and they also relations for Galactic Cepheids (see Table 6) derived by
show a larger spread among the three different NIR PW S11a (red line) and Benedict et al. (2007, hereinafter
relations. Note that the MC relative distance based on B07; blue line). The standard deviations plotted in the
the long–period PW(J,H) relations are systematically same figure clearly indicate that current Magellanic and
smaller than the others, because the zero–point of the Galactic optical PW relations do agree within 1σ. The
long–periodPWrelationforLMCCepheidsislargerthan difference in the slope of the PW(V,I) relation between
the zero–point of the global PW relation (15.949 versus our metal-poor stellar system (SMC, [Fe/H]=-0.75) and
15.876). our metal-rich stellar system (Galaxy, [Fe/H]= -0.18 to
We repeated the same test by using two different +0.25) is, on average, smaller than ∼0.1σ (B07) and
pivotperiods,namelylogP=0.2fortheshort–periodand ∼0.9σ (S11a). The bottom panel of Figure 6 shows the
logP=1.2 for the long–period PW relations and the re- difference between the slope of the PW(V,K ) relations
S
sults are quite similar. We also performed the same test weestimatedforLMC(blackline)andSMC(greenline)
using NIR FO PW relations and the outcome is –once Cepheids with the PW relation for LMC Cepheids (see
again– quite similar. Note that the intrinsic errors on Table6)derivedbyR12(grayline). Dataplottedinthis
the coefficients of the long–period FO PW relations are figure clearly indicate the good agreement between the
larger than the errors of the short–period ones, since the two independent LMC slopes. Moreover, current SMC
Cepheid sample in the former period interval is from a and LMC PW relations do agree within 1σ. The other
factor of five to a factor of 10 smaller than in the latter NIR and optical-NIR PW relations provide similar re-
one. sults. The quoted numbers indicate that the PW rela-
TheabovefindingsindicatethatthePWrelationswith tions are, in the metallicity range covered by Magellanic
arbitrary breaks in period when compared with global Cepheids, independent of metal abundance. The exten-
PW relations have larger intrinsic errors on the coeffi- sion into the more metal-rich regime does require more
cients of the linear regressions and roughly equivalent accurate measurements for Galactic Cepheids.
dispersions.
3.3. Absolute calibration of the PW relations
However, the MC relative distances based on the for-
meronesarecharacterizedbyintrinsicerrorsthatare,on To estimate the distances to the MCs, we combined
average,afactoroftwolargerthanthelatterones. Thus our new comprehensive sets of PW relations with re-
further supporting the use of global NIR PW relations. centfindingsconcerningabsolutemagnitudesofGalactic
This provides an independent support to the results Cepheids. We followed the same approach suggested by
concerning the linearity of both optical and NIR PW P04tocalibratetheLMCPWrelationsandadoptedthe
relations for FU Cepheids by Persson et al. (2004); 10 FU Galactic Cepheids with Hubble Space Telescope
Bonoetal.(2010);Ngeow(2012,andreferencestherein). trigonometric parallaxes (Benedict et al. 2007). To cal-
We found that optical and NIR PW relations for FO ibrate the FO PW relations, we adopted the Hipparcos
Cepheids are also linear over the entire period range, trigonometric parallaxes for Polaris provided by van
supporting previous findings by Ngeow et al. (2005) and Leeuwenetal.(2007). ThemeanJ,H,K magnitudesfor
S
Madore & Freedman (2009). We are thus facing the em- thecalibratingGalacticCepheidsarefromLaney&Sto-
piricalevidencethatopticalandNIRPLrelationsforFU bie(1992). Weestimated thetruedistance modulus–µ–
Cepheids do show a change in the slope for logP ≈0.4 of both LMC and SMC by using the quoted calibrators
(Sasselovetal.1997;Bonoetal.1999;Ngeowetal.2005; andbyimposingtheslopeofindividualPWrelationsfor
Koenetal.2007;Matsunagaetal.2011). Thedifference FU and FO Cepheids (see Column 6 of Table 1).
between the PL and the PW relations is mainly due to Note that the true distance moduli for FU Cepheids
the fact that the latter is mimicking, as originally sug- were estimated as the weighted mean of the µ of in-
i
gested by Bono & Marconi (1999), a PLC relation. dividual calibrating Cepheids. The associated error on
µ is the sum in quadrature of the weighted error on
3.2. Metallicity dependence of the PW relations
the distance and of the intrinsic dispersion associated
To further constrain the metallicity dependence of the with the linear regression (see Column 5 of Table 1).
NIR PW relations, we performed a detailed comparison The weighted means based on the FU PW relations give
with similar estimates available in the literature. The µ(LMC)=18.45±0.02 and µ(SMC)=18.93±0.02 mag,
middle panel of Figure 6 shows the difference between whiletheweightedmeansbasedonFOPWrelationsgive
the slope of the PW(J,K ) relations we estimated for µ(LMC)=18.60±0.03 and µ(SMC)=19.12±0.03 mag.
S
LMC (black line) and SMC (green line) Cepheids with Toconstrainthepossibleoccurrenceofdeceptiveerrors
similarPWrelationsforGalacticCepheids(seeTable6) intheabsolutezero-point,weperformedanindependent
derivedbyStormetal.(2011a,hereinafterS11a;redline) zero-point calibration using predicted FU PW relations
and by Ngeow (2012, hereinafter N12; purple line). The for Magellanic Cepheids provided by Bono et al. (1999)
standard deviations plotted in the same figure clearly andMarconietal.(2005). Recentinvestigationsindicate
Distance to the MCs 5
thattheoryandobservationsagreequitewellconcerning this effect we computed a new set of PW relations by
opticalandoptical-NIRPWrelations(Bonoetal.2010). adoptingthereddeninglawbyMcCall(2004). Wefound
The true distance moduli based on the new zero-point that the difference in the true distance moduli, based
calibrationarelistedincolumnsevenofTable1. Theer- on the two different reddening laws, is on average ∼0.01
ror associated to individual distance moduli is the stan- mag. The mild dependence of current distance determi-
dard deviation from the theoretical PW relation. The nations on the reddening law might also be due to the
new weighted means based on the FU PW relations give fact that the selective absorption ratios of optical–NIR
µ(LMC)=18.56±0.02andµ(SMC)=18.93±0.02mag. In- PWrelationsarelesssensitivetothefinestructureofthe
terestingly enough, the two independent calibrations for reddening law. The selective absorption ratios given in
FU Cepheids do provide weighted true distance moduli Section 3 indicate that the coefficient of the color term
totheMCsthatagreequitewell(DM(cid:46)0.11mag). This of the PW(V,K) relation is at least one order of mag-
finding appears even more compelling if we take into ac- nitude smaller than the coefficients of PW(J,H) and
count that we are using independent NIR and optical PW(H,K ) relations (0.13 versus 1.63 and 1.92 mag).
S
data sets together with independent theoretical and em- This evidence indicates that the difference in the true
pirical calibrators. distance moduli based on PW(J,H) and PW(H,K ) re-
S
Current zero-point calibration for FO PW relations lations might also be caused either by photometric error
relies on the trigonometric parallax of a single object in the mean magnitudes or by changes in the reddening
(Polaris, van Leeuwen et al. 2007). Absolute distances law along the line-of-sight of the HST Galactic calibrat-
for FO Galactic and Magellanic Cepheids based on the ing Cepheids.
IRSB method are not available. To overcome this prob-
lem, we decided to use predicted FO PW relations for 4. SUMMARYANDDISCUSSION
Magellanic Cepheids provided by Bono et al. (1999) We present new true distance modulus determinations
and Marconi et al. (2005). The true distance moduli of the MCs using NIR and optical-NIR PW relations.
based on the new zero-point calibration are listed in The NIR PW relations were estimated adopting the
Column 7 of Table 1. The error associated to individ- largest data set of J,H,K single epoch measurements
S
ual distance moduli are the dispersions from the the- ever collected for MC Cepheids. The optical V,I mea-
oretical PW relation. The new weighted means based surements come from the OGLE-III data set. We ended
on the FO PW relations give µ(LMC)=18.51±0.02 and up with a sample of 4150 (2571, FU; 1579, FO; SMC)
µ(SMC)=19.02±0.02 mag. The two independent em- and 3042 (1840, FU; 1202, FO; LMC) Cepheids. We es-
pirical calibrations for FU and FO Cepheids provide timated independent PW relations for both FU and FO
weighted true distance moduli to the MCs that differ Cepheids. The slopes of the current FU PW relations
from0.15(LMC)to0.19(SMC)mag. Ontheotherhand, agree quite well with similar estimates available in the
the weighted true distance moduli based on the theoret- literature. We found that they agree at 1.2σ level with
icalcalibrationsdifferatthelevelofafewhundredthsof the slopes of the NIR PW relations for LMC Cepheids
mag. The difference between the two empirical calibra- derivedbyP04. Theagreementisevenbetterifwecom-
tionsisduetothefactthattheempiricalcalibrationsfor pare our slopes for the PW(J,K ) relations with the
S
FO PW relations rely on a single object (see Section 4). slopes recently provided by Storm et al. (2011b, here-
However, data listed in Table 1 indicate that the inafter S11b) for the LMC (LMC: -3.31±0.09 versus -
PW(J,H) and the PW(I,H) relations for FU and FO 3.365±0.008). Theabovefindingsareevenmorerelevant
Cepheids, calibrated using the Galactic Cepheids with if we take into account that current slopes are based on
trigonometric distances, provide true distance moduli data samples that are from 80 (S11b) – 30 (P04) times
that differ at the 2σ-3σ level from the weighted mean. to∼3times(Groenewegen2000)largerthanthequoted
TheevidencethatdistancesbasedonPWrelations,cali- samples. We cannot perform a similar comparison con-
bratedusingtheoreticalpredictionsforMCCepheids(L. cerning the slopes of the FO PW relations, since to our
Innoetal. 2013,inpreparation),showsmallerdifferences knowledge they are not available in the literature.
indicates that the main culprit seems to be the precision Moreover, we found that both FU and FO PW re-
of the H band zero-point calibration. However, the dif- lations are linear over the entire period range and their
ference in the weighted mean distances, provided by the slopesattain,withintheintrinsicdispersions,similarval-
twoindependentzero-pointcalibrationsforFUCepheids, ues in the MCs. The difference is, on average, smaller
issmallerthan5%(LMC:49.0±1.2versus51.5±1.2kpc; than 0.8σ. The difference between the slope of our SMC
SMC: 61.1±2.2 versus 68.8±2.3 kpc). Moreover, the to- and Galactic PW(J,K ) relations available in the liter-
S
tal uncertainty of current LMC and SMC distances is ature is, on average, smaller than 0.5σ (0.3σ,N12; 0.4σ,
at the ∼2% and at the ∼4% level, respectively. Note S11b). The same outcome applies to optical bands, and
that we obtain very similar distances if we neglect the indeed the difference in the slope between our SMC and
distances based on the PW(J,H) and PW(I,H) rela- GalacticPW(V,I)relationsavailableintheliteratureis,
tions, namely18.47±0.02(trigonometricparallaxes)and onaverage,smallerthan∼0.1σ (B07)and∼0.9σ (S11a).
18.57±0.03 (theory) mag. This supports the evidence for a marginal dependence
Tofurtherconstrainthepossiblesourcesofsystematic of NIR and PW(V,I) relations on the metal content, as
errors in current distance estimates, we also constrained suggested by pulsation predictions and recent empirical
the impact of the adopted reddening law. In a recent in- investigations.
vestigation Kudritzki & Urbaneja (2012) suggested that The new PW relations were calibrated using two in-
distance determinations based on the PW relations may dependent sets of Galactic Cepheids with individual dis-
be affected by changes in the reddening law either in tancesbasedeitherontrigonometricparallaxesoronthe-
the Galaxy or in external stellar systems. To constrain oretical models. By using FU Cepheids we found a true
6 Inno et al.
distance modulus to the LMC of 18.45±0.02 (random) estimates provided by (Groenewegen 2000, 19.11±0.11
±0.10 (systematic) mag and to the SMC of 18.93±0.02 mag; Hipparcos trigonometric parallaxes and PW(V,I)
(random) ±0.10 (systematic) mag. These estimates are relation) and S11b (18.92±0.14 mag).
the weighted mean over the entire set of distance deter-
5. FINALREMARKS
minations. The random error was estimated by taking
The key feature of current findings is that the random
intoaccounttheintrinsicdispersionofindividualPWre-
errorsassociatedtoourdistancedeterminationsarevery
lations. Thesystematicerroristhesuminquadratureof
small, due to the fact that we adopt an homogeneous
thedifferenceinµintroducedbythechangeinreddening
and accurate NIR data set and also because we are fully
law and in the zero-point calibration.
exploitingtheuseofNIRandoptical–NIRPWrelations.
We found similar distances using FO Cepheids
Moreover,theuseoftwoindependentzero-pointcalibra-
18.60±0.03(random)±0.10(systematic)mag,LMCand
tions and two different reddening laws indicate that the
19.12±0.03 (random) ±0.10 (systematic) mag, SMC.
global uncertainty on the MC distances seems to be of
Once again the random errors were estimated by taking
the order of 1% by using either the 10 NIR/optical–NIR
intoaccounttheintrinsicdispersionofindividualPWre-
PW relations or the seven optical–NIR PW relations.
lations,whilethesystematiconesarethesuminquadra-
However, there are a few pending issues that need to
ture of the difference in µ introduced by the change in
be addressed in more detail in the near future.
reddening law and in the zero-point calibration.
ThetwoindependentempiricalcalibrationsforFUand 1. The very good intrinsic accuracy of NIR and
FO Cepheids provide weighted true distance moduli to optical–NIRPWrelationsfurthersupportthefind-
theMCsthatdifferfor0.15(LMC)and0.19(SMC)mag. ings by Bono et al. (2010, see their Figures 13
On the other hand, the weighted true distance moduli and 14) indicating that the difference between op-
based on the theoretical calibrations differ at the level tical (B,V) and NIR (J,K ) PW relations can be
S
of a few hundredths of mag. The difference between the adopted to constrain the metallicity correction(s)
empirical and theoretical calibrations is due to the fact to the Cepheid distance scale based on optical PL
that the empirical calibrations for FO PW relations rely relations. Moreover, current findings indicate that
on a single object (see Section 3.2). the error budget of the absolute distances based
The relative distance of the MCs, for distance indica- on PW relations is dominated by uncertainties in
torsminimallyaffectedbythemetalcontent,isindepen- the zero–point. The solution of this problem ap-
dentofuncertaintiesaffectingthezero-pointcalibration. pearsquitepromisinginlightofthefactthatGaia
We found that the weighted mean relative distance be- will be launched in approximately one year and
tweenSMCandLMCusingFUCepheidsandthePWre- the number of double eclipsing binaries includ-
lationlistedinTable1(logP=1)is∆µ=0.48±0.03mag. ing classical Cepheids is steadily increasing during
WeappliedthesameapproachbyusingFOCepheidsand the last few years (Pietrzyn´ski et al. 2010, 2011).
wefound∆µ=0.52±0.03mag(logP=0.5). Theerrorson Moreover, new optical (OGLEIV Soszyn´ski et al.
the weighted mean relative distances were estimated by 2012)andNIR(Galaxy:VVV,Minnitietal.2010);
using the dispersions of individual PW relations. The (MCs:VMC, Cioni et al. 2011, R12) surveys will
quoted determinations agree quite well with each other also provide new, homogenous and accurate mean
and with the recent estimate ∆µ=0.47±0.15 mag pro- magnitudes.
videdbyS11bbyusingtheIRSBmethod(seealsoGroe-
newegen 2000; Bono et al. 2010; Matsunaga et al. 2011). 2. The above results provide an independent sup-
ThedistancemodulusweobtainedfortheLMCagrees port to the plausibility of the physical assump-
quite well with the recent estimate provided by S11b tions adopted in current hydrodynamical models
(18.45±0.04 mag) and by P04 (18.50± 0.05mag) by us- ofvariablestars. Indeedthedistancemodulibased
ing the NIR PL, PLC and PW relations. The difference on theoretical calibrations agree well with dis-
is also minimal with the “classical” value –18.50±0.10 tancemodulibasedonempiricalcalibration. How-
mag– (Freedman et al. 2001). The same conclusion can ever, we still lack detailed investigations concern-
be reached if we compare the current estimate with re- ing the pulsation properties of Classical Cepheids
cent distance moduli provided by Benedict et al. (2007, in the metal-intermediate regime. In particular,
18.50±0.03; HST trigonometric parallaxes for Galactic we need a comprehensive analysis of the metallic-
Cepheids and the LMC slope of the optical PW rela- ity dependence of both PW relations and Period-
tion); by Ngeow & Kanbur (2008, 18.49±0.04; optical Luminosity-Colorrelationsintheopticalandinthe
PL and PLC relations); by Freedman & Madore (2010a, NIR regime.
18.44±0.03 (random) ±0.06 (systematic); PW(V,I) re-
3. Accurate spectroscopic iron abundances are only
lation for Galactic and LMC Cepheids ) and by Ngeow
available for roughly the 50% of Galactic Cepheids
(2012, 18.531±0.043 mag; NIR and optical-NIR PW re-
(Romaniello et al. 2008; Pedicelli et al. 2009; Luck
lations)9. Moreover,ourresultalsoagreeswiththemost
& Lambert 2011, and references therein) and for
recent distance modulus – 18.477 ± 0.033– provided by
a few dozen of MC Cepheids. However, the em-
Scowcroftetal.(2011)andFreedmanetal.(2012),using
pirical scenario will have a relevant jump thanks
the Spitzer mid-IR band PL relations.
totheongoingmassiveground-basedspectroscopic
The distance modulus we obtained for the SMC is,
surveys at the 8m class telescopes (Gaia ESO Sur-
onceagain,inverygoodagreementwiththeindependent
vey, Gilmore et al. 2012; Tolstoy et al. 2009)
9 Note that in the comparison of LMC distance moduli, we 4. Plain physical arguments indicate that FO
adoptedtheestimatesthatneglectthemetallicitydependence. Cepheids have the potential to be robust distance
Distance to the MCs 7
indicators (Bono et al. 2000). However, we still It is a pleasure to thank an anonymous referee for
lack for these variables NIR template light curves. his/her pertinent suggestions and criticisms that helped
Moreover,currentFOabsolutecalibrationsarealso us to improve the readability of the paper. We also ac-
hampered by the lack of precise distance deter- knowledge M. Fabrizio for many useful discussions con-
minations based on trigonometric parallaxes for a cerning the use of Biweight and data set cleaning. One
goodsampleofGalacticcalibrators. Thesecircum- ofus(G.B.)thankstheESOforsupportasasciencevis-
stantial evidence limits the precision of MC dis- itor. This work was partially supported by PRIN-INAF
tance determinations based on FO Cepheids. 2011 “Tracing the formation and evolution of the Galac-
tic halo with VST” (P.I.: M. Marconi) and by PRIN-
5. Absolute distances based on PW relations includ- MIUR (2010LY5N2T) “Chemical and dynamical evolu-
ingtheHbandarecharacterizedbyalargespread. tion of the Milky Way and Local Group galaxies” (P.I.:
The reasons for this behavior are not clear. No F. Matteucci).
doubt that new high-resolution, high signal-to-
noise NIR spectra of Galactic Cepheids (Bono et
al. 2012) can shed new lights on this open prob-
lem.
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Distance to the MCs 9
TABLE 1
NIR and Optical-NIR PW relations for LMC and SMC Cepheids.
W(λ2,λ1)a Mode a b σb µπ µtheo
LMC
W(J,KS) FU(1708) 15.876±0.005 -3.365±0.008 0.08 18.44±0.05c 18.53±0.07d
W(J,H) FU(1701) 15.630±0.006 -3.373±0.008 0.08 18.30±0.05c 18.65±0.04d
W(H,KS) FU(1709) 16.058±0.006 -3.360±0.010 0.10 18.54±0.05c 18.46±0.12d
W(V,KS) FU(1737) 15.901±0.005 -3.326±0.008 0.07 18.46±0.05c 18.51±0.08d
W(V,H) FU(1730) 15.816±0.005 -3.315±0.008 0.07 18.40±0.05c 18.56±0.06d
W(V,J) FU(1732) 15.978±0.006 -3.272±0.009 0.08 18.49±0.05c 18.47±0.12d
W(I,KS) FU(1737) 15.902±0.005 -3.325±0.008 0.07 18.46±0.05c 18.52±0.08d
W(I,H) FU(1734) 15.801±0.005 -3.317±0.008 0.08 18.39±0.05c 18.55±0.06d
W(I,J) FU(1735) 16.002±0.007 -3.243±0.011 0.10 18.50±0.05c 18.46±0.12d
W(V,I) FU(1700) 15.899±0.005 -3.327±0.008 0.07 18.47±0.05c 18.53±0.13d
MEAN(FU) 18.45±0.02e 18.56±0.02e
W(J,KS) FO(1057) 15.370±0.005 -3.471±0.013 0.08 18.60±0.08f 18.52±0.06g
W(J,H) FO(1064) 15.207±0.005 -3.507±0.015 0.09 18.60±0.08f 18.56±0.06g
W(H,KS) FO(1063) 15.483±0.007 -3.425±0.017 0.10 18.59±0.08f 18.49±0.07g
W(V,KS) FO(1061) 15.410±0.005 -3.456±0.013 0.07 18.61±0.08f 18.51±0.06g
W(V,H) FO(1071) 15.357±0.004 -3.485±0.011 0.08 18.61±0.08f 18.52±0.06g
W(V,J) FO(1086) 15.475±0.005 -3.434±0.014 0.10 18.62±0.08f 18.48±0.06g
W(I,KS) FO(1059) 15.402±0.005 -3.448±0.013 0.08 18.61±0.08f 18.50±0.06g
W(I,H) FO(1072) 15.351±0.004 -3.489±0.012 0.08 18.62±0.08f 18.51±0.06g
W(I,J) FO(1100) 15.499±0.006 -3.423±0.020 0.13 18.66±0.08f 18.45±0.06g
W(V,I) FO(1081) 15.399±0.003 -3.460±0.009 0.07 18.52±0.06f 18.56±0.06g
MEAN(FO) 18.60±0.03e 18.51±0.02e
SMC
W(J,KS) FU(2448) 16.457±0.006 -3.480±0.011 0.16 18.92±0.05c 19.01±0.10d
W(J,H) FU(2448) 16.217±0.006 -3.542±0.011 0.17 18.74±0.05c 19.02±0.07d
W(H,KS) FU(2448) 16.638±0.006 -3.445±0.011 0.19 19.05±0.05c 19.01±0.14d
W(V,KS) FU(2295) 16.507±0.005 -3.461±0.011 0.15 18.95±0.05c 19.00±0.11d
W(V,H) FU(2285) 16.426±0.005 -3.475±0.010 0.15 18.88±0.05c 19.00±0.10d
W(V,J) FU(2286) 16.614±0.005 -3.427±0.011 0.16 19.00±0.05c 18.98±0.14d
W(I,KS) FU(2294) 16.511±0.005 -3.464±0.011 0.16 18.95±0.05c 19.00±0.10d
W(I,H) FU(2202) 16.417±0.005 -3.480±0.011 0.15 18.87±0.05c 19.00±0.10d
W(I,J) FU(2279) 16.662±0.006 -3.424±0.013 0.18 19.01±0.05c 18.92±0.14d
W(V,I) FU(2260) 16.482±0.005 -3.449±0.010 0.13 18.95±0.05c 19.03±0.12d
MEAN(FU) 18.93±0.02e 18.99±0.03e
W(J,KS) FO(1461) 15.947±0.005 -3.651±0.022 0.16 19.06±0.08f 19.02±0.04g
W(J,H) FO(1473) 15.778±0.006 -3.722±0.023 0.17 19.17±0.08f 19.05±0.03g
W(H,KS) FO(1456) 16.069±0.007 -3.579±0.027 0.19 19.00±0.08f 19.01±0.04g
W(V,KS) FO(1472) 15.992±0.005 -3.624±0.021 0.16 19.09±0.08f 19.02±0.04g
W(V,H) FO(1482) 15.937±0.005 -3.660±0.020 0.15 19.16±0.08f 19.03±0.05g
W(V,J) FO(1494) 16.074±0.006 -3.578±0.023 0.18 19.17±0.08f 19.02±0.04g
W(I,KS) FO(1471) 15.990±0.005 -3.630±0.020 0.16 19.09±0.08f 19.02±0.05g
W(I,H) FO(1477) 15.932±0.005 -3.667±0.020 0.16 19.17±0.08f 19.02±0.04g
W(I,J) FO(1499) 16.113±0.007 -3.595±0.027 0.20 19.17±0.08f 18.00±0.05g
W(V,I) FO(1465) 15.958±0.005 -3.599±0.019 0.14 19.12±0.06f 19.05±0.03g
MEAN(FO) 19.12±0.03e 19.02±0.02e
a The color coefficients of the adopted PW relations are the following: AK =0.69; AH =1.63;
E(J−KS) E(J−H)
AK =1.92; AK =0.13; AH =0.22; AJ =0.41; AK =0.24; AH =0.42; AJ =0.92;
E(H−KS) E(V−KS) E(V−H) E(V−J) E(I−KS) E(I−H) E(I−J)
AI =1.55
E(I−V)
b Dispersionofthelinearfit(mag)
c Distancemodulusbasedonthezero-pointcalibrationfromBenedictetal.(2007).
d Distancemodulusbasedonthezero-pointcalibrationobtainedbythepredictedFUPWrelationsforMagel-
lanicCepheidsprovidedbyMarconietal.(2005). TheassociatederroristhedispersionofthetheoreticalPW
relation.
e WeighteddistancemodulusestimatedusingthedistancemoduliofindividualPWrelations.
f DistancemodulusobtainedusingPolarisforthezero-pointcalibration(vanLeeuwenetal.2007).
g Distancemodulusbasedonthezero-pointcalibrationobtainedbythepredictedFOPWrelationsforMagel-
lanicCepheidsprovidedbyMarconietal.(2005). TheassociatederroristhedispersionofthetheoreticalPW
relation.
10 Inno et al.
TABLE 2
Difference in the slopes of the PW
relations for LMC and SMC Cepheids.
W(λ2,λ1) Mode ∆bLMC−SMCa σtotb
W(J,KS) FU 0.115±0.014 0.18
W(J,H) FU 0.169±0.014 0.19
W(H,KS) FU 0.120±0.015 0.21
W(V,KS) FU 0.135±0.014 0.17
W(V,H) FU 0.160±0.013 0.17
W(V,J) FU 0.155±0.014 0.18
W(I,KS) FU 0.139±0.014 0.17
W(I,H) FU 0.163±0.014 0.18
W(I,J) FU 0.181±0.017 0.21
W(V,I) FU 0.122±0.014 0.15
W(J,KS) FO 0.180±0.026 0.18
W(J,H) FO 0.215±0.027 0.19
W(H,KS) FO 0.154±0.032 0.21
W(V,KS) FO 0.172±0.024 0.18
W(V,H) FO 0.175±0.023 0.17
W(V,J) FO 0.143±0.027 0.21
W(I,KS) FO 0.182±0.024 0.18
W(I,H) FO 0.178±0.023 0.18
W(I,J) FO 0.172±0.034 0.23
W(V,I) FO 0.139±0.021 0.16
a Theerroronthedifferencewasestimatedbyac-
countingfortheuncertaintiesontheslopesofPW
relations.
(cid:113)
b Total dispersion, i.e. σtot= σL2MC+σS2MC,
where σLMC and σSMC are the individual dis-
persions of the PW relations for LMC and SMC
Cepheids,respectively.