Uncertainties in The Interstellar Extinction Curve and the Cepheid Distance to M101

0.25 MB·English

by  David M. Nataf

Mon.Not.R.Astron.Soc.000,1–??(2014) Printed23January2015 (MNLATEXstylefilev2.2)
Uncertainties in The Interstellar Extinction Curve and the
Cepheid Distance to M101
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1 David M. Nataf1⋆
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2 1Research School of Astronomy and Astrophysics, The Australian National University,Canberra, ACT 2611, Australia

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J
Accepted2015January21.Received2014December 26;inoriginalform2014October27

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ABSTRACT
]
A I revisit the Cepheid-distance determination to the nearby spiral galaxy M101 (Pin-
wheel Galaxy) of Shappee & Stanek (2011), in light of several recent investigations
G
questioning the shape of the interstellar extinction curve at λ ≈ 8,000 ˚A(i.e. I-
h. band). I find that the relatively steep extinction ratio AI/E(V − I) = 1.1450
p (Fitzpatrick & Massa 2007) is slightly favoured relative to AI/E(V − I) = 1.2899
- (Fitzpatrick 1999) and significantly favoured relative the historically canonical value
o of A /E(V −I) = 1.4695 (Cardelli et al. 1989). The steeper extinction curves, with
tr lowerI values of AI/E(V −I), yield fits with reduced scatter, metallicity-dependences
s
to the dereddened Cepheid luminosities that are closer to values inferred in the lo-
a
[ cal group, and that are less sensitive to the choice of reddening cut imposed in the
sample selection.The increase in distance modulus to M101 when using the preferred
1 extinction curve is ∆µ ∼ 0.06 mag, resulting in an estimate of the distance modulus
v toM101relativetotheLMCof∆µLMC ≈10.72±0.03(stat).Thebest-fitmetallicity-
1 dependence is dM /d[O/H]≈(−0.38±0.14 (stat)) mag dex−1.
1 I
3
Key words: distance scale – stars: variables: Cepheids – ISM: dust, extinction –
5
galaxies:individual: (M101)
0
.
1
0
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1 1 INTRODUCTION theirfunctionsyieldRI ≈1.45.TheresultsofCardelli et al.
: (1989) are a linchpin of astronomy as a whole, with over
v Interstellar extinction causes luminosity sources to appear
5,000 refereed citations at thetimeof writing. Thesevalues
i fainter and redder, and is thus somewhat degenerate with
X havehadconvincingindependentsupportelsewhere.Udalski
r distance which causes luminosity sources to appear fainter (2003) measured RI =1.44±0.03 toward theLargeMagel-
butnotredder.Inprinciple,thisdifference(thecolouroffset)
a lanic Cloud (LMC), which is the anchor of the extragalac-
can allow one to break the degeneracy between interstellar
tic distance scale (Freedman et al. 2001) and many investi-
extinctionanddistance.Ifoneassumesaconsistenttotal-to-
gations of Cepheids. Pejcha & Kochanek (2012) developed
selective extinction ratio RI = AI/E(V −I) = AI/(AV − a comprehensive physical model and matched to ∼177,000
AI), one can estimate a“Wesenheit1 magnitude”(Madore
photometric measurements from a sample of 287 LMC,
1982) that is nominally reddening-independent:
Small Magellanic Cloud (SMC), and Milky Way Cepheids.
WI =I−RI×(V −I). (1) They measured a best-fit mean extinction curve of RV ≈
3.127, assuming the formalism from Cardelli et al. (1989).
The values of RI regularly used in the literature range Similarly, Pejcha & Prieto (2014), matched to ∼6,800 pho-
from1.60(Paczynskiet al.1994),1.55(Majaess et al.2011; tometric measurements over a broad range of wavelengths,
Ngeow 2012), down to 1.45 (Macri et al. 2006; Gerkeet al. and showed that the RV = 3.1 extinction curve from
2011; Shappee& Stanek 2011). There is certainly a strong Cardelli et al. (1989) is an effective fit to the UBVRI light
empirical basis for this assumption. Cardelli et al. (1989), curvesof Type-IIplateau supernovae.
in their seminal investigation of extinction from the ultra-
violet to the near-infrared, yielded parametric fits for the There has been recent evidence that the extinction
extinction curve as a function of wavelength and the free- curve of even the diffuse interstellar medium may be vari-
parameter RV = AV/E(B −V). For the case RV = 3.1, able on a systematic basis, or simply distinct than as pa-
rameterised byCardelli et al.(1989).Schlafly & Finkbeiner
(2011) studied reddening values toward Milky Way halo
⋆ Email:[email protected] stars, and found that the exitnction curve of Fitzpatrick
1 “Wesenheit”istheGermanwordfor“essential”. (1999), with its different method of derivation with the ex-
2 Nataf
tinction curve fit to some cubic spline anchor points rather of RV = 4.9, which is extremely shallow, using a combina-
than seventh degree polynomials among other distinctions, tion of UBVR photometry.
and its steeper extinction in the wavelength range 6,000 Having worked extensively on some of these issues,
˚A6λ69,000˚A,wasmoreconsistentwithobservationsthat I cannot argue at this time that there is a convincing
of Cardelli et al. (1989). This finding contributed to a re- framework unifying these disparate, seemingly mutually-
vision of the SFD extinction maps (Schlegel et al. 1998). inconsistent findings. What I am confident in, is that more
Similarly, Sung& Bessell (2014) showed that reddening to- investigation is needed, both of the shape of the extinction
ward open clusters within 3 Kpc of the Sun is well-fit by curve, how it varies with direction, and how this hitherto
anRV =3.1Fitzpatrick(1999)extinctioncurve,whichpre- largely ignored source of systematic error has metastasised
dicts RI ≈ 1.27 for hot stars. Further, it is by now well- into the general astronomy literature and its library of ac-
documented that the inner-parts of the Milky Way, which cepted values. There is an abundance of data available in
arerigorously investigated,arefitbyasteeperstandardex- a broad range of bandpasses for a broad range of objects
tinction curvethan the RV =3.1 curvefrom Cardelli et al. observed in a broad range of contexts, and thus further re-
(1989). In their study of 17,000 Galactic bulge RR Lyrae search that could elucidate theseissues is possible.
stars identified in OGLE-III photometry (Szyman´skiet al. Thus, I tackle the Cepheid distance to M101 for two
2011), Pietrukowicz et al. (2012) measure RI = 1.080 ± reasons.First,asaprobeoftheinterstellarextinctioncurve
0.007. Nataf et al. (2013) used red clump stars (which are in and of itself. The data products of Shappee& Stanek
∼2,000 Kelvin colder and ∼ 10× more metal-rich) mea- (2011) are of high quality, with the photometry obtained
sured with the same OGLE-III photometry and obtained from the Hubble Space Telescope (HST) and reduced via
<RI >=1.218, with significant variations confirmed span- a suite of state-of-the-art software tools. The observations
ning a range 1.0.RI .1.4. The large shifts in theextinc- areofaspiralgalaxyofsimilarmassandmorphologyasthe
tioncurveareobservedtotakeplacetowardsightlinescloser MilkyWay.AsM101isviewednearlyface-on,thereddening
to one another than 0.5 degrees on the sky, or a transverse valuesaresufficientlysmallthatalargenumberofCepheids
distancenogreaterthan75parsecs.Finally,fromtheextinc- canbeidentified.Indeed,thecatalogueofShappee& Stanek
tionstudyofBerdnikov et al.(1996),whichbasedpurelyoff (2011) is one of the largest homogenously-measured extra-
photometry of Cepheids2,RI ≈1.07. galactic catalogues of Cepheids, containing 1,227 Cepheid
Readingthissequenceof findingssome may arguethat candidates.Second,thisinvestigationcanhelpdiscernwhat
the astronomical community should simply switch to using impact these uncertainties might have on the field of the
the Fitzpatrick (1999) extinction curve as default over that extragalactic distance ladder,where Cepheidsare a widely-
ofCardelli et al.(1989).Thatmayturnouttobethecorrect used standardisable candle (Macri et al. 2006; Riess et al.
courseofaction,butasofnowthereatleastthreecausesfor 2011;Gerke et al.2011;Efstathiou2014).Astheeraofpre-
concernwiththisapproach.First,asdiscussedearlierinthe cision cosmology is now over a decade old (Spergel et al.
introduction, the extinction curve of Cardelli et al. (1989) 2003),withthereportederrorbarsgrowingsmallerandpo-
does have convincing independent empirical support, and tentialtensionsgrowinggreater(Planck Collaboration et al.
this would need to be explained if the RV =3.1 extinction 2013), the requirementsfor measurement precision are now
curveofCardelli et al.(1989)turnsouttobeincorrect.Sec- higher-than-ever,necessitatingdiligent investigationsofpa-
ond,theevidenceiscurrentlyoverwhelmingthattheextinc- rameters such as extinction coefficients.
tion curve of Fitzpatrick (1999) fails in the near-IR, where
Fitzpatrick (1999) predicts AJ/AK ≈ 2.31 that is nearly
independent of RV. However, the most precisely and accu-
2 DEFINING THE PROBLEM AND
ratelymeasuredvalueintheGalacticastronomyliteratureis
AJ/AK ≈ 3.02 (Nishiyama et al. 2009). Finally, buoyed by METHODOLOGY
more abundantdata and a different mode of analysis, Fitz- Asdiscussedintheintroduction,virtuallyanyextinctionco-
patrick himself argued for a differentmean Galactic extinc- efficientintherange1.05.RI .1.45canbeassignedsome
tioncurveinFitzpatrick & Massa(2007)(seetheirTable5), empirical support ascribing it the designation of“the stan-
which is as distinct from Fitzpatrick (1999) as Fitzpatrick dard extinction ratio for the diffuse interstellar medium.”
(1999) is from Cardelli et al. (1989). That is problematic and a source of major systematic error
Separately and independently to these issues, evidence previouslyundiagnosedandunquantifiedintheliteratureon
hasrecentlyemergedthatthewavelength-dependenceofin- theuseof Cepheidstoprobetheextragalactic distancelad-
terstellar extinction is a function of the spectral type and der.In thispaper, I test for threedifferent cases. These are
thespecific-star-formationrateofagalaxy(Kriek & Conroy the extinction curves of Cardelli et al. (1989), Fitzpatrick
2013), and even location within a galaxy (Zasowski et al. (1999), and Fitzpatrick & Massa (2007), which are shown
2009;Phillips et al.2013;Donget al.2014).Duringtheref- in Figure 1. I convolve these curves with the transmission
ereeprocessforthispaper,Fausnaugh et al. (2014)founda functions of the Landolt (1992) V and I filters (also shown
best-fit extinction curve toward the Cepheids of NGC 4258 in Figure 1), and a synthetic spectrum of a Teff = 5,750
Kelvin, [Fe/H]= 0, logg = 1.0 star kindly sent to me by
LucaCasagrande, wheretheparametersarechosen totypi-
cal of Cepheids as modelled by Pejcha & Kochanek (2012).
2 From Table 4 of Berdnikovetal. (1996) one can derive RI = Thepredicted extinction coefficients are listed in Table 1.
0.84, but that is because the I-band filter used in that study is Attherequestofthereferee,IalsolistinTable2what
centredatλ≈8,800A˚,whichisatalongerwavelengththanthe the extinction coefficients would be for different assumed
standardLandoltfilter. parameters. Shifting the temperature by 1000 Kelvin only
Interstellar Extinction and M101 Cepheids 3
Table 1. Predicted extinction coefficients for the Lan- Table 2. Predicted extinction coefficients for the Lan-
dolt, 2MASS, ACS, and WFC3 filter transmission dolt, 2MASS, ACS, and WFC3 filter transmission
curvesconvolvedwiththesyntheticspectrumofaTeff = curvesconvolvedwiththesyntheticspectrumofaTeff =
5,750Kelvin,[Fe/H]=0,logg =1.0staraswellas0.40 6,750Kelvin,[Fe/H]=0,logg =1.0staraswellas0.40
mag of extinction at λ = 5500˚A. These are the coeffi- mag of extinction at λ=5500˚A.
cients assumed by this study.
CCM89 F99 FM07
CCM89 F99 FM07 A /E(V −I) 1.4524 1.2721 1.1304
I
AI/E(V −I) 1.4695 1.2899 1.1450 AU/A5500A˚ 1.5395 1.5407 1.5151
AU/A5500A˚ 1.5492 1.5532 1.5276 AB/A5500A˚ 1.3129 1.3233 1.2979
AB/A5500A˚ 1.2893 1.3022 1.2774 AV/A5500A˚ 1.0078 1.0085 1.0035
AV/A5500A˚ 1.0020 1.0015 0.9965 AR/A5500A˚ 0.8258 0.7933 0.7768
AR/A5500A˚ 0.8187 0.7854 0.7683 AI/A5500A˚ 0.5969 0.5646 0.5325
AI/A5500A˚ 0.5963 0.5641 0.5319 AJ/A5500A˚ 0.2900 0.2702 0.2388
AJ/A5500A˚ 0.2981 0.2694 0.2380 AH/A5500A˚ 0.1826 0.1717 0.1411
AH/A5500A˚ 0.1825 0.1716 0.1410 AKs/A5500A˚ 0.1178 0.1160 0.0853
AKs/A5500A˚ 0.1178 0.1160 0.0853 AF555WACS/A5500A˚ 1.0435 1.0503 1.0432
AF555WACS/A5500A˚ 1.0367 1.0423 1.0356 AF606W,ACS/A5500A˚ 0.9491 0.9360 0.9244
AF606W,ACS/A5500A˚ 0.9339 0.9178 0.9058 AF814W,ACS/A5500A˚ 0.5711 0.5417 0.5090
AF814W,ACS/A5500A˚ 0.5699 0.5406 0.5079 AF555W,WFC3/A5500A˚ 1.0636 1.0698 1.0583
AF555W,WFC3/A5500A˚ 1.0482 1.0521 1.0414 AF606W,WFC3/A5500A˚ 0.9447 0.9309 0.9195
AF606W,WFC3/A5500A˚ 0.9304 0.9138 0.9019 AF814W,WFC3/A5500A˚ 0.6016 0.5684 0.5368
AF814W,WFC3/A5500A˚ 0.6001 0.5671 0.5354 AF110W,WFC3/A5500A˚ 0.3429 0.3234 0.2904
AF110W,WFC3/A5500A˚ 0.3379 0.3184 0.2855 AF125W,WFC3/A5500A˚ 0.2895 0.2699 0.2385
AF125W,WFC3/A5500A˚ 0.2881 0.2686 0.2372 AF160W,WFC3/A5500A˚ 0.2045 0.1910 0.1606
AF160W,WFC3/A5500A˚ 0.2042 0.1907 0.1603
informationevenifoneassumesthatallsourcesoferrorare
known,since χ2 is a correlation-dependentquantity.
shifts the extinction coefficients by ∼1% or less. The dom-
(iii) I fit for the metallicity-dependence of the dered-
inant uncertainty lies in the assumed extinction curve, and
dened Cepheid luminosities concurrently with the fit for
not the convolution of the stellar spectrum with which the
the relative distance modulus of M101 with respect to
transmission filters are convolved. Nevertheless, should one
the LMC using a multilinear least-squares fit. In con-
actually be attempting “1% cosmology”, then one should
trast, Shappee& Stanek (2011) computed the metallicity-
compute slightly different extinction coefficients for every
dependence using two sequential least-squares fit, with
Cepheid. With the two bandpasses used in this work, the
the distance modulus computed first independently of the
shift in distancemodulus is only ∼0.003 mag, with theval-
metallicity-dependence, and the scatter to the first relation
uesof Table 1 yieldingthemarginally smaller distances.
thenregressed with respect to themetallicity.
I thenfollow thesample selection outlined in Section 4
(iv) Shappee& Stanek (2011) set their metallicity zero-
andSection5ofShappee& Stanek(2011),whichisbasedoff
point to [O/H]= 8.50, which is thus their assumed metal-
the work of Macri et al. (2006), including the same period-
licity for the LMC. I instead use [O/H]= 8.36, as ar-
luminosityrelationsfromUdalski et al.(1999),andsample-
guedbyBresolin (2011),which was assumed byRiess et al.
cutsbasedoncolourandvariabilityamplituderatiosmeant
(2011) and is consistent with the measurement of [O/H]=
to reduce blends. However, I make a few modifications to
8.37 in HII regions and supernovae remnants of the LMC
themethodology:
(Russell& Dopita1990).
(i) I use recursive 3-σ outlier rejection rather than itera- (v) As this investigation is concerned with quantifying
tiveweighted-mediansigmaclippingtoremoveoutliers.This oneparticularsystematicerror,theestimatesofvariouspa-
consistently leads to 3 of the 231 clean Cepheids being re- rametersstateonlythemaximum-likelihooodvaluesandthe
moved from the fit, independent of the assumptions made statistical errors. In contrast to Shappee& Stanek (2011)
in thefit. who report estimates of the total systematic error separate
(ii) The errors in the relations are computed assum- from theirstatistical errors.
ing homoscedastic errors on the data points. I argue that
the χ2 estimates from the method of Macri et al. (2006)
andShappee& Stanek(2011) areproblematic.Thevarious 3 RESULTS
sources of systematic error (such as the uncertain extinc-
tion curve) are in need of characterisation. and these will 3.1 Metallicity-Dependence as a Free Parameter
add to the existing errors in unexpected ways, rather than
Assuming the extinction curve of Cardelli et al. (1989), I
simplyasare-scalingofexistingerrors.Further,thereisno
obtain:
correlation givenfortheerrors onvariousvariables,suchas
the error on the mean I-band magnitude or V-band mag- ∆µLMC =(10.663±0.031)+(−0.433±0.145)([O/H]−8.36)
nitude of the Cepheids, which could be correlated. Thus it δ=0.1680,
is actually impossible to compute a χ2 from the available (2)
4 Nataf
Figure 1. The extinction curves of Cardelli et al. (1989) as the dotted-blue line, Fitzpatrick (1999) as the short-
dashed-green, and Fitzpatrick & Massa (2007) as the long-dashed-salmon line, as a function of wavelength. Also
shownaretheLandolt(1992)V andLandoltI filtersinblack.Thedifferenttrendsofthe extinctioncurvesoverthis
wavelength regime lead to different predictions for the extinction ration A /E(V −I).
I
where δ is the 1-σ scatter on the relation. If I assume the that Shappee& Stanek (2011) derive using two different
extinction curveof Fitzpatrick (1999): methods. That may be due to the different method of
∆µLMC =(10.692±0.031)+(−0.406±0.144)([O/H]−8.36) fitting. The value derived here is closer to other literature
estimates derived from other estimates, as will be shown in
δ =0.1671,
thesubsequentsubsection.
(3)
andfor theextinctioncurveofFitzpatrick & Massa (2007):
3.2 Metallicity-Dependence Fixed to Literature
∆µLMC =(10.716±0.031)+(−0.384±0.144)([O/H]−8.36) Values
δ =0.1674,
It is of interest to verify how results differ when
(4) the metallicity-dependence is fixed to literature values.
Ireiteratethattheerrorsquotedarerandomerrorsresulting Sakaiet al. (2004) estimated γ = −0.24±0.05 mag dex−1
from the assumption of homoscedastic errors on the data by comparing tip of the red giant branch magnitudes to
points. A complete inventoryof thesystematics involved in Cepheid magnitudes for 7 nearby galaxies images in V and
Cepheid determinations and their associated correlations is I with HST, as well as 10 additional values found in the
not available at this time and is beyond the scope of this literature. Storm et al. (2011) estimated γ = −0.23±0.10
work.Onlyonesystematicisbeingfocusedon:theshapeof mag dex−1 for a sample of 51 Cepheids from the SMC, the
theextinction curve. LMC, and the Milky Way. I adopt the value of γ = −0.23
The relative distance estimate from Equations 2,3,4 is mag dex−1 though the two values are so similar that the
∼0.03maggreaterthanthatfromShappee& Stanek(2011) effect of thischoice is negligible.
in spite of assuming the same extinction curve and nearly The relation obtained for the extinction curve of
thesame selection function.The offset is largely dueto the Cardelli et al. (1989) is:
d∼o0w.1n4wdaerdx.adjustment of the assumed LMC metallicity by ∆µLMC =(10.622±0.011) (5)
δ=0.1687,
For thedistance relations fit by Equation 2 through to
Equation 6 in the following subsection, thesame threeout- for theextinction curveof Fitzpatrick (1999):
liers and no others are always removed: F2-3598, F1-3546,
and F2-1458. Their respective inferred distances are ∼0.60 ∆µLMC =(10.657±0.011)
(6)
mag,∼-0.70mag,and∼1.20magfurtherthantherelations. δ=0.1676,
Due to these large offsets and the fact that it’s the same
andfortheextinctioncurveofFitzpatrick & Massa (2007):
threeoutliersremoved eachtime, Iargue thattherecursive
3-σ outlierrejection doesnotdetrimentallybiastheresults. ∆µLMC =(10.685±0.011)
The metallicity dependence derived, γ = (7)
dMI/d[M/H] ≈ 0.40 mag dex−1, is substantially lower δ=0.1678,
than the values of 0.72 mag dex−1 and 0.80 mag dex−1 M101 isshiftedtoadistancethatis∼0.04magfurther
Interstellar Extinction and M101 Cepheids 5
Table3.Theslopeoftheshiftininferreddistancemod-
ulus per 1 magnitude increase in the reddening cut, as
a function of assumed extinction curve. The curve of
Fitzpatrick & Massa (2007) yields the smallest depen-
dence to the choice of colour cut.
CCM89 −0.063
F99 −0.027
FM07 −0.017
away in all threecases relative tothevalues obtained when
the metallicity-dependence is floated as a free parameter.
That offset comes from the product of the mean [O/H] of
M101 relative to the LMC (∼0.20 dex) and the shift in the
slopeofthemetallicity-dependence(∼0.15-0.20magdex−1).
Though this was interesting as an exercise, I note that
this assumption of a metallicity-dependence form the liter-
ature is inconsistent with other assumptions in this inves-
tigation. Storm et al. (2011) assumed a universal, constant
extinctionfunctionofRV =3.23fromCardelli et al.(1989),
corresponding to AI/E(V −I) ≈ 1.50. That’s marginally Figure 2. TOP: The distance modulus of M101 rela-
shallowerthantheLMCvalueofAI/E(V −I)=1.44±0.03 tive to that of the LMC as a function of the extinction
(Udalski 2003), and substantially shallower than the Milky curves and as the maximum reddening E(V − I)Max
WayvalueofAI/E(V −I)≈1.27 suggested bythework of of Cepheids included in the calculation. The extinc-
Schlafly& Finkbeiner (2011). It may also be distinct from tion curve of Fitzpatrick & Massa (2007) is the least
theSMCvalue.Thereisanurgentneedforaninvestigation sensitive to the choice of E(V − I)Max, whereas that
of the metallicity-dependence of Cepheid luminosities that of Cardelli et al. (1989) is the most sensitive. BOT-
accountsforextinctioncurveuncertaintiesandvariationsin TOM: Same as top panel, but with the distance mod-
theMilky Way Galaxy and its satellites. ulus for E(V − I)Max = 0.39 (the value assumed by
Shappee & Stanek 2011), shifted to zero.
3.3 Shifting the Maximum-Colour Cut
Table 4. Scatter in distance modulus as a func-
Shappee& Stanek (2011) removed Cepheids with E(V − tion of colour-cut on the Cepheid sample and the
I)>0.39 from theirfit,on thebasis that theymight either choice of the extinction curve. The extinction curve of
beredblends,orhavehigh-reddeningvaluesthatwouldlead Fitzpatrick & Massa(2007)yieldsthesmallestincrease
in scatter as the colour cut is increased.
toanerrorlinearlyproportionaltotheerrorintheassumed
extinction curve. Of interest would be to test which of the E(V −I)Max CCM89 F99 FM07
three extinction curves yields a distance least sensitive to
the choice of E(V −I) cut (hereafter: E(V −I)Max). For 0.39 0.1687 0.1676 0.1678
0.99 0.1844 0.1839 0.1766
this calculation, I fix the metallicity-dependence to the lit-
eraturevalueofγ =−0.23magdex−1(Storm et al.2011)to
restrictthenumberofdegreesoffreedom,thoughitisnoted track the scatter in the relations rather than the shift in
that the results are nearly identical if I fix the metallicity distance modulus, for which the results are listed in Table
dependenceto thevaluesfound in Equations2, 3, and 4. 4. Assumingtheextinction curveof Cardelli et al. (1989), I
With this test, of which I plot the results in Figure find that the scatter increases from σ = 0.1687 at E(V −
2,theextinctioncurveofFitzpatrick & Massa(2007)isthe I)Max=0.39toσ=0.1844atE(V−I)Max=0.99.Withthe
mostsuccessfulatmatchingthedataforM101,whereasthat extinction curveof Fitzpatrick (1999), the scatter increases
of Cardelli et al. (1989) which is the most standard in the from σ =0.1676 to σ =0.1839. Finally, with the extinction
Cepheid literature is the least successful. The inferred rel- curve of Fitzpatrick & Massa (2007), the scatter increases
ative distance modulus decreases rapidly as more reddened from σ = 0.1678 to σ = 0.1766. The increase in variance
sources are included when I assume the extinction curve of for the shallowest extinction curve as the reddening cut is
Cardelli et al. (1989), exactly what one would expect if the increasedisonly∼10%,lessthanhalfwhatitisfortheother
extinction curve is too shallow. The distance modulus also two extinction curves.
decreaseswhenIassumetheextinctioncurvesofFitzpatrick
(1999) Fitzpatrick & Massa (2007), but by a much smaller
amount,∼−0.027and∼−0.017respectivedecreasesindis-
4 DISCUSSION AND CONCLUSION
tancemodulusper1magnitudeincreaseinE(V −I)Max.In
contrast,useoftheextinctioncurveofCardelli et al.(1989) Inthisinvestigation IhavedemonstratedthattheCepheid-
yieldsamuchsteepersensitivityof∼−0.063. Theseresults distance to the spiral galaxy M101 is measured with
are listed in Table 3 . a reduced scatter and reduced sensitivity to systemat-
The same conclusions are reached if one would rather ics if I assume the mean Galactic extinction curve of
6 Nataf
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Kriek M., Conroy C., 2013, ApJ, 775, L16
now well-documented that the shape of extinction curve
Landolt A.U., 1992, AJ, 104, 340
is a function of location even in one particular galaxy
MacriL.M.,StanekK.Z.,BersierD.,GreenhillL.J.,Reid
(Zasowski et al. 2009; Phillips et al. 2013; Donget al.
M. J., 2006, ApJ, 652, 1133
2014). I thus argue that a new phenomenological model to
Madore B. F., 1982, ApJ,253, 575
deal with interstellar extinction is needed, both to under-
Majaess D. J., Turner D. G., Lane D. J., Henden A. A.,
stand extragalactic stellar populations and to precisely and
Krajci T., 2011, Journal of the American Association of
accurately calibrate thedistance ladder.
VariableStar Observers(JAAVSO),39, 122
The referee brought up the possibility of varying RV.
Nataf D. M. et al., 2013, ApJ, 769, 88
Giventhattheinvestigationofthisworkhadaccesstodata
Ngeow C. C., 2012, ApJ, 747, 50
inonlytwobandpasses,varyingRV fromafixedfamilyofex-
NishiyamaS.,TamuraM.,HatanoH.,KatoD.,Tanab´eT.,
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SugitaniK., Nagata T., 2009, ApJ,696, 1407
tioncurveatfixedRV.FromtheformalismofCardelli et al.
Paczynski B., Stanek K. Z., Udalski A., Szymanski M.,
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KaluznyJ., KubiakM., Mateo M., 1994, AJ, 107, 2060
a value common in Type Ia SNe cosmology (Phillips et al.
Pejcha O., Kochanek C. S., 2012, ApJ, 748, 107
2013).Thedistinctioncannotbevisitedinthiswork,itcould
Pejcha O., Prieto J. L., 2014, ArXiv e-prints
in principlebeinvestigated iftherewerealarger numberof
Phillips M. M. et al., 2013, ApJ, 779, 38
bandpassesavailable, in particular B-bandwould obviously
Pietrukowicz P. et al., 2012, ApJ, 750, 169
bea significant degeneracy-breaker.
Planck Collaboration et al., 2013, ArXive-prints
Somereadersmayworrythattheeraofworryingabout
RiessA.G.,FliriJ.,Valls-GabaudD.,2012,ApJ,745,156
extinctionasasourceof errorinthedistanceladderisend-
Riess A.G. et al., 2011, ApJ,730, 119
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Russell S.C., Dopita M. A.,1990, ApJS,74, 93
period-luminosity relations for a sample of 68 Cepheids in
Sakai S.,Ferrarese L., Kennicutt Jr. R. C., Saha A., 2004,
the Andromeda galaxy (M31). This strategy is promising,
ApJ,608, 42
astheextinctioninWFC3 filterF160W isonly ∼30% that
Schlafly E. F., FinkbeinerD.P., 2011, ApJ, 737, 103
of the extinction in the Landolt I-band filter, and the dis-
SchlegelD.J.,FinkbeinerD.P.,DavisM.,1998,ApJ,500,
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525
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Spergel D.N. et al., 2003, ApJS,148, 175
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Storm J., Gieren W., Fouqu´e P., Barnes T. G., Soszyn´ski
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Sung H., Bessell M. S., 2014, in H.W. Lee, Y.W. Kang,
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ACKNOWLEDGMENTS Udalski A., Soszynski I., Szymanski M., Kubiak M.,
Pietrzynski G., Wozniak P., Zebrun K., 1999, Acta. As-
I thank Benjamin J. Shappee, Brian P. Schmidt, and Mar-
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tinAsplund,forhelpfuldiscussions.Ithanktheanonymous
Zasowski G. et al., 2009, ApJ, 707, 510
referee for a constructivereview of themanuscript.
DMN was supported by the Australian Research Council
grant FL110100012.