Using Ultra Long Period Cepheids to Extend the Cosmic Distance Ladder to 100 Mpc and Beyond
aa r X i v : . [ a s t r o - ph ] J a n A CCEPTED FOR PUBLICATION IN A P J. Preprint typeset using L A TEX style emulateapj v. 12/14/05
USING ULTRA LONG PERIOD CEPHEIDS TO EXTEND THE COSMIC DISTANCE LADDER TO 100 MPC ANDBEYOND J ONATHAN
C. B
IRD , K. Z. S
TANEK , J
OSÉ
L. P
RIETO
Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, [email protected],[email protected], [email protected]
Accepted for publication in ApJ.
ABSTRACTWe examine the properties of 18 long period (80 -
210 days) and very luminous (median absolute magnitudeof M I = - .
86 and M V = - .
97) Cepheids to see if they can serve as an useful distance indicator. We find thatthese Ultra Long Period (ULP) Cepheids have a relatively shallow Period-Luminosity (PL) relation, so in factthey are more “standard candle”-like than classical Cepheids. In the reddening-free Wesenheit index, the slopeof the ULP PL relation is consistent with zero. The scatter of our sample about the W I PL relation is 0 .
23 mag,approaching that of classical Cepheids and Type Ia Supernovae. We expect this scatter to decrease as biggerand more uniform samples of ULP Cepheids are obtained. We also measure a non-zero period derivative forone ULP Cepheid (SMC HV829) and use the result to probe evolutionary models and mass loss of massivestars. ULP Cepheids main advantage over classical Cepheids is that they are more luminous, and as such showgreat potential as stellar distance indicators to galaxies up to 100 Mpc and beyond.
Subject headings:
Cepheids — stars: distances — stars: mass loss — distance scale INTRODUCTION
A reliable method of measuring the physical distance toastrophysical objects has always been sought after in obser-vational astronomy (e.g., Bessel 1839). In the era of “pre-cision cosmology”, the need for accurate physical distancemeasurements has been amplified (e.g., Spergel et al. 2003;Riess et al. 2004; Tegmark et al. 2004). Accurate and pre-cise distance indicators hold the key to pinning down thevalue of the Hubble constant ( H ) and many other cosmo-logical parameters (see discussion in, e.g., Macri et al. 2006).A number of methods have been employed to determine ex-tragalactic distances, with varying degree of success (e.g.,Freedman et al. 2001). The construction and reliability of the“cosmological distance ladder” depends crucially on Cepheidvariables being able to provide precise and accurate distancesto nearby ( d .
20 Mpc) galaxies. The quest for such distanceshas been an arduous journey for almost a hundred years, withmany dramatic twists and turns (for a review of early years,see Baade 1956, for a recent review see, e.g., Macri 2005).Cepheids offer several advantages as distance indicators.Massive stars ( ≥ M ⊙ ) make an excursion through the in-stability strip and most, if not all, of them become Cepheidvariables. These variable stars are relatively bright ( M V ∼ - P ∼
10 day Cepheid) and often have large brightnessvariations (amplitude ∼ ∼
5% (e.g.,Macri et al. 2006). For these reasons, Cepheids are commonlyused to calibrate other distance indicators, forming the base ofthe cosmological distance ladder.Despite their many advantages as a distance indicator,Cepheid distances also have some shortcomings. Most Cepheids have an intrinsic brightness of M V ≥ -
5, so withthe current instrumentation they can be only used to mea-sure distances to .
30 Mpc (the largest Cepheid distancein Freedman et al. 2001 is ∼
22 Mpc). Observations ofCepheids in distant galaxies are also hindered by blend-ing (Mochejska et al. 2000)— as young stars, Cepheids livein close proximity to the crowded star-forming regions oftheir host galaxies, and are thus likely to have another starof similar brightness on the scale of a typical instrumen-tal point-spread-function (PSF). The effect of blending be-comes worse as the square of the distance to the host galaxy(Stanek & Udalski 1999), again limiting the usefulness ofCepheids to measuring distances .
30 Mpc even with highresolution instruments such as the Hubble Space Telescopes(
HST ). Ideally, we would like to find a distance indicator thatshares the good properties of classical Cepheids, but is evenmore luminous, allowing us to observe it further away and beless susceptible to blending. In this paper we discuss such apossible distance indicator, namely Ultra Long Period (ULP)Cepheids.We define ULP Cepheids as fundamental mode Cepheidswith pulsation periods greater than 80 days. Several suchCepheids have been already discovered in the pioneeringstudy of Leavitt (1908). However, ULP Cepheids have tra-ditionally been ignored for distance measurements as theyare PL outliers. Indeed, the observed PL relation flat-tens for Cepheids with periods greater than 100 days (e.g.,Grieve et al. 1985; Freedman et al. 1992). Grieve et al. (1985)suggests that long period Leavitt Variables could be used fordistance measures— unfortunately that idea has not perme-ated through the community. We argue that the flattening ofthe PL at long periods actually improves the usefulness ofULP Cepheids as distance indicators because it makes thema good standard candle in the traditional sense. We note sev-eral additional advantages of ULP Cepheids over lower periodCepheids due to their increased luminosity. ULP Cepheidscould be used as a stellar distance measure to the Hubble Flow(up to ∼
150 Mpc)— several times the current observationallimit. In Section 2 we describe our sample compiled from Bird, Stanek, & Prietothe literature. The ULP Cepheid PL relation is discussed inSection 3. Section 4 demonstrates how ULP Cepheids mayprovide the additional benefit of testing massive stellar evolu-tionary models. We summarize our results in Section 5. SAMPLE
We have assembled a sample of ULP Cepheids from the lit-erature and list their reported positions, periods, and mean V and I magnitudes (see Table 1). We adopt the periods, redden-ing values, and distance moduli found in these sources exceptin the case of the Magellanic Clouds (see below). Our pri-mary criteria for selecting the sample was the existence of V and I data calibrated on the standard Johnson/Kron-Cousinsmagnitude system using Landolt standards (with the possibleexception of the Magellanic Clouds; see below). The ULPdistinction is applied to fundamental mode Cepheids with pe-riods greater 80 days. We combed the recent literature forreports of such variable stars. Magellanic Clouds
Our sample includes four LMC andthree SMC ULP Cepheids. Freedman et al. (1985) calibratedphotoelectric observations of these Cepheids and transformedthem to the Johnson/Kron-Cousins standard system. Themean flux-weighted photometry for the six Cepheids reportedin Freedman et al. (1985) agrees with the Landolt standardstar calibrated results of Moffett et al. (1998) to within 0 . V light curvesof six of these ULP Cepheids were obtained from ASAS.HV2883 was not targeted by ASAS, and its V light curvephotometry was obtained from Madore (1975), van Genderen(1983), and Moffett et al. (1998). Moffett et al. (1998) pro-vide the I light curve data for the entire sample. We appliedthe analysis of variance technique (Schwarzenberg-Czerny1989) to the seven Harvard Variable light curves in Figure 1 toobtain the periods listed in Table 1. We adopt total reddeningvalues of E ( B - V ) = 0 .
14 mag and E ( B - V ) = 0 .
09 mag forthe LMC and SMC, respectively (Udalski et al. 1999). We as-sume a distance modulus (DM) of ( m - M ) = 18 . m - M ) = 18 .
93 mag (Hilditch et al. 2005;Keller & Wood 2006). The LMC (SMC) hosts ULP Cepheidswith periods of 98.6, 109.2, 118.7, and 133.6 (84.4, 127.5,and 210.4) days. The LMC has gas phase oxygen abundance12 + log(O/H) = 8 . ± .
10 (Pagel et al. 1978) while the SMCis 12 + log(O/H) = 7 . ± .
10 (Peimbert & Torres-Peimbert1976).The Araucaria Project (Pietrzy´nski et al. 2002) is a photo-metric survey of Local and Sculptor Group galaxies and theirCepheid populations. The primary goal is to more accuratelydetermine the distances to these galaxies and to character-ize the dependence of various stellar distance indicators onmetallicity and age. The Araucaria Project has observed ULPCepheids in the following galaxies.
NGC 55
Five ULP Cepheids were found in NGC 55(Pietrzy´nski et al. 2006). Observations were taken with theOptical Gravitation Lensing Experiment (OGLE) detector onthe Warsaw 1.3 m telescope at Las Campanas Observatory.They estimate that the calibration procedure used to transformtheir photometric data from the OGLE filters to the standardsystem produced errors ≤ .
03 mag. Follow up observationsin the IR revealed a total reddening of E ( B - V ) = 0 .
13 mag(Gieren et al. 2008). Their multi-wavelength PL analysis pro- duced a DM to NGC 55 of 26 . ± . ± .
08 mag (statisti-cal and systematic errors, respectively). NGC 55 hosts ULPCepheids with periods of 85.1, 97.7, 112.7, 152.1, and 175.9days. The oxygen abundance of NGC 55 is 12 + log(O/H) =8 . ± .
10 (Tüllmann et al. 2003).
NGC 6822
One ULP Cepheid was found in NGC 6822(Pietrzy´nski et al. 2004). The filters and telescope used areidentical to those of NGC 55 (Pietrzy´nski et al. 2006). Sim-ilarly, the reported calibration error onto the standard systemis ≤ .
03 mag. As in the multi-wavelength follow up studyof NGC 6822 (Gieren et al. 2006), we adopt a total redden-ing of E ( B - V ) = 0 .
36 mag. The lone ULP Cepheid in NGC6822 has a period of 123.9 days. Gieren et al. (2006) calcu-late a DM to NGC 6822 of 23 . ± . ± .
06 mag (statisticaland systematic errors, respectively). NGC 6822 has a similaroxygen abundance to NGC 55 of 12 + log(O/H) = 8 . ± . NGC 300
Gieren et al. (2004) found three ULP Cepheidsin NGC 300. Again, OGLE filters were used for the obser-vations. Their calibration onto the standard system has a re-ported error ≤ .
03 mag. A multi-wavelength study of NGC300 (Gieren et al. 2005) determined a reddening-free DM of26 . ± . ± .
03 mag (statistical and systematic, respec-tively) using a total reddening of E ( B - V ) = 0 .
10 mag. ULPCepheids of 83.0, 89.1, and 115.8 days are observed in NGC300. NGC 300 has a strong metallicity gradient; therefore weadopt mean Cepheid radial distance of 4 kpc and apply theaveraged gradient of Urbaneja et al. (2005) to obtain a meanoxygen abundance value of 12 + log(O/H) = 8 . ± . I Zw 18
Aloisi et al. (2007) discovered three ULP Cepheidsfrom the extremely metal poor galaxy I Zw 18, thoughthey could not confirm one candidate. A follow-up study(Fiorentino et al. 2008) presents flux weighted mean photom-etry but no data, so the light curves of these objects couldnot be included in Figure 1. The ULP Cepheids have peri-ods of 129 . . E ( B - V ) = 0 .
032 mag, Aloisi et al. (2007) use thered giant branch tip to determine a DM of 31 . ± .
17 magwhile Fiorentino et al. (2008) find a DM of 31 . ± .
26 magvia pulsation models. We use the former measurement as itis considered more reliable by the authors. We do not includethese two Cepheids in the upcoming PL determination as I Zw18 is a full dex more metal poor than the other galaxies in thissample (12 + log(O/H) = 7 . ± .
10; Skillman & Kennicutt1993). There is an increasing amount of support for a metal-licity dependent PL (e.g. Sandage et al. 2008) and includingthese Cepheids in our PL analysis would greatly increase themetallicity dispersion of the host galaxies in our sample. Wedo, however, make use of them to examine the ULP PL rela-tion dependence on metallicity.
Absolute Photometry
The ULP Cepheid sample and its mean, flux-weighted pho-tometry in the standard system can be found in Table 1. Weassume that the photometric error associated with each ULPCepheid is negligible when compared to the intrinsic scatterof the PL relation. We transform these measurements to ab-solute magnitudes via: M i = m i - DM - A i , i = I , V (1)where M i is the absolute magnitude in either the V or I , m i isthe apparent magnitude; DM is the reddening free distancemodulus; and A i is the extinction in the V or I . We usethe extinction law A V = 3 . E ( B - V ) and A I = 1 . E ( B - V )LP Cepheids 3 F IG . 1.— The V (open circles) and I (filled circles, where available) band light curves of the ULP Cepheids. Each panel spans 2.4 magnitudes along the y-axis.The phase is given along the x-axis. The Cepheid identification (see column 1, Table 1) is listed in the upper left of each plot while the period (in days) is in theupper right. (Schlegel et al. 1998). We define the Wesenheit magnitudesas: W I = I - . V - I ) (e.g., Udalski et al. 1999).The color-magnitude diagram (CMD) highlights severalimportant characteristics of the ULP Cepheid data set (Fig-ure 2). ULP Cepheids are the luminous counterparts toshorter period Cepheids in color magnitude space. Our sam-ple clearly populates the luminous region of the instabil-ity strip. Future Cepheid studies can use ULP Cepheids topush Cepheid distance measurements well beyond the current ∼
30 Mpc limit as our sample’s median absolute magnitude isM I (M V ) = - . - .
97) (see Section 5). The intrinsic bright-ness of ULP Cepheids makes them ideal candidates for dis-tance indicators to galaxies where classical Cepheids cannotbe observed. DISTANCE MEASUREMENTS WITH ULP CEPHEIDS
The Cepheids in our sample have been ignored as dis-tance indicators as they do not follow to the standard period-luminosity relationship (e.g., Freedman et al. 1992). In thissection, we examine the characteristics of our ULP Cepheid sample in the period-luminosity plane and explore their via-bility as a distance indicator. We determine PL relations ofour sample in the V , I , and W I in Section 3.1 while the metal-licity dependence of our results is presented in Section 3.2. Period Luminosity Relations
Using the data in Table 1, we construct PL diagrams in V , I , and W I (Figures 3, 4, 5, respectively). In each case, ULPCepheids are compared to fundamental mode SMC Cepheids(hereafter, this control sample will be referred to as OGLECepheids). The OGLE Cepheid sample contains over 1100fundamental mode Cepheids with periods ranging from 0 . ∼
50 days; however, we only plot the 70 Cepheids withperiods of greater than 10 days. To quantify our compari-son, we perform a linear fit on both samples in each PL dia-gram: the slopes of the OGLE Cepheid PL relations (here-after PL
SMC ; dotted lines in the figures) are adopted fromUdalski et al. (1999) while the intercepts are chosen to mini-mize chi-square. We employ linear least square fitting of theULP Cepheid sample to identify their PL relation (hereafter Bird, Stanek, & Prieto
TABLE 1U
LTRA L ONG P ERIOD C EPHEIDS
ID Host Galaxy RA DEC P < V > ( V - I ) W I E ( B - V ) (m-M) V ( V - I ) W I + log(O/H) References(J2000.0) (J2000.0) (days) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) dex(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)LMC HV883 LMC 05 : 00 : 08 . -
68 : 27 : 03 133 . .
12 1 .
09 9 .
34 0 .
14 18 . - .
83 0 . - .
16 8 . ± .
12 1,2,3LMC HV2447 LMC 05 : 19 : 31 . -
68 : 41 : 12 118 . .
99 1 .
12 9 .
13 0 .
14 18 . - .
96 0 . - .
37 8 . ± .
12 1,2,3LMC HV2883 LMC 04 : 56 : 27 . -
64 : 41 : 26 109 . .
41 1 .
07 9 .
68 0 .
14 18 . - .
54 0 . - .
82 8 . ± .
12 1,2,3LMC HV5497 LMC 04 : 55 : 40 . -
66 : 25 : 39 98 . .
92 1 .
11 9 .
09 0 .
14 18 . - .
03 0 . - .
41 8 . ± .
12 1,2,3SMC HV1956 SMC 01 : 04 : 15 . -
72 : 45 : 20 210 . .
28 0 .
83 9 .
95 0 .
09 18 . - .
94 0 . - .
98 7 . ± .
10 5,2,3;4SMC HV821 SMC 00 : 41 : 43 . -
73 : 43 : 24 127 . .
92 1 .
03 9 .
29 0 .
09 18 . - .
30 0 . - .
64 7 . ± .
10 1,6,3;4SMC HV829 SMC 00 : 50 : 28 . -
72 : 45 : 09 84 . .
97 0 .
91 9 .
65 0 .
09 18 . - .
25 0 . - .
28 7 . ± .
10 1,6,3;4NGC 6822-1 NGC 6822 19 : 45 : 02 . -
14 : 47 : 33 123 . .
86 1 .
40 14 .
29 0 .
36 23 . - .
60 0 . - .
02 8 . ± .
10 7,8,9NGC 55-1 NGC 55 00 : 14 : 13 . -
39 : 08 : 42 175 . .
25 0 .
84 17 .
11 0 .
13 26 . - .
60 0 . - .
33 8 . ± .
10 10,11,12NGC 55-2 NGC 55 00 : 15 : 12 . -
39 : 12 : 18 152 . .
56 0 .
95 17 .
14 0 .
13 26 . - .
28 0 . - .
29 8 . ± .
10 10,11,12NGC 55-3 NGC 55 00 : 14 : 36 . -
39 : 11 : 09 112 . .
18 1 .
05 17 .
51 0 .
13 26 . - .
67 0 . - .
92 8 . ± .
10 10,11,12NGC 55-4 NGC 55 00 : 15 : 14 . -
39 : 13 : 17 97 . .
54 1 .
25 17 .
35 0 .
13 26 . - .
31 1 . - .
08 8 . ± .
10 10,11,12NGC 55-5 NGC 55 00 : 15 : 10 . -
39 : 12 : 26 85 . .
84 1 .
38 17 .
32 0 .
13 26 . - .
01 1 . - .
12 8 . ± .
10 10,11,12NGC 300-1 NGC 300 00 : 55 : 11 . -
37 : 33 : 55 115 . .
13 0 .
97 17 .
66 0 .
10 26 . - .
55 0 . - .
71 8 . ± .
22 13,14,15NGC 300-2 NGC 300 00 : 54 : 35 . -
37 : 35 : 01 89 . .
71 1 .
02 17 .
12 0 .
10 26 . - .
97 0 . - .
25 8 . ± .
22 13,14,15NGC 300-3 NGC 300 00 : 54 : 54 . -
37 : 37 : 02 83 . .
26 0 .
77 17 .
30 0 .
10 26 . - .
42 0 . - .
07 8 . ± .
22 13,14,15I Zw 18-1 I Zw 18 ··· ··· . .
56 0 .
74 21 .
67 0 .
03 31 . - .
84 0 . - .
63 7 . ± .
10 16,17I Zw 18-2 I Zw 18 ··· ··· . .
47 0 .
91 21 .
15 0 .
03 31 . - .
93 0 . - .
15 7 . ± .
10 16,17R
EFERENCES . — References: 1. Freedman et al. (1985); 2. Pagel et al. (1978); 3. Udalski et al. (1999); 4. Hilditch et al. (2005) and Keller & Wood (2006); 5. Pojmanski (1997, ASAS survey);6. Peimbert & Torres-Peimbert (1976); 7. Pietrzy´nski et al. (2004); 8. Peimbert et al. (2005); 9. Gieren et al. (2006) 10. Pietrzy´nski et al. (2006); 11. Tüllmann et al. (2003); 12. Gieren et al. (2008)13. Gieren et al. (2004); 14. Urbaneja et al. (2005); 15. Gieren et al. (2005); 16. Fiorentino et al. (2008); 17. Skillman & Kennicutt (1993).N
OTE . — ULP Cepheids in our sample grouped by host galaxy. (1): Cepheid Identification. (2): Host galaxy name. (3,4): Right Ascension and Declination in J2000 coordinates. (5): Periodin days. (6): Apparent mean V magnitude of Cepheid. (7): Apparent ( V - I ) color of Cepheid. (8): Apparent Wesenheit magnitude (definition in text). (9): Reddening towards host galaxy. (10):Reddening-free distance modulus. (11): Absolute V magnitude. (12): Absolute ( V - I ) color. (13): Absolute Wesenheit magnitude. (14): Metallicity: 12 + log(O/H). (15): First reference is forphotometry, reddening, and distance modulus (except where noted in text). Second reference refers to metallicity. If third reference is present, its reddening and distance modulus measurementssupercedes the first. PL ULP ). We omit errors in distance moduli and extinction inthis demonstration as they are small when compared to theoverall scatter of the sample. The parameters of these fits andthe RMS of each data set in V , I , and W I are listed in Table 2.Despite our sample ranging in period from 83 to 210 days,ULP Cepheids occupy a small region of luminosity space. Wenote that the ULP Cepheids from I Zw 18 are not included inthis analysis for reasons outlined in Section 2.The V PL diagram is Figure 3. The PL
SMC fit has a slopeof - .
76 and the RMS of the OGLE Cepheid sample aboutthis fit is 0 .
25 mag. The ULP Cepheid sample has 76% morescatter (RMS=0 .
44 mag) about the PL
SMC fit. This discrep-ancy in scatter has led to the standard practice of removingULP Cepheids from PL relation studies (e.g., Freedman et al.1985) and the significant increase in RMS suggests that theULP Cepheids do not conform to the classical PL relation.If we determine the PL relation of ULP Cepheids alone wefind PL
ULP has a slope ( - . ± .
94) that is flatter thanPL
SMC (though the slopes are within 2 σ of each other, seeTable 2). The RMS of our sample to PL ULP is 0 .
40 mag; onlymarginally better than the ULP Cepheid scatter about the es-tablished PL
SMC relation. In V , the ULP Cepheid sample doesnot follow a statistically distinct and unique PL.The longer the wavelength the less reddening is a con-cern. The accuracy of distance measurement with Cepheidsincreases going from V to I (PL diagram in Figure 4). PL SMC has a slope of - .
96 and the OGLE Cepheid sample’s RMS is0 .
19. The ULP Cepheid scatter about this fit is 116% larger(0 .
41 mag). The RMS of the ULP Cepheids is reduced to 0 . ULP fit (slope= - . ± . ULP isapproximately five times as flat as PL
SMC and the two slopesare distinct at the 3 σ level. While ULP Cepheids show thesame general trends with regards to period, luminosity, andcolor as normal Cepheids, significant statistical differencesbetween the two populations are apparent in the I -band PL relation.To further reduce the uncertainty associated with red-dening in our PL analysis, we repeat the procedure us-ing the reddening-free Wesenheit Index (W I ) introduced inMadore & Freedman (1991). The W I PL diagram illuminatesthe advantages of this reddening-free index for Cepheid dis-tance measurements (Figure 5). The OGLE Cepheid samplehas a very tight relation between period and luminosity; withsmall scatter about the PL
SMC fit (slope of - .
28; RMS of only0 .
12 mag). The ULP Cepheid RMS about PL
SMC is 0 .
47 mag.The 4-fold increase in scatter implies the ULP Cepheid andthe OGLE Cepheid samples do not conform to the same PLrelation. The PL
ULP fit slope is flatter than its PL
SMC coun-terpart at the 6 σ level ( - . ± .
54 vs. - .
28) and the ULPfit slope is consistent with zero slope. The scatter of the ULPCepheids is only 0 .
23 mag about the PL
ULP relation. Thisscatter is still 92% more than that of the OGLE Cepheid sam-ple; however, the ULP sample is relatively small and hetero-geneous. We note that the scatter of ULP Cepheids about thePL
ULP fit is smaller than that of the OGLE Cepheid sampleabout the nominal PL relation in V and on par with the samein I .Several trends in PL space are apparent as one examinesthe ULP Cepheid sample in V , then I , and finally in the W I index. As reddening is reduced, the PL ULP parameters are in-creasingly different from those of PL
SMC . The PL
ULP fit ismore shallow as one moves from V to W I . In the W I , thePL ULP relation reveals that ULP Cepheid luminosity becomesstatistically independent of period. In essence, ULP Cepheidsbehave as bright, standard candles in the reddening-free in-dex.
Metallicity Dependence
An uncertainty of the Cepheid PL and its derived distancemeasurement is its sensitivity to the metallicity of the starsLP Cepheids 5
I Zw 18NGC 300NGC 55NGC 6822SMCLMC F IG . 2.— M V versus ( V - I ) color CMD of our ULP sample (open symbols) with the OGLE SMC Cepheids (black dots) and OGLE SMC stars (gray dots) forcomparison. The legend denotes the host galaxy of each ULP Cepheid. For reference we label the main sequence (MS), blue supergiant (BSG), red supergiant(RSG), and red giant (RG) sequences. (e.g., Freedman & Madore 1990; Kennicutt et al. 1998). Oursample of ULP Cepheids contains six different host galax-ies that span a range of ∼ . + log(O/H) from7.22 to 8.39, providing an opportunity to investigate the de-pendence of the ULP Cepheid PL on metallicity. We plotthe residual of each ULP Cepheid to the PL ULP , W I fit listedin Table 2 as a function of metallicity (Figure 6). In otherstudies, linear fits of PL residuals have determined a correc-tion factor, γ , between 0 . - . - (see Figure1 of Romaniello et al. 2008). Recently, Macri et al. (2006)used the metallicity gradient in NGC 4258 to determine γ = - . ± . ± .
05 mag dex - (random and systematic errors,respectively). We overlay this relation (normalized to our dataset) in Figure 6 for reference. If the I Zw 18 Cepheids are con-firmed, it suggests a stronger correlation between PL offsetand metallicity than is evident in lower period Cepheids (e.g.,Kochanek 1997; Kennicutt et al. 1998). However, we notethat we do not take into account any reddening or DM errorsin this analysis. As such, we do not claim a specific metal-licity dependence for ULP Cepheids. We simply demonstrate TABLE 2L
EAST S QUARE F IT V ALUES : y = b + a ∗ x Relation Subset Shorthand Intercept (b) Slope (a) RMS(1) (2) (3) (4) (5) (6)Period-Luminosity: V SMC Cepheids PL
SMC , V - . - .
76 0 . V ULPs PL
ULP , V - . ± . - . ± .
94 0 . I SMC Cepheids PL
SMC , I - . - .
96 0 . I ULPs PL
ULP , I - . ± . - . ± .
73 0 . WI index SMC Cepheids PL SMC , WI - . - .
28 0 . WI index ULPs PL ULP , WI - . ± . - . ± .
54 0 . OTE . — The fit values of the PL relationships in V , I , and W I . For each photometric system, we calculate the PL relationof classical SMC (PL SMC ) and ULP (PL
ULP ) Cepheids. that the residuals to the PL
ULP fit are broadly consistent withthe range of values presented in the literature to date.At this time we do not apply a metallicity correction to ourULP Cepheid PL relations. Precise gas phase oxygen abun-dance measurements are difficult to obtain (for a review seeBresolin 2006) and we adopt a minimum metallicity error of0 . I Zw 18NGC 300NGC 6822NGC 55SMCLMC F IG . 3.— The V Period Luminosity relationship for the OGLE SMC Cepheids (black dots) and ULP Cepheids (open symbols). The dashed line is the PLrelation adopted from Udalski et al. (1999), with a slope of - .
76. The least square fit of the ULP Cepheid subsample yields a flatter slope of - . ± .
94 (redline) and the RMS is 0 .
40 mag. The residuals to the PL
SMC fit are shown in the bottom panel (black, open squares). Residuals to the PL
ULP are given for the ULPCepheid sample (red symbols). is an exception and to characterize the functional form of theULP Cepheid PL sensitivity to metallicity. USING ULP CEPHEIDS TO PROBE THE EVOLUTIONARYMODELS OF MASSIVE STARS
Most Cepheid variables cross the instability strip threetimes (e.g., Bono et al. 2000; Pietrukowicz 2001). One candetermine which crossing a Cepheid is undergoing by mea-suring its period change, dP / dt . The first and third crossingsare associated with positive dP / dt while Cepheids exhibit adecreasing period on their second crossing. We investigatedthe light curves of our sample for signs of period changesby comparing photometry taken over the last 30 years. OneULP Cepheid, HV829, exhibits a negative period change ofabout 1.5 days. For this Cepheid, we compiled photomet-ric data taken during 1970-1976 from Madore (1975) andvan Genderen (1983) and 2000-2004 data from the ASAS cat-alog (See Figure 7). This result is confirmed by a measuredperiod of 87 .
63 days in Payne-Gaposchkin & Gaposchkin(1966) and 85.2 days by Moffett et al. (1998), firmly estab- lishing HV829 as a Cepheid on its second crossing. No otherCepheid in our sample exhibited a measurable period change.ULP Cepheids occupy a mass range that is ideal to probehigh mass evolutionary models along the instability strip. Weplot the CMD of our ULP Cepheid sample and overlay theevolutionary tracks of Lejeune & Schaerer (2001) (Figure 8).The location of ULP Cepheids in the color magnitude dia-gram suggest masses between 13 and 20 M ⊙ , depending onthe assumed metallicity (here, we choose SMC metallicity).Our sample clearly probes a mass range unexplored by cur-rent Cepheid studies. Note the evolutionary tracks at 15 and20 M ⊙ only cross the instability strip once, regardless of as-sumed mass-loss rate. However, we have shown and con-firmed that HV829 is undergoing its second crossing; a resultat odds with the models. We note that the evolutionary modelrepresents some “mean” behavior based on assumptions ofstellar chemical composition, overshooting, and other param-eters. Nevertheless, our result is one of the few observationalconstraints on high mass stellar evolutionary models. HV829LP Cepheids 7 I Zw 18NGC 300NGC 6822NGC 55SMCLMC F IG . 4.— The I Period Luminosity relationship for the OGLE SMC Cepheids (black dots) and ULP Cepheids (open symbols). The dashed line has a slope of - .
96 and is the PL relation adopted from Udalski et al. (1999). The least square fit to the ULP Cepheid subsample produces a flatter slope of - . ± .
73 (redline) and the RMS is 0 .
31 mag. The residuals to the PL
SMC fit are shown in the bottom panel (black, open squares). Residuals to the PL
ULP are given for the ULPCepheid sample (red symbols). may indicate that massive stars behave differently than ex-pected. Future stellar evolutionary models in this mass regimeshould take this into account. DISCUSSION
We have presented, for the first time, a collection of Ul-tra Long Period ( P >
80 days) Cepheids from the literatureand demonstrated their viability as a distance indicator. In thepast, ULP Cepheids have been ignored as distance indicators,and in fact many stellar variability searches did not extendtheir cadence and search strategy to allow for their discovery.In V , I , and especially reddening-free W I magnitude, ULPCepheids have a relatively flat PL relation compared to the re-spective relations for classical Cepheids (Udalski et al. 1999).The dispersion in both the classical and ULP Cepheid popula-tions about their respective PL relationships becomes smalleras one moves from V to I to W I , and the discrepancy be-tween the slopes increases. Most notably, the slope of theULP Cepheid W I PL relation is significantly shallower than the standard SMC PL relation (slope is - .
05 vs. - . .
23 mag (See Fig-ure 5). Other papers (e.g. Kanbur et al. 2007) have found non-linearites in the PL relationship at lower periods. However,the change in slope seen here is much more dramatic and itis unlikely that it shares a physical connection with the PLchanges at lower periods.Our ULP PL scatter in W I is already less than that of theinitial peak brightness vs. absolute magnitude relation forType Ia Supernova ( ∼ . . .
20 mag scat-ter in the relation seen today (e.g., Jha et al. 2007). We expectfuture observational and theoretical studies of ULP Cepheidswill further decrease the already fairly small scatter found inthis first analysis.We strove to find all the known ULP Cepheids in the liter- Bird, Stanek, & Prieto
I Zw 18NGC 300NGC 6822NGC 55SMCLMC F IG . 5.— The absolute Wesenheit magnitude Period Luminosity relationship for the OGLE SMC Cepheids (black dots) and ULP Cepheids (open symbols).The dashed line is the PL relation adopted from Udalski et al. (1999) and has a slope of - .
28. The least square fit to the ULP Cepheid subsample produces a flatslope of - . ± .
54 (red line) with a ULP Cepheid RMS = 0 .
23 mag. If we assume that PL
ULP has zero slope (intercept of - . SMC fit are shown in the bottom panel (black, open squares). Residuals to the PL
ULP are given for the ULP Cepheid sample (red symbols). ature, but our sample is likely not a complete census of ULPCepheids. We note that the Araucaria Project found ULPCepheids in three of the five galaxies they observed at thetime of this analysis, so the ULP Cepheid sample should growat a reasonable rate as Cepheid studies are extended to moregalaxies and previous data sets are reanalyzed with longer pe-riod searches. There is also evidence ULP Cepheids exist ina broad range of metallicities, as preliminary data analysis ofa M81 variability survey with the Large Binocular Telescopehas already discovered at least one ULP Cepheid (Kochanek,private communication).In addition to following a fairly tight PL relation, the ULPCepheids are also very luminous, with a median absolutemagnitude in I ( V ) for our sample of - . - . HST can obtain 10% photometry at V = 28 or I = 27 (DM = 35 — distance of 100 Mpc for the median ULPCepheid) in about 10 orbits, while only two orbits are neededto reach a DM of 34. As one would only need a few orbitsper epoch, one could detect the median ULP Cepheid (with a period of ∼
121 days) at 100 Mpc and the brightest ULPCepheids at ∼
150 Mpc in a reasonable amount of time. Sincethe luminosity of an ULP Cepheid is a weak function of its pe-riod, relatively accurate distances would not require as preciseperiod measurements as is needed for classical Cepheids. Weencourage future variability proposals to search for Cepheidswith periods greater than 100 days.We note two concerns in using ULP Cepheids for distancemeasurements. It is obvious from our sample size that ULPCepheids are far less common than classical Cepheids. Therelatively small ULP Cepheid population will make preci-sion distance measurements less practical. As the sample sizegrows and the ULP Cepheid PL relations become established,a single ULP Cepheid observation may yield distance mea-surements accurate to 10 - I Zw 18NGC 300NGC 6822NGC 55SMCLMC F IG . 6.— Residual to the Wesenheit index PL relation (See Table 2, PL ULP , W I ) versus metallicity. The open symbols are ULP Cepheids from the sample. Thedotted line corresponds to the luminosity correction of - . ± .
10 mag dex - determined by Macri et al. (2006) and normalized to our sample. The residualsof the sample, minus the two I Zw 18 Cepheids, are consistent with the Macri et al. (2006) result. a problem for our ULP Cepheids even at large distances sim-ply because they are so bright and there are very few stars ofcomparable brightness in a given galaxy. The effect of blend-ing on ULP Cepheid observations will need to be investigatedfurther as the sample is increased.The data set and analysis herein provides meaningful con-straints on theoretical work on Cepheids in this mass and pe-riod range. We have shown that ULP Cepheids show strongevidence for a different, flatter PL relation than their lowerperiod cousins. Several papers have modeled Cepheid pul-sations and mapped these to theoretical PL relations (e.g.,Bono et al. 2002). However, this work has not been reliablyextended to the period range of our sample. Pulsation modelsin this period range would also help determine the intrinsicscatter to the PL ULP relation.Our current sample is not large enough to constrain the sen-sitivity of the ULP Cepheid PL to metallicity. The PL resid-uals as a function of metallicity are consistent with the re-sults for shorter period Cepheids ( γ = - . ± . ± .
05 magdex - ; Macri et al. 2006). Note that the median 12 + log(O/H) value for a galaxy in our sample is about 0 . HST