Inspecting the Cepheid distance ladder: The Hubble Space Telescope distance to the SNIa host galaxy NGC 5584
Behnam Javanmardi, Antoine Mérand, Pierre Kervella, Louise Breuval, Alexandre Gallenne, Nicolas Nardetto, Wolfgang Gieren, Grzegorz Pietrzy?ski, Vincent Hocdé, Simon Borgniet
DDraft version February 26, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Inspecting the Cepheid distance ladder:The
Hubble Space Telescope distance to the SNIa host galaxy NGC 5584
Behnam Javanmardi , Antoine M´erand, Pierre Kervella , Louise Breuval , Alexandre Gallenne ,
3, 4, 5
Nicolas Nardetto , Wolfgang Gieren, Grzegorz Pietrzy´nski ,
3, 4
Vincent Hocd´e, and Simon Borgniet LESIA, Observatoire de Paris, Universit´e PSL, CNRS, Sorbonne Universit´e, Universit´e de Paris, 5 place Jules Janssen, 92195 Meudon,France European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland Universidad de Concepci´on, Departamento de Astronom´ıa, Casilla 160-C, Concepci´on, Chile Unidad Mixta Internacional Franco-Chilena de Astronom´ıa (CNRS UMI 3386), Departamento de Astronom´ıa, Universidad de Chile,Camino El Observatorio 1515, Las Condes, Santiago, Chile Universit´e Cˆote d’Azur, Observatoire de la Cˆote d’Azur, CNRS, Laboratoire Lagrange, France
ABSTRACTThe current tension between the direct and the early Universe measurements of the Hubble Constant, H , requires detailed scrutiny of all the data and methods used in the studies on both sides of thedebate. The Cepheids in the type Ia supernova (SNIa) host galaxy NGC 5584 played a key role in thelocal measurement of H . The SH0ES project used the observations of this galaxy to derive a relationbetween Cepheids’ periods and ratios of their amplitudes in different optical bands of the Hubble SpaceTelescope (HST), and used these relations to analyse the light curves of the Cepheids in around halfof the current sample of local SNIa host galaxies. In this work, we present an independent detailedanalysis of the Cepheids in NGC 5584. We employ different tools for our photometric analysis and acompletely different method for our light curve analysis, and we do not find a systematic differencebetween our period and mean magnitude measurements compared to those reported by SH0ES. Byadopting a period-luminosity relation calibrated by the Cepheids in the Milky Way, we measure adistance modulus µ = 31 . ± .
047 (mag) which is in agreement with µ = 31 . ± .
046 (mag)measured by SH0ES. In addition, the relations we find between periods and amplitude ratios of theCepheids in NGC 5584 are significantly tighter than those of SH0ES and their potential impact on thedirect H measurement will be investigated in future studies. Keywords: cosmology: distance scale – methods: data analysis – methods: observational – galaxies:distances and redshifts – stars: variables: Cepheids – techniques: photometric INTRODUCTIONThe current expansion rate of the Universe, known asthe Hubble constant or H , is one of the fundamentalparameters of the standard model of cosmology and ofany viable cosmological model. A few decades after theinitial estimate of around 500 km s − Mpc − by Hubble(1929), H became a place for debate with values either ≈
100 km s − Mpc − (e.g. van den Bergh 1970; de Vau-couleurs 1972) or ≈
50 km s − Mpc − (e.g. Sandage & Corresponding author: Behnam [email protected], [email protected]
Tammann 1975). The debate was finally settled afterthe findings of the HST H Key Project whose final re-sults was H = 72 ± − Mpc − (Freedman et al.2001). This value was found to be in agreement with thesubsequent results from the observations of the CosmicMicrowave Background (CMB) by the Wilkinson Mi-crowave Anisotropy Probe (WMAP, e.g. Spergel et al.2003) based on the standard Lamda-Cold-Dark-Matter(ΛCDM) model. However, in the recent years and withthe improved precision of the measurements of H , a sig-nificant tension has again risen this time between the socalled early-Universe cosmology-dependent approachesfinding H ≈
67 km s − Mpc − and late-Universe directmeasurements mostly finding H ≈
73 km s − Mpc − . a r X i v : . [ a s t r o - ph . GA ] F e b Javanmardi et al.
On the one hand, using the precise observations ofthe CMB from the Planck satellite, Planck Collabo-ration et al. (2018) concluded that the ΛCDM pro-vides an excellent explanation of the CMB data andreported a model-dependent prediction of the Hubbleconstant H = 67 . ± . − Mpc − . This resultis in good agreement with other early Universe mea-surements. For example, by combining baryon acous-tic oscillation (BAO) and Big Bang nucleosynthesis(BBN) data, Addison et al. (2018) reported a CMB-independent value of H = 66 . ± .
18 km s − Mpc − ,and by combining BBN and BAO data with galaxy clus-tering and weak lensing data, the Dark Energy Surveyreported H = 67 . +1 . − . km s − Mpc − (Abbott et al.2018). In a recent study and based on new high reso-lution CMB observations from the Atacama CosmologyTelescope, Aiola et al. (2020) reported H = 67 . ± . − Mpc − , consistent with previous early Universeresults. All these results are based on the ΛCDM model.On the other hand, the SH0ES (Supernovae H for theEquation of State) project, that uses the Cepheid cal-ibrated SNeIa data, finds a significantly higher locallymeasured H value. Cepheids are one of the most reli-able distance indicators and, using more than a decadeof observations(see e.g. Riess et al. 2005), the SH0ESproject measures H = 73 . ± . − Mpc − for theHubble constant (Riess et al. 2019; Riess 2019). This isone of the most precise determinations of H and is inmore than 4 σ tension with the early-Universe results.There are also other direct but Cepheid-independentmethods for measuring H . Using time-delay dataof gravitationally lensed quasars, the H0LiCOW (H0lenses in COSMOGRAIL’s Wellspring) project reported H = 73 . +1 . − . km s − Mpc − (Wong et al. 2020). In an-other gravitational lensing study, Birrer et al. (2020)employed a different lens mass profile modeling ap-proach and found H = 67 . +4 . − . km s − Mpc − and H = 74 . +5 . − . km s − Mpc − using two different datasets. Using yet another independent method of geomet-ric distance measurements to megamaser-hosting galax-ies, Pesce et al. (2020) reported H = 73 . ± . − Mpc − . Another late Universe method to measurethe H is to calibrate the SNeIa with the tip of the red gi-ant branch (TRGB), using which the Carnegie-ChicagoHubble Program (CCHP) found H = 69 . ± . − Mpc − (Freedman et al. 2019).Although some late Universe results are in agreementwith those from early Universe approaches, the absolutemajority of direct methods find H values larger thanthe early Universe model-dependent methods, and cur-rently different combinations of the late Universe mea-surements are in 4 to 6 σ tension with the early Universe ΛCDM predictions (Verde et al. 2019; Riess 2019), andremoving any one method does not appear to resolvethe tension. In fact, the general consistency of the di-rect methods on the one hand, and of those of the early-Universe methods on the other hand, significantly re-duces the possibility that systematics in one method,data, or analysis would solve this problem.However, since the persistence of the H tension wouldmean the failure of the base ΛCDM model, and giventhe generally understood success of the ΛCDM in ex-plaining the CMB and the large-scale structure data,it is absolutely necessary to not only take different ap-proaches for measuring H , but also, as emphasized byRiess et al. (2020), to scrutinize in detail all the data,methods, and the studies that have led to this cosmicdiscordance.The main three rungs of the Cepheid distance ladderare i) calibration of the period-luminosity relation usinggeometric distance measurements to nearby Cepheids,ii) calibration of the SNIa absolute magnitude usingCepheids in SNIa host galaxies out to around 40 Mpc,and iii) using SNIa out to redshift 0.15 to measure H .On the first rung, different studies (e.g. Nardetto 2018;Borgniet et al. 2019; Kervella et al. 2019b; Gallenne et al.2019; Anderson 2019; Hocd´e et al. 2020a,b; Musella et al.2020) have focused on enhancing our understanding ofthe different properties of Cepheid variables, and in arecent study, Breuval et al. (2020) presented a new cal-ibration of PL relation for Milky Way Cepheids usingtheir companion parallaxes from Gaia (Kervella et al.2019a). In addition, the high precision measurement ofthe distance to the Large Magellanic Cloud (LMC) byPietrzy´nski et al. (2019) provides an accurate calibra-tion of the Cepheid period-luminosity relation in thissatellite galaxy of the Milky Way.On the third rung, the impact of SNeIa environment(Roman et al. 2018) and in particular that of the starformation rate (Rigault et al. 2015) of their host galaxieson distance measurements has been investigated. Joneset al. (2018), however, concludes that the environmen-tal dependency of SNeIa properties have negligible ef-fect on the H measurements. Dhawan et al. (2018)and Burns et al. (2018) used near-infrared observations,where SNeIa luminosity variations and extinction bydust are less than in the optical observations, and con-cluded that the H tension is likely not caused by sys-tematics like dust extinction or SNeIa host galaxy mass.Also, Hamuy et al. (2020) reported that different meth-ods for standardization of SNeIa light curves yield con-sistent results with a small standard deviation, conclud-ing that SNeIa are robust calibrators of the third rung. epheid distance to the SNIa host galaxy NGC 5584 andWFPC2 , using F555W (V), F814W (I), and F160W(H) bands for measuring mean magnitudes and peri-ods of their Cepheid variables . However, for 9 out of19 of these galaxies, the photometric time series neces-sary for identifying the Cepheids, measuring their lightcurves and estimating their periods, have been obtainedusing the wide band HST F350LP filter available onWFC3/UVIS. The wavelength range of this so called”white light” filter covers those of V and I bands, henceis suitable for the detection of faint sources. The 9 galax-ies mentioned above currently have much fewer randomphase observations in V and I bands, not sufficient forlight curve analysis. NGC 5584, however, has time se-ries observations in all these three bands. Using thedata of this galaxy, the SH0ES team obtained a relationbetween the periods of the Cepheids and the ratio oftheir amplitudes in V and I relative to those in F350LPband. Then, assuming that these relations derived fromNGC 5584 also hold in other SNIa host galaxies, theSH0ES project correct for the effect of random phaseobservations of Cepheids in the galaxies with few V andI observations. Therefore, the Cepheids in the galaxyNGC 5584 played a key role in obtaining the periodsand mean magnitudes of the Cepheids in almost half ofthe current SH0ES sample of SNeIa host galaxies, andin turn in the final measurement of H .For our inspection, we use the same observations ofNGC 5584 that were used by SH0ES. Hence, this workis not a complete reproduction of the original experi- Near Infrared Camera and Multi-Object Spectrometer. Wide Field and Planetary Camera 2. In this paper F555W, F814W, and F160W are used interchange-ably with V, I, and H, respectively. ment, since we do not repeat the observations them-selves. However, where possible, we intentionally ex-plore different numerical methods and tools than thoseused by SH0ES to provide an independent insight to the H problem. The goal of this work is to inspect the foun-dations of the Cepheid distance scale, independently ofany input on our analysis from the SH0ES team.This paper is organized as follows. In Section 2, webriefly outline the method. Section 3 presents a fulldescription of the data. We describe our analysis inSection 4, present our results in Section 5, and finallyconclude in Section 6. METHODA standard approach for distance measurements usingthe Cepheid variables (Leavitt & Pickering 1912) is touse reddening-free ”Wesenheit” index (Madore 1982) inthe H band defined by R16 as W H = H − R H ( V − I ) (1)where H , V , and I are mean magnitude of the Cepheidsin F160W, F555W, and F814W, respectively. In ouranalysis, we adopt R H = 0 .
386 which is derived fromCardelli et al. (1989) and Fitzpatrick (1999), and is alsoadopted by e.g. Riess et al. (2019), Bentz et al. (2019),and Breuval et al. (2020). The distance to a nearby SNIahost galaxy can be measured by obtaining the relationbetween the pulsation period and W H of its identifiedCepheids, and by adopting a W H vs. period relationcalibrated by the Cepheids in e.g. the Milky Way orthe LMC. The observations of NGC 5584 for the mea-surements of periods and the mean magnitudes of itsCepheids in the above-mentioned bands are describedin the next section. DATA3.1.
Archival Observations
We obtain the data of NGC 5584 from the Mikul-ski Archive for Space Telescopes (MAST) database .NGC 5584 has been observed by the Wide Field Cam-era 3 (WFC3) between January and April 2010 withthe purpose of measuring a Cepheid distance to type Iasupernova SN 2007af hosted by this galaxy (PI: AdamRiess, Cycle: 17, Proposal ID: 11570). WFC3 has beeninstalled on the HST in 2009 replacing the WFPC2.It has two imaging cameras: the UV/Visible channel(UVIS) and the near-infrared (IR) channel. UVIS hastwo mosaics of 2051 pixel × ×
162 arcsec , and a resolution of https://archive.stsci.edu/access-mast-data Javanmardi et al. h m s s s s -0°22'23'24'25' RA D E C h m s s s RA WFC3/IR (F160W)
Figure 1.
Examples of the HST images from the NGC 5584 in the F350LP (left) and F160W (right) bands. The former imageis from the WFC3/UVIS which has two mosaics of 4096 × ≈ . (cid:48)(cid:48) ) gap, and the latter isfrom the WFC3/IR with a dimension of 1014 pix × × ×
123 arcsec , and aresolution of 0.13 arcsec/pixel.NGC 5584 has been observed in 13 epochs (in total45540 sec) in F555W band, 6 of which also accompa-nied by F814W observations (in total 14400 sec). Intwelve of these epochs, this galaxy has also been ob-served in the F350LP band (in total 15000 sec). In addi-tion, NGC 5584 has also been observed with WFC3/IRchannel with the F160W or the H band in 2 epochs (intotal 4929 sec). 3.2. Calibrations
In all cases, we obtain the calibrated cosmic-raycleaned (i.e. the flc.fits files for WFC3/UVIS, and flt.fits files for the WFC3/IR observations) dataprovided by the MAST database. In the case ofWFC3/UVIS, the flc.fits files are also corrected forthe charge-transfer efficiency loss . We list the full in-formation regarding these observations in Appendix D. WFC3/IR observations do not suffer from this loss.
Similar to H16, we use the
TweakReg software for im-age registration and alignment. For all the images of allthe bands we achieve an alignment better than 0.1 pix-els, the same precision is also reported by H16. We usethe coordinates of the ”local standard stars” providedby H16 (see section 3.3 for more details on these stars)in order to have the same absolute astrometry as theirs.This provides an exact identification of the Cepheids us-ing the RA and DEC reported by H16.Each observation epoch consists of multiple exposures.For example, 11 out of 13 epochs in F555W bands con-sist of six different exposures, and the other two, consistof four different exposures (see Appendix D). We usethe AstroDrizzle software to combine all the expo-sures of each epoch (and of the same filter) to obtainfinal distortion-corrected drizzled science images for thepurpose of our analysis.Figure 1 shows examples of UVIS and IR images ofthe NGC 5584. Part of the
DrizzlePac software package provided by STScI. epheid distance to the SNIa host galaxy NGC 5584
The Cepheids in NGC 5584
After performing Point-Spread Function (PSF) pho-tometry for all the sources in the galaxy image, H16uses the Welch & Stetson (1993) variability index toidentify variable objects. This procedure requires com-paring fluxes of each epochs with non-variable sources.A list of visually inspected such ”local standard stars”is provided by H16 in their table 3. H16 fits all vari-able objects with Cepheid light curve templates fromYoachim et al. (2009), which have been generated forV and I bands and by a combination of Fourier decom-position and principal component analysis from a sam-ple of Cepheids in the MW, the LMC, and the SmallMagellanic Cloud. After template fitting, H16 visuallyinspects the six best solution for all the variables, andrejects the variables that are poorly fitted. The detailson further criteria that H16 applied to get to their finalCepheid sample are presented in their section 4.2.In this work, rather than redoing the Cepheid iden-tification process, we use the same identified Cepheidsprovided and used by H16 and R16. This enables us todirectly compare our photometry and light curve mod-eling results with those of SH0ES for each and all of theidentified Cepheids in NGC 5584. ANALYSIS4.1.
Photometry
Our precise alignment of the images using the localstandard stars of H16 provides an exact identification ofthe Cepheids using the RA and DEC reported by H16.In the left panel of Figure 1, we mark the positions ofthe 199 optically identified Cepheids. Out of these, only82 are identified in F160W and measured by R16. Theseare marked with red dots on both panels of Figure 1.4.1.1.
PSF Modelling
To measure the brightness of the Cepheids at eachepoch, we use the PSF photometry routines of the
Photutils package of
Astropy (Bradley et al. 2019)that provides tools similar to, but also more generalthan, DAOPHOT (Stetson 1987) which is used byH16. For optical bands, we perform the PSF pho-tometry on 100 pix ×
100 pix (4 by 4 arcsec ) por-tions of the image centered on each Cepheid for allthe epochs. The background is locally estimated foreach Cepheid and is automatically subtracted from theCepheid flux. Similar to H16, we use the TinyTim package that provides PSF models for various cam-eras and different HST bands (Krist et al. 2011). Wechecked various fitting algorithms and background esti-mators and found that the choice has negligible effecton the flux measurement. Therefore, similar to R16,
Figure 2.
Our PSF photometry for the representativeCepheids in Figure 4 of H16. The left column shows 40 × Javanmardi et al. we use a Levenberg–Marquardt-based algorithm (pro-vided by
Astropy as LevMarLSQFitter ) for determin-ing the best-fit parameters which are the (x,y) positionand the flux (plus their uncertainties) for the Cepheids,and
MMMBackground routine which calculates the back-ground using the DAOPHOT MMM algorithm (Stetson1987).For IR photometry, i.e. for the F160W band, our pro-cedure is the same as in the optical analysis, except that(similar to R16) the (x,y) positions of the Cepheids arefixed to their best-fit values from the F814W band andthat the PSF photometry is performed on 50 pix × ) portions of the imagecentered on each Cepheid. The reason for fixing the(x,y) position is that the significantly lower resolutionof IR images may lead the fitting algorithm to pick awrong neighbouring source rather than the Cepheids if(x,y) are allowed to vary as free parameters.Examples of our PSF photometry results are shownin Figure 2. We choose to show those Cepheids that arepresented as representative by H16 (in their Figure 4).4.1.2. Epoch-to-epoch offset
The observation condition varies from epoch to epochand would affect the flux of the Cepheids. To correct forthis, we use the local standard stars which were intro-duced earlier. For each band, we perform a PSF pho-tometry of these non-variable stars and measure theiraverage fluxes in all epochs, ¯ F all , and also for each epoch,¯ F epoch . The Cepheid fluxes at each epoch is then scaledby ¯ F all ¯ F epoch to correct for the epoch-to-epoch offset .4.1.3. Magnitude zero-points and aperture correction
The magnitude zero-point, ZP, for different HSTbands are provided by Kalirai et al. (2009), Deustuaet al. (2017), and on the STScI calibration pages . TheseZP values are based on WFC3 standard aperture ra-dius of 0.4 arcsec. Therefore, the difference between thisstandard aperture and the PSF modeling should be mea-sured and corrected for. A customary approach adoptedalso by H16 is to perform both PSF and aperture pho-tometry on a sample of ideally isolated and relativelybright stars in the image and to obtain a statistical meandifference between the two.In this work, we take a rather different approach. Ide-ally, for a single isolated star the difference between the Since we scale the Cepheid fluxes by the ratio ¯ F all ¯ F epoch , the differ-ence between the choice of a statistic (whether mean or median)is negligible. F555W F814W F350LP F160WZP (mag) 25.737 24.598 26.708 24.5037AP cor (mag) 0.032 0.034 0.032 0.049
Table 1.
The zero-point (ZP) and the aperture correction(AP cor ) values both in mag for the different HST bands usedin this study. See Section 4.1.3. aperture and PSF photometry should be directly depen-dent on the aperture size and the PSF model, while thebackground should be the same. Here, given that theaperture size for the purpose of correction is fixed to0.4 arcsec, the difference is basically caused by the ex-tra light captured by the tails of the PSF model beyond0.4 arcsec radius. Therefore, one way to directly obtainthis difference is to measure the flux of the PSF modelusing a 0.4 arcsec radius aperture (10 pixels for UVISand around 3 pixels for IR). The magnitude difference,hence the aperture correction (AP cor ), would then beAP cor = 2 . [ F ap F PSF ] − . [ EE ( r = 10)] , (2)where F ap is the fraction of the PSF flux inside the aper-ture, F PSF is the total flux of the PSF model, and EE ( r )is the encircled energy for different aperture radius r (seeDeustua et al. 2017, for further details). We comparethe two methods of measuring the aperture correctionin Appendix A.The ZP and AP cor values used in this study are listedin Table 1 for each band .4.2. Crowding Bias
At distances larger than ≈
10 Mpc, despite the largeluminosity of Cepheids, their light often cannot be sep-arated from their stellar crowds (Riess et al. 2020). Theflux of the neighboring stars entering the same resolu-tion element as the Cepheid alters the statistical estima-tion of the background, therefore biasing the Cepheidflux (Anderson & Riess 2018). This bias is one of themost significant challenges for Cepheid measurementsat distances larger than 20 Mpc (Freedman et al. 2019).In particular for NGC 5584, at a distance of around23 Mpc, each pixel of the WFC3/UVIS camera spansaround 4 pc. Therefore, it is very likely that the pixelthat contains a given Cepheid also encompasses otherstellar sources either physically near the Cepheid, oralong the line of sight. The pixel size of UVIS/IR isaround three times larger than that of WFC3/UVIS,hence covering a larger physical size at the distance men- We note that R16 and H16 used 25.741, 24.603, and 24.6949 asZP values for F555W, F814W, and F160W, respectively epheid distance to the SNIa host galaxy NGC 5584
TinyTim
PSF models) 20 artificialstars per epoch and add them to the same image por-tions used for their PSF photometry (Section 4.1.1). Inthe case of the F160W band, because only two epochsare available, we use 50 artificial stars per epoch. Thefluxes of these artificial stars are then measured usingthe same PSF approach explained in Section 4.1.1. Priorto obtaining a mean value for the magnitude differences,H16 directly removes the artificial stars that land within2.5 pixels of another source that is up to 3.5 mag fainter.Instead of this direct removing approach, we apply a 2 σ clipping which automatically rejects the artificial starsthat are blended with another bright source. We thenmeasure the mean magnitude difference as the crowdingbias estimate for each Cepheid.For the optical observations, the SH0ES team uses themean value of crowding bias in a galaxy as a single biasvalue for all the Cepheids in that galaxy. By doing that,the local bias are over estimated for some Cepheids, andare underestimated for some others. Crowding is anenvironment dependent effect and, in principle, it shouldnot be averaged over a galaxy. In our analysis, we take adifferent but accurate approach and apply the crowdingbias estimated at the position of each Cepheid on themeasured magnitudes of that Cepheid before templatelight curve fitting. We investigate the crowding bias inmore detail in Appendix B where we derive a relationbetween crowding bias and local surface brightness andwe also compare our results with those of SH0ES.4.3. Light curve fitting using Templates from GalacticCepheids
The data collected for each Cepheid consists of sev-eral epochs for different pass bands. From this data, weneed to derive the pulsation period, as well as the meanmagnitudes in each band. In H16, this was done usingtemplate light curves from Yoachim et al. (2009). In this eff (K)254060100160250400 R a d i u s ( R ) Anderson+ 16 35916295190 P e r i o d ( d ) Figure 3.
Radius vs. Temperature diagram for the GalacticCepheids. The dots are the average values (over the pulsa-tion), whereas the thin lines show the values over the pulsa-tion. The color code refers to the pulsation period. Thedotted lines are the borders of the theoretical instabilitystrip, using mild rotation (0.5) and solar metallicity (An-derson et al. 2016). We only use the Cepheids with periodgreater than 12 days for building our template light curves,see Section 4.3.1 for further details. work, we use different template light curves and fittingstrategy so that all bands are analysed simultaneously.We derive synthetic light curves in the HST photomet-ric bands for various known Galactic Cepheids, coveringthe instability strip (in effective temperature and pe-riod). The radius, effective temperature, and period ofthese Cepheids are shown in Figure 3. We then use adimensionality reduction algorithm to parametrize anylight curve using only a few parameters.4.3.1.
Data set for the templates
We choose to use observational data as basis for ourtemplates, fitted with our modeling tool SPIPS (M´erandet al. 2015) which synthesizes photometric observationsbased on variations of the stellar radius and effectivetemperature. We collect high quality spectro-, photo-and interferometric data for many Galactic Cepheidsand fit their SPIPS models. It should be noted that theknowledge of the distance and/or the projection factorof these Galactic Cepheid does not play a role in buildingthe light curve templates.Our final sample comprises of 28 stars with periodsranging from 12 to ∼
90 days (Breuval et al., in prep).
Javanmardi et al.
F350LP F555W F814W F160Wdata PCA4
Figure 4.
The training set (continuous lines) and recon-structed (doted line) light curves, sorted by pulsation period:from shortest (bottom) to longest (top). See Section 4.3.2. F L P C1C2C3C4mean F W F W F W PCA basis (mag) c u m u l a t i v e v a r i a n c e ( % ) , r e s i d u a l s ( m a g ) Figure 5.
Top four panels: PCA components, in blue theaverage light curve, and in shades of gray the first 4 com-ponents (the darkest is the first component). Bottom: theincrease of the training data set variance covered as a func-tion of number of components used in the reconstruction. epheid distance to the SNIa host galaxy NGC 5584 l o g ( P ) ( d ) component 1 component 2 l o g ( P ) ( d ) component 3 component 4 Figure 6.
The color coded PCA coefficients as function ofCepheids’ effective temperature and period. Interestingly,component 1 is strongly correlated with temperature, andcomponent 3 is strongly correlated with period.
We do not include Cepheids with period shorter than12 days because i) Cepheids observed in distant galaxiesare biased towards the brightest ones, which results in anobservational cut around ∼
20 days and ii) Cepheids lightcurves change dramatically around 9-10 days, which hasbeen long noticed ever since Fourier decomposition wasapplied to Cepheids’ light curves (see e.g. Simon & Lee1981). We do not apply any selection cut on radiusand effective temperature, as our intent is to sampleCepheids in the instability strip.The SPIPS models are based on radial and tempera-ture variations enabling the synthesize of any photomet-ric light curve using the filter band pass definition andatmospheric models. The advantage of this method isthat it can accurately extrapolate light curves in passbands for which we do not have data. We use the HST band passes and zero points defined at the Spanish Vir-tual Observatory’s Filter Profile Service .4.3.2. Reduction of dimensions in templates
Our 28 Galactic Cepheids light curves contain alot of information which needs to be reduced intoparametrised templates. We reduce the dimensions ofour template data set with a principal component analy-sis (PCA), using the scikit-learn
Python library (Pe-dregosa et al. 2011). The training data set for PCA are28 vectors composed of the concatenated light curves(one for each band) over a single pulsation cycle, cen-tered around their means (see Figure 4). When it comesto choosing how many components to keep to fit ourlight curves, it is customary to consider the amount ofvariance reproduced by a given number of most signif-icant components. In our dataset, at any given phaseand for any bands, the standard deviation is nevergreater than 0.2 mag, with a total standard deviationof 0.13 mag (around the average light curve). Usingenough PCA components to reproduce 95% of the vari-ance should reproduce light curves within ∼ Fitting strategy
For a given NGC 5584 Cepheid, we have a list of ob-servations in various pass bands and at different dates.The initial period is estimated by a computed peri-odogramme on the F555W and F350LP data. Then,a full model is fitted to the data using the PCA lightcurves. Our model also includes reddening, using theformula contained in SPIPS and parametrised usingthe color excess E(B-V). We fix the reddening to E(B-V)=0.035, which we estimate using
DUST We iterate on the initial parameter by randomisingthe period ( ± http://svo2.cab.inta-csic.es/theory/fps/ https://irsa.ipac.caltech.edu/applications/DUST/ Javanmardi et al. prior constrains the coefficient to only evolve inside therange of values observed on the template stars. Fromthe randomised starting periods, we keep the fit with theglobal lowest reduced χ . Using the best fit parametersand covariance matrix, we can compute the domain ofuncertainty for the synthetic light curves and derive theaverage magnitudes and amplitudes.Our fitting method has several differences with theone presented in H16 using Yoachim et al. (2009). Firstof all, we fit all data at once. This is feasible sinceour model include realistic information about the offsetbetween bands and the shape of the light curve. Anexample can be seen for star 347072 in Figure 7 (whichwe discuss further in Section 5). The F814W data ofthis Cepheid are very noisy and the fitted light curveis constrained mostly by the F555W and F350LP data,which are of much better quality. Even if the modeledlight curve in F814W is systematically above the datapoints, it is the most realistic within our hypothesis andpriors derived from Galactic Cepheids. RESULTS5.1.
Light Curves, Mean Magnitudes, and Periods
Using the light curve template fitting explained in Sec-tion 4.3, we obtain the periods and the mean magnitudesfor all the identified Cepheids in the four HST bands.Figure 7 presents our results for the light curves of theCepheids we showed in Figure 2, they are chosen byH16 as the representative Cepheids of NGC 5584. Ourlight curves can be directly compared with those of H16shown in their Figure 4. Most of the light curve modelsnicely represent the data. One exception among these isthe Cepheid 347072, which as discussed earlier, has poorquality data points in F814W. This Cepheid is not de-tected in the F160W band and therefore is not includedin the measurement of distance neither by SH0ES norby us in this work.Figure 8 provides one-on-one comparisons of our re-sults with those of SH0ES reported in H16 and R16.The top row provides comparisons for the mean mag-nitude measurements in V , I , and H bands, as wellas the ( V − I ) color. For the H band, we only showthe uncertainties on the Y axis (i.e. from our results),since R16 publishes only the so called total uncertainties( σ tot ) and not those of the mean magnitudes in the H band. A generally good agreement can be seen betweenthe two results, especially for the H band and the V − I color both of which directly contribute to the distancemeasurement (see Equation 1).The left-most panel on the bottom row of Figure 8provides a comparison for period measurements. As canbe seen, although we use a different approach for tem- Phase F L P + . F W F W - . Figure 7.
Our light curves of the Cepheids presented byH16 as representative Cepheids (see their Figure 4). Oneach panel, the bottom (blue), middle (black), and top (red)curves are light curves in F350LP, F555W, and F814W, re-spectively. Two cycles are plotted and F350LP and F814Whave 1.25 and 0.25 mag offsets, respectively. The shadedtransparent regions represent the model uncertainties andare present for every curve on all panels. For some curves,they are too small to be seen by eye. plate fitting and hence the period measurements, thetwo results are in general agreement with only a fewexceptions.Regrettably, H16 does not provide mean magnitudesin F350LP band, we therefore cannot have a direct com-parison for this quantity. However, we can compare am-plitude measurements in F350LP band as discussed inthe next sub-section.5.2.
Amplitude Measurements
We remind the reader that H16 uses the amplituderatios vs. period relation of the Cepheids in NGC 5584to correct the random-phase observations of other SNIahost galaxies in the V and I band. Therefore, an ac-curate and precise measurement of these relations canpotentially impact the final H measurements. Thethree panels (from the right) on the bottom row of Fig-ure 8 provide comparisons for our amplitude measure-ments vs. those of the SH0ES team. We perform two epheid distance to the SNIa host galaxy NGC 5584 V (mag) I (mag) H (mag) V I (mag)
50 10020406080100120
Period (days) A I PTP (mag) A LP PTP (mag) A V PTP (mag)
SH0ES T h i s W o r k Figure 8.
Comparing our results (Y axes) with those the SH0ES (X axes) team for mean magnitudes (LP: F350LP, V: F555W,I: F814W, H:F160W), V − I color, period, and light curve amplitudes ( A ) of the Cepheids in NGC 5584. For the H band, weonly show the uncertainties on the Y axis (i.e. from our results), since R16 publishes only the so called total uncertainties ( σ tot )and not those of the mean magnitudes in the H band. PTP stands for peak-to-peak and is one of the methods of determiningthe pulsation amplitudes (see Section 5.2 for more details). The equality lines are plotted with solid black on all panels. different measurements of the amplitudes: 1) peak-to-peak (PTP) which measures the magnitude differencebetween the maximum and minimum of the light curvemodel, and 2) the root-mean-square (RMS) which is thestandard deviation of the light curve (regularly sampled)from their mean value. While the PTP results (whichare the ones shown in Figure 8) are in general agree-ment with the amplitude measurements of SH0ES, it isnot robustly estimated in our method. Our PCA-basedfits allow variations in the shape of the model, especiallybetween phase 0.8 an 1.0, which is where the amplitudeis measured (see for example F350LP light curve of star258671 in Figure 7). On the other hand, the amplitudeis directly one of the template fitting parameter in theSH0ES analysis. While PTP and RMS differ by a fac-tor of 2 √ ≈ .
83 for a pure sinusoidal wave, the valuevaries with the exact shape of the light curve. Fromour high definition template sample star, we find that (cid:0)
PTPRMS (cid:1) I = 3 . ± .
12 and (cid:0)
PTPRMS (cid:1) V = 3 . ± .
14. Weare interested in ratios between bands, and the com-parison with SH0ES’ results. For the amplitude ratioswe find that (cid:16)
PTP I PTP V (cid:17) = 0 . ± . (cid:16) RMS I RMS V (cid:17) . In otherwords, the ratio of amplitudes are almost independentof the amplitude measurement method and our ampli-tude ratios computed from RMS (which we use in our subsequent analysis) are comparable to those of SH0ESwith a scatter of 6%.In Figure 9, we compare our results and those ofSH0ES for the amplitude ratio vs. period relation. Theblue squares and red diamonds are our A V /A LP and A I /A LP , respectively. The grey plus and cross sym-bols are the same quantities as published by SH0ES inH16 and have significantly larger scatters. The dots andempty circles are, respectively, A V /A LP and A I /A LP forthe Milky Way Cepheids. The blue solid line, and thered dashed line are our results of linear fits on A V /A LP and A I /A LP vs. log P . While for the linear fitting weonly used the data from the Cepheids in NGC 5584,and while only 28 of the MW Cepheids with period > ≈ .
3. From the linear fitting we find A V /A LP = 1 .
167 + 0 . P − . , σ fit = 0 . ,A I /A LP = 0 .
757 + 0 . P − . , σ fit = 0 . , (3)where σ fit values are the standard deviations of the fitsand are an order of magnitude smaller than those of2 Javanmardi et al. A V / A L P A V / A LP (This Work) A V / A LP (SH0ES) A V / A LP (MW Cepheids) A I / A L P A I / A LP (This Work) A I / A LP (SH0ES) A I / A LP (MW Cepheids) Figure 9.
RMS (root-mean-square) amplitudes in V (toppanel) and I (bottom panel) bands relative to F350LP (LP)band vs. period. The plus and cross symbols are SH0ESresults for A V /A LP and A I /A LP , respectively. Our resultshave a significantly lower scatter than those of SH0ES. Thesolid blue and red dashed lines are linear fits as explainedin Section 5.2 and shown in Equation 3. We also show theMW Cepheids as filled dots and empty circles, for A V /A LP and A I /A LP , respectively. We note that while for the linearfitting only the results from the Cepheids in NGC 5584 wereused, and while only 28 of the MW Cepheids with period > SH0ES (see Table 2 of H16). The small scatter in thisrelation means that our amplitude ratio measurementis less noisy and is indicative of a high quality lightcurve modelling approach. We note that in H16 thelight curves of different bands are fitted separately (us-ing Yoachim et al. (2009) templates), and then the am-plitudes resulting from the different fits are divided toyield the amplitude ratios. This could be the reason for the large scatter in their amplitude ratios. On the otherhand, in our approach, all the light curves (of all bands)are fitted simultaneously, hence the amplitudes are notestimated independently from one another, leading to alower scatter.5.3.
Uncertainties on the Wesenheit H Magnitudes
In their section 2.2, R16 describe a σ tot as the totaluncertainty on their Cepheid distance measurements.They refer to the uncertainty of the crowding bias inthe H band as σ sky and that of the optical observationsas σ ct and they add them as a single value for all theCepheids in a given galaxy. Since we apply the crowdingbias (in all bands) for each Cepheid before the templatefitting, the values of mean magnitudes already includethe effect of crowding bias and their uncertainties. Inaddition, our template light curve fitting method anal-yses all the data together, therefore, the uncertainty onthe H band mean magnitudes, already includes the effectof limited phase coverage.Therefore, for the total uncertainty on W H we have σ W H = [ σ H + R H ( σ V + σ I ) + σ int ] / , (4)where σ int is the intrinsic dispersion due to the nonzerowidth of the instability strip. To estimate σ int , we followthe procedure of Riess et al. (2019). Using the Cepheidobservations in the LMC, Riess et al. (2019) present PLrelations and their scatter in different HST bands. Toestimate σ int , they subtract (in quadrature) the meanCepheid measurement errors from the scatter of the PLrelation for a given band. Their mean measurement er-ror for different bands are given in their section 2.2 andthe values for the scatter of the PL relations are listedin their Table 3. For W H , the intrinsic dispersion isestimated to be σ int = 0 .
069 mag.5.4.
The Period-Luminosity Relations
In addition to the PL relation in W H , we also presentPL relations for all the bands F350LP, F555W, F814W,F160W, as well as for optical Wesenheit index, W I inFigure 10. The latter is defined as W I = I − R I ( V − I )with R I = 1 . σ int explained in the previous sec-tion . We note that the data points in the PL relationsshown in Figure 6 of H16 appear to contain only themeasurement uncertainties which are comparable in sizeto this work’s results as shown in our Figure 8. We calculate the σ int for different bands based on the informationgiven in section 2.2 and Table 3 of Riess et al. (2019) in the sameway as explained in Section 5.3. epheid distance to the SNIa host galaxy NGC 5584 F L P ( m a g ) Scatter: 0.388 mag V ( m a g ) Scatter: 0.411 mag I ( m a g ) Scatter: 0.360 mag H ( m a g ) Scatter: 0.233 mag
20 30 40 60 80 120Period (days)21232527 W I ( m a g ) Scatter: 0.347 mag
20 30 40 60 80 120Period (days)21232527 W H ( m a g ) Scatter: 0.261 mag
Figure 10.
Period-Luminosity relations in the four HST bands and also for the W I and W H Wesenheit indices. The uncertaintieson individual Cepheids in this figure also includes the contribution from the σ int explained in Section 5.3. The solid lines representthe results of fitting a linear relation of the form m = α log P + β with a 3 σ clipping. The slopes ( α ) are fixed to the values forLMC Cepheids given in Table 3 of Riess et al. (2019), see Section 5.4. The solid lines represent the results of fitting a linearrelation of the form m = α log P + β , where m is themean magnitude. We fix the slope α to the values givenin Table 3 of Riess et al. (2019) (which lists the PL re-lations from Soszynski et al. (2008), Macri et al. (2015),and R16), and fit for the intercept with a 3 σ clipping.The slightly larger scatter in our PL relations comparedto those found by SH0ES for NGC 5584 is most probablydue to our different treatment of the crowding bias. Asstated earlier in the text, SH0ES add a single value ofcrowding bias for all the Cepheids in a galaxy whichshifts the PL relation slightly towards fainter values.However, we add the crowding bias values estimated atthe location of each Cepheid separately which introducesa somewhat larger scatter in the PL relation .5.5. The Distance to NGC 5584
In this section, we derive the distance modulus ofNGC 5584, based on apparent Wesenheit magnitudes We note that the scatter in the PL relation is not influenced byamplitude ratios which together with mean magnitudes are bothproducts of the same template fitting. W H of our sample of 82 Cepheids in this galaxy. By ap-plying an existing W H PL relation to the known periodof our stars, we derive the absolute magnitude M WH foreach Cepheid and then their individual distance modu-lus µ = W H − M WH .We perform this calculation using two different PL re-lations: one calibrated in the Milky Way (Breuval et al.2020), M WH = − .
432 ( ± . − .
332 ( ± . P − . M WH = 15 . − .
26 log P . For the slope of thelatter relation, a 0.02 mag uncertainty is stated in Riesset al. (2019) while they mention no uncertainty on theintercept. Therefore, we assume a conservative uncer-tainty of 0.02 mag error also for the intercept (the in-tercept uncertainties in Macri et al. (2015) are muchsmaller than 0.02 mag). We then subtract the LMC dis-tance modulus as measured by Pietrzy´nski et al. (2019).For both PL relations, the individual distance moduliobtained for each Cepheid are represented in Figure 11.The Galactic PL relation yields a weighted mean dis-tance modulus of 31 . ± .
047 mag, while the LMC cal-ibration results in 31 . ± .
038 mag. The 1 σ confidenceregions of these weighted mean values are also shown in4 Javanmardi et al.
Figure 11. The distance modulus from the Galactic PLrelation is in agreement with µ = 31 . ± .
046 (mag)measured by SH0ES in R16. The distance modulus fromthe LMC PL relation, however, is smaller though still inagreement within 2 . σ with SH0ES result.It is not surprising to obtain different distances basedon LMC and MW PL relations, given that LMC has asmaller metallicity compared to the MW (Romanielloet al. 2008), i.e. the larger distance inferred from LMCPL relation is consistent with its smaller metallicity.The difference in terms of distance modulus obtainedwith MW and LMC PL relations highlights the needfor a metallicity correction which has been extensivelystudied (see e.g. Pietrzy´nski et al. 2004; Gieren et al.2018; Groenewegen 2018; Ripepi et al. 2019, 2020, andBreuval et al. 2021, in prep.), though yet with no clearconsensus. However, NGC 5584 is a spiral galaxy with astructure similar to that of MW and, in fact, its metal-licity gradient is very similar to that of the MW (seetable 6 of Balser et al. 2011, and table 8 of R16). TheMW PL relation, therefore, is more appropriate for mea-suring the distance to NGC 5584.From our µ for NGC 5584 based on MW PL relation,we calculate a distance of d NGC 5584 = 23 . ± .
05 Mpc. CONCLUSIONThe 4 − σ tension (Riess 2019) between the directand the early Universe measurements of H asks for de-tailed investigations in the different methods involved.NGC 5584 played a key role in the direct measurementof H from the Cepheid distance ladder by the SH0ESteam (Riess et al. 2016). Observations of this galaxywas employed to derive a relation between the ratio ofpulsation amplitude of Cepheids in V and I bands rel-ative to the wide F350LP HST band and the period.The F350LP band has been used by the SH0ES teamfor detection and light curve measurement of Cepheidsin around half of the current SNIa host galaxies used for H measurements and the relation mentioned above hasbeen used to obtain mean V and I magnitudes from thespars sampling of Cepheid light curves in these bands.In this contribution, we provided an independent anddetailed analysis of the HST data from NGC 5584.Where possible, we intentionally used methods and toolsdifferent from those used by SH0ES. This allowed theinvestigation of possible influence of these methods ondistance measurements. The key parts of our detailedanalysis can be listed as follows: • applying PSF photometry routines of Photutils package of
Astropy (Bradley et al. 2019), insteadof the classic DAOPHOT software (Stetson 1987),
20 30 40 60 80 100Period (days)31.031.532.032.533.0 ( m a g ) Distance to NGC 5584
Weighted Mean from MW PL: 31.810 ± 0.047 (mag)Weighted Mean from LMC PL: 31.639 ± 0.038 (mag)Riess et al. (2016): 31.786 ± 0.046 (mag)Cepheids From MW PLCepheids From LMC PL
Figure 11.
Distance modulus µ measured from W H vs.period for Cepheids in NGC 5584 using two PL relations fromMW (red squares) and LMC (blue circles) Cepheids. Thehorizontal filled rectangles show the 1 σ confidence regions formeasured distances. The uniformly red and the blue crossed-diagonal hatched regions represent our measurements basedon the MW and LMC PL relations, respectively, and arethe weighted means of the µ values measured for individualidentified Cepheids. The black back-diagonal hatched regionrepresent the estimated distance reported by R16. • testing and finding negligible influence of thechoice of PSF modelling and background subtrac-tion algorithms, • applying a different aperture correction procedurefor the PSF photometry, • adopting a slightly modified approach for crowdingbias estimation (using a sigma-clipping approachon the artificial stars flux measurement ratherthan directly removing bright estimated sourcesdone by SH0ES), • a different approach for applying the crowding biascompared to SH0ES (applying the bias separatelyfor each Cepheid rather than averaging over thewhole galaxy for the optical observations), and epheid distance to the SNIa host galaxy NGC 5584 • employing a completely different approach forCepheid light curve modelling for measurement ofmean magnitudes, amplitudes, and periods.And our main results can be summarised as follows: • Our measurements of Cepheids’ mean magnitudesand period and those of SH0ES are in good agree-ment. In particular, we find no systematic dif-ference in our H band mean magnitudes and (V-I)color, both of which directly influence the distancemeasurements, compared to SH0ES. • We derived a significantly tighter amplitude ratiovs. period relation compared to the one derivedby SH0ES. • We measure two distance moduli for NGC 5584using two different PL relations calibrated in MWand LMC. The result from the former is in agree-ment with the value from SHOES within 1 σ , andthe result from the latter is 0 . ± .
060 magsmaller than that of SH0ES, though still within2 . σ .We do not attempt at reporting a value for H based onthe distance to only one SNIa host galaxy, and we onlynote that a smaller distance to NGC 5584 points towardsa higher H value. However, we consider the MW PL re-lation to be more appropriate for distance measurementsto NGC 5584, due to similar metallicity and structure ofthese two galaxies. Nevertheless, the effect of metallicityand its measurement methods (Bresolin et al. 2009; Ku-dritzki et al. 2012) on extragalactic Cepheid distancesrequires further investigations.The main conclusion of the current study is that ourinspection of NGC 5584 Cepheids does not yield any sys-tematic hints towards the resolution of the H problem.However, it would be important to also independentlyinspect for systematics in the distance measurements toall the galaxies used for calibration of SNeIa absolutemagnitude. For doing so, and until reasonably fine-sampled time series data of all SNeIa calibrators becomeavailable, it would certainly be better to use our preciseamplitude ratio vs. period relations for light curve anal-ysis of Cepheids in SNeIa hosts with limited time seriesdata as they would potentially yield more accurate meanmagnitudes in V and I bands. This would also providean investigation into the potential statistical effect ofthese relations in H measurements.While it is important to continue the investigationson the H measurements, the current findings seems tobe pointing towards a non-trivial solution to this prob-lem. This could mean that our current understanding of the local or early Universe may require modifications ora complete change of paradigm. In the local Universe,presence of a large local underdensity (which is incom-patible with LCDM, Haslbauer et al. 2020) has beenpresented (Shanks et al. 2019; Haslbauer et al. 2020)as a possible cause of the H discrepancy (but see alsoRiess et al. 2018a and Shanks et al. 2018). In the earlyUniverse, various scenarios such as non-standard recom-bination, dark matter/dark energy interaction, and self-interacting neutrinos have been presented, however, sofar no consensus has been reached (for reviews and sum-maries see Verde et al. 2019; Poulin 2020; Knox 2020).While it is important to seek alternative ideas on thetheoretical side, the improvement of current observa-tional methods as well as the development of new in-dependent ones are necessary for a progress towards asolution to the H problem. For the Cepheid distanceladder, the number of SNeIa calibrators observed bythe HST is soon to be doubled by the SH0ES program(Riess et al. 2019), hence the statistical uncertainty on H measured by this method would be reduced. In ad-dition to strong lensing, megamasers, and TRGB meth-ods (see also Beaton et al. 2016; Kim et al. 2020) men-tioned in the Introduction, other Cepheid-independentroutes would also soon contribute to H measurements.Huang et al. (2020) presents Mira variables for calibra-tion of SNeIa absolute magnitudes. Also, using the ad-vanced LIGO and Virgo gravitational wave detectors,The LIGO & Virgo Collaborations et al. (2019) have re-ported an H measurement using standard sirens (seealso Coughlin et al. 2020). As the number of detectedstandard sirens increases in future, the currently largestatistical uncertainty in their resulting H measure-ment would decrease, making them an important in-dependent way of measuring the cosmic expansion rate(Feeney et al. 2019).One of the most promising contributions to the ac-curacy of the cosmic distance scale in the near futurewould be from Gaia. The impact of the first (see, e.g.,Casertano et al. 2017; Gaia Collaboration et al. 2017)and second (see, e.g., Groenewegen 2018; Riess et al.2018b; Clementini et al. 2019; Breuval et al. 2020; Ripepiet al. 2020) data releases of Gaia on the calibration ofthe Cepheid PL relation is already considerable. It ishowever still limited by the persistently uncertain valueof the instrumental parallax zero point (see, e.g., Are-nou et al. 2018; Khan et al. 2019). The early Gaiadata release 3 (EDR3) published on 4 December 2020(Gaia Collaboration et al. 2020) significantly improvedthe accuracy of the measured MW Cepheid parallaxesof MW Cepheids. A mitigation of the uncertainty dueto the instrumental parallax zero point through an ad6 Javanmardi et al. hoc position-, color- and magnitude- dependent calibra-tion is also presented by Lindegren et al. (2020). Asdiscussed by Riess et al. (2021) (see also Breuval etal. 2021, in prep.), this improvement brings the calibra-tion of Cepheids luminosities to a 1% level, which makesthem the most accurate distance indicators available todate. As the number of measurement epochs and theunderstanding of the Gaia instrument increase, the DR3and DR4 will eventually provide trigonometric reliableparallax measurements at a few percent level or betterfor hundreds of Milky Way Cepheids. Combined withaccurate photometry and extinction corrections from 3Dextinction maps (see, e.g., Chen et al. 2019; Hottieret al. 2020), this set of absolutely calibrated distanceswill result in a very tight set of Cepheid PL relations,calibrated for the solar metallicity. Our Galaxy there-fore appears as a particularly appealing alternative tothe Magellanic Clouds as the primary anchor for extra-galactic Cepheid distances, thanks to the similarity ofits metallicity with those of distant SNeIa host galaxies.Relying on Milky Way Cepheids presents the advantageof reducing the possible bias introduced by the metallic-ity correction. This will effectively bypass the metallic-ity correction, thus increasing the overall robustness ofthe SNeIa calibration.As also noted in Riess (2019), precise measurement of H provides a powerful end-to-end test of the LCDMstandard model of cosmology. Future observationalprogress and inspections such as the current study wouldeventually conclude whether the H tension is caused by a measurement error, or it means that the LCDM shouldbe abandoned as a correct model of the Universe.ACKNOWLEDGMENTSWe thank the anonymous referee for the constructivecomments. The research leading to these results hasreceived funding from the European Research Coun-cil (ERC) under the European Union’s Horizon 2020research and innovation program under grant agree-ment No 695099 (project CepBin). WG and GPgratefully acknowledge financial support for this workfrom the BASAL Centro de Astrofisica y Tecnolo-gias Afines (CATA) AFB-170002. GP also acknowl-edges the support from NCN MAESTRO grant UMO-2017/26/A/ST9/00446 and DIR/WK/2018/09 grants ofthe Polish Ministry of Science and Higher Education.PK, NN, VH and SB acknowledge the support of theFrench Agence Nationale de la Recherche (ANR), undergrant ANR-15-CE31-0012-01 (project UnlockCepheids).We acknowledge the use of the HST observations ofNGC 5584 performed by the SH0ES team (PI: AdamRiess, Cycle: 17, Proposal ID: 11570) which are pub-licly available on the MAST database. This researchmade use of Photutils, an Astropy package for detectionand photometry of astronomical sources (Bradley et al.2019). Facility:
HST, MAST
Software:
DrizzlePac , Astropy (Bradley et al.2019), scikit-learn .REFERENCES
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Pesce, D. W., Braatz, J. A., Reid, M. J., et al. 2020, TheAstrophysical Journal, 891, L1,doi: 10.3847/2041-8213/ab75f0Pietrzy´nski, G., Gieren, W., Udalski, A., et al. 2004, AJ,128, 2815, doi: 10.1086/425531Pietrzy´nski, G., Graczyk, D., Gallenne, A., et al. 2019,Nature, 567, 200, doi: 10.1038/s41586-019-0999-4Planck Collaboration, Aghanim, N., Akrami, Y., et al.2018, arXiv e-prints, arXiv:1807.06209.https://arxiv.org/abs/1807.06209Poulin, V. 2020, in H epheid distance to the SNIa host galaxy NGC 5584 h m s s -0°25'24'23' RA D E C EN1kpc V B i a s ( m a g ) d cen (deg) V B i a s ( m a g ) local (mag/arcsec ) Figure 12.
Left: V band crowding bias ( V Bias ) vs. the projected angular distance d cen in degrees from the center of the galaxy.Middle: V Bias vs. local surface brightness µ local . Right: Distribution of the Cepheids in the NGC 5584 with the color codebeing the estimated crowding bias at the position of each Cepheid in the V band. The same color code is also used in the otherpanels. The Cepheids that are most affected by the crowding bias are statistically closer to the centre of the galaxy, however,the bias is found to be more correlated with local surface brightness. The linear correlation coefficient between the absolutevalue of the crowding bias and d cen and µ local are r = − .
24 and r = − .
40, respectively. See appendix B for details.
APPENDIX A. APERTURE CORRECTIONHere, we compare aperture correction using the aperture photometry of the PSF model with the approach usingaperture and PSF photometry of stars in the image. For this purpose we compare the PSF and aperture photometryof thirteen uncrowded stars using the stacked version of all the F555W band images. For these stars we crop a 50pixel ×
50 pixel portion of the image and perform the PSF photometry in the same way as described in Section 4.1.1.All the sources except from the central star are removed using the PSF modelling prior to the aperture photometrywith an aperture radius of 10 pixels. The difference is then measured using Equation 2 and we find a mean value of AP cor = 0 . ± .
024 mag for the F555W band. It is 1 σ larger than the value obtained using aperture photometryof the PSF model. We expect a similar result for F814W band. For the F160W band, the AP cor we measure usingthe PSF model, i.e. 0.049 mag, is also around 1 σ smaller than the 0 . ± .
01 measured by Huang et al. (2020) forF160W images of the SNIa host NGC 1559. The difference of these two methods is most probably due to imperfectsubtraction of the background noise in the actual images and the absence of this noise in the PSF model. Therefore,by noting that the difference in the F160W band is most relevant for distance measurement (Equation 1), measuring AP cor using aperture photometry of the PSF model rather than using uncrowded stars in the image leads to around0 . ± .
01 mag decrease in the distance modulus. B. CROWDING BIASIn Section 4.2 we explained our method of estimating the crowding bias at the location of each Cepheid. Here weinvestigate the environmental dependence of crowding bias in the F555W band. Figure 12 shows the distribution ofcrowding bias across the galaxy (right panel), bias vs. the projected angular distance d cen in degrees from the center ofthe galaxy (left panel), and bias vs. local surface brightness, µ local (middle panel). The Cepheids that are most affectedby the crowding bias are statistically closer to the centre of the galaxy where the stellar density is generally higher.However, small bias values can also be found at smaller d cen and we measure a correlation coefficient of r = − . d cen . The small correlation is possibly due to spiral structure ofNGC 5584, i.e. even at small galactocentric distances, there are less crowded regions.We also check the crowding bias vs. µ local . The latter is measured using the following three step method: i) wefirst measure the average sky background using around twenty 40 ×
40 pixel square regions outside the parts of theimage covered by NGC 5584, ii) we then used the same size squares at the location of each Cepheid (where we alreadyestimated crowding bias) and measured the total flux inside them, iii) in the end, the average sky background issubtracted from the local total fluxes and the result is converted to surface brightness using the angular area in arcsecand the magnitude zero point. We measure a correlation coefficient of r = − .
40 between the crowding bias and µ local .0 Javanmardi et al. V B i a s ( m a g ) Mean: -0.045±0.072 I B i a s ( m a g ) Mean: -0.044±0.066
20 30 40 60 80 120Period (days)0.20.10.00.1 R H × ( V I ) B i a s ( m a g ) Mean: -0.0004±0.0265 V ( m a g ) I ( m a g ) V I ( m a g ) Figure 13.
Crowding bias in V and I bands, as well as R H ( V − I ) vs. period. This figure can be directly compared to Figure14 of H16 (see appendix B for a discussion). This relatively larger correlation implies that the local surface brightness is a better proxy to crowding bias comparedto galactocentric distance. Using a second order polynomial fit we findBias = − . µ local + 0 . µ local − . σ fit = 0 . µ local (cid:38)
23 mag/arcsec , the effect of crowding bias is negligible.To compare our crowding bias measurements with those of H16, we also show the bias as a function of period inFigure 13. This figure can be directly compared to Figure 14 of H16. Our results is (within 1 σ ) in agreement withthose of the H16. In particular, as can be seen in the lowest panel, the effect of the crowding bias on the V-I colormeasurement is very small. We remind the reader that unlike the approach of SH0ES (averaging over the galaxy forthe optical observations), we apply the crowding bias estimated for individual Cepheids on their photometric resultsbefore the template fitting. epheid distance to the SNIa host galaxy NGC 5584 C. CEPHEID PROPERTIESOur results for the photometric properties of the identified Cepheids in NGC 5584 are listed in Table 2.
Table 2 . Our measurements for the photometric properties of the Cepheids in the NGC 5584.
ID RAJ2000 DECJ2000 LP σ LP A LP V σ V A V I σ I A I H σ H (deg) (deg) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag)82928 215.5872 -0.3685 26.717 0.019 0.313 26.943 0.024 0.36 25.899 0.044 0.231 24.859 0.186318 215.5892 -0.3676 26.985 0.023 0.274 27.286 0.025 0.326 26.04 0.024 0.22 - -91999 215.5886 -0.3682 27.392 0.047 0.306 27.696 0.046 0.361 26.442 0.05 0.243 - -96368 215.584 -0.3708 26.841 0.018 0.214 27.11 0.023 0.255 25.945 0.039 0.17 - -97566 215.5886 -0.3685 26.3 0.019 0.203 26.6 0.02 0.244 25.35 0.019 0.166 24.107 0.023111577 215.5875 -0.3698 25.58 0.008 0.18 25.793 0.012 0.21 24.773 0.017 0.133 23.775 0.042121760 215.588 -0.3701 27.399 0.059 0.29 27.701 0.07 0.343 26.453 0.107 0.231 - -134935 215.5855 -0.372 25.963 0.011 0.232 26.213 0.015 0.272 25.099 0.02 0.179 - -143986 215.5898 -0.3703 25.809 0.019 0.168 25.984 0.028 0.192 25.067 0.026 0.116 24.187 0.065151156 215.5928 -0.3691 27.043 0.055 0.186 27.282 0.074 0.22 26.193 0.07 0.143 - -156158 215.5903 -0.3706 26.541 0.019 0.245 26.715 0.026 0.277 25.808 0.031 0.171 - -157119 215.5914 -0.3701 25.616 0.016 0.234 25.824 0.019 0.269 24.823 0.027 0.171 23.838 0.059172880 215.589 -0.3721 25.385 0.036 0.172 25.673 0.04 0.205 24.444 0.039 0.128 23.24 0.062175404 215.591 -0.3712 26.232 0.018 0.182 26.528 0.019 0.221 25.284 0.016 0.149 - -175413 215.5939 -0.3697 26.399 0.02 0.206 26.69 0.026 0.25 25.463 0.026 0.169 24.233 0.061185292 215.5952 -0.3696 25.475 0.008 0.211 25.635 0.012 0.237 24.761 0.009 0.144 23.914 0.025191706 215.5961 -0.3695 26.359 0.017 0.17 26.569 0.023 0.198 25.558 0.029 0.124 24.575 0.067197260 215.59 -0.3729 27.219 0.03 0.26 27.521 0.03 0.308 26.268 0.031 0.208 - -200467 215.5944 -0.3707 26.947 0.033 0.285 27.253 0.033 0.338 25.992 0.034 0.227 24.72 0.045200686 215.5899 -0.3731 25.929 0.022 0.186 26.234 0.024 0.229 24.97 0.024 0.157 - -208725 215.5952 -0.3708 26.322 0.016 0.266 26.524 0.021 0.304 25.543 0.027 0.193 - -211148 215.5834 -0.3769 27.295 0.035 0.299 27.546 0.043 0.347 26.435 0.076 0.226 - -216328 215.5967 -0.3704 26.468 0.037 0.21 26.767 0.038 0.255 25.52 0.038 0.176 - -220248 215.5879 -0.3751 26.293 0.016 0.294 26.526 0.021 0.339 25.462 0.023 0.219 24.399 0.051229600 215.5929 -0.373 26.922 0.027 0.252 27.162 0.032 0.293 26.076 0.041 0.191 - -230093 215.5895 -0.3747 26.99 0.017 0.207 27.263 0.021 0.248 26.085 0.029 0.165 24.914 0.067238461 215.5937 -0.373 26.733 0.022 0.268 27.037 0.023 0.319 25.781 0.021 0.216 24.51 0.023247527 215.5757 -0.3826 26.551 0.019 0.296 26.801 0.024 0.343 25.691 0.037 0.225 - -253461 215.5963 -0.3724 26.342 0.018 0.193 26.636 0.018 0.235 25.4 0.019 0.16 24.163 0.024254240 215.6057 -0.3677 26.154 0.013 0.319 26.418 0.016 0.371 25.27 0.023 0.243 - -258671 215.5955 -0.3731 27.075 0.04 0.223 27.349 0.051 0.266 26.172 0.081 0.179 - -267902 215.5968 -0.373 25.861 0.014 0.227 26.066 0.02 0.261 25.072 0.021 0.166 - -271193 215.5966 -0.3732 26.321 0.019 0.171 26.569 0.028 0.204 25.456 0.029 0.133 - -271677 215.5882 -0.3775 27.113 0.024 0.23 27.413 0.024 0.277 26.166 0.025 0.188 - -276835 215.5827 -0.3806 26.582 0.036 0.243 26.696 0.047 0.266 25.948 0.068 0.157 - -281768 215.5913 -0.3764 27.006 0.02 0.284 27.277 0.028 0.331 26.111 0.039 0.219 24.945 0.092290494 215.6083 -0.3682 26.103 0.012 0.267 26.304 0.015 0.305 25.322 0.025 0.195 - -295981 215.5898 -0.3779 25.913 0.013 0.193 26.104 0.016 0.221 25.145 0.027 0.138 24.21 0.062298430 215.6007 -0.3724 26.845 0.024 0.41 27.071 0.03 0.469 26.031 0.047 0.302 24.993 0.107321323 215.5979 -0.375 26.971 0.038 0.218 27.269 0.037 0.262 26.027 0.041 0.178 - -321793 215.5995 -0.3742 26.995 0.031 0.196 27.164 0.038 0.221 26.266 0.062 0.135 - -325206 215.5894 -0.3795 25.933 0.018 0.207 26.226 0.024 0.25 24.994 0.029 0.17 23.76 0.069325458 215.5992 -0.3745 27.414 0.102 0.286 27.723 0.103 0.338 26.453 0.102 0.228 - -325693 215.5909 -0.3788 27.443 0.056 0.264 27.636 0.074 0.3 26.678 0.113 0.191 - -325718 215.5996 -0.3744 25.435 0.011 0.178 25.726 0.011 0.215 24.492 0.011 0.14 23.272 0.013326705 215.5967 -0.3759 27.603 0.037 0.443 27.754 0.046 0.5 26.917 0.075 0.312 - -329366 215.6014 -0.3736 26.959 0.028 0.193 27.255 0.029 0.235 26.012 0.03 0.159 24.771 0.039 Table 2 continued Javanmardi et al.
Table 2 (continued)
ID RAJ2000 DECJ2000 LP σ LP A LP V σ V A V I σ I A I H σ H (deg) (deg) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag)330805 215.599 -0.3749 26.173 0.015 0.183 26.361 0.02 0.21 25.411 0.021 0.13 - -339133 215.5806 -0.3847 25.609 0.009 0.185 25.813 0.013 0.213 24.817 0.014 0.135 - -340379 215.5949 -0.3775 26.966 0.055 0.203 27.119 0.076 0.227 26.263 0.1 0.137 25.44 0.237342112 215.5925 -0.3788 26.002 0.015 0.175 26.278 0.019 0.212 25.09 0.025 0.141 - -347072 215.5997 -0.3754 25.593 0.018 0.164 25.803 0.02 0.191 24.791 0.044 0.12 - -353561 215.594 -0.3786 26.399 0.046 0.164 26.642 0.064 0.195 25.54 0.096 0.126 - -354807 215.594 -0.3787 25.535 0.018 0.159 25.757 0.026 0.184 24.707 0.026 0.111 23.699 0.064374736 215.5992 -0.377 26.048 0.013 0.242 26.286 0.015 0.281 25.205 0.024 0.183 24.136 0.055378235 215.6091 -0.3721 26.737 0.016 0.264 26.989 0.022 0.308 25.873 0.028 0.201 24.76 0.065390652 215.6005 -0.3771 26.415 0.021 0.239 26.603 0.026 0.272 25.656 0.037 0.17 24.731 0.084395114 215.5969 -0.3792 25.537 0.017 0.184 25.853 0.019 0.228 24.557 0.022 0.157 23.258 0.04396420 215.6059 -0.3747 26.928 0.018 0.213 27.224 0.018 0.258 25.984 0.019 0.177 - -399436 215.5982 -0.3788 26.727 0.029 0.332 26.893 0.04 0.375 26.011 0.044 0.233 - -411135 215.597 -0.3799 25.921 0.012 0.281 26.153 0.017 0.325 25.091 0.025 0.21 24.039 0.062412396 215.6 -0.3785 26.137 0.023 0.192 26.308 0.033 0.218 25.403 0.044 0.133 24.528 0.105418643 215.5894 -0.3842 26.447 0.016 0.3 26.743 0.023 0.353 25.511 0.03 0.236 - -419182 215.5993 -0.3792 26.311 0.023 0.196 26.476 0.027 0.221 25.587 0.048 0.134 - -420418 215.5948 -0.3815 26.579 0.026 0.219 26.83 0.035 0.258 25.712 0.037 0.17 - -421192 215.5971 -0.3804 26.244 0.009 0.362 26.511 0.012 0.419 25.36 0.017 0.273 - -424677 215.5991 -0.3795 27.785 0.033 0.158 28.065 0.045 0.192 26.863 0.07 0.125 - -427599 215.5982 -0.3801 26.055 0.021 0.178 26.269 0.028 0.208 25.25 0.033 0.131 - -437977 215.5933 -0.3831 27.197 0.053 0.234 27.283 0.074 0.253 26.609 0.082 0.145 - -446943 215.5947 -0.3829 25.601 0.011 0.212 25.858 0.014 0.252 24.725 0.019 0.166 - -449157 215.5933 -0.3837 26.347 0.018 0.169 26.578 0.025 0.199 25.511 0.026 0.127 24.467 0.061449432 215.6042 -0.3782 25.017 0.012 0.197 25.248 0.016 0.23 24.18 0.013 0.15 23.139 0.031455910 215.6028 -0.3792 27.031 0.033 0.216 27.304 0.041 0.258 26.126 0.053 0.174 - -455911 215.6042 -0.3785 26.348 0.016 0.276 26.63 0.022 0.324 25.433 0.022 0.216 - -464626 215.5896 -0.3864 26.954 0.029 0.371 27.26 0.038 0.432 26.002 0.045 0.287 24.728 0.102466137 215.6009 -0.3807 27.027 0.023 0.33 27.334 0.025 0.388 26.072 0.023 0.26 - -469580 215.5999 -0.3814 26.119 0.015 0.177 26.358 0.022 0.21 25.269 0.025 0.136 - -473829 215.6056 -0.3787 25.629 0.012 0.201 25.906 0.015 0.243 24.716 0.02 0.164 23.527 0.045475792 215.5941 -0.3846 27.131 0.086 0.379 27.223 0.088 0.421 26.541 0.09 0.254 - -477073 215.6036 -0.3799 26.683 0.025 0.205 26.822 0.036 0.228 26.004 0.04 0.135 - -478350 215.602 -0.3807 26.604 0.028 0.289 26.915 0.03 0.34 25.638 0.029 0.23 24.359 0.041481285 215.5936 -0.3852 26.15 0.017 0.202 26.342 0.025 0.232 25.383 0.02 0.145 - -487089 215.5934 -0.3855 26.549 0.029 0.217 26.72 0.038 0.246 25.816 0.053 0.151 - -491027 215.5998 -0.3825 27.04 0.037 0.389 27.245 0.046 0.443 26.261 0.088 0.282 - -493790 215.5985 -0.3833 26.514 0.016 0.203 26.72 0.025 0.235 25.722 0.029 0.149 24.748 0.071494049 215.6008 -0.3821 26.727 0.032 0.209 26.918 0.049 0.24 25.962 0.049 0.149 - -495038 215.5946 -0.3853 26.722 0.026 0.224 26.807 0.026 0.242 26.132 0.026 0.138 - -502797 215.6009 -0.3825 25.936 0.015 0.274 26.2 0.017 0.321 25.052 0.029 0.211 23.902 0.064504490 215.5963 -0.3849 26.289 0.017 0.237 26.475 0.02 0.27 25.533 0.032 0.169 24.614 0.071511109 215.6 -0.3833 26.693 0.022 0.384 26.982 0.027 0.445 25.772 0.042 0.293 24.54 0.097513372 215.6028 -0.382 26.463 0.013 0.342 26.73 0.019 0.396 25.576 0.023 0.26 24.417 0.056513827 215.5974 -0.3849 26.571 0.023 0.31 26.878 0.024 0.366 25.617 0.022 0.246 24.335 0.025516608 215.596 -0.3857 27.256 0.031 0.221 27.478 0.048 0.257 26.44 0.067 0.165 - -519642 215.5948 -0.3864 26.551 0.014 0.335 26.761 0.016 0.383 25.759 0.026 0.245 - -521128 215.5939 -0.387 26.545 0.024 0.235 26.832 0.028 0.28 25.62 0.044 0.188 24.405 0.096534937 215.5823 -0.3936 27.038 0.039 0.306 27.277 0.047 0.354 26.199 0.076 0.228 25.115 0.169540558 215.5994 -0.3851 26.528 0.036 0.201 26.689 0.046 0.226 25.811 0.064 0.138 - -543151 215.6031 -0.3834 26.431 0.021 0.208 26.732 0.022 0.25 25.479 0.022 0.17 24.231 0.029549082 215.5961 -0.3872 25.888 0.011 0.207 26.132 0.016 0.244 25.035 0.018 0.159 23.947 0.044549585 215.5937 -0.3885 26.751 0.019 0.345 26.926 0.03 0.39 26.021 0.041 0.244 25.13 0.101 Table 2 continued epheid distance to the SNIa host galaxy NGC 5584 Table 2 (continued)
ID RAJ2000 DECJ2000 LP σ LP A LP V σ V A V I σ I A I H σ H (deg) (deg) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag)550433 215.6125 -0.3789 26.398 0.015 0.342 26.691 0.022 0.399 25.468 0.027 0.265 24.227 0.067550434 215.6129 -0.3787 27.084 0.022 0.349 27.391 0.022 0.408 26.132 0.023 0.272 24.848 0.03552392 215.5834 -0.3939 26.655 0.061 0.188 26.872 0.064 0.219 25.843 0.121 0.139 - -556696 215.6031 -0.384 26.784 0.022 0.214 27.081 0.023 0.258 25.839 0.023 0.175 - -562692 215.6024 -0.3847 26.409 0.03 0.384 26.659 0.033 0.441 25.555 0.058 0.285 - -562960 215.6016 -0.3851 27.236 0.041 0.389 27.548 0.04 0.452 26.275 0.045 0.301 - -563696 215.6054 -0.3832 27.128 0.041 0.354 27.361 0.048 0.406 26.301 0.057 0.262 25.241 0.118567349 215.6029 -0.3846 25.978 0.02 0.191 26.264 0.025 0.232 25.05 0.039 0.157 - -571414 215.6052 -0.3837 26.151 0.016 0.314 26.445 0.021 0.367 25.218 0.032 0.245 23.982 0.077584459 215.5942 -0.3899 27.753 0.094 0.289 28.06 0.101 0.342 26.795 0.089 0.23 - -584466 215.5955 -0.3893 26.698 0.036 0.208 26.844 0.048 0.232 26.008 0.068 0.139 - -589456 215.6036 -0.3854 26.996 0.039 0.188 27.29 0.04 0.229 26.055 0.038 0.155 24.823 0.037594530 215.5833 -0.396 26.777 0.017 0.191 27.021 0.021 0.225 25.922 0.04 0.147 - -602554 215.6093 -0.3831 26.817 0.019 0.365 27.126 0.02 0.427 25.863 0.02 0.284 24.57 0.026603762 215.6004 -0.3877 26.322 0.022 0.176 26.618 0.021 0.216 25.374 0.022 0.146 - -605531 215.593 -0.3916 26.61 0.017 0.257 26.858 0.021 0.3 25.753 0.042 0.196 24.646 0.096606041 215.6089 -0.3835 25.872 0.012 0.184 26.059 0.016 0.21 25.11 0.018 0.13 24.19 0.042607520 215.6078 -0.3841 25.387 0.012 0.226 25.648 0.015 0.267 24.503 0.02 0.177 23.368 0.047610213 215.604 -0.3862 26.119 0.011 0.198 26.413 0.016 0.24 25.18 0.018 0.164 23.944 0.043611528 215.6102 -0.3831 26.571 0.03 0.239 26.763 0.039 0.273 25.805 0.058 0.171 - -620130 215.5825 -0.3977 26.604 0.016 0.3 26.868 0.02 0.349 25.723 0.023 0.229 - -628911 215.6084 -0.3849 25.437 0.012 0.178 25.685 0.015 0.212 24.573 0.023 0.138 23.476 0.052633407 215.6025 -0.3881 26.726 0.02 0.176 27.016 0.02 0.215 25.788 0.021 0.145 - -640109 215.5982 -0.3906 27.413 0.03 0.18 27.663 0.042 0.214 26.547 0.069 0.14 - -644384 215.5912 -0.3945 26.944 0.024 0.357 27.171 0.03 0.409 26.126 0.042 0.263 - -648122 215.5924 -0.394 27.972 0.045 0.173 28.263 0.045 0.213 27.032 0.045 0.143 - -648136 215.5955 -0.3924 26.563 0.046 0.158 26.855 0.047 0.193 25.621 0.045 0.127 - -656817 215.609 -0.386 25.391 0.012 0.169 25.566 0.016 0.193 24.648 0.021 0.117 23.767 0.05668576 215.5936 -0.3944 27.419 0.045 0.186 27.711 0.046 0.227 26.479 0.045 0.154 - -673309 215.5921 -0.3954 26.015 0.018 0.186 26.313 0.018 0.227 25.067 0.018 0.155 23.825 0.021673828 215.6087 -0.387 25.579 0.013 0.168 25.833 0.018 0.201 24.702 0.015 0.131 - -674808 215.6013 -0.3908 27.467 0.032 0.262 27.768 0.032 0.311 26.519 0.033 0.21 - -696165 215.6089 -0.388 26.487 0.016 0.252 26.64 0.019 0.283 25.787 0.029 0.172 - -697115 215.6045 -0.3902 27.061 0.028 0.193 27.351 0.034 0.235 26.127 0.05 0.159 - -708572 215.5999 -0.3932 26.214 0.018 0.33 26.408 0.025 0.375 25.45 0.034 0.236 - -711358 215.6128 -0.3867 26.85 0.021 0.327 27.106 0.029 0.379 25.981 0.044 0.248 - -715226 215.5996 -0.3937 26.214 0.017 0.194 26.509 0.017 0.236 25.269 0.017 0.161 24.028 0.02715986 215.6103 -0.3882 26.597 0.023 0.298 26.906 0.024 0.351 25.637 0.025 0.236 24.36 0.037718451 215.5968 -0.3952 26.225 0.082 0.278 26.43 0.107 0.319 25.439 0.12 0.202 - -727892 215.6143 -0.3868 26.128 0.013 0.305 26.362 0.019 0.352 25.298 0.019 0.227 24.233 0.048729270 215.5882 -0.4002 26.763 0.013 0.36 27.005 0.016 0.414 25.923 0.028 0.267 - -735368 215.614 -0.3873 25.286 0.016 0.189 25.53 0.025 0.223 24.429 0.03 0.146 23.349 0.076735776 215.5832 -0.403 26.776 0.019 0.302 27.007 0.024 0.348 25.949 0.03 0.225 - -738261 215.5993 -0.3949 26.753 0.021 0.339 27.063 0.021 0.397 25.795 0.022 0.265 24.509 0.031740028 215.601 -0.3942 26.777 0.03 0.238 27.077 0.03 0.286 25.831 0.03 0.194 24.577 0.038741044 215.6151 -0.387 27.273 0.036 0.233 27.48 0.048 0.268 26.482 0.078 0.17 - -744518 215.6091 -0.3902 27.905 0.098 0.351 28.051 0.118 0.392 27.225 0.127 0.24 - -757081 215.6052 -0.3929 26.076 0.015 0.242 26.334 0.019 0.284 25.2 0.024 0.187 - -758598 215.607 -0.3921 26.075 0.02 0.247 26.365 0.027 0.294 25.145 0.029 0.197 - -762356 215.6121 -0.3896 25.773 0.012 0.201 26.071 0.012 0.243 24.825 0.012 0.165 - -763038 215.5999 -0.3959 26.461 0.021 0.273 26.65 0.029 0.312 25.7 0.044 0.197 24.77 0.103766511 215.616 -0.3879 26.237 0.011 0.258 26.498 0.015 0.303 25.358 0.02 0.199 24.219 0.047767732 215.6132 -0.3893 26.605 0.025 0.231 26.696 0.028 0.25 26.007 0.047 0.144 - - Table 2 continued Javanmardi et al.
Table 2 (continued)
ID RAJ2000 DECJ2000 LP σ LP A LP V σ V A V I σ I A I H σ H (deg) (deg) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag)770504 215.6101 -0.3911 26.921 0.039 0.175 27.211 0.05 0.214 25.984 0.058 0.144 - -770520 215.6157 -0.3882 25.923 0.011 0.166 26.215 0.011 0.203 24.982 0.011 0.135 - -775000 215.6133 -0.3896 26.341 0.015 0.216 26.641 0.016 0.262 25.392 0.015 0.179 24.135 0.02781327 215.606 -0.3937 25.326 0.022 0.156 25.545 0.03 0.183 24.506 0.029 0.114 - -781586 215.6048 -0.3943 25.501 0.016 0.179 25.625 0.02 0.197 24.845 0.025 0.114 - -784855 215.6052 -0.3943 26.72 0.023 0.244 27.021 0.023 0.293 25.773 0.022 0.199 - -787283 215.6034 -0.3953 27.786 0.116 0.43 27.946 0.171 0.485 27.085 0.101 0.303 26.234 0.268789264 215.6083 -0.3929 26.913 0.054 0.229 27.053 0.067 0.255 26.235 0.107 0.154 - -789518 215.6123 -0.3909 26.569 0.028 0.327 26.719 0.023 0.367 25.879 0.06 0.226 - -797934 215.613 -0.391 27.463 0.048 0.331 27.702 0.063 0.381 26.625 0.077 0.246 - -801059 215.5983 -0.3986 25.378 0.013 0.188 25.64 0.018 0.225 24.49 0.024 0.15 23.35 0.057810216 215.6005 -0.3979 26.559 0.025 0.187 26.805 0.033 0.221 25.699 0.029 0.144 24.608 0.065810479 215.6089 -0.3936 27.076 0.024 0.383 27.272 0.03 0.435 26.314 0.049 0.275 - -811974 215.614 -0.3911 26.005 0.011 0.257 26.213 0.019 0.295 25.214 0.019 0.189 24.22 0.051823580 215.6078 -0.3949 26.309 0.016 0.212 26.612 0.016 0.258 25.355 0.018 0.177 24.09 0.027825506 215.5976 -0.4002 27.509 0.031 0.326 27.726 0.035 0.373 26.706 0.05 0.238 - -835494 215.6062 -0.3963 26.917 0.021 0.318 27.167 0.03 0.368 26.059 0.038 0.24 - -835998 215.6124 -0.3932 25.91 0.03 0.229 26.231 0.03 0.276 24.924 0.035 0.19 23.611 0.051845553 215.6017 -0.3991 26.156 0.017 0.296 26.371 0.021 0.339 25.357 0.033 0.216 - -845788 215.604 -0.3979 26.537 0.023 0.214 26.646 0.025 0.234 25.908 0.051 0.136 - -852752 215.6107 -0.3948 26.762 0.017 0.393 27.064 0.022 0.457 25.821 0.026 0.302 24.546 0.059853244 215.6125 -0.394 27.121 0.029 0.436 27.355 0.034 0.498 26.295 0.054 0.319 - -858989 215.6027 -0.3992 25.717 0.035 0.196 26.016 0.036 0.239 24.769 0.034 0.164 23.52 0.035859454 215.5889 -0.4063 26.043 0.014 0.304 26.292 0.019 0.351 25.184 0.025 0.231 - -859464 215.5917 -0.4049 26.866 0.019 0.306 27.102 0.025 0.353 26.031 0.036 0.228 - -871337 215.6125 -0.3949 25.846 0.027 0.208 25.971 0.038 0.229 25.191 0.04 0.135 - -874062 215.6038 -0.3994 27.225 0.03 0.269 27.424 0.043 0.306 26.45 0.068 0.198 - -886741 215.6152 -0.3943 27.512 0.034 0.173 27.805 0.035 0.212 26.571 0.034 0.143 - -889136 215.5984 -0.4029 26.991 0.022 0.244 27.288 0.022 0.293 26.049 0.023 0.2 24.795 0.032892554 215.6117 -0.3963 27.154 0.047 0.3 27.46 0.043 0.353 26.2 0.056 0.237 24.93 0.075905168 215.6032 -0.4013 26.533 0.035 0.262 26.751 0.047 0.301 25.727 0.04 0.195 - -912240 215.6097 -0.3984 27.281 0.065 0.35 27.379 0.072 0.385 26.681 0.114 0.23 25.999 0.244918325 215.6105 -0.3982 26.659 0.018 0.378 26.885 0.02 0.432 25.842 0.033 0.277 24.796 0.072927325 215.6134 -0.3973 27.113 0.028 0.291 27.418 0.028 0.345 26.163 0.029 0.233 24.886 0.037938088 215.6156 -0.3967 27.187 0.034 0.246 27.487 0.038 0.295 26.24 0.032 0.2 - -976489 215.6084 -0.4023 27.078 0.024 0.208 27.356 0.028 0.25 26.165 0.038 0.169 - -979358 215.6001 -0.4067 27.343 0.033 0.179 27.615 0.04 0.217 26.437 0.062 0.144 - -981628 215.6116 -0.4009 26.472 0.016 0.263 26.732 0.017 0.309 25.595 0.034 0.203 - -1003917 215.6038 -0.406 26.428 0.018 0.287 26.733 0.018 0.339 25.476 0.02 0.228 - -1015181 215.6113 -0.4028 26.043 0.012 0.253 26.26 0.016 0.292 25.236 0.019 0.187 24.229 0.0471023938 215.6121 -0.4028 26.433 0.02 0.289 26.604 0.029 0.327 25.706 0.041 0.204 - -1031574 215.6126 -0.4029 25.969 0.016 0.253 26.223 0.022 0.295 25.099 0.035 0.194 23.983 0.0851038160 215.6101 -0.4045 26.795 0.038 0.259 26.928 0.046 0.287 26.129 0.063 0.174 - -1045353 215.6116 -0.4041 26.64 0.016 0.427 26.838 0.021 0.485 25.875 0.032 0.309 - -1055460 215.6116 -0.4045 27.006 0.045 0.296 27.244 0.059 0.342 26.167 0.063 0.222 - -1073816 215.6089 -0.4068 26.942 0.021 0.253 27.242 0.022 0.303 25.995 0.021 0.205 24.735 0.027 Note —The ID and the coordinates are those of H16. LP: F350LP, V: F555W, I: F814W, H:F160W. Note that not all the Cepheids that areidentified in the optical bands are detected in the H band. D. DATA FILES OBTAINED FROM MASTWe list the information about all the data files weretrieved from the MAST database in Table 3. epheid distance to the SNIa host galaxy NGC 5584 Table 3.