Measuring Infrared Surface Brightness Fluctuation Distances with HST WFC3: Calibration and Advice
Joseph B. Jensen, John P. Blakeslee, Zachary Gibson, Hyun-chul Lee, Michele Cantiello, Gabriella Raimondo, Nathan Boyer, Hyejeon Cho
DD RAFT VERSION O CTOBER
10, 2018
Preprint typeset using L A TEX style emulateapj v. 01/23/15
MEASURING INFRARED SURFACE BRIGHTNESS FLUCTUATION DISTANCESWITH
HST
WFC3: CALIBRATION AND ADVICE J OSEPH
B. J
ENSEN
Utah Valley University, Orem, Utah 84058, USA; [email protected] J OHN
P. B
LAKESLEE
NRC Herzberg Astrophysics, Victoria, British Columbia, Canada Z ACHARY G IBSON
Utah Valley University, Orem, Utah, USA H YUN - CHUL L EE The University of Texas Rio Grande Valley, Edinburg, Texas, USA M ICHELE C ANTIELLO AND G ABRIELLA R AIMONDO
INAF–Osservatorio Astronomico di Teramo, Teramo, Italy N ATHAN B OYER
Brigham Young University, Provo, Utah, USA H YEJEON C HO Department of Astronomy and Center for Galaxy Evolution Research, Yonsei University, Seoul 120-749, Korea
Draft version October 10, 2018
ABSTRACTWe present new calibrations of the near-infrared surface brightness fluctuation (SBF) distance method forthe F110W ( J ) and F160W ( H ) bandpasses of the Wide Field Camera 3 Infrared Channel (WFC3/IR) onthe Hubble Space Telescope . The calibrations are based on data for 16 early-type galaxies in the Virgo andFornax clusters observed with WFC3/IR and are provided as functions of both the optical ( g − z ) and near-infrared ( J − H ) colors. The scatter about the linear calibration relations for the luminous red galaxies inthe sample is approximately 0.10 mag, corresponding to a statistical error of 5% in distance. Our results implythat the distance to any suitably bright elliptical galaxy can be measured with this precision out to about 80 Mpcin a single-orbit observation with WFC3/IR, making this a remarkably powerful instrument for extragalacticdistances. The calibration sample also includes much bluer and lower-luminosity galaxies than previously usedfor IR SBF studies, revealing interesting population differences that cause the calibration scatter to increase fordwarf galaxies. Comparisons with single-burst population models show that, as expected, the redder early-typegalaxies contain old, metal-rich populations, while the bluer dwarf ellipticals contain a wider range of ages andlower metallicities than their more massive counterparts. Radial SBF gradients reveal that IR color gradientsare largely an age effect; the bluer dwarfs typically have their youngest populations near their centers, while theredder giant ellipticals show only weak trends and in the opposite sense. Because of the population variationsamong bluer galaxies, distance measurements in the near-IR are best limited to red early-type galaxies. Weconclude with some practical guidelines for using WFC3/IR to measure reliable SBF distances. Subject headings: distance scale — galaxies: clusters: individual (Virgo, Fornax) — galaxies: distances andredshifts — galaxies: elliptical and lenticular, cD — galaxies: stellar content INTRODUCTION1.1.
Distance Measurements in the Big Picture
Accurate distance measurement is central to both astro-physics and cosmology. Reliable distances are needed to con-vert observed properties of galaxies (fluxes and angular sizes) Based on observations with the NASA/ESA
Hubble Space Telescope ,obtained at the Space Telescope Science Institute, which is operated by theAssociation of Universities for Research in Astronomy, Inc., under NASAcontract NAS 5-26555. These observations are associated with Program into absolute physical quantities such as luminosities, masses,ages, star formation rates, and dynamical time scales. In thelocal universe where peculiar velocities are significant, thedistance estimate is often a major source of uncertainty onthese physical properties. For instance, a recent review ar-ticle on supermassive black holes (Kormendy & Ho 2013)notes that for many galaxies, the errors in the central blackhole masses are dominated by the uncertainty in distance; yet,many authors neglect to include this important contribution tothe uncertainty. a r X i v : . [ a s t r o - ph . GA ] J un Jensen et al.In the field of cosmology, the acceleration of the cosmic ex-pansion was first revealed by accurate distance measurementsof Type Ia supernovae (Riess et al. 1998; Perlmutter et al.1999). The supernova distance estimates, combined with flat-ness constraints for the universe provided by the cosmic mi-crowave background (CMB) power spectrum, are primarilyresponsible for inaugurating a new era of “precision cosmol-ogy,” central to which is the conclusion that the mass-energybudget of the universe is dominated by “dark energy.” Now,with the exquisite constraints on the CMB power spectrumat z ∼ H to a pre-cision of 1% (Riess et al. 2011; Freedman et al. 2012). Asdiscussed in the foregoing references, this level of precisionis required for firm simultaneous constraints on cosmic ge-ometry, the dark energy equation of state, and the number ofneutrino species.Of course, the value of H has been controversial fordecades, primarily owing to systematic calibration errors(e.g., Freedman & Madore 2010). Determining H with a to-tal uncertainty of no more than 1% remains beyond the abilityof any single distance measurement technique. In order toachieve the required level of precision, it is helpful to havemultiple high-precision distance indicators to provide robustconstraints on the contributions from systematic errors.The surface brightness fluctuation (SBF) method providesa measurement of the mean brightness of the red giant branchstars in an early-type galaxy even though individual stars can-not be resolved (Tonry & Schneider 1988). It was introducedas a way to estimate distances with ∼
10% uncertainty out toabout 20 Mpc from ground-based astronomical images (seeTonry et al. 1990). More recent applications have shown sub-stantial improvements in both the precision of the method anddepth to which it can be applied (see the reviews by Blakeslee2012 and Fritz 2012), so that it has become one of a smallnumber of methods capable of making a significant contribu-tion to the problem of constraining H to 1%. In the follow-ing sections, we discuss these recent developments with themethod and the need for a new calibration at near-IR wave-lengths. 1.2. The Key Role of HST
The latest revolution in our knowledge of the extragalacticdistance scale (decreasing the uncertainty from nearly a factorof two to less than 10%) has resulted primarily from obser-vations made with the
Hubble Space Telescope ( HST ). Start-ing in the mid-1990s,
HST was used to measure light curvesfor samples of Cepheid variable stars in late-type galaxies outto ∼
20 Mpc, mostly as part of the Key Project on the Dis-tance Scale (e.g., Freedman et al. 1994; Ferrarese et al. 1996;Kelson et al. 1996; Saha et al. 1996, 1997; Silbermann et al.1999). The resulting Cepheid distance estimates were usedto calibrate various secondary distance indicators and therebyderive the value of the Hubble constant H (Ferrarese et al.2000; Gibson et al. 2000; Sakai et al. 2000; Mould et al.2000). The resulting value of H from the Key Project was72 ± − Mpc − (Freedman et al. 2001) where the totaluncertainty includes both random and systematic contribu-tions. More recent Cepheid-based estimates are very similarto this value, but with reduced uncertainties of 3 to 4% (Riesset al. 2011; Freedman et al. 2012; Sorce et al. 2012). The excellent angular resolution and photometric stabilityof HST has also made it possible to measure SBF with farbetter precision and to much larger distances than was possi-ble from the ground. For instance, Jensen et al. (2001) cal-ibrated the SBF method for the near-IR F160W bandpass ofthe NICMOS NIC2 camera on
HST (Thompson et al. 1999)and measured SBF distances to 16 galaxies beyond 40 Mpc,including the first SBF distances reaching beyond 100 Mpc.Stellar population effects on the NICMOS F160W SBF mag-nitudes were explored in detail by Jensen et al. (2003) usinga larger sample of 65 galaxies. In general, the SBF absolutemagnitude in a given bandpass depends on stellar populationand must be calibrated using a population indicator, typicallya broadband color.Following the installation of the Advanced Camera for Sur-veys (ACS) on
HST , Mei et al. (2005b) produced the first cal-ibration of the SBF method for the ACS Wide Field Channel(ACS/WFC) using F475W ( g ) and F850LP ( z ) data for84 galaxies from the ACS Virgo Cluster Survey (ACSVCS;Côté et al. 2004). In that work, the z SBF measurementswere calibrated for stellar population variations based on theobserved ( g − z ) color; the resulting distances enabled thefirst clear resolution of the depth of the Virgo cluster and pro-vided constraints on its triaxial structure (Mei et al. 2007). Inother studies based on ACS/WFC observations, Cantiello etal. (2005, 2007) measured multi-band SBF and color gradi-ents in 21 galaxies, and Biscardi et al. (2008) made the firstoptical SBF measurements beyond 100 Mpc. As part of theACS Fornax Cluster Survey (ACSFCS; Jordán et al. 2007),Blakeslee et al. (2009) refined the SBF calibration for theACS F850LP bandpass and determined the relative distanceof the Virgo and Fornax clusters to a precision of 1.7%. Ad-ditional ACS/WFC SBF measurements and a new calibrationfor the F814W bandpass were published by Blakeslee et al.(2010). The launch of Wide Field Camera 3 with its powerfulIR channel (WFC3/IR) has greatly increased the distance towhich SBF measurements can be made within a single HST orbit. However, the method must first be calibrated for se-lected WFC3/IR passbands as done previously for NICMOSand ACS; this is the primary goal of the present work.1.3.
SBF Measurements in the Infrared
The development of new infrared detectors in the 1990s al-lowed researchers to successfully apply the SBF techniquesto IR images for the first time (Luppino & Tonry 1993; Pahre& Mould 1994; Jensen, Luppino, & Tonry 1996). Becausethe SBF signal is dominated by the most luminous stars in apopulation, and these tend to be quite red for evolved galax-ies, SBF magnitudes are much brighter in the near-IR than atoptical wavelengths. Additionally, extinction by dust (both inour Galaxy and in the target galaxy) is much lower at near-IR wavelengths. Depending on how it is distributed, dust caneither reduce the fluctuation signal (as for a uniform screenof foreground dust in the Galaxy), or, more commonly, biasthe fluctuation signal towards higher amplitudes and shorterSBF distances, as would occur if dusty regions were clumpyon scales comparable to the size of the point-spread function(PSF). Clumpy dust is often associated with recent star for-mation, and bright young stars seriously bias SBF measure-ments as well. The contrast between the fluctuations and otherpoint-like sources (globular clusters and background galax-ies) is also higher in the near-IR bands, reducing yet anothersource of uncertainty in the SBF measurement. While thebackground in the IR is higher than at optical wavelengths,nfrared SBF Distances Using WFC3 3the increased strength of the SBF signal more than compen-sates, especially from space, where the thermal backgroundat 1.1 and 1.6 µ m is not significant. The benefit of the muchlower background, combined with the excellent image qual-ity and a very stable PSF, usually makes near-IR SBF mea-surements with HST much more accurate than measurementsfrom ground-based facilities.However, the calibration of the SBF magnitudes as a func-tion of stellar population is potentially more complicated inthe near-IR. As noted above, the trend of SBF magnitudewith galaxy color is used for calibrating the SBF distancemeasurements, both at optical and IR wavelengths. At op-tical wavelengths, the effects of age and metallicity variationson the SBF calibration relations are largely degenerate, butthis degeneracy begins to break down in near-IR, and thiscan reveal interesting differences in the stellar populationsof galaxies. Bluer elliptical and S0 galaxies typically showsigns of intermediate-age populations, and the asymptotic gi-ant branch (AGB) stars associated with those populations pro-duce brighter fluctuations (Jensen et al. 2003; Mieske, Hilker,& Infante 2003, 2006). The stellar population variations maytherefore produce more scatter in IR SBF distance calibration,but the brightness of the fluctuations at these wavelengthsmake them measurable to much larger distances; thus, it isworth characterizing the behavior and limits of the calibrationas well as possible.In this paper we report the results of a study to calibratethe IR SBF distance measurement technique using new SBFmeasurements in the F110W ( J ) and F160W ( H ) band-passes of WFC3/IR on HST . The calibration sample includes16 galaxies spanning a wide range in galaxy luminosity andcolor. The following section describes the observations andsample in more detail. Section 3 discusses the data reductionsand SBF measurements. New SBF calibrations in J and H are presented in Section 4, while implications of the SBFmeasurements for the galaxy stellar populations are discussedin Section 5. We provide our recommendations for measuringSBF distances with WFC3/IR in Section 6, before concludingwith a summary. WFC3/IR OBSERVATIONSIn order to calibrate the SBF method for WFC3/IR, weselected 16 early-type galaxies, eight in each of the Virgoand Fornax clusters, that already had high-quality ACS SBFmeasurements in z and ( g − z ) colors (Blakeslee et al.2009). Table 1 lists the properties of the galaxies that weretargeted in HST program GO-11712 (PI: J. Blakeslee). Thegalaxies were chosen to cover the full color range of theACSVCS and ACSFCS samples so that the resulting cali-bration would be as generally applicable as possible. More-over, the NICMOS SBF calibration exhibited increased scat-ter for bluer galaxies (Jensen et al. 2003), as have ground-based I -band SBF measurements (Mieske et al. 2006); ex-ploring a broad color range should help us understand wherethe WFC3/IR calibration becomes less reliable.Each of these 16 galaxies were observed for one orbit, splitapproximately equally between the J and H filters, withfour dithered exposures in each filter and total exposure timesvarying with target visibility. The same dither pattern wasused for each galaxy.For this study we also downloaded archival WFC3/IR H data for NGC 4258 (GO-11570, PI: A. Riess) and NGC 1316(GO-11691, PI: P. Goudfrooij). NGC 4258 is a late-typegalaxy with a H O masers in Keplerian orbits around a cen- tral black hole, enabling a geometric estimate of the distance(Greenhill et al. 1995; Miyoshi et al. 1995; Herrnstein et al.1999). While not ideal for SBF analysis, the importance ofthis galaxy to the absolute calibration of the extragalactic dis-tance scale makes it an important target worthy of a trial SBFmeasurement. NGC 1316 is an early-type S0 galaxy in theFornax cluster with extensive dust and signs of recent merg-ing. Although it is also a poor SBF candidate, it is a usefulcomparison galaxy for this study because it has hosted four type Ia supernovae.Tables 2 and 3 list the exposure times and sky brightnessesfor the all the J and H observations used in this study.Additional information in these tables is discussed in the fol-lowing sections. SBF MEASUREMENTSThe spatial fluctuations in the surface brightness of asmoothly distributed population of stars, as found in ellip-tical and lenticular galaxies, arise due to the Poisson statis-tics of the discrete stars making up the galaxy, even whenthe stars cannot be resolved or detected individually (Tonry& Schneider 1988). The SBF amplitude scales inversely withthe square of the distance: nearby galaxies appear “bumpy”compared to more distant galaxies, where more stars are sam-pled by each resolution element and the √ N variation be-tween regions is therefore a smaller fraction of the total num-ber of stars. The fluctuations, which are dominated by themost luminous stars in a population, are blurred by the PSF;additional contributions to the fluctuation signal arise fromclumpy dust, globular clusters, background galaxies, and fore-ground stars. The process of making an SBF measurementconsists of extracting and fitting the spatial Fourier powerspectrum of the stellar fluctuations convolved with the PSFpower spectrum and removing the contributions from extrane-ous sources. The resulting fluctuation power is used to com-pute the fluctuation magnitude.Procedures for measuring surface brightness fluctuationshave been described in detail by several authors (e.g., Tonryet al. 1990, 1997; Blakeslee et al. 1997; Jensen et al. 1998;Mei et al. 2005a; Fritz 2012). The description here providesa concise overview of the process steps that are either uniqueto this study or are particularly relevant to the WFC3/IR SBFmeasurements. 3.1. Data Reduction
The first step in the SBF data reduction process involvesproducing a calibrated, combined, and background-subtractedimage ready for further SBF analysis. We used the imagesfrom the
HST archive reduced using the standard pipelinethrough the flat-fielding stage ( flt files). From that point, weadopted a reduction procedure that differs from the standardpipeline.We combined the individual flat-fielded exposures using in-teger pixel shifts after fitting each image for background andidentifying cosmic rays; in order to avoid introducing corre-lated noise between pixels, fractional pixel registration was not used. Using integer pixel shifts results in slightly lowerspatial resolution in the combined image, but preserves theindependence of noise from pixel to pixel, which is importantfor fitting the SBF power spectrum.In a second difference from the standard pipeline reduc-tion, the clean combined images were not corrected for theWFC3/IR geometrical distortion nor combined using astro-drizzle . Our analysis therefore includes the ∼
10% difference Jensen et al.
TABLE 1G
ALAXY P ROPERTIES
Galaxy Cluster a Type b m B c R e d M B e R e f A J g Alt ID h (mag) (arcsec) (mag) (kpc) (mag)IC 1919 F dS0 13.5 21.2 − − − − − − − − − − − − − − − − a Cluster: V for Virgo and F for Fornax. b Morphological type from the ACSVCS (Côté et al. 2004) and ACSFCS (Jordán et al. 2007). c Apparent B -band magnitude (Vega). d Effective radius in arcseconds, determined from the ACS and/or SDSS imaging (Ferrarese et al.2006; Chen et al. 2010; P. Côté, priv. comm.). e Absolute B magnitude (Vega), corrected for Galactic extinction, and assuming distances of 16.5and 20.0 Mpc for galaxies in Virgo and Fornax, respectively. f Effective radius in kpc, assuming same Virgo and Fornax distances as above. g Galactic extinction (Vega mag) in J -band, from Schlafly & Finkbeiner (2011). h Alternate names from Virgo and Fornax Cluster Catalogs (Binggeli et al. 1985; Ferguson 1989),or alternate NGC designation in the case of NGC 1344. in plate scale between the x and y axes, causing our imagesto appear somewhat narrower horizontally than they do on thesky (Fig. 1). The SBF procedure involves taking the spatialFourier power spectrum, and correlated noise between pix-els resulting from fractional pixel shifts and interpolated pixelvalues when correcting for geometrical distortion can producea slope in the white noise component of the power spectrum.Finally, we chose not to apply the correction to pixel sizein the y -axis of WFC3/IR images. The pixel map correctionusually used for WFC3/IR corrects for PSF variations but isinappropriate for extended objects. The WFC3/IR focal planeis tilted, and the size (area) of the pixels on the sky variesby ∼
8% from the center to the upper and lower edges ofthe frame (Kalirai et al. 2010). When the data are dividedby the flat field image (as is done for the flt files in the HST archive), the varying pixel sensitivity is removed, effectivelymaking the pixels equally sensitive to uniform illumination.Flattening the images in this way creates a variation in sensi-tivity for point sources from the center to the top and bottomedges that is usually corrected in the pipeline data reductionprocess using astrodrizzle . Since we are interested in accu-rately measuring the surface brightnesses of the galaxies andavoiding correlated noise between pixels, we chose not to cor-rect for pixel size variation in our SBF data reduction process.The practical effect of this decision is that the PSF at the ex-treme upper and lower regions of the image does not matchthe PSF near the center. We have carefully chosen PSF refer-ence stars from the same vertical region of the field of viewas the galaxies being analyzed (usually very near the center)to avoid any systematic offset between the PSF photometricnormalization or power spectrum shape and the galaxy fluc-tuations. The chosen PSF stars were all unresolved, isolatedfrom other bright objects, and much brighter than the globularcluster population. 3.2.
Measuring Fluctuations
SBF measurements are made by fitting the Fourier spatialpower spectrum of the stellar fluctuations in a given regionof a galaxy with the normalized power spectrum of the PSF.There are several steps to produce the spatial power spec-trum: (i) the background level is estimated and subtracted;(ii) extraneous objects (globular clusters, background galax-ies, and dusty regions) are identified, measured, and masked;(iii) a smooth isophotal model is fitted to the galaxy profileand subtracted; (iv) isolated bright stars are extracted and usedto determine the power spectrum of the PSF; (v) the Fourierpower spectra are computed for the stellar fluctuations, themasked galaxy profile, and the PSF; and (vi) the power spec-trum of the data is fitted and normalized to determine the SBFpower in units of flux, with the power from undetected globu-lar clusters and galaxies subtracted, from which a fluctuationmagnitude is computed in the established way (e.g., Tonry &Schneider 1988; Jensen et al. 1998; Mei et al. 2005a).It is important to accurately measure and subtract the IRbackground before computing fluctuation magnitudes. Esti-mating the background level was done in an iterative processof cross-checking values measured in different ways. Forthe small galaxies, we measured the flux in the corners ofthe frames. For the larger ellipticals, we also determined thebackground using the best fit to a r / profile for each galaxy.These estimates were then compared to a measurement of thebackground made by iteratively computing a smooth modelfor each galaxy and looking at the residual background in thefield of view. By adjusting the sky level offset, we optimizedthe galaxy models such that the residual background was notsystematically positive or negative. The difference betweenthe sky values determined using the different methods wasused as an estimate of the uncertainty in the sky level, andnfrared SBF Distances Using WFC3 5 TABLE 2 J SBF M
EASUREMENTS
Galaxy Exposure Background Annulus (cid:104) gal / sky (cid:105) a gal/sky SBF S / N b m
110 c (sec) (AB mag/arcsec ) (arcsec) average range ( P − P r ) / P (AB mag) Fornax
IC 1919 997 21.74 8 – 33 1.3 0.9 – 2.6 33 28 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . Virgo
IC 3025 997 21.84 8 – 17 0.8 0.8 17 28 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . Supernova host
NGC 1316 1396 22.08 33 – 67 15 8 – 34 166 28 . ± . a Weighted average ratio of the galaxy surface brightness to sky background surface brightness within the measurementregion. b Weighted average ratio of the SBF fluctuation power to the white noise component P of the spatial power spectrum. c SBF magnitudes have been corrected for Galactic extinction using values from Schlafly & Finkbeiner (2011).TABLE 3 H SBF M
EASUREMENTS
Galaxy Exposure Background Annulus (cid:104) gal / sky (cid:105) a gal/sky SBF S / N b m
160 c (sec) (AB mag/arcsec ) (arcsec) average range ( P − P r ) / P (AB mag) Fornax
IC 1919 997 21.90 8 – 33 1.8 1.3 – 3.8 43 27 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . Virgo
IC 3025 997 21.76 8 – 17 0.3 0.3 27 27 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . Supernova host
NGC 1316 2796 21.85 33 – 67 21 9 – 36 111 27 . ± . Maser host
NGC 4258 2012 21.91 irreg. 10 47 47 25 . ± . a Weighted average ratio of the galaxy surface brightness to sky background surface brightness within the measurementregion. b Weighted average ratio of the SBF fluctuation power to the white noise component of the spatial power spectrum. c SBF magnitudes have been corrected for Galactic extinction using values from Schlafly & Finkbeiner (2011).
Jensen et al. F IG . 1.— Fornax (top two rows) and Virgo cluster galaxies (bottom two rows). Each image is displayed with background subtracted and using the same upperand lower limits and logarithmic stretch, within the same field of view 100 arcsec on a side. The bluer galaxies are on the left and the redder giant ellipticals areon the right. Measured values of ( g − z ) (AB) are shown next to the galaxy labels. nfrared SBF Distances Using WFC3 7 F IG . 2.— Fits to the spatial power spectra for the 16 galaxies in Fornax and Virgo (superimposed white line). The dashed lines indicate the scaled PSF powerspectrum and the white noise (flat) components. the SBF analysis was repeated to determine the uncertainty influctuation magnitude due to sky level uncertainty. The SBFmagnitude is normalized by the mean galaxy brightness at thelocation of the SBF measurement. For the smaller galaxieswith the lowest surface brightness (see Fig. 1), the backgroundlevel was most accurately measured. For the largest galaxiesthat extend beyond the limits of the field of view, the back-ground was most difficult to measure accurately, but its influ-ence on the SBF measurement was also minimal. The uncer-tainty in the SBF magnitude is therefore relatively insensitiveto the uncertainty in the background measurement.Typical background levels at J were 1.3 e − s − pix − , or22 . ± .
23 AB mag arcsec − ; at H we measured 0.67e − s − pix − , or 21 . ± .
15 AB mag arcsec − (see Tables 2 and3). These sky values were found to be consistent with pub-lished empirical measurements of the HST
IR background,which is dominated by scattered zodiacal light in the SolarSystem (Pirzkal 2014). The J background levels were alsoaffected by the diffuse upper-atmosphere He emission lineat 1.083 µ m (Brammer et al. 2014). While very few indi-vidual exposures were strongly affected, the residual back-ground variation among the data is larger at J than at H .The background variability between observations of differentgalaxies (see Tables 2 and 3) is not directly related to theuncertainty in the background measurement for a particulargalaxy, which was determined independently for each galaxy.After the background had been subtracted, we then iden- tified and masked any non-fluctuation point sources in thefield of view. Background galaxies and globular clusters wereidentified and their brightnesses measured using the SExtrac-tor software (Bertin & Arnouts 1996) and adopting aperturecorrections taken from the WFC3 instrument webpage. Westarted by making an initial fit to the galaxy and subtractingit to make it easier for SExtractor to identify and measure allthe compact objects in the field (we used a noise model forSExtractor that accounts for the subtracted galaxy and pre-vents the software from confusing the stellar fluctuations withglobular clusters). Using the SExtractor output, we then cre-ated a fit to the luminosity functions of the globular clustersand background galaxies. For most of the galaxies, we used aGaussian of width 1.2 mag to fit the luminosity functions; wefound that a width of 1.35 mag fit better for NGC 1399 andNGC 4472. We adopted a luminosity function peak absolutemagnitude of M V = − . M J = − .
26, and M H = − .
29 (e.g.,Harris 2001; Frogel et al. 1978). The background galaxies areassumed to follow a power law distribution with power lawslope of 0.25, which for most of our observations results in anormalization of about one to two galaxies per square arcsecat 34.50 mag AB (Retzlaff et al. 2010; Windhorst et al. 2011).These fits allowed us to integrate the contribution to the SBFsignal fainter than the completeness limit and correct the finalSBF magnitude accordingly. A mask was then created fromthe list of objects that removed all objects brighter than the Jensen et al.limiting cutoff magnitude.The next step was to fit a final smooth model to the galaxyprofile with the sky and point sources removed. We used aniterative procedure of fitting elliptical isophotes to the galaxysurface brightness profile, allowing the procedure to adjustthe centers, ellipticities, and orientations of the elliptical aper-tures. This model galaxy was later used to normalize the fluc-tuation signal.With the sky background and mean galaxy surface bright-ness removed and contaminating point sources masked, wethen computed the Fourier transform and spatial power spec-trum of the data in circular annuli (see Tables 2 and 3 forthe sizes of the annular regions). The measurements were re-peated using elliptical annuli for the six most elongated galax-ies with apparent radial gradients in their SBF magnitudes.The power spectrum was normalized by the mean galaxy lu-minosity so that the fluctuation amplitude should be the samein each annulus. The purpose of measuring fluctuations inmultiple annuli was to look for consistency between regionswith varying surface brightness, globular cluster population,and distance from the center. It also allowed us to measurethe radial gradients in fluctuation amplitude, and thus stellarpopulation, as described in Section 5.5.The measured fluctuation power spectrum is a convolutionof the pixel-to-pixel variation in the number of stars and thePSF of the instrument. We therefore require a robust measure-ment of the PSF power spectrum to determine the fluctuationamplitude. We extracted isolated bright stars from the centralregion of the detector field of view and computed their powerspectra. Because PSF stars are not all uniformly centered onthe pixels, there is some variation that naturally arises in thePSF power spectra. To determine which PSF stars best fit-ted the power spectrum for a particular galaxy, we combinedthe cleanest and brightest PSF stars from several observations,and then repeated the SBF measurements using a variety ofPSF stars. We computed the uncertainty in SBF magnitudeattributable to the PSF variations by determining the range ofplausible PSF fits based on the shape of the power spectraand the quality of the fits. We then used a common compos-ite PSF to measure SBF consistently in all the galaxies (thesame dither pattern was used for all the observations). As anadded check on the PSF uniformity and fit quality, we alsofitted the observed power spectra to the “Tiny Tim” PSF mod-els (Krist et al. 2011). The Tiny Tim model PSF for eachfilter was convolved with Gaussians of various widths to con-struct a library of model PSFs to provide better matches to thedata, which had been combined using integer pixel offsets andno geometrical distortion corrections (see Sec. 3.1). The SBFmagnitudes computed using the Tiny Tim model PSFs werethen compared to those derived from the combined empiricalPSFs and the range of plausible fits was used to determine theuncertainty due to PSF variations (typically 0.04 mag).Fluctuation magnitudes were computed by fitting the nor-malized PSF power spectrum to the galaxy power spectrum P ( k ) = P E ( k ) + P , where E ( k ) is the expectation power spec-trum, which includes the smooth galaxy profile and the com-bined annular region and external object mask, all convolvedwith the normalized PSF power spectrum (see Fig. 2 forpower spectra and fit components). The fits excluded thelowest wavenumbers k <
10, which are affected by large-scalegalaxy and sky subtraction errors. P is the white noise com-ponent, which is flat for uncorrelated pixel-to-pixel noise. The http://tinytim.stsci.edu/cgi-bin/tinytimweb.cgi scale factor used to best match the data corresponds to the fluxin SBF power in units of e − s − . It is then straight-forward tocompute the fluctuation magnitude: m = − . P − P r ) + M where P is the fluctuation power and P r is the contributionfrom point sources fainter than the completeness limit. M is the zero point for the filter+detector (26.8223 AB for J and 25.9463 AB for H ). The AB magnitude is 0.7595 maglarger than the Vega equivalent at J , and 1.2514 mag largerthan the Vega magnitude at H . AB magnitudes and colorswere corrected for Galactic extinction using the values pub-lished by Schlafly & Finkbeiner (2011). The ( g − z ) col-ors from Blakeslee et al. (2009) were adjusted to make themconsistent with the Schlafly & Finkbeiner extinction values.Individual sky background levels, exposure times, and SBF S / N values are listed in Tables 2 and 3.Absolute fluctuation magnitudes M and M (Table 4)were then computed using both individual distance modulusmeasurements and average cluster distances of ( m − M ) =31.51mag for the Fornax cluster and 31.09 for Virgo (all from theoptical ACS SBF measurements of Blakeslee et al. 2009). Theradial extent of each cluster (0.053 mag for Fornax and 0.085mag for Virgo) was adopted as the uncertainty on the aver-age cluster distance moduli. The colors originally reportedby Blakeslee et al. (2009) were recomputed for the aperturesused in this study (circular and elliptical).There are several sources of uncertainty in the SBF mea-surement procedure that we quantified by exploring the rangeof input parameters, as we did for the uncertainty due to thePSF fit. Average values (and ranges) of the uncertainties wemeasured and adopted for the final SBF measurements arelisted in Table 5. Not all sources of uncertainty are com-pletely independent—residual errors in sky subtraction canaffect the galaxy or PSF fit, for example—so the total uncer-tainties listed in Table 4 are not a simple quadrature additionof all sources listed in Table 5; we estimated the fraction ofthe power spectrum fit ( P ) uncertainty that results from thePSF fit and sky subtraction separately before adding all inde-pendent sources of error in quadrature. The distance modulusuncertainties were included in the individual-distance valuesof M . The cluster-distance M values include the cluster dis-tance dispersion values from Blakeslee et al. (2009) in thetotal uncertainty. ANALYSIS4.1.
Calibration of the WFC3/IR SBF Distance Scale
The SBF signal can be detected with
HST in modest J and H exposures (an orbit or less) out to ∼
100 Mpc (e.g.,Jensen et al. 2001). To take full advantage of WFC3/IR ob-servations of early-type galaxies collected for a variety ofpurposes and measure accurate distances, we calibrated theWFC3/IR J and H SBF distances by fitting the abso-lute fluctuation magnitudes M as a function of both optical( g − z ) and IR ( J − H ) colors. Determining the M val-ues requires us to adopt a distance modulus ( m − M ) for eachgalaxy. We used the z SBF distance moduli measured usingACS (Blakeslee et al. 2009). These measurements provide aconsistent distance reference accurate to (cid:46) g − z ) < .
05 mag. We also adopted( g − z ) values from the same ACS data, supplementingnfrared SBF Distances Using WFC3 9 TABLE 4A
BSOLUTE
SBF M
AGNITUDES
Galaxy ( m − M ) a ( g − z ) b ( J − H ) M M M M Fornax
IC 1919 31 . ± .
073 1 . ± .
037 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
086 1 . ± .
013 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
068 1 . ± .
007 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
070 1 . ± .
011 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
072 1 . ± .
029 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
075 1 . ± .
007 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
091 1 . ± .
005 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
072 1 . ± .
006 0 . ± . − . ± . − . ± . − . ± . − . ± . Virgo
IC 3025 31 . ± .
130 0 . ± .
074 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
133 1 . ± .
030 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
134 1 . ± .
060 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
080 1 . ± .
040 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
070 1 . ± .
049 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
075 1 . ± .
006 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
069 1 . ± .
014 0 . ± . − . ± . − . ± . − . ± . − . ± . . ± .
079 1 . ± .
006 0 . ± . − . ± . − . ± . − . ± . − . ± . Supernova host
NGC 1316 31 . ± .
065 1 . ± .
007 0 . ± . − . ± . − . ± . − . ± . − . ± . Maser host
NGC 4258 29 . ± .
048 1 . ± . ··· ··· ··· − . ± . ··· N OTE . — All magnitudes are on the AB system and extinction corrected. a Blakeslee et al. (2009) except NGC 4258, Humphreys et al. (2013). b Galaxy colors from Blakeslee et al. (2009) have been updated to match the apertures used in this study, and corrected for extinctionusing Schlafly & Finkbeiner (2011). c M computed using the individual distance moduli shown in the second column. d M computed using average cluster distances of 31.51 mag for Fornax and 31.09 for Virgo. Uncertainties on M include the cluster depthsof 0.053 mag (Fornax) and 0.085 mag (Virgo).TABLE 5A VERAGE U NCERTAINTIES
Source σ (mag) Range (mag)Power spectrum fit P g − z ) color uncertainty 0.025 0.005 – 0.074( J − H ) color uncertainty 0.013 0.002 – 0.036Distance modulus (individual) 0.086 0.068 – 0.134Distance modulus (Virgo) 0.085 0.085Distance modulus (Fornax) 0.053 0.053Total statistical M uncertainty 0.10 0.08 – 0.17 the published values from Blakeslee et al. (2009) with up-dated color measurements made using the original images inannuli that matched our IR observations. The ACS colors anddistance moduli used to calibrate the IR SBF distance scaleare listed in Table 4. Extinction-corrected ( J − H ) colorswere measured using our WFC3/IR images.As in optical bandpasses, the intrinsic luminosity of IR fluc-tuations varies with galaxy color. The SBF amplitude is sen-sitive to the brightness of the most luminous stars in a pop-ulation, and bluer galaxies with a significant component ofyoung or intermediate-age stellar populations have luminousAGB stars that enhance the SBF signal (e.g., Jensen et al.2003). An accurate IR SBF distance calibration must takeinto account the brightening of fluctuations at intermediateand bluer colors. As in the previous F160W NICMOS cali-bration (Jensen et al. 2003), a linear fit to the red end of thesample was found to best represent the SBF calibration fordistance measurements of typical giant elliptical galaxies. Todetermine the best slope of M as a function of galaxy color (see Figs. 3 and 4), we adopted an iterative procedure thattakes into account the uncertainties in both the M and coloraxes. We started by making an initial approximate fit ignoringthe color uncertainties (i.e., using a standard least-squares ap-proach). We computed the error ellipse for each point and thedistance from the fitted line in units of the combined x and y uncertainties. Because the z SBF distances are also a func-tion of ( g − z ), there is a small correlation between the x and y -axis uncertainties when fitting the individual-distance M values vs. ( g − z ). We included the rotation of the er-ror ellipse for that subset of the calibration fits. We then iter-atively adjusted the fit coefficients to minimize the combineddifference between the line and the data points, and then com-puted the rms in M . This procedure was repeated for each ofthe filters for both ( g − z ) and ( J − H ), and for the twosets of M values derived from individual and common clus-ter distances. The coefficients and rms scatter for each fit arelisted in Tables 6 and 7.The intrinsic scatter in the optical SBF distance measure-ments is comparable to the Virgo and Fornax cluster depthsas estimated by Blakeslee et al. (2009) (0.053 mag for For-nax, 0.085 mag for Virgo). Depending upon the location ofthe galaxy within the cluster, the error in the estimated dis-tance may be larger when adopting the cluster mean or whenusing the individual galaxy distance. If the typical distancemeasurement error (including intrinsic scatter about the stel-lar population calibration) is less than the magnitude of thescatter from cluster depth, then it makes sense to calibrate theIR measurements using individual optical SBF distances. Ifthe optical SBF distance measurement errors dominate, thenit would be better to average all the optical SBF measure-ments and use a common cluster distance to calibrate the IRmeasurements. In the case of Fornax, the individual distance0 Jensen et al. F IG . 3.— Fits to the absolute fluctuation magnitudes M as a function of ( g − z ) color. We also plot M for NGC 4258 for comparison. The calibration shownon the left is based on distances derived using the individual z -band SBF distances. The panel on the right shows the calibration using average cluster distancesfor Virgo and Fornax. Red points indicate H measurements (top set) and blue symbols are the J measurements (lower set). The dashed calibration linesshow the quadratic fit and the linear calibration including IC 1919; the color of IC 1919 is intermediate between the other blue dwarf galaxies and the ellipticalgalaxies in our sample. errors are larger than the scatter from cluster depth; the situ-ation is less clear in Virgo, especially for the bluer galaxies.Table 6 presents calibrations computed using both individualdistance moduli and average cluster distances of 31.09 magand 31.51 mag for Virgo and Fornax, respectively (Blakesleeet al. 2009). The linear calibrations using cluster distances arenot significantly different, particularly for the bright ellipticalslocated near the centers of the clusters, but the rms scatter issomewhat lower using the cluster distances.The downturn in absolute SBF magnitude at the blue endis dominated by the four dwarf galaxies in Virgo. The fourbluest galaxies have the largest color uncertainties and ranges,the lowest SBF S / N ratios, the lowest galaxy brightness com-pared to the sky, and the largest radial gradients in fluctuationamplitude. They also show evidence of a wide range in stellarpopulation age and metallicity, as manifested in their large ra-dial color and fluctuation magnitude gradients (the error barsshown in Figures 3 and 4 are larger than the measurement er-rors, and include the range of values due to radial gradientsas described below in Section 5.5). These four Virgo galaxieswere excluded from the linear calibration fits; IC 1919 wasexcluded from the ( g − z ) fits as well. Because the fluc-tuation amplitude is significantly lower in the bluest galaxiesin this sample, we also present an alternative second orderpolynomial distance calibration fit that can be used for loweraccuracy distance measurements of bluer galaxies (Figs. 3 and4). The quadratic fits were computed using the same iterativeprocedure that was used to make the linear fits, as describedabove. Higher-order fits are not justified given the samplesize, measurement uncertainties, and large population varia-tions between blue dwarf elliptical galaxies. The linear cali-bration is not useful for the bluer galaxies; they have too muchpopulation variation for SBF to be generally useful as a dis-tance indicator. The quadratic calibration may be used to getapproximate distances for bluer galaxies when necessary.Calibration coefficients are shown in Tables 6 and 7. The coefficients are defined as follows: M = a + b [( g − z ) − . + c [( g − z ) − . (1) M = a + b [( J − H ) − . + c [( J − H ) − . (2)where c = 0 for the linear fits.For ( g − z ) > .
2, researchers measuring distancesshould use the appropriate linear calibrations centered at themean galaxy color as follows: M = ( − . ± . + (2 . ± .
15) [( g − z ) − .
4] (3) M = ( − . ± . + (2 . ± .
27) [( g − z ) − . . (4)The quadratic fits may be used for bluer galaxies, bearingin mind that the intrinsic scatter between blue galaxies islarge. Quadratic fits are not shown for M computed usingcluster distances because two of the bluest Virgo galaxieshave individual optical SBF distance moduli that differ fromthe mean cluster modulus for Virgo by − probably outside theVirgo cluster core and should not be included in a calibrationbased on mean cluster distances.If ( g − z ) colors are not available, distances may becomputed using the ( J − H ) color instead. The scat-ter in the calibration with ( J − H ) is larger than with( g − z ) because the color range spanned is much smaller.For ( J − H ) > .
2, the following relations centered at themean galaxy color should be used: M = ( − . ± . + (6 . ± .
9) [( J − H ) − .
27] (5) M = ( − . ± . + (7 . ± .
1) [( J − H ) − . . (6)For magnitudes on the Vega system, subtract 0.7595 mag from J AB and 1.2514 mag from H AB for the WFC3/IR fil-ters. The ( J − H ) color can be shifted to the Vega systemby adding 0.4919 mag.The results of our calibration analysis show that IR SBFmeasurements, especially in F110W, can produce high-nfrared SBF Distances Using WFC3 11accuracy distance measurements for red early-type galaxieswith ( g − z ) > . J − H ) > . Independent Checks of the IR SBF CalibrationZero Point
Now, as for several decades, the forefront of progress in themeasurement of extragalactic distances is limited primarily bythe uncertainty in the calibration zero point (e.g., Freedman &Madore 2010; Riess et al. 2011). We have chosen to calibratethe WFC3 IR SBF distance scale using the extensive Virgoand Fornax optical SBF measurements made by Blakeslee etal. (2009) and their collaborators. This guarantees that theIR observational uncertainties and population variations willdominate the calibration uncertainty, not the precision of thereference distances. It does not, however, reduce the system-atic zero point uncertainty present in the optical SBF mea-surements, which in turn were based on
HST
Cepheid dis-tances (Freedman et al. 2001). Blakeslee et al. (2010) dis-cuss in detail the small offsets between several of the largestSBF surveys, including Tonry et al. (2001) and Jensen et al.(2003), and the application of metallicity corrections to the
HST
Cepheid distance scale of Freedman et al. (2001). Thesystematic uncertainty in the SBF distance scale due to theuncertainty in the Cepheid zero point is about 0.1 mag (Freed-man & Madore 2010; Blakeslee et al. 2010).One approach for avoiding the Cepheid zero point uncer-tainty would be to use theoretical stellar population modelpredictions to calibrate the absolute M in galaxies of varyingages, metallicities, and colors. This model-based approachwould therefore make SBF a primary distance indicator inde-pendent of all other distance measurements, dependent onlyon our understanding of the luminosities and colors of redgiants and other evolved stars of a particular age and metal-licity. Comparisons with several different stellar populationmodels are presented below in Section 5. As will be shown,infrared stellar population models are not sufficiently consis-tent to provide a robust zero point for distance calibration atthe 10% level. At present, we find that observed IR SBFmagnitudes are more useful for constraining stellar populationmodels than the models are for constraining the SBF distancecalibration in the IR.Another approach is to find other distance indicators thatare independent of the Cepheid calibration, such as the ge-ometrical distance to NGC 4258. Water masers orbiting thecentral black hole in NGC 4258 have now been used to ac-curately determine the distance to this galaxy using a purelygeometrical technique based on the Keplerian orbits of themasers (Humphreys et al. 2013). While SBF magnitudesare best measured in early-type galaxies, archival H im-ages of the central bulge of NGC 4258 (GO-11570) providedus with an opportunity to explore the SBF calibration inde-pendent of the Cepheid distance scale. Given that an SBFmeasurement to NGC 4258 could allow us to bypass the sys-tematic uncertainty in the Cepheid calibration, we felt it was worth an attempt. Unfortunately, the presence of clumpydust and recent star formation prevented us from achievingan accurate calibration using this galaxy, even when opticalcolor images were used to identify dusty regions. The maser-calibrated fluctuation magnitude is significantly brighter (by ∼ . g − z ) colors (see Fig. 3). This result was not asurprise; patchy dust adds to the fluctuation signal, as doesthe presence of younger populations containing bright AGBstars. Unfortunately, the geometrical distance to NGC 4258does not provide a useful direct calibration of the SBF tech-nique for elliptical galaxies. Given that optical Cepheid dis-tances to NGC 4258 have now been published by Macri etal. (2006), Fausnaugh et al. (2015), and Hoffmann & Macri(2015), the future value of NGC 4258 in calibrating IR SBFis therefore most likely to be through an improved calibrationof the Cepheid distance scale zero point and metallicity cor-rections.Type Ia supernovae are one of the most accurate andwidely-used distance measurement techniques in use today.In a recent paper, Cantiello et al. (2013) reported WFC3 J and H measurements of the SBF distance to NGC 1316, atype Ia supernova host galaxy in the Fornax cluster. They usedthe Jensen et al. (2003) F160W SBF calibration for NICMOS(including a metallicity correction to the Freedman et al. 2001Cepheid zero point) and applied a 0.2 mag offset to the NIC-MOS zero point to account for the difference in filter widthbetween NICMOS and WFC3/IR, based on predictions of theSPoT stellar population models (Raimondo 2009; Raimondoet al. 2005). To avoid uncertainties arising from differencesbetween the methods used by Cantiello et al. and those usedherein, we repeated the SBF analysis for NGC 1316 using theoriginal WFC3/IR data (GO-11691) and the procedures de-scribed above. Our measured SBF magnitudes are listed inTables 2 and 3; they are consistent with the Cantiello et al.(2013) values within the stated uncertainties. This galaxy isnot an ideal SBF candidate due to the presence of extensivepatchy dust near the center, but the regions farther out fromthe center appear relatively clean and the SBF signal is verystrong. If we adopt the Blakeslee et al. (2009) z -band SBFdistance (Table 4), the M values we find for NGC 1316 arebrighter than the calibration prediction by ∼ I -band SBF measure-ment of 31 . ± .
17 supports the Blakeslee et al. (2009) dis-tance for NGC 1316. If NGC 1316 is located at the same dis-tance as the core ellipticals in Fornax, then it appears to havea significant population of younger AGB stars, most likely theresult of star formation that took place during a major merg-ing episode a few Gyr ago, that biases the IR SBF magni-tude. It may also have additional undetected dust contribut-ing to the fluctuations. On the other hand, the IR and opticalSBF distances are inconsistent with the published type Ia su-pernova distances, which place NGC 1316 ∼ .
25 mag closerthan the Fornax cluster core. If we adopt the Ia supernovadistance modulus for the three normal supernovae publishedby Stritzinger et al. (2010) of 31 . ± . ± .
04 insteadof the z -band SBF distance, our IR SBF measurements wouldbe much more consistent with the elliptical galaxy calibration.Additional work is needed to reconcile the SBF and supernovadistances to this galaxy.The IR SBF measurements of the maser host galaxyNGC 4258 and the supernova host galaxy NGC 1316 are not2 Jensen et al. F IG . 4.— Fits to the absolute fluctuation magnitudes M as a function of ( J − H ) color derived using individual distances (left) and average cluster distances(right). Red symbols indicate H measurements (top set of points), and lower set of blue points are the J measurements. Symbol definitions are the same asin Figure 3. TABLE 6L INEAR C ALIBRATION C OEFFICIENTS
Calibration a b χ / dof rms Distances N gala M vs. ( g − z ) − . ± .
015 2 . ± .
15 0.48 0.075 clust 11 M vs. ( g − z ) − . ± .
017 1 . ± .
16 0.86 0.086 clust 12 M vs. ( g − z ) − . ± .
032 1 . ± .
32 1.23 0.101 indiv 11 M vs. ( g − z ) − . ± .
034 1 . ± .
34 1.40 0.105 indiv 12 M vs. ( J − H ) − . ± .
032 6 . ± . M vs. ( J − H ) − . ± .
047 5 . ± . M vs. ( g − z ) − . ± .
028 2 . ± .
27 1.35 0.114 clust 11 M vs. ( g − z ) − . ± .
029 1 . ± .
28 1.59 0.114 clust 12 M vs. ( g − z ) − . ± .
042 1 . ± .
42 2.49 0.138 indiv 11 M vs. ( g − z ) − . ± .
043 1 . ± .
44 2.45 0.134 indiv 12 M vs. ( J − H ) − . ± .
035 7 . ± . M vs. ( J − H ) − . ± .
050 6 . ± . OTE . — Linear fits for ( g − z ) > . J − H ) > .
22. For Vega magnitudes,subtract 0.7595 mag from WFC3/IR J and 1.2514 mag from H AB. a IC 1919 was excluded from the ( g − z ) calibration because ( g − z ) < .
2. The( J − H ) color for IC 1919 is greater than 0.22, so it was included in the ( J − H )calibration. We have included ( g − z ) calibrations with and without IC 1919 to showthe relatively small influence this one galaxy has on the ( g − z ) calibration. The recom-mended calibration in Equations (3) and (4) exclude IC 1919.TABLE 7Q UADRATIC C ALIBRATION C OEFFICIENTS
Calibration a b c χ / dof rms (mag) Distances M vs. ( g − z ) − . ± .
004 1 . ± .
025 4 . ± .
12 1.11 0.115 indiv M vs. ( J − H ) − . ± .
011 6 . ± . ± M vs. ( g − z ) − . ± .
003 1 . ± .
022 3 . ± .
09 2.17 0.128 indiv M vs. ( J − H ) − . ± .
030 6 . ± . ±
15 1.74 0.149 indivN
OTE . — Quadratic fits for all 16 galaxies. Use only when necessary for ( g − z ) < . J − H ) < . nfrared SBF Distances Using WFC3 13sufficiently accurate at present to reduce the systematic un-certainty in the IR SBF distance scale calibration to less thanthe 10% that we currently inherit from the Cepheid calibrationof the optical SBF distances used for this study (Blakeslee etal. 2009, 2010). These galaxies have significant patchy dustand recent star formation, both of which enhance the IR SBFsignal over what is typically observed in quiescent ellipticalgalaxies.4.3. Comparison of WFC3 and NICMOS SBF Magnitudes
Eight galaxies in our current sample, mostly in the Fornaxcluster, were included in the NICMOS NIC2 calibration of M (Jensen et al. 2003). A comparison of the SBF magni-tudes is shown in Figure 5. To make the comparison using ABmagnitudes, we added 1.313 mag to the published NIC2 SBFmagnitudes to shift from the Vega magnitude system used byJensen et al. (2003) to the AB mag system. The difference between NIC2 and WFC3/IR F160W SBFmagnitudes shows a modest color dependence (left panel inFig. 5). We fitted the slope (the color term in the conversionof NIC2 SBF magnitudes to WFC3/IR) including uncertain-ties in both ( J − H ) color and m SBF magnitudes; therms for the fit is 0.055 mag and the χ per degree of freedom is0.66. The right panel of Figure 5 compares the NIC2 F160Wapparent SBF magnitudes to WFC3/IR, with and without thecolor correction. The dashed line in the right panel of Fig-ure 5 is not a fit, but shows the 45-degree perfect correlationline. SBF m measurements made using NIC2 prior to theinstallation of the NICMOS cryocoolers may be compared toWFC3/IR measurements using the relation m = m , NIC2 − . J − H ) + .
46 (7)(all AB magnitudes). Because we are comparing apparentfluctuation magnitudes directly, we do not need to be con-cerned about differences in distance scale calibrations be-tween the two studies or cameras. STELLAR POPULATION MODELSWe turn now to how IR SBF measurements, with their sen-sitivity to red giant branch and intermediate-age AGB stars,can expose interesting differences between galaxies with dif-ferent star formation histories and better constrain single-burst stellar population models.The brightening of the SBF magnitudes in elliptical and S0galaxies at intermediate colors seen in the centers of Figures 3and 4, and the subsequent drop in SBF brightness in the bluestdwarf ellipticals in this sample, provide powerful new con-straints for stellar population models, which have only beencompared to redder galaxies in previous near-IR SBF studies.The scatter among the bluest galaxies in our sample is muchlarger than the observational uncertainties, and many of thesegalaxies exhibit significant radial gradients in IR fluctuationmagnitude, color, or both. The current sample includes bluerand fainter galaxies than are typically targeted for SBF dis-tance measurements, and the breaking of the age-metallicitydegeneracy in near-IR fluctuations provides a unique oppor-tunity to explore the stellar populations in these galaxies.Single-burst stellar population (often abbreviated SSP)models with constant age and metallicity are frequently usedto interpret broad-band colors and other properties of unre-solved stellar populations in distant galaxies, including SBF magnitudes. These models are usually calculated by integrat-ing collections of properly-weighted isochrones, and can beused to compute predicted SBF magnitudes directly withoutany need to link the apparent SBF magnitudes to an exter-nal distance scale calibration. Examples of theoretical SBFcomparisons include Worthey (1993, 1994), Liu et al. (2000,2002), Blakeslee et al. (2001), Cantiello et al. (2003), Rai-mondo et al. (2005), Marín-Franch & Aparicio (2006), Bis-cardi et al. (2008), and Lee et al. (2010).We compared our SBF measurements to three recent setsof SSP models for which J and H SBF magnitudes havebeen computed. The purpose of these comparisons is to ex-plore the limitations of our SBF distance calibration and pro-vide input to researchers working to improve stellar popu-lation models, particularly for understanding galaxy evolu-tion, when the observations may not so easily distinguish theeffects of age and metallicity as our near-IR SBF measure-ments do. While we compared our IR SBF measurements tosingle-burst population models, real galaxies are composedof composite stellar populations with potentially many burstsof star formation. Because the fluctuations are dominated bythe most luminous stars weighted as L , they are even morestrongly weighted towards young, luminous populations thanare broad-band galaxy colors (Tonry & Schneider 1988). Acomposite population model will therefore predict an SBFmagnitude close to that of the younger (or brighter) modelcomponent, even when the young population is only a smallfraction ( ∼
10% to 20%) of the galaxy by mass (Jensen et al.2003; Blakeslee et al. 2001; Liu et al. 2002). The comparisonto SSP model ages shown in this section should be consideredthe time since the most recent episode of star formation, notthe average age of the dominant stellar population by mass.5.1.
Teramo BaSTI Models
The first set of stellar population models we consider hereare based on the Teramo BaSTI models using a standardSalpeter initial mass function (IMF) with a low-mass cutoff of0.5 M (cid:12) (Lee, Worthey, & Blakeslee 2010; Pietrinferni et al.2004, 2006; Cordier et al. 2007). We compared our observedfluctuation magnitudes M to absolute fluctuation magni-tudes computed for two variants of the BaSTI models: thesolar-scaled abundance ratio models without convective over-shoot, and the α -enhanced version of the models describedby Lee et al. (2010). The latter models have a mean [ α /Fe]of ∼ α elements (i.e., O, Mg, Si,S, Ca, Ti); the [Fe/H] abundances in these models have beencorrespondingly reduced to keep a fixed [Z/H].The solar-scaled models shown in the top panel of Figure 6do not match the reddest giant ellipticals as well as the α -enhanced models shown in the lower panel (the solar-scaledmodels are included here to provide a point of referencewith past SBF-model comparisons that only used solar-scaledmetallicity models). Both model variations suggest that theintermediate-color galaxies in our sample have younger pop-ulations, as expected due to the presence of intermediate-ageAGB stars. The models imply that the bluest galaxies are oldand metal-poor. While we have chosen to show the compar-ison for M and ( g − z ), the conclusions are the samewhen we compare the models to M instead of M or( J − H ) instead of ( g − z ). http://193.204.1.62/index.html F IG . 5.— Comparison of NICMOS NIC2 and WFC3/IR H SBF measurements. The left panel shows the fit to the color term used to correct the points in theright panel, which shows the corrected NIC2 SBF magnitudes plotted as a function of the WFC3/IR SBF magnitudes. For reference, the SBF magnitudes withno color correction are shown with × symbols.F IG . 6.— Teramo BaSTI models compared to M as a function of galaxy( g − z ) color for two metallicity variants of the models computed usingthe individual galaxy distances: the “SSS” models (top panel) are solar-scaledabundances spanning the range from [Fe/H]= − .
659 to +0.395. The “AES”models (lower panel) have enhanced α element compositions and reduced[Fe/H] to make the overall metallicity Z the same as the solar-scaled modelsshown in the top panel. The range of [Fe/H] spanned by the AES modelsis − Teramo SPoT Models
The second set of models was developed by the TeramoSPoT group (version BaSeL3.1, Raimondo 2009; Raimondoet al. 2005). The Teramo SPoT models pay special attentionto the thermally-pulsating asymptotic giant branch (TP-AGB)stars, particularly in young to intermediate-age populations.The SPoT model SBF magnitude predictions in the near-IRhave been empirically compared to a variety of clusters in theLarge Magellanic Cloud and have been shown to match em-pirical measurements of SBF magnitudes, integrated magni-tudes, star counts, and colors (Raimondo 2009; Cantiello etal. 2007; Cantiello 2012).The SPoT models in Figure 7 differ significantly fromthe BaSTI models in Figure 6, although they are based onthe same stellar evolutionary tracks as the BaSTI models inthe upper panel of Fig. 6. The SPoT models derive SBF F IG . 7.— Recent versions of the Teramo SPoT models compared to M measurements as in Figure 6. The metallicity range for these models spans[Fe/H]= − .
66 to +0.4 and the ages from 2 to 14 Gyr. The lines and symbolsare defined in the same way as in Figures 3 and 6. magnitudes in a procedure that allows modelers to statisti-cally combine various stellar population models produced bystochastic variations in the number and properties of brightand rare stars, including the TP-AGB and horizontal branchpopulations in intermediate-age and old stellar populations.Overall, the SPoT and BaSTI models agree for the red andintermediate-color ellipticals, with somewhat fainter SBFmagnitudes for the oldest and most metal-rich giant ellipti-cals. The SPoT models predict a larger spread in SBF mag-nitude at younger ages and imply that the bluer galaxies inthe sample are all younger than about 5 Gyr, in contrast withthe BaSTI models, which span a narrower range in M andimply ages greater than 5 Gyr for the bluest galaxies.5.3. Padova Models
The third set of models are based on the Padova isochrones(Fig. 8), which include sophisticated handling of the TP-AGBevolutionary phase. The Padova tracks use solar-scaled metal-licity abundance ratios and do not include α -element enhance-ment. SBF magnitudes were computed by Lee et al. (2010)using the evolutionary tracks of Marigo et al. (2008).The Padova SSP models show the largest spread in M of all the models considered here. At the red end, the giantellipticals again agree with old, metal-rich population mod-nfrared SBF Distances Using WFC3 15 F IG . 8.— Stellar population models based on the Padova isochrones com-pared to M measurements computed using individual SBF distances. Thesymbol definitions are the same as in Figure 3. Lines of constant metallicityfrom [Fe/H]= − .
705 (in the extreme lower left corner) to 0.0 and +0.222(overlapping at right) are shown with red dashed lines. Lines of constant agefrom 2 to 13 Gyr are plotted with dotted blue lines. els, with the intermediate bluer galaxies having brighter fluc-tuations and younger populations. The bluest galaxies inthe sample are consistent with ages intermediate between theBaSTI and SPoT models, in the range 3 to 7 Gyr. Because oftheir larger spread in SBF magnitude predictions, the Padovamodels, as compared to the other sets of models, suggestthat the data provide better discrimination between ages andmetallicities. 5.4.
Fluctuation Colors
SBF measurements at two wavelengths can be used to elim-inate uncertainties resulting from distance error; for instance,the “fluctuation color” ( m − m ) can be compared to stel-lar population models in a distance-independent way. Figure 9compares ( m − m ) to the Teramo BaSTI solar-scaled and α -enhanced models as a function of ( g − z ). As discussedby Lee et al. (2010), the predicted SBF magnitudes are sen-sitive to α -element abundance mostly because of the effectsof oxygen-enhancement on the upper red giant branch andAGB phase. The data in Figure 9 agree on average with the α -enhanced models relatively well, but only poorly with thesolar-scaled models. However, this set of α -enhanced mod-els also predicts a narrower range of ( m − m ) than is ob-served. In particular, the low-mass dwarf IC 3032 in Virgoagrees better with the locus of the solar-scaled models; thismay indicate real variation in α -element abundance ratiosamong the sample galaxies. We conclude that fluctuation col-ors can provide useful information on elemental abundanceratio trends with age and metallicity in elliptical galaxies, in-dependent of the uncertainties in the distance calibration. Inaddition, comparisons with other observables that are sen-sitive to age, metallicity, or α -enhancement should providepowerful joint constraints for future stellar population mod-els. 5.5. Radial SBF Gradients
To further explore the origins of the scatter in SBF mag-nitude among the low-luminosity blue dwarf ellipticals, wemeasured the radial behavior of the SBF amplitude. Manyof the galaxies in our sample, particularly the low-luminositygalaxies, are quite elliptical. To get the cleanest gradient mea-surements possible, we repeated the SBF analysis and mea-sured ( g − z ) colors in elliptical annuli for a subset of the F IG . 9.— Distance-independent IR fluctuation colors for the solar-scaledand α -enhanced Teramo models. Blue dotted lines indicate lines of con-stant age, from 2 to 13 Gyr. Red dashed lines show constant metallicitytracks, from [Fe/H]= − .
659 at the left to +0.395 at right (upper panel) and[Fe/H]= − .
01 to +0.05 (lower panel). The two points that are not labeled forclarity are NGC 1399 in Fornax and NGC 4636 in Virgo. Symbol definitionsare the same as in Figures 3 and 6.F IG . 10.— Radial SBF and color gradients for the survey galaxies, withlarger symbols corresponding to the inner annuli in which SBFs were mea-sured and smaller symbols being outer regions. Black lines link measure-ments in the same galaxy. The measurements are compared to the BaSTI α -enhanced models; the conclusions are the same for the other models be-cause they all have lines of constant metallicity with similar slopes for thiscolor range. IC 2006 is not labelled but falls very close to NGC 1374. galaxies with significant M gradients (IC 1919, NGC 1375,NGC 1380, IC 3025, IC 3487, and IC 3586; see Fig. 1). Forthe rest of the sample we used the circular annulus SBF and( g − z ) color measurements previously used for the cali-bration. The results are plotted in Figure 10.The comparison of radial SBF gradients to the modelsshows a significant difference between the giant ellipticalsand the smaller galaxies. Most of the galaxies show a gra-dient sloping from upper left to lower right in Figure 10,roughly along lines of constant metallicity. While the vari-ous models look quite different in detail, they all have linesof constant metallicity sloping in approximately the same di-rection at the relevant colors. The lower-luminosity galax-ies have centers (larger symbols in Fig. 10) consistent withyounger stellar populations (brighter fluctuations) and nearlyconstant metallicities: IC 1919, IC 3025, IC 3487, IC 3586,and NGC 1375 all have brighter fluctuations near their cen-6 Jensen et al.ters. In contrast, the giant ellipticals on the red end of thediagram tend to show older, and sometimes more metal-rich,populations in their centers: IC 3032, IC 2006, NGC 1374,NGC 1399, NGC 1404, NGC 4458, and NGC 4649 havefainter fluctuations towards their centers. Four of the sixteengalaxies (NGC 1380, NGC 1344, NGC 4458, and NGC 4472)appear to have color and SBF gradients consistent with littleor no age variation. The majority of the galaxies show gradi-ents consistent with primarily age variations, however.The IR SBF and color gradients hint at differing formationhistories for the galaxies. As noted above, low-luminosityblue elliptical galaxies usually have older populations at largeradii, and thus to have formed stars more recently near theircenters from metal-poor gas, while the giant ellipticals formedstars in their cores long ago from enriched gas. Optical studiesof SBF gradients, in contrast, suggest that the outer parts ofgiant ellipticals have colors and fluctuation magnitudes con-sistent with lower metallicity populations and little or no agegradient (Cantiello et al. 2005, 2007). Our IR measurementsdo not cover as large a range in radius as the optical studiesbecause of the smaller field of view spanned by the IR detec-tors and the brighter sky background. Because the data hereare confined within the effective radius of the several largestgalaxies (Table 1), we cannot derive strong constraints on thelarge-scale stellar population gradients in these giant galax-ies. Interestingly, the physical size ( r (cid:46) along the direction of the linear cal-ibration. These galaxies are ideally suited for distance mea-surement because variations from galaxy to galaxy in age ormetallicity are adequately accommodated by the calibrationslope with ( g − z ). On the other hand, the radial gradi-ents in SBF magnitude in the bluer dwarf galaxies (the graysymbols in the left half of Fig. 10 are perpendicular to thequadratic calibration relation, leading to greater scatter in thedistance calibration. These low-luminosity dwarfs show awide range of ages and metallicities, with several showing ev-idence of recent star formation near their centers, as revealedby their SBF magnitudes.Only one set of SBF measurements and models is shownin Figure 10; the general conclusions, however, are consistentfor all the models discussed herein. The radial variations are F IG . 11.— Lick index measurements for eleven of the galaxies in our sam-ple (Kuntschner 2000; Trager et al. 2000; Caldwell et al. 2003) as comparedwith the α -enhanced models from Lee & Worthey (2005). H β is more age-sensitive, while Mg b is metallicity-sensitive. Such data provide an indepen-dent way of checking the SBF model comparison conclusions; see text. consistently sloped along lines of constant metallicity for allthe models, so even though the models might not agree on thespecific age and metallicity of a particular galaxy, the trendtowards younger ages in the centers of bluer dwarf galaxies isconsistent for all the models.5.6. Line Index Age and Metallicity Constraints
Eleven of the galaxies in our sample have published H β and Mg b Lick index measurements from Kuntschner (2000),Trager et al. (2000), and Caldwell et al. (2003). The formerindex is more sensitive to age, and the latter to metallicity.Figure 11 compares these data with the + α -enhancedmodel predictions from Lee & Worthey (2005). The line in-dex measurements generally sample different regions of thegalaxies than our SBF data, but we see again that the red-dest ellipticals agree with the old, metal-rich population mod-els. The youngest galaxies as determined using absorptionlines do not always agree with the SBF models. IC 3487has the strongest H β index but the faintest M among thebluer galaxies, implying a relatively older age compared toNGC 1375, which has somewhat weaker H β and brighter M (although there is considerable variation between SBFmodels at the youngest ages). Further work is needed to ex-plore the radial behavior of Mg b and H β as compared to ourSBF measurements on the same scales, particularly since wedetect a significant radial age gradient in many of the lower-luminosity galaxies.5.7. Model Comparison Summary
The SBF models shown in Figures 6, 7, and 8 agree for old,metal-rich populations such as those commonly found in gi-ant elliptical galaxies, and for which extensive comparisonshave been made in the past (e.g., Jensen et al. 2003; Cantielloet al. 2012; Fritz 2012). At younger ages and lower metallici-ties, the three sets of models are significantly different, andthe conclusions we draw about the ages of the blue dwarfellipticals are strikingly different. These three sets of mod-els allow for the blue, low-mass dwarf ellipticals to poten-tially have a range of ages from 2 to 14 Gyr, and [Fe/H] fromabout − − I -band SBF measurements of bluedwarf ellipticals (Mieske et al. 2006) also show a large spreadof fluctuation magnitudes and younger implied ages. Sinceeach set of models was computed with the aim of understand-nfrared SBF Distances Using WFC3 17ing something different—the role of α -enhancement in early-type galaxies for the BaSTI models (Lee et al. 2010) and theTP-AGB phase for the SPoT and Padova models (Raimondo2009; Cantiello et al. 2007, 2012; Lee et al. 2010)—the differ-ences shown here provide the starting point for future detailedcomparison of the near-IR properties of actual red giant andAGB stars in unresolved stellar populations with model pre-dictions. We have chosen to show model comparisons using M plotted against ( g − z ) computed using the individ-ual galaxy optical SBF distances. The general trends and con-clusions are similar when the models are compared to M orplotted against ( J − H ).It is beyond the scope of this study to provide a critical anal-ysis of the strengths and shortcomings of each of these sets ofmodels. For the purposes of this study, we conclude that theIR SBF distance calibration is robust when applied to old, red,metal-rich galaxies like the giant ellipticals typically found inenvironments like Virgo and Fornax, and even to some withintermediate-age populations and somewhat bluer colors. Thebluer dwarf ellipticals, on the other hand, provide importantnew observational constraints that should be of interest to re-searchers constructing the next generation of stellar popula-tion models. It is clear that better constraints from data suchas these will be valuable in better defining the properties ofyoung, metal-poor populations, and the brightness of the TP-AGB stars within these populations. RECOMMENDATIONS FOR MEASURING IR SBFDISTANCES WITH WFC3WFC3 on the
HST makes it possible to measure IR SBFmagnitudes at relatively large distances in modest exposuretimes. Based on our experience with the Fornax and Virgocluster calibration data presented here, as well tests withWFC3/IR observations in the Coma cluster from
HST pro-gram GO-11711 (see Blakeslee 2013) and with the instrumentexposure time calculator, we provide the following guidelinesto help other astronomers plan WFC3 SBF observations andmake use of existing data in the
HST archive.1. The fluctuations are brighter at H than at J , but the J filter is signficantly wider than H (by 0.8 mag),which largely cancels out the brightness advantage. Theimage quality is slightly better at J than H , and thebackground is slightly lower. The net effect is that ex-posure times to achieve a particular SBF S / N ratio isabout the same in the two filters, but the ability to de-tect and remove contaminating point sources (primar-ily globular clusters) is better at J , and there is lessscatter in the calibration. We therefore advise choos-ing J over H when possible. The broad F140Wfilter would be a good alternative, unhampered by the1.083 µ m He emission line in the upper atmosphere, butthat bandpass remains uncalibrated for SBF.2. Typical one-orbit exposure times ( ∼ J or H out to about80 Mpc. This distance limit is imposed by the pointsource sensitivity required to detect and remove glob-ular clusters from the image, with the goal of reachingwithin ∼ J , or ∼ H , for which the fluctuations are relatively brighter(Jensen et al. 1998). The SBF signal itself can be de-tected to much larger distances (beyond 100 Mpc) in a single orbit, but the large correction for contaminatingpoint sources would then dominate the uncertainty.3. Exposure times for more distant galaxies should bescaled to achieve a point source sensitivity sufficientto detect and remove globular clusters 1 to 1.5 magbrighter than the peak of the globular cluster luminos-ity function. The exposure time needed to detect thestochastic fluctuations that comprise the SBF signalgoes as d , but the time required to detect the globu-lar clusters increases significantly faster, scaling as d to d , because of the bright background on which theglobular clusters are superimposed.4. To avoid issues with correlated noise, do not use thedefault HST pipeline-combined images. Use the flt fileswithout correcting the WFC3/IR field distortion. It maybe possible to recreate the drz files using the lanczos3kernel in the astrodrizzle package; this approach wasnot tested for WFC3/IR as part of this study, but hasbeen used successfully in the past for ACS data (cf.Cantiello et al. 2005; Mei et al. 2005a).5. Because SBF magnitudes depend on the properties ofthe stellar populations, high-quality color data are es-sential to determine accurate distances. For the most ac-curate SBF distances, one should target giant ellipticaland S0 galaxies with old stellar populations, for which( g − z ) colors are greater than 1.2 or ( J − H ) aregreater than 0.22 AB mag. The population variationsat bluer colors are too great for robust distance mea-surements. If possible, it is best to use ACS ( g − z )colors, but WFC3/IR ( J − H ) colors are an accept-able alternative. If necessary, other color indices maybe translated to ( g − z ) or ( J − H ) using well-constrained empirical or model relations for old, metal-rich populations. SUMMARYWe have measured J and H SBF magnitudes and( J − H ) colors for 16 early-type galaxies in the Virgo andFornax clusters observed with WFC3/IR. All of these galaxieshave previously measured SBF distances and ( g − z ) col-ors from ACS. We find that the luminous red galaxies in thesample follow linear relations between absolute SBF magni-tude and optical or IR color; SBF distances to such galaxiescan be determined within a statistical uncertainty of 5% us-ing the calibration relations that we have presented in Equa-tions (3) through (6). The systematic uncertainty of this cali-bration is ∼
10% due to the uncertainty in the Cepheid calibra-tion on which this work is based. Stellar population modelsare not consistent enough to provide a direct calibration of theIR SBF technique accurate to 10%, but they are valuable forinferring age and metallicity trends in and among the samplegalaxies. The scatter in SBF magnitude among bluer galax-ies is large, indicating that a wider variety of stellar popula-tions dominate the light from these galaxies and that a simplebroadband color does not adequately parameterize the com-plexities inherent in such populations. Some galaxies, partic-ularly those of intermediate color, clearly have younger (4 to8 Gyr) populations, likely with AGB stars that enhance the IRfluctuation amplitude. Bluer galaxies, primarily dwarf ellip-ticals, may have very-low metallicities and/or younger ages,with the interpretations varying among different sets of stellar8 Jensen et al.population models. Finally, we have provided practical adviceto guide researchers interested in undertaking SBF measure-ments with WFC3/IR.Based on observations made with the NASA/ESA
Hub-ble Space Telescope , obtained at the Space Telescope Sci-ence Institute, which is operated by the Association of Uni-versities for Research in Astronomy, Inc., under NASA con-tract NAS 5-26555. These observations are associated withprogram
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