THE ASTROPHYSICAL JOURNAL, 516:626–646, 1999 May 10
© 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.

The Hubble Space Telescope Key Project on the Extragalactic Distance Scale. XX. The Discovery of Cepheids in the Virgo Cluster Galaxy NGC 4548 1

JOHN A. GRAHAM, 2 LAURA FERRARESE, 3, 4 WENDY L. FREEDMAN, 5 ROBERT C. KENNICUTT, JR., 6 JEREMY R. MOULD, 7 ABHIJIT SAHA, 8 PETER B. STETSON, 9 BARRY F. MADORE, 10 FABIO BRESOLIN, 6, 11 HOLLAND C. FORD, 12 BRAD K. GIBSON, 13 MINGSHENG HAN, 14 JOHN G. HOESSEL, 14 JOHN HUCHRA, 15 SHAUN M. HUGHES, 16 GARTH D. ILLINGWORTH, 17 DANIEL D. KELSON, 2, 17 LUCAS MACRI, 15 RANDY PHELPS, 5 SHOKO SAKAI, 8 N. A. SILBERMANN, 10 AND ANNE TURNER 6

Received 1998 October 9; accepted 1998 December 16


ABSTRACT

     We report on the discovery and properties of Cepheid variable stars in the barred spiral galaxy NGC 4548, which is a member of the Virgo cluster of galaxies. This is one of the galaxies being observed as part of the Hubble Space Telescope (HST) Key Project on the Extragalactic Distance Scale, which aims to determine the Hubble constant to 10% accuracy. Our analysis is based on observations made with the Wide Field and Planetary Camera 2 during 1996 and 1997. We identify 24 probable Cepheids with periods between 16 and 38 days. They were observed over 13 epochs with the F555W filter and eight epochs with the F814W filter. The HST F555W and F814W data have been transformed to the Johnson V and Cousins I magnitude systems, respectively. Photometry has principally been carried out using the DAOPHOT/ALLFRAME package. A comparison is made with parallel measurements using the DoPHOT package. Apparent period-luminosity relations for V and I have been constructed. Assuming values of μ$\mathstrut{_{0}}$=18.50±0.10 mag and E(B-V)=0.10 mag for the distance modulus and reddening of the Large Magellanic Cloud, a true distance modulus of 31.01±0.28 mag is derived corresponding to a distance of 15.9±2.0 Mpc. HST Cepheid distances of other spiral galaxies in the Virgo Cluster are discussed. Their good agreement with the new NGC 4548 distance strengthens the evidence that this galaxy lies within the Virgo cluster core.

Subject headings: Cepheids—distance scale—galaxies: clusters: individual (Virgo)—galaxies: individual (NGC 4548)

FOOTNOTES

     1 Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc. under NASA Contract No. NAS5-26555.

     2 Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, DC 20015.

     3 Hubble Fellow.

     4 California Institute of Technology, Pasadena, CA 91125.

     5 Carnegie Observatories, Pasadena, CA 91101.

     6 Steward Observatories, University of Arizona, Tucson, AZ 85721.

     7 Mount Stromlo and Siding Spring Observatories, Institute of Advanced Studies, ANU, ACT 2611, Australia.

     8 Kitt Peak National Observatory, NOAO, Tucson, AZ 85726.

     9 Dominion Astrophysical Observatory, Victoria, British Columbia V8X 4M6, Canada.

     10 NASA/IPAC, California Institute of Technology, Pasadena, CA 91125.

     11 European Southern Observatory, Garching b. München, Germany.

     12 Johns Hopkins University and Space Telescope Science Institute, Baltimore, MD 21218.

     13 CASA, University of Colorado, Boulder, CO 80309-0389.

     14 University of Wisconsin, Madison, WI 53706.

     15 Harvard Smithsonian Center for Astrophysics, Cambridge, MA 02138.

     16 Royal Greenwich Observatory, Cambridge, CB3 OHA, UK.

     17 Lick Observatory, University of California, Santa Cruz, CA 95064.

§1. INTRODUCTION

     The ultimate aim of the Hubble Space Telescope (HST) Key Project on the extragalactic distance scale is to enable the Hubble constant to be determined within 10% (Kennicutt, Freedman, & Mould 1995). The essence of this HST program is to determine Cepheid distances via the period-luminosity (PL) relation to 18 galaxies with redshifts out to about 1500 km s-1. The Virgo Cluster galaxies are playing a significant part in providing the calibration for the secondary distance indicators that bridge local flow perturbations and enlarge the volume over which a global Hubble constant can be derived. As well as NGC 4548, the subject of this paper, two other Virgo galaxies are included in the HST program. They are NGC 4321 (Ferrarese et al. 1996) and NGC 4535 (Macri et al. 1999). We are also rereducing archival HST data obtained by others for three additional galaxies in the Virgo Cluster, NGC 4496A, NGC 4536, and NGC 4639.

     We chose NGC 4548 as a well-resolved spiral galaxy that has a high a priori probability of membership in the Virgo Cluster (de Vaucouleurs & de Vaucouleurs 1973; Binggeli, Tammann, & Sandage 1987). It is centered at α$\mathstrut{_{2000}}$=12$\mathstrut{^{{\rm h}}}$35$\mathstrut{^{{\rm m}}}$26&fs;3, δ$\mathstrut{_{2000}}$=+14$\mathstrut{^{{\circ}}}$29$\mathstrut{^{{\prime}}}$49$\mathstrut{^{{\prime}{\prime}}}$. The heliocentric velocity is 475 km s-1 (Rubin, Waterman, & Kenney 1999), which is small compared to that of the Virgo Cluster as a whole but is in no way exceptional. The galaxy type is SBb(rs)I–II (Sandage & Tammann 1981) and SBb(rs) (de Vaucouleurs et al. 1975). The nucleus shows low-ionization emission (Ho, Filipppenko, & Sargent 1995). Rubin et al. (1999) estimate an isophotal inclination of 37°. Ground-based images are published in the Carnegie Atlas of Galaxies (Sandage & Bedke 1994). The galaxy appears similar to NGC 3351, which was the subject of one of our earlier papers (Graham et al. 1997). Van den Bergh (1976) refers to it as "a fine example of an anemic spiral." NGC 4548 can probably be identified with Messier 91, although some historical uncertainty exists (Mallas & Kreimer 1978).

§2. OBSERVATIONS AND DATA REDUCTION

     Our observing strategy is discussed in detail in previous papers of this series (e.g., Ferrarese et al. 1996, 1998) and we refer to these for more complete descriptions. Here we discuss only those issues that relate directly to NGC 4548. The HST observations began on 1996 April 16 using the Wide Field and Planetary Camera 2 (WFPC2). For the principal data set, a total of 40 V images at 12 epochs, spaced over a 60 day interval, was accumulated using the F555W filter. Within this same interval 24 additional images were obtained at eight of the 12 epochs with the F814W filter to measure I magnitudes. All observations were carried out at the same telescope pointing and roll angle. For this series of observations, a displacement of a few pixels was introduced between each epoch of observation to improve the sampling capability and the removal of bad pixel elements for each frame. An additional follow-up pair of images, with the F555W filter only, was obtained during a revisit on 1997 May 5, 324 days after the last observation of the main data set. This pair was used to improve the precision of the Cepheid periods.

     The region we have observed in NGC 4548 is shown in Figure 1, which is taken from an image obtained with the 1.2 m telescope at the F.W. Whipple Observatory of the Smithsonian Institution. It is centered 43&arcsec; east, 79&arcsec; south of the nucleus of the galaxy. The PC chip covers the smallest field. We refer to this as chip 1. The three WFC chips cover the three larger fields. We will refer to these as chips 2, 3, and 4 as encountered when one moves counterclockwise from the PC field in the figure. The summary of observations and exposure times is given in Table 1. The sampling strategy has been discussed by Freedman et al. (1994). The actual observations followed very closely our requested sampling sequence. Figure 2 gives a measure of the uniformity with which a light curve of period P will be covered, given the sampling strategy adopted (Madore et al. 1999). The calculation excluded the revisit epoch because these observations were not used for the variable star search. Incompleteness due to magnitude selection effects is not taken into account. This becomes severe for faint stars because of the large measuring errors in the magnitudes. From the slope of the period-luminosity (PL) relation and the incompleteness at fainter magnitudes, Cepheid variable stars are unlikely to be discovered at periods less than 15 days in this galaxy.

Fig. 1 Fig. 2

     Routine calibration via the standard pipeline maintained by the Space Telescope Science Institute (STScI) has been carried out as described in previous papers of this series. All exposures were taken at the low CCD operating temperature of -88° so that the hot pixel problem and the "charge transfer" photometry gradient (Holtzman et al. 1995a; Hill et al. 1998) were reduced. Although this latter gradient has now been more precisely specified (Whitmore & Heyer 1997), no additional corrections have been made at this time. The residual uncertainty is expected to be less than 0.02 mag.

§3. PHOTOMETRIC REDUCTION

     Photometric analysis of HST frames was carried out independently by Graham using DAOPHOT and ALLFRAME (Stetson 1994) and by Ferrarese using DoPHOT (Schechter, Mateo, & Saha 1993). As pointed out in earlier papers (e.g., Ferrarese et al. 1996), the philosophy behind the two program packages is quite different. Thus there is a useful check on the results for systematic errors that might otherwise go unnoticed if a single program were used. For example, noise events cause different responses in the two programs and the methods for determining sky background are not the same.

     Procedures described in the earlier papers were again followed in the ALLFRAME measurements. Small corrections are necessary to bring the photometry to the standard systems used by others with the HST (Hill et al. 1998). These include the aperture corrections that were computed to bring the ALLFRAME magnitudes to the equivalent of aperture photometry with an aperture diameter of 0&farcs;5 (Holtzman et al. 1995b). Approximately 25 isolated stars were selected from the ALLFRAME photometry lists to determine, with the DAOGROW routine, image growth curves showing magnitude as a function of aperture. The initial solutions, particularly those for the PC (chip 1) and WF2 (chip 2) frames were ill defined and did not lead to credible results. This was largely because of the lack of stars of sufficient brightness with low measuring errors. New solutions were therefore made for all chips by averaging image growth curves computed for other galaxies of the Key Project along with some star cluster and parallel field data. The resulting aperture corrections are given in Table 2. The values agree well with those derived earlier for chips 3 and 4 using the NGC 4548 frames alone and are more precise than those first determined for chips 1 and 2.

     The DoPHOT photometry was performed using a variant of the DoPHOT package (Schechter et al. 1993; Saha et al. 1994), which was developed especially to deal with the photometry of undersampled images such as those obtained with the HST. Discussion of this application of DoPHOT to photometry of HST images can be found in Saha et al. (1996a), Ferrarese et al. (1996, 1998), and Hill et al. (1998).

     A color correction was also applied. We again used the following relations suggested by Holtzman et al. (1995b) to obtain V and I magnitudes on the Johnson and Cousins systems, respectively,







Except for very red stars, the color correction is small, no more than a few hundredths of a magnitude. We have again included the correction of 0.05 mag to our long exposure frames as discussed in Hill et al. (1998).

     The bright stars used to determine the ALLFRAME aperture corrections are convenient reference stars for present and future comparisons of our photometry, and we list them in Table 3 along with x, y positions, right ascension and declination with the mean ALLFRAME and DoPHOT magnitudes converted to the standard VI system. In the identification column the first figure refers to the chip number and the second figure refers to the number of the reference star on that chip. Identical procedures were followed in processing the photometry of the Cepheid variable stars (§ 5). In every case the x, y coordinates refer to the first frames at the first epoch of the set. The equatorial coordinates are based on the nominal pointing of HST and are calculated using the metric program in the IRAF/STSDAS software package. The actual pointings of the telescope agree with the planned ones to within 0&farcs;6, well within the overall uncertainty (≈1&arcsec;) of the coordinate system as a whole.

§4. COMPARISON BETWEEN ALLFRAME AND DoPHOT MAGNITUDES

     The independent data reductions using ALLFRAME and DoPHOT provide an external test of the point-spread function (PSF) fitting accuracy in these crowded and complicated star fields. A detailed discussion and comparison will be presented in a future paper (Stetson et al. 1999). Here we summarize the results of our comparisons for NGC 4548. We first compared the photometry for the isolated bright stars (Table 3) and then performed the same comparison for the Cepheid variable stars of our final sample (Table 5). The differences are plotted in Figure 3 and listed in Table 4. The agreement is not uniformly good, illustrating the difficulty in analyzing fields as distant and as crowded as those found in NGC 4548. Chip-to-chip differences as large as 0.14 mag are found. The average difference for all Cepheids is small in V (+0.02 mag) but large in I (+0.09 mag), and this directly affects our distance determinations (§ 7). When separated according to different chip numbers, it can be seen in Table 4 that the large differences in the Cepheid photometry are associated with large (but generally more precisely determined) differences in the photometry of the bright stars. For both groups of stars, the largest differences are found for chip 3 and chip 4, which (cf. Fig. 1) include the brightest background contribution from the NGC 4548 itself. Crowding of faint, partially resolved stars must complicate the definition of a background "sky measurement" in these fields. In addition there is the problem of separating close, and frequently redder, companion stars. Tests conducted with artificial stars have shown that ALLFRAME may not resolve close companions stars, as well as DoPHOT, although both procedures are likely to be deficient in fields as crowded as these. The same tests point to errors in determining the aperture corrections as the largest source contributing to the discrepancy. With the few bright, isolated stars available, their determination remains a formidable task. However, the use of two separate photometry packages does allow us to quantify external uncertainties of this type.

Fig. 3

§5. VARIABLE STAR SEARCH

§5.1. DAOPHOT/ALLFRAME Data Set

     Two methods have been used to search the DAOPHOT/ALLFRAME data set for variability. They complement each other by emphasizing in turn the tasks of detecting variability and searching for periodicity. The first method is described by Welch & Stetson (1993). It depends on the simple concept that although photometric measuring errors have a random distribution with time, residuals due to intrinsic variability are expected to be strongly correlated. The method works especially well with the HST data sets in which observations are purposely grouped for random event (cosmic ray) removal. A variability index is computed for each of the stars measured by ALLFRAME. A filter is incorporated into the program to remove the large differences that may be introduced by isolated erroneous magnitudes. This filter also serves to remove epochs for which ALLFRAME finds itself unable to measure a sensible magnitude and outputs instead an unrealistically large one. A lower limit on the correlation index needs to be specified in order to limit the suspect list to those stars that are likely variable. With star lists often containing several thousand stars, random positive correlations naturally occur. The resulting list is then sorted in decreasing value of the index. The true variable stars are usually found at the top of this list. Occasionally, a bad pixel measurement will produce a single epoch magnitude that will distort the index and give an erroneous detection. Such cases are easily spotted by inspection.

     Another powerful method of Cepheid detection is to attempt to fit a period for the sequence of measured magnitudes. For this, a version of the Lafler & Kinman (1965) technique as formulated by Stellingwerf (1978) has been used. The "phase dispersion minimization" (PDM) program takes the data set and, with a trial period, computes phases. The magnitude list is reordered in phase and the program computes a difference sum for a succession of trial periods. The spacing of the trial periods depends on the time base of the data set. When there is a real periodic variation, the difference sum becomes small as the best period is approached. Some caution has to be used to eliminate spurious periods, which, for example, may represent two cycles, not just a single cycle. The method is most effective at finding periods between 0.25 and 1.0 times the time base of the data set. For shorter periods, it gets confused by photometric errors and will contribute spurious periods. Experience has shown that the PDM method is more sensitive to large errors in the photometry (e.g., from random events on the chip) than the correlated residuals method. The initial search and period search were derived only with the main data set of V magnitudes from the 12 epochs covering a time base of 60 days. Periods around the reported PDM period were then examined, and the best period was selected by taking into account the observational uncertainty and phase value of individual magnitudes in the sequence. The best period was usually within a day of the reported PDM period. The mean magnitude of the revisit observation, made 324 days later, was then incorporated into the data set and, again with the recognition of the measuring uncertainties, was used to refine the period of the variable star. Final periods are listed in Table 5 with estimates of their uncertainties.

§5.2. DoPHOT Data Set

     The search for variable stars was performed on the V band images following the procedure described by Saha & Hoessel (1990). We required that a star be detected in at least 10 of the 12 epochs in order to be checked for variability. We also excluded all stars in crowded regions by rejecting candidates with a companion contributing more than 50% of the total light in a two-pixel radius. A detailed discussion of search procedure can be found in Ferrarese et al. (1996). A star meeting the above constraints was flagged as a variable if χ$\mathstrut{^{2}_{r}}$≥8 or Λ≥3 where χ$\mathstrut{^{2}_{r}}$ and Λ are as used by Saha & Hoessel (1990).

     Several spurious variables were registered by this procedure as a consequence of non-Gaussian sources of error and various anomalies of the images (e.g., residual cosmic-ray events) along with the crowding referred to earlier. Each potentially variable star was visually inspected by blinking several of the individual frames against each other. With the DoPHOT data set, the best period for each variable was selected by phasing the data for all periods between 3 and 100 days in incremental steps of 0.1 days. Although in most cases the final period adopted corresponds to a minimum value of the phase dispersion, in a few cases here also, an obvious improvement of the light curve was obtained for a slightly different period.

§5.3. Search Results

     Our aim is to obtain a sample of Cepheid variable stars with properties similar to those known in the Galaxy and the Large Magellanic Cloud (LMC). Thus the prime criterion for accepting a star as such in NGC 4548 is the appearance of the light curve relating magnitude to phase-wrapped epoch. Numerical parameters, such as those based on correlated residuals or phase dispersion minima are invaluable for discovery but quantitatively are susceptible to random events and photometric errors. They are not helpful in distinguishing long-period variables, eclipsing stars and novae, for example, from Cepheids. More sophisticated routines for doing just this are currently being tested at the Dominion Astrophysical Observatory by Stetson (1996). Typical Cepheid light curves are well known from the LMC sample (e.g., Wayman, Stift, & Butler 1984). They are sometimes sinusoidal but more often show a more rapid rise in brightness than decline. In some senses, discrimination by light curve–shape parameters alone is a more quantitative procedure but decisions about the critical values used for the parameters are themselves based on personal experience. Thus the decision process is only moved back one step. Inclusion of Cepheid variables pulsating in the first overtone (Böhm-Vitense 1988) is a concern only for stars with periods less than 10 days. Although Population II W Virginis stars might be expected in a spiral galaxy with a type as early as that of NGC 4548, reference to published PL relations (Nemec & Lutz 1993) shows that even the brightest, longest period examples of these stars would be much fainter than our detection limit.

     After engaging in separate searches with ALLFRAME and DoPHOT, we compared candidate lists and examined in detail those stars flagged in only one search. We found this double search reassuring. Most variables (28) indeed were found independently in both data sets. In seven cases with only a single discovery, the explanation lay in the different treatment of random events by the two different procedures. Subsequent examination of these produced a list of 24 stars that we consider bona fide Cepheids. A thorough analysis of the effect of samples found separately by ALLFRAME and DoPHOT is given by Ferrarese et al. (1996). Artificial star simulations on crowded fields (Ferrarese et al. 1999), show that incompleteness biases are negligible (less than 10% of stars are lost) at V magnitudes brighter than 26.5 mag. V=27.5 mag or fainter stars need to be reached before more than 50% of the sample is lost. These numbers refer to a complete list of stars and grossly overestimate the number of stars lost in uncrowded parts of the field, where almost all of the Cepheids used in fitting the PL relation are found. The tests by Ferrarese et al. (1999) predict that a significant loss of Cepheids due to magnitude incompleteness is present in the NGC 4548 field only at periods shorter than 20 days.

     Our final list of 24 Cepheid variables is presented in Table 5. The ALLFRAME and DoPHOT periods were reviewed by Graham and a consensus value determined that is entered into Table 5 with the appropriate uncertainty. Coordinates based on WFPC2 measurements and the nominal position of the telescope are given. Finding charts are provided in Figures 4 and 5. The photometry is given in Tables 6 and 7. Table 8 contains a list of variable stars that are either not Cepheids or are suspected Cepheids that were excluded from the main list because of unconvincing light curves or poor photometry. Finding charts for these stars are also given in Figures 4 and 6.

Fig. 4 Fig. 5 Fig. 6

§6. LIGHT CURVES AND MEAN MAGNITUDES

     The light curves, based on the V magnitudes phased to the periods in Table 5, are reproduced in Figure 7. They are arranged in order of decreasing period and are lined up so that phase=1.0 corresponds to maximum brightness. They are folded over two cycles to highlight their morphology. The adopted period is shown in each panel. A characteristic error reported by ALLFRAME for the magnitudes in each set is shown in the lower left corner of each panel. A perusal of the panels in Figure 7 confirms that they are typical of curves expected from normal Cepheid variable stars with the rise to maximum being faster than the decline to minimum.

Fig. 7

     Mean V and I magnitudes are routinely computed in two different ways: as intensity-averaged magnitudes 〈V〉i, 〈I〉i and as phase-weighted magnitudes 〈V〉ph, 〈I〉ph (see Saha & Hoessel 1990). For variable stars with uniformly sampled light curves, these coincide, but whenever the phase coverage of the light curve is not uniform, higher weighting of the less common phase points provides a more accurate estimate of the mean magnitude than a simple intensity average. Both are listed in Table 9 for each Cepheid variable star along with the period. In the NGC 4548 data set, I magnitude coverage (eight epochs) is almost as good as that for V (12 epochs) and, for this galaxy, we did not see the need for computing 〈I〉ΔI, which results from mapping the I magnitudes onto the V magnitude light curve (see Freedman 1988; Graham et al. 1997). A comparison between intensity-averaged magnitudes and phase-weighted magnitudes for V and I confirms that the phase sampling is not a problem. The mean &angl0;V&angr0;$\mathstrut{_{i}}$-&angl0;V&angr0;$\mathstrut{_{{\rm ph}}}$=-0.029 mag with an average numerical difference per star of 0.05 mag. The mean &angl0;I&angr0;$\mathstrut{_{i}}$-&angl0;I&angr0;$\mathstrut{_{{\rm ph}}}$=-0.008 mag with an average numerical difference per star of 0.04 mag.

     An I, V-I color-magnitude diagram for all stars is shown as Figure 8. Cepheids are marked as filled circles, other stars as points. The Cepheids lie in a band bounded by V-I=0.6 and 1.4 mag. The color-magnitude diagram for all stars that we measured illustrates mainly the color characteristics of the faint magnitude cutoff. It is similar to that of NGC 3351 (Graham et al. 1997) if allowance is made for the greater distance of NGC 4548.

Fig. 8

§7. PERIOD-LUMINOSITY RELATIONS AND THE DISTANCE TO NGC 4548

     Following other papers in this series, the apparent V and I distance moduli to NGC 4548 are to be based on the DAOPHOT/ALLFRAME data set. Again, the V and I PL relations found by Madore & Freedman (1991) are used. These depend on LMC Cepheid data scaled to a true modulus of 18.50 mag corrected for an average line of sight E(B-V) reddening of 0.10 mag [E(V-I)=0.13 mag]. They are







     Note that these calibration relations include overtone pulsating variable stars. They would be different, and more physically correct, if these short-period stars had been excluded. However, we have chosen to adopt this calibration as it is for all Key Project galaxies. The effect is a small one, introducing errors of only a few hundredths of a magnitude. Our current procedure assures homogeneity and does not introduce biases in the derived distances since the shape of the PL relations is kept fixed throughout. Only the zero point is allowed to vary, not the slope. Larger samples of LMC Cepheids are becoming available, and it is foreseeable that an improved, more precise PL calibration will be available in the near future. Indeed, we plan to revise all of the derived distances when this calibration is redone.

     Phase-averaged magnitudes are used in our fitting procedure. Using the ALLFRAME data set, we plot the V and I PL plots shown in Figures 9 and 10 for the 24 stars in Table 9. The solid lines represent the best unweighted fit. The dashed lines, drawn at ±0.54 mag in Figure 9 and at ±0.36 mag in Figure 10, reflect the full width of the Cepheid instability strip. The functional relations are







These lead to V and I moduli of 31.29±0.07 and 31.17±0.05 mag, respectively, with E(V-I)=0.11±0.04 mag for the NGC 4548 Cepheids. Using the procedures described in earlier papers of this series, one finds that the apparent moduli are related through a dust extinction law. An extinction law consistent with that of Cardelli, Clayton, & Mathis (1989) with A$\mathstrut{_{B}}$:A$\mathstrut{_{V}}$:A$\mathstrut{_{I}}$=1.3:1.0:0.6 and R$\mathstrut{_{V}}$=A$\mathstrut{_{V}}$/E(V-I) of 2.45 that takes into account the actual effective wavelength of the Cousins I band is used to derive a true modulus of 31.01±0.05 mag corresponding to a distance of 15.9±0.4 Mpc. This assumes R$\mathstrut{_{V}}$=A$\mathstrut{_{V}}$/E(B-V)=3.3. Lanoix, Paturel, & Garnier (1999) have questioned the extent to which solutions such as these might be influenced by selection biases related to the magnitude limit of the sample. Kelson et al. (1999) have shown that the size of the effect predicted in their paper is exaggerated because of their neglect of the narrower intrinsic width of the I band PL relation but, in any case, we believe that we have largely eliminated it by including only Cepheids with periods greater than 15 days. As a test, we carried out a solution for 13 stars (slightly over half of the sample) with periods greater than 20 days. These gave apparent V and I moduli of 31.33 and 31.19 mag corresponding to a true modulus of 30.99 mag. These values are well within the uncertainties of the values derived for the full sample and confirm that sample selection effects are not important. We cannot determine from our data alone whether the small amount of dust reddening is produced within NGC 4548 or is largely foreground reddening. However, reference to the DIRBE dust maps (Schlegel, Finkbeiner, & Davis 1998) shows that, for the Virgo galaxies, E(B-V) is unlikely to be more than 0.02 mag and that the dust absorption is in fact largely internal.

Fig. 9 Fig. 10

     The corresponding relations for the DoPHOT data are







These lead to V and I moduli of 31.25±0.07 and 31.07±0.05 mag, respectively, with E(V-I)=0.18±0.03 mag and a true modulus of 30.81±0.07 mag. The errors as before are internal errors and for the individual apparent moduli are correlated. Thus the true modulus has a smaller error than one would expect if the V and I moduli were completely independent. The DoPHOT true modulus corresponds to 14.5±0.4 Mpc. The difference between the two distances draws attention to the disturbing sensitivity to the reddening determinations based on two-color photometry alone. They are a direct consequence of the mean difference in the DoPHOT and ALLFRAME photometric scales in the I band (§ 3). DoPHOT, it will be recalled, determines I magnitudes for Cepheids that are on the average 0.09 mag brighter than from ALLFRAME, although the mean differences in V are close to zero. The different internal reddening implied levers the change in the internal absorption estimate that is then responsible for the different distances. Although the photometry is capable of some improvement, we feel strongly that the only way to firmly address this problem is to push our photometry further to the infrared, which has distinct advantages once the period of the Cepheid is known (McGonegal et al. 1982). At present, we can do no better than to propose the ALLFRAME values and to embrace the difference with DoPHOT in our overall error assessment by including the uncertainty with the I photometry calibration error.

     Distances based on Cepheid absolute magnitudes are no more accurate than the calibrating period-luminosity relations on which they are based. All the galaxy distances listed in Table 11, for example, rest on the same LMC Cepheid calibration published by Madore & Freedman (1991) and will change together, should that calibration be improved. Following the publication by Feast & Catchpole (1997) of the first results of Hipparcos parallaxes for Galactic Cepheids, Madore & Freedman (1998) have reexamined their earlier calibration to see whether modifications are appropriate at this stage. They use the new individual distances to calibrate the PL relation at six wavelengths (BVIJHK). Current parallax errors dominate the uncertainty and they conclude that the above LMC modulus is still the most consistent one to use.

     The effect of metallicity on Cepheid distances remains a controversial issue. Kennicutt et al. (1998) found only a weak dependence of the inferred distance modulus on metal abundance with δ(m-M)$\mathstrut{_{0}}$/δ[O/H]=-0.24±0.16 mag dex-1. We have decided not to attempt a correction to our Key Project distances at this time but a recent measurement of [O/H]=0.45±0.2 for this galaxy (Kennicutt et al. 1999) obliges us to point out that the effect could be appreciable. Skillman et al. (1996) noted that the Virgo spirals tend to be significantly more metal rich in [O/H] than field spirals so that any adjustment would affect all Cepheid distances given in Table 11 in the same direction. As in previous papers, an error budget has been drawn up for our new distance and is shown in Table 10. We incorporate an uncertainty of ±0.10 due to the metallicity correction. Also included is the uncertainty of the LMC distance modulus (±0.10). Assessing all errors, both correlated and uncorrelated (cf. Kelson et al. 1996), we conclude with a mean modulus of 31.01±0.28 mag for NGC 4548, which corresponds to a distance of 15.9±2.0 Mpc.

§8. CEPHEID DISTANCES FOR GALAXIES IN THE VIRGO CLUSTER

     As Aaronson & Mould (1986) made clear, Cepheid variable stars are widely regarded as the best primary indicators of distances to external galaxies. The basic physics is well understood. The dispersion in absolute magnitude is small and quantifiable. Cepheids can be measured in enough galaxies for the calibration to be checked and rechecked and for its sensitivity to parameters such as metallicity and interstellar absorption to be evaluated. However, it has only been with the HST that routine observation of the Cepheid variables in many galaxies has become possible. Only fragmentary observations, for example, could be made of Virgo Cluster galaxies from the ground (e.g., NGC 4571; Pierce et al. 1994). Yet, the Virgo Cluster contains so many galaxies of such diverse types that, regardless of the uncertain dynamics and the probable extension in depth, it is an essential staging post for the calibration of those secondary distance indicators that can extend our measuring capability far beyond.

     Over the last few years, several new distances to Virgo cluster galaxies have been published based on Cepheid variable star observations with the HST and the consequent PL relations. These are listed in Table 11 along with the Revised Shapley Ames type (Sandage & Tammann 1981) and the angular distance of each galaxy from the luminosity-weighted cluster center at 12$\mathstrut{^{{\rm h}}}$27&fm;8+12$\mathstrut{^{{\circ}}}$56$\mathstrut{^{{\prime}}}$ (Huchra 1985). We have in progress a reanalysis of the HST data for NGC 4496A, NGC 4536, and NGC 4639 following our own Key Project procedures. These results will be discussed by Gibson et al. (1999). Even with the results presently at hand it is evident that most of the galaxies in Table 11 have distances very close to our value for NGC 4548, the main exception being NGC 4639, which, according to Saha et al. (1997) has a distance several Mpc beyond the other Virgo galaxies in Table 11. However, perhaps the general agreement is not surprising since, in the view of Böhringer et al. (1997), NGC 4548 is likely to be near the center of the cluster because it shows signs of being stripped of its H I, which is consistent also with its "anemic" appearance. The proximity of the giant elliptical galaxy, Messier 87, only 2&fdg;4 southwest is another argument for NGC 4548 being close to the Virgo core. Ideally, more Cepheid distances for other Virgo spiral galaxies could constrain the distance to the Virgo core more tightly, but it may be many years before these become available. In the interim, the compactness of the core might best be evaluated by studying the relative dispersion of secondary distance indicators in individual galaxies. For example, Jacoby, Ciardullo, & Ford (1990) noted from their study of planetary nebulae around six other galaxies of earlier Hubble type that the dispersion in distance among galaxies within the Virgo cluster core was also small, probably less than 1.0 Mpc. Their mean distance was 14.7 Mpc, not significantly different from the mean Cepheid distance when uncertainties in calibration zero points are taken into account.

ACKNOWLEDGMENTS

     We are most grateful to the referee David Branch who provided several helpful comments that enabled us to improve the original version of the paper. We would again like to thank Doug Van Orsow, the program coordinator for this Key Project, as well as the rest of the STScI and NASA support staff. Financial support for this work was provided by NASA through grant GO-2227-87A from STScI. L. F. acknowledges support by NASA through Hubble Fellowship grant HF-01081.01-96A awarded by the Space Telescope Science Institute. P. B. S. and S. M. G. H. are grateful to NATO for travel assistance via a Collaborative Research Grant (960178).

REFERENCES

FIGURES


Full image (311kb) | Discussion in text
     FIG. 1.—Ground-based R image of NGC 4548 with the Hubble Space Telescope field marked. It is adapted from a CCD image taken with the 1.2 m telescope of the F.L. Whipple Observatory on Mount Hopkins, Arizona. The long side of the L-shaped HST footprint is 150&arcsec;. The PC chip (chip 1) covers the smallest field of the four chips. Moving counterclockwise, the other three WF2 fields correspond to chips 2, 3, and 4.

Full image (19kb) | Discussion in text
     FIG. 2.—Sampling variance of light curves from data taken using the exposure sequence given in Table 1. The variance plotted is a measure of the amount by which the observed phase sampling deviates from that of uniform phase sampling. The variance is normalized such that the zero variance corresponds to the case where the light curve is uniformly sampled. The 1997 revisit observation is not included in this calculation.

Full image (50kb) | Discussion in text
     FIG. 3.—ALLFRAME-DoPHOT magnitude differences plotted against ALLFRAME magnitude for both bright reference stars and Cepheid variables in each of the four chips. Open triangles correspond to chip 1, filled triangles to chip 2, open circles to chip 3, and filled circles to chip 4.

Full image (200kb) Full image (136kb) Full image (167kb) Full image (182kb) | Discussion in text
     FIG. 4.—Deep HST F555W images of NGC 4548 obtained by combining with median filtering all F555W epochs. The 24 Cepheids and the additional 11 variables are identified on each of the chips. The vignetted edges of each field are shown masked.

Full image (348kb) Full image (357kb) | Discussion in text
     FIG. 5.—Finding charts for the Cepheids listed in Table 5. Each finding chart covers a 5$\mathstrut{^{{\prime}{\prime}}}$×5$\mathstrut{^{{\prime}{\prime}}}$ region and has the same orientation as the corresponding chips in Fig. 4. The contrast and intensity have been adjusted differently for each finding chart; therefore, the relative brightness of the Cepheids cannot be inferred from them.

Full image (313kb) | Discussion in text
     FIG. 6.—Finding charts for the additional variable stars listed in Table 8. Each finding chart covers a 5$\mathstrut{^{{\prime}{\prime}}}$×5$\mathstrut{^{{\prime}{\prime}}}$ region and has the same orientation as the corresponding chips in Fig. 4.

Full image (43kb) Full image (40kb) Full image (42kb) Full image (41kb) Full image (38kb) Full image (38kb) | Discussion in text
     FIG. 7.—ALLFRAME V magnitude light curves for each Cepheid variable. The adopted period is shown along with a characteristic uncertainty range as reported by ALLFRAME for a typical point.

Full image (48kb) | Discussion in text
     FIG. 8.—An I, V-I color-magnitude diagram constructed using the mean photometric magnitudes of all stars measured in ALLFRAME. Cepheids are shown as filled circles and populate the instability strip.

Full image (15kb) | Discussion in text
     FIG. 9.—V PL relation for the sample of Cepheids. The solid line represents the best unweighted fit using phase-weighted mean magnitudes and corresponds to a modulus of 31.29±0.07 mag. The dashed lines drawn at ±0.54 mag reflect the full width of the Cepheid instability strip.

Full image (16kb) | Discussion in text
     FIG. 10.—I PL relation for the sample of Cepheids. The solid line represents the best unweighted fit using phase-weighted mean magnitudes and corresponds to a modulus of 31.17±0.05 mag. The dashed lines drawn at ±0.36 mag reflect the full width of the Cepheid instability strip.

TABLES

TABLE 1
LOG OF OBSERVATIONS
Observation Date JD (Midexposure) Exposure Time
(s)		 Filter
1996 Apr 16... 2,450,189.820 1200 F555W
1996 Apr 16... 2,450,189.836 1200 F555W
1996 Apr 16... 2,450,189.886 1200 F555W
1996 Apr 16... 2,450,189.904 1300 F814W
1996 Apr 16... 2,450,189.954 1300 F814W
1996 Apr 16... 2,450,189.970 1300 F814W
1996 Apr 24... 2,450,197.998 1100 F555W
1996 Apr 24... 2,450,198.013 1100 F555W
1996 Apr 24... 2,450,198.062 1100 F555W
1996 Apr 24... 2,450,198.078 1100 F555W
1996 Apr 24... 2,450,198.130 1200 F814W
1996 Apr 24... 2,450,198.142 1200 F814W
1996 Apr 24... 2,450,198.013 1200 F814W
1996 May 5... 2,450,208.920 1200 F555W
1996 May 5... 2,450,208.936 1200 F555W
1996 May 5... 2,450,208.985 1200 F555W
1996 May 5... 2,450,209.002 1300 F814W
1996 May 5... 2,450,208.053 1300 F814W
1996 May 5... 2,450,208.070 1300 F814W
1996 May 7... 2,450,211.065 1200 F555W
1996 May 7... 2,450,211.065 1200 F555W
1996 May 7... 2,450,211.081 1200 F555W
1996 May 7... 2,450,211.130 1300 F555W
1996 May 7... 2,450,211.147 1300 F555W
1996 May 10... 2,450,213.947 1200 F555W
1996 May 10... 2,450,213.963 1200 F555W
1996 May 10... 2,450,214.011 1200 F555W
1996 May 10... 2,450,214.029 1300 F814W
1996 May 10... 2,450,214.079 1300 F814W
1996 May 10... 2,450,214.095 1300 F814W
1996 May 14... 2,450,217.900 1200 F555W
1996 May 14... 2,450,217.916 1200 F555W
1996 May 14... 2,450,217.965 1300 F555W
1996 May 14... 2,450,217.982 1300 F555W
1996 May 17... 2,450,221.050 1200 F555W
1996 May 17... 2,450,221.066 1200 F555W
1996 May 17... 2,450,221.115 1200 F555W
1996 May 17... 2,450,221.132 1300 F814W
1996 May 17... 2,450,221.181 1300 F814W
1996 May 17... 2,450,221.199 1300 F814W
1996 May 21... 2,450,225.272 1200 F555W
1996 May 21... 2,450,225.288 1200 F555W
1996 May 21... 2,450,225.337 1300 F555W
1996 May 21... 2,450,225.354 1300 F555W
1996 May 26... 2,450,229.895 1200 F555W
1996 May 26... 2,450,229.911 1200 F555W
1996 May 26... 2,450,229.959 1200 F555W
1996 May 26... 2,450,229.976 1300 F814W
1996 May 26... 2,450,230.027 1300 F814W
1996 May 26... 2,450,230.044 1300 F814W
1996 May 31... 2,450,235.122 1200 F555W
1996 May 31... 2,450,235.138 1200 F555W
1996 May 31... 2,450,235.186 1300 F555W
1996 May 31... 2,450,235.203 1300 F555W
1996 Jun 7... 2,450,241.960 1200 F555W
1996 Jun 7... 2,450,241.975 1200 F555W
1996 Jun 7... 2,450,242.023 1200 F555W
1996 Jun 7... 2,450,242.040 1300 F814W
1996 Jun 7... 2,450,242.090 1300 F814W
1996 Jun 7... 2,450,242.107 1300 F814W
1996 Jun 15... 2,450,249.736 1200 F555W
1996 Jun 15... 2,450,249.752 1200 F555W
1996 Jun 15... 2,450,249.800 1200 F555W
1996 Jun 15... 2,450,249.816 1300 F814W
1996 Jun 15... 2,450,249.866 1300 F814W
1996 Jun 15... 2,450,249.883 1300 F814W
1997 May 5... 2,450,574.239 2300 F555W
1997 May 5... 2,450,574.305 2600 F555W

Images of typeset table: 1 2 | Discussion in text
TABLE 2
ALLFRAME APERTURE CORRECTIONS
Chip Correction Standard Error
A. F555W (V)
1... -0.17 0.01
2... -0.04 0.01
3... -0.01 0.01
4... +0.00 0.01
B. F814W (I)
1... -0.17 0.01
2... +0.00 0.01
3... +0.01 0.01
4... +0.01 0.01

Image of typeset table | Discussion in text
TABLE 3
POSITIONS AND MAGNITUDES OF BRIGHT STARS
Star x y R.A. (2000) Decl. (2000) VALL IALL VDoP IDoP
1-1... 264.70 279.27 12 35 29.76 14 28 21.77 24.44 24.46 24.51 24.53
1-2... 243.63 327.97 12 35 29.73 14 28 19.41 23.49 23.22 23.60 23.32
1-3... 493.97 383.56 12 35 30.53 14 28 19.33 23.48 23.09 23.60 23.19
1-4... 506.68 539.21 12 35 30.67 14 28 12.54 27.03 23.87 27.14 24.02
2-1... 232.91 125.31 12 35 28.54 14 28 09.87 24.20 24.32 24.23 24.27
2-2... 511.05 133.28 12 35 28.90 14 27 42.77 24.48 24.22 24.47 24.16
2-3... 374.74 156.48 12 35 28.55 14 27 55.48 24.43 24.13 24.40 24.09
2-4... 543.40 198.06 12 35 28.52 14 27 38.22 26.80 24.09 26.71 24.00
2-5... 300.36 270.59 12 35 27.67 14 28 00.22 26.14 23.80 26.09 23.70
2-6... 294.16 393.16 12 35 26.85 14 27 58.16 24.18 23.90 24.23 23.87
2-7... 304.62 394.10 12 35 26.86 14 27 57.12 24.75 23.76 24.71 23.70
2-8... 263.74 428.99 12 35 26.56 14 28 00.32 23.64 23.46 23.70 23.40
3-1... 550.00 149.82 12 35 25.33 14 28 28.82 23.31 23.07 23.21 22.93
3-2... 565.53 242.54 12 35 25.09 14 28 37.46 23.44 22.38 23.40 22.27
3-3... 533.72 243.60 12 35 25.30 14 28 38.23 23.45 22.92 23.38 22.78
3-4... 731.42 245.20 12 35 23.98 14 28 34.27 23.91 23.69 23.81 23.56
3-5... 760.02 293.73 12 35 23.72 14 28 38.37 25.27 23.93 25.14 23.79
3-6... 360.20 364.21 12 35 26.28 14 28 53.60 22.99 22.92 22.97 22.78
3-7... 404.33 498.48 12 35 25.79 14 29 05.71 23.69 23.35 23.67 23.19
4-1... 281.70 125.74 12 35 29.13 14 28 54.41 23.52 22.60 23.54 22.54
4-2... 88.31 261.54 12 35 30.31 14 28 38.38 23.29 23.03 23.25 22.94
4-3... 453.94 383.97 12 35 30.62 14 29 16.37 23.41 23.31 23.55 23.22
4-4... 633.13 415.02 12 35 30.58 14 29 34.42 24.76 22.69 24.69 22.59
4-5... 233.22 436.05 12 35 31.28 14 28 55.94 24.32 22.76 24.36 22.67
4-6... 153.55 446.14 12 35 31.46 14 28 48.40 26.88 24.13 26.88 24.08
4-7... 207.41 491.78 12 35 31.69 14 28 54.56 23.33 23.03 23.36 22.94
4-8... 108.29 493.04 12 35 31.83 14 28 44.99 23.54 23.25 23.55 23.19
4-9... 360.70 523.57 12 35 31.69 14 29 10.12 23.06 22.36 23.13 22.29
4-10... 736.20 589.20 12 35 31.60 14 29 47.84 23.40 23.24 23.44 23.19
4-11... 718.24 647.92 12 35 32.02 14 29 47.26 23.96 23.56 23.94 23.44

     NOTE.— Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds.

Image of typeset table | Discussion in text
TABLE 4
DAOPHOT/ALLFRAME MINUS DOPHOT PHOTOMETRY
Chip Number of Stars $\mathstrut{\overline{{\Delta}V}}$ Number of Stars $\mathstrut{\overline{{\Delta}I}}$
A. Bright Stars
1... 4 -0.10±0.01 4 -0.11±0.03
2... 8 +0.01±0.02 8 +0.06±0.01
3... 7 +0.07±0.02 7 +0.14±0.01
4... 11 -0.02±0.02 11 +0.08±0.01
B. Cepheids
1... 4 -0.10±0.07 4 -0.08±0.04
2... 4 +0.06±0.03 3 +0.11±0.05
3... 8 +0.13±0.01 8 +0.12±0.07
4... 8 -0.03±0.02 8 +0.14±0.03

Image of typeset table | Discussion in text
TABLE 5
POSITIONS AND PERIODS FOR CEPHEID VARIABLES
Star Chip x y R.A. (2000) Decl. (2000) P
(days)
C01... 3 768.83 239.70 12 35 23.74 14 28 32.97 33.2±0.1
C02... 3 752.23 165.29 12 35 23.96 14 28 26.15 18.4±0.1
C03... 3 694.22 262.29 12 35 24.20 14 28 36.69 24.8±0.1
C04... 2 99.62 664.26 12 35 24.75 14 28 11.02 29.5±0.2
C05... 2 199.52 587.17 12 35 25.41 14 28 03.09 24.2±0.2
C06... 2 212.35 553.53 12 35 25.65 14 28 02.59 19.1±0.5
C07... 3 331.86 359.76 12 35 26.48 14 28 53.77 17.1±0.1
C08... 3 164.31 514.70 12 35 27.37 14 29 12.35 38.2±0.2
C09... 3 179.16 311.60 12 35 27.57 14 28 52.34 18.8±0.1
C10... 3 79.84 400.76 12 35 28.10 14 29 03.08 23.7±0.1
C11... 3 51.98 337.40 12 35 28.38 14 28 57.53 29.4±0.1
C12... 2 317.56 158.00 12 35 28.45 14 28 00.98 18.0±0.2
C13... 4 440.26 275.85 12 35 29.91 14 29 12.85 31.0±0.1
C14... 4 393.44 279.03 12 35 30.00 14 29 08.37 17.5±0.2
C15... 1 357.13 559.09 12 35 30.23 14 28 10.23 17.5±0.2
C16... 1 529.87 394.30 12 35 30.65 14 28 19.20 35.0±0.2
C17... 1 541.11 727.13 12 35 30.90 14 28 04.57 16.5±0.1
C18... 1 558.87 666.46 12 35 30.92 14 28 07.41 17.5±0.1
C19... 4 275.85 425.79 12 35 31.15 14 28 59.87 28.2±0.1
C20... 4 386.47 478.48 12 35 31.35 14 29 11.71 16.9±0.1
C21... 4 346.62 492.30 12 35 31.50 14 29 08.11 21.2±0.1
C22... 4 599.65 603.94 12 35 31.89 14 29 34.96 20.2±0.1
C23... 4 273.89 730.72 12 35 33.19 14 29 05.89 23.3±0.1
C24... 4 267.47 771.26 12 35 33.47 14 29 06.09 17.0±0.1

     NOTE.— Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds.

Image of typeset table | Discussion in text
TABLE 6
ALLFRAME V PHOTOMETRY FOR NGC 4548 CEPHEIDS
V±σ$\mathstrut{_{V}}$
JD 2,450,000+ C1 C2 C3 C4 C5 C6
189.847... 25.91±0.11 26.24±0.14 26.60±0.16 25.36±0.08 26.05±0.13 26.39±0.16
198.024... 26.44±0.16 26.74±0.19 26.07±0.13 25.48±0.10 26.66±0.25 26.63±0.16
208.947... 26.69±0.18 26.04±0.11 26.06±0.09 25.48±0.08 26.04±0.09 26.28±0.14
211.106... 26.17±0.13 26.18±0.16 26.24±0.12 25.26±0.06 25.97±0.10 26.67±0.16
213.640... 26.02±0.12 26.46±0.15 26.48±0.12 25.24±0.08 26.23±0.13 26.78±0.19
217.940... 25.74±0.09 26.62±0.15 26.47±0.16 25.37±0.08 26.37±0.14 27.06±0.24
221.077... 25.92±0.11 27.56±0.36 26.23±0.05 25.51±0.07 26.32±0.11 27.18±0.44
225.313... 26.12±0.13 26.94±0.13 25.64±0.15 25.76±0.09 27.16±0.23 25.87±0.09
229.922... 26.32±0.13 26.03±0.13 25.72±0.09 25.80±0.10 26.82±0.19 26.30±0.13
235.162... 26.77±0.18 26.42±0.13 26.13±0.13 25.96±0.13 25.98±0.10 26.80±0.18
241.986... 26.54±0.15 26.57±0.21 26.69±0.19 25.17±0.07 26.33±0.18 27.14±0.28
249.763... 25.82±0.10 26.09±0.11 25.77±0.08 25.48±0.07 26.67±0.16 26.55±0.18
574.203... 26.51±0.18 27.06±0.21 25.67±0.07 25.47±0.13 25.95±0.27 26.40±0.10
C7 C8 C9 C10 C11 C12
189.847... 25.86±0.11 25.41±0.08 26.58±0.20 26.50±0.18 25.40±0.09 26.71±0.18
198.024... 26.90±0.18 26.09±0.13 25.91±0.13 26.29±0.16 25.65±0.12 26.76±0.25
208.947... 25.90±0.11 26.33±0.19 26.25±0.38 26.56±0.16 26.22±0.16 26.77±0.20
211.106... 26.34±0.30 26.48±0.17 25.56±0.09 26.63±0.17 26.34±0.14 26.95±0.22
213.640... 26.66±0.15 26.45±0.25 25.66±0.10 26.84±0.26 26.21±0.16 26.88±0.21
217.940... 26.72±0.25 26.45±0.18 26.18±0.18 25.87±0.11 25.55±0.09 26.78±0.20
221.077... 26.45±0.17 26.90±0.11 26.61±0.16 26.08±0.13 25.18±0.08 26.22±0.14
225.313... 26.04±0.12 25.43±0.09 26.89±0.20 26.60±0.15 25.51±0.09 26.39±0.17
229.922... 26.47±0.15 25.71±0.10 25.42±0.09 26.66±0.18 25.84±0.11 27.19±0.28
235.162... 27.03±0.18 25.89±0.11 25.79±0.10 26.59±0.25 26.20±0.15 26.87±0.17
241.986... 25.98±0.11 26.22±0.15 26.75±0.19 26.88±0.12 26.42±0.23 26.58±0.15
249.763... 26.76±0.24 26.49±0.22 25.32±0.08 26.27±0.16 25.17±0.09 27.27±0.30
574.203... 26.86±0.15 25.62±0.08 25.93±0.07 25.89±0.13 25.29±0.12 27.18±0.19
C13 C14 C15 C16 C17 C18
189.847... 26.01±0.12 25.54±0.08 27.03±0.29 26.16±0.14 26.92±0.23 25.85±0.12
198.024... 25.97±0.12 26.62±0.18 25.94±0.11 26.82±0.16 26.87±0.24 27.00±0.20
208.947... 25.35±0.08 25.87±0.12 27.02±0.25 27.30±0.22 26.74±0.20 26.09±0.12
211.106... 25.50±0.09 26.04±0.13 27.00±0.21 27.47±0.23 26.97±0.18 26.40±0.13
213.640... 25.47±0.08 26.56±0.14 26.08±0.10 26.41±0.34 26.87±0.22 26.70±0.16
217.940... 25.84±0.10 26.93±0.25 26.48±0.11 25.96±0.09 25.98±0.10 26.86±0.18
221.077... 26.03±0.12 26.80±0.18 27.07±0.20 26.04±0.08 26.26±0.12 26.67±0.15
225.313... 26.12±0.12 25.82±0.09 27.38±0.24 26.38±0.13 27.07±0.22 25.98±0.10
229.922... 25.58±0.08 26.10±0.10 27.00±0.18 26.76±0.15 26.92±0.19 26.51±0.16
235.162... 25.03±0.07 26.89±0.21 26.43±0.14 26.92±0.22 26.02±0.12 26.75±0.20
241.986... 25.36±0.10 25.58±0.08 27.13±0.24 26.92±0.27 26.49±0.21 26.13±0.11
249.763... 25.72±0.08 26.42±0.24 26.11±0.12 26.49±0.17 25.39±0.15 26.78±0.23
574.203... 25.11±0.06 25.86±0.08 26.83±0.29 26.11±0.11 26.76±0.14 26.13±0.08
C19 C20 C21 C22 C23 C24
189.847... 25.42±0.07 26.76±0.23 26.34±0.14 26.16±0.14 25.37±0.07 25.71±0.10
198.024... 25.92±0.12 25.80±0.11 25.49±0.09 26.82±0.16 25.85±0.11 26.45±0.18
208.947... 26.32±0.17 26.43±0.19 25.80±0.10 27.30±0.22 25.82±0.10 26.07±0.12
211.106... 26.46±0.19 26.20±0.13 25.99±0.11 27.47±0.23 25.22±0.11 26.27±0.12
213.640... 25.56±0.09 25.69±0.12 25.11±0.08 26.41±0.34 25.41±0.08 26.56±0.17
217.940... 25.19±0.07 25.97±0.11 25.57±0.09 25.96±0.09 25.83±0.11 26.63±0.21
221.077... 25.33±0.07 26.80±0.18 25.70±0.09 26.04±0.08 25.86±0.09 26.59±0.26
225.313... 25.51±0.13 26.66±0.21 25.98±0.12 26.38±0.13 26.14±0.10 25.88±0.12
229.922... 25.59±0.14 25.41±0.08 26.04±0.10 26.76±0.15 26.36±0.16 26.41±0.18
235.162... 26.11±0.14 25.99±0.14 25.31±0.07 26.92±0.22 25.12±0.08 26.79±0.22
241.986... 26.04±0.09 26.41±0.17 25.84±0.10 26.92±0.27 25.75±0.10 25.84±0.10
249.763... 25.41±0.07 25.71±0.09 26.18±0.11 26.49±0.17 26.30±0.11 26.45±0.18
574.203... 26.31±0.11 26.10±0.10 25.35±0.19 26.11±0.11 26.16±0.09 26.67±0.17

Image of typeset table | Discussion in text
TABLE 7
ALLFRAME I PHOTOMETRY FOR NGC 4548 CEPHEIDS
I±σ$\mathstrut{_{V}}$
JD 2,450,000+ C1 C2 C3 C4 C5 C6
189.943... 24.68±0.10 25.39±0.14 25.47±0.13 24.52±0.08 25.26±0.13 25.15±0.16
198.117... 25.05±0.10 25.74±0.19 25.08±0.12 24.83±0.08 25.57±0.15 25.87±0.21
209.042... 25.21±0.11 25.72±0.20 25.58±0.12 24.68±0.07 25.03±0.11 25.52±0.19
214.067... 24.94±0.10 25.63±0.17 25.60±0.14 24.46±0.08 25.12±0.12 25.53±0.16
221.171... 24.87±0.10 26.05±0.25 25.47±0.14 24.65±0.08 25.43±0.10 26.24±0.32
230.036... 25.21±0.13 25.41±0.10 24.86±0.11 24.90±0.10 25.56±0.13 25.23±0.15
242.079... 25.24±0.13 25.91±0.22 25.79±0.21 24.63±0.07 25.34±0.14 25.74±0.43
249.855... 24.88±0.17 25.82±0.16 25.00±0.12 24.63±0.08 25.51±0.09 25.31±0.32
C7 C8 C9 C10 C11 C12
189.943... 25.37±0.27 24.48±0.10 25.67±0.30 26.24±0.15 24.76±0.12 25.37±0.27
198.117... 25.81±0.23 24.53±0.09 25.41±0.17 25.02±0.11 24.59±0.09 25.81±0.23
209.042... 25.26±0.15 24.92±0.11 25.51±0.38 25.86±0.19 24.87±0.08 25.26±0.15
214.067... 25.88±0.26 25.20±0.14 24.71±0.25 25.58±0.15 25.05±0.10 25.88±0.26
221.171... 25.69±0.17 24.56±0.10 25.62±0.14 25.15±0.11 24.41±0.08 25.69±0.17
230.016... 25.71±0.18 24.61±0.08 25.33±0.11 25.39±0.12 24.56±0.10 25.71±0.18
242.079... 25.25±0.13 24.78±0.09 26.17±0.30 25.11±0.12 25.08±0.11 25.25±0.13
249.885... 25.87±0.19 25.25±0.10 25.20±0.10 25.39±0.14 24.35±0.08 25.87±0.19
C13 C14 C15 C16 C17 C18
189.943... 24.85±0.10 25.22±0.11 25.63±0.16 24.92±0.14 25.73±0.17 25.18±0.10
198.117... 24.87±0.09 25.78±0.23 25.58±0.15 25.24±0.17 25.80±0.19 25.56±0.16
209.042... 24.42±0.08 25.34±0.17 26.48±0.37 25.48±0.19 25.72±0.18 25.20±0.16
214.067... 24.66±0.13 25.80±0.24 25.37±0.11 25.35±0.34 25.86±0.36 25.76±0.17
221.171... 24.91±0.10 26.02±0.17 25.95±0.26 24.73±0.10 25.36±0.12 26.17±0.27
230.016... 24.73±0.08 25.42±0.15 25.57±0.14 25.02±0.14 25.89±0.21 25.76±0.18
242.079... 24.61±0.08 25.23±0.11 25.38±0.26 25.59±0.13 25.87±0.22 25.06±0.13
249.885... 24.92±0.15 25.72±0.16 25.26±0.12 25.33±0.15 25.03±0.09 25.76±0.16
C19 C20 C21 C22 C23 C24
189.943... 24.58±0.09 25.71±0.16 25.27±0.12 25.18±0.14 24.69±0.08 25.22±0.13
198.117... 24.88±0.12 25.01±0.10 24.86±0.09 24.15±0.13 25.07±0.10 25.77±0.23
209.042... 25.45±0.17 25.56±0.14 24.93±0.10 25.06±0.12 24.79±0.09 25.17±0.14
214.067... 24.70±0.08 25.28±0.15 24.78±0.10 24.69±0.11 24.89±0.09 25.46±0.19
221.171... 24.56±0.10 25.27±0.15 25.08±0.12 25.00±0.13 24.93±0.09 25.32±0.18
230.016... 24.86±0.09 25.07±0.12 25.19±0.15 25.38±0.20 25.40±0.14 25.49±0.16
242.079... 25.51±0.13 25.51±0.14 25.08±0.14 24.83±0.12 24.77±0.07 25.09±0.16
249.885... 24.37±0.08 25.13±0.13 25.21±0.12 25.04±0.13 25.18±0.11 25.51±0.14

Image of typeset table | Discussion in text
TABLE 8
POSITIONS AND MEAN MAGNITUDES FOR OTHER VARIABLE STARS
Star Chip x y R.A. (2000) Decl. (2000) 〈V〉 〈I〉 Notes
V01... 3 720.46 531.16 12 35 23.64 14 29 02.16 26.22 25.63 Prob. Ceph. P=16.2 days
V02... 3 711.12 565.65 12 35 23.65 14 29 05.69 25.90 25.97 Blue
V03... 2 211.93 540.57 12 35 25.73 14 28 02.91 25.61 24.84 Poss. Ceph. P=26.0 days
V04... 2 138.04 429.69 12 35 26.37 14 28 12.48 25.63 24.63 No good period
V05... 2 340.89 447.83 12 35 26.55 14 27 52.43 26.23 25.04 Ceph. flat min. P=31 days
V06... 3 211.13 340.17 12 35 27.32 14 28 54.43 25.96 24.98 Prob. Ceph. P=24.8 days
V07... 1 265.56 369.23 12 35 29.82 14 28 17.78 25.18 25.33 Blue
V08... 1 266.04 635.60 12 35 30.00 14 28 05.98 24.44 23.30 Small variation
V09... 1 347.54 553.91 12 35 30.20 14 28 10.36 26.04 25.26 Peculiar. P=29 days?
V10... 4 417.91 438.86 12 35 31.04 14 29 13.97 22.13 21.80 Blue supergiant vbl?
V11... 4 113.37 486.37 12 35 31.78 14 28 45.34 25.32 24.94 Poss. Ceph. P=24.1 days

     NOTE.— Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds.

Image of typeset table | Discussion in text
TABLE 9
PERIODS/MEAN MAGNITUDES FOR CEPHEID VARIABLES
Star P
(days)		 log P &angl0;V&angr0;$\mathstrut{^{{\rm ALL}}_{i}}$ &angl0;V&angr0;$\mathstrut{^{{\rm ALL}}_{{\rm ph}}}$ &angl0;I&angr0;$\mathstrut{^{{\rm ALL}}_{i}}$ &angl0;I&angr0;$\mathstrut{^{{\rm ALL}}_{{\rm ph}}}$ &angl0;V&angr0;$\mathstrut{^{{\rm DoP}}_{{\rm ph}}}$ &angl0;I&angr0;$\mathstrut{^{{\rm DoP}}_{{\rm ph}}}$
C01... 33.2 1.521 26.18 26.20 24.99 25.00 26.03 24.83
C02... 18.4 1.265 26.46 26.53 25.68 25.72 26.31 25.47
C03... 24.8 1.394 26.08 26.07 25.32 25.28 25.98 25.07
C04... 29.5 1.469 25.47 25.53 24.65 24.68 25.50 24.63
C05... 24.2 1.384 26.30 26.37 25.33 25.33 26.28 25.13
C06... 19.1 1.281 26.56 26.58 25.53 25.64 26.45 25.42
C07... 17.1 1.233 26.39 26.37 25.57 25.59 26.19 25.32
C08... 38.2 1.582 25.97 25.98 24.76 24.72 25.88 24.56
C09... 18.8 1.274 25.96 26.07 25.38 25.42 25.96 25.23
C10... 23.7 1.375 26.31 26.36 25.40 25.41 26.21 25.15
C11... 29.4 1.468 25.68 25.78 24.68 24.70 25.68 25.07
C12... 18.0 1.255 26.77 26.68 25.52 25.43 26.70 …
C13... 31.0 1.491 25.56 25.54 24.73 24.71 25.55 24.55
C14... 17.5 1.243 26.13 26.25 25.53 25.60 26.31 25.34
C15... 17.5 1.243 26.64 26.64 25.60 25.70 26.64 25.64
C16... 35.0 1.544 26.50 26.55 25.17 25.16 26.58 25.26
C17... 16.5 1.217 26.44 26.37 25.61 25.52 26.67 25.61
C18... 17.5 1.242 26.39 26.48 25.50 25.57 26.54 25.68
C19... 28.2 1.450 25.74 25.76 24.80 24.87 25.80 24.74
C20... 16.9 1.228 26.07 26.10 25.29 25.29 26.14 25.04
C21... 21.2 1.326 25.69 25.72 25.04 25.02 25.71 24.86
C22... 20.2 1.305 25.88 25.86 25.00 24.92 25.91 24.84
C23... 23.3 1.367 25.72 25.78 24.94 24.95 25.79 24.89
C24... 17.0 1.230 26.28 26.29 25.36 25.35 26.27 25.30

Image of typeset table | Discussion in text
TABLE 10
ERROR BUDGET
Source of Uncertainty Error Comment
a: F555W calibration... ±0.04
b: F814W calibration... ±0.08
c: V photometry zero... ±0.03
d: I photometry zero... ±0.04
     A: Cumulative error V... ±0.05 Errors uncorrelated
     B: Cumulative error I... ±0.09
e: PL fit (V)... ±0.07
f: PL fit (I)... ±0.05
     C: True modulus... ±0.23 Due to A, B, e, f (errors correlated)
g: Metallicity... ±0.10 Systematic
h: LMC modulus... ±0.10
i: V PL zero point... ±0.05
j: I PL zero point... ±0.05
     D: Systematic uncertainty... ±0.16 g, h, i, j
     E: Total uncertainty ... ±0.28 C, D

Image of typeset table | Discussion in text
TABLE 11
HST CEPHEID DISTANCES TO GALAXIES IN VIRGO
Galaxy RSA Type Δ
(deg)		 Distance
(Mpc)		 Reference
NGC 4321... Sc(s)I 3.6 16.1±1.3 Ferrarese et al. (1996)
NGC 4496A... SBcIII–IV 8.7 16.1±1.1 Saha et al. (1996b)
NGC 4535... SBc(s)I.3 4.6 16.0±1.8 Macri et al. (1999)
NGC 4536... Sc(s)I.3 10.5 16.6±1.2 Saha et al. (1996a)
NGC 4548... SBb(rs)I–II 2.2 15.9±2.0 This paper
NGC 4639... SBb(r)II 3.1 25.5±2.6 Saha et al. (1997)

Image of typeset table | Discussion in text