A . 1997, ApJ, 475, 399 , A. 1999, astro-ph/9907062

, G., Soszynski, 1., Wozniak,

Cosmic Flows 1999: Towards an Understanding of Large-Scale Structure ASP Conference Series, Vol. 201, 2000 S. Courteau, M.A. Strauss and I .A . Willick, eds.

The Calibration of the Tully-Fisher Relations and the Value of Hubble Constant

Shoko Sakai\ Jeremy R . Mould2, John Huchra3

, Shaun Hughes4, Lucas M. Macri3 and Robert C. Kennicutt, Jr.5

1 Kitt Peak National Observatory, NOAO, Tucson AZ, USA

2 Mount Stromlo Siding Spring Observatory, Australia

3 Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA

4 Institute of Astronomy, Cambridge University, UK

5 Steward Observatory, University of Arizona, AZ, USA

Abstract. We present the calibration of BV RI H -0.5 Tully- Fisher re­lations based on Cepheid distances to 21 galaxies within 25Mpc. These relations are then applied to four distant cluster surveys (in B, R, I and H) to derive a value of Ho. Taking a weighted average of the estimates, we obtain Ho = 71 ± 4 (random) ±7 (systematic) km sec-1 Mpc-1 . We also investigate how various systematic uncertainties affect this value .

1. Introduction

As part of the final stage of the HST Key Project on the Extragalactic Distance Scale, four secondary distance indicators were used to measure accurately Ho: Tully-Fisher (Sakai et al. 2000), fundamental plane (Kelson et al. 2000), Type Ia supernovae (Gibson et al. 2000) and surface brightness fluctuations (Ferrarese et al. 2000) . were used to measure the accurate value of Ho (see Ferrarese [tcl for a review). This paper presents a summary of the calibration of Tully-Fisher relations for spiral galaxies, and the application of this method to measure Ho. The details are found in Sakai et al. (2000).

2. The Absolute Calibration of TF Relations

The objective is to bring the calibrator sample to the same photometric and linewidth systems as the cluster surveys that will be used later to measure Ho. We have a sample of 21 calibrating galaxies whose distances had been measured accurately using the period-luminosity relations of Cepheid variable stars. Their TF data were compiled from various databases. The optical total magnitudes mainly come from Macri et al. (2000), while the H-band aperture magnitudes were taken from the database of Aaronson et al. (1980, 1982, 1986). For the rotational velocity data, we have used both the digitized 21cm HI profiles pro­vided by Martha Haynes, as well as those scanned from literature, to re-derive the linewidths measured at both 20% and 50% levels. The magnitudes are cor-

129

130 Sakai et aI .

rected for both the Galactic (Schlegel et al. 1998) and internal extinctions (Tully et al. 1998), and for the K-correction (Han 1992), and the linewidths for the in­clination and redshift effects. For the inclination angles, we have used only the photometric measurements even though for most calibrators, (more accurate) kinematical data were available. This was to maintain the consistency between the calibrators and the distant cluster data for which only the photometric incli­nation angles were available . The following absolute TF relations in BVRI and H_O.5 bands are derived, which are also shown in Fig . 1:

B¥ = - 7.49(logWg :....- 2.5) - 19.72 [/Tint = 0.25]'

vf = -9.01(10gWg - 2.5) - 20.27 [/Tint = 0.22],

R~ = - 8.53(10gWg - 2.5) - 20.59 [/Tint = 0.25],

I¥ = -9 .55(logWg - 2.5) - 21.02 [/Tint = 0.20],

(17)

(18)

(19)

(20)

H~0.5 = -11 .03(10gWg - 2.5) - 21.74 [/Tint = 0.19J . (21)

The intrinsic dispersion for each relation, after subtracting observational errors, is shown in square brackets (observed dispersions are 0.35-0.42 mag). We observe that : (1) the slope increases as a function of wavelength; (2) the intrinsic disper­sion is 0.20-0.25 mag for all wavelengths; (3) the residual in absolute magnitude is insensitive to color; and (4) the usage of photometric rather than kinemat­ical inclination angles for barred galaxies tend to over-estimate their inclinations (too edge- on) (see Sakai et al. 2000 for details).

3. Hubble Constant

We now apply the absolutely calibrated Tully-Fisher relations to several all-sky surveys of spirals galaxies, in order to measure accurate distances to the clusters of galaxies, and thus the value of Ho. Four surveys used in the analyses are: (1) ScI I-band sample by Giovanelli et al. (1997a) consisting of > 500 galaxies in 24 clusters, (2) H-band database of 173 galaxies compiled by Aaronson and collaborators, and (3) & (4) B- and V-band surveys by Bothun et al. (1985)which are much smaller than the former two surveys, consisting only of 57 galaxies in five clusters. Again, to make the calibrators and cluster samples consistent with each other, we have posed a lower linewidth cutoff oflog W :::: 2.35. Furthermore, galaxies that are nearly face-on (i :::: 80°) and edge-on (I :::; 40°) were excluded from any further analyses. We obtain for the BVIH surveys, respectively, Ho = 74 ± 2 (undorn) ± 7 (ayllerno.ic), 67 ± 2 ± 10, 72 ± 2 ± 11, and 68 ± 2 ± 10. Taking a weighted average, Ho = 71 ± 4 ± 7. The following assumptions and models have been adopted in determining Ho: (1) the distance to and the reddening in the line of sight of LMC are 18.5 ± 0.13 mag and 0.13 mag respectively; (2) velocities are measured in the CMB reference frame; (3) Cepheid distances to the calibrators have not been corrected for a possible metallicity dependence of the Cepheids; (4) individual distances to clusters have been corrected for the cluster population incompleteness bias (see below); and (5) internal extinction model by Tully et al. (1997) has been used.

-23

-22 /

-21

-20

-19

-16

2.4 2.6 2.6 log W (20%)

-24

-23

-22

-21

-20

- 19

2.4 log '

Figure 1. Calibratic

internal extinctions (Tully L the linewidths for the in­Les, we have used only the Librators , (more accurate) n the consistency between Jnly the photometric incli­TF relations in BVRI and .1:

Tint = 0.25], (17)

Tint = 0.22]' (18)

Tint = 0.25], (19)

rint = 0.20], (20)

[Uint = 0.19]. (21)

Lcting observational errors, 1.35-0.42mag). We observe th; (2) the intrinsic disper­Lual in absolute magnitude ~tric rather than kinemat­-estimate their inclinations

relations to several all-sky .te distances to the clusters ; used in the analyses are: :msisting of > 500 galaxies :ompiled by Aaronson and . Bothun et al. (1985)which sting only of 57 galaxies in ter samples consistent with og W :::: 2.35. Furthermore, m (1 ::; 40°) were excluded surveys, respectively, Ho = L, and 68 ± 2 ± 10. Taking 19 assumptions and models ance to and the reddening 0.13 mag respectively; (2)

~; (3) Cepheid distances to e metallicity dependence of .ave been corrected for the and (5) internal extinction

TF Relation and Ho 131

-23 -23

-23 -22 B V

/ -22 -21

-22

-21 -21

-20 -20

-19

-IB -19

-IB 2.4 2.B 2 .B 2.4 2.6 2.6 2.4 2 .6 2.B

log W (20%) log W (20%) log W (20%)

-24 -25

-23 -24

-22 -23

-21 -22

-20 -21

-19 -20

2.4 2.6 2.B 2.4 2.B 2.B log W (20%) log W (20%)

Figure 1. Calibration of Tully-Fishel' Relations

132 Sakai et al .

Ho derived here is ",15% smaller than, for example, that derived by Pierce & Tully (1992) or Aaronson et al. (1980) . Almost all of this difference comes from the difference in the calibration sample: the four calibrators whose distances had been determined from the ground-based observations before the launch of HST all fell below the mean TF relation (thus fainter zero point, yielding shorter distances and a higher Ho). The errors in the value of Ho are explained in Ferrarese et al. (this vol). However, those specific to the TF analysis include the uncertainty originating from the extinction corrections, and also the discrepancy between the I-band and H-band distances. The Ho values obtained from these two surveys (which are larger and should be better sampled than the B and V databases) disagree by as much as 15%. Although we have investigated various possibilities for the origin of this discrepancy, including the inconsistencies in the linewidth definitions and the hybrid nature of the H-band aperture magnitudes, no single source has been found. However, there is a systematic photometric difference between the calibrators and cluster galaxies in H-O.5 magnitudes which are circular aperture magnitudes : we find that the calibrators are systematically redder in I - H - 0.5 color compared to the cluster samples . This issue will be investigated in more detail in the future.

4. Systematic Uncertainties in Ho

TF Slope and Shape: By artificially varying the TF slope, we have examined whether using an incorrect TF slope would yield a significantly different result. We have also tested the case using quadratic TF relations. We find that neither case will affect Ho significantly, perhaps 1 - 2% at most.

Cluster Population Incompleteness Bias: A minimal effect on the Tully- Fisher distances is expected due to incomplete cluster sampling. This is because ofthe small TF dispersion we observe (",0 .2 mag). We have also run two series of Monte Carlo simulations, including an extensive method introduced by Giovanelli et al. (1997b), to see the effect of the cluster population incomplete­ness bias. For each cluster, the bias was found to be less than "'0.08 mag, or <3- 4% in distance. This was used to correct the cluster distances in measuring Ho ·

Velocity Field: We have determined Ho using the velocities in the CMB frame. Using a simple flow model in which three attractors, Virgo cluster, the Great Attractor and the Shapley concentration, were considered (Mould et al. 2000), Ho remains unchanged.

Extinction Correction Method: We have used the internal extinction correction algorithm from Tully et al. (1998) which is dependent on the rota­tional velocity, but not on the morphological type. On the other hand, Han (1992)'s method is dependent on the morphology, while that of Giovanelli et al. (1994) depends on both morphology and rotational velocity. Using all three to estimate Ho, we find that the value of Ho is insensitive to the extinction correction method used, varying by 1 % at most.

Metallicity Dependence of the Cepheid PL Relation: If there is a strong dependence of the Cepheid magnitudes on metallicity, then a more metal- rich Cepheid would appear redder. If not corrected for this systematic dependence, then the reddening would be overestimated, thus yielding an un-

derestimated distance (f( the TF calibrators are m of our Cepheid distance! dependence (-0.24±0.U zero point brighter, ther. survey) from 74 ± 2 to 7

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TF Relation and Ho 133

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