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9.4 Calibration

A real strength of the fluctuation method is that it is based on the luminosities of stars for which we think we have a good fundamental understanding. Thus, the luminosities of the stellar populations we observe can be evaluated theoretically or empirically in systems whose distance we know.

Tonry et al. (1990) discussed the fluctuation luminosities of theoretical stellar populations constructed from the Revised Yale Isochrones (RYI - Green et al. 1987). The results were that the fluctuation luminosity in blue photometric bands depended strongly on the metallicity, age, and IMF of a stellar population, but that the luminosities were quite insensitive to population parameters in the I band. These theoretically calculated values for barMI showed a small scatter of about 5% around a mild dependence on the mean color of the population, with redder stars having brighter barMI. However, observations of M32 (Tonry et al. 1990) gave barmI = 22.81. If M32 is 0.7 Mpc distant, this corresponds to barMI = -1.42. These theoretical isochrones predicted barMI = -1.87 for the (V - I) color of M32, so there was a discrepancy of 0.45 magnitudes.

The numerator in the expression for barLI given in Equation (20) is proportional to the square of the luminosity at the tip of the giant branch and the number of stars there. It appears that the reason for the discrepancy between M32 and the RYI is that the RYI bolometric corrections for these very luminous, very red stars do not adequately account for molecular opacity of their atmospheres at the solar metallicities found near the centers of external galaxies. It seems expedient therefore to abandon temporarily the use of isochrones to calibrate barMI, and turn to clusters and local group galaxies.

Tonry et al. (1990) found that the Virgo galaxies show a scatter in barmI which is consistent with the depth of the Virgo cluster, confirming the expectation that barMI is quite uniform (varying less than about 20%), but precluding the possibility of investigating the variation in barMI from barmI. This situation was addressed by Tonry (1991), where observations of the much more compact Fornax and Eridanus clusters permitted this comparison to be made.

Without any correction for galaxy color, the scatter in barmI measured among the galaxies in these clusters was about 0.15 magnitude. The data spanned a range of galaxy luminosity of about a factor of 50, and included both E and S0 galaxies. There was a trend for redder galaxies to have fainter barmI, contrary to the predictions of the RYI. The scatter was reduced to about 0.08 magnitude about this trend, and a suggestive correlation with galaxy type. The two galaxies observed in the Leo cluster confirmed this predicted trend, but again, the Virgo cluster has too much depth to be useful at this level of precision. Nevertheless, the derived distance moduli for Virgo galaxies showed no trend with color or luminosity over a range of 100 in luminosity.

The barmI in the bulge of M31, M32, and NGC 205 also confirm this relationship, and give us an absolute calibration. For an assumed distance of 0.77 Mpc, and an assumed AB extinction of 0.31 magnitudes to M31, Tonry (1991) derived

Equation 22 (22)

This, of course, should be modified for different assumptions about the distance and extinction to M31, and the uncertainty in the zero point depends directly on these assumptions. There also appears to be an intrinsic scatter of about 0.08 magnitude about this relation. Figure 21 illustrates this relation for the Local Group, Leo, Fornax, and Eridanus clusters by shifting the observed barMI by the assumed distance modulus for M31 and the derived relative distance moduli.

Figure 21. barMI plotted for cluster galaxies as a function of mean galaxy color (V - I). The adopted distance modulus for each cluster is indicated in parantheses. The Local Group (LG) galaxies M31 (red) and M32 (blue) are shown as larger symbols; different patches of NGC 205 comprise the remaining LG points.

Comparison with other distance estimators suggests that this relation is universal. Tonry (1991) found that surface brightness fluctuation distances agree with the PNLF distances for 10 galaxies in common with a scatter in the difference of 7%. The relative mean distances of the four clusters (Virgo, Leo, Fornax, and Eridanus) agree with the results of the infra-red TF relations with a scatter in the difference of only 2%. The relative distance between M31 and M81 determined by surface brightness fluctuations agrees well with the relative distance from Cepheids. Figure 3 of Tonry (1991), however, shows that agreement with the Dn - sigma results is much poorer for reasons not yet understood. (We discuss comparisons between the surface brightness fluctuation distances and the other methods in greater detail in Sec. 11.)

Recent work on the fluctuation luminosity in galactic globular clusters (whose distances can be determined from their horizontal branches) indicates that they also agree with this relation, and can serve to establish the zero point to about 10% (Ajhar 1992). Globular clusters with a metallicity of about 0.1 solar lie just at the intersection of the empirical calibration shown here for galaxies and the RYI calibration from Tonry et al. (1990).

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