In order to work as a distance indicator, the stellar population dependence of the SBF magnitude must be well calibrated. This has worked best in the I and z bands, where the relation between and galaxy color has the smallest scatter (e.g., Blakeslee et al. 2001; Côté et al. 2004). We now discuss the most recent calibrations of the SBF method and the difficulties (and opportunities) in modeling the stellar population effects on SBF magnitudes at various wavelengths.
2.1. SBF as a Distance Indicator: Some Recent Work
Most of the recent work on SBF distances has focused either on dwarf galaxies in southern groups and clusters observed with large aperture ground-based telescopes (e.g., Jerjen et al. 2004; Mieske et al. 2006; Dunn & Jerjen 2006) or on early-type galaxies observed with the HST Advanced Camera for Surveys Wide Field Channel (ACS/WFC). SBF studies with ACS/WFC F814W bandpass (similar to I) include the first optical SBF distances out to ~ 100 Mpc or beyond (Biscardi et al. 2008; Blakeslee et al., in preparation), a measurement of the distance of the peculiar gas-rich lenticular galaxy NGC 1533 in the Dorado group (Barber Degraaff et al. 2007), and studies of SBF gradients in galaxies (Cantiello et al. 2005, 2007b; discussed below).
The most extensive SBF work with the ACS to date has been in the F850LP band (z850) as part of the ACS Virgo and Fornax cluster surveys (Côté et al. 2004; Jordán et al. 2007). Mei et al. (2005, 2007) present the SBF analysis, calibration, distance measurements for 90 early-type galaxies in the ACS Virgo survey, and Blakeslee et al. (2009) present the same for 43 galaxies in the ACS Fornax survey. The latter study also presents a recalibration based on the combined Virgo and Fornax samples.
Figure 1 shows the resulting z850-band SBF calibration from Blakeslee et al. (2009). The dependence of 850 on (g475 - z850) is nonlinear and can be well described by a cubic polynomial. The fit yields a highly precise relative distance modulus of 0.42 ± 0.03 mag (including systematic uncertainties) for Fornax with respect to Virgo. The intrinsic scatter in the method is estimated empirically to be just 0.06 mag for galaxies with (g475 - z850) > 1, but increases at bluer colors (the compactness of Fornax makes it possible to measure this small intrinsic scatter). Mei et al. (2005) showed that the general behavior (with a zero-point shift) of SBF in z850 was reasonably approximated by predictions from Bruzual & Charlot (2003) simple stellar population (SSP) models of varying age and metallicity. However, it is not possible to predict the scatter in the SBF relations from SSP models. Chemo-evolutionary or semi-analytic models are required for this, although some estimates can be made from simple monte carlo simulations (Blakeslee et al. 2001). A fully successful model should predict the very tight 850 vs (g475 - z850) relation with increased scatter at the blue end.
Figure 1. Combined SBF 850 vs (g475 - z850) color calibration for our ACS Virgo and Fornax cluster survey galaxies (from Blakeslee et al. 2009). SBF magnitudes for the Fornax galaxies are shifted brighter by the best-fit relative distance modulus of 0.42 ± 0.03 mag. The curve represents the best-fit cubic polynomial calibration for the dependence of 850 on (g475 - z850).
At present, significant uncertainties remain in SBF model predictions even in well-studied bandpasses. For instance, Figure 2 compares SBF predictions in the I band from Padova and Teramo/BaSTI SSP models (see Lee et al. 2009 for full details). The predictions are given both with and without the contributions from the thermally pulsing AGB (TP-AGB) stage. Two things are worth noting: there are large differences between the two sets of model predictions (left panel), and the highly uncertain TP-AGB stage has a very large effect (compare left and right panels). The agreement between the sets of models is better when this stage is omitted, but of course it is needed to match the observations (represented by the thick lines).
Figure 2. Comparison of Padova and Teramo/BaSTI stellar population model SBF predictions in the I band, with (left) and without (right) the thermally pulsing AGB (TP-AGB) stage, adapted from Lee et al. (2009). At each of four different ages, models with five different metallicities are connected by the thin lines. For reference, the large solid squares mark the solar metallicity models of varying age. The empirical I-band SBF relations are shown by the bent thick lines (see Lee et al. 2009 for details).
2.2. Multi-band SBF: Hot Horizontal Branches, TP-AGB, Post-AGB, etc.
Worthey (1993b) showed theoretically that SBF measurements in the UV could provide quantitative information on the presence of extended hot horizontal branch stars in elliptical galaxies and other unresolved stellar systems. According to the models used by Worthey, the presence of a hot horizontal branch could make the U-band SBF magnitude brighter by 3 mag in a metal-rich early-type galaxy. The effect at shorter wavelengths, such as the F284W band of HST/WFPC2, was even larger. However, the SBF signal is very faint at these wavelengths, and to date there have been no practical demonstrations of the usefulness of U-band SBF for this purpose. With the coming of large ground-based telescopes equipped with blue sensitive detectors (and hopefully the UVIS channel of WFC3) this may soon change.
Although the ACS/WFC has no sensitivity shortward of 4000 Å, this instrument (before its sad demise) afforded the first samples of reliable B-band (F435W) SBF measurements beyond the Local Group (Cantiello et al. 2007b), which have proven to have interesting implications for stellar population synthesis. Cantiello et al. (2007b) demonstrated the sensitivity of SBF - colors to the rate of post-AGB evolution. The observational data disagreed with standard model predictions, but Cantiello et al. showed that the models could be brought into agreement with the data by adjusting the post-AGB evolution to agree with that inferred for resolved stars in M32. The hot post-AGB stars have a proportionately larger effect on than on .
However, this solution was not unique, since an unmodeled hot horizontal branch or other missing components could also cause the observed discrepancy. Additional SBF measurements in the UV (to constrain further the properties of the hot component) and near-IR (sensitive to the post-AGB star progenitors) could fully resolve this issue. Multi-band optical/IR SBF data are thus relevant to such problems as AGB evolution and the UV excess in elliptical galaxies (e.g., Buzzoni & Gonzalez-Lopezlira 2008).
Blakeslee et al. (2001) found that the treatment of the AGB phase was responsible for some large discrepancies in the near-IR SBF predictions of different models; see also the discussion by Liu et al. (2000). Figure 3, adapted from Lee et al. (2009) shows a dramatic demonstration of the effects of the TP-AGB phase on near-IR SBF (in the HST F160W bandpass). For both the Padova and Teramo/BaSTI sets of models, the inclusion of the TP-AGB phase actually reverses the sense of the dependence of the SBF magnitude on integrated color (at least for age 1 Gyr).
Figure 3. Comparison of Padova and Teramo/BaSTI stellar population model SBF predictions, similar to Figure 2, but here shown for the HST NICMOS F160W band. The empirical relation from Jensen et al. (2003) is shown as a thick solid line. The importance of the TP-AGB phase is considerably greater in the near-IR. The effect of these stars in fact reverses the sense of the dependence of the SBF magnitude on color, so that the near-IR SBF brightens as observed at bluer colors, instead of becoming fainter as it would without the TP-AGB. See Lee et al. (2009) for details.
The original expectations from models were that near-IR SBF magnitudes would brighten at redder colors (e.g., Worthey 1993a). It was a surprise when the reverse was found observationally (Jensen et al. 1998, 2003). The modeling of the AGB phase was likely much of the reason for the erroneous prediction. For the most part, the inclusion of the AGB in population synthesis relies on imperfectly constrained empirical prescriptions, rather than true evolutionary models. It is evident from the figures and comparisons with observations that nature has ordained a better behaved AGB phase than those included in the population models. The relations between SBF magnitude and integrated color are tighter than might be expected from current models. Multi-band SBF data can provide powerful constraints to aid in the development of true AGB evolutionary codes for inclusion in the next generation of stellar population models.