A NEW REDDENING LAW FOR M4

We have used a combination of broadband near-infrared and optical Johnson–Cousins photometry to study the dust properties in the line of sight to the Galactic globular cluster M4. We have investigated the reddening effects in terms of absolute strength and variation across the cluster field, as well as the shape of the reddening law defined by the type of dust. All three aspects had been poorly defined for this system and, consequently, there has been controversy about the absolute distance to this globular cluster, which is closest to the Sun. Here, we determine the ratio of absolute to selective extinction ( R V ) in the line of sight toward M4, which is known to be a useful indicator for the type of dust and therefore characterizes the applicable reddening law. Our method is independent of age assumptions and appears to be significantly more precise and accurate than previous approaches. We obtain A V / E ( B − V ) = 3.76 ± 0.07 (random error) for the dust in the line of sight to M4 for our set of filters. That corresponds to a dust-type parameter R V = 3.62 ± 0.07 in the Cardelli et al. reddening law. With this value, the distance to M4 is found to be 1.80 ± 0.05 kpc, corresponding to a true distance modulus of ( m − M ) 0 = 11.28 ± 0.06 (random error). A reddening map for M4 has been created, which reveals a spatial differential reddening of δ E ( B − V ) ⩾ 0.2 mag across the field within 10' around the cluster center; this is about 50% of the total mean reddening, which we have determined to be E ( B − V ) = 0.37 ± 0.01. In order to provide accurate zero points for the extinction coefficients of our photometric filters, we investigated the impact of stellar parameters such as temperature, surface gravity, and metallicity on the extinction properties and the necessary corrections in different bandpasses. Using both synthetic ATLAS9 spectra and observed spectral energy distributions, we found similarly sized effects for the range of temperature and surface gravity typical of globular cluster stars: each causes a change of about 3% in the necessary correction factor for each filter combination. Interestingly, variations in the metallicity cause effects of the same order when the assumed value is changed from the solar metallicity ([Fe/H] = 0.0) to [Fe/H] = -2.5. The systematic differences between the reddening corrections for a typical main-sequence turnoff star in a metal poor globular cluster and a Vega-like star are even stronger (∼5%). We compared the results from synthetic spectra to those obtained with observed spectral energy distributions and found significant differences for temperatures lower than ∼5000 K. We have attributed these discrepancies to the inadequate treatment of some molecular bands in the B filter within the ATLAS9 models. Fortunately, these differences do not affect the principal astrophysical conclusions in this study, which are based on stars hotter than 5000 K. From our calculations, we provide extinction zero points for Johnson–Cousins and Two Micron All Sky Survey filters, spanning a wide range of stellar parameters and dust types. These extinction tables are suited for accurate, object-specific extinction corrections.

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