AbstractsLaw & Legal Studies

We have used broad-band near infrared photometry in combination with optical Johnson-Cousins photometry to study the dust properties in the line of sight to the Galactic globular cluster M4. These data have been used to investigate the reddening effects in terms of absolute strength, distribution and variations across the cluster field, as well as the shape of the reddening law defined by the type of dust. All three aspects were poorly defined for this system and therefore there has been controversy about the absolute distance to the globular cluster which is closest to the sun. Here, we introduce a new method to determine the ratio of absolute to selective extinction (RV ) in the line of sight toward resolved stellar populations, which is known to be a useful indicator for the type of dust and therefore characterizes the applicable reddening law. This method is independent of age assumptions and appears to be significantly more precise and accurate than existing approaches. In a first application, we determine AV /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 RV = 3.62 ± 0.07 in the Cardelli, Clayton & Mathis (1989) reddening law. With this value, the distance to M4 is found to be d = 1.80 ± 0.05 kpc, corresponding to a true distance modulus of (m − M)0 = 11.28 ± 0.06. These uncertainties do not include possible systematic errors in the theoretical isochrones. A reddening map for M4 has been created which reveals a spatial differential reddening of δE(B − V ) ≥ 0.2 mag across the field within 10′ around the cluster centre; this is about 50% of the total mean reddening, which has been 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, a computer code has been written to investigate 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 similar sized effects for the range of temperature and surface gravity typical of globular cluster stars: both cause 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. Our analysis showed that the systematic differences between the flux of 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 in detail for temperatures lower than 5 000 K. We have attributed these discrepancies to the inadequate treatment of molecular bands in the B filter within the ATLAS9 models. Accordingly, for those cooler…