A reprocessed cropped portion of the 2MASS mosaic of the Milky Way (Cutri et al. 2003). The Galactic bulge exhibits a peanut-like morphology.The Galactic Center cannot be studied at visible, ultraviolet or soft X-ray wavelengths, because of the interstellar dust that hides it from observation. The available information comes from observations at radio, infrared, sub- millimeter and hard X-rays.
The main problem in estimating the distance to the Galactic Center is a proper calculation of extinction.
Extinction is the dimming of light from stars and other distant objects, due the combined effects of interstellar absorption and scattering of light by dust particles. Interstellar extinction increases at shorter wavelengths, resulting in interstellar reddening. Extinction is minor in longer wavelengths - radio and infrared, which makes them more suitable for observing at large distances in the galactic.
Because many of the GCs, which Shapley studied, are out of the dusty Galaxy plane, the distances that he found were not too severely affected by extinction.
The Shapley’s main argument was that such massive objects as GCs are most likely to be centered on the galactic center. However Shapley's conclusions remained controversial at the beginning, they were eventually accepted by majority of astronomers, and his technique is still considered one of the primary means of determining the distance to the center of the Galaxy.
Similar studies in the 1970s and 1980s with much better data and absorption corrections yielded half shorter distances - 8 instead of 15 kpc.
The exact distance from the Earth to the Galactic Center is still uncertain. The latest estimates based on both - geometric-based methods and standard candles produce distances of 7.6–8.7 kpc with more than 1Kpc uncertainty.
Eisenhauer, F. et al. (2005) used geometrical-based method combined with near IR imaging spectroscopy (with astrometric accuracy of 75 mas) to observe the central 30 light-days close to the Galactic Center. They determined radial velocities for 9 of 10 stars in the central 0.4”, and for 13 of 17 stars out to 0.7”, limiting stars magnitudes to K~16. They combined the calculated radial velocities with astrometrical data, and then used a global fit technique to derive new improved three-dimensional stellar orbits for 6 S stars in the central 0.5” region. This result in the updated estimate for the distance to the Galactic Center Ro= 7,62 +-0,32 kpc.
The instrumentation they used is SINFONI - a near-infrared (1.1 - 2.45 µm) integral field spectrograph connected to an adaptive optics module, installed on ESO VLT. The instrument operates with 4 gratings (J, H, K, H+K) providing a spectral resolution around 2000, 3000, 4000 in J, H, K, respectively, and 1500 in H+K. For more information about SINFONI, please refer to the following page: http://www.eso.org/sci/facilities/paranal/instruments/sinfoni/overview.html
Vanhollebeke, Groenewegen, and Girardi (2009) employed the different approach. They used the star population synthesis code called TRILEGAL (TRIdimensional modeL of thE GALaxy, Girardi et al. 2005) to compute colour-magnitude diagrams (CMD) towards the galactic bulge (GB) and Galactic Center. They simulated the photometric properties of stars located towards a given direction and limited simulations to given magnitudes. The simulations were run for several star formation rates and metallicity distributions. Extinction was calculated for each object separately based on its visual extinction value and the distance modulus of the object. Based on their simulations, the distance to the Galactic Centre was determined as R0 = 8.7+-0.57 - 0.43 kpc.
Majaess (2010) used sample RR Lyrae variables from the OGLE survey of Galactic bulge fields to estimate R0 using the standard candles method. Majaess (2010) paid a special attention to the effects that can bias the accurate measurements of R0. These include a) an ambiguous extinction, which in turn imposes a preferential sampling of stars toward the near side of the GB, resulting in a smaller mean value of R0, and b) an uncertainty in characterizing how a mean distance to the group of variable stars relates to R0. The result is R0=8.1+-0.6 kpc.
Eisenhauer, F. et al. 2005, "SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month". AJ. 628
Vanhollebeke E., Groenewegen M. A. T., Girardi L.. "Stellar populations in the Galactic bulge. Modelling the Galactic bulge with TRILEGAL". A&A 498: 2009. Bibcode 2009A&A...498...95V.
Majaess, D."Concerning the Distance to the Center of the Milky Way and Its Structure". Acta A.. 60 (2010)Cutri R.M., et al. 2003, The IRSA 2MASS All-Sky Point Source Catalog of Point Sources, NASA/IPAC, Infrared Science Archive.