At what wavelengths can black hole Sagittarius A* be observed from Earth? The supermassive black hole in the center of the Milky Way is blocked by dust and gas clouds as seen from where we are. Which wavelengths are blocked and which are most undisturbed for observation of Sagittarius A* and its immediate neighborhood? Does the matter between us change for example polarization at some wavelengths or cause disturbances other than blocking the light? Could galactic cosmic rays, heavy ions, from it be detected if they were emitted, or would they be deflected by magnetic fields?

By the way, at what distance from us is the most dust located? Is it concentrated in one region or are there several dust clouds in the way?
From Genzel et al. (2010), here's part of Fig. 7.7.1:



This is part of the spectral energy distribution of Sagittarius A*, a flot of $\nu$ (frequency) vs. $\nu L_{\nu}$ (frequency times luminosity). For comparison, visible light is in wavelengths from $\sim4\times10^{14}\text{ Hz}$ to $\sim8\times10^{14}\text{ Hz}$, which happens to be around the bottom of the trough of nonthermal electron emission. Right away, this makes submillimeter and millimeter wavelengths good candidates, leading to studies using Very Long Baseline Interferometry. Likewise, infrared emissions are a good target, and so the Spitzer Space Telescope, for instance, has been used. X-ray flares of up to $\sim10^{36}\text{ erg/s}$ also occur from time to time,1 so that part of the spectrum is sometimes used to observe this activity. Finally, of course, Sagittarius A* is a very strong radio source, and it was initially observed in radio wavelengths (and it still is!).

As Fish &amp; Doeleman 2010 write,2


  Interstellar scattering, which varies as $\lambda^2$, dominates over intrinsic source structure at longer wavelengths, and the emission from Sgr A* transitions from optically thick to optically thin near $\lambda = 1\text{ mm}$ (Doeleman et al. 2001). 


This means that the visible part of the spectrum is dimmed even more. Combine that with relatively low emission at those wavelengths, and you have a pretty poor target for optical telescopes, and a pretty good target (all other factors considering) at other wavelengths, especially near the emission peak.



1 Flares also are visible in other wavelengths, but I mention X-rays here because Sagittarius A* is typically much less luminous in X-rays.

2 I believe they mean $\lambda^{-2}$. Power laws for scattering in the area vary, but they are generally given between as $\lambda^{-1.5}$ and $\lambda^{-2}$. At any rate, the index may differ over different regimes.