Are there any brown dwarfs optically visible from Earth?
A typical brown dwarf has 0.01% of the luminosity of the Sun, with the peak in infrared. There is still some output in visible light, probably around 0.001% of the Sun’s output. That is 100,000 times less (to use a popular way to phrase the ratio). The log of 100,000 is 5, which, divided by 0.4, yields 12.5 The Absolute magnitude of a brown dwarf would be 12.5 magnitudes fainter (thus, greater) than the Sun’s. M_bd = M_sun + 12.5 = 4.8 + 12.5 = +17.3 This is the magnitude that the star would have (in visible light) at a distance of 10 parsecs (from the definition of Absolute magnitude). To be visible to the naked eye, we have to bring it close enough for the apparent magnitude to be +6.0 A difference of 11.3 magnitudes 11.3 * 0.4 = 4.52 antilog(4.52) = 33,111. 10 parsecs / 33,111 = 0.0003 parsec = 0.001 light-year = 62.3 astronomical units. To be [barely] visible to the naked eye, the brown dwarf that we have modeled in this example would have to be within the Oort cloud, almost as far
