Re: At what distance from Earth will R136a1 appear to be as bright as the Sun?

When I first saw your answer of 3162 AU, I said, "that is clearly right." After reading your friend's reply, I realized that I was thinking mechanically in astronomical jargon. Your friend is right in worrying about the wavelength of the light from the star. We have to be more specific here. When astronomers speak of the luminosity of the star, they usually mean the luminosity summed at all wavelengths. This is really a theoretical term because it is very difficult to measure the luminosity of a massive star. Stars with hundreds of solar masses emit most of their light at ultraviolet wavelengths and some X rays, and it is not easy to measure ultraviolet light because that light is heavily absorbed by the interstellar medium and the Earth's atmosphere. Astronomers have to resort to models of such stars in order to guess the luminosity of a star at all wavelengths. The procedure is to compare the light at visible wavelengths with calculations of a model star of certain luminosity. If the observed and calculated lights intensities coincide, we assume that the star has that luminosity. Doing so, Crowther and coworkers in a recent article to be published in the Monthly Notices of the Royal Astronomical Society concluded that the luminosity of R136a1 must be around 10 million solar luminosities. But remember: this is the luminosity summed over all wavelengths of light.

Your friend poses an interesting question. How would such a star look like to the human eye? Your friend is right in that massive stars are much bluer than our Sun. Their light tends to concentrate at blue and ultraviolet wavelengths, which our eyes cannot perceive. According to the article by Crowther's research team, the absolute magnitude of R136a1 at visible wavelengths is M_R136a1=-7.41. The absolute magnitude of a star is the magnitude that the star would have if it were placed at 10 parsecs from the observer. If we placed the Sun at 10 parsecs from us, it would have a magnitude of M_S=4.83 at visible wavelengths. To convert absolute magnitudes to luminosities, use the formula: log(L/L_s)=0.4(M_s-M) where L and M are the luminosity and magnitudes of the star, and L_s and M_s are those of the Sun. Notice that L grows as M decreases (and becomes more negative). Just in case, log(L/L_s) equals the exponent x of 10 such that 10^x=L/L_s. Thus I get log(L/L_s)=4.90, or L=10^4.90L_s at visible wavelengths. That is almost 100,000 times the solar luminosity at visible wavelengths. You can see that most of the light from R136a1 is at invisible wavelengths to the eye. At visible wavelengths this star is much dimmer. If we wanted to see this star just as we see the Sun at visible wavelengths, it would have to be placed at 280 AU from us. Of course we would be unable to see its strong ultraviolet light, or even guess it because that light would be enough to kill all life on Earth at that distance.

Greetings,

Vladimir Escalante Ramírez
National University of Mexico