Question

Problem 3 (6 pts) Use the filter bandwidths for the UBV system shown in the table below to determine through which filter Vega (effective temperature 9600 K) is the brightest. Assume that the sensitivity function is within the bandwidth of each filter, and 0 outside. Hint. It is helpful to remember that fv 10 Av(A)dλ and that s proportional to plank function Name Central λ Width (tım) 0.37 0.45 0.55 (pin) μιιι 0.066 0.094 0.088

Answer 1

Given that, the effective temperature of Vega = T = 9600 degrees k Again, the filter band widths of DBV system is given. We know that m = -2.5 log (f/f_0) M - absolute magnitude f - flux of the star f_0 - flux of standard star = 1 (say) Thus, we need to find f in different bonds Again, we have f = integral_0^infinity f_lambda s_gamma (lambda) d lambda s_gamma (lambda) - sensitivity function = {1 with filter boundaries 0 outside filter boundaries f (lambda) alpha B (lambda) (flack distribution) B (lambda) = 2hc^2/lambda^5 1/e^hc Vertical-bar lambda k Vertical-bar - 1 in case of high temperature, we have hc Vertical-bar lambda k Vertical-bar = 1 + hc/lambda k T + 1/2 [hc/lambda k T] + ------- e^hc Vertical-bar lambda k Vertical-bar - 1 = hc/lambda k T (neglecting higher order terms) \r\n thus B_lambda = 2hc^2/lambda^5 lambda k T/hc = 2 kTc/lambda^4 = f = integral_0^infinity 2 ktc/lambda^4 s_gamma (lambda) d lambda (1) u filter (0.309 - 0.936 mu m)