Finding magnitude of part of binary system

[elliottmarter]

3. A very cool, faint white dwarf is identified as such from its spectrum and is known to have an apparent visual magnitude, mv = 16.73. A series of observations over several years yields a parallax measurement of 171±2 mas (milli-arcseconds).

(i) How far away is the white dwarf, and what must its absolute visual magnitude be?

(ii) Repeated spectroscopic observations of the white dwarf provide evidence that the white dwarf is in fact a close binary system, in which the brighter component contributes twice as much visual light as the fainter component. What would the apparent magnitude of the fainter star be, in the absence of its brighter companion?

I have done part i) but i can't do part ii) my attempt is below

My Attempt:

Ma: apparent mag of brighter star
Mb: apparent mag of dimmer star

Ma-Mb = 2.512 x log(Fa/Fb)

16.73-Mb = 2.512 x log(2) [as the brighter star is twice as bright]

Mb = 15.97

but this number is lower and so means it is brighter than the brightest star?

any help would be much appreciated TIA

 

[NateD]

Part (i): The distance to the white dwarf is 5.8 parsecs, and its absolute visual magnitude must be 12.41. Part (ii):The apparent magnitude of the fainter star, in the absence of its brighter companion, would be 15.97.