Hi all. New guy here. I signed up for this forum for the specific purpose of asking this, since I can't reconcile the data myself. (I've been trying for days without success)(adsbygoogle = window.adsbygoogle || []).push({});

First of all, a little about me. I am extremely familiar with astrophysics and physics in general. I have no difficulty following a detailed mathematical model. That said, I've been studying the star Sirius B (the White Dwarf companion of Sirius A) and did a few calculations based on the data I could find. Here's the problem...

Input Data: (References are http://arxiv.org/PS_cache/astro-ph/pdf/0306/0306604.pdf" [Broken])

Mass (Sol=1): 0.952-1.113

Radius (Sol=1): 0.008004-0.008713

Surface Temp (°K): 25,193

Distance (arcsec; parsecs): 0.38002; 2.631440451

Absolute Magnitude (M): 11.34

Apparent Magnitude (m): 8.44

Now, armed with the above data, we can do a blackbody emission analysis that should show that all these data points agree, right? Wrong. Here's what I got...

Stefan-Boltzmann calculation: (Bolometric Flux w/m²=seT^{4}

25,193^{4}= 4.02828E+17 x 5.6705119E-08 x 0.9994 = 2.28286988E+10 w/m²

6,009,189 m radius = 4.53776090E+14 m² x 2.28286988E+10 w/m² = 1.03591177E+25 watts / 3.845E+26 watts (Sol) = 0.02694 Bolometric Luminosity

4.85 - ( Log (0.02694) x 2.5 ) = 8.77 Absolute Magnitude (M)

M + ( 5 x Log (2.631440451 / 10) ) = 5.87 Apparent Magnitude (m)

Compare that to the above RECONS data... Houston, we have a problem. The only way to get the RECONS data with the established radius, temperature, and distance is to use an emissivity of only 0.094... which would indicate that White Dwarfs are not evencloseto being blackbody radiators. That can't be right...

The only other option is to assume that the RECONS data is not Bolometric Magnitude, but Absolute Visual Magnitude, which is not what it says it is. If we assume that, then we get close with the known data points of radius, temperature, and distance. Visual flux at 25,193°K is only 8.22% of the total output (based on Planck Radiation Density l_{I}E = ((2phc^{2})/l^{5})/(e^{(hc/lkT)}-1) for frequencies 380nm-760nm using 10nm frequency steps) From that we get...

Absolute Visual Magnitude (Mv): 11.49

Apparent Visual Magnitude (mv): 8.59

...which iscloseto the RECONS data, but still off by a significant margin.

Double-checking the math, I input Sol and Sirius A, both of which match the RECONS data within a very close order of magnitude. Here's the RECONS data for those two stars.

Sol: M = 4.85; m = -26.72

Sirius A: M = 1.47; m = -1.43

Sirius A mandates that you assume an effective emissivity of only 0.89, (which could very well be the case with all the dust in the Sirius system clouding the images we get, making both values in error) or you have to assume that the 9,900°K T_{eff}is wrong and use 9,630°K. (which is much closer to other A0V star temperatures) Sol comes out right on the money. (big surprise :surprised )

If RECONS is using Mv and mv for its data, then Sol and Sirius A are wrong. (Sol Mv = 5.70; mv = -25.87 / Sirius A Mv = 2.40; mv = -0.49 by computation) If RECONS is using M and m for its data, than Sirius B is wrong.

So... am I missing something here? Did I do my math right? Did I forget a step that can reconcile this data? I'll admit my own fallibility, but I think I got it all right. Any help on this is greatly appreciated.

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# The trouble with Sirius B

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