Mass uncertainties and the calculation of accretion disks

[Ikendo]

I'm currently writing an extended essay about black holes in binary systems and accretion disks, and I wonder how I should proceed when calculating the size of the accretion disk.

Take, for instance, the binary system A 0620-00 where the mass of the black hole is said to be 5-10 solar masses, and the companion star is said to be 0.2-0.7 solar masses. The period is 0.323 days. To calculate the size of the accretion disk I use these equations:

The distance between the star and the black hole (assuming circular orbits):
a=2.9 ×10^6 x M_1^(1/3) x (1+q)^(1/3) x P^(2/3) km

q=M_2/M_1

The size of the accretion disk:
R_circ/a=(q+1) x (0.500 - 0.227log q)^4

Will it be very wrong to use the min. value of the black hole and the min. value of the companion star to calculate the min. size of the accretion disk, and then the max. values for the max. size? Or should I use the max. value of the black hole and the min. value of the companion star, and then the other way around?

I suddenly feel like I lack some very basic knowledge in this...

 

[jbsteele]

The answer depends on what you are trying to achieve. If you are looking to calculate the range of possible sizes for the accretion disk, then it is appropriate to use the min and max values of the black hole and companion star to get the min and max values for the size of the accretion disk. However, if you are looking for a more precise measurement of the size of the accretion disk, then you may need to use intermediate values for both the black hole and companion star, or take an average of the two. It is important to note that there is no one-size-fits-all approach, and the best approach will depend on the particular system you are studying.

 

[tomcue]

As a scientist, it is important to acknowledge and account for uncertainties in any calculations or measurements. In this case, the uncertainties in the mass of the black hole and the companion star can have a significant impact on the calculated size of the accretion disk.

To address this, it would be best to use a range of values for both the black hole and companion star masses, rather than just the minimum or maximum values. This will give a more accurate and realistic range for the size of the accretion disk.

Additionally, it is important to consider the sources of these uncertainties. Are they based on observational data or theoretical models? Understanding the limitations and assumptions in these values can also help in interpreting the results.

Overall, it is important to be cautious and transparent in accounting for uncertainties when making calculations in any scientific research.