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I was researching the formation of brown dwarfs, and I stumbled into the paper "The minimum mass for star formation, and the origin of binary brown dwarfs", and I am attempting to code a function in Python for equation (42), where c is the speed of light, h is the Planck constant, a is the isothermal sound speed, K(T) is the mean opacity (given by equation 3 in the paper), G is the gravitational constant, and m is the mean molecular weight.

The equation

My functions are:

def opacity(temp):
    return (1e-4)*((temp)**2) #divide by a factor of 10^-3 and multiply by 10^-4 because of conversion to km

def minmass(molweight, temperature, soundspeed):
    cons = 60/(np.pi**7)  #constant
    numer = (scipy.constants.c**2)*(scipy.constants.h**3)*((soundspeed*1000)**5)*opacity(temperature) #numerator
    denom = (scipy.constants.G**5)*((molweight*0.001)**4) #denominator
   
    total = cons*(numer/denom) #putting it all together
    final = (total**(1/3))/(1.989e30) #division by constant converts kg to solar mass
    return final

print(minmass(4.0e-24, 10, 1.8e4))

As you'll notice, I've attempted to run my function with the test case of contemporary star formation described in the paper (T ≃ 10 K, ¯m ≃ 4.0×10^−24 g, a ≃ 1.8×10^4 km s^−1, κ1 ≃ 10^−3 cm^2 g^−1 and β ≃ 2.) I have also multiplied the inputs in the function so that all lengths are in terms of meters and so that all masses are in kilograms. However, even after extensively combing over the function, I keep achieving an answer that is thousands of magnitudes greater than the expected output, 0.001 M.

I would appreciate it a lot if anyone were to were to assist me on this issue and possibly guide me to a solution.

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  • $\begingroup$ Images of text or mathematics are very strongly discouraged. Please use Mathjax instead. $\endgroup$
    – StephenG - Help Ukraine
    Dec 20, 2022 at 10:14
  • $\begingroup$ The code returns 0.0015 solar masses. $\endgroup$
    – ProfRob
    Dec 20, 2022 at 10:53
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    $\begingroup$ Yeah, that's my bad. The *1e24 term in the denominator variable shouldn't be there, it was just me tweaking around and forgetting to delete it from the code. $\endgroup$
    – Ankit Biswas
    Dec 20, 2022 at 14:00
  • $\begingroup$ I got 0.0015 solar masses with the code as you originally presented it. Now it gives a crazy answer. I suggest you start checking your units. $\endgroup$
    – ProfRob
    Dec 20, 2022 at 16:33

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