CarterBoyerLindquist rms function doesn't account for spin for arbitrary masses.

[dangoh123]

When testing around with various changes, we noticed something odd with the CarterBoyerLindquist.rms() function you provided us, compared to the r_isco() function we made.

CarterBoyerLindquist.rms(M, 0.998) = 1.194e31
CarterBoyerLindquist.rms(M, 0.0) = 1.194e31
r_isco(0.998, M) = 2.4615716037986176e30
r_isco(0.0, M) = 1.194e31

For a mass of 1 solar mass in kg.

CarterBoyerLindquist.rms(M, 0.998) = 1.2369706551751847
CarterBoyerLindquist.rms(M, 0.0) = 6.0
r_isco(0.998, M) = 1.2369706551751847
r_isco(0.0, M) = 6.0

For a mass of just 1.

Does this function only work with a mass of 1?

[fjebaker]

Compare CarterBoyerLindquist.jl implementation

Z₁(M, a) = 1 + ∛(1 - (a / M)^2) * (∛(1 + (a / M)) + ∛(1 - (a / M)))
Z₂(M, a) = √(3(a / M)^2 + Z₁(M, a)^2)
rms(M, a, ±) = M * (3 + Z₂(M, a) ± √((3 - Z₁(M, a)) * (3 + Z₁(M, a) + 2 * Z₂(M, a))))
rms(M, a) = a > 0.0 ? rms(M, a, -) : rms(M, a, +)

with the ISCO here

AccretionFormulae.jl/src/emission_profile.jl

Lines 7 to 18 in 6a0a99f

	function r_isco(a_star, M)
	a = a_star
	r_g = 2*G*M/(c^2) # this should be removed
	# r_g = M This will be what is used once the eddington limit is sorted.
	z1 = 1+∛(1-a^2)*(∛(1+a)+∛(1-a))
	z2 = √(3*a^2+z1^2)
	if a >= 0
	r_isco = (3+z2-√((3-z1)*(3+z1+2*z2)))*r_g
	elseif a < 0
	r_isco = (3+z2+√((3-z1)*(3+z1+2*z2)))*r_g
	end
	end

The CarterBoyerLindquist.jl implemented the function from Bardeen et al. (1972), which doesn't use a dimensionless spin parameter.

I can update CarterBoyerLindquist.jl if you like, since it doesn't really make a difference for me, or else you can just pass in a*M.