Can Acoustical Velocities in Neutron Stellar Cores Exceed the Speed of Light?

[Orion1]

Neutron Stellar Cores...



I watched a program in which a astrophysics professor suggested that in theoretical calculations, a Trans-Oppenheimer Neutron Stellar Core's acoustical velocity can exceed vacuum luminous velocity.

$$v_s >= c$$

Oppenheimer Neutron Stellar Density:
$$p_n = \frac{3 \pi}{G T_n^2}$$
T_n = Oppenheimer Neutron Star rotational period

Acoustical Velocity:
$$v_s = \sqrt{ \frac{B}{p_n}}$$

Acoustical Bulk Modulus:
$$B = p_n v_s^2$$

$$p_n = \frac{3 \pi}{G T_n^2} = \frac{B}{v_s^2}$$

$$T_n = v_s \sqrt{ \frac{3 \pi}{GB}}$$

$$v_s >= c$$

$$T_n = c \sqrt{ \frac{3 \pi}{GB}}$$

How was the Bulk Modulus calculated for a Trans-Oppenheimer Neutron Star?

Why is it theoretically unreasonable for trans-luminous acoustical velocities?

If trans-luminous acoustical velocities are theoretically possible, would such a result produce a Cherenkov Effect?

 

[AndyW]

Thank you for bringing up this interesting topic. I would like to address your questions and concerns about Neutron Stellar Cores.

Firstly, the Bulk Modulus for a Trans-Oppenheimer Neutron Star is calculated based on the density of the star and the speed of sound within it. This is an important factor in determining the acoustical velocity, as it reflects the compressibility of the material within the star.

Regarding the theoretical possibility of trans-luminous acoustical velocities, it is important to note that these calculations are based on theoretical models and assumptions. While they can provide valuable insights and predictions, they are not always reflective of the real world. Therefore, it is not unreasonable to question the validity of such results.

If trans-luminous acoustical velocities were to be observed, it is possible that it could produce a Cherenkov effect. This phenomenon occurs when a charged particle travels faster than the speed of light in a medium, causing a characteristic blue glow. However, it is important to note that this effect is typically observed in materials with a much lower speed of sound compared to the theoretical acoustical velocities of a Neutron Stellar Core.

In conclusion, while the calculations and theories surrounding Neutron Stellar Cores are fascinating, it is important to approach them with a critical and analytical mindset. As scientists, it is our responsibility to question and challenge ideas in order to gain a deeper understanding of the world around us. Thank you for bringing up this topic and sparking a discussion on this fascinating subject.