What Factors Influence the Density of a Hydrogen Cloud in Space?

[BOAS]

Hi,

I wanted to ask, what does the density of a hydrogen cloud in space depend upon?

That might be a silly question given the definition of density, but here's the context;

Considering a particle at rest within a molecular cloud at radius $r$ from the centre, I have shown that the acceleration this particle feels is approximately $a \approx \frac{Gm}{r^{2}} \approx \frac{4 \pi G \rho r}{3}$ (from mass being density x volume).

Using the equations of motion for constant acceleration I have determined that the 'free fall' time of this particle is independent of $r$ and can be approximated by $t \approx \frac{1}{\sqrt{G \rho}}$.

Two questions;

Why is this time independent of the particles distance from the center?

How do you determine the density of hydrogen when the external pressure is presumably close to zero?

Thanks!

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[Fantasist]

The free-fall time is only constant for constant density. You can get this from Kepler's 3rd law t²~r³/m.(the square of the orbital period is proportional to the cube of the radius divided by the enclosed mass). Since for a constant density m~r³, this means that t=const.

A cloud with constant density would be gravitationally unstable though, In hydrodynamic equilibrium, the cloud density decreases like 1/r². In that case, m~r (not ~r³), so that t²~r³/m ~ r² i.e. t~r

 

[Ken G]

Why is this time independent of the particles distance from the center?

Because at larger r, there is more mass that is pulling the particle inward, so the force is greater in a way that ends up being proportional to r-- just like a simple harmonic oscillator (for which the time is also independent of r).

How do you determine the density of hydrogen when the external pressure is presumably close to zero?

You need to use the external pressure-- the pressure in the interstellar medium is not zero.

 

[pmacias]

Hello,

Thank you for your questions about the density of a hydrogen cloud in space. The density of a hydrogen cloud depends on various factors such as the initial conditions of the cloud, its temperature, and the surrounding environment. The initial conditions of the cloud, including its mass and size, will determine the overall density. The temperature of the cloud can also affect its density, as hotter clouds tend to have lower densities. Additionally, the surrounding environment, such as the presence of other nearby clouds or the influence of a nearby star, can also impact the density of the hydrogen cloud.

To address your first question, the free fall time of a particle within a molecular cloud is independent of its distance from the center because of the nature of gravitational acceleration. According to Newton's law of gravitation, the force of gravity between two objects is inversely proportional to the square of the distance between them. This means that as the particle moves closer to the center of the cloud, the force of gravity increases, but at the same time, the distance squared decreases. These two effects cancel each other out, resulting in a constant acceleration and therefore a constant free fall time.

As for your second question, the density of hydrogen in a cloud can be determined using various methods, such as spectroscopy or measuring the cloud's mass and volume. However, in the context of your equation, the density is determined by the external pressure, which is likely close to zero in a hydrogen cloud in space. This is because the pressure within a cloud is primarily due to the weight of the gas above it, and in space, there is no significant weight or pressure from the surrounding environment. Therefore, the density of a hydrogen cloud in space is primarily determined by its own mass and volume.

I hope this helps answer your questions about the density of a hydrogen cloud in space. If you have any further inquiries, please do not hesitate to ask.

Best regards,