Interstellar Medium Shielding

It might surprise you that you need to shield your ship from the interstellar medium, specifically at velocities greater than 40% of c. This is a result of interstellar space being filled with a diffuse medium of mostly hydrogen, which when relative to a ship at high enough velocities, comes to increasingly resemble ionizing radiation.

The main danger is heating and not erosion – erosion is insignificant enough that a 1 cm thick carbon shield can go 25,000 light-years (at a speed regime of 0.3 c), ignoring that not all particles displaced will be lost to space, instead landing back on the shield.

Interstellar Medium Density

To begin with, the interstellar medium density varies greatly, ranging from 10^-4 particles per cubic centimeter in the coronal gas component of the galactic halo of the Milky Way, to 10^6 particles per cubic centimeter in molecular clouds.

This is important in calculating the flux that the forward portion of the ship will receive at a particular velocity.

Particle Density Table

(In units of particles per cubic centimeter)

Component	Particle Density
Molecular clouds	102-106
H II regions	102-104
Cold neutral medium	20-50
Warm neutral medium	0.2-0.5
Warm ionized medium	0.2-0.5
Coronal gas (Hot ionized medium)	10-4-10-2

The local neighborhood around the sun is assumed to have a particle density of 1 particle per cubic centimeter on average.

Interstellar Medium Composition

By mass, the interstellar medium is 70% hydrogen, 28% helium and 2% heavier elements.
By number of atoms, the interstellar medium is 91% hydrogen, 8.9% helium and 0.1% heavier elements.

Erosion

Erosion is not taken to be a significant component of the danger in interstellar shielding. For example, at 0.3 c a ship's forward shield will encounter 1E+18 ISM particles per square centimeter per light-year traveled (ignoring differences in ISM density through the journey).
A light year contains 946.1 quadrillion centimeters. In that length, there are thus 946.1 quadrillion cubic centimeters, and assuming a particle density of one per cubic centimeter, there are 9.467E+17 particles in that volume, rounding up to 1E+18.

If each impact displaces 2 atoms from the shield, every light year traveled will cause the loss of 2E+18 atoms per square centimeter. For carbon shields, this is a loss of 40 micrograms per light year per square centimeter, ignoring that not all particles displaced will be lost to space, instead landing back on the shield.

To get the mass loss rate, 2E+18 times the atomic mass of carbon gives 40 micrograms.

This means that a 1 cm thick shield, can survive a trip of 56,250 light-years before being worn through. At high relativistic velocities however, space-time contraction is significant enough that the effective ISM density increases.

The density of carbon, times the length, divided by mass loss rate gives the max trip length due to erosion.

Calculating the Flux

Before we can begin calculating the flux, the mass density of the interstellar medium first be known.
The mass density is given by:

$\rho =mp$

• where $/rho$ is the mass density of the interstellar medium
• where $m$ is the mass of the particle
• where $p$ is the particle density of the interstellar medium