# Column densities A region of the sky called the "Lockman Hole", located in the constellation of Ursa Major, is one of the areas surveyed in infrared light by the Herschel Space Observatory. Credit: ESA/Herschel/SPIRE/HerMES.

A column density is the number of units of matter observed along a line of sight that has an area of observation. This area has a height that is the distance to an object, or through which observation is taking place.

## Astronomy

"A region of the sky [at top right] called the "Lockman Hole", located in the constellation of Ursa Major, is one of the areas surveyed in infrared light by the Herschel Space Observatory. All of the little dots in this picture are distant galaxies. The pattern of their collective light is what's known as the cosmic infrared background. By studying this pattern, astronomers were able to measure how much dark matter it takes to create a galaxy bursting with young stars."

## Theoretical column densities

Def. a total amount per unit area of a material suspended in a fluid or in a cloud in space, measured along the length of a column is called a column density.

Usage notes:

• Quoted in terms of mass per (cross-sectional) area, or number per area.

## Lockman Hole

"We have made a detailed 21 cm study of areas that have the smallest known amount of H I in the northern sky. These observations were corrected for stray radiation using a method described in an Appendix and have an estimated uncertainty in NH I of ≤ 5 x 1018 cm-2. The region of main interest, around α = 10h45m, δ = 57°20', has a minimum NH I of 4.5 x 1019 cm-2."

Probably "most of the [neutral] hydrogen is extended and not contained in very small, unresolved, clouds. For example, there would have to be ~100 small clouds in the ~0.2 deg2 of the 43 m beam to produce the observed σ/〈NH I〉≈ 0.1. At a distance of 100 pc, each would have a diameter ~0.1 pc and a density 〈n〉~ 200 cm-3."

## Problem 1

Using the numbers in the above section for the beam diameter at the antenna, the distance of 100 pc, the number of clouds, assume a uniform distribution of neutral hydrogen, and the neutral hydrogen particle density, calculate the column density along the line of sight and compare it to the column density mentioned above.

## Problem 2

Using the uncertainty in the column density, calculate the approximate uncertainty in the hydrogen density.

## Problem 3

Using the column density for the Lockman Hole, calculate the apparent neutral hydrogen flux in units of m-2 sr-1. Calculate the uncertainty in units of flux.

## Problem 4

In regions like the Lockman Hole "the dust particles are small (radii a < 0.25 m)". The dust column density (DT) is 0.44 MJy sr-1 so that the DT/N(H I) = 0.077.

Using this information, calculate the dust column density in number of dust grains cm-2.

## Problem 5

According to SIMBAD there are some 1217 objects within 30' radius of the centered position for the Lockman Hole. Although these are mostly astronomical infrared sources and galaxies, if these are large dust particles, calculate their column density.

Of these only 349 are X-ray sources, calculate their column density.

## Hypotheses

1. Probably the number one reason the sky is black at night is the absorption due to media between stars, galaxies, etc.