<p>A column density is just the integral of a (number) density along the line of sight.</p>

<p>Often, you would get the same observational absorption or emission signature from a number density of $n$ molecules cm$^{-3}$, spread along a line of sight through a cloud of diameter $x$, as you would with a density of $0.1n$ spread over $10x$. </p>

<p>In other words, all we can infer is the product or, more accurately, the integral of $n\ dx$, and this is known as the column density.</p>

<p>In the paper you refer to, I doubt they know the thickness of the shock they are investigating, so a column density is all that can be determined.</p>

<p>The relative abundance is more straighforward; it is just the ratio of the number densities of the two labelled species.</p>

CC BY-SA 3.0
2016-05-01T07:09:13.560Z
2016-05-01T07:09:13.560Z
ProfRob
<p>I was reading the abstract of a paper regarding attempts at detection of a molecular precursor to the amino acid glycine, and I came across concepts (and notation) that I found confusing. If someone could describe in layman's terms (I've taken an astrophysics class so I'm not totally unaware) that would be great.</p>

<p>In the question I refer to the following section of a paper's abstract:</p>

<blockquote>
  <p>"we derive <strong>upper limit column densities</strong> of NH$_2$OH of $\leq 1.4 \times 10^{13} \mathrm{cm}^{-2}$
  and $\leq 1.5 \times 10^{13} \mathrm{cm}^{-2}$ toward the B1 and B2 shocks, respectively, and
  upper limit relative abundances of $N_\mathrm{NH_2OH}/N_\mathrm{H_2}$
  $\leq 1.4 \times 10^{-8}$ and $\leq 1.5 \times 10^{-8}$, respectively."</p>
</blockquote>

<p>The paper in question is called <em>CSO and CARMA Observations of <a href="https://en.wikipedia.org/wiki/L1157" rel="nofollow">L1157</a>. I. A Deep Search for Hydroxylamine (NH$_2$OH)</em>, and located <a href="https://ui.adsabs.harvard.edu/#abs/2015ApJ...812...76M/abstract" rel="nofollow">here.</a></p>

<astrochemistry>
What does this information about "upper limit column densities" and "upper limit relative abundances" mean?
Pulchritude
# What does this information about "upper limit column densities" and "upper limit relative abundances" mean?

(Asked by: username_0 on 2016-05-01)

I was reading the abstract of a paper regarding attempts at detection of a molecular precursor to the amino acid glycine, and I came across concepts (and notation) that I found confusing. If someone could describe in layman's terms (I've taken an astrophysics class so I'm not totally unaware) that would be great.

In the question I refer to the following section of a paper's abstract:

> "we derive **upper limit column densities** of NH$\_2$OH of $\leq 1.4 \times 10^{13} \mathrm{cm}^{-2}$
> and $\leq 1.5 \times 10^{13} \mathrm{cm}^{-2}$ toward the B1 and B2 shocks, respectively, and
> upper limit relative abundances of $N\_\mathrm{NH\_2OH}/N\_\mathrm{H\_2}$
> $\leq 1.4 \times 10^{-8}$ and $\leq 1.5 \times 10^{-8}$, respectively."

The paper in question is called *CSO and CARMA Observations of [L1157](https://en.wikipedia.org/wiki/L1157). I. A Deep Search for Hydroxylamine (NH$\_2$OH)*, and located [here.](https://ui.adsabs.harvard.edu/#abs/2015ApJ...812...76M/abstract)

**Tags:** astrochemistry


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## 1 answers

### Answer by username_1 on 2016-05-01. Score: 2 | Accepted answer

A column density is just the integral of a (number) density along the line of sight.

Often, you would get the same observational absorption or emission signature from a number density of $n$ molecules cm$^{-3}$, spread along a line of sight through a cloud of diameter $x$, as you would with a density of $0.1n$ spread over $10x$.

In other words, all we can infer is the product or, more accurately, the integral of $n\ dx$, and this is known as the column density.

In the paper you refer to, I doubt they know the thickness of the shock they are investigating, so a column density is all that can be determined.

The relative abundance is more straighforward; it is just the ratio of the number densities of the two labelled species.


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