<p>@tefalya   Somebody told me  "EM is the integral of electron density squared over the emitting volume.  In collisional ionized plasmas, it gives the amount of material emitting at a given temperature.  In the low density regime, temperature, emission measure, and abundance together with an atomic code completely specify the observed spectral energy distribution of coronal plasma.</p>

<p>The normalization parameter you get out of APEC, MEKAL, etc. relate to the emission measure.  If you read the description of the APEC model in XSPEC, you will see that the normalization = 10^-14* n_e^2 dV/(4 !pi distance^2).  The Emission Measure EM is n_e^2 dV, and has units of cm^-3. So the emission measure is an observable, and by assuming that the volume is not changing significantly during the flare, the changing emission measure is a proxy for the changing electron density."</p>

CC BY-SA 3.0
2017-06-23T04:19:48.673Z
2017-06-23T04:19:48.673Z
questionhang
<p>Emission measure is (usually) used in X-ray and EUV astronomy, though I suppose also in cases of optically thin radio emission. It is <em>defined as</em> the square of the number density of free electrons integrated over the volume of the plasma.</p>

<p>$${\rm EM} = \int n_e^2 \ dV$$</p>

<p>The flux of optically thin emission from a plasma (e.g. thermal bremsstrahlung) is then directly proportional to the emission measure of the plasma multiplied by a temperature dependent cooling loss law.</p>

<p>In other words, when you measure the flux of X-rays from an unresolved optically thin emitter, there is a degeneracy between the electron number density (squared) and the overall plasma volume.</p>

<p>When you fit an X-ray spectrum with an optically thin model, the emission measure (divided by $4\pi d^2$, where $d$ is the distance to the object), is a multiplicative free parameter.</p>

<p>Your question about calculation is extremely difficult to answer. Suppose I measure a count-rate of $N$ X-ray counts per second using some X-ray telescope (I can only assume that's what you mean by a "X-ray light curve".).</p>

<p>The count-rate received at the telescope depends on: the emission measure (as defined above) multiplied by a term that depends on the temperature (or temperatures) of the source, the chemical composition of the source and the adopted emission process (is it free-free thermal bremsstrahlung, a thermal plasma or something else). It is then attenuated by any intrinsic absorption in the source and any absorption between us and the source and by the distance to the source (assuming the radiation is isotropic). Finally what is <em>detected</em> is determined by the response of the X-ray detector to X-ray photons as a function of energy.</p>

CC BY-SA 3.0
2016-01-31T15:15:35.920Z
Your answer can be found in general papers, but they do not give a clear and direct definition about EM. There is no direct expression of EM either.  Usually expressions of EM carry electron density, but Ne can not be derived from a light curve.
questionhang
CC BY-SA 3.0
2016-01-31T15:36:39.100Z
@questionhang how much clearer can the definition be? $EM = \int n_e^2\ dV$.
ProfRob
CC BY-SA 3.0
2016-02-01T02:12:25.427Z
What does this interation mean? Why do we integrate like this? You can not say E is $mc^2$ and that is all. We can not derive $Ne$ in a light curve directly. How to derive it then? I have specified my question clearly before your answer, right?
questionhang
CC BY-SA 3.0
2016-02-02T09:19:08.247Z
I know how to calculate it now. Thank you.
questionhang
CC BY-SA 3.0
2016-01-30T23:28:48.820Z
2017-06-23T08:37:38.340Z
2017-06-23T08:37:38.340Z
ProfRob
<p>Many papers mention emission measure, and some of them give the expression of EM, BUT there is no clear definition of EM.</p>

<p>My question is what EM is on earth? Its unit is supposed to be cm-3.</p>

<p>How to calculate EM? <a href="http://www.cv.nrao.edu/course/astr534/FreeFreeEmission.html" rel="nofollow">here</a>(4B5) gives an expression, but it can not be derived from a light curve directly.</p>

<p>Given an X-ray light curve(not from the Sun), probably I need to devide the light curve into many bins and do spectral fitting.</p>

<p>Then what should I do? Rererence papers with clear definition and expression are welcome.</p>

CC BY-SA 3.0
2016-01-30T13:49:53.343Z
The very first [google hit](http://www.cv.nrao.edu/course/astr534/FreeFreeEmission.html) defines it as the integral of $N_2^2$ along the line of sight, where $N_e$ is the electron number density. That gives dimensions of pc cm$^{-6}$, though.
pela
CC BY-SA 3.0
2016-01-30T15:09:56.490Z
@pela Ne is not a direct observational quantity. There are other expressions of EM, which can be derived by analysing a light curve.
questionhang
<terminology><x-ray><flare><synchrotron-radiation>
What is "emission measure"?
questionhang
# What is "emission measure"?

(Asked by: username_0 on 2016-01-30)

Many papers mention emission measure, and some of them give the expression of EM, BUT there is no clear definition of EM.

My question is what EM is on earth? Its unit is supposed to be cm-3.

How to calculate EM? [here](http://www.cv.nrao.edu/course/astr534/FreeFreeEmission.html)(4B5) gives an expression, but it can not be derived from a light curve directly.

Given an X-ray light curve(not from the Sun), probably I need to devide the light curve into many bins and do spectral fitting.

Then what should I do? Rererence papers with clear definition and expression are welcome.

**Tags:** terminology, x-ray, flare, synchrotron-radiation
> **Comments:**
> **username_1**: The very first [google hit](http://www.cv.nrao.edu/course/astr534/FreeFreeEmission.html) defines it as the integral of $N_2^2$ along the line of sight, where $N_e$ is the electron number density. That gives dimensions of pc cm$^{-6}$, though.  
> **username_0**: @pela Ne is not a direct observational quantity. There are other expressions of EM, which can be derived by analysing a light curve.  

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## 2 answers

### Answer by username_2 on 2016-01-30. Score: 8 | Accepted answer

Emission measure is (usually) used in X-ray and EUV astronomy, though I suppose also in cases of optically thin radio emission. It is *defined as* the square of the number density of free electrons integrated over the volume of the plasma.

$${\rm EM} = \int n\_e^2 \ dV$$

The flux of optically thin emission from a plasma (e.g. thermal bremsstrahlung) is then directly proportional to the emission measure of the plasma multiplied by a temperature dependent cooling loss law.

In other words, when you measure the flux of X-rays from an unresolved optically thin emitter, there is a degeneracy between the electron number density (squared) and the overall plasma volume.

When you fit an X-ray spectrum with an optically thin model, the emission measure (divided by $4\pi d^2$, where $d$ is the distance to the object), is a multiplicative free parameter.

Your question about calculation is extremely difficult to answer. Suppose I measure a count-rate of $N$ X-ray counts per second using some X-ray telescope (I can only assume that's what you mean by a "X-ray light curve".).

The count-rate received at the telescope depends on: the emission measure (as defined above) multiplied by a term that depends on the temperature (or temperatures) of the source, the chemical composition of the source and the adopted emission process (is it free-free thermal bremsstrahlung, a thermal plasma or something else). It is then attenuated by any intrinsic absorption in the source and any absorption between us and the source and by the distance to the source (assuming the radiation is isotropic). Finally what is *detected* is determined by the response of the X-ray detector to X-ray photons as a function of energy.

> **Comments:**
> **username_0**: Your answer can be found in general papers, but they do not give a clear and direct definition about EM. There is no direct expression of EM either.  Usually expressions of EM carry electron density, but Ne can not be derived from a light curve.  
> **username_2**: @questionhang how much clearer can the definition be? $EM = \int n_e^2\ dV$.  
> **username_0**: What does this interation mean? Why do we integrate like this? You can not say E is $mc^2$ and that is all. We can not derive $Ne$ in a light curve directly. How to derive it then? I have specified my question clearly before your answer, right?  
> **username_0**: I know how to calculate it now. Thank you.  

---

### Answer by username_0 on 2017-06-23. Score: 1

@tefalya Somebody told me "EM is the integral of electron density squared over the emitting volume. In collisional ionized plasmas, it gives the amount of material emitting at a given temperature. In the low density regime, temperature, emission measure, and abundance together with an atomic code completely specify the observed spectral energy distribution of coronal plasma.

The normalization parameter you get out of APEC, MEKAL, etc. relate to the emission measure. If you read the description of the APEC model in XSPEC, you will see that the normalization = 10^-14\* n\_e^2 dV/(4 !pi distance^2). The Emission Measure EM is n\_e^2 dV, and has units of cm^-3. So the emission measure is an observable, and by assuming that the volume is not changing significantly during the flare, the changing emission measure is a proxy for the changing electron density."


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