<p>If you have some spectral image in the form of a FITS-format file, like you have in the original image to the right of the P-V diagram: I think you will need to look up some reference on Fourier transform. This Fourier transform will take you from the RA-Dec image to the P-V diagram you want to generate. Also, you might need to read about the cross correlation method, as detailed in Tonry and Davis's 1979 paper: <a href="http://adsabs.harvard.edu/abs/1979AJ.....84.1511T" rel="nofollow noreferrer">http://adsabs.harvard.edu/abs/1979AJ.....84.1511T</a></p>

<p>Another method is called fitting which involves emission lines. </p>

<p>The IRAF package you will need to use is called "rvsao". There are some references on some webpages you can follow: </p>

<ul>
<li><a href="http://tdc-www.harvard.edu/iraf/rvsao/papers/rvsao.adass97.html" rel="nofollow noreferrer">http://tdc-www.harvard.edu/iraf/rvsao/papers/rvsao.adass97.html</a></li>
<li><a href="https://arxiv.org/abs/astro-ph/9803252" rel="nofollow noreferrer">https://arxiv.org/abs/astro-ph/9803252</a></li>
</ul>

<p>To generate a P-V digram you will need to map your radial velocity to a 1D-grid, say one depending on the radial position, the mapping should be one-to-one. Otherwise you can also generate a cube, depending what kind of original FITS data files you have from an observation. </p>

<p>I am only providing the details regarding the technical aspect, and am on purpose on explaining anything regarding "distribution"... Every relationship in physics which depends on space (and maybe time also) is some sort of a distribution. </p>

CC BY-SA 3.0
2017-12-29T15:43:01.820Z
This is a lame (I mean *Link Only*) answer. The question begins "Can someone explain to me how..." There is no explanation in your answer.  These could be left as comments, but I don't think these links provide any helpful *explaining* to the OP to begin with.
uhoh
CC BY-SA 3.0
2017-12-31T12:40:26.043Z
Someone else already explained. I am providing the links only for the ones looking for information to do research with. The question was ill-posed anyway. The example given is in itself a P-V diagram already.
Lame Duck
CC BY-SA 3.0
2017-12-31T14:44:51.347Z
You can consider asking a follow-up question and posting this as an answer there instead. That way your answer can match the question asked. You can also add a comment somewhere here linking to that question, and vice-versa. There's nothing wrong with asking and answering your own question from time to time.
uhoh
CC BY-SA 3.0
2017-12-29T15:15:04.247Z
2017-12-31T12:49:11.620Z
2017-12-31T12:49:11.620Z
Lame Duck
<p>Such diagrams are usually called <a href="https://en.wikipedia.org/wiki/Galaxy_rotation_curve" rel="nofollow noreferrer">rotation curves</a>, and show the velocity of stars/gas <em>in a disk galaxy viewed edge-on</em> along the line of sight (LOS) as a function of distance from the center.</p>

<p>That is, the $x$ axis gives the distance of the stars from the center ($x=0$) of the galaxy, and the $y$ axis gives the measured velocities at a given distance. Along a given LOS you'll find not a single velocity, but a (Gaussian-like) distribution of velocities, both because there is a certain scatter in velocities, but also because you only measure the component of the velocities projected onto your LOS, while both speed and direction change along the LOS, as seen here:</p>

<p><a href="https://i.sstatic.net/8usas.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8usas.png" alt="rotvel"></a></p>

<p><em>If</em> they all had the same velocity along the LOS, the plot you show would be a thin line; instead it is smeared out.</p>

<p>Due to mass being concentrated in the center, there's a steep increase in velocity at low $x$. If there were only the mass you can see, the velocity would decrease at larger $x$ due to the larger distance from the central mass. The reason it stay more or less constant is thought to be the extra, invisible mass known as <em>dark matter</em>.</p>

<p>The reason the left side of the plot is similar to the right, but mirrored not only across the $y$ axis but also the $x$ axis, is that on this side, the stars move <em>toward</em> you, while on the right side they move <em>away</em> from you. The whole galaxy evidently moves away from you at $500\,\mathrm{km}\,\mathrm{s}^{-1}$, since this is the velocity at $x=0$.</p>

<p>So, to recap: How do you generate such a plot? You measure the distribution of velocities along many lines of sight in the galactic plane, from one side ($-R_\mathrm{gal}$) to the other ($+R_\mathrm{gal}$). For instance, at $x=14\,\mathrm{kpc}$, you'd measure $V=675\pm12\,\mathrm{km}\,\mathrm{s}^{-1}$:</p>

<p><a href="https://i.sstatic.net/U5JtJ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/U5JtJ.png" alt="los"></a></p>

<p>In practice, images like this is made by using a grism which disperses the light according to its wavelength, together with a slit placed along the galactic plane, such that you block the light from the rest of the field. This is called <em>slit spectroscopy</em>, in contrast to "normal" spectroscopy where you block all light except for a little hole placed on some object (e.g. a star), or integral field spectroscopy, where you get the whole spectrum behind every pixel in an image.</p>

<p><a href="https://i.sstatic.net/sw7C3.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/sw7C3.gif" alt="Slit"></a></p>

CC BY-SA 3.0
2016-02-18T03:42:50.810Z
Wow! That is a very comprehensive answer! The truth is that I am familiar with the rotation curve. So, The P-V diagram is pretty much the rotation curve with the velocity dispersion on the same diagram? So in order to make such plot, you need both the velocity field and the velocity dispersion field, OR the intensity/spectral cube?
AstrOne
CC BY-SA 3.0
2016-02-18T08:07:52.837Z
@AstrOne: Okay, I can see I got a little carried away, especially for your needs, but yes, in short it's simply a "normal" rotation curve, with the extra information about the spread in velocity. This you could get e.g. with a (2+1)D datacube (2 spatial + 1 spectral) from integral field spectroscopy (in which case you'll have an extra spatial dimension perpendicular to the rotation field which you probably won't be using), or, more commonly, from "normal" spectroscopy placing a slit along the plane of the galaxy.
pela
CC BY-SA 3.0
2016-02-18T16:45:59.157Z
No worries, comprehensive is good actually! Things are clear now! Thanks a lot!
AstrOne
CC BY-SA 3.0
2016-02-18T00:50:20.013Z
2016-02-18T08:19:57.650Z
2016-02-18T08:19:57.650Z
pela
<p>Can someone explain to me how I can generate a Position-Velocity (PV) diagram from a galaxy's radial velocity field? I understand that usually PV diagrams are generated across the major axis of the galaxy, but I am not quite sure why they appear as a distribution. For example:</p>

<p><a href="https://i.sstatic.net/xUolL.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xUolL.gif" alt=""></a></p>

<galaxy><kinematics>
Create Position-Velocity diagram from a velocity field
AstrOne
# Create Position-Velocity diagram from a velocity field

(Asked by: username_0 on 2016-02-17)

Can someone explain to me how I can generate a Position-Velocity (PV) diagram from a galaxy's radial velocity field? I understand that usually PV diagrams are generated across the major axis of the galaxy, but I am not quite sure why they appear as a distribution. For example:

[![](https://i.sstatic.net/xUolL.gif)](https://i.sstatic.net/xUolL.gif)

**Tags:** galaxy, kinematics

---

## 2 answers

### Answer by username_3 on 2016-02-18. Score: 4 | Accepted answer

Such diagrams are usually called [rotation curves](https://en.wikipedia.org/wiki/Galaxy_rotation_curve), and show the velocity of stars/gas *in a disk galaxy viewed edge-on* along the line of sight (LOS) as a function of distance from the center.

That is, the $x$ axis gives the distance of the stars from the center ($x=0$) of the galaxy, and the $y$ axis gives the measured velocities at a given distance. Along a given LOS you'll find not a single velocity, but a (Gaussian-like) distribution of velocities, both because there is a certain scatter in velocities, but also because you only measure the component of the velocities projected onto your LOS, while both speed and direction change along the LOS, as seen here:

[![rotvel](https://i.sstatic.net/8usas.png)](https://i.sstatic.net/8usas.png)

*If* they all had the same velocity along the LOS, the plot you show would be a thin line; instead it is smeared out.

Due to mass being concentrated in the center, there's a steep increase in velocity at low $x$. If there were only the mass you can see, the velocity would decrease at larger $x$ due to the larger distance from the central mass. The reason it stay more or less constant is thought to be the extra, invisible mass known as *dark matter*.

The reason the left side of the plot is similar to the right, but mirrored not only across the $y$ axis but also the $x$ axis, is that on this side, the stars move *toward* you, while on the right side they move *away* from you. The whole galaxy evidently moves away from you at $500\,\mathrm{km}\,\mathrm{s}^{-1}$, since this is the velocity at $x=0$.

So, to recap: How do you generate such a plot? You measure the distribution of velocities along many lines of sight in the galactic plane, from one side ($-R\_\mathrm{gal}$) to the other ($+R\_\mathrm{gal}$). For instance, at $x=14\,\mathrm{kpc}$, you'd measure $V=675\pm12\,\mathrm{km}\,\mathrm{s}^{-1}$:

[![los](https://i.sstatic.net/U5JtJ.png)](https://i.sstatic.net/U5JtJ.png)

In practice, images like this is made by using a grism which disperses the light according to its wavelength, together with a slit placed along the galactic plane, such that you block the light from the rest of the field. This is called *slit spectroscopy*, in contrast to "normal" spectroscopy where you block all light except for a little hole placed on some object (e.g. a star), or integral field spectroscopy, where you get the whole spectrum behind every pixel in an image.

[![Slit](https://i.sstatic.net/sw7C3.gif)](https://i.sstatic.net/sw7C3.gif)

> **Comments:**
> **username_0**: Wow! That is a very comprehensive answer! The truth is that I am familiar with the rotation curve. So, The P-V diagram is pretty much the rotation curve with the velocity dispersion on the same diagram? So in order to make such plot, you need both the velocity field and the velocity dispersion field, OR the intensity/spectral cube?  
> **username_3**: @AstrOne: Okay, I can see I got a little carried away, especially for your needs, but yes, in short it's simply a "normal" rotation curve, with the extra information about the spread in velocity. This you could get e.g. with a (2+1)D datacube (2 spatial + 1 spectral) from integral field spectroscopy (in which case you'll have an extra spatial dimension perpendicular to the rotation field which you probably won't be using), or, more commonly, from "normal" spectroscopy placing a slit along the plane of the galaxy.  
> **username_0**: No worries, comprehensive is good actually! Things are clear now! Thanks a lot!  

---

### Answer by username_1 on 2017-12-29. Score: -1

If you have some spectral image in the form of a FITS-format file, like you have in the original image to the right of the P-V diagram: I think you will need to look up some reference on Fourier transform. This Fourier transform will take you from the RA-Dec image to the P-V diagram you want to generate. Also, you might need to read about the cross correlation method, as detailed in Tonry and Davis's 1979 paper: <http://adsabs.harvard.edu/abs/1979AJ.....84.1511T>

Another method is called fitting which involves emission lines.

The IRAF package you will need to use is called "rvsao". There are some references on some webpages you can follow:

* <http://tdc-www.harvard.edu/iraf/rvsao/papers/rvsao.adass97.html>
* <https://arxiv.org/abs/astro-ph/9803252>

To generate a P-V digram you will need to map your radial velocity to a 1D-grid, say one depending on the radial position, the mapping should be one-to-one. Otherwise you can also generate a cube, depending what kind of original FITS data files you have from an observation.

I am only providing the details regarding the technical aspect, and am on purpose on explaining anything regarding "distribution"... Every relationship in physics which depends on space (and maybe time also) is some sort of a distribution.

> **Comments:**
> **username_2**: This is a lame (I mean *Link Only*) answer. The question begins "Can someone explain to me how..." There is no explanation in your answer.  These could be left as comments, but I don't think these links provide any helpful *explaining* to the OP to begin with.  
> **username_1**: Someone else already explained. I am providing the links only for the ones looking for information to do research with. The question was ill-posed anyway. The example given is in itself a P-V diagram already.  
> **username_2**: You can consider asking a follow-up question and posting this as an answer there instead. That way your answer can match the question asked. You can also add a comment somewhere here linking to that question, and vice-versa. There's nothing wrong with asking and answering your own question from time to time.  

---

