<p>I am wanting to plot a velocity profile (a plot of velocity against the star's distance from the galactic core) from the Gaia DR2, but so far my efforts have been disappointing.</p>

<p>The information I have for each star are the declination ($\delta$), right ascension ($\alpha$), radial velocity ($v_r$), parallax ($\theta_\text{parallax}$) and proper motion ($\mu$) (ra and dec).</p>

<p>I tried to calculate the star's distance from the galactic core using the cosine rule:</p>

<p>$$ d = \frac{1000}{\theta_{\text{parallax}}}$$
$$\theta = \arccos{[\sin{\delta_\text{star}}\sin{\delta_\text{core}} + \cos{\delta_\text{star}}\cos{\delta_\text{core}}\cos{(\alpha_\text{star}-\alpha_\text{core})}]}$$
$$ r = \sqrt{d_\text{core}^2+ d^2 - 2d \times d_\text{core} \times \cos{\theta}} $$</p>

<p>Where $d$ is the distance from the Sun to the star. $d_\text{core}$ is the distance from the Sun to the galactic core. $\theta$ is the angular separation of the star and the galactic core. $r$ is the distance from the star to the core.</p>

<p>And the star's speed using the equations:</p>

<p>$$\mu = \sqrt{\mu_\text{dec}^2 + \mu_\text{ra}^2}$$
$$ v_t = 4.7 \mu d $$
$$ v = \sqrt{v_r^2 + v_t^2} $$</p>

<p>But the plot doesn't show any kind of trend (just a kind of blob). Have I calculated correctly and, if not, how could I calculate the tangential velocities and radius from the galactic core?</p>

<p>Basically, I want to make the kind of plot that helps us identify dark matter in galaxies.</p>

CC BY-SA 4.0
2018-05-21T19:36:03.283Z
Note that I am placing restrictions on the allowed parallax error, as advised
Beta Decay
CC BY-SA 4.0
2018-05-21T23:00:14.380Z
You haven't calculated a velocity, you have calculated a speed. You need the velocity at a tangent to the line from the star to the Galactic centre.
ProfRob
CC BY-SA 4.0
2018-05-21T23:02:15.463Z
Also note that given a 0.1 mas systematic error in parallax, you won't get accurate tangential velocities beyond about 2kpc from the Sun.
ProfRob
CC BY-SA 4.0
2018-05-22T06:14:59.693Z
@RobJeffries Would that be standard for a telescope like Gaia? It seems like a large uncertainty to me
Beta Decay
CC BY-SA 4.0
2018-05-22T07:00:51.600Z
Please read the GaiaDr2 release papers.
ProfRob
CC BY-SA 4.0
2018-05-22T14:17:49.237Z
The radial distance $r$, can you define $d, d_{core}, \theta$?
Kornpob Bhirombhakdi
CC BY-SA 4.0
2018-05-22T14:21:47.070Z
@Kornpob $d$ is the distance from the Sun to the star. $d_\text{core}$ is the distance from the Sun to the galactic core. $\theta$ is the angular separation of the star and the galactic core.
Beta Decay
CC BY-SA 4.0
2021-06-22T12:56:54.080Z
Did you make any progress in the mean time?
B--rian
CC BY-SA 4.0
2021-06-29T13:17:09.207Z
@B--rian I haven't unfortunately, but I might revisit it over the summer
Beta Decay
<data-analysis><astrometry><gaia>
How to calculate the various properties of a star?
Beta Decay
# How to calculate the various properties of a star?

(Asked by: username_0 on 2018-05-21)

I am wanting to plot a velocity profile (a plot of velocity against the star's distance from the galactic core) from the Gaia DR2, but so far my efforts have been disappointing.

The information I have for each star are the declination ($\delta$), right ascension ($\alpha$), radial velocity ($v\_r$), parallax ($\theta\_\text{parallax}$) and proper motion ($\mu$) (ra and dec).

I tried to calculate the star's distance from the galactic core using the cosine rule:

$$ d = \frac{1000}{\theta\_{\text{parallax}}}$$
$$\theta = \arccos{[\sin{\delta\_\text{star}}\sin{\delta\_\text{core}} + \cos{\delta\_\text{star}}\cos{\delta\_\text{core}}\cos{(\alpha\_\text{star}-\alpha\_\text{core})}]}$$
$$ r = \sqrt{d\_\text{core}^2+ d^2 - 2d \times d\_\text{core} \times \cos{\theta}} $$

Where $d$ is the distance from the Sun to the star. $d\_\text{core}$ is the distance from the Sun to the galactic core. $\theta$ is the angular separation of the star and the galactic core. $r$ is the distance from the star to the core.

And the star's speed using the equations:

$$\mu = \sqrt{\mu\_\text{dec}^2 + \mu\_\text{ra}^2}$$
$$ v\_t = 4.7 \mu d $$
$$ v = \sqrt{v\_r^2 + v\_t^2} $$

But the plot doesn't show any kind of trend (just a kind of blob). Have I calculated correctly and, if not, how could I calculate the tangential velocities and radius from the galactic core?

Basically, I want to make the kind of plot that helps us identify dark matter in galaxies.

**Tags:** data-analysis, astrometry, gaia
> **Comments:**
> **username_0**: Note that I am placing restrictions on the allowed parallax error, as advised  
> **username_1**: You haven't calculated a velocity, you have calculated a speed. You need the velocity at a tangent to the line from the star to the Galactic centre.  
> **username_1**: Also note that given a 0.1 mas systematic error in parallax, you won't get accurate tangential velocities beyond about 2kpc from the Sun.  
> **username_0**: @RobJeffries Would that be standard for a telescope like Gaia? It seems like a large uncertainty to me  
> **username_1**: Please read the GaiaDr2 release papers.  
> **username_2**: The radial distance $r$, can you define $d, d_{core}, \theta$?  
> **username_0**: @Kornpob $d$ is the distance from the Sun to the star. $d_\text{core}$ is the distance from the Sun to the galactic core. $\theta$ is the angular separation of the star and the galactic core.  
> **username_3**: Did you make any progress in the mean time?  
> **username_0**: @B--rian I haven't unfortunately, but I might revisit it over the summer  

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## 0 answers

