<p>I'm a high school student but have as much interests in Cepheid variable as the professionalists. I'm trying to derive independent distances to Cepheid with the Baade-Wesselink method. </p>

<p>I got the angular diameter variations data from the paper <a href="https://arxiv.org/abs/astro-ph/0311525" rel="nofollow">Cepheid distances from infrared long-baseline interferometry</a> but I'm stuck from the afterward. I want to know how equation 9 in that paper is derived. Where did the number 9.305 suddenly came up? </p>

<p>The equation is the following:</p>

<p>θLimb-darkened model angular diameter = amplitude of limb-darkened observed angular diameter + 9.305 (∆D/d)</p>

<p>It seems like I need that equation to derive the distance from the angular diameter values with radial velocity values. </p>

CC BY-SA 3.0
2016-10-13T14:53:25.157Z
"This is done by applying a classical χ^2 minimization algorithm between our angular diameter measurements and a model of the star pulsation." It's simply a constant derived from fitting a model to data by minimizing the chi squared value of the fit.
zephyr
CC BY-SA 3.0
2016-10-14T07:02:21.267Z
@zephyr Yeah but the X^2 minimization algorithm is done for angular diameter values but in the equation 9 suddenly distance d and radial amplitude D came up! I don't get this point..
7_G.S.N
CC BY-SA 3.0
2016-10-14T13:35:29.810Z
The minimization is done for $\theta_{LD,model}$ which is a function of $d$ and $D$. That's just [geometry](https://en.wikipedia.org/wiki/Small-angle_approximation#Astronomy).
zephyr
<cepheids><interferometry><angular-diameter>
Calculating angular diameter amplitude from angular diameter variations of Cepheid variable
7_G.S.N
# Calculating angular diameter amplitude from angular diameter variations of Cepheid variable

(Asked by: username_0 on 2016-10-13)

I'm a high school student but have as much interests in Cepheid variable as the professionalists. I'm trying to derive independent distances to Cepheid with the Baade-Wesselink method.

I got the angular diameter variations data from the paper [Cepheid distances from infrared long-baseline interferometry](https://arxiv.org/abs/astro-ph/0311525) but I'm stuck from the afterward. I want to know how equation 9 in that paper is derived. Where did the number 9.305 suddenly came up?

The equation is the following:

θLimb-darkened model angular diameter = amplitude of limb-darkened observed angular diameter + 9.305 (∆D/d)

It seems like I need that equation to derive the distance from the angular diameter values with radial velocity values.

**Tags:** cepheids, interferometry, angular-diameter

> **Comments:**
> **username_1**: "This is done by applying a classical χ^2 minimization algorithm between our angular diameter measurements and a model of the star pulsation." It's simply a constant derived from fitting a model to data by minimizing the chi squared value of the fit.  
> **username_0**: @username_1 Yeah but the X^2 minimization algorithm is done for angular diameter values but in the equation 9 suddenly distance d and radial amplitude D came up! I don't get this point..  
> **username_1**: The minimization is done for $\theta_{LD,model}$ which is a function of $d$ and $D$. That's just [geometry](https://en.wikipedia.org/wiki/Small-angle_approximation#Astronomy).  

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## 0 answers

