<p>It is admirable that you are tackling this type of problem as a high school student, but I really think that some of these topics are out of your grasp currently, partly because of the highly technical nature, but also because of your lack of access to the necessary data. </p>

<p>For one thing, you say you have V-R colors as a function of time, but all these equations were calibrated to use V-K colors. From your linked paper, you're going to need equation 2 for your process to calculate $p$ and equation 3 for getting $\theta_0$. Unfortunately, these equations assume V-K colors. You can redo the analysis done in <a href="http://www.aanda.org/articles/aa/pdf/2009/30/aa12333-09.pdf" rel="nofollow">this paper</a> to calculate $p$ and <a href="http://www.aanda.org/articles/aa/pdf/2007/42/aa8225-07.pdf" rel="nofollow">this paper</a> to get $\theta_0$ for V-R colors, but it's not going to be easy.</p>

<p>For another, you're going to need measurements of the angular size as a function of time (and your cited paper suggests that only exists for a handful of Cepheids and was measured using the VLTI) as well as the RV as a function of time. The $\delta \theta$ that you reference is described exactly in the paper as "a  phase shift  between  the  radial  velocity  curve  and  the  angular  diameter changes measured either interferometrically or via the SB relation." This means if you have $RV(t)$ and $\Delta \theta(t)$, you can determine a phase shift between the two curves, presumably by fitting some equation of the form $f(t) = a\ \mathrm{sin}(bt+c)$ to both equations and saying that $\delta \theta = c_{RV} - c_{\Delta \theta}$.</p>

<p>The analysis you're trying to do requires very specific data and it seems that the relevant papers on this subject have already done the analysis on all stars in which all necessary data existed. You cannot easily apply this process to any Cepheid without significant work.</p>

CC BY-SA 3.0
2016-08-11T18:02:27.187Z
Thanks for your thoughtful and detailed comments. I was actually feeling lots of difficulties and frustration. As you say, it seems like it is almost impossible to derive p-p relation and θ-VR relation by myself in addition to my previous plan, which was relating linear radius variation, (integrated from radial velocity) and angular velocity(derived from θ-VR relation) to derive the distance. So what I thought was just referencing those p-p relation and θ-VR from the literature work, focusing on the later work.
7_G.S.N
CC BY-SA 3.0
2016-08-11T18:06:19.047Z
The data I might use for the radial velocity is in this [link](http://iopscience.iop.org/article/10.1086/426588) and for VR colors in this [database](http://crocus.physics.mcmaster.ca/Cepheid/Classical.html). But again, there's some problem. The data from the database one is quite outdated and I've seen from the other paper that the accuracy falls as the observed time difference gets bigger. So I need to find the lists of VR color values from the other site. I tried to used ESO archive but I couldn't open the file I downloaded from there. (I don't know why) :(
7_G.S.N
CC BY-SA 3.0
2016-08-11T18:08:09.250Z
Like this, I'm facing lots and lots of difficulties not only these things I told you. And I don't know anybody who is professional in this topic. Can I personally contact you in this sense? Asking questions via this stackexchange or any other way? Thank you.
7_G.S.N
CC BY-SA 3.0
2016-08-11T18:09:35.830Z
I cannot tag you. Can you please read my previous comments?
7_G.S.N
CC BY-SA 3.0
2016-08-11T18:19:07.103Z
@7_G.S.N I can't say I'm an expert on this particular method. I just have good technical knowledge of astronomy. I think one major hurdle of your process, like I said, will be that you know V-R colors but all equations referenced are for V-K colors. I'd suggest you try and reproduce the results in the original papers first, for stars already done. It is a viable option to email the authors (most papers list the first author's email) asking for clarifications and/or raw data, but be extremely clear, precise, and respectful if you do, and don't expect an immediate answer (if any).
zephyr
CC BY-SA 3.0
2016-08-11T18:27:17.017Z
But do you not personally suggest just referencing those equations, from the papers you referenced which is in terms of V-K colours?
7_G.S.N
CC BY-SA 3.0
2016-08-11T18:29:35.563Z
I mean there're still lots of jobs to do even I referenced those two particular equations, in the process of deriving the distances.
7_G.S.N
CC BY-SA 3.0
2016-08-11T20:05:43.853Z
You can reference those equations in that you use their mathematical form, but you shouldn't use the constants in those equations because those constants were derived assuming V-K colors. If you try to use them as-is, you're going to wind up with an incorrect answer in the end.
zephyr
CC BY-SA 3.0
2016-08-11T13:54:44.223Z
2016-08-11T13:54:44.223Z
zephyr
<p><a href="https://i.sstatic.net/0jpx9.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/0jpx9.png" alt="enter image description here"></a></p>

<p>The above is the equation used in the Baade-Wesselink method to independently get distances to Cepheid variables (in the process of deriving Period-Luminosity relation).</p>

<p>According to the paper <a href="http://arxiv.org/abs/1003.3854" rel="nofollow noreferrer">New Baade-Wesselink distances and radii for four metal-rich Galactic Cepheids</a>, δθ in the equation accounts for a phase shift between the radial velocity curve and the angular diameter changes measured via surface-brightness relation. My question is how can I calculate this δθ value given that I have lists of radial velocity values and V-R values with the observed HJD dates (which is possible to be converted in terms of phase). </p>

<star><distances><velocity><cepheids>
How to calculate a phase shift in the process of deriving Baade-Wesselinke distance?
7_G.S.N
# How to calculate a phase shift in the process of deriving Baade-Wesselinke distance?

(Asked by: username_0 on 2016-08-11)

[![enter image description here](https://i.sstatic.net/0jpx9.png)](https://i.sstatic.net/0jpx9.png)

The above is the equation used in the Baade-Wesselink method to independently get distances to Cepheid variables (in the process of deriving Period-Luminosity relation).

According to the paper [New Baade-Wesselink distances and radii for four metal-rich Galactic Cepheids](http://arxiv.org/abs/1003.3854), δθ in the equation accounts for a phase shift between the radial velocity curve and the angular diameter changes measured via surface-brightness relation. My question is how can I calculate this δθ value given that I have lists of radial velocity values and V-R values with the observed HJD dates (which is possible to be converted in terms of phase).

**Tags:** star, distances, velocity, cepheids

---

## 1 answers

### Answer by username_1 on 2016-08-11. Score: 2 | Accepted answer

It is admirable that you are tackling this type of problem as a high school student, but I really think that some of these topics are out of your grasp currently, partly because of the highly technical nature, but also because of your lack of access to the necessary data.

For one thing, you say you have V-R colors as a function of time, but all these equations were calibrated to use V-K colors. From your linked paper, you're going to need equation 2 for your process to calculate $p$ and equation 3 for getting $\theta\_0$. Unfortunately, these equations assume V-K colors. You can redo the analysis done in [this paper](http://www.aanda.org/articles/aa/pdf/2009/30/aa12333-09.pdf) to calculate $p$ and [this paper](http://www.aanda.org/articles/aa/pdf/2007/42/aa8225-07.pdf) to get $\theta\_0$ for V-R colors, but it's not going to be easy.

For another, you're going to need measurements of the angular size as a function of time (and your cited paper suggests that only exists for a handful of Cepheids and was measured using the VLTI) as well as the RV as a function of time. The $\delta \theta$ that you reference is described exactly in the paper as "a phase shift between the radial velocity curve and the angular diameter changes measured either interferometrically or via the SB relation." This means if you have $RV(t)$ and $\Delta \theta(t)$, you can determine a phase shift between the two curves, presumably by fitting some equation of the form $f(t) = a\ \mathrm{sin}(bt+c)$ to both equations and saying that $\delta \theta = c\_{RV} - c\_{\Delta \theta}$.

The analysis you're trying to do requires very specific data and it seems that the relevant papers on this subject have already done the analysis on all stars in which all necessary data existed. You cannot easily apply this process to any Cepheid without significant work.

> **Comments:**
> **username_0**: Thanks for your thoughtful and detailed comments. I was actually feeling lots of difficulties and frustration. As you say, it seems like it is almost impossible to derive p-p relation and θ-VR relation by myself in addition to my previous plan, which was relating linear radius variation, (integrated from radial velocity) and angular velocity(derived from θ-VR relation) to derive the distance. So what I thought was just referencing those p-p relation and θ-VR from the literature work, focusing on the later work.  
> **username_0**: The data I might use for the radial velocity is in this [link](http://iopscience.iop.org/article/10.1086/426588) and for VR colors in this [database](http://crocus.physics.mcmaster.ca/Cepheid/Classical.html). But again, there's some problem. The data from the database one is quite outdated and I've seen from the other paper that the accuracy falls as the observed time difference gets bigger. So I need to find the lists of VR color values from the other site. I tried to used ESO archive but I couldn't open the file I downloaded from there. (I don't know why) :(  
> **username_0**: Like this, I'm facing lots and lots of difficulties not only these things I told you. And I don't know anybody who is professional in this topic. Can I personally contact you in this sense? Asking questions via this stackexchange or any other way? Thank you.  
> **username_0**: I cannot tag you. Can you please read my previous comments?  
> **username_1**: @7_G.S.N I can't say I'm an expert on this particular method. I just have good technical knowledge of astronomy. I think one major hurdle of your process, like I said, will be that you know V-R colors but all equations referenced are for V-K colors. I'd suggest you try and reproduce the results in the original papers first, for stars already done. It is a viable option to email the authors (most papers list the first author's email) asking for clarifications and/or raw data, but be extremely clear, precise, and respectful if you do, and don't expect an immediate answer (if any).  
> **username_0**: But do you not personally suggest just referencing those equations, from the papers you referenced which is in terms of V-K colours?  
> **username_0**: I mean there're still lots of jobs to do even I referenced those two particular equations, in the process of deriving the distances.  
> **username_1**: You can reference those equations in that you use their mathematical form, but you shouldn't use the constants in those equations because those constants were derived assuming V-K colors. If you try to use them as-is, you're going to wind up with an incorrect answer in the end.  

---

