Background Physics

Some equations that I needed in a safe place so that I don't have to keep re-deriving these… some are always true, others are true depending on criteria — I remember which are which, but I'm not going to type up the conditions, so use these equations with caution!

(1)
\begin{align} z=\frac{\lambda_{obs}-\lambda_{emit}}{\lambda_{emit}} \end{align}
(2)
\begin{align} z_1-z_2=\frac{\lambda_1-\lambda_2}{\lambda_{emit}}= \Delta z \end{align}
(3)
\begin{align} \frac{\lambda_{emit}}{\lambda_{obs}}=1+\frac{v}{c} \end{align}
(4)
\begin{align} \frac{\lambda_{emit}}{\lambda_{1}} - \frac{\lambda_{emit}}{\lambda_{2}}= 1+\frac{v_1}{c} - 1 - \frac{v_2}{c} \end{align}
(5)
\begin{align} c \left( \frac{\lambda_{emit}}{\lambda_{1}} - \frac{\lambda_{emit}}{\lambda_{2}} \right)=\Delta v \end{align}
(6)
\begin{align} \lambda_{2}\lambda_{emit}-\lambda_{1}\lambda_{emit}=\Delta v * \lambda_{1}\lambda_{2} \end{align}
(7)
\begin{align} \lambda_{emit} \left ( \lambda_{2} - \lambda_{1} \right ) = \Delta v * \lambda_{1}\lambda_{2} \end{align}
(8)
\begin{align} \Delta v = \left ( \frac{\lambda_{emit} \left( \lambda_{2}-\lambda_{1}\right )}{\lambda_{1}\lambda_{2}} \right)* c \end{align}

All right all right.

(9)
\begin{align} z_1=\sqrt{\frac{1+v_1/c}{1-v_1/c}}-1 \end{align}
(10)
\begin{align} z_2=\sqrt{\frac{1+v_2/c}{1-v_2/c}}-1 \end{align}

… algebra

(11)
\begin{align} v_1=\frac{z_1 (2+z_1)}{2+2 z_1 + z_1^2} * c \end{align}
(12)
\begin{align} v_2=\frac{z_2 (2+z_2)}{2+2 z_2 + z_2^2} * c \end{align}

At near the FeII lines 1608 and 1611 (5322/5330 ish angstroms):

we have 1.3 km/s per pixel

$\frac{1}{5325}*c = 56.3$ km/s per Angstrom

Pixels per Angstrom = 43.3 Pixels per Angstrom

The proposal predicts in the Fe-II (1608 and 1611) lines a

Separation of 9.097984552 Angstroms

by: (1611.2005 - 1608.4511) * (2.30908 + 1)

or

Changing Alpha Prediction

(This part is only useful for attaining the predicted separation in Angstroms from the proposal which suggests a 130 m/s increase in separation over the expected value)

9.097984552/1611.2005*300,000,000 = 1,694,013.48 m/s

Add 130 m/s gives:

(130 / 30,000,000) * 5331.6 = 0.00231036 which adds to the separation, giving us a

Separation of 9.100294912 Angstroms


Topics to discuss:
Books:Physical Processes in the Interstellar Medium by Lyman Spitzer absorption lines (curve of growth) - pp 47-57 equations 3-8 and 3-38 optical depth p. 33 oscillator strength f - p 38, 92An Introduction to Modern Astrophysics by Carroll and Ostlie optical depth 126, 266-7, 278, 289, 439
The Physics and Chemistry of the Interstellar Medium by A. G. G. M. Tielens oscillator strength: 44 optical depth, p 50Radiative Processes in Astrophysics by Rybicki and Lightman optical depth: 12-13, 38, 43-44, 50
oscillator strength: 96, 102, 274-7, 280-1
Absorption LinesSpectrographRedshift

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-Share Alike 2.5 License.