What is the relation between redshift and absorption lines in galaxies?

[nietzsche]

I understand the concept, but not the math.

For example, let's say a galaxy is moving away from us, and we observe one absorption line at 400 nm, and another absorption line at 500 nm. Let's also say that we determine that the radiation was emitted originally at 200 nm and 300 nm respectively. Then according to the formula for redshift,

$$z = \frac{\lambda-\lambda_{0}}{\lambda_{0}} = \frac{500-300}{300} \approx 0.67$$

and

$$z = \frac{400-200}{200} = 1$$

Does this mean that every line measured will have a different redshift? Or am I missing something here?

Thanks in advance.

 

[fleem]

I understand the concept, but not the math.

For example, let's say a galaxy is moving away from us, and we observe one absorption line at 400 nm, and another absorption line at 500 nm. Let's also say that we determine that the radiation was emitted originally at 200 nm and 300 nm respectively. Then according to the formula for redshift,

$$z = \frac{\lambda-\lambda_{0}}{\lambda_{0}} = \frac{500-300}{300} \approx 0.67$$

and

$$z = \frac{400-200}{200} = 1$$

Does this mean that every line measured will have a different redshift? Or am I missing something here?

Thanks in advance.

The two lines you describe are redshifted by different factors. Specifically, the multiplier for redshifting one line is not the same for redshifting the other line. So one would have to assume the lines are not from the same object. For a given object, the wavelengths of all its lines are shifted by the same constant multiplier, and its value depends on several factors (object's relative velocity, gravitational redshifting, and Doppler effect).

 

[nietzsche]

The two lines you describe are redshifted by different factors. Specifically, the multiplier for redshifting one line is not the same for redshifting the other line. So one would have to assume the lines are not from the same object. For a given object, the wavelengths of all its lines are shifted by the same constant multiplier, and its value depends on several factors (object's relative velocity, gravitational redshifting, and Doppler effect).

Thanks!