Doppler Shift Calculations

[jagadeeshr]

Hi,

I was looking into Doppler shift calculations, and I came across this blog post (http://jazzistentialism.com/blog/?p=1728). It gives a very simple and straight forward account of calculating the velocity of a star.

Following is the summary the blog post:

Spectrum of Alpha Centauri (A. Cen.) is obtained through Lhires III spectroscope. Spectrum of the sky/sun is used as a reference for calculations since A. Cen. and Sun are G2V type stars.

When the A. Cen.'s spectrum is superimposed on the Sun's spectrum, A. Cen's lines have shifted to the left (blue). Shift is 4 pixels.

From the spectrum, two Iron (Fe) lines are identified at 5371.5 Å and 5424.1 Å. They are 52.58 Å apart, and number of pixels between them is 258 pixels. Therefore 1 pixel = 0.2 Å.

Shift between A. Cen. and Sun is is 4 pixels. Therefore, shift in terms of wavelength is 0.8 Å (-0.8 Å, because of blue shift).

Radial Velocity is calculated using the formula: V = C * (Δλ / λ). Where: C ( speed of light) is 3*10^5 km/s, Δλ is 0.8 Å and λ is 5424.1 Å. The equation gives velocity as -44.25 km/s. Taking into account earth's heliocentricity of 20 km/s, the final velocity of A. Cen. is -44.25 + 20 = -24.25 km/s. This is very close to the astronomical database value of -22.3 km/s.

Here is what I'm confused about: If we use the other Fe line (at 5371.5 Å) as the rest wavelength, the velocity will be -44.68 + 20 = 24.68 km/s (0.4 km/s increase). If we consider spectral lines towards the left (blue region) of the spectrum, the velocity will be higher.

For example, consider an object that emits lines at 4000 Å, 5500 Å and 7000 Å. The shift in wavelength due to Doppler is 1 Å. The Doppler calculations will indicate velocity of 75 km/s at 4000 Å; 54.54 km/s at 5500 Å and 42.85 km/s at 7000 Å.

Therefore, how to identify the appropriate spectral line for Doppler calculation?

[Country Boy]

That depends upon determining which lines correspond to identifiable lines in our sun's spectrum- which depends upon identifying set of spectral lines.

[Strange]

Here is what I'm confused about: If we use the other Fe line (at 5371.5 Å) as the rest wavelength, the velocity will be -44.68 + 20 = 24.68 km/s (0.4 km/s increase). If we consider spectral lines towards the left (blue region) of the spectrum, the velocity will be higher.

 

 

I think the problem is that you have a very limited resolution (at the pixel level). So if we assume that 0.8 is the correct shift for 5424A, then the expected shift at 5371A is about 0.808. You won't be able to see the difference between this and 0.8. So for quite a range of values, you will see the same shift.

 

 

 

For example, consider an object that emits lines at 4000 Å, 5500 Å and 7000 Å. The shift in wavelength due to Doppler is 1 Å. The Doppler calculations will indicate velocity of 75 km/s at 4000 Å; 54.54 km/s at 5500 Å and 42.85 km/s at 7000 Å.

 

That doesn't look right. Wouldn't the amount of shift be different at each wavelength?

[jagadeeshr]

Ah. Based on the image, I had assumed that shift will be uniform across the entire spectrum.

 

So, if an object is moving with a velocity of 10 km/s, Doppler shift will 0.13 Å at 4000 Å and 0.23Å at 7000 Å.

 

Thank you.