Relative distance estimators.IV

The rotational velocity of a spiral galaxy can be measured from the HI integrated spectrum. The HI gas in a spiral follows very closely circular orbits at a speed V_c . If the galaxy is inclined at an angle i to the line of sight, the observed line of sight velocity will vary from + V_c  sin i to - V_c  sin i relative to the systemic velocity of the galaxy. This results in a double horn line profile.


Thus measuring the width of the line we get a direct estimate of the circular velocity. Conventionally, this width is measured by finding the points in the line wings where the intensity has dropped by 20% of the peak value. The difference in Doppler shift between these 2 points is W₂₀.

W₂₀ needs to be corrected for 2 effects. The first one is that HI does not follow perfectly circular orbits, but has some random motion, whose effect is to broaden the observed lines. This can be estimated to be typically 10 km/s. The second effect is due to the inclination. The width that we measure is essentially 2 V_c  sin i. Therefore, the quantity



is an inclination independent measure of the circular velocity of a spiral galaxy.

The best bands to measure the brightness of a spiral galaxy are the infrared bands. The reason is twofold:

• spiral galaxies have large amounts of dust, which produce extinction. The effect of extinction in the infrared is very small
• the light will be dominated by old stars, which are more representative of the overall stellar populations. The observed light does not depend therefore on current star formation activity.

The relations obtained are



and have been calibrated using cepheid distances.