Zenithal hourly rate

All-sky view of the 1998 Leonids shower. 156 meteors were captured in this 4-hour image.

In astronomy, the zenithal hourly rate (ZHR) of a meteor shower is the number of meteors a single observer would see in an hour of peak activity if the radiant was at the zenith, assuming the seeing conditions are perfect^[1] (when and where stars with apparent magnitudes up to 6.5 are visible to the naked eye^[2]). The rate that can effectively be seen is nearly always lower and decreases the closer the radiant is to the horizon.

Calculation

The formula to calculate the ZHR is:

${\displaystyle ZHR={\cfrac {{\overline {HR}}\cdot F\cdot r^{6.5-lm}}{\sin(h_{R})}}}$

where

${\displaystyle {\overline {HR}}={\cfrac {N}{T_{eff}}}}$

represents the hourly rate of the observer. N is the number of meteors observed, and T_eff is the effective observation time of the observer.

Example: If the observer detected 12 meteors in 15 minutes, their hourly rate was 48 (12 divided by 0.25 hours).

${\displaystyle F={\cfrac {1}{1-k}}}$

This represents the field of view correction factor, where k is the percentage of the observer's field of view which is obstructed (by clouds, for example).

Example: If 20% of the observer's field of view were covered by clouds, k would be 0.2 and F would be 1.25. The observer should have seen 25% more meteors, therefore multiply by F = 1.25.

${\displaystyle r^{6.5-lm}}$

This represents the limiting magnitude correction factor (Population index). For every change of 1 magnitude in the limiting magnitude of the observer, the number of meteors observed changes by a factor of r. Therefore, this must be taken into account.

Example: If r is 2, and the observer's limiting magnitude is 5.5, the hourly rate is multiplied by 2 (2 to the power 6.5–5.5), to know how many meteors they would have seen if their limiting magnitude was 6.5.

${\displaystyle \sin(h_{R})}$

This represents the correction factor for the altitude of the radiant above the horizon (h_R). The number of meteors seen by an observer changes as the sine of the radiant height. ^{[dubious – discuss]}

Example: If the radiant was at an average altitude of 30° during the observation period, the observer's hourly rate will need to be divided by 0.5 (sin 30°) to know how many meteors they would have seen if the radiant was at the zenith.

See also

• List of meteor showers

References

1. Cooke, Bill (19 Nov 2019). "About the Upcoming (maybe) Alpha Monocerotid Meteor Shower Outburst". NASA Blogs.
2. Beech, Martin (2006). Meteors and Meteorites: Origins and Observations. United Kingdom: Crowood Press. pp. 80–81. ISBN 9781861268259.

External links

• North American Meteor Network (NAMN)