RZHR computation



In meteoric swarms observation, to count the number of meteors observed at regular intervals is not enough to have a quantitative evaluation of the swarm. Many other factors need to be considered into account, including: the percentage of visible sky, the duration of observation time and especially the radiant height above the horizon.

The more the radiant is low, how few meteors will be visible from the observer, and this is true both for visual observation and for radar observation. The equation that allows to calculate the ZHR, i.e. the number of meteors belonging to the same swarm that are visually observed under standard conditions, with a stellar visual magnitude of 6.5 and free 360 degree sky is:

where


To approximate this correction - typical of the visual observation - adapting it to the radar observations we made the term RZHR (RAMBO Zenithal Hourly Rate).
It therefore represents a corrective factor to the recorded meteor hourly rate, based solely on the radiant height compared to the local horizon.



The RZHR equation

To calculate the RZHR we have done a program in Python. It has an excellent portability and is running on any platform (Linux, Windows and Mac).


- A screen shot of the RZHR program -


The RAMBO data analysis is divided into four subsequent computational phases.

After we have chosen the desired period and the meteor swarm, the program performs the following steps.


1. Sporadic background subtraction

The sporadic background is the number of meteors that are supposed to occur sporadically in a given period of time. The contribution of the sporadic background "contaminates" the the result during a meteoric swarm. So it is necessary to eliminate this contribution. This step is done by computing the mean value of the hourly events in the days immediately preceding (or following) the swarm activity peak, which we arbitrarily consider sporadic, mediated by the number of days and finally subtracted from the number of events recorded hour by hour on the analyzed days.

The equation is:


2. Julian Day

Julian Day (JD) is the integer number of days or fraction thereof passed after midnight Monday, 4712 b.C., January, 1st relative to Greenwich.
JD is a useful method in astronomy to measure time without taking account of calendar variations, leap year and so on.

This equation is:


JD1

where

  Y, M, d are year, month and day to be converted into JD

  and b

JD2


3. Solar Longitude

The year-by-year comparison of swarm behavior forces astronomers to use the geometric position of the swarm along the ecliptic (solar longitude) and not the date, because it involves a quarter-day, year-to-year difference.

Our aim is to provide us with a measure of the longitude of the sun, that is, the angular distance along the ecliptic (on which the Sun moves from South to North) starting from the gamma point Γ (or first point of Aries).

To do this we begin to calculate T in Julian Centuries

ls1

From this we can calculate the average longitude of the Sun

ls2

the average anomaly (i.e. the angular distance from the perihelion that Earth - or any other body of the solar system - would have if it would turn around the Sun at a constant speed)

ls3

and the solar center coordinates

ls4

Finally, we determine the solar longitude:

ls5


In the swarms calculation, a slightly different version is used, in which the longitude must take into account the Sun coordinates J2000.0

ls6


4. Correction due to radiant high

From the radiant coordinates we can calculate the value of its height on the local horizon. We do this by using a Python library (PyEphem) that allows us to determine the location. Finally, the ratio between the number of meteors of the swarm and the radiant height sine is, finally, the RZHR.

rzhr


Here you can see the result.



rzhr


The blue vertical lines represent the RZHR hour by hour, the green dotted line represents the radiant height above the horizon (right axis) and the red line is the instant in which the swarm maximum forecast (IMO and others) is expected.


Other application

rzhr

- Quadrantids - 2019, January -


background

- Subtraction of the "sporadic background" -