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(meteorobs) Fwd Casper ter Kuile: Reply to Assmus & McLeod
To: Meteorobs
cc: Peter
Subject: Reply to Assmus & Mcleod
>From Marco Langbroek, DMS visual section, the Netherlands
Dear Joseph, Norman and others,
Some days ago Meteorobs saw a discussion between Joseph Assmus and Norman
Mcleod about the November 17 Leonid rates and ZHR calculations. I think I
can answer many of the questions and subjects that emerged. Sorry that this
respons comes a little bit late, but I don't have an internet connection
and have to receive everything on paper from Casper and then have to send
him my stuff. Also sorry that this mail wil be rather lengthy, but I'll try
to be as clear and complete on the matter as possible But anyway:
- I think that both Joseph and Norman make some mistakes and that some of
Norman's remarks are due to misunderstandings induced by some failures in
Joseph's analysis. There's nothing wrong with the correction for limiting
magnitudes (sorry Norman, but this is the way it is), but Joseph applies it
in a wrong way. In the equation:
r^(6.5-Lm)
...which corrects for limiting magnitude deviations, Joseph uses r=2.8 for
the outburst Leonids. This however, is close to the value for the annual
Leonids (r=3.0 +- 0.4) which have an emphasis on faint meteors. For the
broad Leonid outburst component, the emphasis is on bright meteors however
(as will be clear to everyone that observed it!), and a more proper
population index r should be ~2.0 (values derived from 1994 and 1995 data).
If you are observing with Lm's poorer than +6.5 (i.e. the Lunsford and
Asmuss data), this will mean that your calculated ZHR's will come down
compared to those calculated with r=2.8. Note: we did use a more fainter
value for r in reducing our own data from France, but that was because
during a limited interval we got many faint Leonids reducing r to ~2.5 or
something like that (more about that in a separate mail).
Usually, you calculate r from your magnitude estimates distribution.
- Norman, it is not true that you 'would have seen almost every one of the
same meteors in a sky a full magnitude poorer' or that this or any other
shower 'should be substantially independant of sky conditions down to
perhaps LM5.5'... There is a psychological pittfall that fooled you in
this. You see many bright meteors yes, and relatively low amounts of
fainties. But: you don't see ALL bright meteors, or ALL fainter ones...!!!
A reduction in LM from say 6.5 to 5.5 does not mean that you lose on the
faint ones alone, but that you lose on the whole trajectory from -3 to +6.
The point is, that even under perfect conditions you don't see ALL +3's or
even ALL -2's! It might be surprising for some of you, but you actually
fail to see a fraction of even the meteors in negative magnitudes, and the
amount that you miss is dependant on limiting magnitude. This was shown in
a classical study by Kresakova back in 1966, who calculated the proportions
of missed meteors for each magnitude class. Several other authors have done
the same. The following data is from Jenniskens, calculated from Dutch DCV
estimates (DCV = Distance from center of vision. It shows you your eye
sensitivity fall-off from the center of view to the edges), and is valid
for an 'average' observer observing with Lm 6.5:
m P m P m P
-2 0.75 +1 0.63 +4 0.09
-1 0.73 +2 0.48 +5 0.009
0 0.70 +3 0.32 +6 0.001
..dot it shows that even with Lm 6.5 you don't see 100% of the -1 meteors that
appear in your field of view, but only 73%, you miss 27%! Of the +4
meteors, you'll only see 9%.
When your LM is lower than 6.5, these values get lower too. With LM 5.8 for
example, you'll only see 0.71 of the -1 meteors and 0.025 of the +4
meteors. The decrease is therefore not only in the +4 meteors, but also in
the observed number of -1's and so on. While you think you'll only lose
some +4's Norman, you'll also lose on the -2, the -1 , the zero's and the
+1 etcetera. This is why your comment is incorrect. The limiting magnitude
formula corrects properly for this because it behaves like a power law as
long as your LM is not too much deviant from +6.5 (the difference should be
no more than 1.3 magnitudes. Usually, you reject all observations with Lm
<5.2 in an analysis). Since it is the fraction of observed meteors that
changes for ALL magnitude classes when the Lm changes, the population index
you use in the limiting magnitude correction equation determines what the
correction amounts to (the population index is a measure of the distributi-
on of meteors over the magnitude classes).
- Norman remarks that his ZHR's would 'shrink to 15-20' using the formula,
and 'that's not the way it is!'. Actally, this is where the 'Cp' or
'personal perception' comes in. Before I continue, I should mention that a
rather unfortunate typographical error appears in Jenniskens' paper of 1994
in Astron. Astroph.: In the equation, it should be Cp^-1 instead of just
Cp, the correct equation being:
ZHR = N/Teff * r^(6.5-Lm) * sin (Hr)^(-g) * Cp^-1
I reduced Norman's data from 1995 some time ago and for that purpose also
calculated his Cp. I found it to be about 0.4, which means he sees 0.4
times the amount of meteors of the 'median' meteor observer and therefore
his rates should be updated by 1/0.4 (or a factor 2.5). Bob Lunsford has a
Cp near 1.0 (and therefore he is hereby exclaimed as the all time high
median NAMN observer...!), so under similar conditions (similar LM and
radiant altitude) Bob would report 2.5 times as much meteors as Norman. I
myself have a Cp of 1.2. I would see 3 times as much meteors as Norman and
1.2 times as much as Bob, and my rates should be corrected by 1.2^-1 or
1/1.2. This shows the importance of including a Cp in data reduction, since
these perception differences as shown introduces major scatter between
observers. Anyway Norman, in the table below you'll notice that your ZHR's
certainly do not shrink to 15-20 with this method. I calculated ZHR's from
the data in your Nov 17 16:40 mail and they end up in the ZHR ~60-90 range.
- In addition to this and in answer to Joseph: the Cp-value of an observer
is NOT (emphasis!) a measure of experience!!! Of course, 'novice' observers
will usually have a low Cp (because they still miss the fainties) and very
experienced observers a higher Cp, but it is certainly not a strict rule
due to various factors. Norman for example has a low Cp but I certainly
would not classify him 'inexperienced'! Also, champion observer George Zay
has a Cp distinctly <1 (0.7 actually). For the larger part, differences in
Cp between observers are a matter of biology. No two persons are genetical-
ly alike. You differ in diameter of your effective field of view, pupil
diameter, eye retina sensitivity, transparancy of your eye lens etc. This
makes up for a large part of the differences in Cp. Age is an important
factor (another one is diet habits). People have best eyesight when in
their teenage years, and your sight (most notably your maximum pupil
diameter and eyelens transparency) already starts to detoriate around age
20! Therefore, it is not surprising to find that 'middle-aged' observers
like Norman or George have a lower Cp than the young Turks in the field
like me.
- In answer to Joseph: it would be a more appropriate aproach to calculate
a Cp from a large sample of sporadic data gathered over SEVERAL nights
instead of one single night. This because while sporadic rates are 'stable'
on a long term, they show significant fluctuations in the short term (in an
earlier mail, Norman pointed to one of these: my 34 sporadics in 35 minutes
of November 17, though I think something else was involved in that case
too) because they behave according to a poisson distribution. I prefer to
calculate a Cp from several nights in August, compute sporadic HR's in ~1
hr intervals, reject the highest and lowest values and average the whole
bunch before applying the formula Cp = Hr_spo / 10. Two things are to be
remarked:
* Sporadic rates vary with time of the day. Highest rates occur in the
morning, lowest in the evening. Therefore, restrict to data from about the
period 22-02h local time (i.e. around local midnight). This is also why I
favour August data, because the short nights automatically result in low
variations.
* Sporadic rates are also dependant of the time of the year. While around
~10 for a 'median' observer around midnight in August, they are around ~12
in Autumn (and around ~8 in spring). When you use November data, divide by
12 instead of 10.
- I agree with Norman that the radiant altitude correction might overcor-
rect for very low radiant altitudes. In a normal analysis, you however do
not use data gathered with Hrad < 30 degrees (at least I do not). I have
myself started to believe that the gamma-value in the correction (c = sin
(H_rad)^-gamma) might be dependant on radiant altitude itself and is ~1.4
for H_rad >30 degrees, ~1.0 for H_rad 20-30 degrees and <<1.0 for H_rad <20
degrees. Alternatively, it might be involved that a low radiant altitude
causes a change to 'brighter' values in the population index. Anyway, be
indeed carefull with interpreting results gained with low radiant altitu-
des. But in the table below you'll notice that Norman's, Bob's and George's
data actually agree well from 9 UT onwards, with radiant altitudes > 20
degrees for Bob and George and >60 degrees for Norman (bear in mind that
there'll always be some statistical scatter playing it's part too. Don't
expect ZHR's to agree exactly. But around 10 UT, they agree very well.
Norman: I think that Bob's sweep in rates when his Lm drops in his final
observing interval has more to do with ambiguities in the Lm determination
(quick LM variation due to start twilight) than with the Lm correction
equation itself).
The rates as observed by Norman, Bob and George (draw a curve of it with
the ZHR on a logarithmic scale: this really helps to see it clear) actually
point to a maximum ZHR around ~85 (annual and outburst combined) around 8h
UT, and a then gradually declining ZHR (to values around ZHR ~55 around the
time (~13h UT) that Bob and George quit) with a slope having a B-index of
~1.0, like 1994 and 1995. With this, I mean the peak of the broad component
of bright meteors of course. This also agrees with reported rates around
the peak time by Peter Jenniskens from the ESO observatory in Chile and
George's observations on November 18 (and our on November 16 from Sexbie-
rum), and the peak position according to radio observers. The narrow peak
of faint meteors we experienced in France which came in addition to the
broad component then stands out well and is odd indeed.
Well, since this message is already very lengthy I think I'll draw an end
to it. I hope it has been of some use. What I want to say as a last word,
is that I think that it is very good that people like Joseph try to do
something with their data, and that people like Norman comment on it. In
this way, you create an active multivoiced environment. Meteor observing as
a hobby and as a 'science' benefits from that. So keep on the statistics
with your data Joseph, keep on presenting them, and keep on discussing
results Norman. And keep on observing and reporting everybody.
-Marco Langbroek.
Dutch Meteor Society
Team Delphinus and visual section
PS: I calculated the following ZHR's for November 17 from Bob Lunsford's,
George Zay's and Norman Mcleod's data:
Observer Norman McLeod (Fort Meyers, Florida). Cp=0.4
Date: November 17, 1996
UT ZHR
5:56 [98 +- 37]* low radiant altitude: 10 degrees
6:56 94 +- 25 *
7:56 69 +- 14
8:56 58 +- 11
9:56 66 +- 11
* Note: In these periods I used r=2.5 instead of 2.0, as it follows from
our observations from France. Actually, rates then closely agree with our
Dutch data from France (the tail of the descending slope of the narrow peak
we observed: see a separate mail). Using r=2.0 these first two observatio-
nal intervals would result in ZHR 117 +- 44 and 112 +- 25.
Observer Bob Lunsford (Descanso, Ca). Cp=1.0
date: November 17, 1996
9:00 85 +- 20
10:00 54 +- 13
11:00 33 +- 8
12:00 43 +- 8
13:00 61 +- 10
Observer George Zay (Descanso, CA). Cp=0.7
Date: November 17, 1996
9:02 127 +- 31
10:04 76 +- 20
11:07 34 +- 10
12:10 83 +- 15
12:57 48 +- 15
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| Casper ter Kuile, Akker 145, NL-3732 XD De Bilt, the Netherlands |
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