A blog about a telescopic system at the Mauna Loa Observatory on Hawaii to determine terrestrial albedo by earthshine observations. Feasible thanks to sheer determination.
This paper develops the theory of the properties of EMCCD cameras, like the Andor 897 that we have:
http://www.aanda.org/articles/aa/pdf/2012/01/aa17089-11.pdf
Very relevant if a new method to handle bias and noise were to be developed in our projects.
In researching material for our first paper we come across the data in Allen for the colour index of Earth: “0.2”. There is no evident source of that piece of information so in order to interpret it and use it in the paper we have to do some detective work. Here it is:
References given by Allen (various editions)
in the table that gives B-V of Earth as ‘0.2’.
==========================
The references are both in the caption of the table, and in the B-V/U-B
column of that table. The table is on page 299 of the fourth edition
by Cox.
reference numbering as in Allen 4th ed.
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1. Astronomical Almanac, 1998, USNO
In the 1997 edition there is on p. E88 a table with a dash ‘-‘ for
Earth’s B-V. For the Moon there is 0.92 without a reference.
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2. Allen 1973 – the two colour columns of the table on page 144 of this
3rd edition – gives references to Irvine and Harris (see below).
In Allen 1955 there is on p. 159 a table with ‘C’ for planets and
Earth has 0.2. In the notes it is explained that C is the ‘colour
index’ and that it is offset from the larger published value by 0.1
to 0.2 … What was ‘C’ as published and where and what is C compared
to B-V? The references on p.160 of the 1955 edition are not specific
for each piece of information, but we find as number [4] a reference to
Danjon. There are two references, it seems – 1936 and ‘Danjon, Comptes
Rendus, 227, 652, (1948)’. The 1936 is an observatory publication on
earthshine observations I am trying to find. The CR reference is about
Mercury and Venus. Using information from Wildey’s paper on Mariner 2 data
for Earth where the mean Danjon C.I. of earthshine/light, BS Moon and Sun
are given, we can estimate the linear transformation from the C.I. system
to B-V. We get, using Wildey’s data for Moon and Sun C.I. but not his
B-V data for same (using instead Holmberg et al for Sun) that
B-V = .112+.671*.(C.I.)
With 0.2 for C.I. we get B-V=0.25.
We can test the effect of using B-V for Moon = 0.92 (an often cited
value), this gives
B-V= -0.0665+.8968*(C.I.)
and C.I. = 0.2,0.3,0.4 gives B-V=0.11, 0.20, 0.29, respectively.
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3. Irvine et al 1968, AJ 73, 251, 807
Paper is on B-V for the planets – not Earth.
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4. Harris, in Vol III, (eds) Kuiper and Middlehurst, p. 272.
The Harris chapter in the book briefly discusses the photometry of Earth
– mainly in the form of a citation to Danjon’s chapter in Book II of the
series by Kuiper and Middlehurst. The Danjon phase law is given for earth,
but no comment on colours.
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Summary: The source of the ‘0.2’ for Earth in Allen is thus not source 1,
nor 3 – but 2 and 4 point at Danjon. The 1933 An. d’Obs. Strasbourg Vol
3 reference is in fact available online (now) at ADS. It is in French, and
it is long – but towards the end things hot up because a summary of color
index data for the Earthshine (Lumiere cendree) and Earthlight (Earth
itself) are discussed, although in the Rougiere system. The effective
wavelengths of this system are given in chapter 4 on p 171 and are
Rouge 606 nm
Vert 545 nm
Bleu 467 nm
so Rouge is between Johnson V and R, Vert is between Johnson B and
V, closer to V, and Bleu is between Johnson B and V, closer to B.
Of interest is a description of the areas on the Moon used – it seems
Crisium and Fecunditatis are used but only after 1928 is this fixed.
Also of interest are mean values (mean over several years) for the colour indexes,
given on
p 174 earthlight C.I. = 0.33 from -0.01 to 0.6
p 175 earthshine C.I. = 0.62
The variability is large and is said to be mainly seasonal. Note the
addendum at the very end (p. 179) where everything important seems to be
updated in a breathless paragraph! An updated value for C.I. for the Moon
by Rougiere is given as 1.10 (cited by Wildey in the Mariner 2 paper),
and the EarthSHINE C.I. is therefore updated to 0.64. There is a note
that there isn’t space to also update the earthLIGHT number but I assume
it is upped by 0.02 also. So, if Allen is referring to Danjon’s C.I.
as 0.2 and states that it is 0.1 to 0.2 lower than the published value,
we can see that Allen is talking, indeed, about the C.I. for Earth itself
– earthLIGHT – and not earthSHINE.
So, using the linear equation developed above
B-V = .112+.671*.(C.I.)
and now inserting C.I.=0.35 (with limits at +0.01 to 0.62)
we have for the earthLIGHT B-V = .35 (with limits from 0.12 to 0.53).
For an earthSHINE colour of C.I. =0.64 +/- 0.3 we get a B-V range of 0.54 +/- 0.2
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Conclusion: This spans our observation as well as Franklin’s, but with large uncertainties. Note the numerically identical B-V and C.I. values – so Allen is right in as much as replacing the ‘C’ from the 1955 edition with the ‘B-V’ of the 1973 (and on) editions.
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Data to plot
Year (B-V)ds-(B-V)bs
————-
1926-1935 0.54(+/- 0.2) to 0.85 = -0.31 to -0.11
1967 -0.17 +/- 0.05
2012 -0.16 +/- 0.02
Plotting this we have:
The Danjon data are an average of measurements from 1926 to 1935 and upper and lower end of the bars indicate the extent of seasonal variability, surmized by Danjon. The Franklin bars represent +/- 1 standard deviation based on the 12 determinates from 2 nights in his paper, and our error bars represent +/- 1 standard deviation based on scatter due to photon statistics in our measurement from a single night in two images.
Minnaert 1941 paper on the ‘reciprocity principle’ and other symmetry-considerations:
Photometry of the bright side of the Moon has been carried out for at least 100 years. An important paper is the one by van den Bergh:
He observed the Moon at 5 different occassions – two of them at Full Moon and one of them at half Moon, and derived B-V colours for 12 regions, measured relative to Mare Serenitatis. He also observed standard stars and tied photometry of Mare S. to these – thus tying the B-V photometry of the 12 regions to the standards.
Here are some results and insights:
For Mare S. he found B-V = 0.876 +/- 0.022. Over the 12 regions on the Moon (20” to 40” large) he reports B-V relative to M. Ser. This offset has mean value -0.017 +/- 0.005, where the mean was weighted (by me) with the square of the mean error reported by vdB. Knowing B-V for M. S. we can say that an average over 11 regions on the Moon (I dropped one measurement as it was flagged problematic) is 0.859 +/- 0.023.
I would say that this is what vdB62 reports. From somewhere we have the notion that he reports 0.92 for B-V – I do not see that in his paper. But he does quote Harris for saying that the mean over many regions on the Moon is 0.92, but does not comment further on that.
I notice that vdB does not allow for the different phases of his observations, and I think I know why – the photometry may depend on the lunar phase, but the colour does not (at least for these phases). We should check that, as we have BS B and V images galore!
Another paper, that by Wildey and Pohn:
contains masses of UBV photometry, and seems to discuss lunar phase and corrections thereof. Should be looked at. Many tables to digitize, though. Bachelors project?
Franklin paper:
This is the digital atlas of the Moon produced by Wildey which we scale the Clementine map to.
The Earthshine is usually a small fraction of the total light we receive from the Moon. But near new Moon the BS is very small and the DS starts to dominate – but at which phase?
Using Hans’ synthetic lunar-image code (based on Hapke 63 reflectances and thus UNDERestimating DS intensity and OVERestimating BS intensity for phases close to New) we get:
It seems the ES contributes 10% or more of the Moonlight at phases closer than 10 degrees to New Moon, and more than 1% at 30 degrees from new Moon.
Now, the SOLSTICE instrument in space has produced data for total lunar irradiance at angles all the way up to 180 (or is it just 170?) degrees from Full, so potentially they have data that contains 1% and more earthshine. The LRO data mentioned in Buratti et al 2010 does not cover to near New Moon. BBSO only gets out to 140 degrees or so (i.e. 40 from NM).
Due to the simplicity of the Hapke63 reflectance there is potential for a brighter ES and fainter BS near NM so that a larger fraction of the Moonshine is due to reflected earthshine. (the above is thus a lower limit on the fraction of Moonshine that is ES, in other words).
Is there potential for using LLAMAS data from SOLSTICE to do some clever work on Earthshine intensity?
2004: The BBSO group’s Science paper:
2005 Controversial multi-dataset compilation:http://adsabs.harvard.edu/abs/2005GeoRL..3221702P
2006: Frida Bender et al at MISU gets in the act:
2006: Palle has a shot back ati Bender:
2007:
Langley/NASA is not amused:
Langley revises their methods:http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007GeoRL..3403704L&db_key=AST&link_type=ABSTRACT
BBSO shoots back:
2009:
BBSO rumbles some more:
And so does NASA:
I stumbled across these, which look interesting:
Just for fun: this in yesterday’s “The Age”, from an article originally in the Guardian:
“Albert Einstein with an equation for the density of the Milky Way.”
Oh how we pine for an equation for Earth’s albedo!
Andor camera test report, Darudi.
Darudi and Rodrigo report on Spectral Analysis of Earthshine telescope.
Astro-Physics v4.12 manual for Keypad:
SPIE paper by the team, on the telescope:
Dravins et al 1998:
Dravins et al 1997a (the scintillation figure is on p 186):
Dravins et al 1997b:
Bernstein 2007 (with table of PSF alfa’s):
Middlemass et al 1989 (interesting discussion of color-dependency in PSFs):
The Chae paper showing the alogorithm for calculating flat fields from dithered observations of extended sources.
