J/AN/341/827 Magnitude accuracies in pre-telescopic catalogs (Protte+, 2020)
Accuracy of magnitudes in pre-telescopic star catalogues.
Protte P., Hoffmann S.M.
<Astron. Nachr. 341, 827-840 (2020)>
=2020AN....341..827P 2020AN....341..827P (SIMBAD/NED BibCode)
ADC_Keywords: Historical catalog ; Magnitudes
Keywords: history of astronomy ; magnitudes ; applied historical astronomy ;
Ptolemy, al-Sufi, Tycho Brahe, Almagest
Abstract:
Historical star magnitudes from catalogues by Ptolemy (137 AD),
al-Sufi (964) and Tycho Brahe (1602/27) are converted to the
Johnson V-mag scale and compared to modern day values from the
HIPPARCOS catalogue. The deviations (or "errors") are tested for
dependencies on three different observational influences. The relation
between historical and modern magnitudes is found to be linear in all
three catalogues which yields a linear conversion of the old
magnitudes to the modern scale. A slight dependency on the colour
index (B-V) is shown throughout the data sets and al-Sufi's as
well as Brahe's data also give fainter values for stars of lower
culmination height (indicating extinction). In all three catalogues, a
star's estimated magnitude is influenced by the brightness of its
immediate surroundings. After correction for the three effects, the
remaining variance within the magnitude errors can be considered as
approximate accuracy of the pre-telescopic magnitude estimates.
Description:
The data consist of magnitude data from 3 historical catalogues, taken
from Verbunt & von Gent (2010A&A...516A..28V 2010A&A...516A..28V, Cat. J/A+A/516/A28,
2012A&A...544A..31V 2012A&A...544A..31V, Cat. J/A+A/544/A31) and additional data was taken
from the HIPPARCOS-catalogue (ESA, 1997, Cat. I/239) The tables list
the original historical magnitudes and the historical magnitudes,
converted to the modern scale, as well as the final corrected
magnitudes. Additionally, they list Colour index, Culmination altitude
and background brightness for every star, as well as the associated
single corrective terms.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
brahe.dat 88 938 Conversion and correction data for brahe
magnitudes
ptolemy.dat 89 992 Conversion and correction data for Ptolemy
magnitude
sufi.dat 88 990 Conversion and correction data for alSufi
magnitudes
--------------------------------------------------------------------------------
See also:
I/239 : The Hipparcos and Tycho Catalogues (ESA 1997)
J/A+A/516/A28 : Star catalogue of Tycho Brahe (1627) (Verbunt+, 2010)
J/A+A/544/A31 : Star catalogues of Ptolemaios, Ulugh Beg (Verbunt+, 2012)
Byte-by-byte Description of file: brahe.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 6 I6 --- HIP Number of Star in Hipparcos catalog (Cat. I/239)
8- 11 I4 --- NoB Number of Star in Keplers 1627 version of
Brahe catalogue (c.f. Verbunt & van Gent, 2010,
Cat. J/A+A/516/A28)
13- 17 F5.2 mag mHIP Modern Johnson V-magnitude taken from
Hipparcos catalog (Cat. I/239)
19- 23 F5.2 deg Culm Culmination height above horizon for Hven
at 1601 C.E.
25- 29 F5.2 mag B-V ? Colour-index B-V taken from Hipparcos catalog
(Cat. I/239)
31- 35 F5.2 mag/sr Back ? Background brightness (as defined in the paper)
37 I1 --- InMW? [0/1]? Is the star within ±10° of the
galactic equator (1=yes/0=no)
39 I1 mag mB [1-6] Numerical magnitude given by Brahe
41 A1 --- qual [b/f] qualifier, added by Brahe:
b(righter)/f(ainter)
43- 45 F3.1 mag mOld Brahe magnitude with qualifier converted to
±0.5mag
47- 50 F4.2 mag m Brahe magnitude converted to the modern scale by
a linear transformation, m=(mOld-0.92)/0.75
52- 57 F6.3 --- d(B-V) ? Corrective term for the colour-dependency
linear model (only for stars FAINTER than
2.3mag): d(B-V)=0.11*(B-V)-0.06mag
59- 64 F6.3 --- d(Ext) Corrective term for the extinction-effect
non-linear model (G1)
66- 71 F6.3 --- d(beta) Corrective term for the Background-dependency
linear model: d(beta)=-0.37*Back-0.69mag
73- 76 F4.2 --- m* Final converted magnitude including all
corrective terms, m*=m-d(B-V)-d(Ext)-d(beta)
78- 82 F5.2 --- dm Magnitude error, dm=m-mHIP
84- 88 F5.2 --- dm* Corrected magnitude error dm*=m*-mHIP
--------------------------------------------------------------------------------
Byte-by-byte Description of file: ptolemy.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 6 I6 --- HIP Number of Star in Hipparcos catalog (Cat. I/239)
8- 11 I4 --- NoP Number of Star in the Almagest (c.f.
Verbunt & van Gent, 2012, Cat. J/A+A/544/A31)
13- 17 F5.2 mag mHIP Modern Johnson V-magnitude taken from
Hipparcos catalog (Cat. I/239)
19- 23 F5.2 deg Culm Culmination height above horizon for
Alexandria at 137 C.E.
25- 29 F5.2 mag B-V ? Colour-index taken from Hipparcos catalogue
(Cat. I/239)
31- 35 F5.2 mag/sr Back ? Background brightness (as defined in th paper)
37 I1 --- InMW? [0/1]? Is the star within ±10° of the
galactic equator (1=yes/0=no)
39 I1 mag mP [1-6] Numerical magnitude given by Ptolemy
41 A1 --- qual [b/f] qualifier, added by Ptolemy:
b(righter)/f(ainter)
43- 45 F3.1 mag mOld Ptolemian magnitude with qualifier converted
to ±0.5mag
47- 50 F4.2 mag m Ptolemian magnitude converted to the modern
scale by a linear transformation,
m=(mOld-0.92)/0.75
52- 57 F6.3 mag d(B-V) ? Corrective term for the colour-dependency
linear model (only for stars FAINTER than
2.3 mag): d(B-V)=0.11*(B-V)-0.06mag
59- 64 F6.3 mag d(Ext) Corrective term for the extinction-effect
non-linear model (G1)
66- 71 F6.3 mag d(beta) Corrective term for the background-dependency
linear model: d(beta)=-0.37*Back-0.69mag
73- 77 F5.2 mag m* Final converted magnitude including all
corrective terms, m*=m-d(B-V)-d(Ext)-d(beta)
79- 83 F5.2 mag dm Magnitude error dm=m-mHIP
85- 89 F5.2 mag dm* Corrected magnitude error dm*=m*-mHIP
--------------------------------------------------------------------------------
Byte-by-byte Description of file: sufi.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 6 I6 --- HIP Number of Star in Hipparcos catalog (Cat. I/239)
8- 11 I4 --- NoS Number of Star in Ulugh Begs catalogue (c.f.
Verbunt & van Gent, 2012, Cat. J/A+A/544/A31
13- 17 F5.2 mag mHIP Modern Johnson V-magnitude taken from
Hipparcos catalog (Cat. I/239)
19- 23 F5.2 deg Culm Culmination height above horizon for
Shiraz at 964 C.E.
25- 29 F5.2 mag B-V ? Colour-index taken from Hipparcos catalog
(Cat. I/239)
31- 35 F5.2 mag/sr Back ? Background brightness (as defined in the paper)
37 I1 --- InMW? [0/1]? Is the star within ±10° of the
galactic equator (1=yes/0=no)
39 I1 mag mS [1-6] Numerical magnitude given by al-Sufi
41 A1 --- qual [b/f] qualifier, added by al-Sufi:
b(righter)/f(ainter)
43- 45 F3.1 mag mOld al-Sufi magnitude with qualifier converted to
±0.5mag
47- 50 F4.2 mag m al-Sufi magnitude converted to the modern scale
by a linear transformation, m=(mOld-0.92)/0.75
52- 57 F6.3 --- d(B-V) ? Corrective term for the colour-dependency
linear model (only for stars FAINTER than
2.3 mag): d(B-V)=0.11*(B-V)-0.06 mag
59- 64 F6.3 --- d(Ext) Corrective term for the Extinction-effect
non-linear model (G1)
66- 71 F6.3 --- d(beta) Corrective term for the Background-dependency
linear model: d(beta)=-0.37*Back-0.69mag
73- 76 F4.2 --- m* Final converted magnitude including all
corrective terms, m*=m-d(B-V)-d(Ext)-d(beta)
78- 82 F5.2 --- dm Magnitude error dm=m-mHIP
84- 88 F5.2 --- dm* Corrected magnitude error dm*=m*-mHIP
--------------------------------------------------------------------------------
Global notes:
Note (G1): d(Ext)=-0.01+0.01/(sin(Culm)+25*exp(-11*sin(Culm)))
--------------------------------------------------------------------------------
Acknowledgements:
Philipp Protte, philipp_protte(at)gmx.de
(End) Patricia Vannier [CDS] 10-Aug-2020