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The star observations of Kolev

Considering the observation database

• The Rozenberg's Airmass formula quoted by Kolev (f8, page 235) has a '+' changed into '-'. That is why the values are so weird! The correct Rozenberg formula is relatively accurate (Schaefer, 1993, page 80).
• The evaluation of Schaefer (Kolev, 2013, page 235) is based on Schaefer's older journal articles (Schaefer, 1987), no comparison has been done to this newer one (Schaefer, 1993).
  
• An error in a Mars observation. The observation date 12 April 2007 CE (Kolev, 2013, page 247) seems not really possible (checking with Schaefer's criterion and PLSV). No idea what date it could/should have been.
• Several stars have different dates for the same heliacal event, year, observer and location:
  
• with different AEC:
  Alniyat/sSco (Kolev, 2013, page 256)
• with same AEC:
  Acrab (Kolev, 2013, page 254)
  Tejat (Kolev, 2013, page 256)
  Theta2Tauris (Kolev, 2013, page 256)
  Zubenelgenubi (Kolev, 2013, page 256)

Errors around derived/calculated values:

• Magnitudes are different than other literature values:
  
  • Mercury: Kolev explicitly uses Schoch values (Kolev, 2013, page 245), which look to be too low (Siedelmann, 2013, page 410).
  • Theta2Tauris and Heka: both have a magnitude some 0.5 lower than SwissEphemeris star database (close to SIMBAD) values. This magnitude difference is observable, because the Just Noticeable Difference [JND] is around 0.2 (Farquhar, 1879, page 504).
• Two objects seems to have a larger (calculated?) |DAzi| then from SwissEphemeris/Stellarium calculations
  
  • Venus: 15 June 2012 (Kolev, 2013, page 241)
  • Zavijava: 13 Oct. 2002 (Kolev, 2013, page 258)
• The examples in The Virtual Heliacal Rise Table section (Kolev, 2013, page 261-262) don't show the calculation of |DAzi|'s influence properly: the minus sign is forgotten. The Helical Rise Table Table XLVI is correct (Kolev, 2013, page 263)
  

Star coordinates and magnitudes

Some evaluation points

• It was tested if Kolev's observations can be mapped with Schaefer's criterion. If not, it might be that: Schaefer's criterion is wrong; in reality a different AEC; or otherwise.
• Some 13% of the observations can not be mapped (by changing the Atmosphere Extinction Coefficient (AEC)) on Schaefer's criterion (even using a slightly higher acuity [1.4] than the average 17-18 year person's acuity of 1.3+/-0.2 (Ohlsson and Villarreal, 2005)). Around 11% needs an unrealistic small AEC (<0.15), while some 2% needs an unrelatistic high AEC (>0.75).
  
• After mapping the observations on the Schaefer's criterion, the following AEC distribution is seen:
  
  This could indicate real atmospheric influences. This is different then seen in Ptolemy's AEC distribution. Due to the difference in AEC (or |DAzi|) distribution the below formula might not be easily comparable to other formula in literature!!!
  
• Relatione between AEC and the season (month of the year)
  
  So there migth be a slight increase of AEC in summertime. This is also expected due to variability of k_a during the year.
  
• Relation m and TopoAV (regardless of |DAzi| and AEC) for Kolev's observations is (blue in below graph):
  TopoAV(m) = 13.1 + 2.5*Magn [deg]   (1)
  <Schaefer's criterion has not been used to derive this formula>
  
  
  
  
• When using Kolev's criterion to calculate the TopoAV, the following formula can be derived (grey in above graph):
  TopoAV(m) = 13.2 + 2.4*Magn [deg]   (2)
  <Schaefer's criterion has not been used to derive this formula>
  
• From the above picture it is clear that the variation of the Sun's altitude at the heliacal events is less than the celestial object's altitude variation. The large variation in the object's altitude is mainly due to the atmospheric conditions. The stability of Sun's altitude maps Ptolemy's view. The larger variation of the Sun's altitude above magnitude of 2.5 is related to the change from photopic to scotopic vision.
  
• The TopoAV for all heliacal events (MF, ML, EF, EL, AR and CS) is seeen below.
  
  
  
  
• The above TopoAV-|DAzi| behavior is not as clear as seen in Ptolemy's events, where it looks to stabilise from above 100 degrees.
  
• Kolev (2013, page 260) though recognises this stabilisation. He sees the boundaries for magnitudes above -2 and below 1.9 to be stabilise from above 90 degrees and for magnitudes between -2 and 1.9 to stabilise above 45 degrees.
  
• We can determine a combined formula for Kolev's observations. This (using Excel's GRG Nonlinear Solver) gives an idea of a three parameter behavior of Kolev's observations for TopoAV and Arcus Visionis:
  TopoAV(Magn,|DAzi|,AEC) = 6.6 + 3.0*Magn  + 0.017*|DAzi| + 22.9*AEC [deg]   (4)
  Arcus Visionis(Magn,|DAzi|,AEC) = 7.1 + 1.3*Magn + 0.014*|DAzi| + 3.9*AEC [deg]   (5)
  <Schaefer's criterion has not been used to derive this formula>
  
  
  
• Looking at the above formulas (4) and (5): the Arcus Visionis (5) is much less depending on Magn, |DAzi| and AEC than the TopoAV (4). The Arcus Visionis is some five times less dependent on AEC than the TopoAV! This was also derived in another analysis.
• Looking at the above: the single parameter criterion of Schoch (1924, page 734) misses the significant influence of |DAzi| (assumed smaller than 25 degrees) and AEC (assumed low and  constant?). The heliacal angles derived by Schoch are tabled here.
• Kolev's criterion has parameters which are depending on Magn: AltSun(Magn), BaseAltObj(Magn), dAlt/|DAzi|(Magn) and dAlt/dAEC(Magn). See below table (Kolev, 2013, page 260)
  

  Magn	AltSun [Deg]	BaseAltObj [Deg]	ThresDAzi [Deg]	dAlt/|DAzi| [-]	dAlt/dAEC [Deg]
  -4	-4	1.6	90	-0.075	1.3
  -3	-5	1.5	90	-0.018	3.3
  -2.3	-7	0.7	90	-0.018	6.6
  -2	-7	1.1	90	-0.018	10
  -1.7	-7	3.1	45	-0.075	13
  -1.5	-7	4.4	45	-0.075	13
  -0.8	-7	4.9	45	-0.075	13
  0	-7	5.7	45	-0.06	16
  0.34	-9	3.7	45	-0.06	17
  0.5	-9	4.7	45	-0.06	17
  0.85	-9	5.1	45	-0.055*	20*
  1.35	-9	6.1	45	-0.055	27
  1.6	-9	6.4	45	-0.05	27
  1.9	-12	3,6	90	-0.03	19
  2.1	-12	4.5	90	-0.03	19
  2.5	-12	7	90	-0.03	19
  2.8	-12	8	90	-0.03*	19
  3	-12	8.6	90	-0.03	37
  4	-12	11	90	-0.03	50
  5	-14	20	90	-0.02	55
  6	-16	36	90	-0.011	58

  * there is some uncertainty
  
  TopoAV(Magn,|DAzi|,AEC) = -AltSun(Magn) + BaseAltObj(Magn) + min(|DAzi|,ThresDAzi(Magn))*dAlt/|DAzi|(Magn) + (AEC-0.16)*dAlt/dAEC(Magn) [deg]   (5)
  
• Comparing the TopoAV differences between (Kolev's observations - Kolev's criterion) [DiffRKAV] with (Schaefer's mappings - Kolev's criterion) [DiffRKAVSch] we see the following graph:


The standard deviation (the red error bar in above graph) of DiffRKAV is somewhat larger than DiffRKAVSch's, so Schaefer's criterion results maps a little better than Kolev's observations on Kolev's criterion. Don't know what this at the end means!

• If we combine the (Schaefer's criterion) mapped calendar entries of Ptolemy (filled marks) and observation of Kolev (open marks) into one graph, we get the following picture:
  
  The likely minimum altitude of the object (regardless of |DAzi| and AEC) is the dashed blue line. The likely maximum altitude of the Sun (regardless of |DAzi| and AEC) is the dashed brown line. These lines are simple linear interpolations, so handle with care!
  What does the above formula in the graph say:
• no TopoAV formula is given in the graph, but add the two together:
  TopoAV(Magn) = 8.8 + 1.5*Magn [deg]   (6)
  <Schaefer's criterion has not been used to derive this formula>
  
• formula earlier in the text (1) and (2) are based on the average;
  
• formula (1) and (2) are quite depending on the AEC and |DAzi| distribution; and
  
• formula (6) from above graph is determined by the maximum Sun and minimum object altitudes.
  
• The AR&CS observations done by Kolev's observations still need an evaluation. There are some 20 of them, so it might not be enough to derive something reliable.
• A teaser of the dependency of TopoAV on magnitude for AR&CS events can be seen below:
  
  It looks that Kolev's criterion (grey) compares (~1.5 degree higher) to the observed TopoAV. The Arcus Visionis (-AltSun) looks to be some 1 degrees smaller than for the MF&ML&EF&EL events. 
  
• The observations (blue) are depending on the magnitude and seem to be overall higher compared to Ptolemy's calendar events (remember the different AEC distribution for both evaluations).
  
• The AltObj (= 3.1 + 0.76*Magn [deg]) (black dots in below graph) looks to be close to the topocentric extinction angle (green circles) of the stars (North, 1996, page 34). A difference is expected due to the observational definition of the AR&CS events by Kolev (2006). The difference is around 2 degrees; so around 0.5 degree might be due to the definition of AR&CS events (Kolev, pers. comm). Is the remaining difference due to North's observed extinction angle at 'under favourable viewing conditions from the downs of southern England' (North, 1996, page 34), while Kolev's is under less clearer skies perhaps (average higher AEC)? But North's observed extinction angles look to be for an AEC of around 0.3, so close to the above shown average AEC of Kolev (close to 0.25).
  
  
• The variation of the Object's and the Sun's altitude at AR&CS events looks to be similar (there are not many data points, so this is not statistically proven). The Sun's altitude is normally not very depending on the AEC, and perhaps the Object's altitude at AR&CS events is also quite independent of the AEC.  Not sure why this happens, as the extinction angle is dependent on the AEC.
• Kolev (2013, Appendix E) also provide criterions for MF, ML, EF and EL from: Ptolemy, Hindu, Lockyer, Neugebauer, Schoch, Meeus and Wislicenus. And Kolev also provides criterions for AR and CS from: Lockyer, Neugebauer, Schoch and Wislicenus.
  Here is a comparison between Kolev's observations and the MF, ML, EF and EL criterions:
  
  For magnitudes lower than 1 the criterions are in the region of the observations, for higher magnitude the criterions are below the observations. The criterions should be at a low AEC (for the location the criterion is made), while Kolev's observations have a AEC of around 0.25.
  
• And here is a comparison Kolev's observations and the AR and CS criterions:
  
  For all magnitudes the criterions are below the observations. The criterions should be at a low AEC (for the location the criterion is made), while Kolev's observations have a AEC of around 0.25. But the criterions are consistently lower, so would Kolev's observation method be different than the observational method used for the criterions?
  

References

Farquhar, Henry, 'The brightness and distribution of the fixed stars', The popular science monthly, no. August (1879): 503-13.
Kolev, Rumen, 'Witnessing the heliacal rise of Sirius and Procyon', Journal for the History of Astronomy 32, no. 107 (2001): 152-53.
Kolev, Rumen, Personal observations of heliacal phases of Mercury: A detailed account, Varna, Bulgaria: Placidus research center, 2006.
Kolev, Rumen, 'Six observations of the heliacal rise of Sirius', Journal for the history of astronomy 38, no. 131 (2007): 227-28.
Kolev, Rumen, The Babylonian astrolabe: The calendar of creation. Edited by Simo Parpola. Vol. XXII, State archives of Assyria studies, Helsinki: Neo-Assyrian Text Corpus Project, 2013.
North, John D., Stonehenge: Neolithic man and the cosmos: HarperCollins, 1996.
Ohlsson, Josefin, and Villarreal Gerardo, 'Normal visual acuity in 17-18 year olds', Acta ophthalmol Scand. 83, no. 4 (2005): 487-91.
Schaefer, Brad E., 'Astronomy and the limits of vision', Archaeoastronomy: The journal of astronomy in culture XI (1993): 78-91.
Schoch, Carl. 1924. 'The 'Arcus Visionis' of the planets in the Babylonian observations', Monthly Notices of the Royal Astronomical Society, Vol 84: pp. 731-34.
Seidelmann, P. Kenneth, and Urban Sean E., Explanatory Supplement to the Astronomical Almanac. 3rd ed: University Science Books, 2013.

Acknowledgements

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