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What prominent star could be at the beginning of April?

Saad Al Akhbia 9 10 11 12 13 (324)
April 1 2 3 (93) 4 5
Ca1-11 Ca1-12 Ca1-13 Ca1-14 Ca1-15
te Rei kua hakagana te henua honu te henua

To exactly adjust calendar time according to the position of a star can hardly be done otherwise than via observing its culmination at midnight.

The answer to my question could therefore be Regulus, because in my star list I have no other great star culminating close to April 3:

  365 days
  (80 + RA / 24h * 365¼)   Day of culmination  
Alphard August 10 (222) 227 March 26 (450) 136
10 0   0
Regulus August 21 (233) 227 April 6 (461) 136
12 +1   -1
Alkes September 3 (246) 228 April 20 (475) 135

But I am not satisfied, 3 days' difference it too much and cannot be accepted.

The heliacal time at Ca1-12 was (92 - 80) / 365.25 * 24h = 0h 47m and therefore the nakshatra time was 12h 47m:

Caph β Cassiopeiae 2.28 58º 52' N 00h 06m 1.5  
Sirrah α Andromedae 2.07 28º 49' N 00h 06m 1.5 AH
Algenib Pegasi γ Pegasi 2.83 14º 54' N 00h 11m 2.8 CH
  θ Andromedae 4.61 38° 41′ N 00h 15m 3.7  
Delta δ Andromedae 3.27 30º 52' N 00h 37m 9.4  
Schedir α Cassiopeiae 2.24 56º 16' N 00h 38m 9.6  
Deneb Kaitos β Ceti 2.04 18º 16' S 00h 41m 10.4  
Achird η Cassiopeiae 3.46 57º 33' N 00h 46m 11.7  
  η Andromedae 4.40 23° 25′ N 00h 49m 12.4 C
Cih γ Cassiopeiae 2.15 60º 26' N 00h 53m 13.4  
Porrima γ Virginis 2.74 01° 11′ S 12h 39m 192.5  
  γ Centauri 2.20 48° 58′ S 12h 39m 192.5  
  β Muscae 3.04 68° 06′ S 12h 43m 193.5  
Mimosa β Crucis 1.25 59° 41′ S 12h 44m 193.9  
  ψ Virginis 4.77 09° 32′ S 12h 51m 195.5  
Alioth ε Ursa Majoris 1.76 56° 14′ N 12h 52m 195.8  
Minelauva δ Virginis 3.39 03° 40′ N 12h 53m 196.1  
Cor Caroli α Canum Ven. 2.89 38° 35′ N 12h 54m 196.3  
  δ Muscae 3.61 71° 33′ S 12h 59m 197.5  

The nakshatra day numbers above indicate a position close to RA day 193. And - we should remember - Mimosa was in rongorongo times rising heliacally in day 192.9 (12h 40m). 12 * 60 + 40 = 760 = 40 * 19.

193 - 181 (equal to the distance from e.g. Aldebaran to Antares and possibly a standard) = 12 = Gregorian day 92, April 2. When Mimosa was seen close to the full moon it meant the beginning of April.

Below I have added also the pair Regulus / Sadalmelik to my earlier table:

Heliacal stars RA distances Nakshatra stars
Achird (10.7) 182.2 Mimosa (192.9)
η Andromedae (11.4) 181.5
Polaris (26.6) 181.9 Benetnash (208.5)
Aldebaran (68.2) 180.9 Antares (249.1)
Wezen (107.1) 181.3 Nunki (288.4)
Regulus (152.7) 181.9 Sadalmelik (334.6)
Dubhe (166.7) 181.1 Fomalhaut (347.8)

Achird is rising somewhat too early in order to serve as a star on the other side of the sky compared to Mimosa. Furthermore, although I have no name in my list for η Andromedae it was important in China:

1 Horn α Virginis Crocodile
2 Neck κ Virginis Dragon
3 Root α² Librae Badger
4 Room π Scorpii Hare
5 Heart σ Scorpii Fox
6 Tail μ¹ Scorpii Tiger
7 Winnowing Basket γ Sagittarii Leopard
8 South Dipper φ Sagittarii (?) Unicorn
9 Ox / Herd Boy β Capricornii Buffalo
10 Girl ε Aquarii Bat
11 Emptiness β Aquarii Rat
12 Rooftop α Aquarii Swallow
13 House α Pegasi Pig
14 Wall γ Pegasi Porcupine
15 Legs η Andromedae (?) Wolf
16 Bond β Arietis Dog
17 Stomach 4¹ Arietis (?) Pheasant
18 Hairy Head η Tauri (?) Cockerel
19 Net ε Tauri Crow
20 Turtle λ Orionis Monkey
21 Three Stars ζ Orionis Gibbon
22 Well μ Gemini Tapir
23 Ghost ρ Gemini ? Goat
24 Willow δ Hydrae Stag
25 Star α Hydrae Horse
26 Extended Net ε Hydrae / μ Hydrae Ox
27 Wings α Crateris Snake
28 Chariot γ Corvi Worm
Gb3-20 (311) Gb3-21 Gb3-22 Gb3-23 Gb3-24 (*378)
Schedir (8.6), Deneb Kaitos (9.4)   Achird (10.7), η Andromedae (11.4) Cih (12.4)  
March 29 30 31 (90) April 1 (457) 2
Saad Al Akhbia 6 7 8 9 (320) 10

I have here counted the glyph numbers as 230 (Gb8-30 +  side a) + 61 (Gb1+Gb2) + e.g. 20 = 311 at the first of the fishy birds. 314 will then be at Gb3-23 and 314 + 64 = 378 (the synodic cycle of Saturn, the great time giver).

"... it is essential to recognize that, whether one has to do with the Mesopotamian Saturn, Enki / Ea, or with Ptah of Egypt, he is the 'Lord of Measures' - spell it 'me' in Sumerian, 'parshu' in Akkadian, 'maat' in Egyptian. And the same goes for His Majesty, the Yellow Emperor of China - yellow, because the element earth belongs to Saturn - 'Huang-ti established everywhere the order for the sun, the moon and the stars' ..." (Hamlet's Mill)

For η Andromedae (possibly a sign of the Wolf) the position in a rongorongo text ought to be 11.4 + 365.25 = ca 377 (= 12 + 365). 80 + 12 = 92 (April 2). Right ascension day 377 is here based on 11.4 but my operations have changed the day value to 12, and kua hakagana is at the 12th glyph in the Mamari text:

Saad Al Akhbia 9 10 11 12 13 (324)
April 1 2 3 (93) 4 5
Ca1-11 Ca1-12 Ca1-13 Ca1-14 Ca1-15
te Rei kua hakagana te henua honu te henua
  Achird (10.7), η Andromedae (11.4) Cih (12.4)    
Mimosa (192.9)

... Allen does not mention Achird and he has no other name for η Cassiopejae, but I guess the star could be connected with α Leonis, Regulus, once named Achir (Possessing Luminous Rays):

'Naturally sharing the character of its constellation as the Domicilium Solia, in Euphratean astronomy it was Gus-ba-ra, the Flame, or the Red Fire, of the House of the East; in Khorasmia, Achir, Possessing Luminous Rays; and throughout classical days the supposed cause of the summer's heat, a reputation that it shared with the Dog-star.'

The Chinese list has Dog in their lunar station after that of the Wolf, and I guess the wild Wolf personifies the dark forces in contrast to the domesticated and friendly Dog. April 1 could be the first day after the dark reign of winter (north of the equator).