J/ApJ/773/1 Period of HD 19356 recorded in the Cairo Calendar? (Jetsu+, 2013) ================================================================================ Did the ancient egyptians record the period of the eclipsing binary Algol --The Raging one? Jetsu L., Porceddu S., Lyytinen J., Kajatkari P., Lehtinen J., Markkanen T., Toivari-Viitala J. =2013ApJ...773....1J (SIMBAD/NED BibCode) ================================================================================ ADC_Keywords: Binaries, eclipsing Keywords: binaries: eclipsing; history and philosophy of astronomy; methods: statistical; stars: evolution; stars: individual (Algol, Bet Per, HD 19356) Abstract: The eclipses in binary stars give precise information of orbital period changes. Goodricke J. (1783RSPT...73..474G) discovered the 2.867d period in the eclipses of Algol. The irregular orbital period changes of this longest known eclipsing binary continue to puzzle astronomers. The mass transfer between the two members of this binary should cause a long-term increase of the orbital period, but observations over two centuries have not confirmed this effect. Here, we present evidence indicating that the period of Algol was 2.850d three millennia ago. For religious reasons, the ancient Egyptians have recorded this period into the Cairo Calendar (CC), which describes the repetitive changes of the Raging one. CC may be the oldest preserved historical document of the discovery of a variable star. Description: Ancient Egyptian Scribes (AES) wrote Calendars of Lucky and Unlucky Days that assigned good and bad prognoses for the days of the year. These prognoses were based on mythological and astronomical events considered influential for everyday life. The best preserved calendar is the Cairo Calendar (CC) in papyrus Cairo 86637 dated to 1271-1163B.C. Here, we concentrate on statistics, astrophysics, and astronomy. We show that n~200 good prognoses would induce P_Moon_ and P_Algol_ in CC, even if the remaining n~700 good and bad prognoses had aperiodic origins. The connections between Algol and AES are discussed in detail in S. Porceddu et al. (2013, in preparation, Paper III), where we date CC to 1224 B.C. Objects: ------------------------------------------------ RA (ICRS) DE Designation(s) ------------------------------------------------ 03 08 10.13 +40 57 20.3 Algol = NAME ALGOL ------------------------------------------------ File Summary: -------------------------------------------------------------------------------- FileName Lrecl Records Explanations -------------------------------------------------------------------------------- ReadMe 80 . This file table1.dat 50 30 Cairo Calendar (CC) prognoses for one Egyptian year table3.dat 59 915 Time points for all prognoses of Table 1 -------------------------------------------------------------------------------- See also: J/A+A/542/A38 : LQ Hya V-band differential light curve (Lehtinen+, 2012) J/A+A/527/A136 : HD 116956 V-band differential light curve (Lehtinen+, 2011) J/MNRAS/405/1930 : Per changes of EA-, EB- and EW-types binaries (Liao+, 2010) J/A+A/383/197 : BV light curves of V511 Lyr in 1994-1996 (Lyytinen+, 2002) J/A+A/362/223 : 1984-1998 BV photometry of V815 Her (Jetsu+, 2000) J/A+A/351/212 : V1794 UBVR time series (Jetsu+, 1999) J/A+A/321/L33 : Terrestrial impact cratering rate (Jetsu 1997) Byte-by-byte Description of file: table1.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 I2 --- D [1/30] Day of month (1) 4- 6 A3 --- AI Prognoses of Aket I (Month=1) (2) 8- 10 A3 --- AII Prognoses of Aket II (Month=2) (2) 12- 14 A3 --- AIII Prognoses of Aket III (Month=3) (2) 16- 18 A3 --- AIV Prognoses of Aket IV (Month=4) (2) 20- 22 A3 --- PI Prognoses of Peret I (Month=5) (2) 24- 26 A3 --- PII Prognoses of Peret II (Month=6) (2) 28- 30 A3 --- PIII Prognoses of Peret III (Month=7) (2) 32- 34 A3 --- PIV Prognoses of Peret IV (Month=8) (2) 36- 38 A3 --- SI Prognoses of Shemu I (Month=9) (2) 40- 42 A3 --- SII Prognoses of Shemu II (Month=10) (2) 44- 46 A3 --- SIII Prognoses of Shemu III (Month=11) (2) 48- 50 A3 --- SIV Prognoses of Shemu IV (Month=12) (2) -------------------------------------------------------------------------------- Note (1): The ancient Egyptian year had 365 days. It contained 12 months of 30 days (D). Every month had 3 weeks with 10 days. The year was divided into the flood (Akhet), the winter (Peret), and the harvest (Shemu) seasons. Note (2): Cairo Calendar (CC) gave three prognoses a day, except for the five additional "epagomenal" days of the year. We use the German notation G = "gut" = "good" and S = "schlecht" = "bad" (Leitz C. 1994, Tagewahlerei (Agyptologische Abhandlungen 55; Wiesbaden, Germany: Harrassowitz Verlag). The notation for unreadable prognoses is "-." The Egyptian day began from dawn. Daytime and nighttime were divided into 12hr. For example, GGS for "I Akhet 25" means that the first two parts of this day were good, but the third part was bad. See section 2 for further details. -------------------------------------------------------------------------------- Byte-by-byte Description of file: table3.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 I2 --- D [1/30] Day number 4- 5 I2 --- M [1/12] Month number 7- 9 I3 --- NE [1/360] Egyptian day; NE=30(M-1)+D 11 A1 --- X [GS] Prognosis 13- 19 F7.3 d ti(2_62) N_0_=62 in Eq. 1 and day division of Eq. 2 (1) 21- 27 F7.3 d ti(2_187) N_0_=187 in Eq. 1 and day division of Eq. 2 (1) 29- 35 F7.3 d ti(2_307) N_0_=307 in Eq. 1 and day division of Eq. 2 (1) 37- 43 F7.3 d ti(3_62) N_0_=62 in Eq. 1 and day division of Eq. 3 (1) 45- 51 F7.3 d ti(3_187) N_0_=187 in Eq. 1 and day division of Eq. 3 (1) 53- 59 F7.3 d ti(3_307) N_0_=307 in Eq. 1 and day division of Eq. 3 (1) -------------------------------------------------------------------------------- Note (1): We computed Gregorian days (NG=1=January 1) from Equation (1): {NG=NE+N_0_-1, NE<=366-N_0_ NG=NE+N_0_-366, NE>366-N_0_} where NE=30(M-1)+D, and N_0_=62, 187 or 307. Assuming that Ancient Egyptian Scribes (AES) divided l_D_(NG) into three intervals gave Equation (2): t_1_(NE)=(NE-1)+(1/6)[l_D_(NG)/24] t_2_(NE)=(NE-1)+(3/6)[l_D_(NG)/24] t_3_(NE)=(NE-1)+(5/6)[l_D_(NG)/24] with l_D_(NG), the daytime at Middle Egypt ({phi}=26{deg}41'). In our other alternative, the daytime was divided into two intervals and the nighttime was the third interval, Equation (3): t_1_(NE)=(NE-1)+(1/4)[l_D_(NG)/24] t_2_(NE)=(NE-1)+(3/4)[l_D_(NG)/24] t_3_(NE)=(NE-1)+1/2+(1/2)[l_D_(NG)/24] See section 2 for further explanations. -------------------------------------------------------------------------------- History: From electronic version of the journal ================================================================================ (End) Prepared by [AAS], Emmanuelle Perret [CDS] 31-Aug-2016