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Towards new nutation theory

V.E.Zharov Physics Faculty, Sternberg State Astronomical Institute Moscow, Russia
JournИes 2014, St-Peterburg 22 ­ 24 September 2014


Goals of work
1) Use the ARIADNA software and the IVS database

for calculations of the nutation angles 2) Comparison of them with the predicted ones by the IAU 2000/2006 nutation theory 3) Some ideas to improve the IAU 2000/2006 nutation theory


The IVS database
1) Observations during period 1984 - 2013 2) Session Earth Orientation Parameter Series (EOP-S) ­ duration of each session 24 hours, during of which 3 or more telescopes observed 10-70 radio sources

3) Number of sessions is ~5500


Main stages of reduction of VLBI observations:
1. Theoretical value of calculated delay:

1 c B s c
c (t ) F (t , X j , j ,UT 1, x
i , Yi , Z i , X i , Yi , Z i , X i , Yi , Z i ,
p , y p , ( , )(or dX , dY ),)

2.

Subtraction of it from observed delay and estimation of parameters Pk of the linearized model:

o

ct




k

c Pk (t ) Pk t

l Ax


Corrections for nutation angles


Spectrum of complex residuals


Some questions (1)
1) Free Core Nutation (FCN) line has significant width. Why? According theory it is free motion (mode) with f = -1.002324 (P = -430.23 d)

SOFA subroutine (Lambert, 2007) realized a free motion of the CIP in the GCRS with a variable amplitude
a) It is mathematical model b) What is an excitation process with the FCN frequency? c) What is physical reason of variability of the FCN amplitude?


Spectral density of atmospheric pressure term around the FCN frequency


Amplitude modulation of signal
a(t ) A(t ) cos(0t 0 ) A(t ) A0 A cos(t ) A0 [1 m cos(t )] MA0 a(t ) A0 cos(0t 0 ) cos[(0 )t (0 )] 2 MA0 cos[(0 )t (0 )] 2


Annual variation of amplitude of S1 tide Semiannual variation

K1; P1 1; 1

S1

(t ) A cos 2 f S1t B sin 2 f S1t


Amplitude modulation of complex signal

P 430 (410; 480) f 1.002324 (1.002439; 1.002083) f modulation (0.000115 0.000241) Pmodulation (8700 6100) 18.6 years?


Simulation

dX (t )


i 1

4

Ai cos(2 fi t i ) dY (t ) B 0.06 0.09 0.09 0.06


i 1

4

Bi cos(2 fi t i )

A P 1/ f 0.09 7275.44 2.23 0.01 493.72 -69.49 0.12 417.26 -91.98 0.09 406.67 -35.48

P 1/ f 6838.33 165.60 446.43 99.30 415.80 -18.87 405.37 39.60


Some questions (2)
2) There is significant power in harmonics with periods in range (-3200;-8200 days) that is close to the main retrograde nutation terms -9,3 and -18,6 years and prograde term with period +18.6 years. Reason is non-perfect modeling of the long nutation terms. What are the Earth structure parameters necessary to correct?


Conclusion
30 ­ years the IVS data base were used for analysis of the nutation angles and comparison with the IAU 2000/2006 nutation series Excitation of the FCN is connected with the atmospheric tide 1 that is one of harmonic results from semi-annual modulation of the thermal S1 tide Is the FCN frequency splitting due to modulation by main nutation harmonic with period 18.6 years? Modeling of main nutation terms with periods 18.6, 9.3 years is not perfect and has to be improved.


Thank for attention !