MEMORANDUM

On the optimization of the RadioAstron mission

by using advanced observing methods

at ground radio telescopes and tracking stations,

and the advantages of using on-board H-maser frequency standard

and on-board accelerometer

Astro Space Center, Moscow, June 2003

1. Objectives

One of the main peculiarities of the RadioAstron mission is its high-apogee orbit where the spacecraft is moving at distances much greater than the Earth diameter during the significant portion of its rotation period. Except of more higher angular resolution a such situation has a number of peculiarities in comparison with low-orbit SVLBI missions: the spacecraft is moving smoothly because of much weaker effects of Earth atmosphere and irregularities of Earth gravitation field, high altitudes provide more stable thermal regime (illumination by the Sun), more convenient condition to use reference sources; easier access for tracking station at lower tracking velocities; slow pass through the UV-cells.

All these peculiarities of high-orbit SVLBI can be used to increase the sensitivity (longer possible integration time for a given UV-point) and the accuracy of measurements of position of radio sources. High accuracy measurements of spacecraft position (or orbit parameters) are necessary to materialize these possibilities.

Calculated sensitivity of space-ground interferometer with the upgraded VLA at 18-25 GHz ( l = 12 – 17 mm) for integration time of 300 s (no loss of coherence) is about s ~ 3 mJy with the fringe size at maximum base line B = 350 000 km of 7.1 ¸ 10 microarcseconds. At the SNR of about 30 it would provide the accuracy of position measurements of about 0.2÷0.3 μas.

In this Memo we consider the advanced methods of ground radio telescopes and tracking stations (TS) operation, on-board H-maser frequency standard (SHM - already planned for the mission) and high-accuracy on-board accelerometer applications to solve this objective.

2. Sensitivity

The sensitivity of space-ground interferometer is defined by the parameters of space (SRT) and ground (GRT) radio telescopes under the condition of high precision time and frequency synchronization (see for ex. [1-3])

s = (T_sys1 T_sys2)^0.5(C h_s)^–1 (2 Dν t K₁ K₂)^-0.5 Jy,

where K_1,2 = ( h_1,.2 А_1,2) (2e)^-1, h_1,2 – aperture efficiency of antennae, А_1,2 – theirs geometric area, h_s – recorder/processor efficiencies (one/two-bit sampling, fringe rate rotation sampling, etc.,), Dν – recorded bandwidth, t - coherent integration time (fringe detection), N – efficiency of phase coherence. Under the assumption of Gauss noise spectrum of phase fluctuations the loss of coherence can be expressed as:

N ≈ 1 – 0.5 s_o²,

where s_o is the RMS value of residual phase fluctuations during the integration time (N ≡ 1 for hundred-per-cent coherence).

The value of s_o is determined by the phase instabilities in all elements of space-ground interferometer: instabilities of local oscillators and other circuits in space and ground receivers and data acquisition systems, mechanical vibrations of SRT and GRT’s, on-board and ground tracking antennas; phase fluctuations due to propagation of the signal through the atmosphere in data transfer (down link) and synchronization (phase-locked loop PLL); inaccuracy of the knowledge of spacecraft acceleration.

The contribution from all electronic circuits to residual phase fluctuations can be made lower than from phase instability of the H-maser frequency standard. At the VLA, the residual phase fluctuations s_e » ν (GHz)/4, which corresponds to s_e = 5^o.5 at ν = 22 GHz [4]. We expect that for the SRT electronics residual phase fluctuations will be at a level of s_e ~ 8º.

One can evaluate the total impact from mechanical vibrations by taking into account allowable vibrations of 0.05 mm (RMS) for SRT and GRT along theirs axes, this will give us at 22 GHz s_m » 4^o when using on-board H-maser frequency standard (SHM), and s_m » 10^o when using up-down link synchronization with 0.1 mm RMS vibration for the on-board VIRK antenna and 0.05 mm RMS vibration for the TS antenna along theirs axis. The conclusion is that usage of SHM considerably reduces phase fluctuations from mechanical vibrations.

From the VSOP mission experience it is known that the main reason limiting the coherence time was phase fluctuations due to propagation of the signal through the Earth atmosphere. These fluctuations reduce the stability of reference frequency by an order of magnitude at the up-down link synchronization [5,6].

Lastly, there is one more reason in coherence loss for space-ground interferometer: this is an uncertainty in the determination of the SRT acceleration. The uncertainty can be caused by the inaccuracy of the reconstructed orbit and by the non-gravitational acceleration, which are difficult to simulate and to take into account.

The atmospheric effects and the anomalies in the acceleration behavior of the SRT will be considered later in this Memo together with suggestions on the possible way of corrections for these effects.

3. Sensitivity in fringe fitting by selfcalibration,

and sensitivity in image reconstruction and in differential astrometry

The problem of self-calibration at very long baselines is connected with the a priori uncertainty in the intrinsic structure of the source under the investigation, which is the ultimate objective of the VLBI study. As a result of VLBA study at 15 GHz [7,8] it was found that in 160 compact radio sources with flat spectra and with total flux densities above 1.5 Jy there are 97, 117, and 151 sources which have correlated flux densities ³0.5, ³0.3, and ³0.1 Jy at maximum baselines correspondingly. One can make the conclusion that there are more than 6000 radio sources with the total flux density ³300 mJy, and more than a half of such sources will have correlated flux densities ³100 mJy at the maximum baselines of the VLBA system.

Mean angular distance between such sources on the sky will be about 3^o. Time necessary to re-point RadioAstron SRT to the sources at angular distance of ~ 10^o is about 10 minutes with the slewing rate of 0.3 degree/s and necessary stabilization time (as specified by the Technical Task for the project); there are about 10 sources available for differential astrometry in such area.

Angular diameter of a compact radio sources (or its component) with the flux density of 100 mJy and circular Gaussian brightness distribution is equal to 16 mas for maximum brightness temperature of T_max = 10¹² K. For the same brightness temperature a source component with elliptical Gaussian brightness distribution (jet) and with the major axis of 100 mas will have the minor axis of only 2.5 mas. Characteristic angular sizes in these models correspond to maximum angular resolution in the RadioAstron mission.

Conclusion: self-calibration may be used for the simplest models of source structure if 100 mJy correlated flux is reliably detected during fringe search.

4. Atmospheric effects and the possibility to correct phase errors

Phase fluctuations caused by the propagation of radio signals through the Earth atmosphere are the main effects limited the coherent integration time in VLBI measurements. This statement was confirmed also for the space-ground radio interferometer HALCA [5,6]. The possibility to make corrections to atmospheric phase fluctuation was studied by many researches, and there were developed some approved technique [9-11]. For space-ground interferometer atmospheric effects are relevant only to GRT’s and to TS’s. Two methods can be used to reduce the phase errors caused by the troposphere: radio monitoring of the atmosphere brightness in several frequencies around of water vapor line at 22 GHz in the direction of the observed radio source (WLM – Water Line Monitoring), and/or self-calibration GRT’s using one reference radio telescope located at the high mountain (HMRT - for example, VLBA antenna at the Hawaii) observing the same source. In the last case the reference antenna will be nearly free from the atmospheric effects and all ground baselines (small compared to the space-ground baselines) can be corrected for atmospheric effects.

Test WLM experiments and regular observations conducted at the Owens Valley Radio Observatory (OVRO) demonstrated an accuracy in the measurements of the atmospheric path delay at a level of 0.15 mm, and it is planned to improve the accuracy down to the level of about 0.05 mm [9]. Such accuracy provides the possibility to conduct regular interferometer observations even at the millimeter wavelength with future extension to submillimeter wavelengths. WLM method was planned to be used in VSOP mission [12], but it was not realized.

Conclusion: observing techniques presented above provide potential capability to reduce atmospheric effects to such level when they will not constitute the main reason limiting the coherence time in VLBI at high frequencies. We propose to develop both methods of phase corrections at 22 GHz with ground radio telescopes during the pre-launch time.

5. High accuracy orbit determination and anomalous acceleration

Space-ground radio interferometer HALCA has demonstrated in practice high accuracy of orbit determination [13]. The same technique of orbit measurements and reconstruction will provide for RadioAstron mission the accuracy in SRT position of about 5 m and with the accuracy of about 0.1 mm/s in STR velocity for each 1÷5 minutes. Even better accuracy will be achieved in orbit reconstruction based on long-term measurements and in post-correlation analysis.

Spacecraft in the RadioAstron mission will move along elliptical high-apogee orbit with the major semi axis nearly 30 times larger than the Earth diameter. The accuracy of the measurements of radial distance and radial velocity will be sufficiently good, but the determination of the tangential components for SRT position and velocity will request some special approaches. It seems that phase-reference observations of two or more radio sources will be necessary for accurate determination of full vectors for the position, velocity and acceleration. Such measurements cannot be conducted continuously because of relatively slow slew speed of the SRT and limited number of re-pointings per day. Therefore, there is necessity for independent monitoring of small and probably variable SRT accelerations especially between the reference source observations.

The estimations show that the accuracy of acceleration measurements which can be achieved by all facilities available in the TS-SRT orbit measurements system including on-board SHM and reference-sources observing technique will be limited by ~ 1÷2ּ10^-8 m/c² in the time intervals between reference-sources observation. The errors are connected with the uncertainties in the model of the Earth gravitation field near the SRT perigee (R_min ~ 10⁴ km) and with the inaccuracy of the calculations of solar light pressure along the whole orbit. For the last effect 10% inaccuracy in the albedo and midship of the spacecraft with SRT at different orientations relative to the Sun direction will cause uncertainty in the SRT acceleration of about σ_a ~ 10^-8 m/c². Acceleration due to solar wind pressure is about ~ 1÷20ּ10^-10 m/c², and it varies by several times in the magnitude (inside the magnetosphere even in direction) during a few seconds. The same acceleration is expected due to gas evaporating from the SRT.

SuperSTAR accelerometer (AM) recently developed and tested by ONERA provides the accuracy of 10^-10 m/c²along all three axis of the spacecraft [7]. The evaluations presented above have shown that solar pressure, solar wind (variable in strength and direction) especially inside the magnetosphere, and evaporation of gas from the spacecraft will cause SRT acceleration in the range of 10^-10 - 10^-8 m/c².

The following Table 1 shows the magnitudes of uncontrolled SRT displacement due to anomalous acceleration acting for some period of time Δt.

Table 1

τ (c)	10^2	10^3	10^4	10^5
∆l = 0,5a(Δt)^2 (mm) for a (a= 3σa = 3ּ10^-8m/c^2) (a= 10^-10m/c^2)	0.15 5ּ10^-4	15 5ּ10^-2	1.5ּ10^3 5	1.5ּ10^5 5ּ10^2

At λ = 13.5 mm uncontrolled SRT displacement by Δl ~ 2 mm will cause 10% loss in coherence in accordance with the expression σ = 2π(0.5Δl/λ) ~ 0.45.

Conclusion: AM will provide a possibility to reduce considerably the effects of errors in SRT acceleration thus increasing coherent integration time from several minutes to several hours when new reference-sources observations could be done. AM will also help to decrease time of fringe search at the correlator because of smaller values in uncertainty of delay and fringe rate.

6. Main parameters of the SuperSTAR accelerometer

High sensitive on-board AM developed in France by the IEA firm (Instrumentation & Aerospace Equipments Research Unit) belonging to the Office National d'Etudes et de Recherches Aerospatiales (ONERA) is successfully operating at the two satellites launched by Russian rocket in 2002 from the cosmodrome Plesetsk (project GRACE, Germany and USA) for the measurements of the Earth gravitation field.

Main parameters:

· acceleration range - ±5 10^-5 m/c²,

· sensitivity - 10^-10 m/(c² Hz^0.5),

· size - 6-liter cube,

· mass - 6 kg,

· power consumption - 2 W,

· analog output.

The accelerometer may be installed at the RadioAstron spacecraft near the mass center. The output information can be included into the science data headers transmitted by the VIRK. The possibility to use such device in VSOP-2 mission is also under discussion.

7. The scheme of frequency synchronization using on-board H-maser

The scheme of frequency synchronization using on-board H-maser and up-down phase loop is shown in Figure 1. On-board H-maser provides steady-going (without interruptions connected, for example, with switching between tracking stations) reference signal for local oscillators, sampling frequencies and the carrier of 15 GHz downlink data transmitter (VIRK). Phase loop produced by H-maser with the receiving science data tracking station will permit necessary data for orbit measurements and time alignment. The backup way of synchronization using standard up-down phase loop providing reference frequency from the ground H-maser at the tracking station is also possible.

The development of the on-board H-maser (SHM) was started in 1996 according to the international agreement between the ASC and ESA signed on January 15 1996 and proved by RosAviaKosmos. Neuchatel Observatory in the Switzerland is the institution responsible for the development, manufacturing, tests and delivery of the on-board H-maser. All tasks necessary for the integration of the SHM at the RadioAstron spacecraft (such as mounting, thermo stabilization, power supply, control, and interfaces with VIRK) were completed in the ASC and in Lavochkin Association. At present the development of SHM at the Neuchatel Observatory is continuing but with the goal to install SHM at the ACES satellite.

Main SHM specification requested by RadioAstron were conserved, they are presented in the Table 2 below.

Table 2

Time interval ∆t (c)	1	10	10^2	10^3	2 10^3
Allan deviation ∆ν/ν	1,5 10^-13	2,1 10^-14	5,1 10^-15	2,1 10^-15	2,0 10^-15
Coherence loss 1-N = 0,5(2π∆ν∆t)^2 (at ν = 22 GHz)	2 10^-4	4,2 10^-4	2,5 10^-3	4,2 10^-2	0,15

Conclusion: the retention of SHM in RadioAstron science package will provide estimated coherent integration time of 300 s, and it would provide possibility to achieve longer integration time (up to 2000 s) under no other constraints.

8. Conclusion

On-board H-maser frequency standard and high accuracy on-board accelerometer included into the scientific payload of RadioAstron mission will permit us to increase the coherent integration time up to 5-30 minutes at the correlator before fringe detection. This will be resulted in 2-5 times improvement in sensitivity by increasing the coherence time up to 5-30 minutes. To reach these potential figures we propose advanced observing methods using the measurements of the atmospheric path delay variations by the monitoring of 22 GHz water vapor line emission along a line of sight to the observing source (WLM) and/or by using reference radio telescope located at high mountain. Additional gain in sensitivity can be obtained by applying self-calibration in fringe-fitting procedure during image reconstruction.

As it is known from regular ground VLBI observations, maximum coherence time at 22 GHz is about 80 seconds. WLM observing technique or/and usage of reference radio telescope on high mountain (HMRT) will increase the integration time by 2-3 times. On-board H-maser frequency standard will also provide the possibility to increase the integration time by 2-3 times. On-board accelerometer will provide necessary accuracy of orbit determination to realize potential maximum integration time by 2-3 and to simplify fringe search at the correlator.

Table 3

Option	Coherent integration time (s)
No HMRT/WLM, SHM and AM	80
HMRT without SHM and AM	160-240
HMRT/WLM and SHM, but no AM	320-720
HMRT/WLM, SHM and AM	720

Table 3 shows that necessary sensitivity of space-ground radio interferometer could be achieved only with on-board H-maser frequency standard and advanced observing techniques.

On-board accelerometer and SHM will provide the possibility to obtain three-dimensional distribution of the Earth gravitation field on the distance scales of R_min ³ 10⁴ km with the high accuracy for the first time.

We propose to stimulate scientific and technical investigations for the implementation of these approaches in the nearest future.

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