Improving Doppler Tracking Sensitivity

7 Improving Doppler Tracking Sensitivity

What would be required to improve broadband¹⁰ burst sensitivity ten-fold, to $≃$ 2 $×$ 10^–16 (thus, in a 40 day observation, have sensitivity to periodic waves of $≃$ 10^–17)? Assuming that there is not some unexpected systematic effect entering between 10^–15 and 10^–16 and that the noises are independent (thus variances add and each component must be brought to $≃$ 10^–16), Table 4 shows the required improvements in the principal subsystems.

Table 4:

Required improvement in subsystems to improve overall Doppler sensitivity by a factor of 10.



Noise source	Comment ( $σy$ at $τ$ = 1000 s)	Required
		improvement


Frequency standard	currently FTS + distribution $≃$ 8 $×$ 10^–16	$≃$ 8X
Ground electronics	currently $≃$ 2 $×$ 10^–16	$≃$ 2X
Tropospheric scintillation	currently $≃$ 10^–15 under favorable conditions	$≃$ 10X
Plasma scintillation	Cassini-class radio system probably adequate for calibration to $≃$ 10^–16	$≃$ 1X
Spacecraft motion	currently $≃$ 2 $×$ 10^–16	$≃$ 2X
Antenna mechanical	currently $≃$ 2 $×$ 10^–15 under favorable conditions	$≃$ 20X

Update

Ten-times better FTS stability is said to be “technologically straightforward” [78 ] and there are published reports [99 ] that 10^–18 or better frequency stability may be possible. (If high-stability flyable frequency standards become available in the future, they would allow simultaneous mulitple one- and two-way Doppler measurements. These multiple observations would give excellent diagnostics of many instrumental noises and provide further rejection of systematic effects [118 , 8 ]). Better frequency standards would require better frequency distribution. Prototypes for frequency distribution within the Atacama Large Millimeter Array achieve stability 10^–16 or better for time scales of about 1000 seconds [36 ].

Improving ground electronics noise by 2X is probably possible by even more careful design. Reducing tropospheric scintillation by 10X will require either an antenna at very high altitude, improvements in AMC technology (e.g., exactly coincident beams, better water vapor radiometry technology), or perhaps an interesting idea (suggested independently by Estabrook [45 ] and Hellings [56 ]) whereby a second ground station (listen-only, at high altitude) could be employed to synthesize a Doppler observable which has the (presumably much lower) tropospheric phase scintillation noise of the higher-altitude receive-only station. Plasma scintillation correction technology is already adequate to reach an Allan deviation of $∼$ 10^–16. Cassini spacecraft unmodeled motion was measured to be within a factor of about 2 of 10^–16 (see Section 4.8); it is not clear what actually limited the Cassini motion measurement so additional analysis/design might be required to assure that this component entered at the 10^–16 level or lower.

The largest required improvement is in antenna mechanical noise. It is impractical to build a large, steel, earth-based, moving structure (such as a 34-m antenna) which has intrinsic $≃$ 10^–16 mechanical stability; performance at this level will probably require a separate calibration/removal of mechanical noise. One suggestion is to exploit the differing transfer function of antenna mechanical noise to two- and three-way observations [15 ]. Suppose that a stiffer (that is, smaller mechanical noise) ancillary antenna is co-located with the two-way tracking antenna. The ancillary antenna takes data in the “listen-only” (three-way) mode. The desired Doppler signal, y_s, and mechanical noises of the two antennas enter the time series of fractional Doppler fluctuation according to

where M₂ and M₃ are the time series of mechanical noise at the two and three-way stations. The data combination [15 ]

has the signal content of the standard two-way observation but antenna mechanical noise

as if the ancillary antenna were both transmitting and receiving. If the ancillary antenna is sufficiently stiff (i.e. if the magnitude of M₃ is small compared with the magnitude of M₂) then mechanical noise in the observation can in principle be reduced substantially.

This idea was tested during an otherwise-routine Cassini observation [15 ]. The Cassini spacecraft was tracked in the conventional two-way mode using NASA’s DSS14 70-m station while simultaneous three-way data were taken at a nearby antenna (DSS 25). During the track DSS 14’s subreflector was deliberately articulated to introduce a large, artificial “antenna mechanical variation” (the signal path within the antenna was described in Section 4). Figure 24 shows the two- and three-way Doppler time series during the test. The upper panel shows the “two-pulse” signature of antenna mechanical variation in the two-way data (Equation (6 ) and Figure 7 ). The lower panel shows the effect of the deliberate subreflector motion in the three-way Doppler (Equation (7 )).

Figure 24:

Time series of DSS 14 two-way (upper panel) and DSS 25 three way (lower panel) Doppler during the 2007 March 15 antenna mechancial noise test. At about 04:30 UT the subreflector at DSS 14 was deliberately articulated to produce large antenna mechanical noise variation. The effect in the two-way Doppler is seen immediately and at a two-way light time (T₂ = 8341.6 s) later (see Figure 7

). The receive-only three-way station is unaffected at 04:30 UT (it is receiving a signal transmitted a two-way light time earlier) but observes the effect of the deliberate subreflcetor motion a two-way light time later (lower panel). (The three impulsive glitches in the two-way time series are unrelated to this mechanical noise test.) Figure adapted from [15

].Update

Figure 25 shows a blowup of the time series of the two-way Doppler during the subreflector motion event (upper panel) and the data combination E(t) formed using the two- and three-way data. The two-way mechanical variability cancels to the level of other noises.

Figure 25:

Blowup of DSS 14 two-way Doppler time series (upper panel) near the deliberate subreflector articulation. The lower panel shows the data combination E(t), which cancels the antenna mechanical noise in the two-way time series leaving the antenna mechanical noise of the three-way station (DSS 25) and other secondary noises. Figure adapted from [15 ].Update

Suitably stiff antennas (i.e. antennas with mechanical stability at least an order of magnitude better than that of DSS 25) have been built for radio astronomy applications [97 ]. These or comparable antennas could be used to reduce the antenna mechanical noise in Doppler gravitational wave tracks to $∼$ 10^–16 or lower for $τ$ = 1000 s. Of course one would not use this technique except in situations where the antenna mechanical noise dominates. Some considerations for a practical implementation of this method are discussed in [14 ].

There is no currently-planned mission that requires Doppler stability at the $≃$ 10^–16 level. Indeed unless such stability can be achieved inexpensively that level of Doppler performance might have to be justified by a mission dedicated to precision radio science. As outlined above, however, $∼$ 10^–16 burst sensitivity may be possible with extensions of current technologies. To do several orders of magnitude better than 10^–16, however – e.g., to achieve sensitivity adequate to detect the very weak GWs from known Galactic binaries – would almost certainly require a different utilization of electromagnetic tracking [24 ], discussed briefly in Section 8.