PhD Research @ Stanford: Precision Thermal Control for LISA

I just wanted to say a few words about what I’ve worked for my Ph.D. dissertation at Stanford.

(Photo Courtesy of NASA/JPL)

I’ve been working for the Laser Interferometer Space Antenna (LISA) project for the last several years. LISA is designed to directly detect the gravitational waves in space for 0.1 mHz to 1 Hz.

The gravitational wave is time-varying strains in space-time and it is detectable as a fractional change in a proper distance. In Einstein’s theory of general relativity, the gravity is due to curvature of space-time, which is caused by the presence of objects. 
The more massive the object is, the greater the curvature becomes and thus the more intense the gravity. 
When the objects move around in space-time, the curvature will be changed.
 Then, ripples in space-time can spread outward just like ripples on the surface of a lake.
They are usually produced in an interaction between two or more masses including the binary orbit of two black holes, a merge of two galaxies, or two neutron stars orbiting each other. 
However, once the waves reach the Earth, they are extremely small because they attenuate in strength with distance as they move away from the source. 
Plus, space-time is very stiff. Even for the most powerful sources, the waves reaching the Earth produce extremely small strains. 
Therefore, gravitational wave detectors need to have extremely high strain-sensitivity along with precision drag-free control.

We need two free-floating inertia objects, which are called proof-mass. When gravitational waves pass through them, they are moved back and forth as the space-time is stretched & compressed. Since we know the nominal distance between the PMs, all we want to do is measure the displacement. But, these distances have a lot of zeros, which makes the problem challenging:  Especially for the LISA mission, PMs separate by 5,000,000,000 m and the displacement will be as small as 10 picometer (or, 10/1,000,000,000,000 m). And the resulting strain is in the order of 1E-21.It is equivalent to measure the diameter of an atom from the distance between the Earth and the Sun.

Gravity waves reaching in the vicinity of earth are so weak and the proof-mass are easily disturbed by external forces, for example, the radiation pressure from the sun. Thus, we build drag-free spacecraft around the proof-masses to shield the external disturbance forces. (In the picture above) LISA consists of 3 identical drag-free spacecraft forming an equilateral triangle orbiting around the Sun, 20-degree behind the Earth. And then, the spacecraft follow the motion of the proof-masses as the gravitational waves pass through. At the same time they protect from external forces.

Temperature variations are expected to be one of the major contribution to acceleration disturbance sources particularly at low frequency range. We have reviewed proof-mass acceleration noise estimate and corresponding LISA’s strain sensitivity. Temperature stability must be in the order of microkelvin to achieve LISA’s scientific goal. Both temporal & spatial stabilities are important. Temperature variations brings several negative effect: (1) radiometer effect
, which could be caused by fluctuations in the temperature difference across each the proof-mass housing if the residual gas pressure is larger than the differential thermal pressure. (2) Thermal radiation (3) Gravitational distortion
: small temperature fluctuation can even produce distortions in the surrounding aluminum structure. This produces a gravitational disturbance, or mass attraction force. Moreover, temperature variations also have negative effects on optics. For example, laser frequency stability and optical path length variation due to thermal distortion. Thus, I decided to focus on “microkelvin temperature stability” for protecting the proof-mass from external disturbances.

I shouldn’t disclose much details about the approaches and results here though, we are essentially working on the following 3 things at Stanford.

(1) temperature sensor that has a resolution as low as microkelvin (~1e-6 K).

(2) passive thermal isolation system

(3) active thermal compensation system

Since the thermal mass of the spacecraft is limited, it calls for active compensation system particularly at the low frequency range. Thermal problems seem to be innocent problems to deal with (for many people), however, it’s not that straightforward when you have to regulate such a tiny amount of temperature variations.