ATMOSPHERIC TURBULENCE IN ASTRONOMY. Marc Sarazin European Southern Observatory. List of Themes How to find the ideal site...and keep it good?. Optical Propagation through Turbulence Mechanical and Thermal Index of Refraction Signature on ground based observations Correction methods
European Southern Observatory
The VLT Observatory at Paranal, Chile
The ESO-VLT Observatory at Paranal, Chile
Effelsberg 100m radiotelescope
ESO OWL project
Big whorls have little whorls,
Which feed on their velocity;
Little whorls have smaller whorls,
And so on unto viscosity.
L. F. Richardson (1881-1953)
Vertical gradients of potential temperature and velocity determine the conditions for the production of turbulent kinetic energy
In a turbulent flow, the kinetic energy decreases as the -5/3rd power of the spatial frequency (Kolmogorov, 1941)
within the inertial domain ]l, L[
Outer (injection) Scale:
(L= 100m or more in the free atmosphere, less if pure convection)
Inner (dissipation) scale:
(l~0.1mm in a flow of velocity u=10m/s)
= dissipation rate of turbulent kinetic energy (~u^3/L, m^2s^-3)
= kinetic viscosity (in air, 15E-6 m^2 s^-1)
Structure function of the temperature fluctuations
3D Spectrum (Tatarskii, 1971)
within the inertial domain ]2/L,2 /l[
but L is now the size of the thermal eddies
Index of refraction of air
Assuming constant pressure and humidity, n varies only due to temperature fluctuations, with the same structure function
P,e (water vapor pressure) in mB, T in K, Cn2 in m-2/3
The Long Exposure Parameters
Seeing: (radian, ^-0.2)
Fried parameter: ( meter, ^6/5)
Easy to remember: r0=10cmFWHM=1” in the visible (0.5m)
S= 0.7 à 2.2 um
S=0.3 à 2.2 um
Seeing = FWHM
The Short Exposure Parameters
Shorter exposures allow to freeze some atmospheric effects
and reveal the spatial structure of the wavefront corrugation
Sequential 5s exposure images in the K band on the ESO 3.6m telescope
A Speckle structure appears when the exposure is shorter than the atmosphere coherence time 0
1ms exposure at the focus of a 4m diameter telescope
How large is the outer scale?
A dedicated instrument, the Generalized Seeing Monitor
(GSM, built by the Dept. of Astrophysics, Nice University)
How large is the outer scale?
Overall Statistics for the Wavefront Outer Scale
At Paranal: a median value of 22m was found.
Ref: F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi and M. Sarazin; Astron. Astrophys. Supplement, v.144, p.39-44; June 2000
Structure function for the phase fluctuations:
The number of speckles in a pupil of diameter D is (D/r0)^2
Why looking for the best seeing if turbulence can be corrected?
Adaptive optics techniques are more complex (ND/r0^2),
less efficient (Strehlexp(r0/D^2))
and more expensive to implement
for bad seeing conditions
The many ways to destroy a good observing environment
Incoming neutral flow should enter the building to contribute to flushing, the height of the turbulent ground layer determines the minimum height of the apertures.
Thermal exchanges with the ground by re-circulation inside the cavity zone is the main source of thermal turbulence in the wake.
When a mirror is warmer that the air in an undisturbed enclosure, a convective equilibrium (full cascade) is reached after 10-15mn. The limit on the convective cell size is set by the mirror diameter
The warm mirror seeing varies slowly with the thickness of the convective layer: reduce height by 3 orders of magnitude to divide mirror seeing by 4, from 0.5 to 0.12 arcsec/K
The contribution to seeing due to turbulence over the mirror is given by:
When a mirror is warmer that the air in a flushed enclosure, the convective cells cannot reach equilibrium. The flushing velocity must be large enough so as to decrease significantly (down to 10-30cm) the thickness turbulence over the whole diameter of the mirror.
The thickness of the boundary layer over a flat plate increases with the distance to the edge in the and with the flow velocity.
Access Asphalt Road
Until the 80’s, most astronomical facilities were not properly designed in order to preserve site quality