Techniques Adaptive Optics Coronographs Differential Imaging Results. Direct Imaging of Exoplanets. Challenge 1: Large ratio between star and planet flux (Star/Planet). Reflected light from Jupiter ≈ 10 –9. Challenge 2: Close proximity of planet to host star.
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Challenge 1: Large ratio between star and planet flux (Star/Planet)
Reflected light from Jupiter ≈ 10–9
Direct Detections need contrast ratios of 10–9 to 10–10
At separations of 0.01 to 1 arcseconds
Earth : ~10–10 separation = 0.1 arcseconds for a star at 10 parsecs
Jupiter: ~10–9 separation= 0.5 arcseconds for a star at 10 parsecs
1 AU = 1 arcsec separation at 1 parsec
Younger planets are hotter and they emit more radiated light. These are easier to detect.
f(x) = F(s) e2pixs ds
F(s) = f(x) e−2pixs dx
The Fourier transform of a function (frequency spectrum) tells you the amplitude (contribution) of each sin (cos) function at the frequency that is in the function under consideration.
The square of the Fourier transform is the power spectra and is related to the intensity when dealing with light.
Two important features of Fourier transforms:
1) The “spatial or time coordinate” x maps into a “frequency” coordinate 1/x (= s or n)
Thus small changes in x map into large changes in s.
A function that is narrow in x is wide in s
Period = 1/frequency
Comb of Shah function (sampling function)
Cosine is an even function: cos(–x) = cos(x)
Sine is an odd function: sin(–x) = –sin(x)
The Fourier Transform of a Gausssian is another Gaussian. If the Gaussian is wide (narrow) in the temporal/spatial domain, it is narrow(wide) in the Fourier/frequency domain. In the limit of an infinitely narrow Gaussian (d-function) the Fourier transform is infinitely wide (constant)
All functions are interchangeable. If it is a sinc function in time, it is a slit function in frequency space
Note: these are the diffraction patterns of a slit, triangular and circular apertures
f(u)f(x–u)du = f * f
Background: Fourier Transforms
In Fourier space the convolution (smoothing of a function) is just the product of the two transforms:
Normal Space Fourier Space
f*g F G
Suppose you wanted to smooth your data by n points.
The second important features of Fourier transforms:
2) In Fourier space the convolution is just the product of the two transforms:
Normal Space Fourier Space
f*g F G
f g F * G
Atmospheric turbulence distorts stellar images making them much larger than point sources. This seeing image makes it impossible to detect nearby faint companions.
The scientific and engineering discipline whereby the performance of an optical signal is improved by using information about the environment through which it passes
AO Deals with the control of light in a real time closed loop and is a subset of active optics.
Adaptive Optics: Systems operating below 1/10 Hz
Active Optics: Systems operating above 1/10 Hz
The brain interprets an image, determines its correction, and applies the correction either voluntarily of involuntarily
Lens compression: Focus corrected mode
Tracking an Object: Tilt mode optics system
Iris opening and closing to intensity levels: Intensity control mode
Eyes squinting: An aperture stop, spatial filter, and phase controlling mechanism
This is the Fourier transform of the telescope aperture
Dl = 1.22 l/D = 251643 l/D (arcsecs)
Even at the best sites AO is needed to improve image quality and reach the diffraction limit of the telescope. This is easier to do in the infrared
A Turbulent atmosphere is characterized by eddy (cells) that decay from larger to smaller elements.
The largest elements define the upper scale turbulenceLuwhich is the scale at which the original turbulence is generated.
The lower scale of turbulence Ll is the size below which viscous effects are important and the energy is dissipated into heat.
Lu: 10–100 m
Ll: mm–cm (can be ignored)
ro: the coherence length or „Fried parameter“ is
r0 = 0.185 l6/5 cos3/5z(∫Cn² dh)–3/5
ro is the maximum diameter of a collector before atmospheric distortions limit performance (l is in meters and z is the zenith distance)
r0 is 10-20 cm at zero zenith distance at good sites
To compensate adequately the wavefront the AO should have at least D/r0 elements
to: the timescale over which changes in the atmospheric turbulence becomes important. This is approximately r0 divided by the wind velocity.
For r0 = 10 cm and Vwind = 5 m/s, t0 = 20 milliseconds
t0 tells you the time scale for AO corrections
The Strehl ratio is a figure of merit as to how well your AO system is working. SR = 1 means you are at the diffraction limit. Good AO systems can get SR as high as 0.8. SR=0.3-0.4 is more typical.
Isoplanetic Angle: Maximum angular separation (q0) between two wavefronts that have the same wavefront errors. Two wavefronts separated by less than q0 should have good adaptive optics compensation
q0≈ 0.6 r0/L
Where L is the propagation distance. q0 is typically about 20 arcseconds.
You do not want to correct using a reference star in this direction
An ensemble of rays have a certain optical path length (OPL):
OPL = length × refractive index
A wavefront defines a surface of constant OPL. Light rays and wavefronts are orthogonal to each other.
A wavefront is also called a phasefront since it is also a surface of constant phase.
Optical imaging system:
The aberrated wavefront is compared to an ideal spherical wavefront called a the reference wavefront. The optical path difference (OPD) is measured between the spherical reference surface (SRS) and aberated wavefront (AWF)
The OPD function can be described by a polynomial where each term describes a specific aberation and how much it is present.
SKn,m,1rn cosmq + Kn,m,2rn sinmq
A wavefront sensor is used to measure the aberration function W(x,y)
Focal Plane detector
Adaptive Optical Components:
Wavefront at telescope
corrected wavefront to camera
You need a reference point source (star) for the wavefront measurement. The reference star must be within the isoplanatic angle, of about 10-30 arcseconds
If there is no bright (mag ~ 14-15) nearby star then you must use an artificial star or „laser guide star“.
All laser guide AO systems use a sodium laser tuned to Na 5890 Å pointed to the 11.5 km thick layer of enhanced sodium at an altitude of 90 km.
Much of this research was done by the U.S. Air Force and was declassified in the early 1990s.
The telescope optics then forms the incoming wave into an image. The electric field in the image plane is the Fourier transform of the electric field in the aperture plane – a sinc function (in 2 dimensions this is of course the Bessel function)
Eb∝ sinc(Dl, q)
Normally this is where we place the detector
In the image plane the star is occulted by an image stop. This stop has a shape function w(Dlq/s). It has unity where the stop is opaque and zero where the stop is absent. If w(q) has width of order unity, the stop will be of order s resolution elements. The transfer function in the image planet is 1 – w(Dlq/s).
W(q) = exp(–q2/2)
The occulted image is then relayed to a detector through a second pupil plane e)
This is the convolution of the step function of the original pupil with a Gaussian
One then places a Lyot stop in the pupil plane
To detect close companions one has to subtract the PSF of the central star (even with coronagraphs) which is complicated by atmospheric speckles.
One solution: Differential Imaging
Since the star has no methane, the PSF in all filters will look (almost) the same.
Split the image with a beam splitter. In one beam place a filter where the planet is faint (Methane) and in the other beam a filter where it is bright (continuum). The atmospheric speckles and PSF of the star (with no methane) should be the same in both images. By taking the difference one gets a very good subtraction of the PSF
Structure in the disks give hints to the presence of sub-stellar companions
But there is large uncertainty in the surface gravity and mass can be as low as 4 and as high as 155 MJup.
Another brown dwarf detected with the NACO adaptive optics system on the VLT
M = 4 MJup
P ~ 870 years
Mass < 3 MJup, any more and the gravitation of the planet would disrupt the dust ring
Planet model with T = 400 K and R = 1.2 RJup.
Reflected light from circumplanetary disk with R = 20 RJup
Detection of the planet in the optical may be due to a disk around the planet. Possible since the star is only 30 Million years old.
Marengo et al. 2009
Not detected in the Infrared. Limits of 3 MJup and age of 200 Million years
Kalas et al. 2012
Recent observations by Kalas using HST confirm presence of planet.
Imaged using Angular Differential Imaging (i.e. Spectral Differential Imaging)
Image of the planetary system around HR 8799 taken with a „Vortex Phase“ coronagraph at the 5m Palomar Telescope
The 2009-2010 orbital motions of the four planets are shown in the larger plot. A square symbol denotes the first 2009 epoch. The upper-right small panel shows a zoomed version of e's astrometry including the expected motion (curved line) if it is an unrelated background object. Planet e is confirmed as bound to HR 8799 and it is moving 46 ± 10 mas/year counter-clockwise. The orbits of the solar system's giant planets (Jupiter, Saturn, Uranus and Neptune) are drawn to scale (light gray circles). With a period of ~50 years, the orbit of HR 8799e will be rapidly constrained by future observations; at our current measurement accuracy it will be possible to measure orbital curvature after only 2 years.
Mass ~ 8 MJup
1SIMBAD lists this as an A5 V star, but it is a g Dor variable which have spectral types F0-F2. Tautenburg spectra confirm that it is F-type
Finds planets at large orbital radii. This fills an important region of the parameter space inaccessible with other methods.
Can get spectroscopy of the planet directly
Can Planets around hot stars as well
Seeing is believing!
Only works for nearby stars
Planet mass relies on evolutionary tracks that are model dependent – mass uncertain!
Orbital parameters poorly known (wait a long time!)
Only massive and young planets detected so far
Only planets far from the star have been detected
Smaller, close in planets will require space missions or extemely large telescopes (30m)