Download 4.1 Detectability of extrasolar planets

Extrasolar planet detection with extremely large
telescopes
Bruce Macintosh
James Graham
Steve Strom
Travis Barman
1
Executive summary
Direct detection of extrasolar planets will be easily within the reach of dedicated high-contrast
adaptive optics systems on 30-50 m telescopes. These will build on the results of such systems
on 8-m class telescopes such as the Gemini Planet Imager and the VLT Planet Finder. The 8-m
AO systems will carry out the first surveys of the outer regions of other solar systems with
contrasts of 10-7 from 0.2-1 arcsecond, but will only be sensitive to self-luminous planets that
are young and/or massive.
High-contrast AO on extremely large (25-50m) telescopes will have four key science missions.
We have carried out simulations and analysis to compare the reach of 30 and 50-m telescopes for
these science missions:
Mission 1: Broad and systematic studies of the extrasolar planet population in the solar
neighborhood. Both 30-m and 50-m telescopes can begin to image planets in reflected rather
than emitted light, allowing overlap between imaging and Doppler searches, and extending the
statistics of our knowledge of other solar systems into 1 AU scales and sub-Jovian masses.
Integration time for these missions will scale as D2 to D4, so a 50-m telescope could carry out a
survey in less time. The ultimate contrast floor, however, will likely be set by internal
aberrations, whose effect is roughly independent of telescope size; in this situation, the 50-m
telescope would not discover any significant number of planets inaccessible to the 30-m, it
would merely discover a larger sample of similar planets in less time.
Mission 2: Imaging very young planets (0–15 Myr) in the process of forming or migrating.
Probing 5 AU scales in nearby star-forming regions such as Taurus requires an inner working
distance of ~0.03 arcseconds. This represents 3 /D for a 30-m telescope in H band. While
instrument architectures exist that can achieve this, such architectures are technologically
challenging and unproven. A 50-m class telescope could carry out this science mission with a
more straightforward coronagraph design, or use advanced coronagraphs to probe 3 AU scales.
Mission 3: High-SNR studies of planetary atmospheres and their astrophysics. High-SNR
spectra at moderate resolution (100-1000) can probe the properties of planetary atmospheres
including abundances, which will provide crucial information on their formation and history.
Such spectroscopy will often be photon-noise limited. R=100 spectroscopy is straightforward,
but R=1000 for any but the brightest planets would require a a 50-m telescope. However, most
science questions can be answered at R=100, with the possible exception of abundance
determination.
Mission 4: The studies of circumstellar disks ranging from young protoplanetary disks through
debris disks to high-density extrasolar zodiacal debris in inner solar systems. Since disks are
often resolved objects, there is no strong advantage (beyond increase photon SNR) for a 50-m
telescope.
It is important to note that some science missions remain beyond the reach of ground-based
telescopes. For example, for any plausible performance model, even 100-m telescopes will be
incapable of imaging Earthlike planets around a useful sample of target stars.
2
Introduction
In the closing years of the 20th Century humankind began its exploration of the planetary systems
in the solar neighborhood. Precision radial velocity measurements have now yielded the
discovery of over 160 planets. Direct imaging of these planets, as opposed to detection of the
effects of orbital motion on their parent star, is now feasible, and the first young planet in a wide
orbit may have been detected using adaptive optics systems. Gemini and the VLT are building
the first generation of high contrast adaptive optics systems, which deliver planet-imaging
performance at 0.2 – 1 arcsecond separations of the host star. These systems will make the first
surveys of the outer regions of solar systems by detecting the self-luminous radiation of young
planets. This will help illuminate many aspects of exoplanetary systems and their formation,
including whether Jovian planets form predominantly through “top-down” (global gravitational
instability) or “bottom-up” (core accretion) processes. However, the 8-m “extreme” AO systems
have several limitations. First, they cannot see close enough to host stars at high enough contrast
to image mature planets in reflected light. This limits such systems to detecting high-mass
planets orbiting young stars, and precludes detection of Doppler planets with the possible
exception of exotic cases such as Epsilon Eridani.
Second, photon statistics will limit their spectroscopic capability to relatively low resolution
(R~100). Third, since their inner working angle is at best 0.1”, they cannot reach the relatively
distant, young clusters and associations where planets are forming.
This leads to four key science missions for high-contrast AO on extremely large (25-50 m)
telescopes:
1. Broad and systematic studies of the extrasolar planet population in the solar
neighborhood, spanning semimajor axis separations 0.5 < a/AU < 50 and exoplanet mass
0.3 < M/MJ < 12.
2. Imaging very young planets (0–15 Myr) in the process of forming or migrating at > 100
pc distances
3. High-SNR studies of planetary atmospheres and their astrophysics
4. The studies of circumstellar disks ranging from young protoplanetary disks through
debris disks to high-density extrasolar zodiacal debris in inner solar systems. Since this
white paper is focused on studies of planets, this mission will not be discussed in detail.
Debris disks are mostly resolved objects, which limits the advantage of a 50-m telescope.
Figure 1 shows this in a schematic sense. It is important to note that some science missions
remain beyond the reach of ground-based telescopes. For example, for any plausible
performance model, even 100-m telescopes will be incapable of imaging Earthlike planets
around a useful sample of target stars. Cavarroc et al 2006 reach a similar conclusion, estimating
100-hour integration times to detect Earthlike planets.
Figure 1: Schematic representation of planets in the solar neighborhood in H-band contrast/angular
separation space. Two solar-neighborhood populations are shown: a distribution of rocky planets, and a
distribution of Jovian (0.3 – 10 M_Jupiter, 0.01-50 AU) planets based on extrapolations from radial-velocity
surveys. Different colors are used for Jovian planets based on whether reflected starlight or near-IR emission
dominates. An additional population of Jovian protoplanets (3-10 AU) at the distance of Taurus are also
shown in the top left. Overlaid are contrast curves for 1-hour exposures of an H=6 star on an 8, 30, and 50-m
telescope assuming x10 speckle suppression from multiwavelength imaging. 30 and 50-m AO systems
described in Table 1, 8-m AO system is a full simulation of the Gemini Planet Imager.
Generally speaking, a successful science program of planet detection will require large target
samples and hence both moderate limiting magnitudes and integration times of at most a few
hours per target for initial discovery. Science requires statistics – an ExAO system that could
detect Earthlike planets but requires such bright stars that it can only observe ten targets may find
a single extrasolar planet (or may find none, as shown by early high-precision radial velocity
searches), but such an isolated discovery will shed little light on the formation and nature of most
solar systems.
We generated simulated ExAO models through a variety of modeling techniques (see Appendix
1), cross-checked against long-exposure (20-second) wave optics simulations of ExAO on 8-m
telescopes and moderate-exposure (4-second) simulations on 30-m telescopes. The results
presented here primarily use Monte Carlo simulations with multiple independent phase screens
to represent atmospheric, AO measurement, and static noise. Our simulations generally predict
somewhat worse final contrast than simulations by some other groups (e.g. Chelli et al 2005).
This can be attributed primarily to an unrealistically low assumed lifetime for atmospheric
speckles in many other analytic calculations; see Appendix 2 and the attached SPIE paper for
some discussion of this.
Since this White Paper is intended to address the scaling of sensitivity with telescope size rather
than the details of different telescope architectures, we have treated all telescopes as ideal
unobscured circular apertures. Generally speaking, small-scale structures such as inter-segment
gaps can be easily mitigated in coronagraphs and have little effect on contrast; large structures
such as secondary supports are more significant, especially when attempting to achieve inner
working angles <5 /D. We have also ignored wavefront errors in the telescope itself, since most
ExAO architectures can successfully correct these within the systems’ control region, even for
the case of moderate phase discontinuities (Poyneer and Macintosh 2004).
3
Brief overview of ExAO sensitivity
Ultimately, the ability to detect a faint companion next to a bright star is limited by scattered
light. Light can be scattered both the fundamental process of diffraction (even for a perfect
telescope in space) and by wavefront phase errors both internal and external.
Diffraction is in many ways the easiest to control. A wide variety of coronagraphs have been
developed since Lyot’s original paper (Lyot 1939). The can be characterized by their throughput
for off-axis (planetary) sources and their inner working distance (IWD), the smallest angle at
which a planet can be detected. For some coronagraphs (e.g. hard-edged Lyot coronagraphs) this
IWD is an absolute cutoff; for others, performance degrades more smoothly, but for most
architectures performance drops off very rapidly within the IWD. The IWD for a “typical”
coronagraph such as a band-limited Lyot coronagraph (Kuchner and Traub 2002) or an apodizer
(Kasdin et al. 2005 is usually on the order of 3-5 /D, with some trade between IWD and
throughput. Both techniques have been demonstrated to achieve performance suitable for planet
detection in the laboratory (Trauger et al 2004, Evans et al 2005). More complex coronagraphs
such as four-quadrant phase masks (Rouan et al 2000, Riaud et al 2001), optical vortex masks
(Palacios 2005) and phase-induced apodization (Guyon 2004) can have smaller IWD, but these
techniques are generally challenging to implement on obscured apertures and have not yet been
demonstrated at 10-7-10-9 contrast levels . Again, this paper is not intended to trade the
performance of different coronagraphs against each other, so we have used a simple apodization
of an unobscured telescope pupil for our simulations and assume an IWD of ~4 /D. The details
of the coronagraph are primarily important for companions appearing very close to their parent
star, such as very young planets at 100-150 pc (see below.)
Even in the absence of diffraction, light will be scattered into the wings of the PSF by wavefront
errors, both phase and amplitude. (See for example Perrin et al. 2003.) This remains the most
fundamental limit to high-contrast imaging from Earth or space. The interference of wavefront
errors produces a pattern of /D sized speckles, each (in monochromatic light) resembling a
planet – as a result, sensitivity is often limited by “speckle noise” to far worse than the photon
noise (Poisson statistics) limit. (Racine et al 1999). The temporal behavior of these speckles is
particularly important. If they are produced by a suitably random process, in a long-exposure
image they will ultimately smooth out into a uniform background against which planets may be
seen. Speckles due to atmospheric errors such as fitting or servo/timelag error are relatively longlived (~Dtel/v); speckles due to measurement noise in the wavefront sensor are relatively shortlived. The combination of these error sources provide the most fundamental limits to ExAO
sensitivity. In general, in situations where these fundamental external sources dominate, final
contrast at a given angular separation will scale as telescope diameter D2 – larger telescopes
better concentrate the light from the planet against the halo.
If the speckles are produced by a static process, they will persist in even long-exposure images
and ultimately limit sensitivity (Sivaramakrishnan et al 2002) even if they contain a small
fraction of the total scattered light. These quasi-static speckles could be removed through PSF
subtraction if they were truly static, but often evolve on timescales (tens of minutes) comparable
to those needed to acquire PSF stars (Marois et al 2006); as a result, PSF subtraction typically
only attenuates their noise by factors of a few. Using the Earth’s siderial rotation can provide
some improvement (Marois et al 2006) but only at wide enough angles that siderial rotation over
minutes is >/D, which may favor larger telescopes. The exact effects of static wavefront errors
depend on their source, spatial power spectrum, etc., but it is interesting to note that if they are
internal to the AO system or instrument they are somewhat independent of telescope size –
achieving a contrast of 10-10 at 10 /D requires the same sub-nanometer static wavefront errors
irrespective of telescope size (Cavarroc et al 2006, Chelli 2005). As a result, even if the
atmospheric errors could be overcome, achieving TPF-like performance on a ground-based
telescope requires TPF-like residual static errors and hence TPF-like stability and optics quality,
which may be very challenging in an observatory environment. Figure 2 illustrates that
aberrations larger than 1 nm will significantly limit the achievable contrast for a 30-m telescope.
Speckles have different wavelength behavior than planteary companions, so multi-wavelength
imaging techniques (Marois et al 2000, Sparks&Ford 2000) can be used to discriminate speckles
from planets. To some extent, this relaxes the requirements on static and dynamic wavefront
errors but imposes similarly strict requirements on differential chromatic errors between
wavelength channels. This technique depends either on broad spectral differences between
planets and their host stars, or on operation at wide enough radii (>10 /D) that magnification of
the speckle pattern with wavelength is significant. Experimental implementations have not yet
demonstrated the ability to attenuate speckle noise by a factor of a 2-10 (even at moderate
contrast levels), limited by chromatic aberrations (Marois et al. 2005, Biller et al 2004). We
make the simple assumption that this can only reduce speckle noise by a factor of ten.
4
Sensitivity comparisons
Table 1 lists the properties of the system simulated. Contrast is relatively independent of the
subaperture size, which primarily determines the outer working angle /d.
Table 1: Parameters for AO simulation
Parameter
Telescope diameter D
Subaperture size d
AO update rate
Value
30-m and 50-m
20 cm
2000 Hz
WFS
Spatially-filtered IR self-referencing
interferometer at science wavelength
15% including coronagraph
Pupil apodization
Total science transmission
Coronagraph
Atmosphere
r0=14 cm, v_wind=10 m/s (no scintillation)
Given these assumptions, Figure 2 shows the contribution of different components to the
sensitivity of a typical 30-m telescope in a one-hour integration for planet detection and
broadband photometry. Speckle noise dominates at small radii, while photon noise dominates at
large radii.
Figure 2: Contrast for a 3600-second exposure with a 30-m telescope on an H=7 target star. Three curves
show contributions to contrast from speckle noise, photon noise, and 1 nm static wavefront error (with a
power spectrum typical of optical polishing errors.) [# I could replace this with an H=5 case if that’s
interesting.]
4.1
Detectability of extrasolar planets
Figure 3 compares these sensitivities for a 30 and 50-m telescope. Overlaid are the approximate
contrast for Earthlike and Jovian planets at 20 pc distance and 0.2, 1, and 5 AU.
Generally speaking, the 50-m has slightly broader science reach but not fundamentally so; it
could detect the 1 AU Jovian planet out to 20 pc, which is challenging for the 30-m telescope.
Alternatively, it could carry out the same survey in (30/50)^2=36% of the required telescope
time.
Figure 3: 5-sigma 2-hour contrast for 30 and 50-m telescope. Target is a G star at 10 pc. Assumes H band
with multiwavelength imaging/post-processing with speckle noise reduction of x10. Overlaid are Jovian
planets at 0.2, 1, and 5 AU from a star at 10 pc (based on Burrows et al 2004), and Terrestrial planets at 0.2
and 1 AU.
4.2
Spectroscopy of extrasolar planets
Speckle noise is (roughly speaking) independent of spectral resolution or number of available
photons. Hence at higher spectral resolutions, photon noise becomes more significant. Figure 4
shows the detectable contrast (SNR=5 per spectral element) for R=100 spectroscopy on a 30-m
and 50-m telescope, and for R=1000 on a 50-m telescope. A 30-m telescope is capable of R=100
spectroscopy of reflected-light planets, but a 50-m is required for R=1000 spectroscopy in
reasonable integration times. (Note that both telescopes are easily capable of high-resolution
spectroscopy of self-luminous planets with contrasts of 10-7.)
Figure 4: 5-sigma spectroscopic contrast (SNR=5 per spectroscopic element) in a four-hour exposure on a G
star at a distance of 10 pc. Other parameters as in figure above.; Jovian planets are shown at 0.2 and 1 AU.
Model atmospheres show that R=100 is in fact adequate for determining effective temperature
and gravity over a wide range of planet properties; see Figure 5. At R=1000, individual features
begin to be visible that may allow determination of atmospheric abundances in the cooler
(reflected-light) planets Figure 6. The minimum resolution needed for such determination is
uncertain, however, and remains an area for future modeling and simulation.
Figure 5: Left: Differential exoplanet spectra in magnitude, i.e., flux ratios, illustrating gravity sensitive
indicators in synthetic spectra. The reference spectrum has Teff = 300 K and log g = 3.0. Spectra with log g 
{3.5, 4.0, 4.5, and 5.0} are shown. Evidently the strength of the band index [1.5] – [2.2] is a good gravity
indicator. Right: Differential exoplanet spectra illustrating effective temperature indicators in synthetic
spectra. Spectra with Teff  {400 K, 500 K, 600 K, 800 K} are shown. We calculate these spectra using fully
self-consistent models with the PHOENIX atmosphere code (Barman et al. 2001). The spectral resolution is R
= 100.
-R=1000 can do abundances (see figure below)
Figure 6: A spectral sequence at R = 1000 in the J band for Teff  {300 K, 400 K, 500 K, 600 K,
800 K} (running from bottom to top), log g = 3.5, and solar abundances.
4.3
In-situ observations of planet formation
Imaging Planet Formation and Planet-Forming Disks
Planets are easiest to detect when they are young and hot (Figure 7), because they will be bright
at near infrared wavelengths (2.1.2). This would suggest that studying the earliest phases of
planet formation should be straightforward. The cooling tracks (Figure 7) also illustrate an
important aspect regarding the atmospheres at young ages (< 100 Myr): planetary mass objects in
this age range are expected to exhibit T dwarfs spectra. That is, older and more massive brown
dwarfs with comparable atmospheric conditions have already been discovered, studied, and
modeled. As a consequence, we have high-fidelity spectral templates for these objects, which can
be used to recognize and classify young exoplanets with confidence.
The star formation rate in the Milky Way has been roughly constant for the past 10 Gyr and the
luminous phase of planets is brief: a 2 MJ object has L/L > 10-6 for < 30 Myr. Thus only a
fraction of a percent of the stars in the Milky Way are young enough to host newly formed
planets. Table 2 lists about 300 youthful (< 100 Myr) associations within the solar neighborhood
(< 50 pc). To find large numbers of genuinely young (< 10 Myr) stars forces the search for the
newly formed planets to more distant star forming clouds, such as Taurus,  Ophiuchus, or
Upper Sco. The closest of these regions lie at distances of about 150 pc. The most critical
instrumental parameter for this study is thus the inner working angle, as 5 AU at 150 pc
translates to 33 mas. This inner working angle translates to about 3/D at H and 4/D at J,
making these the instrumental requirements.
Table 2: Young stars in local groups and associations.
The approximate number of members refers to the number of stars with R < 13 mag or H<11.
Name
Age (Myr)
Dist. (pc)
Approx. No.
TW Hya
8
30-60
20
 Pic
8
30-60
20
Tuc/Hor
30
30-50
50
Local Assoc.
60
40
150
AB Dor
70
15-50
20
10-100
<100
40
3
130
~100
Debris Disks Stars
Taurus
Figure 7: Theoretical tracks showing the evolution of effective temperature with age for low-mass stars (red),
brown dwarfs and planets (blue). Tracks are labeled in M. Conventionally, planets correspond to masses
less than 12 MJ (0.011 M). Grey areas delineate the approximate temperature ranges for L and T dwarfs.
The tracks warmer than 1500 K are from Chabrier et al. (2000, using the AMES-dusty models of Allard et al.
2001) and the tracks cooler than 1500 K are from Baraffe et al. (2003, using the AMES-cond models of Allard
et al. 2001).
We expect that ExAO on 8- and 10-m class telescopes will detect the first handful of such very
young, very luminous, hot Jupiters, in the nearest regions of recent star formation—the 8 Myrold 2M1207b probably is the prototype for such objects (Chauvin et al 2004). Thus, the goal for
ExAO on ELTs is to increase the sample space from a few candidate stars into the hundreds, so
that a statistically significant sample of planets can emerge. By reaching stellar distances of 150
pc, the potential source list grows to include about ten well known nearby star-formation regions.
Many of these are much younger than the nearby associations of – young enough that planets
may still be in the accretion phase. This will thus provide an order of magnitude increase in
search volume over that attainable in early searches with existing telescopes, with over 100
candidate young stars per star forming region, spanning the whole process of planetary
formation. Near-IR interferometers will have some ability to image such systems, but their
sparse apertures will limit their ability to reconstruct complex high-contrast target environments.
A separation of 5 AU at a distance of 150 pc corresponds to 0.03 arcseconds. This is ~3 /D for a
30-m telescope in H band. Achieving even moderate contrast at these separations requires on an
obscured aperture requires is beyond the reach of classical/semi-classical coronagraphs and
requires advanced concepts such as nulling interferometery (Mennesson et al. 2004), Phaseinduced apodization (Guyon 2004), etc. These concepts, though promising, are unproven and
may be challenging to implement in practice. A 50-m telescope, with a correspondingly smaller
diffraction limit, can image at 0.03 arcsecond scales with a conventional coronagraph, or if
equipped with an advanced coronagraph can probe 3 AU scales in nearby star-forming regions.
Since 3-5 AU is thought to be a particularly crucial region for planet formation, the 50-m
telescope has a strong advantage in this area.
5
Appendix 1: Modeling technique
Calculating the final sensitivity of an ExAO system is complicated, particularly from anything
less than a full end-to-end simulation running for many seconds. Unfortunately such simulations
are computationally prohibitive for extremely large telescopes. We analyzed ELT ExAO
sensitivity using Monte Carlo simulations in which separate phase screens are generated through
Fourier filtering for each error source at timescale set by its individual speckle lifetime (section
#.) This approach is computationally efficient – generating phase screens requires only 1-3
fourier transforms per timestep, and the timesteps are set by the fastest speckle lifetime (~10 ms
for speckles from WFS measurement noise, ~1-2 seconds for atmospheric speckles) rather than
the AO system update rate (0.5 ms.) The speckle lifetimes were separately verified with full AO
simulations of 8-m telescopes (see attached SPIE paper). In previous studies for 8-m telescopes,
this approach has been cross-checked with full AO simulations and shown to predict contrast
within a factor of 2-3.
As shown by Sivaramakrishnan et al. (2002), the high-contrast PSF in the high-Strehl regime can
be written as the sum of a diffraction pattern term, a “pinned speckle” term which also traces the
diffraction pattern, and a PSF halo term. The first two can be suppressed by a coronagraph. The
third term, which dominates the wings ( >3-5 /D) of an ExAO system with an effective
coronagraph, is essentially the power spectrum of the residual phase errors. This provides a
natural way to predict the long-exposure average PSF and final sensitivity to pointlike
companions. Assuming there are n distinct wavefront error sources i and all are uncorrelated,
n
the total PSF intensity (normalized to unity) is given by P( )    i2 I i ( ) where
i
I i ( )   i ( /  )  /  is a the unity-normalized spatial power spectrum of the phase error i
2
2
i
and i is the magnitude of the corresponding phase error in radians. A phase error of spatial
frequency  in cycles per meter (D in cycles per pupil) will scatter light to an angular radius
.
As shown by Sivaramakrishnan et al. 2002, the high-contrast PSF in the high-Strehl regime can
be written as the sum of a diffraction pattern term, a “pinned speckle” term which also traces the
diffraction pattern, and a PSF halo term. The first two can be suppressed by a coronagraph. The
third term, which dominates the wings ( >3-5 /D) of an ExAO system with an effective
coronagraph, is essentially the power spectrum of the residual phase errors. This provides a
natural way to predict the long-exposure average PSF and final sensitivity to pointlike
companions. Assuming there are n distinct wavefront error sources i and all are uncorrelated,
n
the total PSF intensity (normalized to unity) is given by
P( )    i2 I i ( ) where
i
I i ( )   i ( /  )  /  is a the unity-normalized spatial power spectrum of the phase error i
2
2
i
and i is the magnitude of the corresponding phase error in radians. A phase error of spatial
frequency  in cycles per meter (D in cycles per pupil) will scatter light to an angular radius
. This leads to a useful insight: in order to detect planets at radii between 0.2 and 1 arscecond at
H band, we need to control phase errors between ~3 cycles per pupil and ~30 cycles per pupil.
Lower frequency errors will primarily rearrange light under the coronagraph occulting stop
(though the details of how light leaks through the coronagraph are complex for different designs)
while higher frequencies scatter light to large radii. Reducing the errors at mid frequencies
results in a PSF with a “dark hole” (Malbert et al.) in which planets can be detected.
Instantaneously, the PSF is completely broken up into speckles and these speckles are the main
source of noise in an attempt to detect a pointlike object such as a planet. The noise as a function
2
of radius for a single PSF noise source in monochromatic light is given by  i Ii ( ) - the noise is
roughly equal to the intensity. (In broadband light, an additional term appears decreasing the
noise due to the elongation of the speckles; for clarity we will omit this term in this section,
though it has been included in our error budget in section 4.) Over a long integration, multiple
realizations of the speckle pattern will act to smooth the PSF. We express this by assigning each
error source a characteristic speckle decorrelation timescale tdeci; in an integration time t> tdeci,
1/ 2
 tdeci 
the final noise for a single source will be given by  i I i ( )

 t 
2
If multiple error sources are present, Sivaramakrishnan et al (2002) show that each decorrelates
independently, and the total noise in the final image is given by
1/ 2
n
 tdeci 
2
N ( , t )    i I i ( )

 t 
i
This means that error sources with rapid decorrelation, such as the random measurement noise of
the AO system, are much less significant than errors that decorrelate slowly, such as the
atmospheric fitting and bandwidth terms. Errors that do not decorrelate, such as quasi-static
optical errors, are the worst of all; as shown by Sivaramakrishnan et al, in an extremely long
exposure with both random and static errors, the PSF approaches the noise floor given by the
static errors only – the PSF becomes a smooth halo with imprinted on it a speckle pattern
equivalent to that given only by the static errors.
Even with this approach, simulation times are limited to < 1 minute for practical CPUs. In an
ExAO system, the effects of static wavefront errors may only become apparent on timescales of
tens of minutes. We have chosen to use semi-analytic techniques to calculate limits on the
required static wavefront errors, e.g. in Figure 2.
A key difference between our models and those of other groups – e.g. Chelli 2005 – is the
atmospheric speckle lifetime. Many groups assume that the speckle lifetime is short, r0/v (where
r0 is the Fried parameter and v is the windspeed), or even as the AO update rate (~1 ms, Angel et
al 1994). Extensive end-to-end simulations by our group have shown that this is not the case for
speckles due to atmospheric effects such as servo lag; the atmospheric speckle lifetime is set by
the telescope clearing time ~0.5 D/v. (See attached SPIE paper, Macintosh et al 2005, for some
of these results.) These long-lived atmospheric speckles can severely limit final contrast, even if
partially suppressed by multiwavelength imaging. Of course, quasi-static effects can impose
even more severe limitations on final contrast.
6
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