Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes
The report describes a new effective technique of atmospheric image motion suppression for observations with large ground-based one-aperture telescopes. The method is based on the use of an enhanced symmetrization of star reference fields. Another (optional) element of the technique is a special apo...
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Головна астрономічна обсерваторія НАН України
2005
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| Цитувати: | Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes / P. Lazorenko // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 537-540. — Бібліогр.: 1 назв. — англ. |
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irk-123456789-797172015-04-04T03:02:43Z Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes Lazorenko, P. MS6: New Trends, Research Directions, and Perspective Programs in the Field of Astronomy and Astrophysics The report describes a new effective technique of atmospheric image motion suppression for observations with large ground-based one-aperture telescopes. The method is based on the use of an enhanced symmetrization of star reference fields. Another (optional) element of the technique is a special apodization of the telescope entrance pupil that is especially effective for extremely large (D > 30 m) apertures. Numerical simulations made for a 10 m telescope show that both atmospheric image motion and photon noise of the star images with a 10 min exposure can be reduced to less than 10 microarcsec. Evaluations refer to the Cn² vertical profile, which is typical for the Chilean astronomical sites, a moderate FWHM = 0.4" and star densities at galactic coordinates l = 0°, b = 20°. For a 100 m telescope, the precision is equal to 0.2 microarcsec/10 min for regions of high star density and drops to 1 microarcsec/10 min at the Galactic Pole. For the 10 m telescope, which measures astrometric reflex motion of stars with an accuracy of 10 microarcsec, a detection limit for Saturn- and Jupiter-sized planets is about 0.5–1 kpc. Application of very high precision astrometry is especially useful for searching extrasolar planets around the Pre-Main-Sequence, early Main-Sequence, and low-mass stars whose investigations with the aid of the radial velocity technique is difficult. 2005 Article Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes / P. Lazorenko // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 537-540. — Бібліогр.: 1 назв. — англ. 0233-7665 http://dspace.nbuv.gov.ua/handle/123456789/79717 en Кинематика и физика небесных тел Головна астрономічна обсерваторія НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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MS6: New Trends, Research Directions, and Perspective Programs in the Field of Astronomy and Astrophysics MS6: New Trends, Research Directions, and Perspective Programs in the Field of Astronomy and Astrophysics |
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MS6: New Trends, Research Directions, and Perspective Programs in the Field of Astronomy and Astrophysics MS6: New Trends, Research Directions, and Perspective Programs in the Field of Astronomy and Astrophysics Lazorenko, P. Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes Кинематика и физика небесных тел |
| description |
The report describes a new effective technique of atmospheric image motion suppression for observations with large ground-based one-aperture telescopes. The method is based on the use of an enhanced symmetrization of star reference fields. Another (optional) element of the technique is a special apodization of the telescope entrance pupil that is especially effective for extremely large (D > 30 m) apertures. Numerical simulations made for a 10 m telescope show that both atmospheric image motion and photon noise of the star images with a 10 min exposure can be reduced to less than 10 microarcsec. Evaluations refer to the Cn² vertical profile, which is typical for the Chilean astronomical sites, a moderate FWHM = 0.4" and star densities at galactic coordinates l = 0°, b = 20°. For a 100 m telescope, the precision is equal to 0.2 microarcsec/10 min for regions of high star density and drops to 1 microarcsec/10 min at the Galactic Pole. For the 10 m telescope, which measures astrometric reflex motion of stars with an accuracy of 10 microarcsec, a detection limit for Saturn- and Jupiter-sized planets is about 0.5–1 kpc. Application of very high precision astrometry is especially useful for searching extrasolar planets around the Pre-Main-Sequence, early Main-Sequence, and low-mass stars whose investigations with the aid of the radial velocity technique is difficult. |
| format |
Article |
| author |
Lazorenko, P. |
| author_facet |
Lazorenko, P. |
| author_sort |
Lazorenko, P. |
| title |
Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes |
| title_short |
Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes |
| title_full |
Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes |
| title_fullStr |
Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes |
| title_full_unstemmed |
Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes |
| title_sort |
atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes |
| publisher |
Головна астрономічна обсерваторія НАН України |
| publishDate |
2005 |
| topic_facet |
MS6: New Trends, Research Directions, and Perspective Programs in the Field of Astronomy and Astrophysics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/79717 |
| citation_txt |
Atmospheric limitations to astrometric detection of extra-solar planets with very large telescopes / P. Lazorenko // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 537-540. — Бібліогр.: 1 назв. — англ. |
| series |
Кинематика и физика небесных тел |
| work_keys_str_mv |
AT lazorenkop atmosphericlimitationstoastrometricdetectionofextrasolarplanetswithverylargetelescopes |
| first_indexed |
2025-07-06T03:43:27Z |
| last_indexed |
2025-07-06T03:43:27Z |
| _version_ |
1836867553469661184 |
| fulltext |
ATMOSPHERIC LIMITATIONS TO ASTROMETRIC DETECTION
OF EXTRA-SOLAR PLANETS WITH VERY LARGE TELESCOPES
P. Lazorenko
Main Astronomical Observatory, NAS of Ukraine
27 Akademika Zabolotnoho Str., 03680 Kyiv, Ukraine
e-mail: laz@mao.kiev.ua
The report describes a new effective technique of atmospheric image motion suppression for ob-
servations with large ground-based one-aperture telescopes. The method is based on the use of
an enhanced symmetrization of star reference fields. Another (optional) element of the technique
is a special apodization of the telescope entrance pupil that is especially effective for extremely
large (D > 30 m) apertures. Numerical simulations made for a 10 m telescope show that both
atmospheric image motion and photon noise of the star images with a 10 min exposure can be
reduced to less than 10 microarcsec. Evaluations refer to the C2
n vertical profile, which is typical
for the Chilean astronomical sites, a moderate FWHM = 0.4′′ and star densities at galactic coor-
dinates l = 0◦, b = 20◦. For a 100 m telescope, the precision is equal to 0.2 microarcsec/10 min for
regions of high star density and drops to 1 microarcsec/10 min at the Galactic Pole. For the 10 m
telescope, which measures astrometric reflex motion of stars with an accuracy of 10 microarcsec,
a detection limit for Saturn- and Jupiter-sized planets is about 0.5–1 kpc. Application of very high
precision astrometry is especially useful for searching extrasolar planets around the Pre-Main-
Sequence, early Main-Sequence, and low-mass stars whose investigations with the aid of the radial
velocity technique is difficult.
INTRODUCTION
The list of detected planets orbiting solar type stars contains now more than a hundred of objects, and the num-
ber increases very rapidly. Since the discovery of these planets was performed by measuring fluctuations of star’s
radial velocity, masses obtained indicate only the lower limit which depends on the inclination of the orbit that
is unknown. A shortcoming of the present technique based on reflex velocity measurements is that it can not
be applied to stars with a deficit of absorption lines necessary to determine radial velocities. It is very sensitive
to close massive planet systems (independent upon the distance) but does not provide good data for systems
with a larger star–planet separation.
Astrometric method, on the contrary, is very useful in order to obtain complementary characteristics of
the known planet systems; it may be applied to study systems with a comparatively large star to planet
separation. The precision of the modern ground-based optical astrometry, however, is insufficient and limited to
about � 1 mas/1 hr. This error set is caused by various effects, the most important of which is the atmospheric
image motion. This limitation is not fundamental and caused by the present technique of observations. I suggest
a new unconventional technique of differential astrometric observations that offers a substantial improvement in
the accuracy (a few decades effect in respect to the variance) by means of an enhanced filtration of atmospheric
image motion spectrum. A new approach to the narrow-field astrometry makes it to be quite a powerful tool
for investigations in different fields of astronomy, in particular, for studies of exoplanet systems. A concept of
the method that allows one to reach microarcsecond accuracies by observations with ground-based very large
telescopes, is described in brief below.
THE CONCEPT
An enhanced attenuation of an image motion spectrum is achieved by introducing two principal modifications
to the classic method of differential measurements. The first is some special apodizing mask (light transmission
modulation) applied to the telescope entrance pupil
P (r) = (1 − 4r2/D2)(ν−3)/2, (1)
where D is diameter of the telescope and ν ≥ 3 is an odd integer. In the frequency domain, such a change
causes strong suppression of high-frequency fluctuations of the random phase distortions and corresponds to
c© P. Lazorenko, 2004
537
a filter Y (q) whose response at high spatial frequencies q goes as q−ν . Note that normally ν is equal to 3
(no apodization).
Suppression of image motion spectrum at low-frequencies is realized with the second modification, or intro-
duction of a new measured quantity
W = N−1
N∑
i=1
ai(x̄0 − x̄i) (2)
formed as a weighted sum of measured differences of the target x̄0 and i-th reference star cartesian (standard)
coordinate x̄i; N is the number of stars and ai are weights that satisfy a normalizing condition
N∑
i=1
ai = N. (3)
Expression for the y-axis is in the similar form.
Weights ai are found from a system of equations
∑
ai = N,
∑
ai(xi − x0)α(yi − y0)β = 0, α + β = 1 . . . k
2 − 1,
(4)
allowing to eliminate some first low modes of random phase fluctuations. Here k ≤ k(k + 2)/8 is an optional
even integer, α and β are positive integers, and weights ai can be negative.
It can be shown that introduction of the quantity W instead of the normally non-weighted differential
positions is equivalent to a filter Q(q) with a frequency response ∼ qk at short q. For conventional differential
technique k is equal to 2.
1e-012
1e-010
1e-008
1e-006
0.0001
0.01
1 10
Y
(q
)*
Q
(q
)
q, [D-1]
Figure 1. Combined filter Y (q)Q(q) response for the parameters given in the text
The combined filtering effect of the apodization and of introduction quantity W is shown in Fig. 1, where
we compare the product of Y (q)Q(q) for the classic (k = 2, ν = 3, upper curve) and a new (ν = 9, k = 8, lower
curve) methods. The plot is given for a 100 m telescope, 1′ effective angular size of reference field, and a single
turbulent layer at 20 km altitude. In this case, a gain in attenuation of image motion spectrum reaches 105.
Equations (4) are used for reduction of the variance Δ2 of atmospheric image motion. However, the total
error of the measured quantity W also includes the image-centroiding error component σph caused by a Poisson
photon noise in star images. It is minimized by a condition
∑
a2
i /ni = min (5)
that is added to the system of equations (4); ni is number of photons detected from the i-th star.
538
ASTROMETRIC PERFORMANCE OF VERY LARGE GROUND-BASED TELESCOPES
Realization of the milliarcsecond accuracy requires a good elimination of various noise sources related to optical
aberrations, pixelization effects (especially for small images produced by adaptive telescopes), photon noise in
star images, differential chromatic refraction (DCR), etc. In particular, there are very intricate problems caused
by a DCR that stretches the star images into colored strips. The amplitude of the DCR effect depends on zenith
distance, air temperature and pressure, spectral band, and star colours. Thus, two rays with wavelengths of 500
and 600 nm coming from a star at a zenith distance of 30◦ are imaged with a separation of about 180 mas along
the vertical direction. Fortunately, in the proper motion studies, the DCR effect is residual and essentially weak
since star motions are to be found from residuals of differential star positions at two epochs.
Evaluating astrometric performance of very large ground-based telescopes, we restricted the error budget
by two components: the atmospheric image motion and photon noise with variances Δ2 and σ2
ph, respectively.
A contribution from both effects was estimated as a function of the angular field size R for sky star densities
near the Galactic plane and at the Pole. The analysis was restricted to a case of a future extremely large 100 m
telescope and a modern 10 m class telescope. A vertical profile of C2
n(h) was obtained by averaging data from
the three Chilean sites: Cerro Tololo, Cerro Paranal, and San Pedro Martir.
Estimates for a 100 m telescope assume FWHM = 0.1′′ achievable with low-order adaptive optics, and for
a 10 m telescope a quite conservative FWHM = 0.4′′ was adopted. We assumed that observations are obtained
in zenith, in R band, with a CCD quantum efficiency of 0.85, transmission of optics 0.8 and of atmosphere 0.9.
Total light
∑
ni of the star field was estimated using the Galaxy model from [1]. Stars fainter than V = 23 mag
were not considered as giving low light signal. To obtain the more robust results, the expected star number
in each 1 mag bin was rounded (truncated) to a smaller integer. This procedure trimmed the bright end of
stellar magnitudes owing to which very narrow star fields were formed largely by faintest stars. Photon noise
in the target star image was always neglected.
Results of simulations are shown in Fig. 2. Each curve starts at small R (star field radius) where only low
(k = 2 or k = 4) orders can be realized with 1–3 reference stars; right ends of curves correspond to k = 12
where fields contain N ∼ 100–1000 stars (except for a case of a telescope with D = 10 m operating at the Pole).
From Fig. 2 we may conclude that, by a high star density, an enough good accuracy is expected with a field
size R of 0.4–1′; the frame is to be at least R = 2′ wide at polar regions.
0.1
1
10
100
1000
0.1 1
to
ta
l e
rr
o
r,
m
ic
ro
a
rc
se
c
field radius, arcmin
D=100m
D=100m
D=10m
D=10m
Galactic equator
Galactic pole
Figure 2. Total error of differential observations as a function of stellar field radius R for the 10 and 100 m telescopes
by 10 min exposure; solid lines – at the Galactic plane (l = 0◦, b = 20◦); dashed – at the Galactic Pole. Apodization:
ν = k + 1 for a 100 m telescope; no apodization (ν = 3) for a 10 m telescope
539
0.1
1
10
100
1000
10000
1 10 100 1000
p
la
n
e
te
ry
s
ig
n
a
l,
m
ic
ro
a
rc
se
c
distance, pc
D=10 m
D=100 m
Earth
Jupiter
Saturn
Uranus
Neptun
Pluto
Figure 3. Astrometric planetery signal and astrometric accuracy in a 10 min exposure of the telescopes with diameters
of 10 and 100 m at the Galactic plane (lower limits) and at the Pole (upper limit)
With the above assumptions on FWHM, and an optimal field size, the expected error of ground-based
observations with a 10 m telescope (no apodization) varies from 10 to 60 μas in a 10 min exposure depending
on sky star density. For a 100 m telescope, this estimate is 0.2 to 2 μas.
EXTRASOLAR PLANETS’ DETECTION LIMITS
Astrometric method of extrasolar planets detection requires measuring a star reflex motion around the planetary
system mass center. The planetary signal produced in the solar-type star system is shown in Fig. 3 as a function
of distance. The astrometric accuracies for the cases discussed in this report are also shown. The plot shows that
10 m class telescopes are sufficiently precise to perform a search for extrasolar planets. Depending on the sky
star density, the application of a new method of differential measurements will allow one to detect Jupiter-type
planets at 200 to 1000 pc even with a moderate 10 min exposure.
[1] Bahcall J., Soneira R. Models of the Galaxy and the predicted star counts // Astron. and Astrophys. Suppl.
Ser.–1980.–44, N 2.–P. 73–110.
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