t done

Некоторые вопросы поиска и
формирования планетных
систем
С. И. Ипатов
AESS, Катар; ИКИ, Москва
SIMULATOR FOR MICROLENS PLANET SURVEYS
Модель яркости звездного неба и алгоритм
оптимального выбора целей для
наблюдений при поиске экзопланет
методом микролинзирования.
С. И. Ипатов
• На основе данных наблюдений, полученных в 2011 с помощью
четырех телескопов, использующихся для поиска планет методом
микролинзирования, построена модель яркости звездного неба.
Эта модель является частью алгоритма оптимального выбора
целей для наблюдений при поиске экзопланет методом
микролинзирования. Алгоритм позволяет определять какие цели
доступны для наблюдений в различное время и какие цели
следует выбирать для того, чтобы максимизировать вероятность
обнаружения экзопланет.
An older version of a presentation on this item can be found on
http://star-www.st-and.ac.uk/~si8/skybrightnessiau.ppt
---- Abstract
We summarize the status of a computer simulator for microlens planet
surveys. The simulator generates synthetic light curves of microlensing
events observed with specified networks of telescopes over specified
periods of time. The main purpose is to assess the impact on planet
detection capabilities of different observing strategies, and different
telescope resources, and to quantify the planet detection efficiency of
our actual observing network, so that we can use the observations to
constrain planet abundance distributions.
At this stage we have developed models for sky brightness and seeing,
calibrated by fitting to data from the OGLE survey and RoboNet
observations in 2011. Time intervals during which events are observable
are identified by accounting for positions of the Sun, the Moon and
other restrictions on telescope pointing. Simulated observations are then
generated for an algorithm that adjusts target priorities in real time with
the aim of maximizing planet detection zone area summed over all the
available events.
3
Studying planets by microlensing
•
•
•
•
•
•
There is no single technique
known that can yield the
complete planet demographics.
Microlensing is unique in its
sensitivity to wider-orbit (i.e.
cool) planetary-mass bodies
1) down to the mass of the
Moon, already with groundbased observations,
2) in orbit around distant stars,
even in neighbouring galaxies,
3) in orbit around faint or dark
stars or remnants, such as
brown dwarfs, white dwarfs,
neutron stars, or black holes,
4) not bound at all. It thereby
allows to explore a yet
enigmatic region in mass
separation space, where even a
small amount of data has the
potential to make a large
impact.
4
If the source crosses a caustic, the deviations from a standard event can
be large even for low mass planets. These deviations allow us to infer
the existence and determine the mass and separation of the planet
around the lens. Deviations typically last a few hours or a few days.
Because the signal is strongest when the event itself is strongest, highmagnification events are the most promising candidates for detailed
study. 2009 Gliese 581 e is an exoplanet with 1.9 Earth masses.
Styding planets by microlensing
The 15% blip lasting about 24 hrs that revealed 5-Earth-mass planet OGLE-2005-BLG390 impressively demonstrated the sensitivity of ongoing microlensing efforts to
Super-Earths. Had an Earth-mass planet been in the same spot, it would have been
detectable from a 3% signal lasting 12 hrs. The detection of less massive planets
requires photometry at the few per cent level on Galactic bulge main-sequence
stars, which, given the crowding levels, becomes possible with images of angular
resolution below about 0.4″.
6
• Detection zone
• Based on the approach presented in [3], at
each time step for different events we
calculate the detection zone area and the
probability of detection of an exoplanet. The
event with a maximum probability at a time
step is chosen for observations.
• We define the ‘detection zone’ (зона
обнаружения) as the region on the lens plane
(x,y) where the light curve (кривая блеска)
anomaly δ(t,x,y,q) is large enough to be
detected by the observations (q is the ratio of
the planet to that of the star).
[3] Horne K., Snodgrass C., Tsapras Y.,
MNRAS, 2009, v. 396, 2087-2102
Detection zones on the lens plane indicate the
regions where a planet with mass ratio
q=m/M=10-3 is detected with Δχ2>25. The
light curve A(t) has maximum magnification
Ao=5, and the accuracy of the measurements is
σ=(5/A1/2) per cent.
7
Maximising planet detection zone area
The photometric S/N (signal to noise) ratio and hence the area w of an isolated
planet detection zone scales as the square root of the exposure time :
S/N = (Δt /τ) 1/2 , w = g Δt 1/2 .
Here τ is the exposure time required to reach S/N=1. The 'goodness' gi of an
available target depends on the target's brightness and magnification, the
telescope and detector characteristics, and observing conditions (airmass, sky
brightness, seeing).
The simulator evaluates 'goodness' of available targets in real time, and observes the
one offering the greatest increase in w with exposure time. Moves to a new target occur
when the increase in w for the new target is better than the current target, accounting
for the slew time required to move to the new target.
As the CCD camera takes a finite time tread to read out, and the telescope takes a
finite time tslew to slew from one target and settle into position on the next, the ontarget exposure time accumulated during an observation time t is Δt=t- tslew –n tread
(tslew ~ 1-3 min, tread ~10-20 s).
At a time step Δt the detection area of i-th event increases by gi[(Δt+tdone) 1/2 - tdone1/2 ],
where tdone is an exposure time already has been done. For a new target, the area is gi
(Δt-tslew) 1/2 . See [3] for details.
[3] Horne K., Snodgrass C., Tsapras Y., MNRAS, 2009, v. 396, 2087-2102.
8
Example of comparison of gi[(Δt+tdone) 1/2 - tdone1/2 ] for a choice of the best event to be
observed (OGLE observations of 10 events: 110251 – 110260) at a time step of 200 s
and tslew=100 s. All but one of the targets require slew time before the exposure can
begin.
9
Target observability
•The observability of a target is limited by its own position on the sky,
as well as that of the Sun and the Moon, and telescopes moreover have
pointing restrictions. Taking the LT (from http://telescope.livjm.ac.uk/)
as example, we particularly require not to make observations at:
•Air mass (≈1/cos[zenith angle of a target; зенитное расстояние]) > 3
or Cos (zenith of the Sun) < sin (-8.8o) or
•Altitude of a target (высота цели): alt<altmin=25o or alt>altmax=87o
or Hour angle: ha<hamin or ha>hamax. For LT there are no limits on
ha: hamin=-12 h and hamax=12 h.
•
Telescopes considered:
•1.3m OGLE - The Optical Gravitational Lensing Experiment - Las
Campanas, Chile.
• 2m FTS - Faulkes Telescope South - Siding Springs, Australia.
• 2m FTN - Faulkes Telescope North - Haleakela, Hawaii.
• 2m LT - Liverpool Telescope - La Palma, Canary Islands.
•
10
•Observations analyzed for construction of sky model:
•For studies of sky brightness for FTS, FTN, and LT, we considered
those events observed in 2011 for which .dat files are greater than 1 kbt:
FTS - 39 events; FTN - 19 events, LT – 20 events. For OGLE we
considered 20 events (110251-110270). The observations were infrared.
The used sky model was based mainly on
K. Krisciunas & B. Schaefer, 1991, PASP, v. 103, 1033-1039.
•Calculations of vskyzen (яркости звездного неба в
зените) and the coefficients (k1 and ko) presented in the tables
and on the plots were based on χ2 optimization of the straight line fit
(y=k1·x+ko, χ2=∑[(yi-k1·xi-ko)/σi]2, σi2 is variance - дисперсия).
The value of vskyzen (sky brightness at zenith) was chosen in such a way
that the sum of squares of differences between observational and model
sky brightness magnitudes (разности между наблюдаемыми и
модельными звездными величинами яркости неба) were minimum in
the case when the Moon is below the horizon.
12
Dependences of seeing on air mass and values of sky
brightness at zenith obtained based on analysis of
observations
Values of sky brightness at zenith (I magnitude per square arcsec)
for an extinction coefficient extmag=0.05 (for extmag equal to 0 and 0.1,
values of vskyzen differed by less than 0.3 %):
Telescope
FTS
FTN
LT
OGLE
vskyzen
20.07
19.87
20.74
19.99
Seeing (FWHM in arcsec) vs airmass (χ2 optimization):
seeing=ko+k1×(airmass-1). Seeing is the blurring effects of air turbulence in the
atmosphere (угловой диаметр кружка, в виде которого изображение звезды
предстает в телескопе; эффект расплывчатости изображения из-за
турбулентности в атмосфере). σ– среднеквадратичное отклонение
Telescope
ko
k1
σ - sigma
FTS
1.33
0.52
0.37
FTN
0.68
0.21
0.21
LT
1.35
0.42
0.50
OGLE
1.33
0.29
0.25
13
Seeing vs. air mass.
Seeing (in arcsec) vs. air mass. FTS observations of 39 events. A thick straight line is
based on χ2 optimization (y=a+b(x-1), a=1.334, b=0.519). Thinner straight lines
differ from this line by +/- Ϭ (Ϭ=0.367). Non-straight lines show mean and median
values (the line for the mean value is thicker).
14
)
Sky brightness (mag) (звездная величина яркости неба) vs. air mass. Different points are for
OGLE observations of 20 different events (110251 – 110270) for the Moon below the horizon
and solar elevation < -18o. The lines are for the χ2 optimisation with different ko (different
values for different events) and the same k1. The most solid line is for the model for which ko is
the same for all events.
15
The difference in sky brightness near different events.
Coefficients for sky brightness=bo+b1×(airmass-1).
One value of b1; values of bo are different for different events.
The range of boi for Moon below the horizon and solar elevation < -18o:
• min
max max-min telescope
•19.49 20.41
0.92
FTS
•19.05 20.15
1.10
FTN
•19.89 20.60
0.71
LT
•19.64 20.35
0.70
OGLE
The values of max-min were about 0.7-1.1 mag. The difference max-min characterizes the
difference in sky brightness due to surrounding stars near different events.
The range of boi for FTS for different positions of the Moon and the Sun:
min
max
max-min data considered
• 18.2
20.2
2.0
- all observations
• 19.3
20.4
1.1
- moon below the horizon
• 19.5
20.4
0.9
- moon below and solar elevation < -18o
The upper limit (less bright observations) in the above table does not vary much; the
difference in the lower limit (more bright sky) is greater and is up to 1.5 mag. When
the Moon is below the horizon and solar elevation <-18o , then σ is smaller than that
for all observations by a factor of 3 (0.11 instead of 0.36). The data of the table show
the influence of positions of the Moon and the Sun on a typical sky brightness near
an event.
16
Residuals of sky brightness
Most of residuals (разности) (observations minus χ2
optimization which is different for different events) of sky
brightness are in a small range (-0.4 to 0.4 mag) even for all
Moon and Sun positions; for the Moon below the horizon
there are many of values in the range [-0.2, 0.2]; greater
values of residuals are for a small number of observations.
The range of sky brightness residuals for the Moon below
the horizon and solar elevation <-18o (for example, [-0.42,
0.87] for FTS) is smaller by a factor of several than for all
positions of the Moon and Sun.
For considered observations, there was no bright sky (i.e.
the lower limit of residuals was >-1 mag) only in the case
when both the Moon was below the horizon and the solar
altitude was <-18o.
17
Sky brightness residuals (mag) vs. air mass for the model with different ko for FTS
observations of 39 events. Left plot is for all positions of the Moon and the Sun. Right
plot is for the Moon below the horizon and solar elevation < - 18o.
18
Sky brightness residuals vs. solar elevation
Analysis of the plots shows that the influence of solar elevation (высоты солнца) on
sky brightness began to play a role at solar elevation > -14o, and was considerable at
solar elevation >-7o. For example, if we consider only observations with the Moon
below the horizon, then for FTS: sbr >-0.4 mag at se<-14o, sbr>-1 at se<-8o, sbr can be
up to -3 mag at se in the range (-8o,-7o), where se is the value of solar elevation, and sbr
is the value of sky brightness residual (in mag).
Sky brightness residuals (in mag.) vs. solar elevation for FTS observations of 39 events.
More dense signs are for the Moon below the horizon.
19
Time intervals when it is better observe events
Time intervals for events selected for observations with OGLE. Considered events: 110250110400 (numbered from 1 to 151). 0 event corresponds to ‘no observations’. Initial Julian
time=2455728.5 (June 15, 2011).
20
Light curves
Light curves for events selected for observations with OGLE. Considered events:
110250-110400. Initial Julian time=2455728.5 (June 15, 2011).
21
CONCLUSIONS
At this stage we have developed models for sky brightness and
seeing, calibrated by fitting to data from the OGLE survey and
RoboNet observations in 2011. Time intervals during which events are
observable are identified by accounting for positions of the Sun, the
Moon and other restrictions on telescope pointing. Simulated
observations are then generated for an algorithm that adjusts target
priorities in real time with the aim of maximising planet detection
zone area summed over all the available events.
•
•
•
•
•
REFERENCES
[1] M. Dominik, 2010, Gen. Relat. Gravit. 42, 2075
[2] Y. Tsapras, R. Street, K. Horne, et al., 2009, AN 330, 4
[3] K. Horne, C. Snodgrass, Y. Tsapras, 2009, MNRAS 396, 2087
[4] K. Krisciunas & B. Schaefer,1991, PASP, 103, 1033
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