Transcript NEO lecture 02 - Observations of NEOs

Near-Earth objects – a threat for Earth?
Or: NEOs for engineers and physicists
Image: ESA
Lecture 2 – From observations to measurements
Dr. D. Koschny (ESA)
Prof. Dr. E. Igenbergs (LRT)
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Outline
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Survey programmes
 Catalina Sky Survey
• http://www.lpl.arizona.edu/css/
• Mount Bigelow, north of Tuscon, AZ – 68/76 cm f/1.9
Schmidt telescope
• Mt. Lemmon 1.5 m f/2 telescope
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Survey programmes - 2
 Panoramic Survey Telescope & Rapid Response System
 http://pan-starrs.ifa.hawaii.edu/public/
1.8 m telescope with 3 deg x 3 deg field of view
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Survey programmes - 3
 http://scully.cfa.harvard.edu/cgi-bin/skycov.cgiSky
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TOTAS – Teide Observatory Tenerife Asteroid Survey
 1 m aperture, 10 % obstruction
 Focal length 4.4 m
 Camera with 0.65” per pixel image scale, normally used in 2x2
binning mode
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Survey programmes - 4
 TOTAS = Teide Observatory Tenerife Asteroid Survey
 http://vmo.estec.esa.int/totas/
 Only a few hours every month since 2010 – ca. 1500 new
discoveries, 12 NEOs
 Small field of view => scan 5 x 5 images every 20 min – results
in a field of 4 deg x 4 deg to be covered – first we did 3
‘revisits’, now 4
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The observatory code
 The IAU defines so-called observatory codes
 All asteroid observers must have one
 Defines name, longitude, latitude, elevation, contact person
 Examples:
• J04 – Optical Ground Station, ESA (on Tenerife)
• B12 – The Koschny Observatory (in the Netherlands)
• 230 - Mt. Wendelstein Observatory
• 703 - Catalina Sky Survey
• F51- Pan-STARRS 1, Haleakala
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ESA’s survey
 Observing goal of ESA’s SSA-NEO programme:
• Detect all asteroids in dark sky larger than ~40 m at least 3 weeks before closest
encounter to Earth
 Which size/field of view telescope is needed?
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Modelling the detection system – real life
Telescope
Asteroid
Sun
Camera
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Modelling the detection system - Abstract
Telescope
Asteroid
Sun
Camera
Abstract model
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Modelling the detection system - Parameters
Albedo p
Phase function f()
Effects of the atmosphere
- Transparency
- Seeing
Distance to
Earth
Telescope
Distance to
Sun
- Effective Aperture in m2
- Throughput
Asteroid
Sun
Emitted light – 1362(*) W/m2
Camera
Abstract model
with parameters
(*) Wild 2013
- Quantum efficiency
- Noise
=> Signal-to-Noise of a given asteroid
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Betelgeuze – 0.3..0.6 mag
Alnitak – 1.7 mag
Rigel – 0.1 mag
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Brightness of an asteroid
 Apparent magnitude
• Let F be the flux density (energy per time per area) in W/m2, then
 F2
m2  m1  2.5 log 
 F1



• m = ‘magnitude’, brightness class
• F0 is defined as the flux density of magnitude 0
• Vega (Alpha Lyrae) is the reference
• Sun: Mv = -26.8 mag; MR = -27.1 mag and FSun = 1362 W/m2 (for all
wavelengths)
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Johnson-Cousins Filter bands
passband in nm
average wavelength in nm
U – ultraviolet
300 – 400
360
B – blue
360 – 550
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V – visual
480 – 680
550
R – red
530 – 950
700
I – infrared
700 – 1200
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Name
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Good to know
 Flux density in W/m2 is energy per time and area
 Energy of one photon:
E Phot 
hc

Where h = 6.626.10-34 Js,
c = 2.998.108 m/s
Allows the conversion from flux density to number of photons
Brightness of the asteroid - 2
The flux density (= irradiance) reduces with the square of the distance. The flux density at the
asteroid can be computed with
Fast
FEarth
 1au 

 
 rast 
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Where rast the distance between asteroid and Sun in au.
With the albedo p of the asteroid, the distance asteroid-Earth being rast, Earth, and the crosssectional area S of the asteroid, the flux density at the Earth can be computed with:
Fast , Earth
Fast

1
4r
2
ast , Earth
pSf ( )
Assume a simple sphere, homogeneous (Lambertian) scatterer:
f () = ½ (1 + cos ())
(i.e.: at 90 deg, half of the object is illuminated)
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 In magnitudes:
mast  mSun
 Fast , Earth
 2.5 log
 FSun , Earth




Absolute magnitude versus size
 Absolute magnitude = magnitude of the asteroid at 1 AU from
the Sun, seen from a distance of 1 AU, at a phase angle (angle
Sun – asteroid – observer) of 0 degrees
 Assumption: Albedo is 0.05
Abs. magnitude
Size
14.0
9400 m
16.0
3700 m
18.0
1500 m
20.0
590 m
22.0
240 m
24.0
95 m
26.0
37 m
28.0
15 m
30.0
6m
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The telescope
Definition of the f-ratio:
Focal length
fr =
fl
d
Diameter of lens
Flux at detector:
FDetect  Fin  ( A  Aobstr ) 
where FDetect the detected energy per time, Fin the
incoming flux density from the object, A the
surface area of the prime mirror, Aobstr the area
of the obstruction, and  the throughput.
Typical f-ratios: old telescopes: 1/10
Newer: 1/4
Very ‘fast’: 1/2
Do larger telescopes have larger or smaller field of view?
Sketch of a telescope - incoming flux density F in W/m2,
surface area A in m2.The sensor obstructs the main
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mirror with an area Aobstr.
The detector
 CCD = Charge Coupled Device
 Converts photons into e Readout results in data matrix in
computer containing Digital
Numbers
 Quantum efficiency QE
• Percentage of photons which generate an
electron
 Gain g
• e- per Digital Number
 Full well
• Maximum no. of e- in a pixel
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The detector – 2
Star image taken with CCD
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102
98
100
101
100
99
150
223
140
102
100
150
402
803
400
200
98
102
130
220
130
107
102
98
99
120
98
100
100
Not all light goes to center pixel – the
percentage is ppx
Noise:
comes from different sources:
photon noise, dark noise, readout
noise, bias
Digital Number DN
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The detector - 3
 Signal-to-Noise ratio:
SNR  Signal / Noise 
DN signal
DN signal  DN bias  DN dark  DN readout  DN Sky
 Signal is a function of input flux and detector properties:
DN Signal
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= texp × p px ×
g
ò
FDetect, l
QEl d l
hc / l
 Assume an ‘average wavelength’:
1 F
DN Signal » texp × p px × × Detect QE
g hc / l
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Typical values for TOTAS
 1 m aperture, f/4.4
 CCD camera has one sensor with 4096 x 4096 px2
 Pixel scale 1.3”/px when binning 2x2, field-of-view 0.7 deg x
0.7 deg
 For survey: We use 30 sec exposure time
 Reaches ~21.0 mag
 ‘Deepest’ surveys go to 22.5 mag
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Stephan’s Quintett
2 min exposure
Summary
 We have learned how asteroid surveys work
 We know which parameters are important
• Number of telescopes, sensitivity, field of view
• The same sky area is observed three or four times to detect moving objects
• Many trade-offs are necessary to optimize a survey
 We have modelled the complete observation chain
 We can compute the sensitivity of a telescope
 For modelling the complete survey, a simulator is required
Exercise
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Task: Get a feeling for the sensitivity of ESA’s
1-m telescope
 For a reliable detection, the SNR(*) of an object should be larger than
5. Compute the apparent magnitude of an asteroid with 1 km diameter
at a distance of 2 au to the Sun and 1 au from the Earth, with an
albedo p = 0.05. Do you expect that it can be detected with ESA’s OGS
telescope?
 Compute the Signal-to-Noise ratio of this asteroid when using ESA’s
telescope on Tenerife, the OGS (Optical Ground Station). Assume the
following:
• The camera at ESA’s telescope on Tenerife is cooled by liquid nitrogen to temperatures
such that the dark current and its noise contribution can be neglected. The readout is
slow enough so that also its noise contribution can be neglected. The camera is
operated with a bias of DNbias ~ 3000. The typical exposure time at which the camera
is used is 60 s. QE = 80 %; g = 0.9 e-/DN.
• Assume that all the photons coming from the object are read at a wavelength of
600 nm.
• Assume that the telescope transmits  = 60 % of the photons to the CCD; ppx = 40 %
of the photons fall on the center pixel. The telescope obstruction is 10 % of the area of
the main mirror.
(*) SNR = Signal-to-Noise Ratio
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Necessary formulae/constants
F
m2  m1  2.5 log  2
 F1



Fast,Earth
1
=
pSf (f )
2
Fast
4p rast,Earth
FDetect  Fin  ( A  Aobstr ) 
SNR  Signal / Noise 
E Phot 
hc

F2 / F1 µ ( r2 / r1 )
-2
f () = ½ (1 + cos ())
1 F
DN Signal » texp × p px × × Detect QE
g hc / l
DN signal
DN signal  DN bias  DN dark  DN readout  DN Sky
h = 6.626.10-34 Js,
c = 2.998.108 m/s
Fsun, Earth = 1362 W/m2
Msun = -27.1 mag
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Steps
(a) Compute the flux density in W/m2 at the asteroid
(b) Compute the flux density from the asteroid at the Earth
(c) With the telescope properties, compute the flux on a pixel on
the detector
(d) Using the properties of the CCD camera and assumptions for
the noise, compute the SNR for the 1 km asteroid.
(e) Bonus task: Compute the minimum Digital Number and
magnitude of an asteroid on the sensor for a Signal-to-Noise
ratio of 5.
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 Additional material
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http://www.iac.ethz.ch/edu/courses/master/
modules/radiation_and_climate_change/do
wnload/Lecture7_2013
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