Download NEO lecture 02 - Observations of NEOs

Lecture 2 – From observations to
measurements
Prof. Dr. E. Igenbergs (LRT)
Dr. D. Koschny (ESA)
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Image: © David A. Hardy/www.astroart.org'
Near-Earth objects – a threat for Earth?
Or: NEOs for engineers
See also: final report
from the asteroid retrieval mission study run by JPL and
Caltech,
through the Keck Institute for Space Studies. It's available
here:
http://kiss.caltech.edu/study/asteroid/asteroid_final_rep
ort.pdf
News
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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
• Siding Spring, Australia – 50 cm Schmidt
telescope for survey, 1-m telescope for follow-up
(5 nights per month)
• Mt. Lemmon 1.5 m f/2 telescope
4/574
Survey programmes - 2
 Panoramic Survey Telescope & Rapid Response System
 http://pan-starrs.ifa.hawaii.edu/public/
 Several ‘key projects’ – one of them is Populations of
Objects in the Inner Solar System
 Not observing asteroids all the time –
but very successful when it does
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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 1.26” per pixel image scale
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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. 500 new
discoveries, 2 NEOs
 Small field of view => scan 5 x 5 images every 30 min –
results in a field of 4 deg x 4 deg to be covered
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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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The detection system - 1
 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
 How: Telescope network
• Size and number of telescopes versus field of view
• Location of telescopes (North/South – space-based sensors…)
 Follow the system engineering approach
• Collect activities
• Collect options, visualize them, order them
• Set up matrix, evaluate them
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The detection system - 2
 Main parameter options (to be traded-off)
• Automation versus human recognition – cost versus robustness
• 3 or 4 images of the same field – duration versus robustness
• Repeat cycle - duration
• Pointing direction
• Maximum angular velocity – neglect fast objects versus robustness
• Telescope aperture – detection limit
• Field of view – duration versus constraints on aperture
• Exposure time – detection limit versus duration, smearing
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Modelling the detection system
Telescope
Asteroid
Sun
Camera
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Modelling the detection system
Telescope
Asteroid
Sun
Camera
Abstract model
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Modelling the detection system
Albedo p
Phase function f()
Distance to
Earth
Telescope
Distance to
Sun
- Effective Aperture in m2
- Throughput
Asteroid
Sun
Emitted light - 1366 W/m2
Abstract model
with parameters
Camera
- Quantum efficiency
- Noise
=> Signal-to-Noise of a given asteroid
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Brightness of the asteroid - 1
 Apparent magnitude
•
Hipparcos divided star brightnesses in 6 ‘equal’ classes from 1 – 6, ‘1’ being
the brightest stars
•
Response of the eye: non-linear
•
Objects with flux density relations 1:10:100 look like having the same
brightness difference
•
Pogson 1856 defined the magnitude in a mathematical way… noting that
the brightness difference of 1 mag and 6 mag stars is roughly 100 =>
m
Pogson defined the ratio of the brightnesses
of class n and n+1 to be sqrt
(100) ~ 2.512.
•
Let F be the flux density 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
•
Astronomers use Vega (Alpha Lyrae) as the reference
•
Sun: Mv = -26.8 mag; MR = -27.1mag and FSun = 1366 W/m2
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Johnson-Cousins Filter bands
passband in nm
average wavelength in nm
U – ultraviolet
300 – 400
360
B – blue
360 – 550
440
V – visual
480 – 680
550
R – red
530 – 950
700
I – infrared
700 – 1200
880
Name
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Good to know
 Flux in W/m2 is energy per time and area
 Energy of one photon:
EPhot 
hc

Where h = 6.626.10-34 Js, c = 2.998.108 m/s
Brightness of the asteroid - 2
Fast, Earth
Fast

1
pAf ( )
2
2d ast
Assume a simple sphere, homogeneous (Lambertian) scatterer:
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 In magnitudes:
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
f  ratio 
Flux at detector:
fl
d
Diameter of lens
FDetect  Fin  ( A  Aobstr ) 
where FDetect the detected flux, Fin the
incoming flux from the object, A the
surface area of the prime mirror, Aobstr
the area of the obstruction, and  the
throughput.
Sketch of a telescope - incoming flux F in
W/m2, surface area A in m2
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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
100
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  texp  p px  g 
FDetect,
hc / 
QE d
 Assume an ‘average wavelength’:
DN Signal  texp  p px  g 
FDetect
QE
hc / 
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Typical values for TOTAS
 1 m aperture, f/4.4
 CCD camera has four sensors, 2048 x 2048 px2
 Pixel scale 1.2”/px, field-of-view 0.7 deg x 0.7 deg
 For survey: We use 1 min 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
Workshop
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Impact energies
What was the impact energy of the ‘Sudan event’
compared to the Hiroshima bomb?
 The ‘Sudan event’ (2008 TC3) was an elongated object
with <10 m size – assume 5 m x 5 m x 5 m
 Assume an entry velocity of 15 km/s
 Densities of recovered meteorites varied from 2 to 3
g/cm3 – assume 2.5 g/cm3
 Impact energies are often given in ‘kilotons TNT’ or
‘megatons TNT’
• 1 kt TNT = 4.184 * 1012 J
 The ‘little boy’ Hiroshima bomb had an explosive yield of
15 kt TNT
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Sensitivity of ESA’s 1-m telescope
 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 ~ 8000.
For a reliable detection, the SNR of an object should be larger
than 5. Compute the sensitivity of ESA’s telescope, using the
following assumptions for the CCD camera: QE = 20 %; g =
0.9 e-/DN. Assume that all the photons coming from the object
are red at a wavelength of 600 nm. Assume that the telescope
transmits  = 60 % of the photons to the CCD; ppx = 20 % of
the photons fall on the center pixel. The telescope obstruction is
20 % of the size of the main mirror.
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Step 1
 Compute the flux in W/m2 and the apparent magnitude of
a 1000 m object and an albedo of p = 0.05, 1 AU from the
Earth, 2 AU from the Sun.
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Step 2
 With the flux coming from the asteroid, compute the flux
at the sensor
Step 3
 Using the properties of the CCD camera, compute the SNR
for the 1 km asteroid.
 Bonus task: Compute the minimum Digital Number of the
asteroid on the sensor for a Signal-to-Noise ratio of 5.
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