1 Optical observations of asteroids – and the same for space debris… Dr. D. Koschny European Space Agency Chair of Astronautics, TU Munich Stardust school Feb 2015, Belgrade Image: ESA

2 Survey programmes 2/57 Catalina Sky Survey Mount Bigelow, north of Tuscon, AZ – 68/76 cm f/1.9 Schmidt telescope Mt. Lemmon 1.5 m f/2 telescope

3 Survey programmes Panoramic Survey Telescope & Rapid Response System

4 Survey programmes - 3

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 5

6 Modelling the detection system Sun Asteroid Telescope Camera Emitted light W/m 2 Distance to Sun Distance to Earth - Effective Aperture in m 2 - Throughput - Quantum efficiency - Noise Abstract model with parameters => Signal-to-Noise of a given asteroid Albedo p Phase function f(  )

7

8 Betelgeuze – mag Alnitak – 1.7 mag Rigel – 0.1 mag

9

10 Brightness of an asteroid Apparent magnitude Let F be the flux density (energy per time per area) in W/m 2, then m = ‘magnitude’, brightness class Vega (Alpha Lyrae) is the reference, F 0 is defined as the flux density of magnitude 0 Sun: M v = mag; M R = mag and F sun, Earth = (1366 W/m 2 )

11 Johnson-Cousins Filter bands Name passband in nmaverage wavelength in nm U – ultraviolet300 – B – blue360 – V – visual480 – R – red530 – I – infrared700 –

Good to know Flux density in W/m 2 is energy per time and area Energy of one photon: Where h = Js, c = m/s

Good to know Flux density in W/m 2 is energy per time and area Energy of one photon: Where h = Js, c = m/s  Flux density can be seen as number of photons per time and area

Brightness of the asteroid The flux density reduces with the square of the distance. The solar flux density at the asteroid can be computed with Where r ast the distance between asteroid and Sun in AU. With the albedo p of the asteroid, surface area S, distance asteroid-Earth r ast, Earth, the flux at the Earth can be computed with: Assume a simple sphere, homogeneous (Lambertian) scatterer (real formula depends on surface properties, shape… More complicated!): f (  ) = ½ (1 + cos (  )) (i.e.: at 90 deg, half of the object is illuminated)

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 Abs. magnitudeSize m m m m m m m m m

The telescope 17 where F Detect the detected energy per time, F in the incoming flux density from the object, A the surface area of the prime mirror, A obstr the area of the obstruction, and  the throughput. Definition of the f-ratio: Flux at detector: Sketch of a telescope - incoming flux density F in W/m 2, surface area A in m 2.The sensor obstructs the main mirror with an area A obstr. Focal length Diameter of lens

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 nm 1000 nm Quantum Efficiency in %

The detector – 2 Star image taken with CCD Digital Number DN Noise: comes from different sources: photon noise, dark noise, readout noise, bias Not all light goes to center pixel – the percentage is p px

The detector - 3 Signal is a function of input flux and detector properties: Assume an ‘average wavelength’: Signal-to-Noise ratio: 20

Typical values for OGS 1 m aperture, f/4.4 CCD camera has one sensor with 4096 x 4096 px 2 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 ~21.5 mag ‘Deepest’ surveys go to 22.5 mag Faintest NEO observed by us: 26.3 mag (with Large Binocular Telescope)

Stephan’s Quintett 2 min exposure

Summary We have modelled the complete observation chain We can compute the brightness of an asteroid at a given geometry We can compute the sensitivity of a telescope

Exercise 26

Magnitude of an asteroid (1) How bright will a 40 m diameter asteroid be when at 15 Mio km distance? Use simplifications wherever you can! Which parameters do you need to guess? (2) Which exposure time would you need using ESA’s Optical Ground Station to get a Signal-to- Noise ratio of at least 5 for this object? Instead of turning equations around and having to solve a quadratic equation – compute the SNR for a 21 mag object for 10 s, 30 s, 60 s 27

Parameters of the Optical Ground Station 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 DN bias ~ The typical exposure time at which the camera is used is 60 s. The telescope uses a custom-built CCD camera by Zeiss with the following properties: 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; p px = 40 % of the photons fall on the center pixel. The telescope obstruction is 10 % of the area of the main mirror. 28

Relevant formulae/constants 29 f (  ) = ½ (1 + cos (  )) h = Js, c = m/s F sun, Earth = 1366 W/m 2 M sun = mag