1 Near-Earth objects – a threat for Earth? Or: NEOs for engineers and physicists Lecture 2 – From observations to measurements Dr. D. Koschny (ESA) Prof. Dr. E. Igenbergs (LRT) Image: ESA

2 2 Outline

3 Survey programmes 3/57 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

4 Survey programmes Panoramic Survey Telescope & Rapid Response System m telescope with 3 deg x 3 deg field of view

5 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 6

7 Survey programmes - 4 TOTAS = Teide Observatory Tenerife Asteroid Survey Only a few hours every month since 2010 – ca 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

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) Mt. Wendelstein Observatory Catalina Sky Survey F51- Pan-STARRS 1, Haleakala 8

9 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?

10 Modelling the detection system – real life Sun Asteroid Telescope Camera

11 Modelling the detection system - Abstract Sun Asteroid Telescope Camera Abstract model

12 Modelling the detection system - Parameters Sun Asteroid Telescope Camera Emitted light – 1362 (*) 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(  ) (*) Wild 2013 Effects of the atmosphere -Transparency -Seeing

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14 Betelgeuze – mag Alnitak – 1.7 mag Rigel – 0.1 mag

15 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 F 0 is defined as the flux density of magnitude 0 Vega (Alpha Lyrae) is the reference Sun: M v = mag; M R = mag and F Sun = 1362 W/m 2 (for all wavelengths)

16 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 Allows the conversion from flux density to number of photons

Brightness of the asteroid The flux density (= irradiance) reduces with the square of the distance. The 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, the distance asteroid-Earth being r ast, Earth, and the cross- sectional area S of the asteroid, the flux density at the Earth can be computed with: Assume a simple sphere, homogeneous (Lambertian) scatterer: 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 21 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 Typical f-ratios: old telescopes: 1/10 Newer: 1/4 Very ‘fast’: 1/2 Do larger telescopes have larger or smaller field of view?

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 22

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 WHY?

The detector - 3 Signal-to-Noise ratio: Signal is a function of input flux and detector properties: Assume an ‘average wavelength’: 24

Typical values for TOTAS 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 ~21.0 mag ‘Deepest’ surveys go to 22.5 mag 25

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 30

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 = 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 DN bias ~ 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; p px = 40 % of the photons fall on the center pixel. The telescope obstruction is 10 % of the area of the main mirror. 31 (*) SNR = Signal-to-Noise Ratio

Necessary formulae/constants 32 f (  ) = ½ (1 + cos (  )) h = Js, c = m/s F sun, Earth = 1362 W/m 2 M sun = mag

33 Steps (a) Compute the flux density in W/m 2 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 35

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