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Chapter 6 Telescopes & Instrumentation

Revised 2007

ERAU Astronomical Observatory  Nick Devereux 2006

Meade 12.375 inch Schmidt Cassegrain Reflecting Telescope

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Different Types of Reflecting Telescopes

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Millenium II German Equatorial Mount

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SBIG ST 2000XM CCD Camera

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CCD

CCD Specifications

Kodak KAI-2020M + TI TC-237H Pixel Array Total Pixels Pixel Size Full Well Capacity (Unbinned) Full Well Capacity (Binned) Typical Dark Current 1600 x 1200 pixels, 11.8 x 8.9 mm 1.92 million 7.4 x 7.4 microns ~45,000 e ~90,000 e < 0.1e¯/pixel/sec at 0° C

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Typical Read Noise < 8 e- RMS

SSP-5 Photoelectric Photometer

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Functions

Telescope – Light bucket Mount – Drives the telescope at the sidereal rate CCD camera – Imaging Photometer – monitor time variability  Nick Devereux 2006

Basic Parameters

Telescope Field of View = mirror diameter/focal length = 12.375in (2.54cm/in.)/304.8cm

= 0.1 radians = 5.96 degrees Related to the f#, or “f number” = focal length/mirror diameter = 9.69

Cited by Meade as f/10  Nick Devereux 2006

Pixel Field of View = pixel diameter/focal length = 7.4 x 10 -6 m/ 3.048m

= 2.43 x 10 -5 radians = 0.5 arc seconds The CCD has 1600 x 1200 pixels providing a field of view = 800 x 600 arc seconds = 13.3 x 10 arc minutes There is no angular magnification, since there is no eyepiece!

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Resolving Power of the Mirror

Important Point: The resolution of the telescope is set by the mirror size – not the pixel size!

Angular resolution,  , of the mirror is determined by the diffraction pattern called the “Airy disk”.

As mentioned previously (Ch 3)  = 1.22  /D radians Where  is the wavelength of the light being measured and D is the diameter of the primary mirror.

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Sky Conditions

The brightness of celestial objects depends on where they are located on the sky, because of

atmospheric extinction

.

A given object will look brighter at the zenith than at the horizon, because the starlight has to travel through a smaller column of air. A consideration of the geometry will convince you that the path length increases as 1/cos (zenith angle). The zenith angle is the angle of the object as measured from the zenith, or 90 - elevation.

The atmospheric extinction can be determined by measuring how the brightness of a star varies with elevation and plotting the brightness versus the airmass.  Nick Devereux 2006

I = I o e -kx -2.5 log I = -2.5 logI o –k’x m i = m o –k’x So a plot of instrumental magnitude, m i , vs. airmass, x, yields a straight line, with slope = k, the extinction coefficient  Nick Devereux 2006

Extinction coefficients measured for ERAU B filter 0.23 +/- 0.01 mag/airmass V filter 0.17 +/- 0.01 mag/airmass The extinction is greater at shorter wavelengths because of Rayleigh scattering, whereby short wavelength photons are preferentially scattered off air molecules. It’s the same reason that the sky is blue.

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Seeing

Seeing is a term used to describe the quality of stellar images. Stellar photons travel, unimpeded, for literally thousands of light years until they strike the Earth’s upper atmosphere. Then , in the last 100  s of their journey, the photons become distorted. Temperature and density variations cause differences in the refractive index of the air column that the stellar photons travel through. The consequence is that the stellar image is blurry by the time it gets to the telescope.

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The magnitude of the effect can be to increase the diameter (FWHM) of the stellar image to several arc seconds, regardless of the size of the telescope mirror. Thus, the vast majority of ground based telescopes never achieve their diffraction limited performance, and is, in fact, one of the primary motivations for placing telescopes in space.

The other is to access other regions of the electromagnetic spectrum that are totally absorbed by the Earth’s atmosphere, such as the x-ray, UV, and far infrared windows.

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transparent

All astronomers proposing to use a professional facility must justify, in a proposal, that their project is feasible. This involves a S/N calculation.

W = f .  . a .  P = W/h  = f .  . a .

Watts  = f .  . a .  h  h  ph/s E = P x Q.E e/s Spread over a certain number of pixels, n I = E/n e/s/pixel S = I . t e/pixel N =  ( I.t +  2 r +  2 sky ) e/pixel Usually I.t >>  2 r +  2 sky for bright objects, so S/N =  I . t  Nick Devereux 2006

Definition of terms

W = f is the stellar flux in Wm -2 Hz -1  = efficiency of the optics ~ 75% a = telescope collecting area in m 2  = filter bandpass in Hz h  = photon energy Q.E = CCD quantum efficiency ~ 50% at V.

t = integration time in seconds  r = read noise of the CCD, ~ 8 e/pix  sky = sky noise  Nick Devereux 2006

CCD performance on the 12 inch V filter, 2 x 2 binning (1 arc sec pixels)

The CCD will saturate (full well) on stars brighter than 5 mag in just 1 sec of integration time.

The CCD can detect (S/N ~ 8) objects as faint as 15 mag in 1 sec of integration time.

(Assumes that 100% of the stellar flux is contained within 4 pixels)  Nick Devereux 2006

Photometric accuracy

The inverse of the S/N ratio is a measure of the percentage error, which is directly related to the photometric accuracy. For example; S/N = 50 N/S = 0.02 ie photometric accuracy of 2% Which also corresponds to an uncertainty of 0.02 magnitudes because; m = 2.5 log 10 f m = 2.5 log e 2.3

f (since log e f = 2.3 log 10 f ) So,  m   f and  f = N Thus,  m = N f f S S  Nick Devereux 2006

S/N Ratio can be increased by co-adding multiple frames

Median combining multiple CCD frames will reduce the noise by a factor equal to  n, where n is the number of frames, thereby increasing the S/N ratio in the final image. The signal does not change, only the noise.

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Crab Nebula – A Supernova Remnant

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M13 – A Globular Cluster

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M95 – A Barred Galaxy

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Moon

Photometry

The photometer is a photon counting device just like a CCD, but it has a much smaller field of view, 81 arc seconds on our 12 inch, and is therefore suitable only for measuring individual stars.

Why use a photometer? Because the data reduction is much easier!

particularly when you want to make multiple observations of the same object.

The photometer reports the photon rate as counts per second, and the data reduction package called SSPDATAQ calculates instrumental magnitudes m i = -2.5 log (counts/s)  Nick Devereux 2006

Measuring a standard star, that is a star of known magnitude, allows the instrumental magnitudes to be corrected to apparent magnitudes, m v, But first, the instrumental magnitudes have to be corrected for atmospheric extinction.

m c = m i – kx and then corrected to an apparent magnitude, m c = m v +  For example, you measure  Lyr, the standard star with m v at an airmass = 1.5. You get 2000 counts/sec in the V filter.

= 0, m i = -2.5 log 2000 = -8.25

m c = m i – kx  Nick Devereux 2006

So, m c = -8.25 – (0.17 x 1.5) m c = -8.5

To find  , use m c = m v +  So, -8.5 = 0 +  Now you can use  to correct all the other instrumental magnitudes to find the apparent magnitudes of the other stars you were observing. This is the procedure, but the SSPDATAQ program does it all for you at the press of a button!

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Uncertainty in photometry

The uncertainty in the photometry,  m, is limited ( for bright objects at least) by the uncertainty in the extinction coefficient,  k such that  m = x  k where x is the airmass that the star was measured.

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