Atmospheric Differential Refraction and Spectrometer Slit Rotation

S. Donnell, Kiowa Creek Observatory

AAVSO, Colorado Springs Astronomical Society

donnellsp@gmail.com

Atmospheric Differential Refraction

• Atmospheric differential refraction is the wavelength-dependent refraction as light passes through the atmosphere.
• Blue is refracted more than red.
• Refraction is perpendicular to the horizon – an image of a star is actually a small spectrum in the vertical direction – blue on top and red on the bottom.

Sec z ~ air mass

• Atmospheric differential refraction, or dispersion, varies with zenith angle and wavelength.

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• Dispersion is zero at the zenith and increases with increasing zenith angle.

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• The difference in dispersion in blue and red also increases with increasing zenith angle.

Effect of Slit Orientation

• The amount of dispersion is comparable to the width of a slit in a typical spectrometer
• A slit oriented perpendicular to the horizon will pass most or all of the light across the spectrum.
• A slit oriented horizontal to the horizon will have a decrease in intensity in the blue and red ends.
• Mostly affects slit spectrometers with broad spectral ranges and narrow slits.

• Dispersion results in a decrease in intensity of light passing through the slit on the blue and red ends of the spectrum.

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• This reduction in intensity increases with increasing zenith angle.

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• Reduction in intensity also means a decrease in signal to noise.

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• Relative and absolute flux calibration is compromised.

-18% at sec z = 1.5

Sec z ~ air mass

Effect on Calibration

• Relative Flux Calibration
• Also known as atmosphere/instrument response correction.
• No effect if both the target spectrum and reference star spectrum are obtained with the slit perpendicular to the horizon for both objects.
• If the reference star spectrum was obtained at one slit angle and the target star another, then there will be a difference in the blue/red response that will remain after the atmosphere/instrument response correction has been applied to the target star.
• This will generally be the case for any fixed slit orientation.
• Absolute Flux Calibration
• Same issue as with relative flux calibration.�

Setting the Slit Parallel to RA/Hour Circles

• Typical fixed slit orientation.
• Slit is oriented perpendicular to the horizon when facing south.
• Slit remains fixed thereafter - parallel to the hour circles and in the direction of the pole.

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Parallactic Angle by Declination and Hour Angle�Latitude 40 deg N

Zenith

• Flux loss at 400 nm (relative to 550 nm) for a slit parallel to RA/hour angle circles

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• Zero flux loss at zenith since dispersion is zero.

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• Larger hour angles and lower declinations contribute to increasing air mass with a resulting flux loss

• Flux loss at 750 nm (relative to 550 nm) for a slit parallel to RA/hour angle circles

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• Losses are less than on the blue end, but still a concern for larger hour angles and lower declinations

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The Miracle of Slit Rotation

• By rotating the slit for both target and reference stars to be perpendicular to the horizon you:
1. Minimize or eliminate entirely the loss of flux and signal to noise at the blue and red ends of the spectrum.
2. Allow for the construction of a better atmosphere/instrument response curve by ensuring that the slit orientation for both target and reference is at the same parallactic angle.
3. Generate a more accurate absolute flux calibration.

Rotating the Slit

• Ideally, the slit should be rotated continuously throughout the exposure - generally not practical for amateur setups.
• A compromise solution is to set the slit orientation to be perpendicular to the horizon at the exposure mid time, minimizing slit loss.
• A manual rotator between the spectrometer and scope allows for rotation of the spectrometer while keeping it firmly attached to the scope.
• About $55 from Agena Astro.

Blue Fireball Camera Angle Adjustor / Rotator

Orienting the Slit to Zero Parallactic Angle

• Attach a bubble level to your spectrometer.
• Easy to determine when your slit is perpendicular to the horizon.
• No need to calculate and dial-in parallactic angles.

Bubble Level

• Goal is for the slit to perpendicular to the horizon at the exposure mid-time.

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• Prior to the target or reference star exposure start time, move the scope to the west and rotate the spectrometer so that the slit is perpendicular to the horizon (i.e, the bubble is centered in the level).

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• Move the scope back to the target/reference star and wait until the indicated exposure start time.

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• If all goes well, the slit will be in the correct orientation perpendicular to the horizon at the exposure mid time.

Offset = Delta Time * Earth rotation rate

Example: Delta Time = 21:17 – 21:02 = 15 min

Earth rotation rate ~ 0.25 deg/min

Offset = 15 * 0.25 = 3.75 deg = 3 deg 45 min

Method for Setting the Slit Orientation

Additional Comments

• Applies to broad spectrum spectrometers like the Alpy 600
• Slitless setups need not worry.
• High resolution spectrometers mostly unaffected due to their narrow spectral range.
• A properly rotated slit will still result in some reduction in intensity at the red and blue wavelengths over the exposure time.
• Especially true for long exposures.
• Minimize by setting slit angle for mid-exposure time
• Difference in exposure times between target and reference will introduce some difference in the blue/red flux even if the slit is oriented properly.
• For very long exposures, setting the slit parallel to the horizon may be a better option (Szokoly, 2005)

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Slit Loss Calculator

Input the conditions specific to your equipment and target star to determine the slit loss for any of three slit orientations: 1. Perpendicular to the horizon (ideal), 2. Parallel to RA/hour circles, and 3. Parallel to the celestial equator.

Slit Loss Calculator

Example: Target and Reference Star with Slit Parallel to RA/Hour Circles

Results From Slit Loss Calculator for Target and Reference Stars

Both stars show losses at 400 nm and 700 nm

Difference in slit loss is ~13% for 400 nm and ~2.6% for 700 nm

Black – Spectrum Calibrated with No Slit Losses

Red – Spectrum Calibrated with Slit Losses

Effect on Spectral Profile

-13%

Summary

• Wavelength-dependent atmospheric refraction (dispersion) causes starlight to be differentially refracted in a direction perpendicular to the horizon.
• A slit oriented in any direction other than the perpendicular results in a significant loss of intensity at the blue and red ends of the spectrum.
• This is a problem primarily for spectrometers like the Alpy 600 that produce a spectrum across the visual range.
• This loss of intensity adversely affects the quality of the atmosphere/instrument response correction as well as absolute flux calibration
• This problem is easily mitigated by rotating the slit to the optimal angle for both the target and reference stars.

References

• Alexei Filippenko (1982), The Importance of Atmospheric Differential Refraction in Spectrophotometry, https://articles.adsabs.harvard.edu/pdf/1982PASP...94..715F
• Ref: Szokoly, 2005, Optimal slit orientation for long multi-object spectroscopic exposures
• https://arxiv.org/abs/astro-ph/0506688

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Questions?

Parallactic Angle

• The parallactic angle is the angle between the great circle through a celestial object and the zenith, and the hour circle of the object.