Seeing The Earth’s atmosphere: seeing, background, All ground-based observatories suffer from a major absorption & scattering problem: Observational Astronomy 2019 light from distant objects must pass through the Part 8 Earth’s atmosphere Prof. S.C. Trager recall from our discussion of optics that the atmosphere has refractive power

Seeing Seeing top of atmosphere

turbulent atmosphere The refraction itself isn’t the problem: it’s the variation in the index of refraction that causes problems near ground Wind, convection, and land masses cause turbulence, mixing the layers of different indices of This non-uniform, continuous variation in the index of refraction cause refraction in non-uniform and continuously varying the initially plane-parallel wavefronts to tilt, bend, and corrugate ways This causes the twinkling we see when we look at stars with our eyes Any degradation of images by the atmosphere is called seeing Seeing Seeing

To understand seeing, we need to examine the index of The dominant terms are refraction and its dependence of temperature and 6 1 n 1 = 77.6 10 pT pressure (and humidity, too) air ⇥ Cauchy’s formula, extended by Lorentz to account for Seeing — perturbations of the transiting wavefront — is humidity, gives the excess (over vacuum) index of caused by changes in nair differentially across the refraction of air: wavefront due to turbulence 6 3 77.6 10 7.52 10 v n 1= ⇥ 1+ ⇥ p + 4810 air T 2 T Note that water vapor has little effect on n in the ✓ ◆ where p is the pressure in mbars, T is the ⇣temperature ⌘ optical (except for fog), but can affect columns of air in K, and v is the water vapor pressure in mbars by causing convection: wet air is lighter than dry air!

Seeing Thermal turbulence

Modern observatories are built at very dry sites, so the overall Thermal turbulence in the effect of humidity is typically unimportant for seeing (but atmosphere is created on a important for differential refraction) variety of scales by

Ignoring v above, then, for an ideal gas and adiabatic convection: air heated undisturbed turbulence conditions, by conduction with the wind flow dn p warm surface of the Earth dT / T 2 becomes buoyant and first rises, displacing cooler air mountain Therefore the primary source of index of refraction variations ridge in the atmosphere is thermal variations humid (wet) air also rises and displaces dry ocean We care (mostly) about small-scale variations in T: thermal air turbulence Thermal turbulence Thermal turbulence

wind shear: high winds — in particular the jet stream — generate wind shear undisturbed turbulence disturbances: large undisturbed turbulence and eddies at various wind flow land-form variations — wind flow

scales, creating a first like mountains — can first turbulent interface mountain create turbulence mountain between other layers in ridge ridge laminar (non-turbulent) ocean ocean flow

Thermal turbulence Thermal turbulence

Turbulence occurs when Turbulence is created by eddie transfer inertial forces dominate over viscous forces in a kinetic energy is deposited on large scales, which creates fluid eddies undisturbed turbulence This means that turbulent wind flow these in turn create smaller eddies, and so on... motions — eddies and vortices — dominate over first ...until the shears are so large compared to the eddy smooth (laminar) flows mountain scale that the viscosity of air takes over and the kinetic ridge energy is turned into heat This is true for typical wind speeds and length ocean This stops the turbulent cascade and smooths out the scales temperature fluctuations Thermal turbulence Thermal turbulence

Kolmogorov showed that When turbulence occurs in an the energy spectrum of atmospheric layers with a such a turbulent cascade temperature gradient differing has a characteristic shape from an adiabatic gradient... –5/3 –5/3 inertial rangeκ one in which no heat is inertial rangeκ The inertial range transferred (i.e., the entropy log E external log E external follows a spectrum cutoff does not increase) cutoff 5/3 internal internal E  cutoff ...it mixes air of different cutoff / temperatures at the same where κ is the log κ altitude, producing temperature log κ wavenumber or inverse fluctuations following a length Kolmogorov spectrum

Atmospheric layers Atmospheric layers contributing to turbulence contributing to turbulence

surface or ground layer: ~few to 10’s of meters — up to few arcminutes seeing!

turbulence generated by wind There are effectively four shear due to friction and layers of the atmosphere topographic effects that affect the seeing, with site geometry, trees, gradual transitions of boulders, etc.

properties between them best sites have surface layers <10 m

build telescope above this layer Atmospheric layers Atmospheric layers contributing to turbulence contributing to turbulence

planetary boundary layer: <~1 km above sea level — 10’s of arcseconds seeing atmospheric boundary layer: above planetary both frictional effects and boundary layer day-night heating-cooling cycles not dominated by creates convection up convection but by to inversion layer abrupt changes in topography most observatories built above this layer

Atmospheric layers Seeing contributing to turbulence

free atmosphere: seeing ~0.4″ — best sites mostly see this To understand turbulence in the context of seeing, we layer need to translate the Kolmogorov spectrum into a unaffected by frictional spatial variation influence of ground To do this, we define a structure function: in 1D, large-scale flows 2 tropical trade winds (at DT (r)= [T (x + r) T (x)] lower altitudes), jet stream h i (at higher altitudes) where T(x) and T(x+r) are the temperatures at two points separated by r mechanical turbulence Seeing Seeing

For a Kolmogorov spectrum, 2 2/3 There is a characteristic transverse linear scale over DT (r)=CT r which we can consider the atmospheric variations to 2 where CT is the temperature structure constant and “flatten out” and in which plane-parallel wavefronts are gives the intensity of thermal turbulence transmitted The variation of the index of refraction (of air) is given by over these scales, the images are “perfect” the index of refraction structure constant, 2 2 6 3 2 2 2 This scale is called the Fried parameter r0 C = C [77.6 10 (1 + 7.52 10 )pT ] n T ⇥ ⇥

Seeing Seeing

The Fried parameter is well-described by integrating Cn2 along the line-of-sight through the atmosphere: 2 1 2 3/5 r =[1.67 (cos z) C (z0)dz0] 0 n The Fried parameter is inversely proportional to the size Z where z is the zenith angle and z′ is the distance along the of the PSF transmitted by the atmosphere line of sight The FWHM of the observed PSF can be predicted if A larger Fried parameter is better! Hence the inverse we know the variation of Cn2 along the line-of-sight: dependence on Cn2 3/5 5 1/5 1 2 note also the dependence on cos z, so the Fried parameter ✓ (00)=2.59 10 (cos z) C (z0)dz0 FWHM ⇥ n gets smaller as one looks through more atmosphere  Z Isoplanaticity and the Fried Seeing model

In 1665, Hooke suggested the existence of “small, This is a typical Cn2 profile moving regions of the atmosphere having different Note that FWHM is refractive powers that act like lenses” to explain bigger for larger zenith scintillation, the “twinkling” of stars angles and smaller for longer wavelengths In 1966, Fried showed that this simple model was a reasonable representation of reality...

Isoplanaticity and the Fried Isoplanaticity and the Fried model model

Assume that at any given moment, the atmosphere acts like an array of small, contiguous, wedge- Thus, each isoplanatic patch transmits a quality image shaped refracting cells of the source These locally tilt the wavefront randomly over the The size of this isoplanatic patch is the Fried parameter size scale of the cells r0, roughly the diameter (not the radius!) of the patch each cell imposes its own tilt on the wavefront... This characterizes the seeing

...creating isoplanatic patches in which the wave The more turbulence there is, the smaller r0 is is fairly smooth and has little curvature Isoplanaticity and the Fried Seeing effects model

Typically r0≈10 cm in the optical and varies as λ6/5 Seeing is always better at longer wavelengths! There are primary effects of seeing: The angular size of the isoplanatic patch is Scintillation (“twinkling”) ✓ 0.6r /h Image wander (“agitation”) 0 ⇠ 0 where h is the height of the primary turbulence layer Image blurring (“smearing”) above the telescope

Seeing effects Seeing effects

Scintillation (“twinkling”) is the result of a varying amount of energy being Image wander (“agitation”) is the motion of an image in received over time the focal plane due to changes in the average tilt of the intensity changes wavefront Variations in the shape of the turbulent layer result in moments when it Because the wavefront is locally plane-parallel, the acts like a (net) concave lens, focussing the light, and other moments when it acts like a (net) convex lens, defocussing the light image can actually be diffraction-limited if the aperture is <~r0 This is only obvious when the aperture is <~r0, like for the human eye For larger apertures, these effects average out Then the Airy disk is imaged, but it will wander

Note that planets don’t twinkle, because they’re much bigger than θ0 Larger apertures average over more isoplanatic patches, Because it is an interference effect, scintillation is highly chromatic so this effect is also only present for small apertures Seeing effects Seeing: summary

Airy disk Image blurring (smearing) dominates for D>r0 The size of the PSF at the detector is caused by the Each isoplanatic patch gives rise to its own Airy disk (FWHM ~ λ/D): seeing (for long integrations) these are called speckles The seeing limits the size of the PSF to FWHM ~ λ/r0 Seen together, they have FWHM ~ λ/r0 and give rise to a shimmering instead of the resolution limit FWHM ~ λ/D blur: https://www.youtube.com/watch?v=vD9vqoMqg5U If integrating for long times, they will have this size for the long- since r0≈10 cm in the optical, if D>10 cm, then for a big exposure PSF telescope the “resolution” is the same as a 10 cm In general, the larger the telescope, the more photons it gathers — telescope but the PSF is limited to λ/r0 this is why we are so interested in adaptive optics need adaptive optics (AO) or speckle interferometry (AO)! Remember that FWHM ~ λ–1/5, so seeing is always better in the red

Backgrounds, absorption, Sky brightness at CTIO scattering, and extinction days U B V R I from new In order to get accurate results, we need to correct for 0 22 22.7 21.8 20.9 19.9 the background and for light removed by the atmosphere through absorption and scattering 3 21.5 22.4 21.7 20.8 19.9 Many background sources come from the Earth (its inhabitants and its atmosphere) 7 19.9 21.6 21.4 20.6 19.7 But perhaps the most important background source 10 18.5 20.7 20.7 20.3 19.5

is the sunlight reflected from the moon: moonlight NOAO newsletter #37 from

Surface brightness in mag/sq.arcsec, Surface brightness in mag/sq.arcsec, 14 17 19.5 20 19.9 19.2 1992PASP..104...76O 1992PASP..104...76O 1992PASP..104...76O

Night sky at a “light- polluted” site

Airglow is emission from molecules and some atoms (like O, Na, H) in the atmosphere

this is the source of “sky (emission) lines” we see in spectra taken from ground-based sites 1992PASP..104...76O

Scattered sunlight during twilight is also a problem at the Zodiacal light is sunlight scattered off of Solar System dust, very beginning and end of the night near the plane of the ecliptic

although very useful for flat fields! this is the limiting background on moonless nights at a very dark site (and even in space) away from the Galactic plane We define three “official” twilights according to the Sun’s position with respect to the horizon: Unresolved galaxy and starlight — like in the plane of the Milky Way — can also cause a significant background 6 degree twilight: “civil twilight” — when you need to turn your headlights on In the near- to mid-IR (>2.4 µm), thermal emission from the Earth and the telescope dominate the background 12 degree twilight: “nautical twilight” — sailors can still see the horizon but also see enough stars to fix a position with a Clouds will reflect light back from the Earth, Sun, and Moon sextant Finally, light pollution from poorly-regulated human settlements is 18 degree twilight: “astronomical twilight” — fully dark sky a serious — and growing — problem for astronomy World-wide light pollution Absorption and scattering

The atmosphere not only adds background but also removes flux, decreasing signal-to-noise (or even removing signal altogether)

Absorption and scattering Absorption and scattering

Atmospheric absorption in the optical is minimal

at λ<3100 Å, O3 (ozone) cuts off the “optical window” In the near- to mid-IR, small but annoying regions H2O and CO2 (along with at ~6800 Å and ~7500 Å a little NO2 and CH4) from O2 absorption make life difficult, except in certain windows at λ>8000 Å, H2O vapor causes absorption, defining “windows” at ~1 µm and beyond Absorption and scattering Absorption and scattering

At longer wavelengths, the far-IR is reachable only from space (or very high- flying balloons or airplanes) Wavelengths shorter than 3000 Å are only visible The spectrum opens up from space (or very high- again at λ>850 µm—1 mm flying balloons or (depending on water airplanes) vapor), becoming almost totally transparent at cm– m wavelengths

Absorption and scattering Absorption and scattering

Molecular scattering, where the scattering radius a≪λ Rayleigh scattering is dominant, with a cross- Scattering arises from section two major regimes of 3 2 2 8⇡ (n 1) 2 4 particle-photon scattering ()= N R 3 N 24 / where N is the particle density and is a function of temperature and pressure, and therefore altitude, etc. Absorption and scattering Absorption and scattering

Aerosol scattering, where the scattering radius a & /10 Rayleigh scattering is the main cause of blue This is Mie scattering, extinction and is which has (roughly) responsible for the blue 2 1 sky! a / and so is the main cause of red extinction

Absorption and scattering Absorption and scattering

Aerosols are highly variable from night to In the summer at La night, as they come from Palma, wind-blown air pollution dust (“calima”) from Saharan dust storms is “haze” (dust) particularly annoying, volcanic ash causing a significant increase in optical dust storms extinction etc. Annual variation at ORM (La Palma) Airmass

In order to determine

extinction corrections, top of Long-term variation at ORM we need to define the atmosphere airmass of our observations X We quote magnitudes at z

“the top of the one airmass

atmosphere” top of telescope

Airmass Airmass

Define z as the zenith We define the airmass top of angle (or zenith top of between the top of the atmosphere distance), where atmosphere telescope and the top of z=90º–altitude the atmosphere at the zenith as one airmass or X X z Then in a plane-parallel z

X=1 one airmass approximation to the one airmass Earth’s atmosphere, top of telescope top of telescope X =1/ cos z =secz Airmass Airmass

The plane-parallel Note that the cosine rule approximation is good for z=60º, X=2 of spherical trigonometry z=60º, X=2 z<60º gives X=1 X=1 For larger zenith angles, a z=90º, X=38 cos z =sin sin + cos cos cos h z=90º, X=38 spherical-shell description where ϕ is your is required: At 60º, you look through 2 latitude, δ is the 2 3 airmasses X =secz 0.0018167(sec z 1) 0.002875(sec z 1) 0.0008083(sec z 1) object’s declination, At 71º, you look through 3 and h is its hour angle airmasses (all in radians or At 90º, you look through 38 degrees) airmasses

Atmospheric extinction and Atmospheric extinction and photometry photometry

Although this topic actually belongs with our Because atmospheric discussion of photometry, absorption and scattering we can now discuss the is a radiative transfer effect of atmospheric problem, we can extinction on photometry, characterize it as an the measurement of optical depth problem magnitudes Atmospheric extinction and Atmospheric extinction and photometry photometry Then we can write that Then, in magnitudes, the flux remaining after m = 2.5 log f 10 passing through the = 2.5 log f + k X 10 0 atmosphere is Therefore, in magnitudes, the loss of light per f = f e X/⌧ 0 airmass is linear, with a

where f0 is the original proportionality constant flux of the object above k = 2.5(log e)/⌧ the atmosphere, X is 10 the airmass, and τ is called the extinction the optical depth coefficient

Atmospheric extinction and photometry We will return to the process filter kλ of determining kλ later...

In the meantime, for the sky U 0.55 over La Palma, on average, the extinction per unit B 0.25 airmass is given to the right... V 0.15 Clearly, we want to observe objects in the U R 0.09 band as close to overhead as possible! I 0.06