PHYS216 Practical Astrophysics Lecture 6 – Photometry 2 & Spectroscopy

PHYS216 Practical AstrophysicsLecture 6 – Photometry 2 & Spectroscopy Module Leader: Dr Matt Darnley Course Lecturer: Dr Chris Davis

Calibrating Stellar Magnitudes Pogson’s Ratio gives: m1 – m2 = -2.5 log10 (f1/f2) where f1and f2are measured fluxes. Note that (f1/f2) is dimensionless – sofcan be in any units! . Typically measure the total, integrated counts in an aperture on a CCD image minus counts from the background sky .

Calibrating Stellar Magnitudes • If one of the two stars was Vega, then: • m1 - mvega= -2.5 log10 (f1/fvega) = 2.5 log10 (fvega) - 2.5 log10 (f1) • But mvega= 0 in all bands, so: • m1= 2.5 log10 (fvega) - 2.5 log10 (f1) • 2.5 log10 (fvega) is the Zero-point, Z . • -2.5 log10 (f1) is the instrumental magnitude, minst, of Star 1. Vega Star 1

Calibrating Stellar Magnitudes Relates absolute magnitude of the star to its instrumental magnitude and the telescope+instrument’sZero-point: m1= Z + minst Z and minst must be measured with the same instrument, and in the same manner. Generally speaking: m= Z - 2.5 log10f If you measure the flux, fstd , of a star with a known magnitude, mstd , you can calculate Z. Given Z, then if you measure the flux of a second star, f★ , you can calculate its magnitude, m★. In other words: fstdand mstd Z Z and f★ m★ fstdand f★ must be in the same units (usually integrated counts per second)

Standard Star Catalogues There are a number of standard star catalogues in use by professional astronomers. For example: A portion of the Landolt catalogue of optical standard stars presented on the European Southern Observatory’s (ESO’s) website Only V-band apparent magnitudes provided: magnitudes in other filters can be calculated from the quoted colours. (b) (r) …etc

Zero-points and Airmass (Altitude) Z changes with Airmass. Remember – Airmass is a measure of how low an object is in the sky: AM = 1; Altitude = 90o AM = 2; Altitude = 30o The flux from a star gets fainter as the airmassincreases. Therefore, Z decreases as the airmassincreases(because m = Z - 2.5 log10f )

Zero-points and Airmass (Altitude) We therefore derive Z at airmass=1 (to use as a reference). To do this make measurements of a standard star throughout the night - at different airmasses – and construct an Airmass Curve. The slope of this curve also gives the atmospheric extinction, in magnitudes per airmass. Remember: mstd = Z - 2.5 log10 (fstd) where mstdis the catalogue magnitude of the standard star, and fstdis its flux (in integrated counts per second) Z Airmass = secz (wherezis the zenith angle)

Using Z to calculate stellar magnitudes • Given: Z at AM=1 and knowledge of how atmospheric extinction varies with AM, can calculate the apparent magnitude of any other star observed with the same system (telescope, instrument, filter) under the same observing conditions. • For Example: • Z1AM = 11.35 (measured from our “airmass curve”). • Slope of the airmass curve gives 0.36 mag/airmassof attenuation. • Science target is observed at AM = 1.28 with an integrated flux, f = 3599 counts/sec. • What is its apparent magnitude? • m★ = Z – 2.5 log f★ - airmass correction • = 2.36 f★ = 215,950 counts in 60 sec, or 3599 counts/sec

More on Zero-Points… • Must establish the zero-point for each filter AND for each night. • However, Zero-points calculated for AM=1 are often made available at professional telescopes. • Z at AM=1 should be the same from night-to-night, provided observing conditions (and the instrument itself) don’t change. • A star with the same magnitude as the zero-point would produce only one count per second in an image • Can you see this from the ZP equation (and Pogson’s relationship)? • m★ - Z = - 2.5 log10 (f★) • You’d want to observe stars that are either much brighter than the zero-point, or observe [integrate] for a lot longer than a second to gather more counts/photons! Zero-points for IR filters in WFCAM at UKIRT, quoted for AM=1 and “photometric” conditions.

Zero-points and bad weather! Clear Sometimes, telescopes will monitor Z so that they know how the weather is changing Skycam-Z Cloudy At the LT skycam-Z images the sky every minute! From standard stars in these data we can measure Z every minute and monitor the transparency…

Zero-points and bad weather! Clear Sometimes, telescopes will monitor Z so that they know how the weather is changing Cloudy On the CLEAR night, the zero-point, Zclear≈ 22.8 mag On the CLOUDY night, sometimes Zcloudy ≈ 21.0 mag How does the cloud affect the flux reaching the telescope? mstd = Z – 2.5 log (fstd) But mstd is fixed! Therefore: Zclear – 2.5 log (fstd,clear) = Zcloudy – 2.5 log (fstd,cloudy)

Noise Why can't a detector detect any source, however faint? The reason is - Noise. All measured signals are accompanied by noise: random variations about the mean. Main sources of noise in most astronomical images is photon noise: • Photons arrive at the detector at random. • Probability of arrival is given by the Poisson Distribution, which describes all random events. • For MANY random events, this becomes the Gaussian or Normal Distribution. Gaussian distributions about the expected value, m, with a variance, s.

Noise Both thermal and photon noise have distributions with: standard deviation √N Where N is the number of events (photons, thermal electrons, etc.), and √N is the uncertainty in N. e.g. A person catching kittens in a bucket! If 1,000,000 kittens land in the bucket, that person would in theory count 1,000,000 ± 1,000 kittens. Note that these statistical arguments only apply if there is a very large number of kittens! 999,397… 999,398!

Noise Lets assume we measure a signal A, with uncertainty X, on a CCD detector. If we add togethermultiple measurements of signal A: - for 2 measurements added: signal = 2.A, but uncertainty = √2.X - for 3 measurements added: signal = 3.A, but uncertainty = √3.X … etc. When N measurements are added: signal = N.A, uncertainty = √N.X Integrating the signal over time, t Equivalent to ADDING N measurements. signal tand noise √t Hence, the Signal-to-Noise ratio, SNR t / √tor SNR √t

Noise • Integrating the signal over bandwidth,DnorDl, will also improve S/N. • The signal is DnorDl (i.e. filter bandwidth) • The noise is √(Dn)or √(Dl) • Therefore, the SNR √(Dn)or √(Dl) Narrow “H2” filter Broad K filter Left - image through a narrow-band H2 filter Right – image through a broad, K-band filter (DlK ≈ 10x DlH2). The SNR in the K image should be √10–times better, but the exposure time in the H2 image is 10-times longer, so this cancels out the affect of the wider filter bandwidth.

Other sources of Noise • Background moonlight, twilight, distant (unresolved) stars and galaxies. • Background in an image almost never completely devoid of light! • We can subtract the background signal but NOT the random noise associated with this signal. • For example: • If Total Signal is Sky + Background: • T = S + B • Total signal, including uncertainties: • T ± DT = (S ± DS) + (B ± DB) • = S + B ± √(DS2 + DB2) • Subtract the background B (e.g. by subtracting a blank image): • (T ± DT) - (B ± DB) = S + B ± √(DS2 + DB2) - (B ± DB) • = S ± √(DS2 + 2DB2) • We have made the (noise) situation worse!

Other sources of Noise 2. Dark Current. From thermal excitation of electrons from the conduction to the valence band in the CCD semiconductor material. 3. Read-noise. Inherent uncertainty associated with readout electronics. Left: Readout electronics used with CCD detectors. Right: Noise in a blank image, largely produced by readout but also due to dark current.

Noise • Even the “dark sky” is • noisy! • Average counts in background ≈ 25. • Root-mean-square (rms) noise level is • ≈ 5 counts ( = √25). • Noise in this image is statistical noise from the “bright” sky background! Q. Is a 9.5 mag star detectable in this image? Assume exposure time is 10 sec, the zero-point, Z = 11.35, and the airmass of the star, AM = 1.0. Assume also that the flux is spread evenly over 4 pixels. Remember: apparent magnitude, m★ = Z – 2.5 log f★ - airmass correction.

Background Noise • Object signal is accompanied by Background (Sky) signal; both sources of signal have associated noise. • Subtracting the sky signal from an object signal reduces the SNR. • Must therefore REDUCE sky signal as much as possible:. • Baffles stop stray light from entering the system. • Observe in complete darkness! • In the Infrared, cool EVERYTHING! Baffles Baffles on the WHT primary and secondary mirrors cut down unwanted stray background light entering the system

SPICA The flying fridge! SPICA IR satellite. To reduce background signal from the telescope itself, the whole spacecraft will be cooled to -269o C !

Calculating Signal-to-Noise Ratio (SNR) The ARRAY EQUATION – the basic equation for all SNR calculations for CCDs where: Sobj = signal from the object (electrons, e-, per resolution element per second) Ssky= signal from sky or background (same units) D = Dark current (e- per second) N = number of pixels per resolution element R = rms read or readout noise (e- per pixel) FIG When imaging, “resolution element” means area covered by the star

Calculating Signal-to-Noise Ratio (SNR) Object Signal, Sobj: Sobj = (PlxDl x A) x E Pl - flux density of photons at each wavelength received at the telescope per unit area (i.e. the number of photons per m2 permm, or per m2 per Å). Dl - filter band-width (in mm or Å ) A - telescope collecting area(the area of the primary mirror, in m2). E is the system efficiency; detector quantum efficiency, reflectivity of the telescope mirrors, throughput, etc. CCD A Dl Pl filter E

Calculating Signal-to-Noise Ratio (SNR) • Sky Signal, Ssky : • Ssky = (PlxDl x A) x E • Is a function of the sky brightness, which varies from site to site and from night to night. • Usually quoted in magnitudes per square arc-second • Is very different at different wavelengths (e.g. brighter at longerl). Infrared images, before and after sky subtraction (data courtesy U. Oregon) Sky-subtracted H-band Raw H-band

SNR – Limiting case • From the Array Equation - if Sskyt >> N.R2 + DT : • This is the sky limited or background limited case, where SNR √t . • What SNR is needed? • SNR = 10 means that fluxes measured to an accuracy of 10% • SNR = 100 means that fluxes measured to an accuracy of 1% • SNR = 3 is usually the accepted limit for a simple detection of a signal. This is often known as a `3-sigma' (3s) detection, where s is the standard deviation.

SNR – How does it vary with time? • In the background-limited regime: • If in 2 seconds we measure: • Sobj = 125 counts • Ssky = 1000 counts • SNR = (125 x √2) / √(250 + 2000) • = 3.72 in 2 seconds • SNR of 3.7 is quite low – how long to get SNR ~ 20?? • Clue: SNR √t

SNR – How does it vary with time? • In the background-limited regime: • If in 2 seconds we measure: • Sobj = 125 counts • Ssky = 1000 counts • SNR = (125 x √2) / √(250 + 2000) • = 3.72 in 2 seconds • SNR √t. Therefore: • SNRt1 / SNRt2 = √(t1 / t2) • or t1 = (SNRt1 / SNRt2)2x t2 • If it takes 2 second to get a SNR of 3.72, to get SNR = 20 it would take: • Time = (20 / 3.72)2x 2 = 57.8 sec

Spectroscopy A plot of flux or (more correctly) flux density with frequency or wavelength can be used to figure out the colour, or effective temperature, of a star. But a spectrum constructed in this way doesn’t have very much detail in it. It is for this reason that the field of Spectroscopy has been developed! ✖ V B R v I U Z v v Photometry Spectroscopy

Spectroscopy Sir Isaac Newton’s famous experiment (circa 1660), in which he split sunlight into the colours of the rainbow by passing it through a glass prism. He is widely recognised as the father of spectroscopy. Newton was the first to use the word “spectrum” to describe the rainbow of light produced in this experiment Can you spot the mistake..?

Slit-less vs Long-slit Spectroscopy Spectroscopy provides wavelength info, but usually at the expense of spatial info Image Spectra Slit-less spectroscopy Long-slit spectroscopy Long slit spectroscopy

Spectroscopy • Astronomers use spectroscopy to: • Measure accurate wavelengths of emission and absorption lines. • Measure line widths velocities, or pressures. • Measure strengths densities, temperatures, abundances. • Measure the spectral energy distribution of the continuum radiation. Star’s continuum emission (smooth slope) Absorption lines

Spectroscopy • Emission lines: • Produced by warm gas surrounding a star. • Atoms and molecules thermally excited. • Electrons raised to higher energy states; molecules vibrate/rotate. • Radiative de-excitation – emission of light at specific l. Emission from H atoms heated to thousands of degrees Emission from O atoms Red star – spectrum steadily rises at longerl

Spectroscopy • Absorption lines: • Produced by cooler gas surrounding a star or in the “line-of-sight” (i.e. between the star and the earth). • Atoms/molecules “absorb” starlight and re-radiate it at different l . • Absorption causes dips at specific l . Star’s continuum is much brighter this time! Relatively cold H atoms absorb light from the star Broad absorption caused by O2 and H2O in earth’s atmosphere

Spectroscopy – Resolving lines If the dispersion of your spectrograph is large enough the “shape” of an emission or absorption line can be “resolved”. • Unresolved emission line: • Line shape is more-or-less Gaussian. • Width is simply equal to the resolution of the spectrometer. • Resolved emission line: • Line shape comprises two “Gaussians”. • May be two gas components

Line broadening - 1 • Emission and absorption lines are broadened by three main mechanisms • Natural broadening - caused by the uncertainty in the energy levels due to the Heisenberg Uncertainty Principle: • DE = (h/2p)/Dt - where Dt is the life-time of the state Hydrogen electronic states/transitions

Line broadening - 2 • Emission and absorption lines are broadened by three main mechanisms • Doppler broadening - caused by motion of the emitting particles • Motions can include thermal, turbulence, pulsation, rotation, infall and outflow. • Wavelengths Doppler shifted according to: • Dl/l = vr/c - where vris the radial velocity vector

Line broadening - 3 Emission and absorption lines are broadened by three main mechanisms • Pressure broadening - caused by collisions between particles. • Collisions reduce the lifetime of an excited state, therefore increasing the uncertainty in photon energy and hence the width of the line. • The higher the pressure the more frequent and energetic the interactions, therefore the broader the line.

Line broadening • The observed “width” of a line is usually a combination of these three effects, PLUS the “resolution” of the instrument. • Spectrometer resolution: • Further broaden or “smooth” emission (or absorption) lines • Lines close together in wavelength may be “merged” or “blended”. 3 … further smoothed by spectrometer resolution 2 … Natural, Doppler, and Pressure broadening 1 … Un-broadened, “infinitely narrow”, emission lines.

Complex Line widths • Width of a spectral line – • characterized by full width at half maximum (FWHM) intensity • often measured by fitting a Gaussian distribution to the line • Sometimes a complex line structure can not be approximated by a single Gaussian. Lines can be separated using deconvolutiontechniques. FWHM A single Gaussian profile nicely fits the line on the left: the FWHM can be easily measured. However, two Gaussians are needed to fit the line on the right.

Line Equivalent Widths • Measure the intensity of a line - difficult to quatify if the target is observed through thin cloud or at high airmass. • Equivalent width, W - a measure of line strength. • W is equivalent to the integrated area under the line divided by the continuum flux density, Fc . • W can be measured for an emission line or an absorption line! • Positive numbers used for absorption lines, negative numbers for emission lines Note that W should not be affected by extinction caused by clouds or airmass > 1 – provided the target (and line) are still detected.

Spectroscopy At the end of the day, spectroscopy is a hugely useful tool for astronomers, allowing them to measure velocities, distances (from red-shifted emission or absorption lines), temperatures, densities, chemical abundances, etc. Without spectroscopy we’d know very little about the Universe in which we live… Enjoy the lab classes!

PHYS216 Practical Astrophysics Lecture 6 – Photometry 2 & Spectroscopy