1. Photometry
…Getting the most from your photon

2. Very Brief History:
Hipparcos in 130 B.C. created catalog of stars and the magnitude scale used to this day
In 1800s astronomers decided that the magnitude scale should be logarithmic, determined by physiological response of eye
m1 – m2 = –2.5 log (f1/f2)
Dm = 5 → 100 x decrease in brightness
Remember: Larger magnitude, the fainter the object

3. What do Astronomers use photometric measurements for?
Brightness of objects (Luminosity)
Color of objects (temperature, Hertzprung-Russel Diagrams)
Variability of Objects (variable stars, transiting planets, etc)
Photometry usually requires only small (< 1m diameter) telescopes.

4. Useful terms
Apparent magnitude m: the brightness of a star in traditional magnitude system
standard magnitude U,B,V, I, R: the standard brightness of a star in traditional magnitude system
absolute magnitude M: the magnitude of a star if it is at a distance of 10 parsecs
Bolometric magnitude: Total power of the source
Bolometric correction: must be added to the visual magnitude to get the bolometric magnitude.

5. Useful terms
Bandwidth : wavelength range over which observations are made:
Broadband:
Dl/l
~ 1/4
Narrow band:
Dl/l
~ 10–2
Color index: difference of two magnitudes at two different wavelengths
Standard star: star that provide a reference to a magnitude system
Metallicity index m1 : index that is a measure of the relative abundance of a star
Extinction k: reduction in light due to passage through the Earth‘s atmosphere
Interstellar extinction: reduction in light due to passage through interstellar material (dust, gas).

6. The Hertzsprung-Russel (H-R) Diagram
Astronomers usually measure the color instead of temperature. For stars in a cluster (all at same distance) the apparent magnitude is a measure of the relative luminosity

7. From http://cas.sdss.org/dr5/en/proj/advanced/color/making.asp
Color indices are a measure of the shape of the black body curve and thus the temperature

8. Magnitudes and color indices
Color Index: ∫
Fn WB (n) dn ( )
B–V = –2.5 log ∫
Fn WV (n) dn ∫
Fn WU (n) dn ( )
U–B = –2.5 log
– 1.093 ∫
Fn WB (n) dn
O G M0
B-V –
U-B –

9. Black Body Curves B V
B–V < 0
T = K
T = 4000 K
Flux
B–V > 0
Temperature

10. B-V = –0.46
U-B = –1.33
For T= ∞

11. Filter Characteristics of Astronomical Photometry Systems
Dl1/2
UBV (Johnson-Morgan) U
3650 Å
700 Å B
4400 Å
1000 Å V
5500 Å
900 Å
Six-color (Stebbins-Whitford-Kron)
3550 Å
500 Å
4200 Å
800 Å
4900 Å G
5700 Å R
7200 Å
1800 Å I
10,300 Å
Infrared (Johnson)
7000 Å
2200 Å
8800 Å
2400 Å J
1.25m
0.38m K
2.2m
0.48m L
3.4m
0.70m M
5.0m
1.2m N
10.4m
5.7m
uvbyb (Strömgren-Crawford) u
3500 Å
340 Å v
4100 Å
200 Å b
4700 Å
160 Å y
240 Å
4860 Å
30 Å,150 Å

13. From http://www.ucolick.org/~kcooksey/CTIOreu.html
Giant stars
Main sequence stars
For field stars the apparent magnitude does not tell you the true luminosity. Therefore, color-color magnitude diagrams are often employed

14. Detectors for Photometric Observations
Photographic Plates
1.7o x 2o
Advantages: large area
Disadvantages: low quantum efficiency

15. Detectors for Photometric Observations
2. Photomultiplier Tubes
Advantages: blue sensitive, fast response
Disadvantages: Only one object at a time

16. 2. Photomultiplier Tubes: observations
Are reference stars really constant?
Transperancy variations (clouds) can affect observations

17. Detectors for Photometric Observations
3. Charge Coupled Devices
From wikipedia
Advantages: high quantum efficiency, digital data, large number of reference stars, recorded simultaneously
Disadvantages: Red sensitive, readout time

18. Aperture Photometry Get data (star) counts Get sky counts
Magnitude = constant –2.5 x log [Σ(data – sky)/(exposure time)]
Instrumental magnitude can be converted to real magnitude by looking at standard stars

19. Aperture photometry is useless for crowded fields

20. Term: Point Spread Function
PSF: Image produced by the instrument + atmosphere = point spread function
Camera
Atmosphere
Most photometric reduction programs require modeling of the PSF

21. Crowded field Photometry: DAOPHOT
Computer program developed to obtain accurate photometry of blended images (Stetson 1987, Publications of the Astronomical Society of the Pacific, 99, 191)
DAOPHOT software is part of the IRAF (Image Reduction and Analysis Facility)
IRAF can be dowloaded from (Windows, Mac, Intel) or
(mostly Linux)
In iraf: load packages: noao -> digiphot -> daophot
Users manuals:

22. In DAOPHOT modeling of the PSF is done through an iterative process:
Choose several stars as „psf“ stars
Fit psf
Subtract neighbors
Refit PSF
Iterate
Stop after 2-3 iterations

24. Original Data
Data minus stars found in first star list
Data minus stars found in second determination of star list

26. Improvements to daophot and psf fitting: SExtractor (Source Extractor)
Improvements to daophot and psf fitting: SExtractor (Source Extractor). Allows for elliptical apertures. Better at finding galaxies which can have none circular shapes
Bertin & Arnouts, Astron. Astroph. Suppl. Ser 117, , 1996

27. Special Techniques: Image Subtraction
If you are only interested in changes in the brightness (differential photometry) of an object one can use image subtraction (Alard, Astronomy and Astrophysics Suppl. Ser. 144, 363, 2000)
Applications:
Nova and Supernova searches
Microlensing
Transit detections

28. Image subtraction: Basic Technique
Get a reference image R. This is either a synthetic image (point sources) or a real data frame taken under good seeing conditions (usually your best frame).
Find a convolution Kernal, K, that will transform R to fit your observed image, I. Your fit image is R * I where * is the convolution (i.e. smoothing)
Solve in a least squares manner the Kernal that will minimize the sum:
([R * K](xi,yi) – I(xi,yi))2 S i
Kernal is usually taken to be a Gaussian whose width can vary across the frame.

31. Special Techniques: Frame Transfer
What if you are interested in rapid time variations?
some stellar oscillations have periods 5-15 min
CCD Read out times secs
Solution: Window CCD and frame transfer
E.g. exposure time = 10 secs
readout time = 30 secs
efficiency = 25%

32. Frame Transfer Target Reference
Transfer images to masked portion of the CCD. This is fast (msecs)
While masked portion is reading out, you expose on unmasked regions
Can achieve 100% efficiency
Data shifted along columns
Store data
Mask

33. Sources of Errors Sources of photometric noise: 1. Photon noise:
error = √Ns (Ns = photons from source)
Signal to noise ratio = Ns/ √ Ns = √Ns
rms scatter in brightness = 1/(S/N)

34. Sources of Errors
2. Sky:
Sky is bright, adds noise, best not to observe under full moon or in downtown Jena.
Error = (Ndata + Nsky)1/2
S/N = (Ndata)/(Ndata + Nsky)1/2
rms scatter = 1/(S/N)
Ndata = counts from star
Nsky = background

35. Nsky = 1000
Nsky = 100
Nsky = 10
Nsky = 0
rms
Ndata

36. Sources of Errors 3. Dark Counts and Readout Noise:
Electrons dislodged by thermal noise, typically a few per hour.
This can be neglected unless you are looking at very faint sources
Readout Noise: Noise introduced in reading out the CCD:
Typical CCDs have readout noise counts of 3–11 e–1 (photons)

37. Sources of Errors 4. Scintillation Noise:
Amplitude variations due to Earth‘s atmosphere
s ~ [ (kD2/4L)7/6]–1
D is the telescope diameter
L is the length scale of the atmospheric turbulence

39. For larger telescopes the diameter of the telescope is much larger than the length scale of the turbulence. This reduces the scintillation noise.

40. Light Curves from Tautenburg taken with BEST

41. Sources of Errors 4. Atmospheric Extinction
Atmospheric Extinction can affect colors of stars and photometric precision of differential photometry since observations are done at different air masses
Major sources of extinction:
Rayleigh scattering: cross section s per molecule ∝
l–4

42. Aerosol Extinction
Absorption by gases

43. Atmospheric extinction can also affect differential photometry because reference stars are not always the same spectral type.
A-star
Wavelength
K-star
Wavelength
Atmospheric extinction (e.g. Rayleigh scattering) will affect the A star more than the K star because it has more flux at shorter wavelength where the extinction is greater

44. 6. Interstellar reddening (extinction):
One of the problems of the 1920s was that the observation of O-B stars had red colors. This was later found to be caused by interstellar material.
To measure accurate „real“ colors and to put a star in the Hertzprung-Russel diagram this must be corrected

45. 6. Interstellar reddening:
To correct: assume that stars with identical spectra have similar colors.
A(li) = amount of interstellar absorption in magnitudes. Then the observed magnitudes mi and mj at two different wavelengths li and lj are related to the intrinsic magnitudes, mi0 and mj0 by the expressions:
mi = mi0 + A(li)
mj = mj0 + A(lj)
The observed color index Cij ≡ mi – mj is related to the intrinsic color index Cij ≡ mi0 – mj0 by
Cij = Cij0 + [A(li) – A(lj)] ≡ Cij + Eij

46. 6. Interstellar reddening:
In the UBV system the notation for color excess is:
E(B – V) ≡ (B – V) – (B – V)0
E(U – B) ≡ (U – B) – (U – B)0
Eij is postive, i.e. colors become redder

47. 6. Interstellar reddening:
The reddening lines for stars of different spectral types originate at different points in the two color diagram
Usually can be neglected
E(U – B) =
E(B – V)
E(B – V)

48. 6. Interstellar reddening:
In many cases we do not have spectral types of the stars. The slope of the reddening line can be used to define a photometric parameter that depends only on spectral type and independent of the amount of reddening. In the UBV system:
E(U – B)
Q ≡ (U – B) –
(B – V)
E(B – V)
Q ≡ (U – B) –
0.72(B – V)

49. 6. Interstellar reddening:
Using expressions for color excess:
E(U – B)
Q = (U – B)0 +
E(U – B) –
[(B – V)0 + E(B – V)]
E(B – V)
E(U – B)
Q = (U – B)0 –
(B – V)0
≡ Qo
E(B – V)

50. 6. Interstellar reddening:
(B – V)0 = Q
Spectral Type Q O5
–0.93 B3
–0.57 O6 B5
–0.44 O8 B6
–0.37 O9
–0.90 B7
–0.32 B0 B8
–0.27
B0.5
–0.85 B9
–0.13 B1
–0.78 A0
0.00 B2
–0.70
We can determine (B – V)0 (= intrinsic color) for early-type stars from Q

51. 6. Interstellar reddening:
We can determine (B – V)0 (= intrinsic color) for early-type stars from Q (measured from UBV). Once (B – V)0 and (U – V)0 are known we find E(B – V) from (B – V).
This only works for stars up to spectral type A0. Reason: The reddening happens to have the same slope as unreddened main sequence stars for late-type stars.
Reddening free indices can also be defined for other photometric systems as well.

52. 6. Interstellar reddening: Extinction in magnitudes (Al)
Intensity drop of light Il through a slab of thickness dx:
dIl = –Iln(x)kldx
n = number density of grains along the line of sight
k = cross section per particle
nkdx is often called the incremental optical depth dt

53. ∫ Optical depth Il + dIl Ilkl
The radiation sees neither klr or dx, but a the combination of the two over some path length L. ∫ o L
tl =
klr dx
Optical depth gm
cm3
Units:
cm2 gm cm

54. dIl = –Ildt Il = Il (0)e–tl
6. Interstellar reddening: Extinction in magnitudes (Al)
Intensity drop of light Il through a slab of thickness dx:
dIl = –Ildt
Il = Il (0)e–tl
Absorption of the starlight in magnitudes:
Al ≡ –2.5 log10(Il/Il(0)) = –2.5 (log10 e)ln(e–tl) = 1.086tl

55. 6. Interstellar reddening: Extinction in magnitudes (Al)
Using expressions for Al, Cij, and t : AV tV kV
RV ≡ = =
E(B – V)
(tB – tV)
(kB – kV)
The absorption AV is proportional to color excess E(B–V) and the constant of proportionality, RV, is fixed by the wavelength dependence of the extinction coefficient. Once you determine RV, observe E(B–V) to determine AV
Need to determine RV

56. To determine RV compare at several wavelengths the energy distribution of a reddened star to one with no reddening and that has the same spectral type. A comparison of the colors results in color excess in each band referenced to one (V for instance). Since different stars have different color excess it is customary to normalize E(B–V) to unity.
Assume that E(X-V) goes to zero at infinite wavelengths (extrapolate). This gives AV

57. Standard Stars
For most photometric measurements (exception: differential measurements for variable star work) you need to put your relative photometric measurements on a reference magnitude scale.
What about fainter stars? Use Landolt standards.
Observations of standard stars should be made as close in time and at similar air mass as your other observations

58. Landolt standards.