Download B – V

Photometry
…Getting the most from your photon
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
What do Astronomers use photometric
measurements for?
1. Brightness of objects (Luminosity)
2. Color of objects (temperature, Hertzprung-Russel Diagrams)
3. Variability of Objects (variable stars, transiting planets, etc)
Photometry usually requires only small (< 1m diameter)
telescopes.
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.
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).
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
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
Magnitudes and color indices
Color Index:
Fn WB (n) dn
∫
B–V = –2.5 log(
)
∫ Fn WV (n) dn
+ 0.710
Fn WU (n) dn
∫
U–B = –2.5 log(
)
∫ Fn WB (n) dn
– 1.093
B-V
O5
G0
M0
–0.35 +0.58 +1.45
U-B
–1.15 +0.05 +1.28
Black Body Curves
B
V
B–V < 0
T = 10000 K
Flux
T = 4000 K
B–V > 0
Temperature
For T= ∞
B-V = –0.46
U-B = –1.33
Filter Characteristics of Astronomical Photometry Systems
System
UBV (Johnson-Morgan)
Six-color (Stebbins-Whitford-Kron)
Infrared (Johnson)
uvbyb (Strömgren-Crawford)
Filter
U
l0
3650 Å
Dl1/2
700 Å
B
V
U
4400 Å
5500 Å
3550 Å
1000 Å
900 Å
500 Å
V
B
G
R
I
R
I
J
K
L
M
N
u
v
b
y
4200 Å
4900 Å
5700 Å
7200 Å
10,300 Å
7000 Å
8800 Å
1.25m
2.2m
3.4m
5.0m
10.4m
3500 Å
4100 Å
4700 Å
5500 Å
4860 Å
800 Å
800 Å
800 Å
1800 Å
1800 Å
2200 Å
2400 Å
0.38m
0.48m
0.70m
1.2m
5.7m
340 Å
200 Å
160 Å
240 Å
30 Å,150 Å
b
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
Detectors for Photometric Observations
1. Photographic Plates
Advantages: large area
Disadvantages: low
quantum efficiency
1.7o x 2o
Detectors for Photometric Observations
2. Photomultiplier Tubes
Advantages: blue sensitive, fast response
Disadvantages: Only one object at a time
2. Photomultiplier Tubes: observations
• Are reference stars really constant?
• Transperancy variations (clouds) can affect observations
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
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
Aperture photometry is useless for crowded fields
Term: Point Spread Function
PSF: Image produced by the instrument + atmosphere =
point spread function
Atmosphere
Most photometric reduction
programs require modeling of
the PSF
Camera
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 http://iraf.net (Windows, Mac, Intel)
or
http://star-www.rl.ac.uk/iraf/web/iraf-homepage.html (mostly Linux)
In iraf: load packages: noao -> digiphot -> daophot
Users manuals: http://www.iac.es/galeria/ncaon/IRAFSoporte/Iraf-Manuals.html
In DAOPHOT modeling of the PSF is done through an
iterative process:
1. Choose several stars as „psf“ stars
2. Fit psf
3. Subtract neighbors
4. Refit PSF
5. Iterate
6. Stop after 2-3 iterations
Original Data
Data minus stars found in first
star list
Data minus stars found in
second determination of star
list
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, 393-404, 1996
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
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:
S ([R * K](xi,yi) – I(xi,yi))2
i
Kernal is usually taken to be a Gaussian whose
width can vary across the frame.
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 30-120 secs
E.g. exposure time = 10 secs
readout time = 30 secs
efficiency = 25%
Solution: Window CCD and
frame transfer
Target
Reference
Frame Transfer
Transfer images to masked
portion of the CCD. This is
fast (msecs)
Data shifted along columns
While masked portion is
reading out, you expose on
unmasked regions
Can achieve 100%
efficiency
Store data
Mask
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)
Sources of Errors
2. Sky:
Sky is bright, adds noise, best not to observe
under full moon or in downtown Jena.
Ndata = counts from star
Error = (Ndata + Nsky)1/2
Nsky = background
S/N = (Ndata)/(Ndata + Nsky)1/2
rms scatter = 1/(S/N)
Nsky = 1000
Nsky = 100
Nsky = 10
rms
Nsky = 0
Ndata
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)
Sources of Errors
4. Scintillation Noise:
Amplitude variations due to Earth‘s atmosphere
s ~ [1 + 1.07(kD2/4L)7/6]–1
D is the telescope diameter
L is the length scale of the atmospheric turbulence
For larger telescopes the diameter of the telescope is much
larger than the length scale of the turbulence. This reduces the
scintillation noise.
Light Curves from Tautenburg taken with BEST
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:
–4
• Rayleigh scattering: cross section s per molecule ∝ l
• Aerosol Extinction
• Absorption by gases
Wavelength
Atmospheric extinction can also affect differential photometry because
reference stars are not always the same spectral type.
A-star
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
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
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
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
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)
=
0.72 + 0.05 E(B – V)
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:
Q ≡ (U – B) –
Q ≡ (U – B) –
E(U – B)
E(B – V)
(B – V)
0.72(B – V)
6. Interstellar reddening:
Using expressions for color excess:
Q = (U – B)0 + E(U – B) –
Q = (U – B)0 –
E(U – B)
E(B – V)
E(U – B)
E(B – V)
(B – V)0
[(B – V)0 + E(B – V)]
≡ Qo
6. Interstellar reddening:
(B – V)0 = 0.322 Q
Spectral Type
Q
Spectral Type
Q
O5
–0.93
B3
–0.57
O6
–0.93
B5
–0.44
O8
–0.93
B6
–0.37
O9
–0.90
B7
–0.32
B0
–0.90
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
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.
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
Optical depth
L
Il + dIl
Il
kl
The radiation sees neither klr or dx, but a the combination
of the two over some path length L.
tl =
L
∫ k r dx
l
Optical depth
o
Units: cm2 gm cm
gm cm3
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
0
Absorption of the starlight in magnitudes:
Al ≡ –2.5 log10(Il/Il(0)) = –2.5 (log10 e)ln(e–tl) = 1.086tl
6. Interstellar reddening: Extinction in magnitudes (Al)
Using expressions for Al, Cij, and t :
RV ≡
AV
E(B – V)
=
tV
(tB – tV)
=
kV
(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
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
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
Landolt standards.