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Observational Methods
1. Spectroscopy
2. Photometry
Prof. Dr. Artie Hatzes
[email protected]
036427-863-51
www.tls-tautenburg.de -> Lehre -> Jena
Spectroscopic Measurements
Observations of oscillations in stars and the sun focus on
measuring the velocity field (Doppler measurements) and
brightness variations caused by the oscillations.
What is the expected amplitude of such variations?
Classical Cepheids
have brightness
variations of few tenths
of a magnitude and
velocity variations of
many km/s
Solar-like oscillations have much lower amplitudes
because these are not ‚global‘ variations like Cepheids
The magnitude of „solar-like“ observations can be
estimated using the scaling relationships of Kjeldsen
& Bedding (1995)
Velocity:
vosc
=
L/L‫סּ‬
23 cm/sec
M/M‫סּ‬
Sunlike stars: 0.2 – 1 m/s
Giant stars: 5 – 50 m/s
The magnitude of „solar-like“ observations can be
estimated using the scaling relationships of Kjeldsen
& Bedding (1995)
Light:
dL/L ≈
L/L‫סּ‬
4.7 ppm
M/M‫סּ‬
Sunlike stars: 4.7 ppm
Giant stars: a few milli-mag
ppm = 10–6
Doppler Measurements
Measurement of Doppler Shifts
In the non-relativistic case:
l – l0
l0
=
We measure Dv by measuring Dl
Dv
c
Spectrographs
camera
detector
corrector
Cross disperser
From telescope
slit
collimator
From telescope
collimator
corrector
slit
Without the grating a spectograph is just
an imaging camera
camera
detector
A spectrograph is just a camera which produces an image of the
slit at the detector. The dispersing element produces images as a
function of wavelength
slit
without
disperser
with disperser
fiber
with disperser
without
disperser
5000 A
n = –2
4000 A
5000 A
4000 A
4000 A
5000 A
n = –1
Most of
light is in
n=0
n=1
4000 A
n=2
5000 A
The Grating Equation
s
bb
a
a
ml
s =
sin a + sin bb
1/s = grooves/mm
Modern echelle gratings are used in high order
(m≈100). In this case all the orders are stacked
on each other
Cross-dispersion: dispersing element perpendicular to dispersion of
echelle grating
m m+1 m+2
m
m+1
m+2
m+3
m+4
dl
Free Spectral Range Dl = l/m
m-2
m-1
m
m+2
m+3
y
Dy ∞ l2
Grating cross-dispersed echelle spectrographs
y
x
On a detector we only measure x- and y- positions, there is
no information about wavelength. For this we need a
calibration source
Traditional method:
Observe your star→
Then your
calibration source→
CCD detectors only give you x- and y- position. A
Doppler shift of spectral lines will appear as Dx
Dx → Dl → Dv
How large is Dx ?
Spectral Resolution
← 2 detector pixels
dl
Consider two monochromatic
beams
They will just be resolved when
they have a wavelength
separation of dl
Resolving power:
l1
l2
l
R=
dl
dl = full width of half
maximum of calibration
lamp emission lines
R = 50.000 → Dl = 0.11 Angstroms
→ 0.055 Angstroms / pixel (2 pixel sampling) @ 5500 Ang.
1 pixel typically 15 mm
v =
Dl c
l
1 pixel = 0.055 Ang → 0.055 x (3•108 m/s)/5500 Ang →
= 3000 m/s per pixel
A Cepheid variable would produce Doppler shift of
several CCD pixels
Solar like oscillations will produce a shift of 1/1000 pixel
Dv = 1 m/s = 1/1000 pixel → 5 x 10–7 cm = 50 Å
The Radial Velocity Measurements of g Cep between 1975 and 2005
Up until about 1980 Astronomers were only able to measure the Doppler
shift of a star to about a km/s
Radial Velocity (m/s)
Radial Velocity (m/s)
Year
Year
The Radial Velocity error as a function of year. The reason for the sharp
increase in precision around the mid-1980s is the subject of this lecture
To get a precise radial velocity meausurement you need:
• Many spectral lines
• High resolution
• High Signal-to-Noise Ratio
• A Stable wavelength reference
• A Stable spectrograph
Wavelength coverage:
• Each spectral line gives a measurement of the Doppler shift
• The more lines, the more accurate the measurement:
sNlines = s1line/√Nlines
→ Need broad wavelength coverage
Wavelength coverage is inversely proportional to R:
Low resolution
Dl
detector
High resolution
Dl
Noise:
s
I
I = detected photons
Signal to noise ratio S/N = I/s
For photon statistics: s = √I → S/N = √I
Exposure
factor
1 4 16 36
Price: S/N  t2exposure
144
400
s  (S/N)–1
Obtaining high signal-to-noise ratio for pulsating stars
is a problem:
Time (min)
To detect stellar oscillations you have to sample
many parts of the sine wave. If you exposure time is
comparable to your pulsation period you will not
detect the stellar oscillations!
Frequency of the maximum power is found:
nmax
M/M‫סּ‬
=
(R/R‫)סּ‬2√Teff/5777K
3.05 mHz
For stars like the sun, the oscillation period is 5 min → 1 min
exposure time
For good RV measurement you need S/N = 200
On a 2m telescope with a good spectrograph you can get S/N = 100
(10000 photons) in one hour on a V=10 star → 400.000 photons on a
V=6 star in one hour, 6600 photons in one minute (S/N = 80). To get
S/N = 200 in one minute will require a 5 m telescope
→ the study of solar like oscillations in other stars requires 8m
class telescopes
The Radial Velocity precision depends not only on the
properties of the spectrograph but also on the properties of the
star.
Good RV precision → cool stars of spectral type later than F6
Poor RV precision → cool stars of spectral type earlier than F6
Why?
A7 star
K0 star
Early-type stars have few spectral lines (high effective
temperatures) and high rotation rates.
Instrumental Shifts
Recall that on a spectrograph we only measure a Doppler shift in Dx
(pixels).
This has to be converted into a wavelength to get the radial velocity
shift.
Instrumental shifts (shifts of the detector and/or optics) can
introduce „Doppler shifts“ larger than the ones due to the stellar
motion
z.B. for TLS spectrograph with R=67.000 our best RV
precision is 1.8 m/s → 1.2 x 10–6 cm →120 Å
Problem: these are not taken at the same time…
... Short term shifts of the spectrograph can limit precision
to several hunrdreds of m/s
Solution 1: Observe your calibration source (Th-Ar) simultaneously
to your data:
Stellar
spectrum
Thorium-Argon
calibration
Spectrographs: CORALIE, ELODIE, HARPS
Advantages of simultaneous Th-Ar calibration:
• Large wavelength coverage (2000 – 3000 Å)
• Computationally simple
Disadvantages of simultaneous Th-Ar calibration:
• Th-Ar are active devices (need to apply a voltage)
• Lamps change with time
• Th-Ar calibration not on the same region of the
detector as the stellar spectrum
• Some contamination that is difficult to model
• Cannot model the instrumental profile, therefore you
have to stablize the spectrograph
Th-Ar lamps change with time!
The Instrumental Profile
What is an instrumental profile (IP):
Consider a monochromatic beam of light (delta function)
Perfect
spectrograph
Modelling the Instrumental Profile
We do not live in a perfect world:
A real
spectrograph
IP is usually a Gaussian that has a width of 2 detector pixels
The IP is not so much the problem as changes in the IP
No problem with this IP
Or this IP
Unless it turns into this
Shift of centroid will appear as a velocity shift
HARPS: Stabilize the instrumental profile
Solution 2: Absorption cell
a) Griffin and Griffin: Use the Earth‘s atmosphere:
O2
6300 Angstroms
Example: The companion to HD 114762 using the telluric
method. Best precision is 15–30 m/s
Filled circles are data taken at McDonald Observatory
using the telluric lines at 6300 Ang.
Limitations of the telluric technique:
• Limited wavelength range (≈ 10s Angstroms)
• Pressure, temperature variations in the Earth‘s
atmosphere
• Winds
• Line depths of telluric lines vary with air mass
• Cannot observe a star without telluric lines
which is needed in the reduction process.
b) Use a „controlled“ absorption cell
Absorption
lines of star +
cell
Absorption lines of the
star
Absorption lines of cell
Campbell & Walker: Hydrogen Fluoride cell:
Demonstrated radial velocity precision of 13 m s–1 in 1980!
A better idea: Iodine cell (first proposed by Beckers in 1979 for
solar studies)
Spectrum of iodine
Advantages over HF:
• 1000 Angstroms of coverage
• Stablized at 50–75 C
• Short path length (≈ 10 cm)
• Can model instrumental profile
• Cell is always sealed and used for >10 years
• If cell breaks you will not die!
Spectrum of star through Iodine cell:
Use a high resolution spectrum of iodine to model IP
Iodine
observed
with RV
instrument
Iodine
Observed
with a
Fourier
Transform
Spectrometer
Observed I2
FTS spectrum rebinned to
sampling of RV instrument
FTS spectrum convolved
with calculated IP
WITH TREATMENT OF IP-ASYMMETRIES
The iodine cell used at the CES spectrograph at La Silla
Photometric Measurements
And to remind you what a magnitude is. If two stars
have brightness B1 and B2, their brightness ratio is:
B1/B2 = 2.512Dm
5 Magnitudes is a factor of 100 in brightness,
larger values of m means fainter stars.
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/IrafManuals.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
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 planet 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
Reading out a CCD
A „3-phase CCD“
Parallel registers shift the charge
along columns
There is one serial register at the
end which reads the charge
along the final row and records it
to a computer
Columns
For last row, shift is
done along the row
Figure from O‘Connell‘s lecture notes on detectors
The CCD is first clocked along the parallel register to
shift the charge down a column
The CCD is then clocked along a serial register to
readout the last row of the CCD
The process continues until the CCD is fully read out.
Target
Reference
Frame Transfer
Data shifted along columns
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
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
A not-so-nice
looking curve
from an open
cluster
Saturated
bright stars
CCD Counts
Saturation
CCD Counts
t
Saturation + nonlinearity
t
Sources of Errors (less important for
Asteroseismology)
4. Atmospheric Extinction
Atmospheric Extinction can affect colors of stars and
photometric precision of differential photometry since
observations are done at different air masses
Due to the short time scales of stellar
oscillations this is generally not a
problem
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