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Observational Methods
1. Spectroscopy
2. Photometry
Prof. Dr. Artie Hatzes
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)
vosc = L/Lּס
M/Mּס
23 cm/sec
Sunlike stars: 0.2 – 1 m/s
Giant stars: 5 – 50 m/s
Velocity:
The magnitude of „solar-like“ observations can be estimated using the scaling relationships of Kjeldsen & Bedding (1995)
L/L ≈ L/Lּס
M/Mּס
4.7 ppm
Sunlike stars: 4.7 ppm
Giant stars: a few milli-mag
Light:
ppm = 10–6
Doppler Measurements
Measurement of Doppler Shifts
In the non-relativistic case:
– 0
0
= vc
We measure v by measuring
collimator
Spectrographs
slit
camera
detector
corrector
From telescope
Cross disperser
slit
camera
detector
correctorFrom telescope
collimator
Without the grating a spectograph is just an imaging camera
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
without disperser
without disperser
with disperser
with disperser
slit
fiber
5000 A
4000 An = –1
5000 A
4000 An = –2
4000 A
5000 An = 2
4000 A
5000 An = 1
Most of light is in n=0
b
The Grating Equation
m = sin + sin b 1/ = grooves/mm
Modern echelle gratings are used in high order (m≈100). In this case all the orders are stacked on each other
m m+1 m+2
m
m+1
m+2
Cross-dispersion: dispersing element perpendicular to dispersion of echelle grating
m+3
m+4
y ∞ 2
y
m-2
m-1
m
m+2
m+3
Free Spectral Range m
Grating cross-dispersed echelle spectrographs
On a detector we only measure x- and y- positions, there is no information about wavelength. For this we need a calibration source
y
x
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 x
x →→ v
How large is x ?
Spectral Resolution
d
1 2
Consider two monochromatic beams
They will just be resolved when they have a wavelength separation of d
Resolving power:
d = full width of half maximum of calibration lamp emission lines
R = d
← 2 detector pixels
R = 50.000 → = 0.11 Angstroms
→ 0.055 Angstroms / pixel (2 pixel sampling) @ 5500 Ang.
1 pixel typically 15 m
1 pixel = 0.055 Ang → 0.055 x (3•108 m/s)/5500 Ang →
= 3000 m/s per pixel
= v c
v = 1 m/s = 1/1000 pixel → 5 x 10–7 cm = 50 Å
A Cepheid variable would produce Doppler shift of several CCD pixels
Solar like oscillations will produce a shift of 1/1000 pixel
The Radial Velocity Measurements of 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
Year
Rad
ial V
eloc
ity
(m/s
)
Rad
ial V
eloc
ity
(m/s
)
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:
Nlines = 1line/√Nlines → Need broad wavelength coverage
Wavelength coverage is inversely proportional to R:
detector
Low resolution
High resolution
Noise:
Signal to noise ratio S/N = I/
I
For photon statistics: = √I → S/N = √I
I = detected photons
(S/N)–1
Price: S/N t2exposure
1 4Exposure factor
16 36 144 400
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!
max = M/Mּס
(R/Rּס)2√Teff/5777K
Frequency of the maximum power is found:
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 x (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:
Spectrographs: CORALIE, ELODIE, HARPS
Stellar spectrum
Thorium-Argon calibration
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
Filled circles are data taken at McDonald Observatory using the telluric lines at 6300 Ang.
Example: The companion to HD 114762 using the telluric method. Best precision is 15–30 m/s
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.
Absorption lines of the star
Absorption lines of cell
Absorption lines of star + cell
b) Use a „controlled“ absorption 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)
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 iodine
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
FTS spectrum rebinned to sampling of RV instrument
FTS spectrum convolved with calculated IP
Observed I2
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 = 2.512m
5 Magnitudes is a factor of 100 in brightness, larger values of m means fainter stars.
Detectors for Photometric Observations
1. Photographic Plates 1.7o x 2o
Advantages: large area
Disadvantages: low quantum efficiency
Detectors for Photometric Observations
2. Photomultiplier Tubes
Advantages: blue sensitive, fast responseDisadvantages: 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
Advantages: high quantum efficiency, digital data, large number of reference stars, recorded simultaneouslyDisadvantages: Red sensitive, readout time
From wikipedia
Get data (star) countsGet 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
Aperture photometry is useless for crowded fields
Term: Point Spread Function
PSF: Image produced by the instrument + atmosphere = point spread function
CameraAtmosphere
Most photometric reduction programs require modeling of the PSF
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
1. Choose several stars as „psf“ stars
2. Fit psf
3. Subtract neighbors
4. Refit PSF
5. Iterate
6. Stop after 2-3 iterations
In DAOPHOT modeling of the PSF is done through an iterative process:
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:
([R * K](xi,yi) – I(xi,yi))2i
Kernal is usually taken to be a Gaussian whose width can vary across the frame.
• some stellar oscillations have periods 5-15 min
• CCD Read out times 30-120 secs
What if you are interested in rapid time variations?
E.g. exposure time = 10 secs
readout time = 30 secs
efficiency = 25%
Solution: Window CCD and frame transfer
Special Techniques: Frame Transfer
Reading out a 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
A „3-phase CCD“
ColumnsFor last row, shift is done along the row
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.
Figure from O‘Connell‘s lecture notes on detectors
Frame Transfer
Target
Reference
Mask
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
Dat
a sh
ifte
d al
ong
colu
mns
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
Nsky = background
Error = (Ndata + Nsky)1/2
S/N = (Ndata)/(Ndata + Nsky)1/2
rms scatter = 1/(S/N)
Ndata
rms
Nsky = 0
Nsky = 10
Nsky = 100
Nsky = 1000
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
Sources of Errors
Typical CCDs have readout noise counts of 3–11 e–1 (photons)
Readout Noise: Noise introduced in reading out the CCD:
Sources of Errors
4. Scintillation Noise:
Amplitude variations due to Earth‘s atmosphere
~ [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
Saturated bright stars
A not-so-nice looking curve from an open cluster
CC
D C
ount
sC
CD
Cou
nts
t
t
Saturation
Saturation + non-linearity
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
A-star
K-star
Atmospheric extinction can also affect differential photometry because reference stars are not always the same spectral type.
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
Wavelength
Wav
elen
gth