Observational Methods

1. Spectroscopy

2. Photometry

Prof. Dr. Artie Hatzes

artie@tls-tautenburg.de

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