STELLAR POPULATIONS Part 1: photometry, spectroscopy, and astrometry
Anno Accademico 2011-12
Prof. Giampaolo Piotto
Dipartimento di Fisica e Astronomia “Galileo Galilei”
Università degli Studi di Padova
STARS
Stars are a minor component in the Universe. Still…..
STARS
The Sun:
our closest star
Radius: 700 000 km =109 Earth radii
Composition (in mass):
70 % hydrogen, 28 % helium, 2 % other chemical elements
Temperature:
5770 K (at surface)
Luminosity:
3.8 x 1026 Watts
1) THERMAL EMISSION
a) FREE-FREE OR BREMSSTRAHLUNG
(CONTINUUM)
b) BOUND-BOUND (LINES)
c) FREE-BOUND (CONTINUUM)
2) NON THERMAL EMISSION
(CYCLOTRON)
2) NUCLEAR
(FISSION)
Free-bound
BACK BODY RADIATION
It doesn’t matter what the excited emission mechanism is… If the medium is optically thick, when photons are emitted they
are immediately absorbed by atoms and moloculrs or
comptonized,
e.g. by electrons. Thus, other photons are generated which will
probably be also absorbed.
This produces an equilibrium between thermal, excitation, ionisation
and radiation temperatures.
This is the mechanism that leads to Black Body Radiation
Visible light is only a
tiny fraction of the
radiation we receive
from the Universe,
but it still provides us
with the great
majority of the
information we have
on stars (and stellar
populations)
Basic tools to measure stellar parameters
1. Photometry
2. Spectroscopy
3. Astrometry
4. Asteroseismology
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Slide 7 Fig. 6-6, p. 98
BLACK BODY TEMPERATURE & THE COLORS OF STARS
Photometry & Stellar Magnitudes
m
2.5log f
const where const(λ) is set by the photometric system
f1
f2
100m
2m
1 5
m 5 ratio of 100 in f
smaller m brighter star
Relative brightnesses of 2 stars at a given λ:
m2-m1 Log f 1/f2 f1/f2
0 0.00 1
1 0.40 2.512…..
2 0/80 6.31
3 1.20 15.85
4 1.60 39.8
5 2.00 100=102
10 4.00 104
15 6.00 106
20 8.00 108
-1 -0.40 0.40
-5 -2.00 0.01=10-2
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" Absolute Magnitude M " L
M m 5logd
10
m 5 5log d
MV M in the "V " band
Total (Bolometric) L Absolute Bolometric M
Mbol
4.75M
bol
2.5logL
L
and Mbol*
MV * BC "Bolometric Correction"
Conventionally, the absolute
magnitude is the magnitude of a
star at a distance of 10pc from the
Sun.
Observers use absolute
magnitudes in some specific
photometric band (e.g. Mv).
Theoreticians use total flux L.
Need to use the same language!
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Slide 7 Fig. 6-6, p. 98
BLACK BODY TEMPERATURE & THE COLORS OF STARS
Photometric systems are
devised in order to be
able to obtain main
stellar parameters from
wide band (many
photons) photometry
There are hundreds of
photometric systems
defined for this purpose.
Many of them are
conceived in order to
get quantitative
information on some
specific parameter.
But the problem is
always the
CALIBRATION of the
systms, i.e. transform
magnitude and colors in
physical quantities
(energy/sec)
Standard Johnson-Cousins photometric system
Strӧmgren photometric system
J H K
L M
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Color index of the SUN
Indice di
Colore
magnitudine
Indice di Colore
magnitudine
U-B
+0.195
V-I
+0.88
B-V
+0.650
J-H
+0.310
V-R
+0.540
H-K
+0.060
R-I
+0.340
K-L
+0.034
V-K
+1.486 L-M
-0.053
U-B, B-V for a black body
T
U-B
B-V
T
U-B
B-V
4000
+0.37
+1.13
20000
-1.01
-0.16
6000
-0.25
+0.62
25000
-1.06
-0.15
10000
-0.69
+0.14
40000
-1.14
-0.29
15000
-0.91
-0.07
-1.28
-0.44
Photometry: three important issues: Bolometric correction Reddening/absorption Photometric calibration
Photometry: three important issues: Bolometric correction Reddening/absorption Photometric calibration
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Photometry: three important issues: Bolometric correction Reddening/absorption Photometric calibration
Reddening: E(B-V)=(B-V) - (B-V)0
Average Milky Way extinction law with Rv=3.1 (Cardelli et al. 1989)
Rv towards specific directions within the Galaxy can vary
Color-color diagrams to determine reddening and extinction
It works only for early spectral types
Photometry: three important issues: Bolometric correction Reddening/absorption Photometric calibration
Going towards the physical world
A number of scientific applications need to have the stellar fluxes (or
magnitudes) in some physical units.
Therefore, we need to calibrate (*) our instrumental magnitudes into
some, properly defined photometric system.
(*) Note that the term “calibration” might generate some confusion. Someone uses
the term calibration to indicate the CCD pre-processing operations (bias, dark,
flatfielding corrections). I personally prefer to use this term to indicate the
complex operations needed to transform the instrumental magnitudes into a
properly defined phot. system.
We need to match
photometries from
different
observations/data sets:
1. For comparison;
2. Variability studies;
3. Extend magnitude/color
coverage;
4. etc.
(Bedin, Anderson, King, Piotto, 2001)
NGC 6397
M4
(King, Anderson, Cool, Piotto, 1999)
We need to compare
observations with models.
Observations and models
need to be compared on the
same photometric system
Low
metallicity
Intermediate
metallicity
This implies to be able to
transform models from the
theoretical plane to some
properly defined photometric system.
And here the real trouble starts….
The Asiago Data Base on Photometric Systems lists 218 systems
(see http://ulisse.pd.astro.it/ADPS/enter2.html)!!!
But, even when you have chosen your photometric system, you
might still be in trouble!
The unbelivable
CMDs!
Theory predicts
that no stars can
be cooler than
the red giant
branch location!
But theory cannot
predict that
astronomers can
be so foolish to
change the
bandpasses of
their observation
without
properly
accounting
for these changes
If observations are properly calibrated
and models transformed into the correct observational plane
(not necessarely a standard system), theoretical
tracks can correctly reproduce the observed CMD (apart from
intrinsic failures of the models…but this is a different story!).
How to operate properly
A general lesson
From the previous examples we have learned a few important
things:
1. Observations must be calibrated and models must be
transformed into the same photometric system;
2. We need to use as much as possible a “standard”
photometric system;
3. If your photometric bandpasses are far from any existing
photometric system, you have the responsibility to
calibrate your system (good luck!);
4. In any case, ALWAYS trasform the models to the
observational plane, and not viceversa.
Photometric calibration of groundbased observations
Let’s suppose that we have collected a set of images of our program
objects through a set of filters properly designed to reproduce a
“standard” photometric system.
First of all, a clarification is needed:
Here, by “standard” I intend some widely used photometric system for
which a large set of standard stars, well distributed in the sky, and
which span a large color interval (at least as large as our program
objects) are available in the literature. And by standard stars I mean
stars for which accurate magnitudes and colors in the given
photometric system are available. Indeed:
the standard stars define our photometric system.
In order to calibrate the magnitudes and colors of our program objects, we need to observe also the standard star fields, at different times during the night, making sure that the observed standards cover a sufficently large color interval.
Just an example (for the Johnson-Cousins system):
Landolt, 1983, AJ, 88, 439
Landolt, 1992, AJ, 104, 340
Photometric information on the standard stars in the
Landolt (1992) catalog
Position information on the
standard stars in the
Landolt (1992) catalog
Most of Landolt’s standards are too bright for modern CCDs.
Better to use Peter Stetson’s extension of Landolt’s catalog in:
http://cadcwww.hia.nrc.ca/standards
Coordinates
Photometry
DSS image General info
It is important to realize that, even if we have collected a set of images
of our program objects through a set of filters properly designed to
reproduce a “standard” system, our observational system is always
different from the standard one.
Indeed, the collected flux depends on at least 6 different terms:
Signal=F()(1-)R()A()K()Q()
F() incoming flux A() atmospheric absorption
fraction of the obscured mirror K() filter trasmission curve
R() mirror reflectivity Q() detector quantum efficency
Red
leakage
Calibration steps (general):
1. Obtain aperture photometry of standard stars;
2. Fit the standard star data with equations of the type:
Where: v, b are the instrumental magnitudes;
V, B the standard magnitudes
X the airmass
t the time of observation (in decimal hours)
ai, bi the unknown transformation coefficents
The instrumental magnitudes must be transformed to a reference
exposure time (e.g. 1 second) and to a reference aperture (fraction of
total light of the star), or to the total light. Big problem (see later)!
For well designed observing
systems, and for not too
extreme colors, a linear fit
may be enough.
3. The next step is to calculate
the aperture correction, i.e.
the zero point difference
between the (fitting)
instrumental magnitudes of
the program stars, and the
aperture photometry used to
obtain the calibr. coefficents.
Finally, once the calibration coefficents have been obtained, the corresponding calibration equations can be applied to the instrumental magnitudes of the program stars, to transform them into the beloved
magnitudes in the standard system!
Example of calibration eq.s to the Johnson-Cousins standard
system for rhe ESO-Dutch telescope (from Rosenberg et al. 2000)
Non-standard photometric systems
What shall we do in case we do not have a standard photometric system,
with an appropriate set of standard stars?
It must be clearly stated that when the transmission curves of the
equipment used to collect the observations are rather different from those
of any existing standard system, the transformation of the data to a
standard system can be totally unreliable, particularly for extreme
stars (i.e., extreme colors, unusual spectral type, high reddening, etc.).
If we are dealing with groundbased obsevations…it is a long, tedious,
delicate job, and I do not have the time to enter into the problem here.
Do you want an advice? Change telescope!
Unfortunatlely, also widely desired (!) and widely used telescopes like
HST….have imagers which do not mount “standard” filters.
Do you want an advice? Do not attempt to transform your WFPC2 or
ACS instrumental magnitudes into any standard system!
So, what shall we do?
Provided that the transmission curves of the complete optical system and
detectors are known, a calibration of the zero points into physical units
is easy to obtain by using a reference star for which the spectral flux
(outside the atmosphere) as a function of the wavelength is known (e.g.
Vega). By multiplying the reference spectrum by the system transmission
curves one obtains the flux within the given pass bands, which can be
easily transformed into magnitudes. If one uses the same procedure
employing model atmospheres and theoretical fluxes, it is possible to
relate the magnitudes and colors to the physical parameters like
temperature and luminosity.
Bedin et al. (2004) have written a paper which describes
in a complete and clear way the methodology, applying it to the
calibration of the HST/ACS camera.
A similar method has been applied by Holtzman et al. (1995) and
Dolphin (2000) for the calibration of the HST/WFPC2 camera.
Example (from Bedin et al. 2005):
The spectrum of Vega from
ftp://ftp.stsci.edu/cdbs/cdbs2/ grid/
k93models/standards/vega_reference.ts
has been multiplied by the (in flight) ACS
trasmission curves on the right, in order to
calculate the ACS Vega-mag flight system
zero point coefficents.
Model atmospheres and theoretical
fluxes have been multiplied by the
same transmission curves in order
to transform the models into
the same (observational) plane
above defined.
Models and observations are
compared on the left panel.
Spectroscopy
RICORDIAMO CHE LE RIGHE POSSONO APPARIRE IN
ASSORBIMENTO O IN EMISSIONE SUL CONTINUO
CONTINU
RIVEDIAMO IL RIVEDIAMO IL
MECCANISMO MECCANISMO
DI FORMAZIONE DI FORMAZIONE
DELLE RIGHE DI DELLE RIGHE DI
ASSORBIMENTO ASSORBIMENTO
E DI EMISSIONE E DI EMISSIONE
Slide 8 p. 99
Slide 9 p. 99 Slide 10 p. 99
Slide 11 p. 99
S l i d e 1 5 p . 1 0 0
ABSORPTION LINES SPECTRUM
Boltzmann Equation
Where, Nn, Nm, are the number of atoms at the excitation
state n and m
k = Boltzmann constant= 1.38x10-16 erg/deg
gn, gm statistical weight of the two energetic levels
Enm = energy difference between the two levels
= photon frequencye
/ /mnE kT h kTn n n
m m m
N g ge e
N g g
Saha Equation (1)
[log X2/(1-X2)]*P=-5040V/T+2.5logT-6.5
where:
X=ionization degree (relative number of ions with respect to the
total number of atoms of a given species)
V= potential of first ionization
T=temperature
P=pressure
X=0 no ions; x=1 all atoms are ionized
X increases, as T increases, X decreases as V and P increase
Saha Equation (2)
Log N(r+1)/Nr = -5040Vr/T+2.5T-0.48+log2B(r+1)/Br-log Pe
N(r+1), Nr number of ions r, and r-1 ionized, respectively
Vr, the potential for the r-ionization
T temperature, Pe the electron pressure
B(r+1), Br ripartition functions
Note the dependence on P. P is smaller in giant stars with respect to
dwarfs. Therefore, the same level of ionization is reached in giants
at smaller temperature than in dwarfs
Solar spectrum
Gli spettri stellari sono descritti da 7 classi spettrali (ciascuna con 10
sottoclassi), O B A F G K M, secondo una sequenza di temperature
decrescenti.
Stellar spectra are divided in 7 main spectral classes (O,B,A,F,G,K,M),
each of them divided into 10 sub classes. From O to M the temperature
decreases.
Spectral classification is morphological, related to the presence of certain lines.
M
K
G
F
A
B
O
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Classification of stars
• O B A F G K M scheme
– Originally in order of H strength – A,B,etc
Above order is for decreasing temperature
– Standard mnemonic: Oh, Be A Fine Girl
(Guy), Kiss Me
– Use numbers for finer divisions: A0, A1,
... A9, F0, F1, ... F9, G0, G1, ...
From our text: Horizons, by Seeds
Line broadening is related to the gas pressure
Giant and supergiant stars has a more extended atmosphere, lower
pressure, smaller interaction among atomos/molecules. Narrower
lines
4
2
24 R
GM
R
FP
grav
gas
Smaller stars have less extended, higher pressure atmosphere.
More interaction among atoms, molecules. Broader lines
Narrow lines = low
pressure
Broader lines =
higher pressure
Very broad lines =
very high pressure
Spectra classification also includes luminosity class Very bright supergiants
Super giants
Bright Giants
Giants
Subgiants
Dwarfs Sun=G2V
Therefore, from the spectra, we obtain -Temperature - Gravity (pressure) - Chemical composition
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Now we anticipate the spectroscopic notation of the Stellar
Chemical Composition.
The chemical composition of celestial bodies and environments is usually given in
terms of X, Y and Z (relative abundances of H, He, and elements heavier than He, in
mass)
However, in spectroscopy, we often do not see some elements when the physical
conditions do dot allow their detection. For example, He is not observed in cold low
mass stars that, instead, show absorption lines due to metals. Hydrogen Balmer
absorptions become relatively weak in very hot stars and even fainter in cold stars.
Obviously, abundance estimates require stellar atmosphere models to fit the observed
spectra.
However, a particular notation was developed to estimate metal abundances.
Since iron is a good metal abundance indicator because its lines are prominent and easy
to measure, the traditional metal abundance indicator is the quantity
Fe
H
log
N(Fe)
N(H )
logN(Fe)
N(H )
esun
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Thus, for the Sun [Fe/H]=0, while stars more metal poor than the Sun have [Fe/H] < 0
Assuming that the conversion from Z to [Fe/H] is universal, being
and we can write
For example, Z=0.001 and Y=0.25 implies [Fe/H]=-1.26; while z=0.04 and Y=0.30
gives [Fe/H]=0.39. However, as, usually He and heavy elements abundance changes are
negligible (x~constant), we can approximately write: [Fe/H]~log(Z/Zsun)
(see Salaris-Cassisi p. 239-241)
Fe
H
log
Z
X
logZ
X
e
logZ
X
1.61 logZ
1Y Z
1.61
Zsun =0.018 Xsun=0.70
sun
IMPORTANT: in old, metal poor ([Fe/H]<-0.6) stellar populations
(halo and globular cluster stars, the so called α-elements (O, Ne,
Mg, Si, S, Ca, and Ti) are overabundant (with respect to the Sun):
[α/Fe]~0.3,0.4
This properties of metal poor stars is
related to the chemical composition of
Type II and type Ia SN. Type II SN
progenitors are massive, short living
stars, which explode earlier. The ejecta of
the Sne are rich in α-elements, and
therefore enrich the interstellar medium
with these elements. Only at a later time
(1Gyr?) Sne Ia start exploding. The ejecta
of these Sne are rich in Fe, with a small
amount of α-elements. Consequently,
younger stellar generations, as the Sun,
have a smalle [α/Fe]
For these α-enhanced mixtures, the general relationshipd between [M/H] and [Fe/H] can
be approximated by:
[M/H]~[Fe/H]+log(0.694fα + 0.306, where fα=10[α/Fe]
For [α/Fe]=0.3, [M/H]=[Fe/H]+0.2
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Astrometry
The major problem we face for the determination of the
main stellar parameters (e.g. mass and age) is the
measurement of their distance
The problem is challenging for stellar associations, clusters,
etc.
The problem is dramatic for single stars
This introduce the problem of the distance scale
Basic distances are coming from parallaxes, as these are
geometrical distances
The concept of parallax
OA=Earth radius for solar system measurements OA=semimajor Earth orbit for stellar distances
